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Evolution of microstructure and texture during continuous annealing of cold rolled, Ti-stablized interstitial-free… Mukunthan, Kannappar 1994

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EVOLUTION OF MICROSTRUCTURE AND TEXTURE DURINGCONTINUOUS ANNEALING OF COLD ROLLED, TI-STABILIZEDINTERSTITIAL-FREE STEELByKannappar MukunthanB. Sc. (Materials Engineering) University of Moratuwa, 1983M.A.Sc. (Metals and Materials Engineering) University of British Columbia, 1987A THESIS SUBMJTTED IN PARTIAL FULFILLMENT OF-THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESMETALS AND MATERIALS ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMay 1994® Kannappar Mukunthan, 1994In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Metals and Materials EngineeringThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5Date:A ii/AbstractInterstitial-Free (I-F) steels are increasingly being used for press forming operations dueto their markedly improved deep-drawability. Additional interest is due to the fact thatthe cold rolled I-F steels can be effectively heat treated in a continuous annealing linewithout the need for any accompanying overaging process.The objective of this study was to characterize the evolution of microstructure andcrystallographic texture of a 80 % cold rolled, Ti-stabilized I-F steel during heatingrates applicable to batch and continuous annealing processes. Isothermal recovery kinetics, as monitored by {220} x-ray peak resolution measurements, were described usinga semi-empirical logarithmic equation. Isothermal recrystallization kinetics were determined by quantitative metallographic measurements and were characterized by bothJohnson-Mehl-Avrami-Kolmogorov and Speich-Fisher relationships. The isothermal recrystallization kinetics were also described in terms of the experimentally determinedmicrostructural path function and an empirical kinetic function relating the interface-averaged growth rate with recrystallization time. The additivity procedure was successfully employed in conjunction with the isothermal kinetic parameters to predict continuous heating recovery and recrystallization kinetics at heating rates simulating batch andcontinuous annealing processing.Microstructural examination showed that the recrystallization event was heterogeneous and related to the cold rolled cell structure. The recrystallized nuclei, developedprimarily by subgrain coalescence occurring during the later stages of recovery, grew intothe cold rolled matrix by the migration of high misorientation boundaries. Large precipitates of TiN and TiS acting as preferred nucleation sites and fine precipitates impeding11the boundary mobility were also observed. The hot band texture with the moderatepresence of (112)[1iO] yielded a strongly developed cold rolled texture extending from(OOi)[iIOj to (112)[1IO]. The recrystallization texture was characterized by the strongpresence of (554)[5] and (111)[1iO]. Grain growth following recrystallization strengthened the existing texture with an accompanying improvement in average strain ratiovalues. The effect of heating rate on the final recrystallization texture was found to beinsignificant.II’Table of ContentsAbstract iiList of Tables vList of Figures viAcknowledgement vii1 Introduction 11.1 Interstitial-Free Steels 11.2 Continuous Annealing Process 41.3 Scope and Objectives 52 Literature Review 92.1 Kinetic Models for Recovery and Recrystallization 92.1.1 Measurement of Recovery and Recrystallization Kinetics 92.1.2 Kinetics of Recovery Processes 152.1.3 Kinetic Models for Isothermal Recrystallization 182.1.4 Additivity and Continuous-Heating Kinetics 322.1.5 Annealing Phenomena in Low-Carbon Steels 422.2 Development of Texture during Cold Rolling and Annealing 572.2.1 Methods of Representation of Texture 582.2.2 Crystallographic Texture and Plastic Anisotropy 612.2.3 The Theoretical Mechanisms of Texture Development 63iv2.2.4 Development and Control of Texture in I-F Steels 673 Experimental Procedure 863.1 Material 863.2 Cold Rolling Schedule . . 863.3 Kinetic Measurements 873.3.1 Apparatus 873.3.2 Diffraction Effects 883.3.3 Annealing Treatment . . . . 893.3.4 Quantitative Metallography 913.4 Electron Microscopic Observations 943.4.1 Gleeble Simulated Annealing Treatment 943.4.2 Thin Foil Preparation and TEM Investigations 953.4.3 SEM/EDX Analysis of Large Precipitates 963.5 Texture Characterization 973.5.1 Specimen Preparation 973.5.2 Pole Figure Determination and ODF Calculations 984 Kinetic Characterization 1054.1 Isothermal Recovery Kinetics 1054.2 Recovery and Recrystallization during Isothermal Heating 1114.3 Isothermal Recrystallization Kinetics 1164.3.1 JMAK/S-F Analysis of Isothermal Recrystallization 1164.3.2 Microstructural Path Concept in Recrystallization Modelling . . 1224.3.3 Recrystallization Kinetics as related to Steel Chemistry and Processing Conditions 1304.4 Recovery and Recrystallization during Continuous Heating 136v4.5 Continuous Heating Recrystallization Kinetics 1405 Microstructural Examination of Structural Changes 1905.1 Structural Changes during Cold Rolling and Annealing 1905.2 Characterization of Large Precipitates 1976 Characterization of Annealing Textures 2247 Conclusions 263Bibliography 266viList of Tables1.1 Typical chemical composition of I-F steel [6] 72.1 Characterization of isothermal recrystallization kinetics for a 89 % coldrolled, rimmed low-carbon steel using the JMAK and the S-F equations [39]. 703.1 Steel composition provided by Stelco and that obtained from chemicalanalysis 994.1 Characterization of isothermal recovery kinetics 1474.2 Characterization of isothermal recrystallization kinetics 1474.3 Characterization of isothermal interface-averaged growth kinetics 1484.4 Experimental and Scheil predicted recrystallization start times (and temperatures) during continuous heating 1486.1 Volume percentages of important texture components calculated from theODF data obtained for the hot band, the cold rolled sheet and annealedspecimens 2426.2 A summary of r at a = 0, 45 and 90°, and Lr predicted from the ODFdata obtained for the hot band, the cold rolled sheet and annealed specimens243viiList of Figures1.1 Comparison of schematic box- and continuous-annealing cycles along withthe Fe-rich side of the Fe-Fe3C equilibrium diagram [24] 81.2 Furnace sections of a continuous annealing line [26] 82.1 Effects of annealing temperature (200, 250, 300, 450°C for 1 hr) on thediffraction peak profiles of the {331} planes in a 90 % cold rolled 70-30brass [49] 712.2 Schematic illustration of the X-ray peak resolution measurement [56, 57] 712.3 Comparison of the % peak resolution (in-situ) and microhardness measurements obtained for a 89 % cold rolled, rimmed low-carbon steel duringcontinuous heating [56] 722.4 Recrystallization behaviour of a 77 % cold rolled, Ti-stabilized extra-low-carbon steel during the simulation of continuous annealing (soak time of40 s at each temperature) [15] 722.5 Isothermal recovery kinetics in polycrystalline iron after 5 % prestrain at0°C, showing fractional residual strain hardening vs. time [40] 732.6 Recovery of x-ray line broadening as measured by the residual line broadening parameter (1-R) for isothermal treatments at 400, 500 and 600°C[53] 732.7 The graph of lnln[1/(1— X)] vs. ln(t) obtained by Rosen et al [72] for a60 % deformed high-purity iron 74viii2.8 Fractional residual strain hardening curves obtained during isothermal annealing of a) copper [92] and b) aluminum (arrows indicate onset of recrystallization) [93] as presented by Furu et al [91] 742.9 Interfacial area per unit volume plotted against the volume fraction recrystallized for a 60 % cold worked 3.25 % Si-steel [90] 752.10 Average boundary migration rates (0) during isothermal recrystallizationof hot-worked 3.25 % Si-Fe [81] 752.11 Schematic representation of the additivity principle [69] 762.12 A schematic TTR diagram with proportionally distributed fractional recrystallization curves to illustrate the validity of the additivity rule. . . 772.13 Comparison of experimental and predicted continuous heating recrystallization kinetics; the isothermal data characterized by both the JMAK andthe S-F equations were used in the additivity calculations [39] 772.14 Schematic illustration of subgrain coalescence by subgrain rotation [53]. 782.15 Schematic representation of nucleation by subgrain growth; boundariesthickly populated by dislocations (dots) have a high misorientation angle,and are the most likely to migrate [131] 782.16 The softening response of three iron alloys recrystallized at 595°C [38]. 792.17 Effect of annealing time at 565°C on the longitudinal properties of a Tistabilized I-F steel cold rolled between 50 and 88 % [21] 792.18 Time-temperature-recrystallization diagram for Ti-stabilized [21], rimmedand Al-killed steels after 50 % cold reduction [138] 802.19 Effect of excess titanium in solid solution and cold reduction on the recrystallization temperature (TF) for annealing soak times of 15 s [16]. . 80ix2.20 Relationship between the recrystallization start temperature, TR, and theamount of Nb in solid solution in ferrite; the points along the curve wereobtained for coarsened precipitates and the open circles include the effectof precipitates as well as Nb in solid solution [17] 812.21 Recrystallization kinetic curves indicating sigmoidal-type behaviour, obtained for a series of I-F steels, cold rolled 75 % and isothermally annealedat 650°C [153] 812.22 Partial (200) pole figures obtained for a rimmed steel (a) in the cold-rolledstate and (b) after recrystallization; the ideal orientations {111} < 112 >,{111} < 110>, {100} <011 > and {211} <011 > are indicated [79]. . 822.23 Normal (ND), rolling (RD) and transverse (TD) direction inverse polefigures obtained for a 70 % cold rolled steel sheet [160] 822.24 Schematic description of crystal orientation by indices of crystal directionsand by Euler angles , and Y2 [157) 832.25 A three-dimensional view and a = 45° section of the Euler space showingthe locations of some important ideal orientations [164, 166] 832.26 Development of recrystallization texture during isothermal annealing (after 2, 3 and 10 s hold at 700°C) of a 90 % cold rolled (CR) Al-killed steel;the plots indicate orientation density along the (a) a (< 110 >11 RD) and(b)-y (< 111 >j ND) fibres [170] 842.27 The effect of the ratio of the intensities of the (111) component to the(001) component on the average strain ratio of low-carbon steel sheets [163] 842.28 Comparison of the relative proportions of different textural componentsin rimmed, Al-killed, and Ti-stabilized interstitial-free as well as highstrength steels [196] 85x2.29 Variation of values with heating rate during annealing for a variety ofsteels subjected to different high temperature processing conditions [23].. 853.1 (a) A strip specimen with thermocouple attached at centre of bottomsurface, and (b) closeup of open hot x-ray camera with specimen in place 1003.2 Schematic diagram illustrating the {220} x-ray peak resolution associatedwith annealing and the procedure for quantifying peak resolution 1013.3 Summary of the isothermal (T-T.-R) and continuous heating (C-H-R) annealing tests performed, together with the parameters measured 1023.4 Comparison of fractional peak resolution, F, based on valley intensity,‘M,as obtained from two different tests 1033.5 Strip specimen thermocouple positions for determining the thermal gradient; C.T. refers to control thermocouple; A, B and C are additionalthermocouple positions 1033.6 Illustration of the measurement of volume fraction recrystallized, X, andthe interfacial area per unit volume, A, by quantitative metallography [90] 1043.7 Through-thickness microstructural variation of a partially recrystallizedspecimen produced by rapid cooling from 750°C after being heated at20.2°C/s, Magnification X 200) 1044.1 Fractional peak resolution (F) calculated at 500°C based on in-situ measurements of x-ray ratio (R1) and valley intensity (IM) 1494.2 In-situ R1 measurements obtained at 500°C, compared with the kineticdescriptions using Eq. 2.3 (ln R1 = K — kt) and Eq. 2.4 (R1 = b — a ln t) 1504.3 (a) In-situ R1 measurements at 500, 550, 600 and 625°C, together withthe kinetic descriptions using Eq. 2.4, and (b) the same kinetic data whenreplotted on a logarithmic time scale 151xi4.4 Time-Temperature-Recovery (T-T-Ry) diagram obtained using Eq. 2.4;experimental measurements corresponding to R1 0.5 and 0.4 are alsoshown 1524.5 (a) Effect of inverse absolute temperature on the natural logarithm of theinstantaneous rate of recovery calculated at constant R1 values, and (b)the calculated activation energy for recovery, Qm,, as a function of theextent of recovery, R1 1534.6 Temperature dependence of parameters b and a; isothermal recovery kinetics has been characterized by the logarithmic relationship, R1 = b — a In t 1544.7 Effect of R1 on in AR and -QR/R; recovery kinetics has been analysed interms of the Arrhenius equation, dR1/dt = —AR exp —(QR/RT) 1544.8 In-situ IM measurements at 500°C, compared with the kinetic curves obtained using Eq. 2.3 (lnJM cx t) and Eq. 2.4 (IM cx int) 1554.9 Rj measurements corresponding to the start of the isothermal hold and theonset of recrystallization, as obtained from the interrupted tests performedat 600, 625, 650 and 675°C 1564.10 Fractional peak resolution, F, calculated at 625°C using interrupted R1values and in-situ IM measurements (obtained from two different tests);metallographically determined recrystallization start time is also indicated. 1574.11 Isothermal 675°C R1 measurements interpreted in terms of recovery (Eq.2.4) based on the total area (RTA) or the unrecrystallized area (RUA),recrystallization (recovery- R1) and measured % recrystallized 1584.12 Isothermal 650°C ‘M measurements interpreted in terms of recovery (Eq.2.4) based on the total area (RTA) or the unrecrystallized area (RUA),recrystallization (recovery- IM) and measured % recrystallized 159xii4.13 Comparison of the fractional peak resolution (F) calculated from interrupted R1 and in-situ ‘M measuremnts, and the fraction recrystallized(X) determined from metallography at (a) 700 and (b) 720°C 1604.14 The effect of isothermal annealing time on the intensity values,‘K1, ‘minand ‘b, as obtained from in-situ peak profile measurements at (a) 500 and(b) 650°C 1614.15 Metallographically determined isothermal recrystallization kinetics at 650°C 1624.16 The JMAK [66, 67, 65] and the S-F [90] analysis of the isothermal dataobtained at 650°C, indicating the best fit lines 1624.17 Temperature dependence of the JMAK time-exponent, n, and the S-Ftime-exponent, m, as obtained from the best fit analysis; the average valuesof n (=0.73) and m (=1.17) are also indicated 1634.18 Recrystallization measurements obtained at 650°C, compared with the kinetic descriptions using the JMAK and the S-F equations; the effects ofusing the original best fit parameters vs. the recalculated average parameters are also shown 1634.19 The JMAK analysis of the isothermal kinetic data obtained at (a) 600,625, 650 and 675°C and (b) 700, 720, 740 and 760°C 1644.20 The S-F analysis of the isothermal kinetic data obtained at (a) 600, 625,650 and 675°C and (b) 700, 720, 740 and 760°C 1654.21 Experimentally determined isothermal recrystallization kinetics at (a) 600,625, 650 and 675°C and (b) 700, 720, 740 and 760°C, compared with thedescriptions using the JMAK and the S-F equations 166xlii4.22 Time-Temperature-Recrystallization (T-T-R) diagram obtained using theJMAK analysis; recrystallization start and finish times for the I-F steelunder investigation, and for a Ti-stabilized [21] and a rimmed [57] low-carbon steels are also shown 1674.23 Temperature dependence of the recrystallization time corresponding to 10,50 and 90 % recrystallization as obtained from the JMAK analysis. . . 1684.24 Temperature dependence of the JMAK parameter, ln b, and the S-F parameter, in k; isothermal recrystallization kinetics has been characterizedby the JMAK and the S-F equations with constant values of n (=0.73)and m (=1.17) 1694.25 Recrystallization start time, as a function of isothermal temperature 1694.26 Typical microstructures of (a) the hot band with an equiaxed grain structure and (b) the 80 % cold-rolled sheet steel with a heavily banded structure along the rolling direction (Magnification X 200) 1704.27 Photomicrographs showing the early stages of recrystallization obtainedfrom specimens held at 700°C for (a) 2 s and (b) 4 s (Magnification X 200). 1714.28 Photomicrographs showing the later stages of recrystallization obtainedfrom specimens held at 700°C for (a) 12 s and (b) 30 s (Magnification X200) 1724.29 Typical microstructure of a fully recrystallized specimen, obtained after a150 s hold at 700°C (Magnification X 200) 1734.30 Photomicrographs at (a) Magnification X 400 and (b) Magnification X1000, showing the initial stages of recrystallization obtained from a specimen held at 650°C for 32 s 174xiv4.31 Interfacial area per unit volume (A) vs. volume fraction recrystallized(X) obtained for all isothermal temperatures and heating rates; the bestfit microstructural path description, A = 2002 (X)°44 (1— X)°94, is alsoindicated 1754.32 Temperature dependence of the interface-averaged growth rate time exponent, riG, as obtained from the best fit analysis; the average G value of-0.58 is also indicated 1764.33 G = KG t (riG = -0.58) analysis of the isothermal growth kinetic dataof (a) 600, 625, 650 and 675°C and (b) 700, 720, 740 and 760°C 1774.34 Effect of inverse absolute temperature on the natural logarithm of theinstantaneous (interface-averaged) growth rate, , calculated at constantgrowth distances, dG 1784.35 Temperature dependence of the growth parameter, KG; isothermal growthkinetics has been characterized by G = KG t with a constant G valueof -0.58 1794.36 The plot of the isothermal G values obtained at all test temperaturesagainst time (both axes on logarithmic scale); the global best fit description line, = is also indicated 1804.37 Modelled X vs. t curves using the microstructural path approach, togetherwith the experimental data points obtained at (a) 600, 625, 650 and 675°Cand (b) 700, 720, 740 and 760°C 1814.38 Schematic diagram illustrating the modelling procedure used in the prediction of recovery and recrystallization kinetics during continuous heating. 182xv4.39 In-situ and interrupted R1 measurements obtained at 0.025°C/s, comparedwith the additivity-predicted recovery kinetics (using ‘activation energy’and ‘empirical’-type isothermal descriptions) and metallographic analysisof % recrystallized 1834.40 Comparison of experimental (interrupted R1) and predicted continuousheating recovery kinetics at 0.025, 1.88, 20.2 and 80°C/s 1844.41 Interrupted R1 measurements obtained at 20.2°C/s interpreted in terms of(predicted) recovery based on the total area (RTA) or the unrecrystallizedarea (RUA), recrystallization (recovery- R1) and measured % recrystallized 1854.42 Temperature effect on (a) the values of (1min - Is), (‘Ka1 - ib) and R1, and(b) the 20 values of the J( peak and the valley 1864.43 Comparison of experimental and predicted continuous heating recrystallization kinetics at 0.025, 1.88 and 20.2°C/s; the predictions are based onthe experimentally determined start times, t. expt’l 1874.44 Comparison of the effect of t expt’l vs. t9 Scheil on the JMAK equation based kinetic predictions at 0.025, 1.88 and 20.2°C/s; experimentallydetermined % recrystallized are also indicated 1884.45 Comparison of the additivity predicted interface-averaged growth rates(G) with the the modelled (using dX/dt from the predicted recrystallization kinetics and A from the derived microstructural path function) andestimated (using the experimental ‘X vs. t’ data and the experimental Avalues) G values at 0.025, 1.88 and 20.2°C/s 1895.1 Bright-field transmission electron micrograph of the 80 % cold rolled I-Fsteel showing the highly dislocated cell structure 204xvi5.2 Microstructures illustrating the heterogeneous nature of the cold rolledcell structure; (a) a reasonably developed cell structure and (b) densedislocation networks with much less developed cell structure 2055.3 Subgrain structure development in a partially recovered specimen heatedat 20.2°C/s up to 580°C; (a) small elongated subgrains and (b) relativelylarge subgrains 2065.4 Well-defined subgrain structure formation in a specimen heated at 20.2°C/sup to 640° C; coalescence of subgrains is suggested by those boundaries indicated by arrows 2075.5 Photomicrograph obtained from a specimen heated at 20.2°C/s up to640°C, indicating the occurence of subgrain coalescence (arrow indicatesthe disappearing boundary); Kikuchi lines corresponding to the subgrainsA and B are also given 2085.6 Microstructure indicating subgrain growth caused by both sub-boundarymigration (indicated by arrow M) and coalescence (indicated by arrow C);the annealing treatment corresponds to quenching from 640°C after beingheated at 20.2°C/s 2095.7 Microstructures obtained from a specimen heated up to 640°C at 20.2°C/s,indicating (a) the effect of a large particle on nucleation (arrow indicatesthe precipitate) and (b) the effect of fine precipitates on sub-boundarymigration (arrow indicates the discontinuity in the boundary curvature.. 2105.8 Recrystallized grain nucleated in the interior of a matrix grain in a specimen heated at 20.2°C/s up to 680°C; selected area diffraction patternsillustrate the orientation of the recrystallized grain A (zone axis < 111 >type) with regard to the matrix subgrain area B (zone axis < 111 > type). 211xvii5.9 Recrystallized grain A (zone axis < 111 > type) bordering a cold rolledgrain B (zone axis < 110 > type) in a specimen heated at 20.2°C/s up to680°C; the pinning of one side of the boundary of the recrystallized grainby fine precipitates is also shown (arrows indicate the precipitates). . . . 2125.10 Photomicrographs obtained from a specimen heated at 20.2°C/s up to740°C ( 50 % recrystallized), showing (a) recrystallized grains growinginto the cold rolled matrix and (b) fully recrystallized grains 2135.11 Fully recrystallized microstructures obtained from the specimens heated(a) at 20.2°C/s up to 800°C and (b) at 0.025°C/s up to 700°C 2145.12 Microstructure of the as-received hot band, showing random distributionof fine precipitates 2155.13 SEM micrograph obtained from a specimen heated up to 800°C at 20.2°C/s,suggesting that the boundary migration had been impeded by fine precipitates (arrows indicate the discontinuities in the boundary curvature). . . 2165.14 SEM micrograph and x-ray spectrum showing the presence of an angular-shaped precipitate in the hot band (arrow indicates the precipitate); thex-ray spectrum is consistent with it being a TiS precipitate 2175.15 SEM micrograph of the hot band showing the larger Ti/S-containing precipitate (appears near the centre) and the smaller precipitates (indicatedby arrows); the associated x-ray spectrum obtained for a smaller precipitate is consistent with it being Ti4C2S 2185.16 SEM micrograph and x-ray spectrum showing the presence of a regularshaped precipitate in the hot band (arrow indicates the precipitate); thex-ray spectrum suggests this to be of the type (Ti,Mn)S 219xviii5.17 SEM micrograph of the hot band showing an angular shaped precipitate(indicated by arrow); the x-ray spectrum is consistent with it being a TiNprecipitate 2205.18 SEM micrograph obtained from the hot band and x-ray spectrum obtainedfrom the particle showing an example where an Al-rich particle (indicatedby arrow Al) acted as the nucleant for Ti-rich precipitates (indicated byarrow Ti) 2215.19 SEM micrograph obtained from the hot band and x-ray spectrum of theprecipitate showing an Al-rich core surrounded by a Ti-rich precipitate,which acted as the nucleant for the sulfide or carbo-sulfide of Ti (the lightercontrast outer layer indicated by arrow) 2225.20 SEM micrograph and x-ray spectrum showing the presence of a P-containingprecipitate in the hot band (arrow indicates the precipitate) 2236.1 (a) Experimental and (b) recalculated (110) pole figures obtained for the80 % cold rolled I-F steel specimen 2446.2 ODFs calculated for the I-F steel hot band (with the grain size of ASTMNo. 7 - 8) presented at constant ço sections; cp2 = 45° section of the Eulerspace is also shown 2456.3 ODFs calculated for the 80 % cold rolled sheet presented at constant ysections; 2 = 45° section of the Euler space is also shown 2466.4 ODFs showing constant cp1 sections for the specimen quenched from 670°Cafter being heated at 20.2°C/s (‘-- 15 % recrystallized); P2 = 45° sectionof the Euler space is also shown 247xix6.5 ODFs showing constant ço sections for the specimen quenched from 720°Cafter being heated at 20.2°C/s (‘-.‘ 40 % recrystallized); c02 = 45° sectionof the Euler space is also shown 2486.6 ODFs showing constant y sections for the specimen quenched from 760°Cafter being heated at 20.2°C/s (‘-. 80 % recrystallized); Cp2 = 45° sectionof the Euler space is also shown 2496.7 ODFs showing constant so sections for the specimen quenched from 800°Cafter being heated at 20.2°C/s (fully recrystallized with the grain size ofASTM No. 9 - 10); Y2 = 45° section of the Euler space is also shown. . 2506.8 ODFs showing constant cc’1 sections for the specimen quenched from 900° Cafter being heated at 20.2°C/s (fully recrystallized with the grain size ofASTM No. 8); cp2 = 45° section of the Euler space is also shown 2516.9 ODFs showing constant coi sections for the specimen quenched from 770° Cafter being heated at 1.88°C/s (fully recrystallized with the grain size ofASTM No. 9 - 10); Y2 45° section of the Euler space is also shown. . 2526.10 ODFs showing constant p sections for the specimen quenched from 700°Cafter being heated at 0.025°C/s (fully recrystallized with the grain size ofASTM No. 9 - 10); c°2 45° section of the Euler space is also shown. . 2536.11 Orientation density along the (a) and (b) y fibres for the as-received hotband and the 80 % cold rolled I-F steel specimens 2546.12 Orientation density along the (a) E and (b) t9 fibres for the as-received hotband and the 80 % cold rolled I-F steel specimens 2556.13 Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolledspecimens annealed at 20.2°C/s; the results are presented as orientationdensity along the (a) a and (b) fibres 256xx6.14 Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolledspecimens annealed at 20.2°C/s; the results are presented as orientationdensity along the (a) E and (b) ‘9 fibres 2576.15 Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolledspecimens annealed at 20.2°C/s; the results are presented as orientationdensity along the c-fibre 2586.16 Effect of heating rate on the annealing texture of fully recrystallized specimens with the grain size of ASTM No. 9 - 10; the results are presentedas orientation density along the (a) a and (b)-y fibres 2596.17 Effect of heating rate on the annealing texture of fully recrystallized specimens with the grain size of ASTM No. 9 - 10; the results are presentedas orientation density along the (a) E and (b) i9 fibres 2606.18 Normal direction inverse pole figures calculated from the ODFs corresponding to (a) the 80 % cold rolled steel and (b) the fully recrystallizedspecimen with the grain size of ASTM No. 9 - 10, annealed at 20.2°C/s 2616.19 Development of plastic anisotropy during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolledspecimens annealed at 20.2°C/s; the results are presented as r (predicted)vs. a (degrees) 262xxiAcknowledgementI would like to express my sincere gratitude to Professor E.B. Hawbolt for his patience,guidance and encouragement throughout the course of this project. Thanks are alsoextended to Professor R.G. Butters (Retired), Mr. Serge Milaire and Ms. Mary Magerfor their help regarding the experimental aspects of this work. Financial assistanceprovided by Natural Sciences and Engineering Research Council of Canada is gratefullyacknowledged.All of the texture measurements of this work were performed in Queen’s Universityand this would not have been possible without the generous help provided by Professor S.Saimoto, Mr. Perry Clarke and Mr. Brad Diak. A special note of thanks to Dr. RajeevKamat for taking the initiative and all the other necessary steps to successfully carry outthe texture measurements.Various aspects of this research work were greatly enhanced by the input provided byseveral researchers of the Metals and Materials Engineering department. In particular,the assistance provided by Dr. R.B. Mahapatra regarding modelling, Dr. F. SaintAntonin regarding transmission electron microscopy and Dr. Fidel Reyes-Carmona regarding precipitate characterization is gratefully acknowledged. A special note of thanksto Dr. Chris Davies for his advice and suggestions in all aspects of this research work.Spontaneous help and friendship shown by fellow graduate students are sincerelyappreciated. In particular, the constant encouragement, help and moral support providedby Mr. Jose Bernardo Hernandez-Morales and Dr. S. Gown are gratefully acknowledged.Thanks are also expressed to the Third World buddies of Metallurgy and the Tamil friendsof British Columbia for making my stay in UBC/Vancouver pleasant and rewarding.xxiiThe debt I owe to my parents cannot be described in words. It is their love andsacrifices that made my education possible and it is to them this thesis is dedicated.xxiiiChapter 1Introduction1.1 Interstitial-Free SteelsLow-carbon steel is one of the most important products of the steel industry today.This is primarily because no other commercial material can offer, at low cost, propertiessuch as strength, good formability, attractive surface finish, and easy weldability. Oneof the most important requirements for many applications involving sheet steel is goodformability. In place of the conventional low-carbon (typically has 0.06 wt % C and0.005 wt % N) sheet steel, further reduction of carbon content to levels of approximately0.005 wt % and additions of Al, Nb, and Ti which combine with interstitial C and N,have long been known to promote recrystallization textures favourable for severe formingoperations such as deep-drawing [1, 2].The annealed sheet steel with very low C and N contents has been produced commercially since the early 1970’s [3]. This constitutes one of the most recent steps in theevolution of formable, cold rolled and annealed sheet steels. Vacuum-degassing and rigorous control of C, N, and 0 pick-up during casting are required to produce these steels,particularly to reduce the carbon levels below 0.005 wt %. Such advanced processingsteps are now commonly applied at a reasonable cost and have led to the commercialproduction of interstitial-free (I-F) steels [3, 4, 5, 6, 7].Interstitial-free or fully stabilized steel sheet is produced from aluminum-killed steelwith extremely low amounts of carbon and nitrogen, treated with one or more of Ti,1Chapter 1. Introduction 2Nb; the typical composition ranges of the elements present in I-F steels are shown inTable 1.1 [6]. Stochiometrically sufficient amounts of Ti and Nb are added to removeC and N completely from the solid solution by forming stable carbides, nitrides, andcarbonitride precipitates. Titanium added to low-carbon steel combines with N, S and Cin that order, primarily in the temperature range of 1400- 900°C, while Niobium almostexclusively combines with the residual C at lower temperatures [4, 6, 8, 9, 10]. Variousstudies on I-F steels dealing with the thermo-kinetic analysis of precipitation as well asthe physical and chemical characterization of different precipitates have been reported[6, 10, 11, 12]. In addition, the Ar3 temperatures of I-F steels are considerably higherthan those of conventional low-carbon steels, and because of this increased range of ferritestability, the temperatures used for finish hot rolling and for annealing after cold rollingare significantly higher for I-F steels [6].The elimination of interstitial elements from the iron matrix has a number of benefitsfor the product, particularly the removal of inhomogeneous deformation associated withstrain aging, decreased yield stress values (140- 180 MPa), significant reduction in theyield strength dependence on grain size, good ductility (40 - 50 % elongation), andmarkedly improved drawability (high ‘average plastic strain ratio’ values) [6, 8, 13]. Thisallows the steel user to produce more complex shapes with fewer forming steps and lowerrejection levels. In deep-drawn oil pan applications, scrap levels were reported to bereduced from 5 % to I % with the replacement of conventional low-carbon steel with 1-Fsteel [14]. However, the manufacturing cost of I-F steel is high and the surface qualitymay be poor due to the presence of a large amount of alloying elements [15].The type and amount of stabilizing element has an effect on the optimum processingconditions and properties. Excess Ti and Nb levels in solid-solution (above what isneeded for stabilizing interstitials) is reported to considerably retard the recrystallizationkinetics in I-F steels [16, 17]. Nb-precipitates, being finer than Ti-precipitates, are moreChapter 1. Introduction 3effective in retarding the growth of new grains, resulting in a fine-grained, recrystallizedmicrostructure [4, 18]. To make up for the loss of strength associated with reducingthe carbon content, P, Si and Mn are the most commonly used alloying elements inI-F steels to impart solid-solution strengthening. In particular, phosphorus additionsstrengthen Ti-stabilized I-F steels very effectively without a significant concurrent dropin deep-drawability [9, 19, 20].In addition to steel chemistry, processing factors have a major influence on the finalproperties of the I-F steels. All of the stabilizing precipitation takes place during the hightemperature processing, and the precipitates are in place prior to cold rolling and annealing. Coarse and widely spaced precipitates allow rapid growth of new grains, therebyhelping to achieve stronger textures favouring deep-drawability. Lower reheat temperatures (1000 - 1100°C), finish rolling temperature values just above Ar3 (‘-‘ 900°C) andhigher coiling temperatures (700- 800°C) are reported to be beneficial for Ti-stabilizedI-F steels [4, 6, 15, 16]. In general, however, Ti-steels are less sensitive to the lowertemperature finish rolling and coiling of the processing schedules due to the presence of astable precipitate distributions in these steels [4, 6]. Coiling temperature control can bequite significant for Nb-steels because this process can occur in the temperature range ofNb(C,N) precipitation [4, 6].The degree of deep-drawability is primarily related to the type of recrystallizationtexture formed. Consequently, cold rolling and annealing, two processing parametersmarkedly affecting texture development, are important processing steps to be controlled.The recrystallization of cold rolled I-F steel is known to be very slow when comparedto other low-carbon steel [21]. Cold reduction of approximate’y 90 % and annealingtemperatures as high as 800° C (independent of the heating rate) are reported to producefavourable textures in I-F steels for deep-drawing applications [4, 6, 14, 22, 23]. Incomparison, Al-killed low-carbon steels are usually cold rolled about 70 %, and annealedChapter 1. Introduction 4by slowly heating at— 0.01°C/s to a temperature of ‘—.‘ 700°C [22, 23].1.2 Continuous Annealing ProcessDuring the cold rolling of steel sheet, the plasticity of the material is exhausted, resultingin limited formability and increased hardness. For the sheet to be used in subsequentforming operations, the ductility must be restored through a heat treatment which resultsin recrystallization. Two processes are employed by the steel industry to accomplish thistask, batch annealing (BA) and continuous annealing (CA).Batch annealing involves heating tight-wound sheet steel coils in a gas fired furnacewith a controlled atmosphere. A typical representation of the annealing cycle experiencedduring batch annealing is shown in Fig. 1.1 (a) [24]. The heating rates are approximately30°C/hr, the soak temperature around 700°C and the entire process taking several daysto complete.Modern CA lines combine several processes including electrolytic cleaning, annealing,overaging and sometimes temper rolling [24, 25, 26, 27]. Sections of annealing and agingfurnaces of a continuous annealing line are shown in Fig. 1.2 [26]. Radiant tubes fired bynatural gas are used for heating. Heating rates of 10 - 40°C/s, soak temperature of around800°C, cooling rates of 20 - 200°C/s and an overaging temperature of approximately350°C are commonly employed to anneal low-carbon steels; the time taken for the totalcycle is only 4- 8 mm. as indicated in Fig. 1.1 (c) [24]. The short heating time minimizesdetrimental carbide coarsening, allowing higher annealing temperatures to be employedto promote recrystallization [24].When carbon-steels are subjected to BA, nearly all the carbide will precipitate duringthe slow cooling cycle. However, the rapid cooling during CA inhibits the completeprecipitation of carbide from ferrite, making subsequent overaging necessary. DespiteChapter 1. Introduction 5overaging, more carbon is retained in solid solution during CA than in BA, and, as aresult, even Al-killed continuously annealed steels show some aging effects [24]. Thisexplains why traditionally BA was preferred over CA in producing the highly formablecarbon-steel sheets, despite the many other advantages offered by CA, such as lower cost,better versatility and more uniform properties in the product [24].Fully stabilized I-F steel is an ideal material for the continuous annealing process dueto the absence of free carbon for subsequent precipitation. With I-F steels, the overagingprocess (as an essential component of a continuous annealing line for low-carbon sheetsteels) can be completely eliminated; this makes CA a much more attractive process thanBA. In fact, almost all of the cold-rolled I-F steel sheet produced today is continuouslyannealed before being subjected to press-forming operations [7].Hot-dip galvanized (HDG) sheet has major use in automotive applications (e.g., doorinners). Most of it is currently produced from cold-rolled, Al-killed low-carbon steel byemploying annealing, hot-dip galvanizing, and overaging processes. However, annealingand galvanizing of the I-F steel can be completed in a single continuous operation toproduce HDG sheet with properties superior to those of Al-killed low-carbon steel sheet[7, 16]. This technology makes I-F steel equivalent in cost to conventional steel for HDGapplications. As a result, manufacturers of HDG sheet using I-F steels are reportedto have significantly increased the production of I-F steel for deep-drawing applications[14, 28].1.3 Scope and ObjectivesThe relationship between microstructure and mechanical properties and the control ofmicrostructure by solid state processing have been important topics of extensive researchChapter 1. Introduction 6in physical metallurgy. However, most of this work has resulted in a qualitative linking of product properties with processing parameters. The current emphasis is focussedon obtaining quantitative product-processing knowledge through the use of knowledgebased computer models, describing microstructure evolution during industrial processing. Although much of the work to date has been based on purely empirical approaches,these have provided short term merits. Models based on sound physical principles withpowers of prediction are now needed to improve process control. This new generationof models must incorporate both microstructure and texture development, to predictthe mechanical properties of the processed product. The emerging field of “microstructural engineering” has as its goal the development of models to quantitatively predict theproperties of a metal product as a function of its composition and thermo-mechanical history. Fundamental to microstructural engineering is the development of a mathematicalmodel that links mechanical properties to processing parameters through the evolutionof microstructure.In the present study, the microstructural engineering approach will be applied to develop a model describing the continuous annealing of a heavily cold rolled, Ti-stabilizedI-F steel with emphasis on kinetic modelling of recovery and recrystallization duringcontinuous heating, associated microstructure and texture evolution, and development ofplastic anisotropy. To accomplish this task, the recrystallization kinetics will be measuredand modelled over an appropriate range of isothermal temperatures and during selectedcontinuous heating cycles applicable to industrial annealing processes. The evolutionof crystallographic texture during simulated continuous annealing will be characterizedquantitatively using orientation distribution functions. Scanning and transmission electron microscopy will also be employed to improve the understanding of the microstructural mechanisms responsible for recovery and recrystallization.Chapter 1. Introduction 7Table 1.1: Typical chemical composition of I-F steel [6]Element Weight PercentageC 0.002- 0.008N 0.001- 0.005S 0.004 - 0.010Si 0.010- 0.030Mn 0.100 - 0.340P 0.010 - 0.020Al 0.030 - 0.070Ti 0.010 - 0.110Nb 0.005 - 0.040Chapter 1. Introduction 8TEMP,A1(a) (b)Fe-FeCEQUILIBRIUMBOX ANNEALING DIAGRAM CONTINUOUS ANNEALING80060040020002 4 6 8TIME, mmFigure 1.1: Comparison of schematic box- and continuous-annealing cycles along withthe Fe-rich side of the Fe-Fe3C equilibrium diagram [24].—AGEING FURNACE—(c)‘ ‘ I -ry + Fe3CI I IHigh Temo4, Rapid CooIngI . OveragingTEM Poc0 1 2 3 .01 .02 M3 .04TIME,days C,wt%— ANNEALING FURNACEFigure 1.2: Furnace sections of a continuous annealing line [26].Chapter 2Literature Review2.1 Kinetic Models for Recovery and RecrystallizationDuring the plastic deformation of a metal, energy will be stored in the material dueto the introduction of defects such as dislocations and their associated strain energy.This stored energy provides the driving force for the two relaxation processes occurringduring annealing; recovery and recrystallization. During recovery, some annihilationand rearrangement of point defects and dislocations takes place, and these processes aidthe formation of recrystallized nuclei. During recrystallization, new relatively strain-freegrains nucleate, and grow by the migration of high-angle grain boundaries until the entirecold-worked matrix is consumed. Grain growth can take place at high temperaturesfollowing recrystallization, with the decrease in the total surface energy of the grainboundaries being the driving force [29, 30].2.1.1 Measurement of Recovery and Recrystallization KineticsThe techniques used for quantifying the effects of an annealing treatment generally involveeither a direct measurement of the release of stored energy (calorimetric techniques) orthe recrystallization event (quantitative metallography), or the measurement of a changein some mechanical or physical property of the alloy associated with the progress ofannealing.9Chapter 2. Literature Review 10Most of the recrystallization studies are based on measurements made at room temperature (e.g., hardness measurements, tensile testing and quantitative metallography)on partially annealed specimens, using interrupted heating-quenching tests. However,microcalorimetry, measurement of electrical resistivity and magnetic permeability, andx-ray diffraction monitoring are a few measurement procedures that permit in-situ measurement of the annealing effects.2.1.1.1 MicrocalorimetryCalorimetric techniques have been used to measure the heat evolved during isothermaland anisothermal annealing [31]; the observations have been interpreted in terms of acombined recovery and recrystallization process [32, 33, 34]. Important information concerning the nature of the annealing mechanisms and the imperfections involved can beobtained thorough this approach. In particular, calorimetric studies have been foundto be very useful in quantifying the effects of competing recovery processes on recrystallization, as a function of temperature and degree of deformation [32, 33]. However,correlating the calorimetric observations to the fraction recrystallized may not be a trivial task. This will be further complicated if additional phase transitions, such as thedissolution or the precipitation of a second phase, occur during recrystallization [34].2.1.1.2 Hardness Measurements and Tensile TestingMicro and macro hardness measurements have been used extensively to measure theprogress of recrystallization due to their ease of use and significance in industrial applications. Recovery seems to play a major role in the softening response of high purityiron [35, 36] and dilute solid solutions of a-iron [37, 38]. However, the observed hardnesschanges in some low-carbon [38, 39] and I-F [15, 17] steels have been attributed almost entirely to recrystallization. Microhardness evaluation methods have been used to monitorChapter 2. Literature Review 11recrystallization of thin specimens. Due to the locallized nature of these microhardnessindentations, a large number of readings must be taken for statistical accuracy [32].The tensile properties that have been used to monitor recrystallization in I-F steelsare yield strength [16, 21], percent elongation [21] and the ratio of tensile strength to yieldstrength (TS/YS) [17]. The changes in yield stress values of iron-based alloys, dependingon the chemical composition, have been found to be related to either recovery [40] orrecrystallization [41], or a combination of both [17, 21]. However, the softening responsein an I-F steel, reflected by the TS/YS ratio, is reported to be due almost entirely torecrystallization [17].2.1.1.3 Quantitative MetallographyIn quantitative metallography, the fraction of recrystallized grains is measured. Despitebeing tedious and prone to error of judgement, this method gives the most appropriatedata for developing a kinetic equation describing recrystallization in terms of nucleationand growth parameters. Microhardness impressions are sometimes made to distinguishbetween the recrystallized and unrecrystallized regions [32]. Precise microstructural measurements are always necessary to validate the recrystallization measurements obtainedfrom other techniques [17, 21, 32, 39]. It has been shown that the systematic two-dimensional point counting method is superior to areal and lineal counting analyses interms of efficiency for a given experimental error [42, 43, 44].2.1.1.4 Measurement of Electrical Resistivity and Magnetic PermeabilityChanges in electrical resistivity [45, 46] and magnetic permeability [47, 48] have alsobeen used to monitor the progress of annealing. Although these methods can be readilyadopted as in-situ techniques, they have been shown to be most effective in monitoringonly the recovery stages [46, 47].Chapter 2. Literature Review 122.1.1.5 X-Ray TechniquesWhen a metal is plastically deformed by rolling, slip occurs in each grain and the grainsbecome flattened and elongated in the direction of rolling. However, contacts amonggrains are retained during deformation, and because of this constraint, a plastically deformed grain will usually also have regions of its lattice left in an elastically bent ortwisted condition. These residual microstresses, the associated non-uniform strain andthe corresponding range of crystallographic plane spacings in the deformed grain structure are all characteristics of the cold-worked state [49, 50].The x-ray line position of the diffracted peaks from different crystallographic planescan be determined from Bragg’s law,A=2d0sinO (2.1)where A is the wavelength of the x-ray beam, 0 is the incident angle the beam makeswith the crystal plane under consideration (2 0 is the angle of diffraction), and d0 is theunstrained lattice spacing of the diffracting plane.For a cold rolled metal, the well-defined K, /iç2 peaks corresponding to the spacingd0, will be replaced by a number of smaller, more diffuse peaks corresponding to therange of spacings in the deformed lattice; combining these peaks, a broadened diffractionpeak is obtained [49, 50, 51, 52]. In addition to non-uniform lattice strain, small coherentcrystallites (fragmented grains) and stacking faults have also been identified by Fourieranalysis of observed diffraction peak profiles and shown to contribute to peak broadening[51, 53]. Based on several such studies, it has been suggested that the non-uniform strainis a major cause of peak broadening in most of the cold-rolled metals and alloys [49].The effect of annealing temperature on the peak profile of a 90 % cold rolled 70-30brass is shown in Fig. 2.1 [49]. A broad diffraction peak for the {331} planes is obtainedafter cold work. The effect of annealing at increasing temperatures causes recovery andChapter 2. Literature Review 13recrystallization processes to occur. Recovery, which dominates the lower temperature response, involves partial stress relief and causes the broad x-ray peak to sharpen and partlyresolve. During recrystallization, new grains form and residual stresses are eliminated,with sharper resolution occurring as recrystallization proceeds. Although, diffractometryprovides a means of monitoring the effects of recovery and recrystallization, it is much lesssensitive to the growth processes that occur following the completion of recrystallization[49].Any kinetic study of recovery and/or recrystallization requires the quantitative characterization of the degree of peak resolution using x-ray diffraction procedures. The parameters used for this purpose are either a measure of the half peak width [47, 48, 52, 54]or a measure of the ratio of intensity of the doublet valley between the K, ‘ç2 peaksand the intensity of any one peak [15, 48, 49, 53, 55, 56, 57]. In x-ray studies of recrystallization in steels, the {211} diffraction peak was monitored using FeKa radiation[48, 56, 57], and the peak resolution has been described in terms of the ‘line sharpeningparameter’, R [56, 57],R= (Iiç— 1mm) (2.2)(‘K1— Ib)where is the intensity of the J(, peak, ‘mm is the intensity of the valley, and ib isthe background intensity, as indicated schematically in Fig. 2.2. Other researchers haveused a ‘residual line broadening parameter’, (1-R), to quantify peak resolution in theirinvestigations [15, 53, 55]. The fractional annealing effects could be estimated using thepeak resolution values for cold-rolled, partially annealed and fully annealed specimens[15, 55, 56, 57].The x-ray peak resolution procedure can be easily adopted for in-situ studies on recrystallization. Fig. 2.3 shows some results where both in-situ fractional peak resolutionand interrupted microhardness measurements were used to characterize the progress ofChapter 2. Literature Review 14annealing of a 89 % cold rolled, rimmed low-carbon steel, continuously heated at 0.02°C/s[56]. Although the exact time corresponding to the onset of recrystallization could notbe determined, both the hardness and the peak resolution profiles change rapidly in thesame time interval, indicating that these two measurement procedures are effective inmonitoring different stages of recrystallization.Although x-ray diffraction peak broadening measurements provide a means of in-situmonitoring of annealing (recovery and recrystallization) processes, no clear distinctionbetween the effects of recovery and recrystallization processes are obtained. In low-carbonsteels, the observed peak resolution prior to the onset of recrystallization, has been foundto vary from 20 % [15, 47, 48, 56] to 70 % [15, 55] of the total peak resolution, dependingon the alloy content, heat-treatment conditions and the particular diffraction peak beingmonitored. Although an inflection point in the peak resolution response corresponding tothe onset of recrystallization has some times been observed [48, 55], no general procedurehas been reported for separating the two effects using x-ray procedures.In cold-rolled metals, recrystallization is normally accompanied by a change in texture. Such a change can also be used as a measure of the degree of recrystallization as theintensity of the diffracted signal from a given texture component is proportional to theamount of material with this texture. Fig. 2.4 shows the results of an investigation wherehardness, fraction of residual line broadening (fractional change in (1-R)), and integratedpole intensity have been measured on a 77 % cold rolled, Ti-stabilized extra-low-carbonsteel subjected to continuous heating-quenching procedure [15]. The integrated pole intensity of some selected diffraction peaks seem to provide a reasonable measure of thedegree of recrystallization. Precipitation during recrystallization [58] and grain growthfollowing it [15] can also influence the integrated intensity measurements, and may haveto be considered in interpreting the experimental observations. This method has the potential to be used for in-situ investigations, as was demonstrated in a recent study whereChapter 2. Literature Review 15the textural evolution was monitored in-situ using neutron diffraction and the measuredintensity values were interpreted in terms of a sigmoidal-type recrystallization kinetics[591.2.1.2 Kinetics of Recovery ProcessesThe rate of recovery of a property from its cold-worked state depends on the instantaneousvalue of that property and results in kinetics exhibiting a continuously decreasing rateof change with increasing time, without any initial incubation period. This response ismarkedly different from the sigmoidal property change usually obtained for nucleationand growth processes, such as recrystallization.Two different expressions have been used in the past to describe the kinetcs of therecovery processes during isothermal annealing. The first equation, based on the asslimption that the rate of decay of a property is proportional to its instantaneous value, canbe expressed as [29],lnx=K—kt (2.3)where x is the instantaneous value of some property measured at time t, and K and kare experimental constants for a given temperature. -An alternative empirical equation is of the logarithmic form [29, 60] and given by,x=b—alnt (2.4)where x is the value of the selected property at time t, and b and a are experimentalconstants for a given temperature. Based on this equation, the rate of recovery, -dx/dt,is equal to a/t.Michalak and Paxton [40] reported detailed studies on the kinetics of recovery ofthe initial flow stress in a 5 % prestrained, polycrystalline iron. The parameter usedto measure the extent of recovery was the fractional residual strain hardening, definedChapter 2. Literature Review 16as the ratio of the difference in flow stress values between partly-annealed and fully-annealed iron to the difference in flow stress between pre-strained and fully-annealediron. Fig. 2.5 shows the results of this study, where fractional residual strain hardeningwas plotted against time for the temperature range 300 to 500°C. These curves are typicalof a recovery process, in that they show a rapid initial decrease with the rate of changedecreasing with increasing time. When the same data were plotted on a logarithmic timescale, linear behaviour was observed, validating the logarithmic recovery relationship (Eq.2.4).Hu [53] investigated the kinetics of recovery in 80 % cold-rolled silicon-iron singlecrystals by monitoring the sharpening of the (002) reflection. The results obtained at400, 500 and 600°C for a (001)[110] crystal are shown in Fig. 2.6 as the residual linebroadening parameter (1-R) vs. log (time). These results support the proposal that theisothermal recovery and the associated peak resolution in iron can be described well byEq. 2.4. In Hu’s study, recovery processes were responsible for the sharpening of thebroadened peak, from (1-R) of 0.55 to 0.15 as indicated in Fig. 2.6; the (1-R) value of0.35 was considered to correspond to approximately 50 % recovery.Although most kinetic recovery models are based on the measurement of specificproperty changes, several researchers have included the details of specific microstructural processes. Li [61] modelled recovery in terms of the kinetics of the annihilation ofdislocation dipoles (pairs of parallel dislocations of opposite signs) through a statisticaltreatment. With some simplifying assumptions, he derived a second-order kinetic relationship of the form, dp/dt cx—p2, where p is the dilocation density. The integration ofthis, with the additional assumption that the stored energy, E, was proportional to thedislocation density, p, led to the kinetic relationship dE/dt cx — t2 [61]. Vandermeerand Gordon [33] monitored recovery in cold worked aluminum in terms of the two distinctstages of stored energy release that were observed. The first energy release, with a rateChapter 2. Literature Review 17proportional to t1, was attributed to the reduction and rearrangement of dislocations insubgrains. The second stored energy release, observed at 139°C with a rate proportionalto t2, was in accordance with the dislocation annihilation model proposed by Li [61],but was attributed to subgrain growth by Vandermeer and Gordon [33].Since recovery is a thermally activated process (or combination of processes), therate of recovery increases with increasing temperature. By assuming Arrhenius rate behaviour, the activation energy corresponding to the recovery process has been calculated,and found to be useful in inferring the mechanisms responsible for recovery. Most of thestudies indicate an activation energy that increases as recovery proceeds [40, 62]; a constant activation energy corresponding to the recovery process has also been reported ina few studies [52, 54].In general, a combination of simultaneous microstructural mechanisms have beenfound to operate during the recovery process. The increase in the activation energyduring recovery can be rationallized in terms of a change in the dominant recovery mechanism [29]. It has been suggested [62], that the activation energy is a function of x, theinstantaneous value of the recovering property. Such an activation energy would havethe form,dx (Qo—Bx”--=—A expRT ) (2.5)where Qo, A and B are experimental constants for a given recovery study, R is the gasconstant and T is the absolute temperature. This equation can be reduced to Eq. 2.4,indicating the validity of the logarithmic time law for an activation energy that varieslinearly with the recovering property [29].Vandermeer and Rath [63] in their recovery studies on iron single crystals used anequation of the same form as Eq. 2.5,dP_ Q0B(PPr)—- ( — r) exp- RT (.)Chapter 2. Literature Review 18where P is the instantaneous value of the stored energy, Pr is the remnant stored energywhich is unrecoverable after long annealing times. They used this equation to analysethe flow stress measurements made by Michalak and Paxton [40] during recovery, basedon the assumption that the flow stress is proportional to the square root of both thedislocation density and the stored energy [64].An increase in the activation energy with the progress of recovery is consistent withrecovery processes initially occurring at severely deformed regions, where mechanismswith a relatively low activation energy can easily operate. Activation energy values of91.9 and 281.7 kJ/mole, corresponding to the start and the end of recovery, were reportedfrom flow stress measurements on 5 % prestrained polycrystalline iron [40]. Based onthese values, it was suggested that simple vacancy migration was rate controlling at thestart, while self-diffusion (due to combined vacancy formation and vacancy migration)was rate controlling towards the end [29]. An activation energy value of 126.2 kJ/moleat 50 % recovery has been reported for 80 % cold rolled silicon-iron single crystals basedon peak resolution measurements [53].2.1.3 Kinetic Models for Isothermal RecrystallizationThe evolution of microstructure during recrystallization can be described phenomenologically as a nucleation and growth process. New strain-free grains emerge from the coldworked microstructure (nucleation) surrounded by high angle grain boundaries whichmigrate (growth) until the cold worked matrix is consumed.2.1.3.1 JMAK Equation - Theoritical DevelopmentMathematical treatment of the kinetics of nucleation and growth processes must compensate for the impingement effects of the new, growing grains with one another. Kolmogorov[65], Johnson and Mehl [66] and Avrami [67] (JMAK) incorporated grain impingementChapter 2. Literature Review 19through an abstract consideration, where the new grains were assumed to grow unimpeded through one another and to continue to nucleate in already-transformed as wellas untransformed regions. The totality of this volume transformed, referred to as theextended volume, could be related to the kinetic laws of growth without considering thegeometric problem of impingement. For a random distribution of the new phase, the realvolume fraction transformed (X) and the extended volume fraction transformed (Xex)could be easily related,dXexlX (2.7)This equation provides the basis for the modelling of phase transformation kinetics bythe JMAK method.The modelling process is implemented by calculating the extended volume fractiontransformed in terms of the nucleation and growth parameters. The following generalcase is used as an illustration [68]. If NT is the nucleation rate, i.e. the number of newgrains appearing per unit volume of material during the time increment between r andT+dT, and v(t — T) is the volume of a new grain nucleated at r and growing unimpingedfor time (t— T) (t is the overall reaction time), thendXex = Nv(t — T)dT (2.8)This ideallization assumes that all new grains have the same geometry and each onegrows independently of the others. For a shape preserved growth of spheroidal shapedgrains,v(t— r) = Ka3 (2.9)where a is the grain radius after time (t — -r) and K is a shape factor, which is forspherical grains. Finally, a may be related to an interface migration rate, 0, and thegrowth time, t’, by the equation,a=jGdt’ (2.10)Chapter 2. Literature Review 20Equations 2.7 to 2.10 are combined and, after carrying out the necessary integrations,yield a relationship between the actual volume fraction transformed, a nucleation rate, agrowth rate, a geometrical factor and the reaction time.In the most general case, NT and G, which are scalar and vector quantities respectively, may vary both spatially and with time. If G is assumed to be isotropic and timeindependent, and NT is treated either as a constant or as a sharply decreasing functionof time (a case where the preferred nucleation sites are quickly exhausted), then for arandom spatial distribution of nucleation sites, the JMAK theory predicts the followingsimple relationship [67],X = 1 — exp(—bt’) (2.11)where X is the volume fraction transformed in time t and n (referred to as the JMAKexponent) and b are constants.For three dimensional growth, n is equal to 3 in the limiting case of early site saturation [67], and equal to 4 when NT is treated as a constant [66, 67]; for a generaldecreasing nucleation rate, the value of n will be between 3 and 4. This general expression remains valid for two- and one- dimesional growth with appropriate n values. TheJMAK exponent, ri, is dependent on the time variation of nucleation and growth ratesand the dimensionality of the growth fronts [69, 70], and is some times independent oftemperature [69]. The constant, b, represents the relative magnitude of the nucleationand growth rates and is often a strong function of temperature [69].2.1.3.2 JMAK Equation - Application to RecrystallizationThe JMAK equation has been used extensively to model the kinetics of phase transformations, including recrystallization in metals. However, in some of the reported studies,Chapter 2. Literature Review 21the observed recrystallization kinetic behaviour could not be adequately described using the JMAK equation. Primarily two types of failure have been observed. First, thetime-exponent, n, was found to assume low values, typically around 1 [33, 38, 39, 71, 72]even though the recrystallized grains were essentially equiaxed and the JMAK theorywould predict 3 < n <4 for such cases. Second, there are a number of studies where thekinetic data, when plotted as In ln[1/(1— X)] vs. ln(t) (the JMAK theory format), showa negative deviation from linear behaviour in the later stages of recrystallization [33, 72].Fig. 2.7 shows the results from one such study by Rosen et al. [72] on a 60 % deformedhigh-purity iron.These discrepencies suggest that one or more of the assumptions involved in thedevelopment of the JMAK equation are not being met. Most of the metallographicobservations indicate that the assumption of a random distribution of nucleation sitesis not valid; in reality, randomness has been observed only in a very few cases, suchas in a lightly deformed metal [73, 74] and in some single crystal studies [75, 76]. Itis common to observe a high density of nuclei only in certain grains of the cold rolledmetal [72, 77], as a result of the non-uniform distribution of stored energy betweengrains of different orientations [78, 79]. Further non-uniformity is due to the presence ofpreferential nucleation sites such as grain boundaries, transition bands and shear bands[33, 80, 81, 82, 83].There have been few attempts to incorporate heterogeneous nucleation into the JMAKanalysis through analytical means. Cahn [70] considered grain boundary nucleated processes, and demonstrated the possibility of n varying between 1 to 3 depending on thenature of the site distribution. A similar study by Vandermeer and Masumura [84]showed that n could assume a value of around 1 depending on the initial grain size.These studies indicate the usefulness of the extended space concept for deriving kineticChapter 2. Literature Review 22equations; the low experimental n values result from the fact that the nuclei are clustered on planes rather than randomly distributed in the volume, and because of this,significant impingement can take place at a very early stage during recrystallization [68].DeHoff [85] recognised this increased impingement, and suggested the use of the equation = (1 — X)2 (as opposed to the random nucleation assumed in Eq. 2.7) toappropriately reduce the real volume fraction recrystallized.The assumption of a constant growth rate (G) in the JMAK analysis, has comeunder considerable scrutiny in the modelling of recrystallization. G, usually obtained bymeasuring the time variation of the largest intercept-free distance in the microstructure,is limited to X < 0.20 due to the impingement effects. Some of the past experimentssuggest a constant growth rate [73, 74, 77, 80, 86], while a decreasing growth rate has alsobeen widely reported, particularly for iron- and aluminum-based alloys [33, 37, 38, 72, 75].Such a decreasing growth rate explains the observed negative curvature away from theexpected JMAK-type linear behaviour towards the completion of recrystallization [87],but may not contribute significantly to the observed low n values [88].The interface migration rate (G), commonly expressed as the product of a drivingforce and mobility, may be reduced considerably due to a decrease in either one of theterms [89]. The dynamic interactions of moving grain boundaries with dissolved soluteatoms and the associated effects on their mobility may partly explain some of the observed decrease in growth rate [68, 81]. However, the observed reduction in interfacemigration rate with increasing recrystallization is thought to be based on the reducingdriving force. This can be attributed to on going recovery effects or the non-uniform distribution of stored energy or a combination of both. No single explanation here satisfiedall researchers. Another proposed explanation for the retardation of interface migrationrate considers growth to be highly anisotropic or the dimensionality of growth to be lessthan three [60, 76].Chapter 2. Literature Review 23Concurrent recovery in the unrecrystallized regions reduces the growth rate by decreasing the stored energy that provides the driving force for the boundary migration[33, 37, 38, 72, 90]. Recovery can play a significant role in high stacking fault energyalloys, as clearly illustrated by Furu et al. [91] in their examination of the low stackingfault copper and high stacking fault aluminum; the softening curves presented by themfor pure copper [92] and for pure aluminum [93] are shown in Fig. 2.8. It is obviousthat in the case of aluminum, a substantial portion of the stored energy evolution occursduring recovery, whereas no recovery effects are visible for copper. Price [94] presentedstrong arguments in favour of the recovery effects, based on the observed linear JMAKbehaviour when recovery was absent as in pure copper [32, 61]. However, the recoveryprocesses are generally rapid at recrystallization temperatures, and consequently, theymay not exhibit the necessary temperature/time dependence to provide a complete explanation for the decreasing interface migration rate, particularly towards the end ofrecrystallization [63, 75, 85].The second major explanation for the decreasing interface migration rate is the nonuniform distribution of stored energy from grain to grain, as well as within a grain [63, 88,95]. Recrystallized grains, being nucleated in the regions of highest stored energy, wouldbe expected to grow along a driving force gradient with a progressively decreasing growthrate. Rollett et al. [96], by neglecting recovery effects and considering such a distributionof stored energy in the simulation of recrystallization, could obtain a negative deviationfrom the linear JMAK behaviour. Additional evidence was provided by the calorimetricstudies of Hutchinson et al. [95], who showed that a given fraction of recrystallization inpure copper was associated with a greater amount of stored energy evolution during theearly stages than during the later stages, even though the stored energy release caused byrecovery was negligbly small. They also rationallized the low n exponents in terms of thisnon-linearity. Vandermeer and Rath [63] used the combined recovery effects and storedChapter 2. Literature Review 24energy gradients to explain their observed non-linear growth in iron single crystals.There are few reported analytical treatments where a varying growth rate has beenincorporated into a JMAK-type equation. Furu et al. [91] have presented one such studyin which the recovery effects were accounted for by,= [1 + (t/Ti)], 0 b < 1 (2.12)where r1 is a temperature dependent relaxation time parameter, and the special caseb 0 corresponds to a constant growth rate 0 = G. If it is assumed that the variationin the growth rate is equal to the variation in the stored energy due to recovery effects,then this equation can be rationallized in terms of subgrain growth as the dominantrecovery mechanism [91]. If the growth rate given by Eq. 2.12 is incorporated into theJMAK derivation procedure for spherically shaped grains, that will lead to,4 3(1—b)=1- exp {- [(1 ‘6)] (—) } (2.13)where r2 = (NG)1/3is a relaxation time parameter for recrystallization. Eq. 2.13corresponds to a limiting case where r,/r2 << 1. Furu et al. [91] successfully modelledthe recovery and recrystallization in aluminum using equations 2.12 and 2.13 respectively,by selecting the appropriate values for r1, 6 and r,/r2. They also rationalized a low rivalue in terms of the slowing down of the growth rate. Vandermeer and Rath [63] followeda similar approach in their kinetic study on iron single crystals, although they used Eq.2.6 to model the recovery kinetics.The assumption of early site saturation in deriving the JMAK equation is usuallya sound one, and not expected to contribute towards any observed failure in recrystallization modelling. This has been shown to be true for large deformations (eg., 60 - 80%); several studies have been reported where the nucleation was found to be effectivelyChapter 2. Literature Review 25instantaneous [33, 37, 38, 75, 80, 81]. However, a constant and an increasing nucleation rates were also reported in a few studies, particularly when the metal was lightlydeformed (eg., 5 - 10 %) [73, 74, 77].The inadequacies of the JMAK equation in describing the recrystallization kineticsand some of the analytical treatments to address this problem were highlighted in thisdiscussion. However, it should be emphasized that the JMAK equation was employedin a vast majority of the reported recrystallization kinetic studies. In many of thesecases, a reasonably good fit to the experimental kinetic data was provided by the JMAKequation, despite the resulting JMAK exponents being considerably different from thosepredicted by the theory. This successful curve-fitting by the JMAK equation is primarilydue to the fact that recrystallization, like other nucleation and growth processes, exhibitsa sigmoidal kinetic behaviour, a form described well by the JMAK equation.2.1.3.3 Improved Models - Microstructural Path ConceptTraditionally, many kinetic studies focussed only on the variation of volume fraction recrystallized (X) with time (t), and such data could be readily analysed using the JMAKequation. However, such an approach invokes the apparent anomaly of using only volumetric terms to model a surface reaction. It has also been shown that useful informationrelated to modelling can be inferred from additional microstructural properties; interfacial area per unit volume separating the recrystallized grains from the cold worked matrix(A) and grain growth rate (0) are two such properties that can be easily determined fromquantitative metallography. Experimental determination of the nucleation rate (NT) isa complicated task. However, a mathematical procedure using Laplace transform techniques has been reported and used for deducing NT and 0 (and growth dimensionality)from the experimentally measured time variation of X and A [75, 97, 98, 99].The characterization of recrystallization kinetics using the A values would require aChapter 2. Literature Review 26set of complementary equations for A, equivalent to the appropriate equations for X.For random nucleation, the relationship corresponding to Eq. 2.7 is given by [85],A=Aex(1X) (2.14)where Aezi. is extended interfacial area per unit volume. If the JMAK theoretical development is adopted for areal terms (instead of volumetric terms), then the followingcomplementary relationship to the JMAK equation can be derived [68],A = (1 — X)Ktk (2.15)where K and k are constants analogous to b and n in Eq. 2.11.The interface-averaged boundary migration rate (0) is another useful parameter inrecrystallization modelling; this can be estimated throughout the transformation by usingthe Cahn-Hagel [100] formulation,AG=4 (2.16)The relationship between the various global microstructural properties (eg., X and A)that describes the microstructural evolution is called the microstructural path function.The nature of this relationship depends on both the distribution of nucleation sites andother geometrical considerations, but is independent of the kinetics [81, 90, 101]. Thepath function, being dependent on the number of nuclei, is usually affected by the amountof deformation [81]. However, a study on aluminum [101] has shown the path functionto be independent of the impurity content, despite the observed reduction in growth rateby three orders of magnitude.Under simplifying JMAK assumptions, both X and Aex will have t’-type timedependence, and this will lead to a relationship in the form of Aex cx (Xe), with q a.constant. Now, if Xe,, and Ae,, are substituted by functions of X and A as given by Eqs.Chapter 2. Literature Review 272.7 and 2.14, then the following path function can be obtained [85, 102],A = C(1 — X)[— ln(1 — X)] (2.17)where C and q are model dependent constants. The following generic semi-empiricalpath function was proposed by Rath [103],A = K(X)(1 — X) (2.18)where K, q and p are model dependent constants with 0 <q,p < 1.When recrystallization is characterized by both X and A, it may be easier to developa microstructural model using a microstructural path function (eg., Eqs. 2.17, 2.18) inconjunction with one kinetic function (eg., Eqs. 2.11, 2.15). The use of the path functionis an advantage when time dependent complications such as competing recovery effectsare present; these factors manifest themselves in the kinetic functions, but do not affectthe path function [102].The approach outlined above forms the basis for developing a comprehensive modelof recrystallization. However, determining the appropriate kinetic function through analitical means remains a formidable task. An alternative approach would be to find anempirical kinetic function. As an example, for deformed iron single crystals, Vandermeerand Rath [75] reported from isothermal measurements that Xex = Bt and Aex = Kt,where B and K were functions of temperature and n and m were constants; X€ and Aexwere obtained using Eqs. 2.7 and 2.14 from the experimentally determined X and A. Itwas also reported from the same study that O decreased with time according to t°at all test temperatures, and this relationship constitutes a simple kinetic function thatcan be readily employed for modelling purposes.Chapter 2. Literature Review 282.1.3.4 S-F Equation - An Empirical ApproachThe model developed by Speich and Fisher [90] was based on two different empiricalrelations. The first, a parabolic equation, was obtained from the metallographic measurements made on a 60 % cold worked 3.25 % Si-steel and given by,A = KAX(1 — X) (2.19)where J(A is a temperature independent constant. The plot of A vs. X obtained in thatwork [90] for the isothermal temperature range of 550 to 1000°C is shown in Fig. 2.9.The second, an empirical inverse time dependence, was reported by English and Backofen[81] for a hot worked Fe-3.25 % Si,G = KG t’ (2.20)where KG was found to be independent of temperature and strain except during theinitial stages of growth, as shown in Fig. 2.10; Leslie et al. [38], and Speich and Fisher[90] have also reported similar vs. t relationships.If the Eqs. 2.19 and 2.20 are combined using the Cahn-Hagel formulation for surface-controlled growth (Eq. 2.16) [100], this will lead to the Speich and Fisher (S-F) equationfor isothermal recrystallization [90],(1 = k tm (2.21)where k is a function of temperature and m(= KAKG) is a constant. It should beemphasized here that the empirical equations 2.19 and 2.20 are quantitative descriptionsof a microstructural path function and a kinetic function, respectively.Speich and Fisher [90] stressed the validity of Eq. 2.19 within the experimental rangeX = 0.02 to 0.95. Cahn [104] showed stereologically that this equation was not rigorouslycorrect at either extreme of X. However, Eq. 2.19 is a simple expression that compensatesChapter 2. Literature Review 29reasonably well for grain impingement during recrystallization. In addition, nucleationis implicit in this model, unlike the JMAK theory, where the nucleation parameters haveto be explicitly specified.It has been shown that 0 is a function of time for 3.25 % Si-steel, but independentof temperature [81, 90]. Both Speich and Fisher [90] and Li [61] rationalised the inversetime dependence, based on concurrent recovery occurring at a rate proportional to t2.The temperature independence, although apparently incompatible with the view thatinterface migration is a thermally activated procees, was explained by invoking the sameactivation energy for the interface-averaged boundary migration rate (0) and the laterstages of recovery 292 kJ/mole in the case of 60 % cold worked 3.25 % Si-steel [90]).Gokhale et al. [105] interpreted the same behaviour solely in terms of the reduction inthe dimensionality of growth during recrystallization. In deformed iron single crystals,Vandermeer and Rath [75] obtained approximately the samet038 dependence for bothG and 0 at all isothermal temperatures. They attributed these observations to thenon-uniform distribution of stored energy in the deformed matrix. The stronger t1time dependence observed by Speich and Fisher [90] was thought to be due to a greaternon-uniformity of stored energy expected in polycrystalline materials [75, 76].Speich and Fisher [90] initially obtained a kinetic equation by combining a constant Gwith Eq. 2.19, and showed that for a silicon steel, the resulting expression overestimatedX during the later stages of recrystallization. Price [87] demonstrated similar effectsin pure vanadium when the JMAK equation was employed. However, in both cases,the kinetics was described well by the S-F equation with its inverse time dependenceof . Based on these observations, Price [87] suggested the S-F equation to be animprovement over the JMAK equation. In a recent study on a rimmed low-carbon steel[39], the recrystallization kinetic data was modelled using both the JMAK and the S-Fequations, and the results, shown in Table 2.1, indicate that both equations describe theChapter 2. Literature Review 30data reasonably well with comparable correlation coefficients, the poorest fit being at thelow and high temperatures.A computer simulation by Price [106, 107] assuming random instantaneous nucleation,showed that both the JMAK type extended volume (Eq. 2.7) and the S-F type empiricalequation (Eq. 2.19) provide reasonable compensation for grain impingement. Based onthe analysis by Price, the major limitation of the JMAK equation is its assumption oflinear growth, while that of the S-F relation is its empiricism. The fact that relationsidentical to Eq. 2.21 have also been derived using a constant growth rate (for example,when increased impingement due to clustering was accounted by (1 — X)2 [85])further emphasizes the empirical nature of the S-F equation.2.1.3.5 Microstructural Evolution - Computer SimulationsAn essential prerequisite for the estimation of the final mechanical properties is theprediction of the microstructure that results from a deformation and annealing treatment.The spatial inhomogenity of the nucleation and growth processes makes this a difficultproblem to be treated analytically. However, computer simulations based on the JMAKapproach [91, 108, 109], Monte Carlo techniques [88, 96, 110, 111] and a network model[112] have enabled the solution of such problems using numerical techniques.In the JMAK-type three-dimensional model [91], the nuclei, distributed in the space,are allowed to grow until they impinge, and the resulting microstructures are analysedfrom two-dimensional sections. The nucleation and growth conditions and rates can beset in accordance with specific models. Monte Carlo simulation methodology [110, 111],originally developed to study grain growth by considering only the grain boundary energy,has been extended to simulate recrystallization by an additional assignment of storedenergy to the lattice sites of each grain in the mapped microstructure. Recrystallizationnuclei with zero stored energy are then introduced, and the boundary motion is simulatedChapter 2. Literature Review 31according to the standard Monte Carlo procedure. A model based on a network of grainsor subgrains, with the capability to simulate recovery and recrystallization, has also beenreported [112]. An equation describing the motion of a boundary is solved for eachboundary, which is then moved accordingly, and the process repeated.The recrystallization kinetics obtained from those models were analysed in terms ofthe JMAK equation, and the grain size distributions were compared with those obtainedexperimentally. The predicted grain size distribution, in general, did not coincide wellwith the experimental curves in terms of the symmetry and spread [88, 91, 112]. However,such simulations have increased the understanding of the JMAK equation as appliedto recrystallization. Furu et al. [911, based on a JMAK-type simulation, showed thepossibility of a transition from three to one dimensional growth (with the associateddecrease in n value) during transformation when nucleation was restricted to certainparallel planes. A JMAK-based simulation by Leffers [108] showed that both randomnucleation combined with a decreasing growth rate (proportional to t°95) and non-random nucleation combined with a constant growth rate, could produce an ii valueof around 0.8. Doherty et al. [88], using Monte Carlo simulation of two-dimensionalrecrystallization, obtained n values in the range of 0.4 to 1.1 by allowing a grain tograin variation in the stored energy; under these conditions, the JMAK impingementcorrection factor (1 — X) (Eq. 2.7) has been shown to seriously underestimate the realimpingement effects [96]. These, and other results obtained from such simulations haveimproved the understanding of the physical processes involved in recrystallization andthus aid in refining the existing analytical models [113].Chapter 2. Literature Review 322.1.4 Additivity and Continuous-Heating KineticsDetermination of the kinetics of recrystallization at a number of different temperatures, allows one to draw a complete isothermal recrystallization diagram. This Time-Temperature-Recrystallization (T-T-R) diagram gives the relation between the temperature and the time for any fixed fractional amount of recrystallization. However, inindustrial practice, the kinetic behaviour of an assembly at constant temperature is frequently of less importance than its behaviour during continuous heating.2.1.4.1 The Concept of AdditivityThe kinetics of phase transformations under non-isothermal conditions has not beenextensively studied using fundamental kinetic equations. Part of the difficulty is thatboth the nucleation rate and the growth rate are time-dependent parameters under suchconditions. One approach to this problem which has been successful is the assumptionthat the transformation is additive. For the application of the ‘additivity principle’, it isnecessary that the transformation behaviour depends only on the state of the assemblyand not on the thermal path by which it is reached. For this to be valid, the instantaneoustransformation rate has to be a function solely of the amount already transformed andthe temperature [69], i.e.,= f(X, T) (2.22)2.1.4.2 Proportional Consumption and the Additivity RuleChristian [69] illustrated additivity by considering a simple non-isothermal reaction combining two isothermal treatments, as shown in Fig. 2.11. The transformation is considered to occur initially at temperature T1, for time t, with the kinetic law X = f1(t) (upto X = X1), and is then continued at a second temperature T2 (after rapidly heated fromChapter 2. Literature Review 33T1 to T2), with the kinetic law X =f2(t), until the total amount transformed is Xa. Ifthe transformation is additive, it will continue at T2 as if the fraction transformed, X1,had been transformed at T2; the time corresponding to that, i.e., t2 in Fig. 2.11, is calledthe ‘virtual time’. If tal and ta2 are the times taken to transform Xa at temperatures T1and T2 respectively, and if the following equation, termed ‘proportional consumption’, isassumed,1 2=— (2.23)then, the following relationship can be easily derived,+2= 1 (2.24)This equation implies that the total time to reach a specified amount of transformation(Xa in this case) under non-isothermal conditions is obtained by adding the fractions oftime to reach this stage isothermally until the sum reaches unity. This concept can begeneralized into the following ‘additivity rule’,t dtL ta(T) = 1 (2.25)where ta(T) is the time to transform Xa isothermally at temperature T, and t and txare the start time and the time to transform Xa respectively, under non-isothermal conditions. Thus, by using the ‘general rate equation’ (Eq. 2.22) for applying the ‘additivityprinciple’, and assuming ‘proportional consumption’ (Eq. 2.23) is valid, the ‘additivityrule’ (Eq. 2.25) is obtained.In this derivation of the additivity rule, certain restrictions have been imposed on theisothermal transformation behaviour through the assumption of proportional consumption. Proportional consumption, as given by Eq. 2.23, implies that a certain fractionof the total reaction time (eg., 10 %) always corresponds to the same fixed percentageChapter 2. Literature Review 34of the transformation event (eg., 6 %), irrespective of the isothermal reaction temperature. In a T-T-T or T-T-R diagram, this requires that the curves representing fractionaltransformation be distributed in a proportional manner within the curves correspondingto the start and the end of the reaction.Fig. 2.12 shows a schematic T-T-R diagram, exhibiting proportional consumption;the validity of the additivity rule (Eq. 2.25) for this situation can be illustrated in anelegant manner. In this illustration, the continuous heating path is considered to consistsof several isothermal steps, the first being time step, dt, at temperature T1. If the timeto transform Xa at T1 is ta(Ti), then the fractional time consumed will be dt/ta(Ti).For the next time step, dt, at temperature T2, the reaction, if additive, will continue asgiven by the isothermal line at T2. Now, if the virtual time at temperature T2 is dt*(the time to produce X1 at T2), as indicated in Fig. 2.12, then according to proportionalconsumption,dt* dtta(T2) = ta(Ti) (2.26)Hence, the addition of the fractional time consumptions corresponding to the first twotime steps will be,dt dt — (dt*+dt)a 1 a 2 a 2Summing the fractional increments to T gives,di ta(Tn)1 228ia(T)—ta(Tn) —.This illustrates the validity of the additivity rule given by Eq. 2.25 for continuous heatingconditions.2.1.4.3 Isokinetic TransformationsChristian [69] showed that the additivity rule, in the form of Eq. 2.25, can be provenanalytically, only if the transformation can be described by a ‘separable rate equation’,Chapter 2. Literature Review 35i.e., in a factorized form,dx h(T)229dtg(X)where, the rate of transformation is a separable function of temperature, T, and fractiontransformed, X. Eq. 2.29 will lead to a relationship of the form,X = F (f h(T)dt) (2.30)where h(T) is a function of temperature oniy (eg., growth rate). Cahn [114] definedreactions of this kind as ‘isokinetic’, where transformation at different isothermal temperatures would take the same course, except for the time scale. It should be notedthat Avrami [67] originally described isokinetic conditions using a constant nucleationrate (Ni) to growth rate (0) ratio; this was recognized as a very limiting condition.not applicable to most transformations. Cahn’s generalized isokinetic condition can befurther illustrated by comparing the isothermal reaction rates (given by Eq. 2.29) at twodifferent temperatures, T1 and T2, for any given X,(dX/dt)T1 h(T1) 2 1(dx/dt)T2 - h(T2) (.3)This equation suggests that the ratio of the isothermal reaction rates depends only on thetemperatures involved, and not on X, whereas Eq. 2.22 would suggest this ratio to be a.function of both T and x. This illustrates a major difference between the requirementsgiven by Eq. 2.22 and Eq. 2.29. Clearly, neither this kind of isokinetic behaviour northe associated additivity rule can be inferred from Eq. 2.22 alone.To examine if proportional consumption is attainable for any isokinetic reaction usingthe JMAK equation (Eq. 2.11), x = 1 — exp(—bt”), requires rearranging of the JMAKequation to obtain the transformation time, t,=[ln(1_X)]* (2.32)Chapter 2. Literature Review 36Differentiating the JMAK equation with respect to time and combining with Eq. 2.32gives,dx— 2 33di— ( ‘ [ 1 ]n_1/n1-X) Fln(1-X)]If the JMAK time-exponent, n, is a constant, and b is a function only of temperature,then Eq. 2.33 will satisfy the isokinetic requirement expressed by Eq. 2.29, as previouslyreported [115]. The validity of the additivity rule (Eq. 2.25) for this condition has alsobeen illustrated [116].To illustrate proportional consumption for the case corresponding to Fig. 2.11, letthe JMAK parameters n1, b1 describe the isothermal event at temperature T1, and ii2, b2at temperature T2. For the notations given in Fig. 2.11 it can be shown, using Eq. 2.32,(ti/ta,)i — ln(1 — X1) (-) 234)(12/1a)T — ln(1— Xa) (Now, if n is a constant,=(2.35)\ aJ’p1 \ a2J7’2This shows the validity of proportional consumption for a constant n. Under theseconditions, the ratio of the isothermal reaction rates for a given X can be calculatedfrom Eq. 2.33,1(dX/dt)T1 (b1’(dx/dt)T2=(2.36)When b is solely a function of temperature, and n is a constant, this satisfies the isokinetic condition expressed by Eq. 2.31. All these illustrations remain valid when theS-F Equation (Eq. 2.21), X/(1 — X) = ktm, is used to describe the isothermal recrystallization kinetics with a constant m and temperature dependent k. These derivationsillustrate that certain transformations are isokinetic, and for those isokinetic reactions,the proportional consumption and hence, the additivity rule (Eq. 2.25) are valid.Chapter 2. Literature Review 372.1.4.4 Kinetic Calculations for a General TransformationThe kinetic calculations during continuous heating are usually performed as follows:• the heating path is divided into several isothermal steps,• at each time step, either the fraction transformed, dX(T), or the fractional timeconsumed, dt/ta(T), is calculated,• the calculated fractions are added until the sum reaches the appropriate fractiontransformed or unity (in the case of fractional time).When proportional consumption is valid, it can be seen from Fig. 2.12 that both thesesums reach the total at the same instant, i.e., >ZdX(T) Xa and d/ta(T) = 1.This is not the case for any general non-isokinetic type transformation. As an illustration, a case with an increasing JMAK exponent, n, with temperature is considered,i.e., n2 > n1 for T2 > T1; such kinetic behaviour has been reported for recrystallizationon a rimmed low-carbon steel [57]. Now, from Eq. 2.34, the following relationship canbe derived since Xa > X1,> (2.37)\ta2IT ‘\taiJjThis equation suggests the fractional time consumption at a lower temperature, T1, tobe equivalent to a larger fraction at a higher temperature, T2. This results, when appliedto Fig. 2.12 as in Eq. 2.27 will give,dt dt (dt*+dt)\ + fm \ (2.38)a1i) tal2) tal2)Now, when the summation is performed in the usual manner, either of the followingcombinations will be possible,EdX(T) = Xa,ta(T)<1 or 1(T) = 1, dX(T) > Xa (2.39)Chapter 2. Literature Review 38These calculations illustrate the difficulties associated with the modelling process if thetransformation is not an isokinetic one.2.1.4.5 A Summary on the Various Conditions of AdditivityThere is some confusion regarding the terminology and the different conditions availableto describe additivity. The different additivity descriptions and their inter-relationshipshave also been studied from the mathematical point of view [117, 118, 119]. Based onthose studies, and from the discussion in this section, it can be concluded that there arebasically three different conditions that have to be met to assume a transformation isadditive:1. the ‘general rate equation’ given by Eq. 2.22 (this is the basic requirement for theapplication of the ‘additivity principle’),2. the ‘separable rate equation’ given by Eq. 2.29 (‘isokinetic condition’ and ‘proportional consumption’ are built-in into this equation),3. the ‘additivity rule’ given by Eq. 2.25.Hayes [117] has derived detailed mathematical relationships linking these three conditions. He has shown the equivalence between condition 2 and Cahn’s generalized isoki—netic condition. Condition 2, a subset of condition 1, has been shown to lead to condition3 [117]. On the other hand, condition 1 will not lead to conditions 2 or 3 without theadditional assumption of isokinetic condition or proportional consumption. Hence, thereare really only two types of additivity conditions. The former one, given by condition1, can be used for a broad range of situations whereas, the later one, given by eithercondition 2 or condition 3, is valid only for the isokinetic-type transformations [117, 119].Chapter 2. Literature Review 39When the JMAK equation describes the isothermal event, isokinetic transformations require ii to be a constant and b to be solely a function of temperature [115, 116, 118], andthese restrictions will lead to a single additivity model since all three conditions are thesame.2.1.4.6 Scheil Equation for Incubation and Its ApplicationsScheil [120] originally proposed an equation similar to Eq. 2.25 to determine the incubation period during a non-isothermal event. He assumed that the time spent at a particular temperature, dt, represented the fractional incubation time consumed, dt/r(T),where r(T) is the isothermal incubation period at temperature T. Then, the start oftransformation is considered to occur when the following condition is fulfilled,J T(T) = 1(2.40)where t is the non-isothermal incubation time. As was the case with the additivity rule(Eq. 2.25), the ‘Scheil equation’ (Eq. 2.40) is also based upon the validity of proportionalconsumption of isothermal incubation.Based on some studies with austenite-ferrite and austenite-pearlite transformations[121, 122] and recrystallization [39], the Scheil equation has been reported to predict considerably longer start times than were actually observed. Recently an attempt [123] wasmade to address this problem in austenite-to-pearlite transformation by incorporatingideal isothermal incubation times into Scheil predictions. These ideal start times, corresponding to an infinite cooling rate rather than an experimental one, could be calculatedeither from experimental CCT curves through an inverse additivity procedure [124] orbased on isothermal experiments performed with two different initial cooling rates [125].Although this approach marginally improved the predictions, it is thought that the mostserious problem with the Scheil equation is its assumption of proportional consumption,Chapter 2. Literature Review 40as was illustrated by Moore [126] in an early work on austenite decomposition.Moore [126] conducted stepped isothermal experiments at two different temperatureswith known incubation times, and observed the start of the reaction microscopically. Thesum of the fractional incubation times corresponding to the start of transformation wasinvariably less than unity during austenite-to-ferrite transformation. He explained this bysuggesting the non-equivalence between a given percentage of the incubation period spentat different temperatures, and correlated these effects to the smaller critical size of theferrite nuclei at lower temperatures. During a step-down experiment, an unstable nucleusat a higher temperature might become a stable one at a lower temperature, suggestingdisproportionately larger effects of early nucleation on later nucleation at a differenttemperature. He also interpreted the experimentally determined incubation period asa composite of two separate processes, a period of nucleation, followed by a period ofgrowth which extends beyond the completion of incubation. Although Moore suggestedthese effects to be minimal during continuous cooling, his study clearly indicates thatincubation may not be an additive process.2.1.4.7 Application of Additivity for Transformation KineticsThe principle of additivity has been successfully applied to predict the kinetics of austeniteferrite and austenite-pearlite transformations [115, 121, 122, 127]. In all of these studies,the JMAK equation was used to descibe the isothermal event. When this equation wasemployed to describe only the transformation event (excluding incubation), the JMAKtime-exponent, n, showed little dependence on temperature and therefore described asa mean ñ value, and b was a strong function of temperature, thus satisfying the isokinetic requirement. Good agreement between the additivity predictions and the experimental measurements during continuous cooling were reported under those conditions[115, 121, 122].Chapter 2. Literature Review 41The same approach was successful in describing the recrystallization kinetics of acold rolled, rimmed, low-carbon steel continuously heated at a rate simulating batchannealing [39, 57, 128]. A comparison of the predicted and experimental kinetics areshown in Fig. 2.13. Fig. 2.13 also compares the effectiveness of the JMAK and theS-F equations in describing the continuous heating recrystallization kinetics. The goodagreement obtained for both approaches supports the experimental validity of applyingthe additivity principle to describe non-isothermal recrystallization.2.1.4.8 Criteria for the Validity of AdditivityIn general, a reaction involving two different time-temperature dependent parameterscorresponding to nucleation and growth, will not be additive. However, if the reaction iscontrolled by a single time-temperature parameter, it is then isokinetic (as indicated byEq. 2.30) and will be additive. Avrami [67] demonstrated the validity of additivity whenthe nucleation rate, N7, is proportional to the growth rate, G, over a range of temperatures. Cahn [114] introduced a less restrictive additivity requirement based on ‘early sitesaturation’, where nucleation sites are rapidly exhausted and the subsequent transformation kinetics are dominated by growth, a temperature dependent parameter. Based onexperimental measurements on the pearlite transformation, Kuban et al. [115] proposedthat ‘effective site saturation’, an even less stringent condition, would also satisfy theadditivity requirement. This condition proposed that the added volume associated withthe incremental growth of the large, early nucleated sites dominate the later stages ofthe transformation kinetics.Recently the principle of additivity was tested by Kamat [129] by examining theproeutectoid ferrite transformation under step-quenching conditions, where the ferritegrowth is controlled by long range diffusion processes. Early site saturation was observedat all temperatures during the transformation. The use of the JMAK equation (as anChapter 2. Literature Review 42empirical equation to describe the sigmoidal transformation kinetics), in conjunction withthe additivity principle was successful in describing the non-isothermal transformationkinetics.The validity of applying the additivity principle to describe non-isothermal recrystallization has not been studied in detail, with the exception of the results shown in Fig.2.13 [39]. During recrystallization of heavily deformed metals, nucleation has often beenreported to be instantaneous [33, 37, 38, 75, 80, 81], thereby satisfying the early sitesaturation condition. For this condition, additive behaviour would be expected.2.1.5 Annealing Phenomena in Low-Carbon Steels2.1.5.1 Structural Changes during Cold-Rolling and AnnealingWhen a cold-worked metal is held at any homologous temperature, TH, above ‘S-’ 0.1, somerecovery occurs. The mechanisms of recovery operating in the region 0.1 < TH < 0.3,are dependent on the motion of point defects. As annealing temperature increases, theenergy input will be sufficient to overcome the activation energy requirements for otherrecovery mechanisms, such as the motion and rearrangement of dislocations [86].In metals of high stacking fault energy such as iron, the initial structure that formsafter heavy deformation (60 - 80 % cold work) consists of cells whose walls are tangleddislocation arrays of very high density, with some dislocations in the cell interiors. Thesemetals, in pure form, when heated to a sufficient temperature, undergo a considerableamount of recovery due to the relative ease with which dislocation motion can occur[130]. In worked metals of low stacking fault energy, no recognisable cell structure formsduring deformation, and the reduced tendency for dislocations to cross-slip leads to theformation of planar dislocation arrays with a high strain energy. This constitutes astrong driving force for recrystallization, so that recrystallization is likely to proceedChapter 2. Literature Review 43before recovery progresses significantly [86].Emphasizing the iron-base alloys, initial recovery results in the tangled dislocationsin the cell walls rearranging themselves into lower energy configuration, and the interiordislocations migrating towards the cell walls. Dislocations are also reduced in numberdue to a variety of annihilation processes. The cell walls become more clearly defined withgreater misorientation and eventually form subgrains of about the same size as the initialcells. These subgrains remain at about the same size until quite late in the recovery process when they may begin to grow [29]. Hu [53] attributed the observed subgrain growthto ‘subgrain coalescence’, based on transmission electron microscopic observations of 80% cold-rolled silicon-iron single crystals. The coalescence process, shown schematicallyin Fig. 2.14, involves a gradual moving of dislocations out of the subgrainboundary between two cells, to the boundaries surrounding them, and a rotation of the subgrain itselfinto the same orientation as its neighbouring subgrain. This mechanism requires latticediffusion, and consequently a moderately high temperature is needed. Misorientationincreases during the coalescence process, and a cluster of coalesced subgrains eventuallybecomes a recrystallization nucleus [53].A ‘subgrain growth’ model, shown schematically in Fig. 2.15, was proposed by Cahn[131] based on the idea of polygonization of macroscopically bent single crystals. He suggested that a small region of high dislocation density, and therefore of high strain gradientand substantial local misorientation, turns into a small strain-free cell by a process ofdislocation climb and rearrangement. Polygonized domains or subgrains thus formed atrelatively high temperatures, are dislocation boundaries of high mobility (misorientationof up to a few degrees) that can migrate into the differently oriented surrounding matrix.Cahn [131] explained that in addition to the preferential growth of a relatively largesubgrairi, a highly misoriented subgrain, even if it is not larger than the average size, canalso grow freely at the expense of its neighbours. A growing subgrain with an increasingChapter 2. Literature Review 44misorientation angle eventually becomes a nucleus for recrystallization.There is considerable debate as to whether the initial growth of subgrains occurs bysubgrain coalescence or by low angle sub-boundary migration. Jones and Hansen [132]concluded the overall kinetics of subgrain growth to be the result of combined subgraincoalescence and low angle boundary migration, no single process being dominant. Experimental observations support the occurrence of both these processes during recovery ofiron based alloys [30]. Cahn [131] suggested that the later stages of growth of a nucleusformed by either mechanism would be due to the migration of boundaries with increasedmisorientation.In some lightly deformed metals, nuclei formation has been attributed to strain-induced boundary migration or grain boundary bulging. When the strain is low, thedislocation density varies from grain to grain. As a result, a short segment of an existing high angle boundary anchored by the substructure in one grain may bulge outinto a region of higher density to produce a roughly spherical volume (relatively free ofdislocations) capable of migrating [133].Solute additions and the presence of fine particles usually retard the recovery processes[130]. Solute additions can hamper climb through the binding energies that tie vacanciesto solute atoms, and also reduce the stacking fault energy permitting dislocations toextend into partials, making climb and cross-slip more difficult. These effects rendernetwork nodes more resistant to unpinning [133]. Solute atoms also reduce sub-boundarymobility, causing further retardation of recovery. When the diffuse cell walls formedduring deformation are broader than the interparticle spacing, the particles can stabilizenetworks of subboundary dislocations, and hence interfere with the conversion of the cellstructure into well-defined subgrains. In addition, small particles retard subgrain growthrate by Zener pinning of migrating low angle boundaries and by hindering coalescencethrough the inhibition of boundary to boundary dislocation transfer [132].Chapter 2. Literature Review 45Recrystallized grains nucleate preferentially in a region where residual damage dueto plastic deformation is greatest. This observation is usually explained in terms of alocalized high dislocation density and a substantial local lattice curvature. Cahn [131]suggested the existance of substantial local lattice misorientation to be a necessary precondition for nucleation of recrystallized grains. A high density of nuclei observed atdeformed grain boundaries, deformation bands and coarse particles can be explained inthis manner [82, 131]. As an example, the nuclei formation in 80 % cold-rolled (001)[100]silicon-iron single crystals has been reported to occur exclusively within the deformationbands; this was attributed to the strong curvature caused by the orientation differences[53]. For the (001)[110] crystals tested in the same study, no deformation bands wereobserved, and consequently no recrystallization occurred even at a temperature as highas 800°C [53].Second phase particles influence the formation of recrystallization nuclei by alteringthe density and distribution of dislocations in the metal matrix [134]. If the particlesare harder than the matrix, the matrix immediately adjacent to the particles will bedeformed to a greater extent. Large particles give rise to an increased local latticemisorientation, and hence will be favoured nucleation sites. A critical particle size of0.74 m was reported for particle stimulated nucleation in a 0.4 wt % carbon steel [135].A smaller particle spacing may decrease the critical particle size due to the formationof joint deformation zones. Other investigations on steels have also indicated that largeparticles with diameters greater than 1 m can act as nucleation sites for recrystallization[1].Talbot [136] investigated the effects of annealing iron of different purity after 96 % coldreduction. For commercially pure iron, cold rolling produced a cell structure, with thecell wall thickness varying widely up to 1 m. Recovery occurred at high temperatureswith an overall reduction in dislocation density. In particular, the tangled dislocationChapter 2. Literature Review 46walls became thinner and more sharply defined, although no significant change in therelative misorientation was observed. A general growth of cells up to approximately 5was reported after 2 h at 550°C, and recrystallization proceeded within the recoveredstructure. However, for the highly pure zone-refined iron, the cells formed after coldrolling were much coarser, and the misorientation across the cell walls was of the orderof 2 to 3°. The nuclei for recrystallization were observed to grow directly from the cold-worked cells at lower temperatures (‘-.. 350°C), without going through any significantstructural changes prior to the onset of recrystallization.Dillamore and co-workers [78, 137] studied annealing of 70 % deformed high purityiron and Al-killed steel by TEM observations. They demonstrated an increasing level ofstored energy in grains in the orientation order of {001} < 110 >, {111} < 110 > and{110} < iTO >. A smaller cell size and a larger average cell boundary misorientationwere associated with an increased stored energy level. For high purity iron, subgrainstructures in {111} < 110 > and {110} < 110 > oriented grains coarsened more rapidlythan in either {0O1} < 110 > or {113} < 110 > oriented grains. A higher growth rate wasattributed to higher stored energy and to a wider initial subgrain size distribution. Otherresearchers have observed more complex deformation patterns and associated smaller,more elongated deformation cell structures with larger mean boundary misorientationsnear grain boundary regions, when compared to grain interior [132].The effects of cold rolling and annealing on the microstructure in rimmed and Alkilled steels were examined by Goodenow [138]. The cold rolled cell structure within anindividual grain appeared to be uniform and arranged in one of two distinct groups; oneconsisted of small, elongated cells of 0.5 to 1 tm arranged in parallel rows and the othercontained large cells of 1 to 2 tm arranged randomly. Some grains appeared to contain both groups separated by a transition zone. Depending on the initial cell structure,two different groups of subgrains were observed after initial recovery. With continuedChapter 2. Literature Review 47annealing, the larger subgrains appeared to grow by a slow sub-boundary migration process. However, the small subgrains were observed to merge with one another, primarilythrough a coalescence process. It was these small subgrains that eventually grew by additional coalescence and boundary migration to form the nuclei. In addition, coalescenceseemed to occur more readily at the relatively finer cell structure observed along grainboundaries and was responsible for most of the nucleation of recrystallized grains [138].The structural changes associated with recovery and recrystallization in cold rolledTi-stabilized [21] and Nb-stabilized [17] I-F steels have been investigated by TEM observations. The general observations were similar to those reported for rimmed and Al-killedsteels, i.e., elongated dislocation cell structures formed as a result of cold rolling; dislocation densities decreased and subgrains formed during recovery; continued subgrainformation, coalescence and growth eventually lead to nucleation. For Ti-stabilized steels,coalescence and growth of subgrains at prior grain boundaries was reportedly the mainsource of recrystallization nuclei [21].Davidson and West [139], in a study on 80 % cold-rolled low-carbon Nb-microalloyedsteels, observed retardation of cell formation and refinement of cell size caused by thedistributions of small Nb(C,N) particles. They also noted these effects to be grain orientation sensitive. In grains with {100} planes oriented parallel to the rolling plane, cellformation was restricted more severely than in {111} oriented grains. A tendency fornucleation to be biased towards grain boundaries has been observed and attributed tothe suppression of general nucleation by particles [139].Recrystallization is considered to commence when the outermost boundary of a grownsubgrain has increased its misorientation to greater than 15 - 20° (at least on one side)with respect to the surrounding matrix and attained a high mobility [82, 140]. Growthinto the deformed material then occurs by the migration of the high-angle boundary. Thedriving force for migration is provided by the reduction in dislocation density, typicallyChapter 2. Literature Review 48from ‘- 10’6m2 to ‘—i 10’°m2,between the interior of a recrystallized nucleus and thesurrounding cold worked metal [29]. The driving force continuously decreases duringannealing due to recovery effects in the unrecrystallized matrix and also due to the factthat grains initially nucleate in the areas of highest stored energy.The mobility of a boundary, as well as the driving force, strongly influences thekinetics of boundary migration. In particular, the misorientation across the boundary,and in some cases the orientation of the boundary itself, significantly influence the rateof migration [140, 141]. The kinetics of grain boundary migration in the absence ofimpurities has been adequately described by considering the transfer of single atomsacross the boundary to be the elementary process involved [140]. Small amounts ofsolutes frequently have a very large effect in reducing the boundary mobility [140, 141].Additional retardation in migration can be caused by Zener drag of a distribution ofsmall particles on the migrating grain boundaries [132].2.1.5.2 Recovery and Recrystallization in Iron and Its Solid-SolutionsPolycrystalline zone-melted iron has been shown to recover relatively easily with an activation energy increasing from 91.9 to 281.7 kJ/mole; these activation energies correlate tovacancy migration and self-diffusion in iron, respectively [40]. However, solute atoms andfine precipitate particles in alloy systems, reduce the relative ease with which recoveryoccurs.Pure iron displayed much more softening (reduction in hardness) during recrystallization than could be attributed to recrystallization alone, due to the concurrent recoveryprocesses [35]. A few ppm of interstitial impurities, carbon [35] and nitrogen [36], whenadded to pure iron, showed a strong effect in reducing recovery; these effects were moreevident for nitrogen than for carbon. For example, at 400°C, recovery processes occurringprior to the onset of recrystallization caused more than 50 % of the total softening inChapter 2. Literature Review 49pure iron, approximately 25 % in carburized iron, and only 10 % in nitrided iron [36].Solute additions of manganese [38, 55] and molybdenum [37] were also found to displaysimilar retardation effects on recovery. Fig. 2.16 [38] shows the effects of increased Mn onpercentage softening during isothermal recrystallization. The combined effect of alloyingadditions in amounts typical of low carbon steel (0.52 Mn, 0.06 C, 0.005 Al) is also shownin Fig. 2.16, indicating that % softening and % recrystallization are approximately equal.These observations suggest that the extent of recovery is considerably reduced with increased alloying additions and that the recovery effects are less important in low-carbonsteel.The recrystallization characteristics of high-purity iron after 60 % cold working wereinvestigated by Rosen et al. [72] in the temperature range of 517 to 632° C. They observedthe formation of nuclei only at certain boundaries of deformed grains; consequently recrystallization was rapid for those grains, but very slow for others. These stable deformedgrains were eventually consumed by an extremely slow growth process from the surrounding grains. They observed a decreasing isothermal growth rate, and associated it withthe very coarse grain size of the stable grains. Leslie et al. [38] observed recrystallizationin iron to be a growth controlled process, with substantial nucleation occurring at zerotime. They attributed the measured decreasing isothermal growth rates to the reductionin driving force resulting from concurrent recovery. The JMAK equation has been shownto describe the kinetic measurements only at the beginning of recrystallization, as canbe seen in Fig. 2.7 [72]. Two distinct stages could be seen in Fig. 2.7; the first wasgrowth-controlled, and the second was attributed to the lack of initial nucleation. Therecrystallization kinetics of iron seems to be strongly dependent on the level of it’s purity.For example, highly pure zone-refined iron was reported to be completely recrystallizedafter 2 h at 350°C whereas commercially pure Armco iron completely recrystallized afterChapter 2. Literature Review 502 h at 600°C [136]. Such anomalous disparities in the recrystallization kinetics, often exhibited by iron, were speculated to be due to the strong interaction between some traceelements (eg., P, As, Sb, Sn) and the boundaries or sub-boundaries [37, 38]Recrystallization kinetics have been characterized either in terms of separate nucleation and growth activation energies, QN and QG, or an overall recrystallization activation energy, QR [142]. Typically, an Arrhenius-type relationship is assumed,Rate = = AR exp ( RT) (2.41)where tR is the time required for a constant fraction of the specimen to recrystallize, Kis a constant, T is absolute temperature, R is the gas constant, AR is a pre-exponentialconstant, and QR is recrystallization activation energy. Rosen et al. [72] reported aconstant QR value of 335.9 kJ/mole for pure iron at temperatures above 590°C, whichthen increased with a decreasing temperature. They attributed this change to the rapidreduction in recrystallization rate observed towards completion. They also reporteda QG value of 155.8 kJ/mole, which was approximately that of grain boundary self-diffusion in iron [72]. Leslie et al. [37, 38] obtained decreasing QR and QG with increasingtemperature, and reported that QR could vary between 125.3 and 367.7 kJ/mole forzone-melted iron. Their studies on dilute binary solid solutions of iron indicated the nonexistence of any simple relationship between temperature, solute content and activationenergy; the effect of solute content on growth rate was observed to change the preexponential constant, rather than affect the activation energy.Small amounts of carbon added to high purity iron were reported to cause only aslight reduction in the recrystallization rate [35]. This, in contrast with the strongereffects of substitutional solutes, was partly explained in terms of the high mobility of theinterstitials. It was further speculated that any reduction in grain boundary mobilitycaused by carbon would be compensated for by the greater stored energy in the system,Chapter 2. Literature Review 51due to the reduced recovery [35]. Similar conclusions were made regarding the nitogenadditions, except for its stronger retarding effect on recrystallization [36].The alloying additions to iron usually have a strong inhibiting effect on the growthof new grains; the effect is greatest for very small additions of the alloying elements[37, 38]. Manganese additions up to 0.30 wt. % [38, 55] and molybdenum additionsup to 0.04 at. % [37] have been shown to considerably reduce the rate of grain growthduring recrystallization. The effect of Mo was reported to be much more pronouncedthan that of Mn. Recrystallization in these dilute iron solid solutions was characterizedprimarily as a growth-controlled process, with a decreasing isothermal growth rate andwith a kinetic response that could not be described well by the JMAK equation [37, 38].The recrystallization response in these alloys is similar to those reported for pure iron[38, 72], indicating only a change of rate caused by the alloying additions. Titaniumand niobium in solid solution were also reported to strongly retard recrystallization iniron-based alloys [130, 143].Several mechanisms have been put forward to explain the retarding effect of soluteatoms on grain boundary mobility. Lucke and Detert [144] assumed an elastic interactionbetween grain boundaries and solute atoms which tends to increase the concentration ofthe solute along grain boundaries. Except at very low solute concentrations or at hightemperatures, the mobility of the boundary is assumed to be controlled by the rate of diffusion of the accompanying solute atoms. This may also explain the previously describedineffectiveness of the highly mobile C and N in reducing the rate of grain boundary migration. Leslie et al. [37] proposed that the growth of recrystallized grains is inhibited byclustering of solute atoms at imperfections (ahead of the migrating boundary) in the Unrecrystallized matrix. Abrahamson and Blakeney [143] considered the electronic effects,and noted a correlation between the rate of change of recrystallization temperature withatomic percent solute and the electron configuration (the number of d-shell electrons) ofChapter 2. Literature Review 52the solute element.In a study by Leslie et al. [38], a low-carbon steel was found to recrystallize considerably faster than high-purity iron. They attributed the rapid recrystallization in thesteel to the increased number of nucleation sites caused by a smaller initial grain size,the presence of large, hard second phase particles (Fe3C, inclusions) and the increaseddriving force due to highly reduced recovery effects. They suggested that these effectscould outweigh any decrease in the growth rate caused by the larger amounts of solutesin the commercial steel. A study on rimmed low-carbon steel [39, 56] revealed negligible changes in hardness and x-ray peak resolution due to the recovery effects occurringduring recrystallization, and the steel recrystallized relatively easily in the temperaturerange of 480 to 560°C with a sigmoidal-shaped kinetic response. The JMAK equationwith a time-exponent of 0.68 described the kinetics reasonably well as indicated in Table2.1 [39].Aluminum-killed low-carbon steels were reported to recrystallize much more slowlythan rimmed steels, and their kinetic response is often not characterized by a sigmoidaltype relationship. In particular, recrystallization at low isothermal temperatures wasobserved to be severely retarded [138]. It was also reported that Al-killed steels sometimesdisplay an initial period of recrystallization, followed by a levelling off period of veryslow kinetics, and then followed by rapid recrystallization [145]. The slower annealingbehaviour and the associated texture development in Al-killed steels were attributedto pre-precipitation clustering of aluminum and nitrogen at subgrain boundary sitesdeveloped by prior cold working [138, 146, 147]. This clustering has been shown to inhibitnucleation by preventing subgrain growth and consequently retard recrystallization [147].Some slowing down of recrystallization was also attributed to the impeding effect ofprecipititates on the mobility of high angle grain boundaries [148].Chapter 2. Literature Review 532.1.5.3 Recovery and Recrystallization Kinetics in I-F SteelsThe matrix of an I-F steel is interstitial-free iron, and consequently these alloys mayundergo considerable amount of recovery, comparable to that of pure iron. However, therecovery may be retarded due to the excessive stabilizing additions in solid solution, i.e.,stochiometrically excess Ti and/or Nb in iron after stabilizing all the interstitials. Thepresence of a fine precipitate distribution may additionally retard the recovery effects inI-F steels.No quantitative studies characterizing the recovery processes occurring in I-F steelsduring recrystallization were found in the published literature. However, several investigations have indicated that a considerable amount of recovery occurs prior to theonset of recrystallization. Fig. 2.17 [21] shows the effect of isothermal annealing onthe yield strength and the % elongation of a cold rolled, Ti-stabilized, I-F steel. Thetensile properties recovered linearly with the logarithm of time until the onset of recrystallization; recovery alone contributed to approximately 50 % of the reduction in yieldstrength. This recovery response is similar to that reported for pure iron [36, 40]. Theresidual line broadening measurements obtained by Satoh et al. [15] on unstabilized andTi-stabilized (see Fig. 2.4) extra-low-carbon steels indicated that considerable recoverycould take place in these alloys (Note: the hardness vs. temperature plot in Fig. 2.4,gives some indication about the possible recovery region). A comparison of their residualline broadening measuments for unstabilized and Ti-stabilized extra-low-carbon steels[15] indicated that Ti additions decrease the extent of recovery. Tensile strength andyield strength of a Nb-stabilized I-F steel decreased by about 15 % before the commencement of recrystallization, while no such recovery effects were visible in terms of the ratioof tensile strength to yield strength or the hardness measurements [17].I-F steels are known to recrystallize in a very sluggish manner. The major retardingChapter 2. Literature Review 54effect is caused by the type and amount of excessive stabilizing elements in the iron matrixand the size and distribution of the associated precipititates. Fig. 2.18 shows isothermalTime-Temperature-Recrystallization (T-T-R) kinetics obtained by Goodenow and Held[21] for a 50 % cold-reduced, low-carbon, Ti-stabilized steel, in combination with thoseobtained for rimmed and Al-killed steels [138]. The retarded recrystallization apparentin the Ti-steel was attributed primarily to the Ti in solid solution, and to a lesser degree,to the presence of numerous fine (< 0.1 tm diameter) Ti(C,N) precipitates. Anotherstudy by Yoda et al. [149] showed that the half-recrystallization temperature was moreclosely related to the content of solute titanium, than the amount of TiC precipitates.The kinetic measurements reported by Satoh et al. [15] for unstabilized and Ti-stabilizedextra-low-carbon steels also indicated the retardation of recrystallization caused by Tiadditions.Goodman et al. [16] simulated continuous annealing cycles with many different Ti-stabilized steels, and measured the recrystallization temperature, TF, i.e., the necessarysoak temperature (soak time of 15 s) for the completion of recrystallization. They attributed the high measured TF values to both the excess Ti content and the TiC precipitate distribution. They also found a relationship between TF and the excess titaniumin solid solution, as shown in Fig. 2.19. Hayakawa et al. [150] also estabilished a similarstrong relationship between the recrystallization temperature and the excess Ti content.In addition, several other continuous annealing simulation studies on low-carbon steelsindicated the retarding effects of Ti and Nb on recrystallization kinetics [7, 151, 152].Hook and Nyo [17] investigated the recrystallization characteristics of a series of Nbtreated I-F steels by softening response and microscopy. The initiation of recrystallizationwas observed at the free surfaces, and these layers thickened with increasing temperatureor time. This observation was explained in terms of the surfaces, having an increaseddislocation mobility, being the preferred nucleation sites when recrystallization is severelyChapter 2. Literature Review 55retarded. The recrystallization start temperature, TR, increased markedly with increasinglevels of Nb in solid solution, as shown in Fig. 2.20 [17]. The values of TR shown as opencircles on the left hand side include the effects of precipitates as well as Nb in solidsolution. The values shown along the curve on the right hand side were obtained afterthe effects of precipitates were minimized by sufficiently coarsening them prior to coldreduction; 0.5 h at 870°C increased the average diameter of the NbC precipititates fromapproximately 5 to 40 nm. These data, being representative of the effect of Nb in solidsolution, indicate its dominance over precipitates in retarding recrystallization. The samestudy also revealed that only those fine precipitates formed in ferrite during hot rolling,not the coarser ones formed in austenite, were effective in retarding recrystallization, dueto the size and density of the precipitate distribution [17].Wilshynsky et al. [153] studied the recrystallization of I-F steels stabilized with Tiand/or Nb, and compared the kinetics obtained with those for an unstabilized, Al-killedsteel. The unstabilized steel recrystallized the most rapidly, followed by Ti-stabilizedand Nb-stabilized steels in that order. The sigmoidal-shaped kinetic curves obtainedfor one testing condition are shown in Fig. 2.21 [153]. They observed the formationof the newly recrystallizing grains only along certain cold-worked boundaries, as wasreported previously for pure iron [72]. Large Ti-rich precipitates, of the order of 1 1umin diameter, were observed to act as preferred nucleation sites in the Ti-steels. Despitethis, the recrystallization kinetics were more sluggish in Ti-steels than in unstabilizedsteels. This was attributed to the fine particle distribution observed in the Ti-steels.Nb-stabilized steels displayed the slowest recrystallization response despite their fine,hot band grain size. This was attributed to the presence of a very high density of fineNb(C,N) precipitates, as well as Nb in solution [153]. This study, together with anothersimilar study conducted by Takechi [7] on recrystallization of Ti- and Nb-stabilized steels,indicate that Nb has the strongest retarding effect on recrystallization.Chapter 2. Literature Review 56Except for the few observations reported by Wilshynsky et al. [153], little informationhas been published concerning the nature of the nucleation and the growth processes thatcontrol the overall kinetics of recrystallization in I-F steels. However, similarities in thegeneral recrystallization response between I-F steels and other dilute solid-solutions ofiron would be expected.The retarding effect of precipitates on recrystallization was treated by Hansen etal. [154} in the following manner. The force of recrystallization, FR, which is the forceper unit area related to the reduction of strain energy, or the reduction of dislocationsgenerated by the cold work, was given by,FR= () (zip) (2.42)where t is shear modulus, b is burger’s vector, and /p is the change in dislocation densitybetween the cold worked and recrystallized grains. The restraining force on boundarymigration per unit area of spherical particles could be written as,= (2.43)where f is volume fraction of particles, ‘y is interfacial energy per unit area of boundaryand r is the particle radius. F will depend on the directional aspects of recrystallization,since is a function of the orientation difference between the cold worked matrix andrecrystallized grains [155]. Boundaries will be pinned only when F is greater than FR.The observation that precipitates impede grain boundary motion in one instance, butnot in another [153], can be explained in terms of the changes in FR and/or F. The largenumber of discontinuities observed in the grain boundaries of a partially recrystallizedNb-steel [153] indicate that the boundary motion has been significantly impeded; thiscan be correlated to a high value of F caused by a high density of fine precipitates, asgiven by Eq. 2.43.Chapter 2. Literature Review 57The precipitates in I-F steels are randomly scattered, and consequently do not appearto exert any significant influence on grain morphology [17, 21, 153]. Goodman et al. [16]obtained recrystallized microstructures consisting of equiaxed ferrite grains, with grainsizes ranging from 0.012 to 0.015 itm for continuous annealed, Ti-stabilised, I-F steel.However, the formation of blocky ferrite grains were reported for a Nb-stabilized steel[153]. The fine precipitate distribution in this steel was thought to allow growth only incertain directions, resulting in the observed blocky grain morphology.Goodenow and Held [21] observed the hot rolled structure of a Ti-stabilized I-F steelto be equiaxed (grain size of ASTM No. 9 - 10), with numerous fine Ti(C,N) particlessmaller than 0.1 1um, uniformly scattered through the grains. A few large particles,thought to be Ti sulfide and oxide, were also present. They reported that the size anddistribution of precipitates were the same for both the initial hot rolled and the finalfully recrystallized specimens. Unlike in Al-killed steels, sigmoidal-shaped isothermalrecrystallization kinetic curves were obtained for all test temperatures between 450 and900°C, giving additional indication for the absence of precipitation or dissolution in thistemperature range [21]. Similar findings were also reported by Wilshynsky et al. [153]based on an investigation of a series of Ti and/or Nb stabilized steels. The precipitatesreportedly present after hot rolling and coiling, survived cold rolling and remained stableduring annealing [153]. Hook and Nyo [17] observed Nb-stabilized steels to recrystallize inthe temperature range of 600 to 700° C, without any change in the precipitate distribution.However, NbC precipitates coarsened and the associated softening was reflected in thehardness measurements after long holding times (3600 s) at temperatures above 700°C[17].Chapter 2. Literature Review 582.2 Development of Texture during Cold Rolling and AnnealingDeformation textures have their origins in the crystallographic nature of the deformationprocesses of slip and twinning. During the slip process, the crystal lattice rotates asa result of the shape change and the geometrical constraints of its surroundings. Therestricted number of slip systems available produces rotations towards a limited number ofend points and consequently a deformation texture is produced. During recrystallization,new grains with different orientations are nucleated and grow at the expense of the coldworked matrix; these processes lead to an overall texture modification. The mechanicalbehaviour of single crystals is anisotropic, and therefore preferred orientations have asignificant effect on the properties of materials. In a strongly textured sheet metal, theyield stress varies with direction in the plane of the sheet as well as across the sheetthickness; such effects are critically important during non-uniform flow encountered indeep-drawing operations [156].2.2.1 Methods of Representation of TextureTexture can be defined as the orientation distribution of all crystallites in an assemblyof grains [157]. Traditionally, preferred orientations are described by means of pole figures. Pole figures are stereographic projections which show the distribution of particularcrystallographic directions and are readily determined using techniques employing theprinciples of x-ray diffraction. The Schulz reflection method [49, 156, 158, 159] is commonly used for determining textures in sheet metals; the peripheral areas of the polefigure are not determined in this method due to some defocussing effects. In the Schulzreflection method, the normal to the diffracting planes {hkl} remains fixed in space whilethe specimen is rotated through a wide range of angles, and whenever a crystal becomesappropriately oriented, a diffracted intensity is measured; the total diffracted intensityChapter 2. Literature Review 59at any instant is then proportional to the volume of grains that are in that orientation.Fig. 2.22 (a) and (b) show two partial (200) pole figures obtained for a rimmed steelin the cold-rolled state and after recrystallization; the presence of the ideal orientations{111} < 112 >, {111} < 110 >, {100} < 011 > and {211} < 011 > are also indicated[79]. (Note: {111} < 112 > type ideal orientation means the {111} planes lie parallelto the sheet surface, and the < 112 > directions in that plane lie parallel to the rollingdirection).For deformation processes of higher symmetry that require only one axis to be specified (e.g., cold drawing), a satisfactory description of the texture can also be given by aninverse pole figure [49, 156]. An inverse pole figure uses a crystallographic unit trangleas a reference frame with contour lines to show the frequency with which the variousdirections in the crystal coincide with the specimen axis under consideration. In the caseof sheet specimens, inverse pole figures are determined for normal (ND), rolling (RD) andtransverse (TD) directions; three such inverse pole figures obtained for a 70 % cold rolledsteel are shown in Fig. 2.23 [160]. Inverse pole figures are of great interest as relatedto the uniaxial properties (properties that depend only on one crystal direction) of atextured material; in this case, the inverse pole figure is the weighting function needed inorder to calculate the mean values of the single crystal properties [161]. In particular, NDinverse pole figures can be determined easily for a sheet metal by the usual difFractometrymethod [49, 156, 158, 162]. These integrated intensity measurements have been foundto be useful in correlating the texture evolution and the associated changes in plasticanisotropy [15, 21, 55, 163].Although pole figures and inverse pole figures provide a useful description of the texture present in a material, the information they contain is at best semi-quantitative;this is due to the fact that while a general orientation has three degrees of freedom, apole figure (or inverse pole figure) specifies only two independent variables [49, 156, 164].Chapter 2. Literature Review 60This difficulty has been overcome by the use of the orientation distribution function(ODF), which describes the frequency of occurence of particular orientations in a three-dimensional orientation space. This space is defined by three Euler angles which constitute a set of three consecutive rotations that must be given to each crystallite in order tobring its crystallographic axes into coincidence with the specimen axes. The descriptionof crystal orientation by indices of crystal directions and by Euler angles p, q and S02are schematically shown in Fig. 2.24 [157]. The complete ODF consists of the sets ofrotations pertaining to all the crystallites in the specimen. The fundamental relationshipbetween pole figure and ODF is based on the fact that the diffraction process does not seea rotation of the crystallites about the normal direction to the reflecting lattice plane. Asa result, a pole figure is an integral over the ODF and consequently, ODFs are calculatedby a method called ‘pole figure inversion’. Mathematical methods have been developedby Bunge [165, 166, 167, 168] and Roe [169] that allow ODFs to be calculated from thenumerical data obtained from several pole figures.According to the analysis (‘series expansion’ or ‘harmonic method’) presented byBunge [165], an ODF may be expressed as a series of generalized spherical harmonics,00 +1 +1f(cp1,q,co2) = CF1m’(q5) exp(imç2 exp(in1) (2.44)1rO m=—1 ,=—.1where C are the series coefficients and p1mn() are certain generalisations of the associated Legendre functions. It is the C-coefficients, C, that are calculated from theexperimentally determined partial pole figures [165].For cubic/orthorhombic crystal/specimen symmetry, a three-dimensional orientationvolume may be defined by using three orthogonal axes for y, q and 2 with each ofthe Euler angles ranging from 0 to 900. Any point in this space corresponds to a singleorientation (hIcl)[uvw] and the density at that point is the strength of the texture component in multiples of random units. A three-dimensional view and a 45° section ofChapter 2. Literature Review 61the Euler space, indicating the locations of some important ideal orientations are shownin Fig. 2.25 [164, 166]. Regions of higher and lower orientation density are separatedby contour surfaces, and the results are usually presented as a series of parallel sections(constant cp1 sections for b.c.c. metals) through this space. Since the ODF image in theEulerian space is not very descriptive, the ODF information is sometimes presented asorientation densities along selected fibres. Fig. 2.26 shows an example where the development of recrystallization texture during isothermal annealing (700°C) of a 90 % coldrolled Al-killed steel is shown as plots of pole density along the a (< 110 > RD) and(< 111 > ND) fibres [170]; such a description is very useful in correlating the texturedevelopment to cold rolling and annealing parameters [170, 171, 172, 173, 174].2.2.2 Crystallographic Texture and Plastic AnisotropyAn important requirement for many applications involving sheet steel is good deepdrawability. Drawability is the capacity to achieve maximum plastic flow in the plane ofthe sheet and maximum resistance to flow in a direction perpendicular to the sheet; thiscondition reflects the normal anisotropy of the sheet. In addition, the plastic flow in theplane of the sheet varies along different directions, and such planar anisotropy leads tothe formation of ears during drawing operations.In phenomenological plasticity theory, the anisotropic plastic behaviour is describedby the anisotropic yield locus [161, 175, 176]. In practice, however, the anisotropy ofplastic flow is often correlated to the Lankford parameter ‘r’ [2, 22, 23, 156, 163], whichis defined as the ratio of the incremental strains in width (dEw) and thickness (dEt)directions for a strip sample deformed in tension, i.e., r = de/dE [175, 176]. Sinceanisotropy has been observed not to change significantly with straining, r is usuallydetermined from the measurements of true finite strains. Typically, the measurementsare made from a standard tensile specimen strained to approximately 15 % elongation;Chapter 2. Literature Review 62conventionally, it is the width (em) and length (1) strains that are measured due to thedifficulty of determining the thickness strain (Et) accurately in a thin sheet [156]. Thus,based on the volume constancy during plastic deformation,—Er=—=In rolled products, r values are usually measured in the rolling direction (ro), at 45°from the rolling direction (r45) and in the transverse direction (r9o). The average strainratio, i (or rm), commonly defined as,= (r0 + 2r45 + rgo) (2.46)is a good characterization of the average anisotropy of the sheet. While is a convenient measure of the normal anisotropy, the extent of planar anisotropy is related to theparameter, r, defined as,(ro — + r90) (2.47)The good correlation between high i values and good deep-drawability has been clearlydemonstrated [175, 177, 178, 179]. It has been suggested that the ideal deep-drawingsteel will have both a high average strain ratio, > 1, and a Lr of almost zero [2, 176].The plastic anisotropy in sheet steels can be understood in terms of the anisotropicflow properties of single crystals and the nature of the existing crystal orientation. Theoretical calculations for single b.c.c. crystals, based on the assumption of pencil glide slipin < 111 > directions, have indicated to be strongly dependent on crystal orientation[2]. It was also reported based on similar calculations that the values of r0, r45 and r90were approximately 2, 2.5 and 3 for (i1i)[iIO] orientation, and 0, 1 and 0 for (001)[110]orientation [22, 180]. For polycrystalline low-carbon steels, the experimental observations indicated that the most desirable texture to yield high values was the {111} type,whereas the most undesirable was reported to be of the type {001} [2, 22, 23, 163]. InChapter 2. Literature Review 63particular, the ratio of the strengths of the {111} and {OO1} texture components has beenshown to correlate well with the measured f values, and an experimental verification ofthis relationship is shown in Fig. 2.27 [163].It is also possible to calculate the anisotropic flow properties such as r values byincorporating texture in the form of an ODF into a theoretical model of polycrystaldeformation. The early theories that described the deformation behaviour of single andpolycrystalline solids were due to Schmid [181] and Sachs [182]. These theories led to theTaylor [183] model of plastic flow where the plastic strain was assumed to be the same forall grains of the aggregate and also equal to the macroscopic strain; this was consideredto be achieved by permitting the simultaneous activation of five slip systems. The modelalso assumed a selection rule for the slip systems based on the principle of minimizingthe internally dissipated deformation work. Another model, proposed by Bishop and Hill[184, 185], using maximum work principle also yielded the same solutions as the Taylormodel. Detailed mathematical methods have been developed to calculate the strain ratio,r, at different a values (a is the angle between the rolling direction of the sheet and thetensile loading direction of the test specimen) by incorporating the texture in the formof ODF into the Taylor model of polycrystal deformation [161, 165].2.2.3 The Theoretical Mechanisms of Texture DevelopmentDuring cold rolling, the texture of b.c.c. metals becomes progressively stronger andsharper with increasing deformation, but the main components that develop are almostindependent of material and processing variables [186, 187]. For these metals, it is slipand the associated lattice rotations (towards the ideal orientations) that are responsiblefor the development of the deformation texture, and the most appropriate deformationmode corresponds to pencil glide on {hkl} < 111 > systems [186, 187]. It has been established that the cold rolled texture of steels comprised of two major orientation spreadsChapter 2. Literature Review 64[23, 160, 188]. One of these is an almost complete fibre texture with {111} planes parallelto the sheet(7-fibre) and the directions < 110 >, < 112> and < 123 > aligned with therolling direction, and the other is a partial fibre texture with < 110 > along the rollingdirection (a-fibre), encompassing the orientations {001} < 110 >, {112} < 110 > and{111} < 110 >. The Taylor-Bishop-Hill theory has been extensively used in the prediction of rolling textures; this is accomplished by calculating the orientation path duringdeformation of arrays of crystals with an initially random distribution of orientations[176, 189]. In general, the calculated results were in good qualitative agreement with themeasured textures [156, 176].Recovery processes in general are reported to have no significant effect on cold rolledtextures. Recrystallization processes on the other hand involve local reorientation andthus cause textural changes [22, 23, 187, 190]. The orientation dependence of the deformation structures (and hence the internal stored energy) are generally responsible for biasingthe recrystallization process in favour of certain texture components. In particular, for a70 % cold rolled iron, Dillamore et al. [78] observed fine cells with large misorientations(and also high internal stored energy) in the { 111 } family, whereas the cells were coarserand less misoriented in {001} family. Nucleation by subgrain growth mechanisms occursmost rapidly within the grains having the greatest stored energy [72, 77, 78, 79]; thenucleation process is also aided by a high local dislocation density and by the presenceof a sharp lattice curvature [33, 80, 81, 82, 83, 156]. These observations suggest thatnuclei are formed in specific orientations (‘oriented nucleation’), and that the resultingannealing texture is characterized by the orientation of these nuclei. Another commonobservation is that the recrystallization texture is related to the deformation texture byrotations around specific axes, e.g., rotations of 25 to 30° around < 110 > direction inb.c.c. single crystals. Experiments have also indicated that grain boundaries with suchmisorientations have high mobility [22, 23, 187, 190]. This concept suggests that theChapter 2. Literature Review 65nuclei with certain orientations grow rapidly (‘oriented growth’), and that these nucleidetermine the resulting annealing texture. The suitability of one theory over the othercontinues to be a source of debate [190, 191]; compromise theories (oriented nucleation-selective growth) have also been proposed [192]. In the case of b.c.c. metals, the orientednucleation is generally the favoured mechanism [156]. Grain growth, occuring after thecompletion of recrystallization, usually strengthens/sharpens the texture [22, 23, 156].This can be understood in terms of the observations that large grains grow at the expenseof small ones during grain growth and that the grain size distribution for grains of strongtexture components are often biased towards larger sizes than the average distribution[79].The observed annealing textures in low-carbon steels [22, 23, 156, 160, 188] consistof two major components which are approximately {111} < 110 > and {554} < 225 >(‘—‘ 6° apart from {111} < 112 >). A comparison of the annealed textures with thecold rolled textures indicates that two main changes take place during recrystallization.One is the significant reduction of {100} < 110 > and much of the spread around itin the partial fibre texture; the other relates to the redistribution of intensity in thefibre texture with {111} planes parallel to the sheet [156]. The texture developmentduring annealing is sometimes monitored through the measurement of integrated poleintensities. Such studies on I-F steels, often indicated a considerable increase iii {111}and a marked decrease in {100}, while the changes in {110} and {211} were relativelynegligible [15, 193, 194, 195].Conventional deep-drawing steels basically fall into three categories, namely rimmed,Al-killed and intestitial-free (Ti/Nb-stabilized). Rimmed steels have values of around1.0- 1.3, and are characterized by a weak texture, while Al-killed steels yield highervalues (1.4- 1.8), and typically have a stronger {111}-type texture and a weaker{ 001}-components. Interstitial-free steels on the other hand have even higher valuesChapter 2. Literature Review 66(1.6 - 2.0) than Al-killed steels, and are characterized by a sharper {111}-type texture (inparticular the {554} < 225 > orientation) [21, 22, 23, 156]. Fig. 2.28 shows a comparisonof the relative proportions of different textural components in rimmed, Al-killed, and Ti-stabilized interstitial-free as well as high strength steels [196].The texture modification in Al-killed steels is usually attributed to the precipitationor the pre-precipitation cluster formation of A1N during the recovery process [138, 145,146, 147, 148]. These clusters, form at dislocations and cell boundaries, and cause retardation of recrystallization, particularly by inhibiting the nucleation event. Althoughthe nucleation of all orientations are inhibited, the chances that the more strongly driven{111} nuclei overcoming these obstacles are relatively high, and this will eventually tiltthe balance more in favour of {111} orientations [23]. However, strict process controlis usually necessary to get the best possible effects. For example, a high soaking temperature (‘-.‘ 1200°C) and rapid cooling from the hot rolling temperature to the coilingtemperature are considered essential to keep Al in solid solution. In addition, a veryslow heating rate (i.e., batch annealing) should be employed during recrystallization toencourage the clustering of Al and N in the deformed structure prior to the onset ofrecrystallization [23, 138, 146, 156].The mechanism by which the annealing textures of I-F steels are developed is notproperly understood [22, 23, 156]. Most researchers [22, 23, 197, 198] have taken the viewthat textures are controlled by the already existing carbonitride particles, which interferewith the nucleation and growth of recrystallized grains (e.g., inhibition of nucleation of allorientations, but in a less pronounced manner on {111} components [21]); in particular,particles in the size range of 4 - 50 nm have been reported to be beneficial [197]. Someauthors suggest the strong presence of the {112} < 110 > component in the I-F steel hotband (attributed to the slowing down of recrystallization of austenite by precipitation),and the subsequent sharpening of this texture during cold rolling as significant [197,Chapter 2. Literature Review 67199, 200]. This was also suggested as the reason for the particularly strong presence of{554} < 225 > in (ferrite) annealing textures of I-F steels [22]. In another view, theabsence of the damaging effects of the interstitials C and N is considered to be the mostimportant factor [23]. This suggestion is based on the observation that higher dissolvedC and N levels were associated with lower {111}, and higher {110} and {100} intensities[201]. Although a fundamental understanding of this observation is lacking, it is generallysuggested that the inhibition of subgrain-growth nucleation of {111} oriented grains issignificantly lessened by the absence of the interstitials [23]. It should be indicatedhowever that such a view does not rule out the influence of the carbonitride particles; inparticular, if these are too finely dispersed they may inhibit the growth of recrystallizinggrains, with detrimental effects to the final texture, and thus the need for relativelycoarse-scale precipitation [23, 202].2.2.4 Development and Control of Texture in I-F SteelsIndustrial control of values of steel sheets depends on the control of the development ofa suitable texture, and this in turn means a careful control of steel composition and othermetallurgical processing parameters [22, 23, 156]. In general, reductions in the amountsof oxygen (0.04 to 0.002 wt %), sulphur (0.01 to 0.001 wt %), carbon (0.15 to 0.0005%) and nitrogen (0.007 to 0.001 wt %) present in low-carbon steels have been reportedto result in progressively increasing f values [22, 23, 149]. These observations clearlyindicate the benefits of using killed and stabilized steels for deep-drawing applications.Numerous investigations have shown that by adding stochiometrically sufficient amountsof Ti and/or Nb to combine with all of the interstitial C and N, significant improvementsin texture and values could be obtained [3, 7, 9, 15, 16, 17, 18, 21, 149, 196, 197,198, 199, 203]. There does not seem to be any obvious conclusion regarding the effectsof excess Ti and/or Nb in solid solution (i.e., after stabilizing the interstitials) onChapter 2. Literature Review 68values; the reported studies indicate all three possibilities, i.e., increasing or decreasingor having no effect at all [7, 9, 15, 16, 149, 150, 204]. The presence of the solid-solutionstrengthening elements Mn and P in low-carbon steels is usually detrimental to deepdrawability. In particular, values have been reported to decrease steadily as the Mncontent was increased from 0.02 to 0.5 wt % [20, 55, 204, 205, 206, 207]. In the case ofP, the adverse effects were reported to be minimal; even an increase in F value has beenreported for P contents as high as 0.1 wt % [9, 20, 149, 204, 207, 208].The effects of processing parameters on values can be understood in terms ofthe hot-rolling, cold-rolling and annealing conditions. In I-F steels, all of the stabilizing precipitation takes place during high temperature processing, and the processing conditions leading to the formation of coarse and widely spaced precipitates aredesirable to obtain high values [22, 23, 202, 209]. The results from several studies[4, 6, 15, 16, 195, 202, 204, 209, 210, 211] relating the processing conditions to textureevolution and values are briefly summarized here. Lower reheat temperatures (1000- 1100°C) are considered beneficial since they prevent complete dissolution Ti and Nbprecipitates, allowing them to coarsen. Finishing below Ar3 (.-‘-‘ 900°C) has been shownto reduce f values in all types of deep-drawing steels. Higher coiling temperatures (700- 800°C) are also generally desirable since they may lead to coarser precipitates. Someof the recent studies on Ti and Nb stabilized I-F steels indicate that carefully controlledfinish rolling in a-region can also lead to improved deep drawability [149, 203, 212]. Ingeneral, controlling the processing conditions are much more important in the case ofNb-stabilized steels than in the case of Ti-stabilized steels because of the relatively lowprecipitation temperatures of the Nb-compounds [4, 6, 15, 213].Obtaining high values is also dependent on optimizing the cold rolling and annealingconditions. For rimmed and Al-killed steels, the optimum amount of cold reduction wasreported to be around 70 to 80 % [22, 210, 214]. It has been pointed out that above 75 %Chapter 2. Literature Review 69cold reduction the value falls off despite the continiously increasing {111} components inthe annealing texture; such effects were attributed to the development of the detrimental{001} components [22, 214]. However, in the case of I-F steels, the {001} componentswere reported to be present to a lesser extent and the highest values were obtained forreductions of around 90 % [210, 215]. In contrast to Al-killed steels, the values obtainedfor I-F steels are not very sensitive to the annealing conditions [22, 23, 156]. The annealingstudies performed on Ti and/or Nb stabilized I-F steels indicate that in general higherannealing temperatures promote increased values; this is primarily due to the largergrain sizes and the associated sharpened texture resulting at higher temperatures [22, 23].Ti and/or Nb-stabilized I-F steels are often annealed in the (soaking) temperature rangeof 850 to 900° C to produce high values [2, 9, 14, 20]. Fig. 2.29 summarizes the resultsfrom several investigations showing the effects of heating rate during annealing onvalues of different grades of steels [23]; when compared to Al-killed steels, the effects ofheating rate on values were negligible in Ti-stabilized I-F steels.Chapter 2. Literature Review 70Table 2.1: Characterization of isothermal recrystallization kinetics for a 89 % cold rolled,rimmed low-carbon steel using the JMAK and the S-F equations [39].Temp. Avrarni. Equation Speich and FisherC (i = 0 L (= .92)in b R2 ink R2440— 9.93 0.88 —12.64 0.88460— 8.81 0.96—11.21 0.96480— 7.56 0.96— 9.59 0.92490— 6.64 0.88— 8.20 0.74500— 6.21 0.95— 7.69 0.93520— 5.17 0.98— 6.34 0.93540—4.32 0.92—5.24 0.87560— 3.24 0.77— 3.58 0.64Chapter 2. Literature Review 71Figure 2.1: Effects of annealing temperature (200, 250, 300, 450°C for 1 hr) on thediffraction peak profiles of the {331} planes in a 90 % cold roIled 70-30 brass [49].—i oFigure 2.2: Schematic illustration of the x-ray peak resolution measurement [56, 57].Chapter 2. Literature Review 728xFigure 2.3: Comparison of the % peak resolution (in-situ) and microhardness measurements obtained for a 89 % cold rolled, rimmed low-carbon steel during continuous heating[56].A x,Id-,oHdANNEALING TEMPJCFigure 2.4: Recrystallization behaviour of a 77 % cold rolled, Ti-stabilized extra-low-carbon steel during the simulation of continuous annealing (soak time of 40 sat each temperature) [15].• E RSIOO2C/aL_z’ —aC..100U)C.,zC.)Za:z<z 05DC.)CflOC.)Chapter 2. Literature Review2!:U::(1)-J4—(-)73Figure 2.5: Isothermal recovery kinetics in polycrystalline iron0°C, showing fractional residual strain hardening vs. time [40].after 5 % prestrain at°55r-o 50 -045!040:0350301025’or020:£00C010!10’ 102ANNEAEING TIME. MINUTESFigure 2.6: Recovery of x-ray line broadening as measured by the residual line broadeningparameter (1-R) for isothermal treatments at 400, 500 and 600°C [53].00 50 100 150 200 250 300 350 400 450TIME — MINUTES0I5Chapter 2. Literature ReviewFigure 2.7: The graph of in in[1/(1— X)] vs. ln(t) obtained% deformed high-purity iron.CCaaaCaFigure 2.8: Fractional residual strain hardening curves obtained during isothermal annealing of a) copper [92] and b) aluminum (arrows indicate onset of recrystallization)[93] as presented by Furu et a! [91].74o:ccItzo1on Tm (Mnoes)by Rosen et a! [72] for a 60T(tl{ h1Chapter 2. Literature Review0I0Figure 2.10: Average boundary migration rates (G)of hot-worked 3.25 % Si-Fe [81].during isothermal recrystallization75-rxFigure 2.9: Interfacial area per unit volume plotted against the volume fraction recrystallized for a 60 % cold worked 3.25 % Si-steel [90].0E.T+ Sn• 812o 812x 812V 75004604503002303S 8025I tO-1102Time (sec)Chapter 2. Literature Review 76TmeFigure 2.11: Schematic representation of the additivity principle [69].TimeFigure 2.12: A schematic TTR diagram with proportionally distributed fractional recrystallization curves to illustrate the validity of the additivity rule.0907060.30.30.20iFigure 2.13: Comparison of experimental and predicted continuous heating recrystallization kinetics; the isothermal data characterized by both the JMAK and the S-F equationswere used in the additivity calculations [39].Chapter 2. Literature Review 770.0 X3 0.99C)zIC)C)HTO -3D0<3CCL6 20 22 2. 76 27 30 32 3.6 36Time (s)Chapter 2. Literature Review 78(c)THE SUOGRAiN STRUCTURE JUSTAFTER COALESCENCETHE FINAL SU8GRAIN STRUCTUREAFTER SOME SU88OUNDARY MiGRATIONFigure 2.14: Schematic illustration of subgrain coalescence by subgrain rotation [53].Figure 2.15: Schematic representation of nucleation by subgrain growth; boundariesthickly populated by dislocations (dots) have a high misorientation angle, and are themost likely to migrate [131].THE ORIGINAL SU8GRAIN STRUCTURE ONE SURGRAIN IS UNDERGOING A8EFORE COALESCENCE ROTATIONz0<I)Chapter 2. Literature Review 7940 600/ RECRYSTALLiZEDFigure 2.16: The softening response of three iron alloys recrystallized at 595°C [38].1050-FE 4i90j-80-0• 88% duton—105. Redooon050% Rodof.on8gionng Of706Gb17.5 -15.0 -12.5 -10.0 -7.5 -5.0 -2.5000.1 10 10 1(30 1000TIUC AT TEMP(RATURE. MINFigure 2.17: Effect of annealing time at 565°C on the longitudinal properties of aTi-stabilized I-F steel cold rolled between 50 and 88 % [21].Chapter 2. Literature Review 80‘yr9-aI-Figure 2.18: Time-temperature-recrystallization diagram for Ti-stabilized [21], rimmedand Al-killed steels after 50 % cold reduction [138].TiME AT TEMPERA TtJRE. MIN.DC.>-a:0a:coto f(OUCT ION• 60P(HC(No 7Pf4CN1YOU6O14601360a:Da:1260I-12001160000 010 021](XC( S TI 1ANU.dFigure 2.19: Effect of excess titanium in solid solution and cold reduction on the recrystallization temperature (TF) for annealing soak times of 15 s [16].C0,>UC,Chapter 2. Literature Review 81975127512 14C12210095030i17 -1150 -ii2 —a900hOC7:3028023PA3C875I I16 .20 .24U00 .04 .08 22WT PCT NbFigure 2.20: Relationship between the recrystallization start temperature, TR, and theamount of Nb in solid solution in ferrite; the points along the curve were obtained forcoarsened precipitates and the open circles include the effect of precipitates as well asNb in solid solution [17].100C10° 101 102 10flm (ieconds)Figure 2.21: Recrystallization kinetic curves indicating sigmoidal-type behaviour, obtained for a series of I-F steels, cold rolled 75 % and isothermally annealed at 650°C[153].Chapter 2. Literature Review 820Figure 2.22: Partial (200) pole figures obtained for a rimmed steel (a) in the cold-rolledstate and (b) after recrystallization; the ideal orientations {111} < 112 >, {111} < 110 >,{100} <011 > and {211} <011 > are indicated [79].111Figure 2.23: Normal (ND), rolling (RD) and transverse (TD) direction inverse pole figuresobtained for a 70 % cold rolled steel sheet [160].(a) (b)100 110Chapter 2. Literature Review 83Figure 2.24: Schematic description of crystal orientation by indices of crystal directionsand by Euler angles ço, q and Y2 [157].— (111)11121—(554)15)— (332)111311113)30(l1211223)Figure 2.25: A three-dimensional view and a = 45° section of the Euler space showingthe locations of some important ideal orientations [164, 166].NO/310 4/ 13(001)11101 ITDU<110>(11311332)20 30 40 %0 40 10 80 I010110112301 11201 1330)0 10 20 30 L0 50 60 70 80 90n •. •‘ • . A p 1 —10204,‘I233040504070ioioi i0( t0I tuG)tf(2_L5ill(0011)110)(114)11101’ —(113)1li) (114)1Oill,(112)1110)’ ND3<1I1>— ‘ 3111)11211 ‘(223)1110) ,-‘ 4(445))1)0)’/RDII<1I0>1(110)1110)pl01I (i211 (332]—(1313 (0211 (132) 11)3.102I 1122180‘050607080— (110)100!) 1121] (1321 1011) (123)11(23(111)110) 12311(332)11131—(221111103(33131103 1233) 11231 (0131[1101 13313 l22111323 )111 (22311112) (i3) (110) (001p133) 10231 1i3].(2321 (1221 (3123Figure 2.26: Development of recrystallization texture during isothermal annealing (after2, 3 and 10 s hold at 700°C) of a 90 % cold rolled (CR) Al-killed steel; the plots indicateorientation density along the (a) a (< 110 >j RD) and (b) y (< 111 >11 ND) fibres [170].0Ia:a:a:<3a:>Chapter 2. Literature Review 841t2,16y_1414CR-—--—2 S-——3 S•— —las60 9028r—242 016120804C01::-10 10.0 1000 10000tNTENSTY 1111:NTENSTY (001Figure 2.27: The effect of the ratio of the intensities of the (111) component to the (001)component on the average strain ratio of low-carbon steel sheets [163].Chapter 2. Literature Review 85Il1llll1 {ooij <110>(iii) <110>(ii2} <110>{‘1 <225>Figure 2.28: Comparison of the relative proportions of different textural components inrimmed, Al-killed, and Ti-stabilized interstitial-free as well as high strength steels [196].Ce2.01.81.611.121.00.1 1 10 100 1000HEATING PATEFigure 2.29: Variation of i values with heating rate during annealing for a variety ofsteels subjected to different high temperature processing conditions [23].3.63.22.8-j 2 4UIcr2.0,J.Typcct 08% T seeI — cii TypcnIb3x-onnea1n0 (Oinç tempercitures Onhnucxjsonneouin,Ai-+Iled steel -colng temperoture-Pinemcig Sleel -low cotrno teopecoIreChapter 3Experimental ProcedureThis chapter describes the techniques and procedures used during the course of thisinvestigation. They can be broadly categorized into the following processes: cold rollingand annealing; kinetic characterization by diffraction effects; quantitative metallography;electron microscopic observations of structural changes, and quantitative characterizationof texture evolution.3.1 MaterialThe material used in this study was a Ti-rich, Nb-lean Interstitial-Free (I-F) steel; itschemical composition, as provided by Stelco, and that obtained from a laboratory chemical analysis, are shown in Table 3.1. This is one of the commercially produced Deep-Drawing Quality (DDQ) steels, designed for the continuous annealing (CAL) process.The material received was hot band, having been subjected to hot rolling in Stelco,with a finishing temperature of approximately Ar3 ( 890°C) and over, and a coilingtemperature of less than 600°C.3.2 Cold Rolling ScheduleThe 2.92 mm thick hot band was subjected to 5 cold rolling reductions using the ‘Stanat’4 in diameter laboratory rolling mill; the sheet thickness at the end of each pass was 2.54,1.96, 1.35, 0.76 and 0.58 mm respectively. The total thickness change from 2.92 mm to86Chapter 3. Experimental Procedure 870.58 mm corresponds to an overall reduction of 80 %, as commonly used in industrialpractice. Cold rolling was performed only in one direction, between clean, dry rolls,without reversal.3.3 Kinetic MeasurementsIsothermal annealing experiments were performed with the objective of characterizingthe isothermal recovery and recrystallization kinetics over an appropriate range of temperatures. The annealing kinetics during selected continuous heating rates simulatingbatch and continuous annealing processes were also determined.3.3.1 ApparatusThe isothermal and continuous heating annealing experiments were performed in a ‘PhilipsPW 1158’ high temperature, x-ray diffraction camera. The original camera was modifiedto incorporate two grooved quartz tracks for supporting the steel strip. Strip specimensof 155 mm x 13.5 mm x 0.58 mm, sheared from the cold rolled steel sheet, were resistively heated using a 60 Hz power supply capable of delivering up to 500 A. The currentto the specimen was controlled by a silicon phase shifter, thermocouple feedback control.The 0.25 mm diameter wires of an extrinsic chromel-alumel (type-K) controlling thermocouple were spot welded at the centre of the bottom strip surface, directly beneaththe focal point of the x-ray beam. A thermocouple-instrumented strip sample in place inthe open hot x-ray camera is shown in Fig. 3.1. All the experiments were performed ina He + 10 % by vol. H2 environment, by maintaining a continuous flow of the mixed gasat the rate of 200 c.c. per minute. The chamber was first evacuated before introducingthe gas flow. The surfaces of the specimens at the end of the heat treatment were shiny,without any sign of scale formation.Chapter 3. Experimental Procedure 883.3.2 Diffraction EffectsInitial experiments were performed with the objectives of establishing the operating parameters of the x-ray diffractometer, to maxiniise the resulting peak/background ratio,and to select a high angle peak to assure resolution of the K, /Ka2 doublet. FeKc, radiation and the {220} diffraction peak were selected for the experiments. The peak profilewas monitored at a scan rate of 1° (20) per minute with a count interval time of 1 second.The x-rays were generated at 30 kV tube voltage and 10 mA tube current. The broad{220} peak, corresponding to the cold worked state, was located at approximately 20 =145.5° at room temperature.A schematic illustration of the progressive resolution of the initially broadened {220}x-ray peak during annealing and the procedure for quantifying the peak resolution areshown in Fig. 3.2. The degree of peak resolution of the Ka,/K2 doublet has beendescribed quantitatively in terms of:(i) the x-ray ratio, R1 (also referred to as ‘residual line broadening parameter’ [15,53, 55]),= ‘mm— ‘b (3.1)‘Ka, —where‘K01, ‘mm and ‘b are the intensities of the K1 peak, the valley between the K,and Ka2, and the background, respectively;(ii) the valley intensity, ‘M,= ‘mm — ‘b (3.2)where ‘mmn and I, are the intensities of the valley and the background, respectively.The fractional annealing effects, i.e., the volume fraction recovered and/or recrystallized, were estimated using the ‘fractional peak resolution’, F, defined in terms of themeasured parameter, F,(3.3)Chapter 3. Experimental Procedure 89where F, P and P correspond to the initial, an intermediate and the final measuredvalues of the parameter P during the annealing treatment. P could be either R1 or IM,as indicated in Fig. 3.2. The initial and the final measurements correspond to the coldrolled and the fully recrystallized states, respectively.3.3.3 Annealing TreatmentIsothermal annealing tests were performed at 500, 550, 600, 625, 650, 675, 700, 720,740, and 760°C and involved an initial heating rate of 80°C/s to the desired isothermaltemperature; a higher heating rate could not be employed due to the necessity to keepthe initial overshoot of temperature associated with the thermal inertia at 10°C. Continuous heating experiments were conducted at 0.025, 1.88 and 20.2°C/s; the slowest andthe fastest heating rates are typical of batch and continuous annealing processes, respectively. The specimens were rapidly cooled to room temperature after various stages ofisothermal or continuous heating annealing by shutting off the power and cooling thespecimen under the flow of the gas mixture. Initial cooling rates as high as 45°C/s (at800° C) were realized using this procedure.Except for the isothermal tests conducted at the low temperatures of 500 and 550°C,the peak profiles in all other isothermal tests were obtained at room temperature on sam-pies prepared from interrupted heating-quenching procedure. The interrupted heating-quenching procedure was also employed to measure peak profiles on specimens heated at0.025, 1.88 and 20.2°C/s. In addition, in-situ peak profiles were obtained during isothermal testing at 500, 550, 600 and 625°C and during continuous heating at 0.025°C/s; thetime corresponding to the in-situ peak profile was recorded as being that at which thevalley intensity measurement was made.The time required to obtain the peak profile, i.e., to scan from the peak to thevalley between the Kcj and Ka2 peaks, was approximately 24 s. This was a prohibitivelyChapter 3. Experimental Procedure 90long time, and restricted the use of the in-situ method to low reaction rates (i.e., isothermal temperatures of 500, 550, 600 and 625°C and continuous heating rate of 0.025°C/s).A very high energy x-ray source with a more rapid scan rate capability would be requiredto overcome this problem. Partly to address this difficulty, and also to simplify the measurement procedure, experiments were performed to determine if the magnitude of theminimum point in the valley, ‘mm (or IM), is sufficient to describe the resolution of thepeak profile. This method of monitoring only the valley was employed at all isothermaltemperatures in the range of 500 to 760°C. However, the x-ray peak shift (and hence theshift in the valley position) with temperature and the necessity to compensate for thisshift by manually adjusting the x-ray detector, allowed this method to be used only atthe very slow heating rate of 0.025°C/s. Fig. 3.3 lists the isothermal and continuousheating annealing tests performed, together with the measurements made on each test.The effect of temperature on the positions (20) of the Kai /K2 valley and the Kai /Kcw2peaks, and on the values of R1 and ‘M were also investigated by obtaining the peakprofiles of a fully recrystallized specimen at different temperatures.A number of isothermal recrystallization tests were performed using the diffractometer to examine the reproducibility of the x-ray data. R1 values in the range of 0.60 to0.15, obtained both during in-situ monitoring and from interrupted tests, were reasonably reproducible. For example, the R1 values obtained from three different specimensproduced by rapid cooling to room temperature after holding for 300 s at 650°C were0.27, 0.30, and 0.32, indicating reproducibility within + 10 %.The reproducibility of the IM data was tested more rigorously, because when IMwas the monitored parameter, a single test was sufficient to characterize the kinetics atany isothermal temperature. To ensure reproducibility, every isothermal test performedbetween 600 and 760° C by valley monitoring, was repeated at least once. From theresults, it was evident that no single‘M value could be assigned to reflect the state ofChapter 3. Experimental Procedure 91annealing of the metal; the values of‘min -tb and consequently ‘M (in arbitrary units)corresponding to the same state of annealing were observed to vary considerably from testto test, some times as much as by 20 %. However, the proportional change in ‘M causedby annealing, i.e., the fractional peak resolution (F), was reproducible. An example ofthis is shown in Fig. 3.4, where F values obtained from two different tests are plotted asa function of time at 650°C, indicating good reproducibility.To determine the temperature variation with position in the resistance heated stripspecimens, four thermocouples were welded onto a typical specimen, at the positionsindicated in Fig. 3.5. The specimen was held isothermally at temperatures over therange of 600 to 800°C, and the difference between the set-temperature maintained at themidpoint by the controlling thermocouple, and that of the three measuring thermocouples(A, B and C), were then determined. The largest temperature differences, measuredat the highest set-temperature of 800°C, were 10, 30 and 15°C at positions A, B andC respectively. The larger thermal gradient, measured along the width direction (asindicated by the temperature differences at A and B), is thought to be due to the taperedheating ends (see Fig. 3.1 (a)) or the quartz specimen holders. As a consequence, thearea covered by the x-ray beam was reduced by employing modified (non-standard) slitarrangements. With this beam configuration, only position A fell within the area exposedto x-rays, making each x-ray scan essentially at constant temperature, within 10°C.3.3.4 Quantitative MetallographySmall rectangular specimens, 10 mm long, were cut along the length of the 13.5 mmwide strip in such a way that the midpoint of the specimen was the same as the originalthermocouple location. The specimens were set in cold-mount, and then ground andpolished using 120, 180, 320, and 600 grit grinding paper, and 5, 1 and 0.06 um aluminapowder. The microstructures of the polished specimens were revealed using an etchantChapter 3. Experimental Procedure 92prepared from 100 ml H20, 5 gm picric acid and 2-3 ml teepol (wetting agent), and etchingby swabbing at 80°C. The optimum etching time was determined to be approximately120 s. The best etching results were obtained when the specimen was washed and driedafter a 60 s etch and then followed by another 60 s etch. The midpoint of the specimenswas examined using an optical microscope to estimate the times corresponding to thestart(‘—i1 %) and the finish (.—‘ 99 %) of recrystallization. For quantifying the degree ofrecrystallization on partially recrystallized specimens, photomicrographs were obtainedusing a ‘Unitron MR2-11’ metallographic microscope at a magnification of 200 for thecoarser recrystallized grains and 400 for the finer recrystallized grains (i.e., near the startof recrystallization). Selected partially recrystallized specimens were also observed at amagnification of 1000 to provide additional microstructural detail on the nucleation andthe growth processes involved during recrystallization in I-F steels.The photomicrographs were analysed according to standard quantitative metallographic techniques applicable to recrystallization. The volume fraction recrystallized, X,and the interfacial area per unit volume between the recrystallized grains and the coldworked matrix, A, were determined, as illustrated in Fig. 3.6 [90]. The point counting(grid) method of Hillard and Cahn [42] was utilized to obtain X according to the relation,X= (3.4)where N is the total number of intersections on the grid and n is the number of intersections that fall on recrystallized grains. Similarly, following the analysis of Smith andGuttman [216], A was determined as follows,A=— (3.5)where n’ is the number of intersections of the grid line and the boundary between recrystallized and unrecrystallized regions, and L is the total length of grid line. No attemptwas made to measure the growth rate or the nucleation rate.Chapter 3. Experimental Procedure 93The grain size of the as-received and other fully recrystallized specimens was determined using the mean linear intercept (m.l.i.) method, which defines it as the averagechord length intersected by the grains on a random straight line in the planar polishedand etched section [44].Efforts were made to reduce any systematic bias or errors into the counting procedure. The grid spacing relative to the scale of the structure is the most critical item indetermining the accuracy of the analysis. While an increased number of points countedwill reduce the statistical errors, it has also been suggested that to improve the efficiencyand to minimize the sampling error for a given number of points counted, the averagenumber of points falling in any one area of the phase to be measured should not greatlyexceed unity [43]. This condition has been met during the counting procedure by usingtwo different grids, one a 108 (12x9) point grid used for coarser recrystallized grains,and the other with 221 (17x13) points used for finer recrystallized grains (i.e., for themicrographs corresponding to the early stages of recrystallization). With the objective offurther reducing the experimental error, at least four different optical micrographs wereobtained for each condition, all from the center area (within 1 mm from the midpoint)of the specimen, but from slightly different locations. The average of these values wasused for the kinetic calculations.During the diffraction studies of the sheet specimen, it is primarily a thin layer beneath the surface that contributes to the total diffracted intensity. The thickness ofthis layer could be estimated by considering the ratios of the diffracted intensities fromdifferent depths [49]; for the {220} diffraction peak of an iron specimen under FeK radiation, this thickness was estimated to be approximately 60tm. During the metallographicstudies, a typical grinding and polishing operation was estimated to remove about 100urn of material from the surface. Microstructural variation through the thickness of theChapter 3. Experimental Procedure 94sheet was also investigated by sectioning a number of partially recrystallized sheet specimens through the thickness of the beam/thermocouple location. The typical uniform,through-microstructure shown in Fig. 3.7, was obtained from a specimen produced byrapid cooling from 750°C after being heated at 20.2°C/s. The negligble through-thicknessvariation in microstructure observed in these specimens supports the assumption that thekinetic measurements obtained from diffraction effects and metallography are comparable.3.4 Electron Microscopic ObservationsThe major aim of this part of the investigation is to study the microstructural evolution during annealing of heavily cold-rolled I-F steel by transmission and scanningelectron microscopy (TEM and SEM). In particular, the influence of the precipitates onthe microstructural evolution was examined during a heating rate simulating the continuous annealing process. In addition, a brief examination of the orientation relationshipsamong subgrains and the nature of the precipitate distributions was conducted. Largeprecipitates were also examined for identification using an energy dispersive x-ray (EDX)microanalyser.3.4.1 Gleeble Simulated Annealing TreatmentCold rolled strip specimens of 100 mm x 30 mm annealed in the ‘Cleeble 1500’ thermomechanical simulator were used for TEM analysis. As with the hot x-ray camera, thesheet samples were resistively heated in a specimen chamber evacuated and back-filledwith inert Ar gas. The specimen temperature was controlled and monitored using a 0.25mm diameter, extrinsic chromel-alumel thermocouple spot welded to the surface of thestrip at its midpoint. Rapid cooling of the specimens after various stages of annealingChapter 3. Experimental Procedure 95was accomplished by shutting off the power and cooling the specimens in the inert Aratmosphere. For a specimen cooled from 800°C, an initial cooling rate of 31.6°C/s wasobtained using this procedure.Thermal gradients in the longitudinal and transverse directions were determined usingadditional thermocouples welded in different positions of a typical specimen. The difference between the set-temperature of 800° C, maintained at the midpoint by the controllingthermocouple, and that of the other measuring thermocouples, were then determined.A difference of oniy 3°C was observed between the midpoint and a point 10 mm acrossthe width, indicating shallow thermal gradients along the transverse direction. However,considerable thermal gradients were observed along the longitudinal direction, and consequently the working length had to be restricted to 3 mm from the midpoint, this beingthe distance corresponding to a difference of 10°C from the midpoint set-temperature of800°C.Different cold-rolled specimens heated at 20.2°C/s were rapidly cooled from the temperatures of 580, 640, 680, 740 and 800°C. These specimens were used to study themicrostructural changes associated with the recovery and recrystallization processes. Inaddition, a single specimen heated at 0.025°C/s was cooled from 700° C to produce a fullyrecrystallized microstructure, typical of that formed by the batch annealing process.3.4.2 Thin Foil Preparation and TEM InvestigationsThin foils for TEM investigations were prepared [217, 218] from the hot rolled, cold rolledand annealed specimens. Discs 3 mm in diameter were cut along the width (through themidpoint) of the annealed and cold rolled strips using electro discharge machining. These0.58 mm (580 jim) thick discs were mounted to a ‘Gatan’ disc grinder and mechanicallythinned in small increments of 50 jim. Wet grinding was done alternatively from bothsurfaces until a final thickness of approximately 80- 90 jim was achieved with a surfaceChapter 3. Experimental Procedure 96finish of 600 grit. The thicker hot rolled (as-received) material was machined first (equalreduction from both surfaces) to a thickness of ‘- 0.58 mm before the discs were cut, priorto the same grinding operation. The ground discs were then electropolished to perforationin a ‘Struers Tenupol-2’ jet polishing unit with an electrolyte of 5 % perchloric acid and95 % glacial acetic acid (by volume) at a polishing current of 60 - 80 mA (potential of60 V) at room temperature [217, 218]. The thin foils thus produced were examined ina ‘Hitachi H-800’ scanning transmission electron microscope operated at an acceleratingvoltage of 200 kV. In addition to the images obtained in the magnification range of 4 kto 40 k, a limited number of diffraction patterns and Kikuchi patterns were also obtainedwith the objective of studying the orientation relationships among subgrains.3.4.3 SEM/EDX Analysis of Large PrecipitatesSelected specimens of as-received hot band and partially and fully recrystallized steelsthat were observed under the light microscope were also examined using an SEM. Theannealed specimens chosen corresponded to the steels produced by rapidly cooling from660, 730 and 800°C, after continuously heating the cold rolled steel at 20.2°C/s. Thespecimens were re-polished (up to 1 tm diamond paste) and lightly etched with 2 %nital, to facilitate the observation of the precipitates, and were examined in a ‘Hitachi 5-570’ scanning electron microscope operated at an accelerating voltage of 20 kV. Images(secondary electrons imaging mode) obtained in the magnification range of 2 k to 10k, were used to study the relationship of the particles to the nucleation and growthprocesses. The precipitates larger than 0.1 4um in diameter were examined with a ‘Kevex8000’ microanalyser using energy dispersive x-ray (EDX) spectroscopy. A ‘Microspec’wavelength dispersive x-ray (WDX) microanalyser was also employed on a limited numberof samples to facilitate the complete chemical identification of some of the particles thatwere larger than 1 im in diameter.Chapter 3. Experimental Procedure 973.5 Texture CharacterizationThe primary objective of this part of the research was to quantitatively characterizethe evolution of crystallographic texture during cold rolling and subsequent annealingoperations. The effects of heating rate and grain growth on the resultant texture werealso briefly examined.3.5.1 Specimen PreparationThe annealing of the 100 mm x 30 mm cold-rolled strips were performed in a ‘Gleeble 1500’ thermomechanical simulator as described previously. Interrupted heating-quenching procedure was adopted to produce specimens reflective of different stages ofrecrystallization. Different cold-rolled specimens heated at 20.2°C/s were quenched inthe Ar atmosphere from temperatures of 670, 720, 760, 800 and 900°C, and two otherspecimens heated at 1.88 and 0.025°C/s were cooled from 770 and 700°C respectively.in addition, the crystallographic texture of the as-received hot band and the cold-rolledstrip was also characterized.Small rectangular specimens of 16 mm long (in rolling direction) x 12 mm wide werecut from the center of the annealed strips, with the center of the long axis coinciding withthe midpoints of the strips. For cold-rolled and annealed sheet steels, some differences intexture through the thickness of the sheet, particularly between the surface and the midplane had been reported [163, 186], and consequently all current texture measurementswere made on the mid-plane of the specimens. Cold rolled and annealed specimens wereground and polished to reduce the thickness to half its original value of 0.58 mm. Thethicker, 2.92 mm hot band was machined first before being ground to remove its halfthickness. All of the prepared specimens were then lightly etched in 2 % Nital.Chapter 3. Experimental Procedure 983.5.2 Pole Figure Determination and ODF CalculationsPartial {110}, {200}, {211} and {310} pole figures were determined in reflection using a‘Huber’ four-circle split ring goniometer with filtered Cu K radiation. The x-rays weregenerated from a ‘Rigatu’ 12 kW rotating anode operated at 55 kV and 180 mA. The data,received through a 2.7 mm slit, were recorded out to 800 from the centre of the pole at 5°intervals and also every 4° during the rotation of the specimen in its own plane through360°. During the measurement, the specimen is oscillated in its own plane in order toexpose more grains to the incident beam so as to improve the statistical accuracy [49, 158].In the present study, the total oscillation of the specimens was restricted to 2 mm becauseof the high temperature gradients observed along the longitudinal direction during theannealing treatment. Orientation distribution functions (ODFs) corresponding to eachspecimen were calculated from the four partial pole figures using the method developedby Bunge [165]. The ODF data was used to calculate the volume fractions of importanttexture components using = 16.5° Gaussian distributions [166, 219]. In addition, thevalues for average strain ratio () were estimated by incorporating texture data into theTaylor model of polycrystal deformation [161, 165]; the predictions were compared to theexperimentally determined values provided by Stelco.Chapter 3. Experimental Procedure 99Table 3.1: Steel composition provided by Stelco and that obtained from chemical analysisElement Nominal (wt %) Actual (wt %)C Max. 0.0028 n/aN Max. 0.003 0.00118S Max. 0.010 0.003P Max. 0.15 0.011Mn 0.10 0.140Al 0.03 - 0.06 0.060Ti+Nb Ti-rich, Nb-lean ( Ti: 0.03 ) Ti : 0.03, Nb : 0.02Chapter 3. Experimental Procedure 100Figure 3.1: (a) A strip specimen with thermocouple attached at centre of bottom surface,and (b) closeup of open hot x-ray camera with specimen in place.(a)(b)Chapter 3. Experimental ProcedurePEAK RESOLUTION DURING ANNEALING101AAS COLD ROLLEDAAPARTIALLY ANNEALED FULLY ANNEALED{220} DIFFRACTION PEAKX-Ray Ratio ( R1)Im.fllbR1 =IKaIbParameters MeasuredValley Intensity (IM)IM LmnIbFractional Peak Resolution (F)—(R1)— (RI)finaj(IM)jnjtjai — (IM)tF(IM) =(IM)jnjtjal — (IM)fjnJFigure 3.2: Schematic diagram illustrating the {220} x-ray peak resolution associatedwith annealing and the procedure for quantifying peak resolution.F(R1) =Chapter 3. Experimental Procedure 102KINETIC MEASUREMENTS I5 passesROLLING: 2.92 mm 0.58 mm80 % reductionX-RAY: Fe Karadiation; Monitoring (220) Peak.Annealing Treatment:_______T-T-R (Initial Heating Rate: 80 °CIs)Test Temperatures (°C) Parameters Measured500, 550 IM(ifl-situ), R1 (in-situ)600, 625 IM(in-situ), R1 (in-situ), R1 (interrupted)650, 675, 700, 720, 740, 760 Iii(in-situ). R1 (interrupted)Heating Rate (b/s) Parameters Measured0.025 IM(in-situ), R1 (in-situ),R (interrupted)1 .88, 20.2 R1 (interrupted)METALLOGRAPHY: On selected specimens from interrupted tests.Figure 3.3: Summary of the isothermal (T-T-R) and continuous heating (C-H-R) annealing tests performed, together with the parameters measured.Chapter 3. Experimental Procedure‘- 0.804-I0.4cICU1-.A-C C.T.CIL —“—H——-——••10.0—Figure 3.5: Strip specimen thermocouple positions for determining the thermal gradient;C.T. refers to control thermocouple; A, B and C are additional thermocouple positions.11030Time (s)Figure 3.4: Comparison of fractional peak resolution,as obtained from two different tests.F, based on valley intensity, ‘M,LENGTH\2.5BCIL LDIMENSIONS IN mmlChapter 3. Experimental Procedure 104Figure 3.6: Illustration of the measurement of volume fraction recrystallized, X, and theinterfacial area per unit volume, A, by quantitative metallography [90].Figure 3.7: Through-thickness microstructural variation of a partially recrystallized specimen produced by rapid cooling from 750°C after being heated at 20.2°C/s, MagnificationX 200).Recrystaflized ractior7- 1ntertacat Area1 EjChapter 4Kinetic CharacterizationThis chapter deals with the kinetic characterization of the recovery and the recrystallization processes operating during isothermal and continuous heating annealing cycles.The recovery process was monitored primarily through the measurement of x-ray ratio(R1), while the fraction recrystallized determined by quantitative metallography was usedin the analysis of recrystallization. Isothermal recovery, as described by a logarithmictype equation, and isothermal recrystallization, as characterized by the JMAK and theS-F equations are presented. In addition, the microstructural path approach was alsoemployed in the kinetic analysis of recrystallization. Finally, the recovery and the recrystallization kinetics during continuous heating were predicted using the principle ofadditivity, and validated through appropriate experimental measurements.4.1 Isothermal Recovery KineticsMetallographic examination of samples rapidly cooled after progressive stages of isothermal annealing established the following• At 500 and 550°C, the observed peak resolution was related solely to recoveryprocesses,• At 600, 625, 650 and 675°C, recovery effects alone caused the initial peak resolution,while combined recovery and recrystallization processes were responsible in the laterstages,105Chapter 4. Kinetic Characterization 106• At 700, 720, 740 and 760° C, recrystallization commenced during the heating to thetest temperature, and consequently the observed peak resolution was due to theconcurrent recovery and recrystallization processes, although recrystallization wasthe dominant cause.The fractional peak resolution (F) calculated at 500°C using both the in-situ x-rayratio (R1) and the in-situ valley intensity (Lw) are shown in Fig. 4.1, indicating thatthe recovery kinetics can be reasonably quantified using either parameter; analysis ofthe measurements made at 550°C also resulted in the same conclusion. In the presentwork, only the in-situ R1 measurements were used in the detailed kinetic analysis of therecovery process.The suitability of the semi-empirical equations 2.3 (in R1 = K — kt) and 2.4 (R1 =b— a in t) [29] for describing the isothermal recovery kinetics was tested first. Fig. 4.2shows the in-situ R1 measurements obtained at 500°C, together with the curves calculatedusing Eq. 2.3 and Eq. 2.4. Similar recovery measurements were also made at 550° C andpreceding recrystallization at 600 and 625°C; very short recrystallization start times (e.g.,15 s at 650°C) precluded any in-situ R1 measurements corresponding to recovery at 650or 675°C. Isothermal recovery data obtained at each temperature have been analysedin similar manner to those at 500°C, the results being summarized in Table 4.1. Thehigh correlation coefficients (R2) clearly indicate that the recovery kinetics in I-F steelscan be adequately described by the logarithmic relationship, Eq. 2.4. This is consistentwith the previously reported annealing studies on iron, where the recovery kinetics werequantified by the measurement of initial flow stress [40] and x-ray peak resolution [53].Fig. 4.3 (a) shows the in-situ R1 measurements at 500, 550, 600 and 625°C, togetherwith the kinetic curves calculated using Eq. 2.4. These are typical of recovery processes,with a continuously decreasillg rate of change and without any initial incubation period.Chapter 4. Kinetic Characterization 107This is a markedly different kinetic response from the sigmoidal property change usuallyexhibited by recrystallization. The validity of Eq. 2.4 in describing the recovery kineticscan be additionally demonstrated by replotting the same data on a logarithmic timescale, as shown in Fig. 4.3 (b).Fig. 4.4 shows the Time-Temperature-Recovery (T-T-Ry) diagram obtained by calculating the time required for R1 to be equal to 0.5, 0.4, 0.3 and 0.15, using Eq. 2.4;several measured values for R1 = 0.5 and 0.4 are also shown. The R1 values can beconverted to % recovery using the maximum possible change in R1, from 0.6 to 0.15, observed in the present study. It should be emphasized, however, that all of the isothermalR1 measurements that could be attributed only to the recovery processes were withinthe range of 0.56 to 0.34 depending on the test temperature, and the development of theT-T-Ry diagram at lower R1 values is totally dependent upon the extrapolation of themodelled expressions outside the experimental range. In practice, recrystallization wasobserved to commence at R1 0.34, making further R1 measurements corresponding torecovery impossible.The kinetics of the thermally activated recovery process was analysed by assumingArrhenius rate behaviour given by,dR1 (Qiy’\--= —Ar, exp—(4.1)where AR is a pre-exponential constant, QRy is the recovery activation energy, R is thegas constant and T is absolute temperature. The analysis was carried out by plotting thenatural logarithm of the instantaneous rate of recovery (in —dR1/dt = in aft), at fixedfractions of recovery (at constant R1 values), vs. the inverse absolute temperature, 1/T,as showil in Fig. 4.5 (a). The linear relationship obtained between ln(—dRijdt) and 1/T(with correlation coefficients of 0.99), shown in Fig. 4.5 (a), was used to calculate therecovery activation energy, QR at R1 values of 0.6, 0.45, 0.3 and 0.15, the results beingChapter 4. Kinetic Characterization 108shown graphically in Fig. 4.5 (b). The apparent activation energy, has been foundto increase from 173.1 kJ/mole at R1 = 0.6 to 312.1 kJ/mole at R1 = 0.15.The recovery of heavily deformed iron based alloys has been reported to occur byannihilation of point defects, rearrangement, migration and eventual annihilation of dislocations and finally the formation and growth of subgrains (described in detail in section2.1.5). The increasing activation energy with increasing % recovery, suggests a change inthe dominant recovery mechanism as recovery proceeds. An increasing activation energywith the progress of recovery is also consistent with recovery processes occurring initiallyat severely deformed regions, where the stored energy is a maximum, and therefore therequired activation energy is a minimum. Such an activation energy would be a functionof the instantaneous value of the recovering property, as indicated in Fig. 4.5 (b).The range of activation energy values obtained, from 173.1 to 312.1 kJ/mole, is comparable to the activation energy values of 91.9 to 281.7 kJ/mole, reported by Michalakand Paxton [40] from flow stress measurements made on lightly deformed polycrystallineiron; they correlated the lower and the upper limits of the reported activation energy values to simple vacancy migration and self-diffusion, respectively [29]. The values obtainedin the present work are higher than those reported by Michalak and Paxton, particularlyduring the early recovery stages, even though the amount of deformation was 80 % inthe present study and only 5 - 15 % in the Michalak and Paxton study. The activationenergy values obtained in the present study are also higher than the activation energyvalue of 126.2 kJ/mole at 50 % recovery, reported for 80 % cold rolled silicon-iron singlecrystals based on line broadening measurements [53]. The presence of the excess soluteTi and Nb in solid solution and the fine stabilizing precipitates of Ti and Nb carbideshave been reported to hinder the recovery processes (discussed in detail in section 2.1.5)[15, 130, 132] and may explain the higher activation energy values obtained in this study.It should be noted that the highest recovery activation energy computed in this work isChapter 4. Kinetic Characterization 109comparable to the reported activation energy for self-diffusion in iron (‘-‘ 275 kJ/mole[29]).The prediction of recovery kinetics during continuous heating requires the characterization of recovery kinetics over a wide range of isothermal temperatures. Fig. 4.6 showsplots of b and a vs. T. Linear relationships with correlation coefficients (R2) of 0.99 wereobtained for both cases, with corresponding equations,b = 0.95 — 0.00072 T (4.2)anda = 0.0072 — 0.000027 T (4.3)The linear relationship between ln —dR1/dt and 1/T (K—’), shown in Fig. 4.5 (a),indicates that the intercept, in AR, and the gradient, -QR/R, as obtained from Eq. 4.1,are dependent on R1. Both the parameters in AR and -QR,,/R were plotted against R1,the graphs being shown in Fig. 4.7, with the following appropriate equations,in AR 23.6 — 0.075 R1 (4.4)and—= —43137.1 + 37182.2 R1 (4.5)This method can also be used to characterize the recovery kinetics during isothermal andcontinuous heating processes.In-situ valley intensity (IM) measurements made at 500 and 550°C, and prior to theonset of recrystallization at 600, 625 and 650° C were also analysed for characterizing therecovery kinetics. Fig. 4.8 shows the IM measurements obtained at 500°C, together withthe modelled curves using Eq. 2.3 (In ‘M CX t) and Eq. 2.4 (IM CX in t). This, along withthe analysis of the data obtained at other temperatures, showed that the ‘M variationChapter 4. Kinetic Characterization 110with time can also be described adequately (R2 0.95) using Eq. 2.4 and consequentlyprovided a simpler method of monitoring the isothermal recovery kinetics. However,the difficulty of comparing the intensity values obtained at different test temperaturesprecluded the use of this method in the calculation of recovery activation energy.Fig. 4.9 shows the R1 measurements corresponding to both the start of the isothermaltreatment (once the test temperature is reached) and the approximate commencementof the recrystallization event (determined from metallography), as obtained from theinterrupted heating-quenching tests performed at 600, 625, 650 and 675°C. These results,when compared to the maximum R1 change of 0.6 to 0.15 observed in the present study,indicate that approximately 45 to 60 % of the total change in the measured R1 values arecaused by recovery alone; this includes the recovery effects occurring during heating to thetest temperature and the isothermal recovery effects prior to the onset of recrystallization.The lower R1 values corresponding to the start of the isothermal treatment obtained athigher test temperatures indicate the higher amount of recovery the steel underwentduring heating to the test temperature. On the other hand, recrystallization commencedwithin a short isothermal hold time, and consequently the R1 values corresponding to theonset of recrystallization were higher at higher test temperatures. The difference betweenthese R1 values at each test temperature, shown in Fig. 4.9, indicates the recovery effectsassociated with the isothermal hold and shows that recovery is more significant at lowerisothermal temperatures. At higher temperatures, recrystallization commences after ashort hold time, thereby reducing the recovery effects on peak resolution.It is clear from the present study that the I-F steel under investigation undergoesa considerable amount of recovery prior to the onset of recrystallization, in agreementwith data reported previously for Ti-stabilized [15, 21] and Nb-stabilized steels [17]. Thissuggests that the absence of C and N in the matrix of the I-F steel is more effective inpromoting recovery than is the presence of Ti and Nb in solid solution and as precipitatesChapter 4. Kinetic Characterization 111in hindering the recovery processes.In summary, the isothermal recovery kinetics as monitored by in-situ R1 measurements have been described using a semi-empirical logarithmic type equation. The kineticcharacterization indicated the recovery activation energy to be a function of the state ofrecovery, an observation attributed to the change in the dominant recovery mechanism,as recovery proceeds. The calculated activation energy values were moderately higherthan those reported for pure iron. This was explained in terms of the possible retardationof recovery caused by the presence of the excess Ti/Nb in solid solution and the fine stabilizing precipitates of Ti and Nb carbides. This I-F steel has been observed to undergoa considerable amount of recovery prior to recrystallization, an observation attributedprimarily to its interstitial-free iron matrix.4.2 Recovery and Recrystallization during Isothermal HeatingAt temperatures > 600°C, concurrent recovery and recrystallization processes contributeto the observed x-ray peak resolution. This is true for the later part of the isothermaltests at 600, 625, 650 and 675°C, and for the entire annealing time at 700, 720, 740and 760°C. The combined recovery and recrystallization kinetics were monitored usinginterrupted R1 and in-situ IM measurements at all test temperatures. In addition, in-situR1 measurements were also made at 600, 625 and 650°C. Fractional peak resolution, F,calculated at every isothermal temperature, was found to vary with time in a similarmanner irrespective of the parameter used in the estimation of F. Fig. 4.10 presentsthe results obtained for the F values as a function of annealing time at 625° C, usingboth the interrupted R1 values and the in-situ ‘M measurements (obtained from twodifferent tests); the metallographically determined recrystallization start time of 240 s isalso indicated. These results indicate that the combined recovery and recrystallizationChapter 4. Kinetic Characterization 112kinetics can be quantified through the measurement of either R1 orThe determination of recrystallization kinetics from these x-ray measurements requires that a procedure be developed to separate the effects of recovery and recrystallization on peak resolution. The contribution of recovery to the measured R1 values, asquantified using Eq. 2.4, was subtracted from the measured total change to yield therecrystallization kinetics. Fig. 4.11 shows a typical example where the isothermal R1(interrupted) data of 675°C is analysed to give the percentage recrystallized. The effectof recovery during recrystallization is shown by extrapolating the recovery kinetics intothe recrystallization zone (RTA) and reducing the magnitude of the recovery effect by theincreasing area recrystallized (RUA). The estimation of the unrecrystallized area for therecovery correction has been accomplished through an iterative procedure. The initialestimation of the fraction recrystallized was made by neglecting the concurrent recoveryeffects, i.e., by attributing all of the R1 change to recrystallization. The resulting unrecrystallized fraction thus estimated was considered to undergo recovery (instead of thewhole area) and the R1 values corresponding to recovery were modified accordingly. Thedifference between these newly calculated R1 values and the experimental R1 values werethen used in the estimation of the new fraction recrystallized. These calculations wererepeated until the difference between two subsequent estimations of fractions recrystallized was no more than 1 %. Usually, the solution was obtained within 3 to 5 iterations.Only the results from the final analysis are shown in Fig. 4.11. The % recrystallizedobtained through this procedure, was compared with the metallographic measurements,as shown in Fig. 4.11. The reasonable agreement validates the separation procedureadopted in the present study. Fig. 4.12 presents the results of a similar analysis appliedto the in-situ ‘M measurements obtained at 650°C.At temperatures of 700°C and above, x-ray measurements could be directly correlated to recrystallization, due to the rapid recrystallization rates and reduced recoveryChapter 4. Kinetic Characterization 113effects. Figs. 4.13 (a) and (b) show two such examples corresponding to 700 and 720°C,indicating reasonable agreement between the fractional peak resolution (F) calculatedfrom interrupted R1 and in-situ ‘M measurements and the fraction recrystallized (X)obtained from quantitative metallography.The results presented in this section, as well as those in the previous recovery section,support the possibility of quantifying the fractional annealing effects, i.e., the F valuesas influenced by the recovery or recrystallization or a combination of both through thex-ray peak resolution measurements of either R1 or ‘M• To test this approach, a series ofin-situ x-ray peak profiles obtained at selected isothermal temperatures, were analysedto study the variation of the peak and valley intensities during the progress of annealing.Figs. 4.14 (a) and (b) show the time variation of the intensity values of the dominantpeak, ‘K1, the valley between the K1 and Ka2 peaks, ‘mm, and the background, ‘b, at500 and 650°C respectively. The intensity of the Ka2 peak was always in the range of 60- 70 % of the intensity of the Kai peak. At 500° C, recovery effects were solely responsiblefor the peak resolution, while at 650°C, recrystallization was the dominant structuralchange.In the present work, the degree of peak resolution associated with the progressiveelimination of non-uniform lattice strain has been characterized primarily through thex-ray ratio, R1 (Note: the contribution to broadening from the relatively coarse particle size involved in the present study is considered to be negligble). The R1 value wasthen correlated to the fractional annealing effects through the fractional peak resolutionfactor, F. The interpretation of F values in terms of recovery and recrystallization wascarried out with the aid of confirmatory microstructural measurements, in particular themetallographically determined recrystallization start time. The fractional peak resolution, F, as defined by Eq. 3.3, is in fact the ratio of change of R1 within the minimumand the maximum measured R1 values. A similar approach has been used in previousChapter 4. Kinetic Characterization 114recovery and recrystallization studies on iron-based alloys [15, 53, 55, 56, 57]. However,in the present work, the valley intensity, IM, also leads to a similar time variation ofF. During recovery, a progressive reduction in ‘mn, as well as a small increase inhas been observed, as shown in Fig. 4.14 (a). This will lead to a faster rate of decreasein R1 than in ‘M However, Figs. 4.2 and 4.8 indicate that both R1 and ‘M obey thelogarithmic-type recovery equation (R1 = — a in t and ‘M = bM — aM in t), and thisobservation explains the same time variation of F (i.e., F(R1) = F(IM) obtained duringrecovery.When recrystallization was the dominant cause for peak resolution, the intensity,remained relatively constant, as shown in Fig. 4.14 (b). In addition, since R1(R1=values generally vary between 0.45 to 0.15 during recrystallization, thelarger variation in ‘mm shown in Fig. 4.14 (b), will have a stronger influence on R1than the smaller variation in Iiç1. These observations provide the necessary explanationfor the same ratio of change (F) obtained with R1 and ‘M during recrystallization. Inaddition, the observation that and I remain unchanged during recrystallization,suggests that the rate of change of R1 will be approximately equal to that of ‘M duringrecrystallization.In general, the intensity measurements were observed to be influenced by severalfactors such as the temperature and the surface conditions of the specimens. Moreimportantly, the development of prefered crystallographic texture and the correspondingchange in the number of planes participating in diffraction, can have a major influencein the absolute intensity measurements such as However, in the case of x-ray ratio,R1, this being the ratio of two different intensities, the influence of these parameters maynot be significant; this will be demonstrated in a later section relating to the influence oftemperature.The preceding arguments clearly indicate that R1 measurements are more suitableChapter 4. Kinetic Characterization 115than ‘M for the detailed kinetic analysis. However, the major advantage with the ‘Mmeasurement is that it allows the complete kinetic characterization of annealing effects atany isothermal temperature to be accomplished by monitoring a single 20 (valley) positionand the background; no 20 scan is required, as it is for R1 measurements. Previousrecrystallization studies on heavily cold rolled low-carbon steels using integrated poleintensity measurements have indicated that the number of {11O} (and therefore {220})planes that were parallel to the rolling plane was not very sensitive to the cold rolling andthe annealing conditions [21, 163]. In particular, recent recrystallization studies on Ti-stabilized extra-low-carbon steels showed the integrated pole intensity of the {11O} planesto remain unchanged during the entire annealing period (see Fig. 2.4) [15, 193]. Thetexture data obtained during the present investigation also showed that the number of{11O} and {220} planes did not change significantly during annealing (the details will bepresented in a later chapter), thereby validating the IM measurements in characterizingthe recrystallization kinetics.In summary, the {220} x-ray peak resolution, a parameter primarily related to thenon-uniform lattice strain, can be successfully employed to characterize the kinetics ofthe recovery and the recrystallization processes. In particular, both R1 and ‘M measurements have been shown to lead to identical kinetic analyses during the time whenrecrystallization dominates. These observations were explained in terms of the relativeconstancy of the number of {220} planes that are parallel to the rolling plane duringrecrystallization. An iterative procedure was adopted in conjunction with confirmatorymicrostructural measurements to separate the diffraction effects associated with the concurrent recovery and recrystallization processes; the concurrent recovery effects werefound to be significant only during the early stages of recrystallization.Chapter 4. Kinetic Characterization 1164.3 Isothermal Recrystallization KineticsFor the isothermal annealing treatments performed at 600, 625, 650, 675, 700, 720, 740and 760°C, quantitative metallography was carried out on samples rapidly cooled afterprogressive stages of annealing. Polished and etched specimens were examined using anoptical microscope to estimate the times corresponding to the onset (‘-.-‘ 1%) and thecompletion 99 %) of recrystallization. Only partial recrystallization was studied at600 and 625° C due to the long recrystallization times involved, and consequently no recrystallization end time was determined at these temperatures. Similarly, only partialrecrystallization could be obtained at 700, 720, 740 and 760°C because recrystallizationinitiated and progressed during heating (80°C/s) to the test temperature. As a result,no recrystallization start time was estimated in these cases. Because of the difficulty ofestablishing an exact start time, an estimated start time range (any value within thisrange is referred to as t) corresponding to the onset of recrystallization was initiallyestablished at 600, 625, 650 and 675°C. At every isothermal temperature, however, photomicrographs were obtained from the partially recrystallized specimens, and were usedto estimate the volume fraction recrystallized, by the point counting grid method [42].4.3.1 JMAK/S-F Analysis of Isothermal RecrystallizationFig. 4.15 shows a typical plot of % recrystallized vs. time (on a logarithmic scale),obtained from the metallographic measurements made at 650° C. Each experimental pointon the curve is the average of four measurements made from different photomicrographs;the two error bars are indicative of the maximum and the minimum variability of themeasurements observed during the evaluation of all specimens.The recrystallization kinetics at each isothermal temperature was characterized interms of the JMAK equation (Eq. 2.11) [65, 66, 67]. Using least square analysis, theChapter 4. Kinetic Characterization 117best fitting line was determined for a plot of lnln(1/1 — X) vs. ln(t— test), and itscorrelation coefficient (R2) was recorded. The value of the estimated start time, test, wasthen varied by a small time increment, and the best fitting line determined once again.This procedure was repeated and the best correlation (max. R2) was obtained, theassociated t being taken as the recrystallization start time, t. The kinetic parametersn and ln b resulting from the analysis, in combination with the computed t9, were usedto characterize the recrystallization kinetics at each temperature.The same isothermal recrystallization results were described using the S-F equation(Eq. 2.21) [90]. This was accomplished by performing a linear regression analysis ofln(X/1— X) vs. ln(t— t8), with the previously established recrystallization start time,t5. Fig. 4.16 shows a comparison of the JMAK and the S-F kinetic characterization ofthe isothermal recrystallization data obtained at 650°C.The results of the JMAK and S-F kinetic characterization of the isothermal recrystallization for test temperatures 600 to 760°C, are summarized in Table 4.2. It is apparentthat the time-exponents n (JMAK) and m (S-F) remain relatively constant over the testtemperatures, while the parameters in b and ln k, being reflective of the temperature-dependence of the nucleation and the growth equations, are strongly dependent on temperature. Fig. 4.17 shows the effect of temperature on the time-exponents, ri, and, m,and the average values of ri. (n = 0.73) and m (n. = 1.17). Obtaining a constant n forthe JMAK analysis implies that the nucleation conditions and the growth dimensionality are similar over the temperature range examined, a condition corroborated by themetallographic observations. In addition, a constant n value is required if the reactionis assumed to be additive (discussed in section 2.1.4). In the present work, the isothermal data has been characterized in terms of constant ñ and i values of 0.73 and 1.17,respectively. Using these values, the appropriate in b and in k values were recalculatedat each test temperature, and in combination with and ñi, were used to characterizeChapter 4. Kinetic Characterization 118the isothermal recrystallization kinetics. Fig. 4.18 shows the experimentally determinedisothermal recrystallization kinetics obtained at 650°C, and those characterized by thebest fitting and constant average time-exponent analyses using the JMAK and the S-Fequations. The constant average time-exponent characterization of both equations gavea good fit and were used for subsequent continuous heating calculations. The isothermalrecrystallization results obtained at 600, 625, 650, 675, 700, 720, 740 and 760°C, togetherwith the JMAK and the S-F descriptions obtained using a mean time-exponent, ñ or ñi,and a recalculated ln b or ln k, are shown in Figs. 4.19 through 4.21.Fig. 4.22 shows the Time-Temperature-Recrystallization (T-T-R) diagram obtainedby calculating the time required for 1, 50 and 99 % recrystallization using the JMAK analysis and includes the calculated recrystallization start time, t, the metallographicallydetermined recrystallization completion times for the present study and those reportedfor a Ti-stabilized [21] and a rimmed [57] low-carbon steels.Recrystallization kinetics have also been characterized in terms of an overall recrystallization activation energy, QR, by assuming an Arrhenius-type rate behaviour in theform of Eq. 2.41 (1/tR cx exp(—QR/RT)). The time, tR, required for 10, 50 and 90 %recrystallization was calculated for each isothermal test temperature using the JMAKanalysis, and the QR value was estimated by plotting ln(1/tR) vs. 1/T (K’), as shownin Fig. 4.23. The linear relationship (R2 = 0.99) obtained between ln(1/tR) and 1/Tdata supports the validity of the Arrhenius relationship in describing the recrystallization kinetics. The parallel lines corresponding to 10, 50 and 90 % indicate an activationenergy of 501.7 kJ/mole for the entire recrystallization event. A similar analysis usingthe S-F equation gave a QR value of 493.9 kJ/mole.The prediction of recrystallization kinetics during continuous heating using the additivity principle [121, 122, 128] requires mathematical expressions describing the temperature dependence of the kinetic parameters, ln b and ln k for the JMAK and S-F equations,Chapter 4. Kinetic Characterization 119respectively. Fig. 4.24 shows the plots of in b and in k vs. T (°C). Linear relationshipswith correlation coefficients (R2) of 0.99 were obtained for both cases, with correspondingequations,ln b = 0.049 T — 36.6 (4.6)andink = 0.077 T — 56.9 (4.7)Similarly, the prediction of recrystallization start time during continuous heating using the Scheil equation (Eq. 2.40) [120] requires the characterization of the isothermalstart time, t, as a function of temperature. Fig. 4.25 shows the in tS vs. T (°C) experimental results obtained for the low temperature recrystallization experiments whererecrystallization was initiated during isothermal annealing. Linear relationship (R2 =0.98) was obtained between lntt and T (°C), with corresponding equation,lntt = 54.7 — 0.079 T (4.8)To facilitate discussion of the recrystallization kinetics, photomicrographs illustratingthe evolution of microstructure during recrystallization are presented. Figs. 4.26 (a) and(b) show the typical equiaxed microstructure of the as-received hot band and the heavilycold worked banded structure of the 80 % cold-rolled sheet, respectively. The averagegrain size of the hot band, estimated using the mean linear intercept (m.l.i) method[44], corresponds to ASTM No. (7 - 8). Figs. 4.27 (a) and (b) and Figs. 4.28 (a) and(b) show four different photomicrographs (all at magnifications of x 200) obtained fromspecimens held at 700°C for 2, 4, 12 and 30 s, respectively. These microstructures, corresponding to approximately 15, 30, 60 and 80 % recrystallization, illustrate the progressof recrystallization. Fig. 4.29 shows the microstructure of a fully recrystallized specimen,obtained after a 150 s anneal at 700°C. The average grain size of a fully recrystallizedChapter 4. Kinetic Characterization 120specimen at the end of the recrystallization event (i.e., without significant grain growth)was estimated to be in the range of ASTM No. (9 - 10). Figs. 4.30 (a) obtained at x400 and (b) obtained at x 1000 show two different microstructures corresponding to theinitial stages (.-.-‘ 6 %) of recrystallization obtained from a specimen annealed for 32 s at650°C.These microstructures confirm that the recrystallization event is heterogeneous, preferential nucleation initiating at cold-rolled grain boundaries and grain intersections ascan be seen in Figs. 4.27 (a), (b), and Figs. 4.30 (a), (b). The same figures also indicatethat the nucleation and growth are rapid in some deformed grains, and not in others.Although no attempt was made during the present investigation to systematically measure the nucleation rates, an observation of the microstructures, shown in Figs. 4.27 (a)and (b), suggests that most of the nuclei form during the early stages of recrystallization.This indicates an early site saturation type nucleation, and consequently, recrystallizationis predominantly controlled by growth processes.Similar microstructural observations have been previously reported from recrystallization studies on high-purity iron and its dilute solid solutions [37, 38, 72, 81]. Thepresent observations are also in general agreement with the microstructural changes reported for rimmed, Al-killed and Ti/Nb-stabilized low-carbon steels [16, 17, 21, 138, 153].The observation that nucleation is heterogeneous clearly violates the random nucleationassumption of the JMAK theory. In reality, the nuclei are clustered on planes rather thanrandomly distributed in volume, and the associated increase in the impingement duringthe early stages of recrystallization is grossly underestimated by Eq. 2.7, as provided inthe random nucleation JMAK treatment [68, 85, 96]. This is thought to be the majorreason for obtaining the low value of apprximately 0.7 (Table 4.2) for the JMAK timeexponent, n, in this study. Isothermal kinetics with such low JMAK time-exponents havebeen widely reported from recrystallization studies on iron and its alloys [38, 39, 71, 72].Chapter 4. Kinetic Characterization 121Another type of failure that has been observed with the JMAK analysis of recrystallization is the negative deviation from the expected linearity between in ln(1/1— X)vs. in(t— t3) [33, 72, 87]. Such effects are visibie in Figs. 4.19 (a) and (b), particularly at 650, 675 and 700°C. The same effect can also be seen in the X vs. t graphs inFig. 4.21 (a) and (b) during the later stages of recrystallization at 650, 675 and 700°C.Since recrystallization was not carried out to completion at lower temperatures, theseeffects could not be seen. No negative deviation was observed at higher temperatures,presumably due to faster growth rates. A decreasing growth rate (G) with time duringrecrystallization is a possible explanation for this observation of negative deviation fromthe linearity, as has already been suggested by other researchers [33, 37, 38, 72, 75].A decreasing growth rate during isothermal recrystallization has been explained primarily in terms of a reducing driving force (for growth), caused either by concurrent recovery effects [33, 37, 38, 72, 90] or by non-uniform distribution of stored energy [85, 88, 95]or by the combination of the two [63, 75] (see section 2.1.3). Figs. 4.11 and 4.12 showthe effects of recovery during recrystallization, by extrapolating the recovery kinetics intothe recrystallization zone. It is clear from these figures that the recovery effects becomenegligibly small during the final 50 % of recrystallization, consistent with their rate progressing inversely proportional to time. This observation suggests that the non-uniformdistribution of stored energy (or growth along a driving force gradient) is the probablecause for any reduction in growth rate that might have occurred during recrystallizationof the present steel.Price [87, 106, 107] recognized the deficiency of the JMAK equation as related to itsassumption of constant growth rate, and suggested the S-F equation with a decreasinginterface-averaged boundary migration rate (G) as a better alternative. When the presentisothermal data was plotted on a standard S-F format, i.e., ln(X/1— X) vs. ln(t —as shown in Figs. 4.20 (a) and (b), no systematic deviation from the linearity could beChapter 4. Kinetic Characterization 122seen towards the end of recrystallization. A careful examination of Figs. 4.21 (a) and(b), where the experimental and the modelled fraction recrystallized were plotted as afunction of time, also reveals that the S-F equation is more suitable in describing thelater stages of recrystallization. However, it is also obvious from Figs. 4.21 (a) and (b)that the JMAK equation provides a better fit to the early portion of the kinetic curve.In summary, both the JMAK and the S-F equations provide reasonable descriptionsof the experimental data as indicated by Figs. 4.19 through 4.21. The comparable correlation coefficients resulting from the regression analysis using either equation, as shownin Table 4.2, are due to the fact that the JMAK and the S-F equations describe differentstages of the recrystallization event particularly well. The microstructural observationsas related to the heterogeneous nature of recrystallization suggest the need to adopt anempirical approach with physical significance to better describe the kinetics of isothermalrecrystallization.4.3.2 Microstructural Path Concept in Recrystallization ModellingThe second approach used in the present study to model the microstructural and kinetic aspects of recrystallization involves the microstructural path concept. The path ofmicrostructural change is the sequence of the microstructural states through which thesystem passes during a process [85]. The instantaneous state of the system undergoingmicrostructural evolution during the process of recrystallization is frequently describedexperimentally in terms of the stereological properties, X, the volume fraction recrystallized, and A, the interfacial area per unit volume separating the recrystallized grainsfrom the deformed matrix. In the present study, the photomicrographs obtained fromthe partially recrystallized specimens were used to estimate the interfacial area per unitvolume (A) according to Eq. 3.5 [216]. Fig. 4.31 shows the resulting A vs. X dataobtained for all isothermal temperatures and heating rates. The existance of a singleChapter 4. Kinetic Characterization 123microstructural path function independent of the thermal path is obvious. Because ofthe assymmetric nature of the A vs. X graph, the semi-empirical equation (Eq. 2.18)proposed by Rath [103], was used to describe the relationship, givingA = 2002 (X)°44 (1 — X)°-94 (4.9)which has a correlation coefficient of R2 = 0.98.In the microstructural path approach, the kinetic function is usually described bythe relationship between the interface-averaged growth rate (C) and the growth time[75, 81, 90]. The C values are estimated throughout the transformation using the CahnHagel formulation (Eq. 2.16), i.e., = A C [100]. In the present study, each isothermaltemperature or heating rate was treated separately to calculate the C values. The Xvs. t data obtained for each annealing condition was subjected to curve-fitting, usinga JMAK-type equation, and the resulting curve was used in the estimation of dX/dt.The resulting dX/dt values and the experimental A values gave C values correspondingto each annealing test. For each isothermal test, the relationship between and t wasdescribed according to the following equation [75],(4.10)where the time-exponent, riG, and the coefficient, KG, are constants, and the time, t,corresponds to the actual recrystallization time. The parameters riG and KG corresponding to each isothermal temperature were obtained through a linear regression analysisof in C vs. ln(t—t) (t8 is the calculated recrystallization start time), performed separately for each isothermal temperature. The results are summarized in Table 4.3. It isapparent that the growth rate time-exponent, G, remains relatively a constant over thetest temperatures, while the parameter log KG is strongly dependent on temperature.Fig. 4.32 shows the effect of temperature on the growth rate time-exponent, riG, and theChapter 4. Kinetic Characterization 124average riG value of -0.58. In explaining this observation, G is expected to be a functionof the growth dimensionality. Since comparable equiaxed grains are obtained at eachtemperature, the nG value remains a constant, comparable to that of the temperature-independent JMAK time-exponent. In addition, a temperature-independent G, alsosatisfies the general isokinetic condition of the additivity requirement (Eq. 2.29) [114],as will be demonstrated in a later section.In the present study, the isothermal interface-averaged growth data have been characterized in terms of the average G value of -0.58. Using this value, the appropriatelog Ka values were recalculated at each test temperature, and in combination with theriG value of -0.58, were used to characterize the isothermal recrystallization kinetics. Theresulting recrystallization analysis is shown graphically in Figs. 4.33 (a) and (b). Fig.4.33 (a) shows the growth rate vs. time (both axes on logarithmic scale) at 600, 625,650 and 675°C, and Fig. 4.33 (b) presents the similar information at 700, 720, 740 and760°C. It should be emphasized that the experimental points in these graphs are specificgrowth rates calculated from experimental measurements and not primary data points.The interface-averaged growth kinetics have also been characterized in terms of agrowth activation energy, QG, by assuming an Arrhenius-type rate behaviour of theform G cx exp(—QG/RT). The activation energy calculations were made at differenttemperatures, but at constant degree of recrystallization. A parameter, called ‘interfaceaveraged growth distance’, dG, was used to fix the state of the reaction (in an analogousmanner to fraction recrystallized, X), and defined as follows,dG=JGdt=‘t+’ (4.11)(riG + 1)By substituting the total recrystallization times obtained at the isothermal temperatures into Eq. 4.11, the total (interface-averaged) growth distance corresponding to theChapter 4. Kinetic Characterization 125complete recrystallization event was estimated to be about 0.0024 cm(‘S-’24 t m). Consequently, the growth rates were calculated at constant growth distances of 0.0005, 0.0010,0.0015 and 0.0020 cm. The activation energy for growth, QG, was calculated by plotting ln G vs. 1/T (K—’), as shown in Fig. 4.34. The linear relationship (R2 = 0.99)obtained between ln G and l/T indicates the validity of the Arrhenius relationship indescribing the growth kinetics. The common slope obtained for each growth distancegave an activation energy of 544.9 kJ/mole for the entire recrystallization event.The prediction of the growth kinetics during continuous heating using the additivityprinciple requires a mathematical expression describing the temperature dependence ofthe kinetic parameter, KG. Fig. 4.35 shows the plot of K (on a logarithmic scale) vs. T(°C). The following linear relationship with a correlation coefficient of 0.99 was obtained,log KG = 0.013 T — 13.2 (4.12)The relationship between the stereological properties A and X obtained in the presentwork, as shown in Fig. 4.31, and the associated microstructural path function, as givenby Eq. 4.9, are asymmetric in nature. A increases rapidly during the early stages ofrecrystallization, remains close to the maximum when the % recrystallized is in therange of 25 to 45 %, and decreases steadily thereafter. The initial rapid rise in A with anincreasing X can be rationalized in terms of the early site saturation type nucleation andthe subsequent growth of these grains in a spherical manner as indicated in Figs. 4.27(a) and (b). The progressive disappearance of the cold rolled matrix, however, occursroughly in the form of pancake shaped manner as shown in Figs. 4.28 (a) and (b); thisprovides the rationale for the slowly decaying A during the later stages.To the author’s knowledge, there is no reported study of the microstructural pathfunction for a heavily deformed polycrystalline low-carbon steel. However, the presentmicrostructural observations are in general agreement with the A vs. X data reportedChapter 4. Kinetic Characterization 126for a deformed iron single crystal [75, 102], and with some of the other recent theoreticaland experimental developments reported on path functions [75, 84, 102, 103]. However,it should be noted that the A vs. X data of Fig. 2.9, and the associated path functiondescribed by Eq. 2.19, as incorporated into the S-F model [90], are considerably differentfrom those obtained in the present study. In particular, the S-F path function, A =KAX(1 — X) (Eq. 2.19), and the corresponding symmetric nature of the A vs. Xrelationship, may not adequately describe recrystallization with early site saturationtype nucleation.The kinetic relationship obtained in the present study between the interface-averagedgrowth rate (G) and the recrystallization time, as shown in Figs. 4.33 (a) and (b), issimilar to the results reported by Vandermeer and Rath [75] for a deformed iron singlecrystal. They obtained a relationship in the form of C cx t0 at all isothermal temperatures, and rationalized this behaviour in terms of a nonuniform stored energy distributionor growth along a stored energy gradient [75]. The stronger t058 time dependence obtained in the present work can be easily explained in terms of the greater non-uniformdistribution of stored energy to be expected in a heavily deformed polycrystalline metal.In the present study, the effect of temperature is incorporated in the coefficient KG in Eq.4.10, as shown by Eq. 4.12. Whereas, the growth equation, Eq. 2.20, incorporated intothe S-F model [90] is considerably different, with a stronger growth time dependence,O o t1, apparently independent of temperature.The quantitative understanding of a strongly time dependent (cx t1), but apparentlytemperature independent, migration rate (C) continues to be a controversial issue. English and Backofen [81] observed this behaviour with the exception of short times, asshown in Fig. 2.10, and attributed it to the time dependence of the extent of solutesegregation to subboundaries in the unrecrystallized material. Speich and Fisher [90] reported the growth equation, 0 8.5x104 to describe the growth rates at all isothermalChapter 4. Kinetic Characterization 127temperatures. They explained this by invoking the same activation energy for both theboundary migration and the later stages of recovery. Gokhale et al. [105] reinterpretedthe same data in terms of the reduction in the dimensionality of growth during recrystallization. Vandermeer and Rath [76] suggested that highly anisotropic three-dimensionalgrowth could also produce the same result, without the need for invoking competingrecovery. The anisotropy was postulated to be due to an orientation effect on boundarymobility. The present investigation, as well as some other reported studies [63, 75, 85],have indicated that recovery can not be responsible for a significant reduction in migration rates during the later stages of recrystallization. On the other hand, in view ofthe fact that the recrystallized grains did not change shape during growth (i.e., isotropicgrowth), the change in growth dimensionality or any other anisotropic effects cannot besignificant.In the present study, isothermal G vs. t data was analysed separately at each temperature. For comparison purposes only, the data from all test temperatures was plottedon a single graph, as indicated in Fig. 4.36. The best fitting line obtained from a linear regression is shown in Fig. 4.36. The equation corresponding to this line, with acorrelation coefficient of 0.95, is given by,= 3.8 x104 (4.13)This temperature independent equation is remarkably close to the one reported by Speichand Fisher [90]. Some resemblance can also be seen with the graph reported by Englishand Backofen [81] (see Fig. 2.10) in terms of the deviation from the linearity at shortrecrystallization times. A closer examination of the regression line, particularly at lowtemperatures, indicates that the data obtained at a single temperature have a slightlydifferent gradient than that corresponding to the global fit. However, the global regressionline does a reasonable job in relating X vs. t. It should be noted that when the isothermalChapter 4. Kinetic Characterization 128data were subjected to the regression analysis, one temperature at a time, all of the time-exponents (riG) obtained were within the range of -0.48 to -0.68, as indicated in Fig. 4.32.However, the global fit with a larger time scale, resulted in a considerably higher timeexponent of -1. This observation provides an additional explanation to the previouslyreported strongly time-dependent growth. However, it should be emphasized that thoughthe G values obtained from the global regression line or Eq. 4.13 may not be very differentfrom the actual calculated ones, the relationship among the points corresponding to asingle temperature or the associated time-exponent is significantly different in the globalrepresentation.The interface-averaged growth rate, G, was measured in the present study throughoutthe recrystallization event using the procedure described previously. The local growthrate, G, usually obtained by measuring the time variation of the largest intercept-free distance on the microstructure, is limited to X < 0.20, due to the impingement effects. Suchmeasurements require several specimens corresponding to the initial stages of recrystallization, and consequently, G was not estimated in this study. English and Backofen [81]measured both G and G, and indicated that 0 also satisfied the relationship obtainedbetween and t. A recent study on iron single crystals by Vandermeer and Rath [75]also revealed approximately the same time dependence for G (o t°40) and oc t°38).They also obtained approximately the same activation energy for both 0 and G, althoughthe pre-exponential constants are slightly different. These arguments suggest the generaltime-dependence of 0 and G to be approximately the same. In addition, for an early sitesaturation type nucleation, one can reasonably expect the same G and G values beforeimpingement. In the present results shown in Fig. 4.33 (a) and (b), the first two pointsat each isothermal temperature, which usually corresponds to X < 0.20, obey the t°58relationship reasonably well. The 0 values corresponding to these points are expectedto be comparable to the G values, suggesting a similar t°58 relationship for 0 vs. t.Chapter 4. Kinetic Characterization 129Combining the microstructural path function, Eq. 4.9, and the isothermal interface-averaged growth kinetic function, Eq. 4.10, obtained in the present study using theCahn-Hagel formulation (Eq. 2.16), the following relationship is obtained,Ix0.44 (1 X)O.94dX 2002 (KG)T Jt_0.58dt (4.14)where (KG)T is the value of KG for a given temperature, T, and can be obtained usingEq. 4.12. Unlike the S-F equation development [90], this integration will not lead to asimple analytical expression to relate to X and t. However, Eq. 4.14 can be numericallyintegrated to yield the fraction recrystallized at any isothermal temperature as a functionof time. Figs. 4.37 (a) and (b) show the calculated X vs. t curves at 600 to 760°C,together with the experimental data, indicating a good description of the isothermalrecrystallization kinetics.The existence of a single microstructural path function independent of the thermalpath implies that the total number of nuclei is more or less fixed, i.e., the number ofrecrystallization centers does not vary markedly with temperature. This is in agreementwith the numerous observations that recrystallization begins at existing sites [33, 37, 38,75, 80, 81], and consequently, the density of nuclei can be expected to remain constantfor a particular grain size, inclusion distribution and degree of cold work. The sameargument also suggests the recrystallized grain size to be independent of the thermal pathand to be a measure only of the density of nuclei. In the present study, irrespective ofthe annealing treatment performed, the recrystallized grain sizes were found to be in therange of ASTM No. 9- 10; this corresponds to a mean linear intercept of 12 m [44]. Theinterface-averaged growth distance, as defined by Eq. 4.11, is related to the recrystallizedgrain structure. The appropriate time required in Eq. 4.11 to obtain the growth distancethat corresponds to the final recrystallized grain size is not known, although the useof an average time at which impingement occurs around most of each grain, has beenChapter 4. Kinetic Characterization 130suggested [90]. However, it suffices to mention here that the growth distance obtained bysubstituting the total recrystallization time obtained at different isothermal temperatureswas approximately 24 t m. This is of the same order of magnitude as the average grainsize of a fully recrystallized microstructure.In summary, modelling recrystallization kinetics is a difficult task due to the heterogenity introduced during the original deformation processes and the subsequent nonhomogeneous nucleation of recrystallized grains and time-dependent growth rate. Additional complication results from the concurrent recovery processes which compete forthe same stored energy. Due to these factors, recrystallization as a process is very resistant to generalizations and simplifying assumptions. In the present work, the basicJMAK assumptions of random nucleation and constant growth rate have been shownto be invalid. The microstructural path and the kinetic functions incorporated into theS-F model have also been shown to be inappropriate. In light of this, the usefulness ofthe JMAK and the S-F equations can be attributed more to their curve-fitting abilitythan to their fundamental significance. However, it should be emphasized that thesetwo expressions still provide a simple empirical relationship for adequately describingthe isothermal recrystallization kinetics. The major advantage with the microstructuralpath approach used in the present study is the absence of any assumption regarding thenucleation and the growth conditions. However, this method suffers from its empiricism,despite its physical significance as related to the evolution of microstructure.4.3.3 Recrystallization Kinetics as related to Steel Chemistry and Processing ConditionsThe T-T-R diagram shown in Fig. 4.22 clearly supports the reported observations thatthe recrystallization kinetics of I-F steel are severely retarded, when compared to thatof rimmed steel [57] and also slower than the recrystallization kinetics of Al-killed steelChapter 4. Kinetic Characterization 131[21]. It should be noted that the JMAK time-exponent obtained in the present study(0.73), and the one reported for the rimmed steel (0.68) are almost identical, suggestingthe similarity of the site-saturation type nucleation and growth dimensionality in both ofthese steels (both steels were subjected to similar amount of cold work). Severe retardation of recrystallization in I-F steels is usually attributed to the reduction in the interfacemigration rate caused by the excess Ti/Nb in solid-solution and by the fine stabilizingprecipitates of Ti and Nb [15, 16, 17, 21, 150, 153]. The recrystallization kinetics reportedby Goodenow [21] for the Ti-stabilized low-carbon steel are similar to those obtained inthe present work (Fig. 4.22). However, the onset of recrystallization occurs later in thework by Goodenow, probably due to the lower amount of cold reduction (50 % as opposedto 80 % in the present study). In addition, the progress of recrystallization in the presentstudy was considerably slower. The hot band grain size of the steel used in the currentwork is considerably larger (ASTM No. 7 - 8) than that used by Goodenow (ASTM No.9 - 10); this is expected to result in a lower nuclei density and slower recrystallizationkinetics.As indicated in Fig. 4.23, the recrystallization kinetics in the present work has beencharacterized in terms of a single activation energy, QR, of 501.7 kJ/mole. QR valuesof 335.9 and 367.7 KJ/mole were reported for high purity iron by Rosen et al. [72]and Leslie et al. [37, 38], respectively. These researchers obtained a higher activationenergy at lower temperatures and towards the end of recrystallization, and explained thisbehaviour in terms of a rapid reduction in the recrystallization rate observed towardscompletion. In particular, Rosen et al. observed two distinct stages of recrystallization(see Fig. 2.7), and attributed the second (slower) stage to the lack of initial nucleation.A slowing down of recrystallization was also observed in the present study, towards theend of the recrystallization event. However, this change is not as sharp as the onereported by Rosen et al., and the recrystallization kinetics in the present work clearlyChapter 4. Kinetic Characterization 132followed the usual sigmoidal behaviour to completion. While both of the previouslydescribed studies dealt with cold deformations of 50 to 60 %, an 80 % cold reductionwas applied in the present case. It is possible that at the higher deformation levels,nucleation sites are more numerous throughout the cold rolled grains. The presence oflarge particles may yet be another source for a high nuclei density (electron microscopicobservations supporting particle induced nucleation will be presented in the next chapter).Such increased nucleation might have prevented the occurrence of the extremely slowgrowth process in the current study. Sigmoidal-type, kinetic behaviour without anysharp discontinuities has also been reported for Ti and/or Nb-stabilized I-F steels after50 to 75 % cold deformation (see Fig. 2.21) [21, 153]. A recrystallization study on a 89 %cold-rolled, rimmed low-carbon steel also resulted in a similar conclusion with a constantQR value of 407.5 kJ/mole.It is obvious that the measured QR value of 501.7 kJ/mole obtained is considerablyhigher than the QR values of around 360 kJ/mole and 407.5 kJ/mole reported for highpurity iron and rimmed low-carbon steel, respectively and is also much higher than 275kJ/mole reported for self-diffusion in iron [29]. The higher QR value reported for therimmed steel, when compared to pure iron, can be explained in terms of the reducedinterface mobility often associated with the presence of the interstitial C and N in steels[35]. The addition of substitutional solutes such as Mn [38, 55] and Mo [37] have alsobeen shown to strongly inhibit the growth of the newly recrystallized grains. In particular, Ti and Nb in solid solution are reported to have a very strong influence in retardingrecrystallization in iron-based alloys [130, 143]. Additional retardation can be due to thepinning of migrating boundaries by the numerous fine (< 0.1k m in diameter) precipitates of Ti and Nb [154, 155], as discussed in section 2.1.5. The electron microscopicobservations obtained in the present study, illustrating the effect of fine precipitates onboundary migration, will be presented in the next chapter. There are several reportedChapter 4. Kinetic Characterization 133studies on I-F steels that demonstrate the effects of these two parameters on retardingrecrystallization [15, 16, 17, 21, 150, 153] and such strong retardation of the recrystallization kinetics is clearly reflected in the high activation energy value obtained in thepresent study. A QR value of 425 kJ/mole, reported from a recent study on I-F steels,was also rationalized in a similar manner [220].A comparison of the recovery and recrystallization activation energies calculated forthe I-F steel with those reported for high purity iron, indicates that the difference causedby solute additions is much more significant in the case of recrystallization. This observation is probably due to the fact that the rate of recrystallization depends on boundarymigration over considerable distances, a process severely retarded by excess solutes andfine precipitates. It should also be indicated that the QR value of 501.7 kJ/mole obtainedfor recrystallization and the Qcj value of 544.9 kJ/mole obtained for interface-averagedgrowth are similar. This observation provides additional support to the suggestion thatrecrystallization in the present I-F steeel is primarily controlled by growth processes.In a Ti-stabilized steel, Ti combines with N, S and C during high temperature processing, and the amount of Ti remaining in solid-solution, TiEX, can be estimated accordingto [4, 6] (all amounts are in weight percentages),TiEx = TiTOTAL — 4C — 3.42N — 1.55 (4.15)In a Nb-stabilized steel, Nb combines only with carbon at relatively lower temperatures,and the NbEx can be calculated from [4, 6) (all amounts are in weight percentages),NbEx = NbTQTAL — 7.75C (4.16)However, the estimation of TiEX and NbEx is difficult for a Ti/Nb-stabilized I-F steel.If all of the precipitation in the present I-F steel, with TiTOTAL = 0.03 and NbTOTAL =0.02, is attributed to Ti alone, then, according to Eq. 4.9, TiEx 0.01. Similarly, if all ofChapter 4. Kinetic Characterization 134the carbide precipitation is due to Nb alone, then, NbEx 0, and corresponding TiEX0.02. In reality, however, carbides of both Ti and Nb are often found [12, 14, 153, 221],and the oniy conclusions that can be made about the excess Ti and Nb are : 0.02 >TiEX 0.01 and NbEx <0.02.The excess amounts of Ti and Nb in solid solution have been reported to have astronger retarding effect on recrystallization than the amount present as precipitates.Correlations have been reported between recrystallization temperatures and TiEX orNbEx (see Figs. 2.19 and 2.20) [15, 16, 17, 21, 149, 150]. The present I-F steel hasvery low amounts of TiEx and NbEX; steels with 10 times higher TiEX and NbEXhave been studied for recrystallization. Based on these arguments, the present steelshould recrystallize with relative ease, within the family of I-F steels, and the measuredrecrystallization temperatures are in general agreement with the reported literature inthis regard. An exact comparison is difficult, since factors such as size and distributionof precipitates and hot band grain size will also have to be considered. In addition, theamounts of carbon (0.0028 wt %) and nitrogen (0.00118 wt %) in the base steel used inthis study is extremely low (compared with the typical I-F steel compositions given inTable 1.1 [6]), and this results in fewer precipitates in the ferrite phase.The size, distribution and volume fraction of each kind of precipitate present, i.e.,nitrides, sulfides and carbides of Ti, and carbides of Nb, will depend on the thermodynamic and kinetic parameters of the precipitation reactions and the high temperatureprocessing conditions [4, 6, 10, 15, 161. Lower reheat temperatures (1000 - 1100°C), finish rolling temperature values just above Ar3 (‘--‘ 900°C) and higher coiling temperatures(700 - 800°C) are reported to be beneficial for Ti-stabilized I-F steels [4, 6, 15, 16]. Theseconditions have been reported to result in coarse and widely spaced precipitates, allowingrapid growth of new grains with favourable textures. The available information regardingthe hot band used in this study indicates a finishing rolling temperature of around 890° CChapter 4. Kinetic Characterization 135and a coiling temperature of less than 600°C. These processing conditions, particularlythe lower coiling temperature, could have resulted in a relatively finer precipitate structure, causing significant retardation of recrystallization kinetics. The relatively large (‘—1 m) precipitates of TiN and TiS have been reported to be effective in causing particleinduced nucleation of recrystallization in Ti-stabilized I-F steels [153]. In the presentstudy, such effects were observed in a very limited manner. A low coiling temperature,together with the fact that the base steel had extremely low amounts of C and N, mayexplain this observation.The recrystallized microstructure obtained in the present study, as shown in Fig.4.29, consists of equiaxed ferrite grains with an average grain size in the range of ASTMNo. 9 - 10. The equiaxed recrystallized grain structure obtained for the present I-F steelindicates that the presence of the randomly scattered fine precipitates has no significantinfluence on the resulting grain morphology. This observation is in agreement with mostof the reported literature on I-Fstee1s [16, 17, 21, 153], with the exception of a study on aNb-stabilized steel where the recrystallized structure exhibited a blocky grain morphology[153]. It should also be noted that the final recrystallized grain size of ASTM No. 9 -10 obtained in the present work is similar to those reported by Hook and Nyo [17] for aNb-treated I-F steel and by Goodman et a!. [16] for a Ti-containing I-F steel.In summary, severe retardation of recrystallization in I-F steels in comparison withother low-carbon steels, has been demonstrated through the development of a T-T-Rdiagram and the measurement of high activation energies. These observations were attributed to the reduced interface migration rates caused by the excess Ti/Nb in solidsolution and the presence of fine stabilizing precipitates of carbides/carbo-sulfides of Tiand Nb. The observed recrystallization kinetics and the microstructural changes were alsoanalysed in terms of the steel chemistry and the high temperature processing conditions.Chapter 4. Kinetic Characterization 1364.4 Recovery and Recrystallization during Continuous HeatingContinuous heating annealing tests have been conducted at heating rates of 0.025, 1.88and 20.2°C/s. The slowest heating rate of 0.025°C/s (89.4°C/h) and the fastest heatingrate of 20.2°C/s are typical of a batch and a continuous annealing process, respectively.Fig. 4.38 schematically illustrates the modelling procedure used for predicting recovery and recrystallization kinetics during continuous heating. The continuous heatingcycle was described by assuming it to be made up of a series of isothermal steps. Thekinetic calculations of recovery, as characterized by the logarithmic relationship (Eq.2.4), or recrystallization, as characterized by the JMAK equation (Eq. 2.11) or the S-Fequation (Eq. 2.21), were performed at each isothermal step. The amount of recovery(as indicated by the change in R1 value), and/or the percentage recrystallized calculatedat each time step, were summed to predict the continuous heating kinetics.As indicated in the isothermal recovery section, two different descriptions were usedto characterize the temperature dependence of the isothermal recovery kinetic parametersto be used to predict continuous heating recovery. One involved Eq. 2.4, and Eqns. 4.2and 4.3 and the other relates the instantaneous rate of recovery, —dR1/dt, to temperaturethrough the recovery activation energy, which in turn, is a linear function of R1 (Eqns.4.1, 4.4 and 4.5).Fig. 4.39 shows the in-situ and interrupted R1 measurements obtained at 0.025°C/s,together with the recovery kinetic predictions and the metallographically determinedrecrystallization start and finish temperatures. As can be seen, the recovery portion ofthe annealing curve has been successfully predicted and no difference appears betweenthe predictions based on the activation energy approach or that using the empiricalrelationships, Eqns. 4.2 and 4.3. For this reason, only the activation energy approachwas used in subsequent recovery predictions. The recovery curve is extrapolated intoChapter 4. Kinetic Characterization 137the recrystallization zone, but, as shown, the agreement between the measured R1 values(without any recovery correction) and the metallographically determined recrystallizationkinetics indicates that recrystallization dominates.The validity of additivity for the recovery process was further tested using the interrupted R1 measurements obtained at 0.025, 1.88, 20.2 and 80°C/s, as indicated inFig. 4.40. The reasonable agreement obtained between the predicted and the experimental R1 values for a wide range of heating rates clearly demonstrates the usefulnessof the additivity principle in predicting the recovery kinetics during continuous heatingprocesses.Fig. 4.41 emphasizes the recrystallization portion of the R1 (interrupted) vs. T(°C) data obtained at 20.2°C/s. The procedure adopted during the isothermal analysisto separate the concurrent recovery and recrystalliztion effects with appropriate areacorrections (see Figs. 4.11 and 4.12), was applied as related to the experimental R1values and the predicted recovery kinetics (RTA). The % recrystallized obtained throughthis procedure is in reasonable agreement with the metallographic measurements.The start of recrystallization at 20.2°C/s corresponds to a higher R1 value of 0.47as opposed to 0.36 at 0.025°C/s (see Fig. 4.39). As a result, more recovery effects canbe expected at 20.2°C/s during the early stages of recrystallization. This explains thegood correlation obtained between the R1 values and % recrystallized at 20.2°C/s oncethe recovery effects were removed from the experimental R1 measurements; whereas, at0.025°C/s, the agreement was good even without any recovery corrections.The effect of temperature on the intensity of the Ka1/K2 diffraction peaks, theKai/Ka2 valley and the background, and on the 20 positions of the peaks and the valleywere also investigated. This was accomplished by obtaining the peak profiles of a fullyrecrystallized specimen heated to different test temperatures through a step-heating procedure. Fig. 4.42 (a) and (b) show the effect of temperature on (imin - Ib), (IK.1 - Ib)Chapter 4. Kinetic Characterization 138and R1, and on the 219 values of the Kci peak and the valley, respectively.Increased thermal vibration of the atoms, as the result of an increase in temperature, isknown to decrease the intensities of the diffraction lines and to slightly increase the background intensity. The former has been explained in terms of the atoms lying no longeron mathematical planes but rather in platelike regions of ill-defined thickness, while thelater is attributed to general coherent scattering in all directions (temperature-diffusescattering) [49, 50]. The experimental observations during the current investigation alsorevealed similar temperature effects on intensity values. The general mathematical treatment of this problem involves the modification of the atomic scattering factor using atemperature dependent term [49, 50]. However, in the present study, only a very simpletreatment is used to illustrate the effect of temperature on intensity and consequently onthe x-ray ratio, R1. A linear regression was performed between the measured intensityvalues of (‘mm - Is), (iK, - Ib) and temperature (°C) yielding,‘mm — ‘b = 7.2 — 0.0046 T (4.17)andIK, — ‘b = 47.3 — 0.03 T (4.18)The lines corresponding to these equations, obtained with correlation coefficients of 0.92,are also shown in Fig. 4.42 (a). Dividing Eq. 4.17 by Eq. 4.18 gives temperature-independent R1 value of 0.15, as indicated in Fig. 4.42 (a).At high temperatures, the unit cell expands, causing changes in plane spacings andtherefore in the 20 positions of the diffraction lines [49]. Linear relationships with R2= 0.99 were obtained between the (20)° values corresponding to the Ka, peak and thevalley, and temperature (°C), as shown in Fig. 4.42 (b). The equation relating the (2&)°value of the K1 peak to the temperature (°C) is,(20)° = 145.9 — 0.0052 T (4.19)Chapter 4. Kinetic Characterization 139In the present study, in-situ x-ray measurements were made oniy at the slowest heatingrate of 0.025°C/s and were correlated well with the kinetics of recovery and recrystallization. If in-situ R1 measurements are to be obtained during high heating rates, theprocess must be fully automated to follow the shift of the {220} peak with temperature,based on Eq. 4.19. Such R1 measurements may be directly correlated to the degree ofannealing since Rj values were shown to be independent of temperature. As in the caseof isothermal studies, in-situ measurements will be considerably easier if only the valleyand the background intensities are monitored. However, unlike in isothermal analysis,IM measurements during continuous heating will be influenced by both the degree ofannealing and the temperature effects. The temperature effect, as characterized by Eq.4.17, may be removed from the total change in ‘M to yield the kinetics of the recoveryand recrystallization processes.In a few isothermal and continuous heating tests, both in-situ and interrupted R1measurements were made to monitor the annealing process. The heating rate of 0.025°C/sis one such case, and both the in-situ and the interrupted R1 measurements made at thisheating rate are shown in Fig. 4.39. The apparent agreement between these two sets ofvalues supports the general assumption that no significant annealing occurred during therapid cooling (- 45°C/s) to room temperature. In addition, Fig. 4.39 clearly indicatesthe effectiveness of the x-ray peak resolution measurements in determining the kineticsof the recovery and recrystallization processes. The designated recrystallization startand finish temperatures shown in this figure were obtained from metallography. Therecrystallization start point is also characterized by a change in the gradient, . Thistransition is particularly clear in this case, since it occurs at a low R1 value of 0.36,where the concurrent recovery effects are expected to be low. At the recrystallizationfinish point, no further decrease in R1 was observed. This observation, together withsimilar findings from previous investigators [49, 57], indicates that grain growth has noChapter 4. Kinetic Characterization 140significant effect on peak resolution.In summary, the usefulness of the additivity principle in predicting the recovery kinetics during continuous heating processes has been demonstrated. The experimental R1measurements have been interpreted in terms of the predicted recovery and recrystallization. The procedure adopted during the isothermal analysis to separate the concurrentrecovery and recrystallization effects on peak resolution has been successfully employedto interprete the interrupted R1 measurements obtained at 20.2°C/s. The temperatureeffect on the intensity values and 20 positions of the Ka, peak and the Ka, /K2 valley has been analysed. The temperature independence of the x-ray ratio, R1, has beendemonstrated.4.5 Continuous Heating Recrystallization KineticsFor heating rates of 0.025, 1.88 and 20.2°C/s, quantitative metallography was performedon samples rapidly cooled after progressive stages of annealing. The specimens weredirectly observed in an optical microscope to estimate the time corresponding to the onset(t3 expt’l) and completion of recrystallization. In addition, photomicrographs obtainedfrom the partially recrystallized specimens, were used to quantify the volume fractionrecrystallized (X) and the interfacial area per unit volume separating the recrystallizedgrains from the unrecrystallized matrix (A).The continuous heating recrystallization kinetics were predicted using the experimentally determined start time (t3 expt’l), the isothermal recrystallization kinetic parameters(JMAK and S-F), and the principle of additivity. As indicated in Fig. 4.38, at each timestep after the onset of recrystallization, i.e., after t expt’l, the fraction recrystallized wascalculated based on the isothermal recrystallization kinetics at the temperature of theparticular isothermal step, and the fraction of the recrystallized material already present.Chapter 4. Kinetic Characterization 141This process was continued until all the cold worked matrix had been consumed. Theisothermal kinetic parameters obtained from both the JMAK and the S-F descriptions,with constant n (n. = 0.73) and m (ñi = 1.17) and temperature-dependent ln b (Eq.4.6) and ln k (Eq. 4.7), were used in the kinetic predictions. A similar procedure wasadopted based on the Scheil equation [120] to estimate the continuous heating ‘recrystallization start time’ (t5 Scheil), as defined by the fractional consumption of the isothermalincubation time determined from Eq. 4.8.The additivity procedure was used in the prediction of continuous heating recrystallization kinetics at 0.025, 1.88 and 20.2°C/s, the predicted and experimental results arecompared in Fig. 4.43. Reasonable agreement is apparent for all three heating rates, indicating that recrystallization is experimentally additive. A comparable level of agreementis obtained irrespective of whether the isothermal recrystallization was characterized bythe JMAK or the S-F equation. However, a careful examination of the comparison showsthat the predictions using the JMAK equation are better in the early stages of recrystallization, while the S-F equation predicted a better fit to the later stages. This observationis a direct result of the fact that the JMAK and the S-F equations describe, respectively,the early and the later stages of isothermal recrystallization particularly well, and anyadditivity-based kinetic prediction would be expected to behave accordingly.The Scheil equation was used to estimate continuous heating recrystallization starttimes (t8 Scheil) at 0.025, 1.88 and 20.2°C/s. The results, in combination with theexperimentally determined recrystallization start times (t3 expt’l), are shown in Table4.4. The temperatures corresponding to the start times, referred to as “T expt’l”and “T Scheil” are also indicated. The Scheil equation consistently overestimates theincubation time associated with the onset of recrystallization; the extent of overestimationis higher at higher heating rates.The continuous heating recrystallization kinetics were also calculated at 0.025, 1.88Chapter 4. Kinetic Characterization 142and 20.2°C/s, based on the Scheil predicted recrystallization start times (t.9 Scheil). Fig.4.44 shows the effect of t. expt’l vs. t Scheil on the JMAK equation-based predictionsfor all three heating rates compared with the experimental % recrystallized. The predictions based on t51 Scheil are virtually identical with the t9 expt’l-based predictionsafter approximately 30 % recrystallization. Despite the higher start times predicted bythe Scheil equation, the increased recrystallization rate associated with a higher starttemperature seems to have quickly compensated for the difference. The correspondinganalysis with the S-F equation-based predictions exhibited similar behaviour.The additivity procedure was also employed in the prediction of the continuous heating interface-averaged growth rates (G) at 0.025, 1.88 and 20.2°C/s. The predictionswere based on the isothermal characterization of the growth kinetics as provided by thetemperature-independent growth rate time-exponent, flu, (= -0.58) and the temperature-dependent parameter, KG, (Eq. 4.12). The primary isothermal equation used in thismodelling exercise was Eq. 4.11, i.e., dG = (n) j(nc+l) With this equation, the stepsinvolved in the continuous heating recrystallization model were converted to predict thegrowth kinetics. The fraction recrystallized, X, was replaced by the interface-averagedgrowth distance, dG, and the final growth rates were calculated from the predicted dGvalues using the equation,ZIG (4.20)where dG is the additional growth distance corresponding to the time step, Lit. Thesecalculations were continued until the experimentally determined recrystallization finishtime was reached.In addition, growth rates during continuous heating were also calculated using theexperimental X vs. t data and the experimental A values; a JMAK-type equation wasChapter 4. Kinetic Characterization 143found to be useful for curve-fitting and for the calculation of dX/dt. Another modelling procedure was also used to calculate the G values during continuous heating. Inthis method, dX/dt was calculated from the JMAK equation based additivity predictedrecrystallization kinetics, as given in Fig. 4.43 and the A values were obtained fromthe experimentally determined microstructural path function, Eq. 4.9. Fig. 4.45 compares the additivity predicted G values with (i) the modelled 0 values obtained usingdX/dt from the predicted recrystallization kinetics and A from the derived microstructural path function and (ii) the estimated 0 values using the experimental X vs. t dataand the experimental A values. The results presented in this graph clearly indicate thatthe interface-averaged growth rate, 0, during continuous heating can be succesfully predicted using the isothermal growth kinetics and the principle of additivity. It can alsobe seen from Fig. 4.45 that the 0 values increase during the progress of recrystallizationdue to the increased thermal activation, despite the fact that the driving force for growthsteadily decreases.To test the validity of the isokinetic concept [114] for recrystallization, as characterizedby its growth kinetics, the Cahn-Hagel formulation, Eq. 2.16, and the growth rateequation, Eq. 4.10, can be writen as,= A KG tnG (4.21)Substituting the time, t, calculated from Eq. 4.11 into Eq. 4.21, and rearranging gives,dX —— / 1— A .J’G+1 17 I______— 11 UG 1kG j KG\ (nG+1)In Eq. 4.22, A and dG are functions of X only, while KG is a function only of temperature.If the growth rate time exponent, riG, is independent of temperature, then Eq. 4.22 willsatisfy Cahn’s [114] isokinetic condition expressed by Eq. 2.29. In the present study,Chapter 4. Kinetic Characterization 144the isothermal growth kinetics have been characterized by a constant riG value of -0.58,indicating the recrystallization process to be isokinetic.The recrystallization in the present I-F steel, with its isothermal kinetics being described by the temperature-independent JMAK, S-F and growth rate time-exponents,can be considered to be an isokinetic-type transformation. Such isokinetic transformations satisfy all of the additivity conditions and lead to a single additivity model (seesection 2.1.4 [114, 115, 116, 118]). Hence, there are no ambiguities in the current modelling exercise to predict the recrystallization kinetics during continuous heating, and thegood agreement obtained between the predicted and the experimental recrystallizationkinetics for a wide range of heating rates (covering 3 orders of magnitude) clearly indicates that recrystallization in the present I-F steel is experimentally additive. A previousrecrystallization study on the rimmed low-carbon steel resulted in the same conclusion[39].The validity of additivity for phase transformations involving nucleation and growthprocesses has been tested in considerable detail; ‘early site saturation’ [114] and ‘effective site saturation’ [115] are two different criteria resulting from those studies. All ofthese studies point to the fact that a reaction will be additive if the transformation isdominated by a single temperature dependent process- ‘growth’. The microstructuresobtained during the present study, conducted over a wide range of isothermal temperatures and continuous heating rates, indicated that nucleation substantially occurredduring the early stages of recrystallization, suggesting the validity of early site saturation. Similar observations have often been reported from recrystallization studies onheavily deformed metals [33, 37, 38, 75, 80, 81]. The early site saturation type nucleationmakes recrystallization primarily a growth-controlled process, a sufficient condition toexplain the experimentally demonstrated validity of additivity in the present study.The fact that a single activation energy (QR = 501.7 kJ/mole) was obtained forChapter 4. Kinetic Characterization 145recrystallization is consistent with the additivity criterian of the dominance of the sameprocess (or mechanism) throughout the transformation; this also implies recrystallizationto be isokinetic [114]. This argument would suggest that the recovery process, with itsincreasing activation energy, QR, from 173.1 kJ/mole at R1 = 0.6 to 312.1 kJ/mole atR1 = 0.15, is not additive. However, the additivity procedure could be used successfullyto predict the recovery kinetics during continuous heating, as shown in Fig. 4.40. Thisis probably due to the fact that all of the predicted R1 values were within the narrowrange of 0.58 to 0.36, and the corresponding change in Qm, values, i.e., from 179.3 to247.2 kJ/mole, is relatively small.As reported in some previous recrystallization [39] and phase transformation studies[121, 122], the present work also showed the tendency of the Scheil equation [120], withits inherent assumption of proportional consumption of isothermal incubation, to overestimate the continuous heating recrystallization start time. This observation suggestsincubation to be a non-additive event. This may be the case if no single mechanism dominates throughout the incubation period. Recovery takes place during incubation, andleads to the formation of recrystallized nuclei. A range of different mechanisms operateduring recovery. This was reflected in the increasing activation energy for recovery as obtained in the present work, providing indirect evidence that incubation is a non-additiveevent.Moore [126j observed similar non-additive behaviour from stepped isothermal testsperformed during the austenite-ferrite transformation. He explained those observationsby suggesting the non-equivalence between a given percentage of the incubation periodspent at different isothermal temperatures, and correlated these effects to the smaller critical size of the ferrite nuclei at lower temperatures. This non-proportional consumptionof isothermal incubation time, may also explain the presently observed overestimationof incubation time during continuous heating. Despite the higher Scheil-predicted startChapter 4. Kinetic Characterization 146times, the additivity procedure resulted in good kinetic predictions, particularly towardsthe (more significant) later part of recrystallization. These results clearly demonstratethe usefuliness of the Scheil equation in kinetic modelling, as it eliminates the necessityto experimentally determine the recrystallization start time for any heating rate.In summary, the isothermal recrystallization kinetics as characterized by the JMAKand the S-F equations, have been successfully used in conjunction with the principle ofadditivity to predict the recrystallization kinetics during continuous heating. A similarprocedure was adopted to predict the interface-averaged growth rates at different heatingrates. These observations have been rationallized in terms of the early site saturationtype nucleation and the isokinetic nature of the subsequent growth. The additivityprocedure also led to useful recovery predictions. This was explained in terms of theactivation energy for recovery not changing significantly within the narrow test range.Despite overestimating the non-isothermal incubation times, the usefulness of the Scheilequation in recrystallization modelling has been demonstrated.Chapter 4. Kinetic Characterization 147Table 4.1: Characterization of isothermal recovery kineticsTemp. In R1 = K — kt = b— a In t°C K k R2 b a R2500 -0.780 8.4 x 10—6 0.71 0.587 0.020 0.95550 -0.838 1.3 x i0 0.70 0.558 0.022 0.96600 -0.738 3.4 x iO 0.89 0.517 0.023 0.99625 -0.804 9.1 x i0 0.83 0.499 0.024 0.96Table 4.2: Characterization of isothermal recrystallization kineticsTemp. JMAK_Equation S-F Equation°C n lnb 1?2 m ink R2600 0.65 -6.63 0.96 0.84 -7.96 0.92625 0.74 -6.31 0.95 0.95 -7.58 0.91650 0.68 -4.34 0.98 0.99 -5.41 0.99675 0.62 -3.09 0.95 0.93 -3.75 0.99700 0.71 -1.89 0.98 1.07 -2.03 0.97720 0.79 -1.52 0.97 1.28 -1.68 0.97740 0.90 -0.65 0.99 1.64 -0.50 0.97760 0.76 0.34 0.99 1.68 1.21 0.98Chapter 4. Kinetic Characterization 148Table 4.3: Characterization of isothermal interface-averaged growth kineticsTemp. G log KG R2(°C)600 -0.56 -5.35 0.97625 -0.48 -5.28 0.97650 -0.61 -4.48 0.96675 -0.68 -4.15 0.93700 -0.59 -3.87 0.96720 -0.53 -3.75 0.91740 -0.48 -3.41 0.91760 -0.67 -3.19 0.97Table 4.4: Experimental and Scheil predicted recrystallization start times (and temperatures) during continuous heatingHeating Rate Experimental Scheil Predictions°C/s (s) T5 (°C) (s) T3 (°C)0.025 23680 600 24080 6101.88 331 630 349 66420.2 31.3 640 34.0 694Chapter 4. Kinetic Characterization 1491—____________-500°C(Recovery Only)0.8 -a R1 (in-situ) aC•_ a-+-+ ‘M (in-situ)0.6l) ++aI0.4O a +a0.2 ++o a 1b’Time (s)Figure 4.1: Fractional peak resolution (F) calculated at 500°C based on in-situ measurements of x-ray ratio (R1) and valley intensity (IM).Chapter 4. Kinetic Characterization 1500.60.546 0.480.420.360.340Figure 4.2: In—situ R1 measurements obtained at 500°C, compared with the kinetic descriptions using Eq. 2.3 (in R1 = K — kt) and Eq. 2.4 (R1 = 6 — a in t).0 10 20 30(Thousands)Time (s)Chapter 4. Kinetic Characterization 1510.60.50.4cix0.30.240(a)0.60.5C0.4>-‘x0.30.2(b)Figure 4.3: (a) In-situ R1 measurements at 500, 550, 600 and 625°C, together with thekinetic descriptions using Eq. 2.4, and (b) the same kinetic data when replotted on alogarithmic time scale.0 10 20 30(Thousands)Time (s)Tirrie (s)Chapter 4. Kinetic Characterization650600550500450101Time (s)152Figure 4.4: Time-Temperature-Recovery (T-T-Ry) diagram obtained using Eq. 2.4; experimental measurements corresponding to R1 = 0.5 and 0.4 are also shown.R1=Time-Temp.-RecoveryPredicted (Eq. 2.4)• Expt’l (R1= 0.5) + Expt’l (R1= 0.4)ib’ ib7Chapter 4. Kinetic Characterization 1530bI—00070 7O0 626O0 50i 5Q0 t5-0- IsothermalRecovery+ 0.450.300.15—3J— I I I I I I I0.96 1.04 1.12 1.2 1.28l03/T (°K1)350300-250-200150— I I0.1 0.2 0.3 0.4 0.5 0.6 0.7X-Ray Ratio, R1Figure 4.5: (a) Effect of inverse absolute temperature on the natural logarithm of theinstantaneous rate of recovery calculated at constant R1 values, and (b) the calculatedactivation energy for recovery, as a function of the extent of recovery, R1.Chapter 4. Kinetic Characterization0.640.60.56- 0.520.48 -0.44-0.4400Temperature (t)0.0280.0260.0240.022• 0.028000.018Ho,O-30 ‘zc.CM154500 600 700in Ap. -QR/RFigure 4.6: Temperature dependence of parameters b and a; isothermal recovery kineticshas been characterized by the logarithmic relationship, R1 = b — a in t.23.61-2023.623.5923.5823.5723.56-25-35C I I I --400.1 0.2 0.3 0.4 0.5 0.6 0.7X-Ray Ratio, R1Figure 4.7: Effect of R1 on in AR and -QR/R; recovery kinetics has been analysed interms of the Arrhenius equation, dR1/dt = —ARk exp —(QR/RT).Chapter 4. Kinetic Characterization 15525C/D-‘S>231cc> 21‘S(I)Q20= 191840Figure 48: In-situ ‘M measurements at 500° C, compared with the kinetic curves obtainedusing Eq. 2.3 (lnIM x t) and Eq. 2.4 (IM x int).0 10 20 30(Thousands)Time (s)Chapter 4. Kinetic Characterization 1560.600.45’C.-+++0.30R1 (interrupted)• Isothermal start+ Recrystallization start• (metallography)0.15- I I580 600 620 640 660 680 700Isothermal Test Temperature (°C)Figure 4.9: R1 measurements corresponding to the start of the isothermal hold and theonset of recrystallization, as obtained from the interrupted tests performed at 600, 625,650 and 675°C.Chapter 4. Kinetic CharacteriEation 157e:stal1iZti‘—‘ 0.8 R1 (interrupted)a- Test 1I-__+ ‘M (in-situ) - Test 2 —CcFJ 0.6- +I)0.4‘aI+1’UIo 1.— a I,4.1 +0 02 + Recryst.starta+0-100 i’o’ ib2 io4Time (s)Figure 4.10: Fractional peak resolution, F, calculated at 625°C using interrupted R1 values and in-situ‘M measurements (obtained from two different tests); metallographicallydetermined recrystallization start time is also indicated.Chapter 4. Kinetic Characterization 1580.5Recryst. start0.4Recoverybased on 1nrecrystallized I(RUA)area ]ased oRecovery I total I(RTA)0.3 La]0______________—4RUA - R1 (interrupted)- 100675a R1 (interrupted)02-- 75% Recrystallized CDC)-500- R1 (intemipted)0a(metallography)(ID0.1-- 25N——100 10’ 102 io3 io4Time (s)Figure 4.11: Isothermal 675°C R1 measurements interpreted in terms of recovery (Eq.2.4) based on the total area (RTA) or the unrecrystallized area (RUA), recrystallization(recovery- R1) and measured % recrystallized.Chapter 4. Kinetic Characterization.1-41592016128 CDC)(ID44-.NCD0Figure 4.12: Isothermal 650°C ‘M measurements interpreted in terms of recovery (Eq.2.4) based on the total area (RTA) or the unrecrystallized area (RUA), recrystallization(recovery- IM) and measured % recrystallized.100755025Time (s)Chapter 4. Kinetic CharacterizationC0Cl)Ce0C)CeCCCl)CeCeCCC-)Ce1600.80.60.40.20C)CC)CCl:><Time (s)(a)0.80.60.40.20-.! I0.8 + 0.8_____:i720C0.2+ R1 (interrupted) 0.21M (in-Situ)o Metallography0 0100. 102Time (s)(b)Figure 4.13: Comparison of the fractional peak resolution (F) calculated from interruptedR1 and in-situ ‘M measuremnts, and the fraction recrystallized (X) determined frommetallography at (a) 700 and (b) 720° C.Chapter 4. Kinetic CharacterizationCD1CeICe>-Cd,16120(Thousands)Time (s)(a)70605040302070aa.a aa a. aa a •a a a aa a. U a• a—S 60-650°C> (Recryst. start = 15 s)50-_______a ‘KAiphal+ ‘nun40-++++++ ++++ ++30 + + +++++ + +— - + ++ ++20-(Thousands)Time (s)(b)Figure 4.14: The effect of isothermal annealing time on the intensity values,‘Ku,, ‘mmand ‘b, as obtained from in-situ peak profile measurements at (a) 500 and (b) 650°C.0 2 3 4Chapter 4. Kinetic Characterization><NCe>0C0Figure 4.16: The JMAK [66, 67, 65] and the S-F [90] analysis of the isothermal dataobtained at 650°C, indicating the best fit lines.a162aa0.8a0.604- a0.20lOl 102Time (s)Figure 4.15: Metallographically determined isothermal recrystallization kinetics at650°C.43a650°Ca Experimental (JMAK) ++ Experimental (S-F) - - - -JMAK (best fit) - +----S-F (best fit)C432+ ---- a2-1-0—l-2-3-4+-22 4-36In (t—t1)8-4Chapter 4. Kinetic Characterization 1634________AIsothermalRecrystallization• n-bestfit3 + m-bestfit—n - average -----rn-average2- 2* ++1 ++ +-.-1+•••• —I I I I I I I I I I I I I i580 620 660 700 740 780Temperature (k)Figure 4.17: Temperature dependence of the JMAK time-exponent, n, and the S-Ftime-exponent, m, as obtained from the best fit analysis; the average values of n (=0.73)and m (=1.17) are also indicated.650tExperimental>< 0.8—JMAK (best fit)-——JMAK (average)N S-F(bestfit)0.6 S-F (average)1:2/I101 i03 10Time (s)Figure 4.18: Recrystallization measurements obtained at 650°C, compared with the kinetic descriptions using the JMAK and the S-F equations; the effects of using the originalbest fit parameters vs. the recalculated average parameters are also shown.Chapter 4. Kinetic Characterization 1642____0--2 --3- I1 11in (t—L,)(a)-2In (t—t)(b)Figure 4.19: The JMAT{ analysis of the isothermal kinetic data obtained at (a) 600, 625,650 and 675°C and (b) 700, 720, 740 and 760°C.JMAKa+ 625C° 6506759D3 5 7 92I0—1-3-1 - 1 3 5Chapter 4. Kinetic Characterization-2165Figure 4.20: The S-F analysis of the isothermal650 and 675°C and (b) 700, 720, 740 and 760°C.kinetic data obtained at (a) 600, 625.420-2-41 3 5 7 9In (t-t)(a)420-4In (t-t)(b)Chapter 4. Kinetic Characterization><‘DN(I)>C-)0C)[10NC,)>00000.81660.40.20Time (s)(a)0.8060.40.2(b)Figure 4.21: Experimentally determined isothermal recrystallization kinetics at (a) 600,625, 650 and 675°C and (b) 700, 720, 740 and 760°C, compared with the descriptionsusing the JMAK and the S-F equations.10’Time (s)102Chapter 4. Kinetic Characterization 167720 -___________________T-T-RN N + N Predicted (JMAK)(, + Start/Finish - Ti-stabilizedUOU N. (Present Work)N. o Start/Finish - Ti-stabilizedN N? (Goodenow)+ N N Start/Finish - Rimmed640-N. ‘N N (Magee)600-560- 1% 50% 99%520 -480- I101 10 i03Time (s)Figure 4.22: Time-Temperature-Recrystallization (T-T-R) diagram obtained using theJMAK analysis; recrystallization start and finish times for the I-F steel under investigation, and for a Ti-stabilized [21] and a rimmed [57] low-carbon steels are also shown.ChapLer 4. Kinetic Characterization 1685- 7qot 6q0°C0(ID.—;-5-— -10--15-0.96 1.04iO3ff (K’)Figure 4.23: Temperature dependence of the recrystallization time corresponding to 10,50 and 90 % recrystallization as obtained from the JMAK analysis.760°C 650°CIsothermalRecrystallization(JMAK)• 10 QR(kJ/mole)+ 501.70 90%J1.00 1.08 1.12Chapter 4. Kinetic CharacterizationFigure 4.24: Temperature dependence of the JMAK parameter, in b, and the S-F parameter, in k; isothermal recrystallization kinetics has been characterized by the JMAK andthe S-F equations with constant values of n (=0.73) and m (=1.17).169-D20-2-4-6-8-10-12580 620 660 700 740 780Temperature (°C)B8642580 600 620 640 660Temperature (°C)680Figure 4.25: Recrystallization start time, t, as a function of isothermal temperature.Chapter 4. Kinetic Characterization 170Figure 4.26: Typical microstructures of (a) the hot band with an equiaxed grain structureand (b) the 80 % cold-rolled sheet steel with a heavily banded structure along the rollingdirection (Magnification X 200).(a)(b)Chapter 4. Kinetic Characterization 171Figure 4.27: Photomicrographs showing the early stages of recrystallization obtainedfrom specimens held at 700° C for (a) 2 s and (b) 4 s (Magnification X 200).(b)Chapter 4. Kinetic Characterization 172Figure 4.28: Photomicrographs showing the later stages of recrystallization obtainedfrom specimens held at 700°C for (a) 12 s and (b) 30 s (Magnification X 200).(b)Chapter 4. Kinetic Characterization 173Figure 4.29: Typical microstructure of a fully recrystallized specimen, obtained after a150 s hold at 700°C (Magnification X 200).Chapter 4. Kinetic Characterization 174Figure 4.30: Photomicrographs at (a) Magnification X 400 and (b) Magnification X 1000,showing the initial stages of recrystallization obtained from a specimen held at 650°C for...(b)32 s.Chapter 4. Kinetic Characterization 1751000 -(-)j :::_______j :::0.’2 ‘ 04 0.6 0.8 1Fraction Recrystallized (X)Figure 4.31: Interfacial area per unit volume (A) vs. volume fraction recrystallized (X)obtained for all isothermal temperatures and heating rates; the best fit microstructuralpath description, A 2002 (X)°44 (1 — X)°94, is also indicated.xxIxIx1+MicrostructuralPath Functionxx -t+÷xx+x600, 625650, 675Z700, 7209740, 7600.025, 1.88, 20.2CC/sBest FitChapter 4. Kinetic Characterization 1760-C-05C-1-0-1.5- Isothermal Growth(interface averaged)• nG-bestfit• nG - average-2- I I580 620 660 700 740 780Temperature (°C)Figure 4.32: Temperature dependence of the interface-averaged growth rate time exponent, riG, as obtained from the best fit analysis; the average G value of -0.58 is alsoindicated.Chapter 4. Kinetic Characterization 1770,Ecit,)Ce0(a)0,EC)ID0C2 100pCDio -10-I(b)Figure 4.33: G = KG t (riG = -0.58) analysis of the isothermal growth kinetic data of(a) 600, 625, 650 and 675°C and (b) 700, 720, 740 and 760°C.Isothermal Growth(interface averaged)• 600°C+ 625°C° 650°C675°Cio-7io° 10 102 1o4Time (s)N0isothermal Growth(interface averaged)• 700°C+ 720°C° 740°C760°C+10Time (s)Chapter 4. Kinetic Characterization 178760°C 700°C 650°C 600°C5 I I I(I) +IC.)-10•.-++C Isothermal Growth +-15 - (interface averaged)Growth Dist. QGIc• 0.0005 ci1 (kJ/mole)+ 0.OOlOcmI0.OOl5cmF 544.9 +0.0020 cm]______________________-20- I I0.96 1.00 1.04 1.08 1.12iO (K1)Figure 4.34: Effect of inverse absolute temperature on the natural logarithm of the instantaneous (interface-averaged) growth rate, G, calculated at constant growth distances,dG.Chapter 4. Kinetic Characterization 179Figure 4.35: Temperature dependence of the growth parameter, KG; isothermal growthkinetics has been characterized by G = KG jlzG with a constant T1G value of -0.58.11io_5 -iO6580I I I I I I I620 660 700 740Temperature (°C)780Chapter 4. Kinetic Characterization 1800+Sci)II+-9101 06110100+++++*++IIsothermal• 600, 625÷ 650, 6759,700, 720Z740, 760ZBest Fit•U.101 101 1Time (s)Figure 4.36: The plot of the isothermal G values obtained at all test temperatures againsttime (both axes on logarithmic scale); the global best fit description line, G 3.810also indicated.Chapter 4. Kinetic Characterization 181>< 0.80C)N.E 0.6v)>0C)0.400ciçs.. 0.20106(a)-0.8C)Ncici0.6C).C00ccl OA0.2Figure 4.37: Modelled X vs. t curves using the microstructural path approach, togetherwith the experimental data points obtained at (a) 600, 625, 650 and 675°C and (b) 700,720, 740 and 760°C.Time (s)Time (s)(b)Chapter 4. Kinetic CharacterizationH182Figure 4.38: Schematic diagram illustrating the modelling procedure used in the prediction of recovery and recrystallization kinetics during continuous heating.RecrystallizationJMAK —-X = 1 - exp(-bt11)S-F —-(XIl-X)=ktmRecovery= b - a ln tTimeChapter 4. Kinetic Characterization 183C-o-25-75NCD-100 Q0.60.50.40.30.20.1RecoveryRecryst.. start.cJ0.025 °CIs• R1 (in-situ)o R1 (interrupted)Predicted Recovery(activation energy)- - -- Predicted Recovery(empirical)% Recrystallized(metallography)RecoveryandRecrystallizationRecryst. finishI I I— ——-——J—— I300 400 500 600 700Temperature (°C)Figure 4.39: In-situ and interrupted R1 measurements obtained at O.025°C/s, comparedwith the additivity-predicted recovery kinetics (using ‘activation energy’ and ‘empirical’-type isothermal descriptions) and metallographic analysis of % recrystallized.Chapter 4. Kinetic CharacterizationC.-Temperature (°C)184Figure 4.40: Comparison of experimental (interrupted R1) and predicted continuousheating recovery kinetics at 0.025, 1.88, 20.2 and 80°C/s.0.6 -0.5 -0.4 -0.3Continuous HeatingRecovery• 0.025 °C/s0+ 1.88 C/s20.2 °C/s80 °C/s—Prediction+.400 440—I I I I I I I I I I480 520 560 600 640 680C.-Figure 4.41: Interrupted Hi measurements obtained at 20.2°C/s interpreted in terms of(predicted) recovery based on the total area (RTA) or the unrecrystallized area (RUA),recrystallization (recovery - H1) and measured % recrystallized.Chapter 4. Kinetic Characterization0.50.40.30.20.10185-100-7c CD‘-‘ C)‘1-25NCD-0 c1Recoverybased ounrecrystallized (RUA)startL area- ‘based O1Rcovery total I (RTA)__________________L area]20.2 °CIsR1 (interrupted) a% Recrystallized a(metallography)RUA- R1 (intemipted)RTA- R1 (intemipted)620I I I I 1660 700 740 780 820 860Temperature (°C)186400Temperature (b)(a)Chapter 4. Kinetic Characterization50 0.62 40 0.5CC0.4 )<ct 301-pV.320— C02-100.I0 0147Cl)a)a)144Cl)CC- 143a)> 142a)141(b)Figure 4.42: Temperature effect on (a) the values of (Jmn - 1J, (j*01 - 16) and B1, and(b) the 20 values of the Ka, peak and the valley.Temperature (t)Chapter 4. Kinetic Characterization 1871580 820Figure 4.43: Comparison of experimental and predicted continuous heating recrystallization kinetics at 0.025, 1.88 and 20.2°C/s; the predictions are based on the experimentallydetermined start times, t expt’l.620 660 700 740 780Temperature (°C)Chapter 4. Kinetic Characterization1580Temperature (Z)188Figure 4.44: Comparison of the effect of t. expt’l vs. t Scheil on the JMAK equation based kinetic predictions at 0.025, 1.88 and 20.2°C/s; experimentally determined %recrystallized are also indicated.ntinuous Heatin[zatiOno 0.025 UCIs1.88 °CIs20.2 °C/s—JMAK(t81exp ’l)- JMAK (tSchei1620 660 700 740 780 820Chapter 4. Kinetic Characterization 1891 02If)10_‘ io601 08600 800Temperature (°C)Figure 4.45: Comparison of the additivity predicted interface-averaged growth rates (G)with the the modelled (using dX/dt from the predicted recrystallization kinetics and Afrom the derived microstructural path function) and estimated (using the experimentalvs. 1’ data and the experimental A values) G values at 0.025, 1.88 and 20.2°C/s.640 680 720 760Chapter 5Microstructural Examination of Structural ChangesThe major aim of this part of the research work is to study the microstructural changesduring annealing of heavily cold-rolled I-F steel by transmission and scanning electronmicroscopy (TEM and SEM). In particular, the influence of the precipitates on thesestructural changes was examined during a heating rate simulating that of the continuousannealing process. In addition, the orientation relationships among subgrains and the nature of the precipitate distributions were briefly studied. The composition of precipitateslarger than 0.1 jim in diameter were also examined with a scanning energy dispersivex-ray (EDX) microanalyser.5.1 Structural Changes during Cold Rolling and AnnealingThe annealing treatments performed correspond to either a heating rate of 20.2°C/s(simulating continuous annealing) after which the specimens were rapidly cooled frompeak temperatures of 580, 640, 680, 740, and 800°C or to a heating rate of 0.025°C/s(simulating batch annealing) where a single specimen was quenched after being heatedto 700° C. Thin foils produced from the as-received hot band, the cold rolled steel and theannealed sheet specimens were examined in a STEM operated at 200 kV to study themicrostructural changes associated with the recovery and the recrystallization processes.Diffraction patterns and Kikuchi patterns were also obtained to determine the orientationrelationships among siibgrains.The heavily cold-rolled interstitial-free steel specimens exhibited a poorly defined,190Chapter 5. Microstructural Examination of Structural Changes 191non-homogeneous cell structure, as shown in Fig. 5.1. The heterogeneous nature of theobserved microstructure is more clearly illustrated in Figs. 5.2 (a) and (b): Fig. 5.2 (a)shows the presence of a reasonably developed cell structure in certain grains while Fig.5.2 (b) indicates the existence of dense dislocation networks and a less developed cellstructure. The cells contain a relatively small number of dislocations, separated fromone another by highly deformed cell boundaries; the cell boundaries contain the greaterfraction of the dislocations introduced by cold rolling. Fig. 5.2 (a) indicates that the cellscan take different sizes and geometric shapes, varying from relatively large equiaxed tosmall elongated cells. For the approximately equiaxed cells, the cell size varied between0.3 to 0.8 jim, while the thickness of the cell walls was typically in the range of 0.2 to 0.4Figs. 5.3 (a) and (b) were obtained from a specimen quenched from 580°C afterbeing heated at 20.2°C/s. These micrographs correspond to a partly recovered state asthe metallographically determined recrystallization start temperature was 640°C andprovide evidence of an overall reduction in the dislocation density during the early phaseof recovery caused by a variety of annihilation processes. In particular, dislocations canannihilate by glide and climb within grains, in addition to migrating to cell walls. Thetangled dislocations in the cell walls rearrange themselves, and, as a result, a reasonablywell defined cell structure evolves, as shown in Figs. 5.3 (a) and (b). These microstructures are characterized by a considerably lower dislocation density in the cell interiorand more sharply defined (thin) cell boundaries. The subgrains thus formed are approximately of the same size and shape as the initial cells; the relatively smaller elongatedsubgrains and the larger ones can be seen in Figs. 5.3 (a) and (b), respectively.With additional recovery, continued subgrain formation and subgrain growth takeplace. These processes eventually lead to the formation of recrystallized nuclei as seenin Figs. 5.4 through 5.7 for specimens heated at 20.2°C/s up to 640°C. Figs. 5.4 (a) andChapter 5. Microstructural Examination of Structural Changes 192(b) show the well-defined subgrain structure developed with continued recovery. Thesefigures also suggest that the early growth of subgrains occurs largely by coalescence,i.e., by eliminating the boundaries between them. The probable positions of eliminatedboundaries are indicated by arrows, based on shape considerations and/or by identifyingthe visible residual dislocations from the coalesced boundaries. Fig. 5.5 shows anotherexample of subgrain coalescence, together with the Kikuchi patterns corresponding toboth of the subgrains. The estimated misorientation of 0.6° (equal to the displacementbetween the corresponding lines divided by the camera length of 0.8 m) provides additional evidence for the possible occurrence of the coalescence process. In addition tocoalescence, sub-boundary migration also contributes to the growth process. Fig. 5.6shows an example where both sub-boundary migration (as suggested by the curvature ofthe boundary) and coalescence seem responsible for subgrain growth. Precipitates influence recrystallization through their effects on nucleation and growth processes. Fig. 5.7(a) shows an example where a relatively large particle of 0.7 um aids in the nucleationprocess (note the preferential formation of dislocation-free subgrains around the precipitate). Fig. 5.7 (b), on the other hand, suggests the retarding effect of fine precipitateson sub-boundary migration; this can be inferred from the sharp discontinuity observedalong the curvature of the boundary.Continued subgrain growth by coalescence and sub-boundary migration leads to theformation of recrystallized nuclei. The subsequent growth of these nuclei into the coldrolled matrix takes place by the migration of boundaries with relatively high misorientation. Figs. 5.8 and 5.9 show two such examples together with the corresponding diffraction patterns; these microstructures were obtained from a specimen quenched from 680°Cafter being heated at 20.2°C/s. Fig. 5.8 indicates that the orientation of the recrystallizednucleus and the recovered parent grain are both {111}; the considerable misorientation(‘-S-’20°) present due to rotation about the normal axis is also evident when comparingChapter 5. Microstructural Examination of Structural Changes 193the two diffraction patterns. Fig. 5.9 shows an example where a fully developed recrystallized grain with {111} orientation borders with a {110} oriented cold rolled grain; thisfigure also suggests that one side of the boundary of the recrystallized grain has beenpinned by fine precipitates.The following microstructures were obtained from a specimen produced by rapidlycooling from 740°C after being heated at 20.2°C/s; this heat treatment produces about 50% recrystallization. Fig. 5.10 (a) shows the fully developed recrystallized grains growinginto the cold rolled matrix, while Fig. 5.10 (b) corresponds to the fully recrystallizedregion of the specimen.Figs. 5.11(a) and (b) show microstructures typical of fully recrystallized materialobtained in specimens heated at 20.2°C/s up to 800°C and at 0.025°C/s up to 700°C.Fig. 5.12 shows the microstructure of the as-received hot band. These microstructures,in general, indicate that the precipitate particles were scattered randomly; in addition,they also suggest that the precipitate particles remain unchanged during the cold rollingand annealing processes. The presence of a moderate number of dislocations in the fullyrecrystallized microstructures is thought to be due to the stabilizing effect of precipitateson dislocations. The limitations of thin foil work, in particular the possibility of foildamage from foil flexing, should also be considered in interpreting these observations.The surface of several lightly etched specimens was examined using the SEM to obtainadditional evidence regarding the effects of precipitates on the nucleation and growthprocesses. Fig. 5.13 was obtained from a specimen heated up to 800°C at 20.2°C/s, andthis corresponds to the fully recrystallized state. The discontinuous boundary curvatureobserved in this figure suggests that the grain boundary migration has been impeded byfine precipitates, most of which are not visible at this magnification.The overall microstructural changes observed in the present study are in general agreement with those reported for high purity iron [136j, rimmed and Al-killed steels [138] andChapter 5. Microstructural Examination of Structural Changes 194I-F steels [17, 21], and consequently, only a brief discussion of these observations are presented here. The development of the cell structure during cold deformation is usuallyexplained in terms of plastic strain accomodation by multislip and energy minimizationof dislocation clusters [222]. The observed heterogeneities in the cold rolled microstructure, as illustrated in Figs. 5.1 and 5.2, are consistent with the previous recrystallizationstudies on high purity iron and low-carbon steels [78, 132, 137, 138, 139], and are usuallyattributed to the dependence of the amount of stored energy on grain orientation. Thereasonably well-developed cells, formed in certain grains of the cold rolled matrix, evolveinto recrystallized nuclei, as illustrated in Figs. 5.3, 5.4 and 5.8. This explains the observed heterogeneous nucleation behaviour during the kinetic characterization (see Figs.4.27 and 4.30); in addition, such observations attribute the origin of the recrystallizationheterogeneity to the cold rolling operation itself. The typical cell sizes of 0.3 to 0.8 tmobserved in the present study are smaller than the 0.5 to 2 1um reported for the rimmedand Al-killed steels [138], but very close to the 0.4 to 0.8 m reported for a low-carbon,Nb-microalloyed steel [139]. A fine dispersion of precipitates has been reported to resultin retardation of cell formation and refinement of cell size [132, 139]; this may also explainthe small cell size observed in the present study.The microstructural observations illustrated in Figs. 5.4, 5.5 and 5.6 indicate thatthe early growth of subgrains occurs primarily by subgrain coalescence; some growthby sub-boundary migration also occurs, as indicated in Fig. 5.6. These observationsprovide stronger support for the subgrain coalescence model proposed by Hu [53, 223]than for the sub-boundary migration concept of Cahn [131]. Coalescence was observedamong different types of subgrains, although it seemed to be more common among therelatively small elongated subgrains, as previously indicated by Goodenow [138]. Thecoalescence process, shown schematically in Fig. 2.14, involves a gradual moving ofdislocations out of the boundary between the subgrains to the boundaries surroundingChapter 5. Microstructural Examination of Structural Changes 195them, and a rotation of the subgrain itself into the same orientation as its neighbouringsubgrain. The example shown in Fig. 5.5 and the corresponding small misorientationof 0.6° between the subgrains, suggests the occurrence of subgrain coalescence by such amechanism. Hu [53, 223] suggested that the angular misfit of the boundary around therotated subgrain may increase, and that a cluster of coalescenced subgrains would havehigher-angle boundaries in addition to being large; the recrystallized nucleus thus formedcould grow into the cold rolled matrix by high angle boundary migration.A limited attempt was made to determine the orientation of the recrystallized nucleiwith respect to the surrounding cold rolled matrix. The example shown in Fig. 5.8indicates that the orientation of the nucleus and the matrix are both { 111); however,a significant misorientation is present due to rotation about the normal axis. A similarrelationship has been previously reported by Goodenow [138] based on an annealingstudy of a rimmed steel. In Fig. 5.9, a fully developed recrystallized grain with {111}orientation is bordering a {110} oriented cold rolled grain. These examples clearly showthat the later stages of growth of the recrystallized grains take place by the migrationof boundaries with relatively high misorientation. They also give some indication aboutthe textural changes associated with recrystallization, a subject to be dealt with in moredetail in the next chapter.The experimental observation shown in Fig. 5.7 (a) indicates that large precipitates(‘—i 0.7 urn) may be preferred nucleation sites. Similar observations have also been reported previously for a Ti-stabilized I-F steel [153], and are usually explained in termsof a localized high dislocation density and substantial local lattice distortion in the surrounding matrix [82, 131). A distribution of fine precipitates, on the other hand, hasbeen reported to retard sub-boundary/boundary migration during recrystallization ofI-F steels [16, 17, 21, 153]; similar effects were observed in the present study in Figs.5.7 (b), 5.9 and 5.13. The discontinuities in the boundary curvature observed in Figs.Chapter 5. Microstructural Examination of Structural Changes 1965.7 (b) and 5.13 suggest that some precipitates are more effective in impeding boundarymigration than others. Such observations are usually explained in terms of the complexinteractions between the migrating boundaries and precipitates, i.e., by considering factors such as the particle radius, the interfacial energy per unit area of the boundary andthe change in dislocation density across the migrating boundary (a detailed treatmentprovided by Hansen et al. [154] is given in section 2.1.5).Fully recrystallized microstructures shown in Fig. 5.11 and the microstructure of thehot band given by Fig. 5.12 suggest that the precipitates do not undergo any significantchanges during cold rolling and annealing operations. This seems to be the case irrespective of whether the heating rate simulates the continuous annealing process (20.2°C/s)or the batch annealing process (0.025°C/s). This observation is consistent with reportedresearch on I-F steels [21, 153] and can be rationallized in terms of the low annealingtemperatures (maximum of 800°C) compared to the precipitation temperatures for mostof the Ti and Nb nitrides, sulfides and carbides which are in the range of 1400- 900°C[4, 6, 9, 101. In addition, Figs. 5.10, 5.11 and 5.12 indicate that precipitates are scattered randomly. A random distribution of precipitates will not significantly influencethe grain morphology. The equiaxed grain morphology observed in the present study(see Fig. 4.29), as well as in most of the other recrystallization studies on I-F steels[16, 17, 21, 153], is a reflection of this.In summary, the heterogeneous nature of the cell structure developed during coldrolling was examined and shown to lead to well-defined subgrain formation during theearly stages of recovery. The subgrain growth, occurring primarily by subgrain coalescence, led to the formation of the recystallized nucleus which grew into the recoveredmatrix by the migration of high misorientation boundaries. Large precipitates (.. 0.7tim) acting as preferred nucleation sites and fine precipitates impeding the boundarymobility were illustrated. The microstructures obtained from the hot band and the fullyChapter 5. Microstructural Examination of Structural Changes 197recrystallized steel suggest that the precipitates remain unchanged during cold rollingand annealing operations.5.2 Characterization of Large PrecipitatesThe as-received hot band and a fully recrystallized steel produced by heating up to 800° Cat 20.2°C/s were examined using an SEM operated at 20 kV. The specimens, groundand polished (up to 1 diamond paste) by conventional metallographic techniques,were lightly etched with 2 % nital to facilitate the observation of the precipitates. Theprecipitates larger than 0.1 itm in diameter were analysed using EDX spectroscopy; WDXspectroscopy was employed in a limited number of cases to confirm the microchemistryof certain precipitates. More than 200 different particles were analysed from the hotband and the fully recrystallized steel specimens. The observations indicate that theprecipitates have the same composition, and consequently, only the results obtainedfrom the hot band are presented.The most common precipitates observed during this study were the sulfides of titanium. Fig. 5.14 is an SEM micrograph of the hot band showing an angular shapedprecipitate of 1 tim; the x-ray spectrum obtained from this precipitate is also shown.The x-ray peaks for Ti and S are comparable in magnitude and breath, the standardlessanalysis indicating an atomic ratio of 1. This suggests that the observed precipitate isTiS (Note: the Fe peak corresponds to the iron matrix surrounding the precipitate). Inaddition, regular shaped precipitates of TiS in the size range 0.3 to 0.8 m were also observed. Fig. 5.15 shows one such example (TiS at the centre), together with some other(smaller) spherical shaped precipitates of 0.1 to 0.2 [Lm; the x-ray spectrum obtainedfor these smaller precipitates, shown in the same figure, indicates the Ti/S atomic ratioto be approximately 2, suggesting that these precipitates are Ti4C2S.It should also beChapter 5. Microstructural Examination of Structural Changes 198emphasized that often the Ti/S atomic ratio obtained from the relatively large (0.3 to 0.8m) precipitates was found to vary between 1 and 2, suggesting the possible coexistanceof TiS and Ti4C2S in the same particle. S-rich, Mn-containing, regular-shaped precipitates were also observed on a few occasions, a 0.8 m diameter example being shownin Fig. 5.16 with its x-ray spectrum. The x-ray peaks shown in this figure suggests thisprecipitate to be of the type (Ti,Mn)S.In addition to sulfides and carbo-sulfides, a second type of Ti-rich precipitate usuallylarger than 1 m in size was also observed during this study. One example (‘-- 2 urn)together with the corresponding x-ray spectrum is shown in Fig. 5.1.7. The characteristicangular shape of this precipitate suggests it to be titanium nitride. The WDX dot mapsobtained on this area confirmed that the precipitate was not enriched in either 0 or C(except for some high concentration of C around the precipitate). This observation isconsistent with the precipitate being TiN; the analysis for N was not carried out due tothe fact that both Ti and N have overlapping peaks.Some other noticeable features regarding the observed larger particles ( 1 urn) areindicated in Fig. 5.18, where the coexistance of two different types of precipitates issuggested. The x-ray spectrum obtained from the different regions in the particle indicatethat Ti-rich precipitates form on the already existing Al-rich particle. Because theseparticles were too small to be clearly resolved in a WDX analysis, the true identityof these phases was not established. However, some confirmatory WDX point analysisindicated the base particle to be alumina, and the characteristic angular shapes suggestthe newly formed precipitates to be titanium nitride. In certain cases, an Al-rich core(probably Al203), a surrounding Ti-rich precipitate (probably TiN) and a third layerof precipitate (the lighter contrast outer layer indicated by arrow) were observed, asshown in Fig. 5.19 and indicated by the EDX analysis performed on this precipitate.This analysis (i.e., the presence of 5) suggests the outer layer to be either a sulfide or aChapter 5. Microstructural Examination of Structural Changes 199carbo-sulfide of Ti. It should also be noted that in certain instances S-containing outerlayer of precipitate was observed directly around the Al-rich core without the secondTi-rich layer. During this study, evidence of the presence of P-containing precipitateswas detected on a few occasions; a typical example and the associated x-ray spectrum,is shown in Fig. 5.20, suggesting the presence of titanium-iron phosphides together withalumina.The characterization of fine precipitates can best be accomplished by studying carbonextraction replicas in a TEM. This method allows one to study precipitates as small as afew nm. In addition, the interference of the matrix in the analysis of the microchemistrycan be avoided. In the present study, however, the precipitates were observed in an SEMand the analysis was done primarily through EDX. The effective magnification that couldbe employed was in the range of x 2k to x 10k, and consequently the smallest precipitatethat could be studied was of 0.1 sum. Almost all the particles studied were within the sizerange of 0.1 to 2 ,um, and because of this, the observed x-ray spectrum invariably had apeak corresponding to the iron matrix (the volume of the material interacting with theelectron beam is typicaly of 2 to 4 im in diameter). In addition to the EDX analysis,the prior knowledge about the existing precipitates in similar I-F steels and the knowninformation regarding the characteristic shapes were also used in the identification. TheWDX spectroscopy was employed in a limited manner primarily to identify the presenceof C, N and 0. However, obtaining proper dot maps was found to be difficult with thesesmall particles (‘ 1 jim); this is mainly due to the fact that even a small movement of thespecimen (instability caused by heating effects due to the high beam current, tilt of thespecimen etc.) becomes critical at the high magnifications necessary for proper resolution.Because of these difficulties, some WDX analyses were done by point analysis, where thepeak/background ratio of the element of interest was measured in the precipitate and inthe matrix, and the comparison of these values indicated the relative presence of C, N orChapter 5. Mjcrostructural Examination of Structural Changes 2000 in the particle. In addition, since Ti and N have overlapping peaks (the ) values for NK and Ti L1 are 31.59 and 31.36 A, respectively [224]), the presence of a TiN precipitatewas confirmed by verifying the absence of C and 0.As illustrated in this chapter, the progress of recrystallization in an I-F steel is influenced by the size and distribution of the precipitates. Coarse and widely spaced precipitates allow rapid growth of new grains with favourable orientation, thereby helpingto achieve stronger textures favoring deep-drawability. In addition, all of the stabilizingprecipitation takes place during the high temperature processing (primarily in the temperature range of 1400 to 900°C [4, 6, 8, 10]), and the precipitates therefore undergo nonoticeable changes during the cold rolling and annealing operations. Thus, it is important to control the size and distribution of the precipitates and the grain size in the hotband in order to achieve good deep drawability. The precipitate size ranges observed forTiN, TiS and Ti4C2S during this study are in general agreement with those reportedfor other Ti-stabilized I-F steels [10, 11, 12, 225]. The present method of analysis wasrestricted to precipitates that are larger than 100 nm, and because of this, other possibleprecipitates, such as TiC and NbC with size ranges of 10 to 40 nm [10, 14, 221] couldnot be observed. In addition, the reported presence of Ti4C2Sas small as 50 nm [10, 12]could not be confirmed. The precipitation sequence of a typical Ti-stabilized I-F steel isreported to be TiN, TiS, Ti4C2S and TiC [4, 10]; the present observations indicate thatthe size of the precipitates decreased in the same order.The present study mainly deals with sulfides and carbo-sulfides of Ti, as shown inFigs. 5.14, 5.15 and 5.16. Previous studies on I-F steels have also indicated the formationof TiS with different morphologies [10, 11, 226], as observed in the present study (seeFigs. 5.14 and 5.15). A direct transformation from TiS to Ti4C2S has been reportedto be responsible for the removal of interstitial C atoms at high temperatures [10, 11,12, 225]; this transformation is considered desirable since C is removed at relatively highChapter 5. Microstructural Examination of Structural Changes 201temperatures (‘- 1200°C) as coarse carbo-sulfides rather than as fine carbides at relativelylower temperatures (‘-‘.‘ 900°C). In addition, it was also reported that TiS and Ti4C2Sphases often coexist as composite particles [12, 225, 226, 227]. The present observationthat the Ti/S atomic ratio was occasionally found to lie between 1 and 2 is consistentwith those findings.The steel used in the present study has a Mn content of 0.140 wt %. However,only a very few Mn-containing precipitates were observed, and they were all of the type(Ti,Mn)S, as indicated in Fig. 5.16. The presence of similar (Ti,Mn)S type inclusionshas been reported in previous studies on steels [228]. The presence of only a very fewMn-rich precipitates indicates that the stabilization of S must have occurred primarilyby Ti. It has generally been reported that when Ti*/Mn 0.125, the precipitation ofMnS could be suppressed, where Ti* refers to that amount of Ti available after formingTiN at high temperatures [229]. Such a condition is easily met in the present steel whichhas the appropriate Ti*/Mn ratio of 0.206; this might explain the noticeable absenceof MnS in this steel. On the other hand, this observation suggests the bulk of the Mnto be present in the solid solution. Mn in solid solution is beneficial in terms of solid-solution strengthening, but may be undesirable as far as deep-drawability is concerned[4, 6, 20, 55].In Ti-stabilized I-F steels, Ti reportedly stabilizes all the N present as TiN at hightemperatures (-... 1400°C) [4, 6, 10, 15, 227, 230]. TiN particles were usually observedto be larger than 1 jim in size [10] and were observed to assume a characteristicallyangular shaped morphology [231, 232]. The present observations of TiN, as shown inFigs. 5.17, 5.18 and 5.19, are consistent with those studies. TiN has been observedeither as a separate particle (independent nucleation and growth) as shown in Fig. 5.17,or in coexistence with alumina particle, as shown in Figs. 5.18 and 5.19. Fig. 5.19 showsan example where in addition to the Al-rich core and the surrounding Ti-rich precipitate,Chapter 5. Mjcrostructural Examination of Structural Changes 202a third layer of Ti/S containing precipitate (either TiS or Ti4C2S)was also observed;the presence of similar three-layered particles, i.e., alumina core, TiN precipitate and thesurrounding layer of TiS, has been reported for a Ti-stabilized stainless steel [232]. Itshould also be noted that an existing particle may act as a preferential nucleation site forthe later formation of a precipitate as was observed in the present study. The presenceof alumina inclusions in the steel can be attributed to the fact that the base steel isan Al-killed steel containing 0.060 wt % Al. Alumina inclusions have been reported toremain in steels from the primary deoxidation process [233, 234]. The relatively small (2to 5 im) isolated alumina particles observed in this study are probably the secondaryinclusions that precipitate from the steel during cooling and solidification, i.e., the resultof the stabilization by Al of the remaining oxygen in steel [15, 231, 233, 234].Phosphorous is commonly used in Ti-stabilized I-F steels as an alloying elementsince it imparts solid-solution strengthening without significantly reducing the deepdrawability [4, 6, 9, 235, 236]; the steel used in the present study has a P content of0.011 wt %. Some previous studies indicate that precipitates of (Ti,Fe)P (titanium-ironphosphide) with sizes ranging from 0.1 to 1 m, form during the high temperature processing [9, 235]. These precipitates have been reported to reduce both the tensile strengthand deep-drawability [235]. In the present study, however, the P-rich precipitates havebeen observed only in a very few occasions, and always together with a large Al-richparticle (probably alumina), as shown in Fig. 5.20. This observation suggests that thebulk of the phosphorous remains in solid solution, a necessary condition to achieve thebeneficial effects of phosphorous as an alloying element. A high coiling temperature (“.‘750°C) has been reported to favour the precipitation process [235]. The current steel wascoiled at a relatively low temperature of around 600° C which may explain the presentobservation of the low amount of P-rich precipitates.The finest precipitates present in I-F steel are usually Ti and Nb carbides (10 to 40Chapter 5. Microstructural Examination of Structural Changes 203nm) [10, 14, 221], and these have been usually observed as individual particles (fromindependent nucleation and growth). However, some epitaxial growth of TiC on Ti4C2Shas also been reported [225]. None of these particles were observed in the present studydue to the method of analysis, and hence, no detailed discussions of these precipitatesare presented. It is worth noting that no Nb-rich precipitate was observed, despite thepresence of 0.02 wt % Nb. This is thought to be due to the fact that except for the possiblestabilization of C as NbC, all of the other stabilization (N and S) results in Ti compounds.It should also be indicated that carbides, being the finest precipitates present in I-F steels,may have the most decisive influence in retarding the growth of the recrystallized grains.A coarser distribution of carbides, as caused by a higher precipitation temperature, isdesirable. One way to achieve this distribution is by facilitating the high temperatureremoval of C by promoting the direct transformation from TiS to Ti4C2S [10].In summary, precipitates larger than 0.1 ,um, i.e., the nitrides, sulfides and carbosulfides of Ti, were characterized. It was shown that the existing alumina particles actas nucleation sites for the precipitation of Ti-compounds. Only a few Mn and P richprecipitates were observed, which suggests the possibility that the bulk of these elementsremain in solid solution. The necessity to control the size and distribution of precipitates,in particular, the beneficial effects of the high temperature removal of C by the directtransformation from TiS to Ti4C2S,was discussed.Chapter 5. Microstructural Examination of Structural Changes 204Figure 5.1: Bright-field transmission electron micrograph of the 80 % cold rolled I-F steelshowing the highly dislocated cell structure.Chapter 5. Microstructural Examination of Structural Changes 205Figure 5.2: Microstructures illustrating the heterogeneous nature of the cold rolled cellstructure; (a) a reasonably developed cell structure and (b) dense dislocation networkswith much less developed cell structure.(a)0.5tmII(b)0.5tmChapter 5. Microstructural Examination of Structural Changes 206Figure 5.3: Subgrain structure development in a partially recovered specimen heated at20.2°C/s up to 580°C; (a) small elongated subgrains and (b) relatively large subgrains.(a)(b)Chapter 5. Mjcrostructural Examination of Structural Changes 207Figure 5.4: We11-defined subgrain structure formation in a specimen heated at 20.2°C/sup to 640°C; coalescence of subgrains is suggested by those boundaries indicated byarrows.(a)(b)Chapter 5. Microstructural Examination of Structural Changes 208Figure 5.5: Photomicrograph obtained from a specimen heated at 20.2°C/s up to 640°C,indicating the occurence of subgrain coalescence (arrow indicates the disappearing boundary); Kikuchi lines corresponding to the subgrains A and B are also given.A BChapter 5. Microstructural Examination of Structural Changes 209Figure 5.6: Microstructure indicating subgrain growth caused by both sub-boundarymigration (indicated by arrow M) and coalescence (indicated by arrow C); the annealingtreatment corresponds to quenching from 640°C after being heated at 20.2°C/s.O5jimHChapter 5. Microstructural Examination of Structural Changes 210Figure 5.7: Microstructures obtained from a specimen heated up to 640°C at 20.2°C/s,indicating (a) the effect of a large particle on nucleation (arrow indicates the precipitate)and (b) the effect of fine precipitates on sub-boundary migration (arrow indicates thediscontinuity in the boundary curvature.(a)p0.5,um(b)Chapter 5. Microstructural Examination of Structural Changes 211Figure 5.8: Recrystallized grain nucleated in the interior of a matrix grain in a specimenheated at 20.2°C/s up to 680°C; selected area diffraction patterns illustrate the orientation of the recrystallized grain A (zone axis < 111 > type) with regard to the matrixsubgrain area B (zone axis < 111 > type).Chapter 5. Microstructural Examination of Structural ChangesV212Figure 5.9: Recrystallized grain A (zone axis < 111 > type) bordering a cold rolled grainB (zone axis < 110 > type) in a specimen heated at 20.2°C/s up to 680°C; the pinningof one side of the boundary of the recrystallized grain by fine precipitates is also shown(arrows indicate the precipitates).I 0.5 imChapter 5. Microstructural Examination of Structural Changes 213Figure 5.10: Photomicrographs obtained from a specimen heated at 20.2°C/s up to740°C (.-- 50 % recrystallized), showing (a) recrystallized grains growing into the coldrolled matrix and (b) fully recrystallized grains.(a)(b)Chapter 5. Microstructural Examination of Structural Changes 214Figure 5.11: Fully recrystallized microstructures obtained from the specimens heated (a)at 20.2°C/s up to 800°C and (b) at 0.025°C/s up to 700°C.(a)(b)Chapter 5. Microstructural Examination of Structural Changes 215Figure 5.12: Microstructure of the as-received hot band, showing random distribution offine precipitates.Chapter 5. Microstructural Examination of Structural Changes 216Figure 5.13: SEM micrograph obtained from a specimen heated up to 800° C at 20.2°C/s,suggesting that the boundary migration had been impeded by fine precipitates (arrowsindicate the discontinuities in the boundary curvature).Chapter 5. Microstructural Examination of Structural Changes 217S Ti FelA:::::.jfl4Figure 5.14: SEM micrograph and x-ray spectrum showing the presence of an angular-shaped precipitate in the hot band (arrow indicates the precipitate); the x-ray spectrum is consistent with it being a TiS precipitate.__________rPrr4... 0.320 Rane= L1.aLi EnergyFigure 5.15: SEM micrograph of the hot band showing the larger Ti/S-containing precipitate (appears near the centre) and the smaller precipitates (indicated by arrows); theassociated x-ray spectrum obtained for a smaller precipitate is consistent with it beingTi4C2S.Chapter 5. Microstructural Examination of Structural Changes 21812725Fel-‘Ij4— 0. 000 Rariie 10. 130 EnergyFeS IJ-6Mn I4— O.[1[ 5nqr= Energyi illFigure 5.16: SEM micrograph and x-ray spectrum showing the presence of a regular-shaped precipitate in the hot band (arrow indicates the precipitate); the x-ray spectrum suggests this to be of the type (Ti,Mn)S.Chapter 5. Microstructural Examination of Structural Changes 219027234 20KV X2:O’KI0uflChapter 5. Microstructural Examination of Structural Changes 220Figure 5.17: SEM micrograph of the hot band showing an angular shaped precipitate(indicated by arrow); the x—ray spectrum is consistent with it being a TiN precipitate.Ti .:Fe4— C.32O Rane= 1C..?C 1eV EnergyL.1O.2.E11 —Chapter 5. Microstructural Examination of Structural Changes£221Al ::.:::....Ac::. .::::: .... . . . v:.:...:. FeTi.:.t.. :2,4— 2. 160 Rnge= 10.230 keV Energy 10.’C —,*Ti),FeAl Iiama LL4— 0.160 Pange= 10.230 6eV EnergyFigure 5.18: SEM micrograph obtained from the hot band and x-ray spectrum obtainedfrom the particle showing an example where an Al-rich particle (indicated by arrow Al)acted as the nucleant for Ti-rich precipitates (indicated by arrow Ti).12230 —Chapter 5. Microstructural Examination of Structural ChangesFeIi-‘ItSr____.tcc.4— 0,480 Panqe= 10.23C.’ keV Energy222Figure 5.19: SEM micrograph obtained from the hot band and x-ray spectrum of theprecipitate showing an Al-rich core surrounded by a Ti-rich precipitate, which acted asthe nucleant for the sulfide or carbo-sulfide of Ti (the lighter contrast outer layer indicatedby arrow).Chapter 5. Microstructural Examination of Structural Changes•:••:••.• Fe . .Ti....Al11$r4— LI. 3.20 Panye= 1.1]. 233 [eV Energy223Figure 5.20: SEM micrograph and x-ray spectrum showing the presence of a P-containingprecipitate in the hot band (arrow indicates the precipitate).Chapter 6Characterization of Annealing TexturesThe primary objective of this part of the research work is to characterize the evolutionof crystallographic texture by means of orientation distribution functions (ODFs) during cold rolling and annealing processes. The basis for the comparison of texture inthis study is primarily three-fold. First, the texture development from the as-receivedhot band to the 80 % cold rolled state was studied. Then, the progressive developmentof recrystallization texture (‘—‘ 15, 40, 80 and 100 % recrystallized) and the additionalchanges caused by grain growth (ASTM No. 9 - 10 to ASTM No. 8) were monitored forthe specimens annealed at 20.2°C/s. Finally, the effect of heating rate on texture development was investigated by comparing the textures of the fully recrystallized specimens(with approximately the same grain size of ASTM No. 9 - 10) produced at the heatingrates of 20.2, 1.88 and 0.025°C/s. In addition, the values for the strain ratio () wereestimated by incorporating the texture data into the Taylor model of plastic flow, andthe predictions were verified against the mechanical measurements.Nine different specimens were subjected to the texture analysis; they correspond tothe as-received hot band, the 80 % cold-rolled strip and other annealed sheet specimens.All texture measurements were made on the mid-plane (i.e., the center-line thickness) ofthe specimens. Most of the continuous heating annealing treatments were performed at20.2°C/s after which the specimens were rapidly cooled from peak temperatures of 670,720, 760, 800 and 900°C. The specimens quenched from 670, 720 and 760°C correspondto approximately 15, 40 and 80 % recrystallized, respectively. The specimen produced by224Chapter 6. Characterization of Annealing Textures 225rapidly cooling from 800°C corresponds to complete recrystallization with an estimatedaverage grain size of ASTM No. 9 - 10. The specimen cooled from 900° C underwentconsiderable grain growth after completion of recrystallization and resulted in an averagegrain size corresponding to ASTM No. 8. Two other cold rolled specimens heated at1.88 and 0.025°C/s were quenched from 770 and 700°C, respectively; these two specimenscorrespond to the fully recrystallized state without any grain growth. The average grainsize of these specimens was estimated to be in the range of ASTM No. 9 - 10. It shouldbe noted that the heating rates of 20.2 and 0.025°C/s are typical of a continuous and abatch annealing process, respectively.Partial (110), (200), (211) and (310) pole figures (measured up to 80° from the centre of the pole figure) were determined for each of the prepared specimen on a texturegoniometer using Cu K radiation. The experimental pole figures were scrutinized forsymmetry aspects [165, 237], and the intensity values confirmed the orthorhombic symmetry of all the pole figures. Orientation distribution functions (ODFs) were calculatedfrom the partial pole figures using the series expansion method (lmar = 22) developedby Bunge [165, 166, 167, 168]. The ODFs were then used to recalculate the pole figures.The comparison of the experimental and recalculated pole figures gives a direct indication of the quality of the measurements and the absence of significant errors in the ODFcalculations [165]. In the present study, good agreement was obtained in all the cases,and a typical example, presented in Fig. 6.1 (a) and (b), compares the experimental andrecalculated (110) pole figures obtained for the 80 % cold rolled I-F steel specimen.The complete ODFs calculated for all nine specimens used in this study are presentednow. Figs. 6.2 and 6.3 were obtained for the as-received hot band and the 80 % cold-rolledsteel, respectively. Figs. 6.4, 6.5, 6.6, 6.7 and 6.8 correspond to the annealing treatmentsin which the 80 % cold rolled sheets were heated at 20.2°C/s to peak temperatures of670, 720, 760, 800 and 900°C and rapidly cooled, in that order. Fig. 6.9 correspondsChapter 6. Characterization of Annealing Textures 226to the specimen heated at 1.88°C/s to 770°C. Fig. 6.10 was obtained for the specimenquenched from 700°C after being heated at 0.025°C/s. The microstructural state of eachspecimen is indicated in the appropriate figure caption. The three-dimensional ODFs arepresented at constant y sections, i.e., coi = 0 to 90° in increments of 5°. For the constantcpi sections, Y2 is given by the horizontal axes, while the vertical axes indicate q5. The S°2= 45° section, which contains most of the important orientations, is also shown at theend of each figure; for this section, ço1 is given by the horizontal axis, while the verticalaxis indicates q.The analysis of the ODF results shown in Fig. 6.2 suggests that no highly developedtexture is present in the hot band. Fig. 6.3 indicates the formation of a reasonablydeveloped texture during cold rolling; this texture is represented by an extended-tube inorientation space. Fig. 6.4 shows the texture near the start of recrystallization ( 15 %recrystallized). A comparison of Figs. 6.3 and 6.4 indicates that the overall nature of thetube-shaped density distribution remains approximately the same. However, a generalsharpening of the texture and the elimination of certain auxiliary texture components(the ones outside the main ‘tube’) can be seen. A careful observation also indicates aredistribution of density within the ‘tube’. In particular, the positions (i.e., 2 andvalues) that correspond to the maximum pole densities could be observed to shift toward{111}-type orientations in most of the sections. It should be noted that the twoblack dotted curves and their intersection point in each y section indicate the three-foldsymmetry elements in the Euler space for cubic/orthorhombic crystal/sample symmetry;the intersection points in all y sections correspond to the 7-fibre where < 111 >11 ND.The shift towards { 111 }-type orientations with increasing % recrystallization is shownin Fig. 6.5, which corresponds to a 40 % recrystallized microstructure; in this casethe maximum intensities in all sections approach near {111}-type components. Withcontinued recrystallization, a general sharpening and strengthening of this texture occursChapter 6. Characterization of Annealing Textures 227without any other significant changes; see for example, Figs. 6.6 and 6.7 that correspondto 80 and 100 % recrystallized microstructures, respectively. A similar trend continueswith grain growth following the completion of recrystallization, as can be seen by comparing Fig. 6.8 (ASTM No. 8) with Figs. 6.9 and 6.10 (both ASTM No. 9 - 10); thesethree fully recrystallized microstructures were obtained at heating rates of 20.2, 1.88and 0.025°C/s, respectively. All of the ODFs obtained from the fully recrystallized microstructures (Figs. 6.7 through 6.10) are comparable; the overall nature of the extended,tube-shaped density distribution is the same in each case and each shows similarities tothat of the cold rolled steel.The development of textures during cold rolling and annealing is most convenientlystudied by expressing the orientation densities along selected fibres (see Fig. 2.26 forexample). In the present study, the development of fibres < 110 > RD (a-fibre),< 111 >11 ND (7-fibre), < 110 >11 TD (e-fibre), < 001 >J ND (t-fibre) and < 110 >ND (C-fibre) were monitored. The pole density along the a-fibre is of importance for hotand cold rolling textures as well as for recrystallization textures. For deep-drawing steels,the course of the pole density in the7-fibre characterizes the recrystallization texture andthese components are highly desirable for good deep-drawability. The e-fibre is presentedsince it contains the important (554)[5] texture component. The t9-fibre marks theundesired components of the deep-drawing texture. The C-fibre development is of someinterest in this particular study since the {220} peak resolution was used in characterizingthe kinetics of the recovery and recrystallization processes. The development of all fivefibres (a, 7, E, t9 and C) were analysed, and all the significant changes are presented here.In the case of and t9 fibres, it is sufficient to show only one third and one half of the fibre,respectively, due to symmetry reasons; however, complete fibres are presented in thisstudy for all the cases. In addition, all of the fibres are plotted with the same maximumorientation density scale of twelve times random to illustrate the relative significance ofChapter 6. Characterization of Annealing Textures 228different texture components.Figs. 6.11 (a), (b) and Figs. 6.12 (a), (b) show the orientation density f(g) alongthe a,-y, e and ?9 fibres for both the as-received hot band and the 80 % cold-rolled I-Fsteel specimens; the important texture components are indicated at appropriate angles.The as-received hot band did not have any highly developed texture, although this is stillfar from a random texture. One observes the presence of a weak partial a-fibre textureextending from (114) [110] to (111)[1I0] with the strength of about four times random near(112)[1I0J. There is also the presence of a weak (two to three times random) but complete7-fibre and a weak E-fibre in between (111)[112] to (110) [001] with a high strength valueof about four times random near (221)[114]. No 9-fibre is observed in the hot band.Cold rolling has resulted in a highly developed texture. One observes the presenceof a strong partial a-fibre texture extending from (001)[1i0] to (112)[1i0], with strengthvalues as high as nine times random for texture components in the vicinity of (114)[1i0].The relatively strong (112) [110] of the hot band seems to have increased moderately (fromthree to five times random) during cold rolling. The 7-fibre remained almost the same atabout two to three times random during cold rolling. There is a general development of Eand ‘0 fibres during cold rolling. In particular, the strong development of (001)[1I0]-typecomponents with considerable spread around them, a slight improvement in (111)[112],and a reduction of the strongly developed (221)[114] to almost the random level couldbe observed.The development of annealing texture from the cold rolled texture during the progressof recrystallization (‘-. 15, 40, 80 and 100 % recrystallized) and grain growth (ASTM No.9 - 10 to ASTM No. 8) are shown in Figs. 6.13 through 6.15. Figs. 6.13 (a) and (b), Figs.6.14 (a), (b) and Fig. 6.15 present this information as plots of orientation density f(g)along the a,,e, ‘0 and fibres, in that order. In the a-fibre, a continious reduction of(001)[1I0] (from eight times random to random) and a continuous increase of (111){1IOjChapter 6. Characterization of Annealing Textures 229(from two times random to ten times random) could be observed during annealing; theplots corresponding to 15 and 40 % recrystallized microstructures indicate the transitionbetween the cold rolled and recrystallized textures. There is a consistent increase in thecomplete 7-fibre from about two to three times random to about ten times random duringannealing. The and 9 fibres also indicate a continuous reduction in the spread aroundthe (001)[1I0J-type texture components during annealing. In the case of t9-fibre, mostof the other components are reduced to below random level during annealing. The efibre indicates the strong development of (554){5J (from two times random to ten timesrandom); while (111)[112] was relatively stronger initially, (554)[5] was more dominanttowards the end of recrystallization. Annealing causes some additional reduction in thealready weak C-fibre components. However, these changes are very small when comparedto the changes in other fibres, and in particular, the changes in the C-fibre componentsare almost negligible after the initial stages of recrystallization.The effect of heating rate (20.2, 1.88 and 0.025°C/s) on the final recrystallizationtexture (grain size of ASTM No. 9 - 10) is shown in Figs. 6.16 through 6.17. Figs. 6.16(a), (b) and Figs. 6.17 (a), (b) show the recrystallization texture as plots of orientationdensity f(g) along the a, 7, 6, 9 and C fibres, in that order. In general, the effectof heating rate on the final recrystallization texture appears to be small. The a-fibreindicates the strength of (111){1I0] to be the minimum (about six times random) for thespecimen produced at 0.025°C/s, while the other two heating rates resulted in almostthe same orientation density of about eight times random. On the other hand, the-fibre indicates the strength of (111)[112] to be the minimum (about six times random)for the specimen produced at 20.2°C/s, while the other two heating rates yielded thesame orientation density of about seven times random; overall however, 1.88°C/s seemsto have resulted in stronger {111}-type components. In the case of 6-fibre, the strengthof (554)[5j increased steadily with a decreasing heating rate, from about seven timesChapter 6. Characterization of Annealing Textures 230random at 20.2°C/s to about ten times random at 0.025°C/s. Although the ‘0-fibrewas reduced almost to the random level during annealing, the remnants of {001}-typecomponents were relatively strong for the specimen annealed at 0.025°C/s.The volume fractions of important texture components were also estimated from theC-coefficients of the ODFs, and the calculations were based on ideal orientations witha spread described by = 16.5° Gaussian distributions [166]. Although the absolutevalues of the calculated volume fractions are questionable, they have been used in relativeterms as supporting evidence in texture studies [219]. The texture analysis presentedso far indicates the most important texture components to be (O01)[1I0], (112)[1I0],(114)[1I0], (111)[1I0] and (554)[5] (6° away from (111)[112]); the volume percentagesof these texture components, calculated for all nine test specimens are presented in Table6.1. The volume fractions obtained for (111)[112] were very close to those obtained for(554) [5] and hence not tabulated. The volume fractions were also calculated for thestandard orientations such as cube (001)[100], goss (011)[100], brass (011)[211], copper(112)[11 1], etc. However, since these texture components were present in relatively smallamounts and also did not undergo any major changes during cold rolling and annealing,they are not presented here. It should be indicated that the calculated values of thevolume fractions are dependent on the orientation density of the considered component,the assumed spread of model function and the multiplicity factor corresponding to thetexture component [238]. The relatively low values obtained for the volume fraction of(001)[1I0], despite the observed high orientation density (compare with (112)[1I0] forexample, in the the cold rolled a-fibre shown in Fig. 6.11 (a) and also in Table 6.1), isprimarily due its low multiplicity factor (24 for (001)[1I0] as against 48 for (112)[1I0][238]). The volume percentages of the important texture components indicated in Table6.1 give a clear indication about the evolution of texture during cold rolling and annealing;they are also useful in assessing the significance of the heating rate and grain growth onChapter 6. Characterization of Annealing Textures 231the annealing texture.Normal direction (ND) inverse pole figures indicate the density of different crystallographic planes that are parallel to the sheet, and consequently they provide a simpler(though not complete) method of monitoring texture development. In particular, thedensities of different principal planes that are parallel to the rolling plane have beenfound to be useful in correlating the texture evolution to the associated changes in plastic anisotropy [15, 21, 55, 163, 193]. While ND inverse pole figures can be determinedeasily for a sheet metal using diffractometry [49, 156, 158, 162], they can also be calculated from the ODFs [165, 166]. In the present study, ND inverse pole figures werecalculated using the ODF data for all nine specimens, and Figs. 6.18 (a) and (b) showtwo such examples corresponding to the 80 % cold rolled steel and the fully recrystallizedspecimen with the grain size ASTM No. 9 - 10 annealed at 20.2°C/s. The general conclusions that could be made from the inverse pole figures were similar to those alreadypresented in this section. Of particular interest are the following observations as relatedto the densities of {111}, {001} and {110} planes that are parallel to the rolling plane(the indicated density values are approximate since they were read from contour plots):• The density of { 111 } planes remained approximately the same at 2.5 times randomafter cold rolling the hot band. The density of {001} planes on the other hand,increased from less than 0.8 times random to 2 times random, while the numberof {110} planes decreased slightly from 1.3 times random to less than 0.8 timesrandom.• For the specimens annealed at 20.2°C/s, the density of {l11} planes increasedsteadily from 2.5 times random for the cold rolled to 8 times random for the annealed during the progress of recrystallization and grain growth. The densities of{ O01} planes decreased in a similar manner from 2 times random to less than 0.8Chapter 6. Characterization of Annealing Textures 232times random during annealing.Among the three different heating rates that were employed to produce fully recrystallized specimens (grain size of ASTM No. 9 - 10), 1.88°C/s yielded thehighest density for {111} planes (8 times random) and the lowest density for {001}planes (less than 0.8 times random). The other two heating rates resulted in approximately the same density of {111} planes (6.4 times random) although thespecimen heated at 0.025°C/s had a relatively higher number of {001} planes (1times random against less than 0.8 times random corresponding to 20.2°C/s).• The densities of {110} planes were always below 0.8 times random, except for thehot band, where it was 1.3 times random.Finally, the anisotropic flow properties, in particular the strain ratio, r, was predictedby incorporating the measured texture in the form of ODF into the Taylor model of poiycrystal deformation [161, 165]. The Taylor factor (or M-factor) calculations were carriedout for simple tensile deformation by assuming glide along (110)[111j and (112)[111] slipsystems. The r values were predicted for the a values of 0, 15, 30, 45, 60, 75 and 90°,where a is the angle between the rolling direction of the sheet and the tensile loadingdirection of the test specimen. Fig. 6.19, a plot of r vs. a, for specimens annealed at20.2°C/s, illustrates the development of plastic anisotropy from the cold rolled textureduring the progress of recrystallization 15, 40, 80 and 100 % recrystallized) and graingrowth (ASTM No. 9 - 10 to ASTM No. 8). The plot corresponding to the 40 %recrystallized microstructure indicates the transition between the cold rolled and the recrystallized states. The r values corresponding to 0, 45 and 90° were also used to estimatethe average properties, f and r, based on Eqs. 2.46 and 2.47. Table 6.2 summarisesthe predicted r values at a = 0, 45 and 90° and the calculated averages i and r for allnine test specimens.Chapter 6. Characterization of Annealing Textures 233The strain ratio (r) values were not experimentally determined during the present investigation. However, some of the plant trial information obtained from ‘Stelco’ regardingI-F steel annealing cycles and mechanical properties is used for validation purposes. Thereported values for the 80 % cold rolled I-F steel subjected to various annealing cycleswere within the range of 1.6 to 1.8. The measured steel temperatures during a typicalcontinuous annealing cycle indicated a heating rate of 46.6°C/s up to the peak temperature of 845°C, a hold of 16s at the peak temperature and final cooling at the rate of7.4°C/s. The I-F steel subjected to this annealing cycle resulted in a microstructure withan average grain size of 25.5 jim and a value of 1.69. For another case with a fairlysimilar temperature profile, the measured properties were an average grain size of 15.1jim and a value of 1.68. These values are in good agreement with the predicted valuesin the present study. In particular, the values of 1.58 for the grain size of ASTM No.9 - 10 (m.l.i. of 12 jim) and 1.71 for the grain size of ASTM No. 8 (m.l.i. of 20 jim)predicted for the specimens annealed at 20.2°C/s agree well with the measured values.Such a comparison is appropriate since the effect of heating rate (thermal history) on thefinal annealing texture has been shown to be relatively minor (see Figs. 6.16 and 6.17).A near random texture with relatively strong {100} < 011 > component is usuallyobserved for the hot-rolled strips of Al-killed and other low-carbon steels, finish-rolled attemperatures of 950° C [172, 239, 240]. This is primarily a consequence of the austeniteto ferrite transformation from a completely recrystallized austenite. Ti/Nb-stabilizedand other microalloyed low-carbon steels, however, develop moderately strong hot bandtextures [172, 239, 240, 241]. These textures are attributed to the retarding effects of thealloying elements on austenite recrystallization, and the consequent transformation of thehighly textured austenite into ferrite. The major components of the deformation textureof austenite are {110} < 112 > and {112} < 111 > which give rise, respectively, to{332} < 113 > and {113} < 110 > orientations in ferrite. The recrystallization textureChapter 6. Characterization of Annealing Textures 234of austenite, {100} < 001 >, is similarly transformed into {100} < 011 > in ferrite[164]. The hot band textures observed in the present study (see Figs. 6.11 and 6.12), inparticular (112)[1I0] (i.e., near (113)[1I0]) in the a-fibre and (221)[114] (6° away from(332)[113]) in the i-fibre, indicate that the origin of the hot band texture was deformedaustenite. These observations and the presence of the moderately strong complete 7-fibre, are consistent with most of the hot band textures reported from similar studies onI-F steels [164, 172, 239, 240, 241].The cold rolled texture obtained in this study consists of a strongly developed partiala-fibre between (001)[1I0] and (112)[1IO] as indicated in Fig. 6.11 (a). In addition,there is also a slight improvement in the 7-fibre components, as can be seen from Fig.6.11 (b) and Table 6.1. The strongest components of the partial a-fibre appear closerto (112)[1i0] (or near (114)[1I0]) rather than near (111)[1I0] (volume fractions shownin Table 6.1 indicate this clearly). This observation indicates that cold rolling reinforcesthe already existing components near (112)[1I0]. It should be noted that {112} < 110 >and {001} < 110 > have been shown to be relatively stable end orientations for {110} <111 >-type glide [240]. While this observation agrees well with other studies on I-F steels[239, 241, 242], this is considerably different from most of the studies on Al-killed andother unalloyed low-carbon steels, where high texture intensities were observed between(112)[1I0] and (111)[1I0], and (111)[1I0] was often found to be the strongest component[172, 239, 240, 241, 242]. Although such differences are primarily due to the strong(112)[1I0] of the I-F steel hot band, another factor that may be important in this regardis the hot band grain size.The effect of hot band grain size on cold rolled texture development, though not investigated in depth, has been demonstrated in a few studies [170, 172, 242]. A comparitivestudy conducted by Bleck et al. [172] on Al-killed steels with two different hot band grainsizes (obtained from different areas of the same strip) indicated that the hot band textureChapter 6. Characterization of Annealing Textures 235of the coarse grain size material was relatively stronger; after about 90 % cold rolling, thecoarse grain hot band (when compared to the fine grain one) resulted in a texture whichconstitutes a relatively stronger partial a-fibre (about 2 times stronger for (114)[1i0]),and a considerably weaker7-fibre (half as strong). The hot band grain size of the presentsteel (ASTM No. 7- 8) is larger than that corresponding to reported studies (for example,hot band grain size of ASTM No. 9 in the study by Schlippenbach and Lucke [170]), andconsequently this difference might have been another contributory factor for the observedstrong a-fibre, particularly for the strong components near (114)[1I0]. More importantly,the grain size effect is the most probable explanation for the presently observed smallincrease in the7-fibre components [170, 172]. It appears that when the components near(112)[1I0] in the hot band are particularly strong, whether caused by a coarse grain sizeor not, the a-fibre, in particular the components near (112)[1i0J and (114)[1i0], stronglydevelop during cold rolling often at the expense of the development of the 7-fibre.Recrystallization texture developments shown in Figs. 6.13 and 6.14 are typical of anylow-carbon ferritic steels [22, 23, 156, 170, 171, 172, 239, 240, 241]. The rolling textureexhibiting high orientation densities along the a-fibre, in particular the strong components stretching from (001)[iIOj to (112)[1I0], continuously decrease to near randomlevel during recrystallization. On the other hand, the recrystallization texture, typicallycharacterized by the orientation of the 7-fibre, especially the (111)[iIo] and (111)[112]components increase throughout recrystallization. The development of the 7-fibre during recrystallization is explained by oriented nucleation of the { 111 }-orientations causedby the relatively higher internal stored energy of the {111}-oriented cold rolled grains[23, 78]. The high strength of the (111)[112] component of the recrystallized texture isalso attributed to oriented growth from the strong (112) [110] component of the cold rolledmatrix, and such growth is because of the favourable orientation relationship betweenthese two components (35° around the < 110 > transverse direction which is close to theChapter 6. Characterization of Annealing Textures 236ideal orientation relationship of 27° < 110 > found for high growth rates) [170, 171, 240].The textural changes indicated by a and 7-fibres in Fig. 6.13 occur in a progressive manner throughout recrystallization, and such an observation can be understood interms of the steady consumption of the cold rolled matrix by differently oriented nuclei. In particular, the a and -y fibres corresponding to the 15 and 40 % recrystallizedspecimens indicate the magnitude of the change to be significant during the early stagesof recrystallization. This observation seems to disagree with two other studies on low-carbon steels where the changes in the texture during the early stages of recrystallizationwas relatively small [170, 171]. In both of those studies, the 7-fibre, and in particular the(111)[1I0] component, was considerably strong (about 4 to 8 times random) before thecommencement of recrystallization, and the overall changes in the -fibre componentsduring recrystallization were small (an increase of about 50 % or less). In the presentstudy, however, all of the -fibre components increased by a magnitude of about 3 to 4times during recrystallization. In particular, the cold rolled -fibre was relatively weakand consequently all of the new grains with { 111 }-orientation would have contributedto a significant change in texture. In addition, the microstructural observations of thepresent study indicated that the initial nucleation preferentially occurred along grainboundaries. Such nuclei and their consequent growth into the differently oriented adjacent grains probably explains the observed significant changes in (111)[1I0] (increase)and (001)[1I0] (decrease) during the early stages of recrystallization.Another noticeable observation in the a-fibre corresponding to the 15 % recrystallizedspecimen (see Fig. 6.13 (a)) is the apparant strengthening of the (112)[1I0] componentduring the early stages of recrystallization. Such an increase can also be seen from thevolume fractions indicated in Table 6.1. A similar increase in the (112)[1I0] component during the early stages of recrystallization was also reported by other researchers[170, 171]. Those researchers suggested a strain-induced boundary migration nucleationChapter 6. Characterization of Annealing Textures 237process favouring the lower energy orientations such as (112)[1I0] as a possible explanation. While such a factor may also explain the present observations, a thorough studywill be required to clarify the matter further.The e-fibre shown in Fig. 6.14 (a) indicates the strong development of the spreadaround (111)[112] during recrystallization. These components are usually enhanced byoriented growth (in addition to the initial oriented nucleation), as explained previously[170, 171, 240]. In I-F and other microalloyed steels, because of the strong presence ofthe (112)[1IO] in the cold rolled steels, the spread around (111)[112] is usually strongerthan the spread around (111)[1I0] [239, 240, 241]. It should be noted that in the case ofAl-killed and other low-carbon steels, (111)[1I0] is often the strongest component of theannealing texture [172, 239, 241]. In addition, the spread was reported to be centeredon (554)[5] rather than (111)[112j, due to a more matching growth relationship of theformer [22, 23, 189, 196, 239]. The present observations indicate (554)[5] to be thestrongest component after about 40 % recrystallization, i.e., after growth has becomedominant. Such observations are consistent with other reported texture studies on I-Fsteels [22, 23, 196, 239, 241].The C-fibre components, shown in Fig. 6.15, undergo very small changes duringrecrystallization. Additionally, the normal direction inverse pole figures indicated thedensity of {110} planes to be less than 0.8 times random throughout recrystallization.Such observations are consistant with most of the annealing studies on I-F steels (seefor example, Fig. 2.4). These observations provide supporting evidence for using the{220} peak resolution, particularly the corresponding valley intensity, in characterizingthe kinetics of recrystallization, as conducted in the present study.The elimination of the partial a-fibre and the development of the y-fibre continuedduring grain growth after the completion of recrystallization. In particular, the 7-fibreexhibited a significant increase during grain growth (ASTM No. 9 - 10 to ASTM No 8).Chapter 6. Characterization of Annealing Textures 238Obviously the grains with {111} orientation have grown selectively at the expense of thedifferently oriented grains. Similar observations have been reported previously based ontexture studies on low-carbon and I-F steels [22, 23, 79, 171].The development of plastic anisotropy (r-value) as related to the texture evolutionduring recrystallization is shown in Table 6.2 and Fig. 6.19. It is important to notethat these r-values were not determined experimentally; they were calculated from themeasured textures. Fig. 6.19 clearly illustrates the change in the nature of the r vs. a (ais the angle to the rolling direction) relationship during the progress of recrystallization.The cold rolled and the 15 % recrystallized specimens exhibit high r45 values, but thevalues for r0 and r90 were relatively low. The recrystallized specimens, i.e., the onescorresponding to 80 and 100 % recrystallized microstructures and the one with additionalgrain growth, exhibit high r values in general, although the values for r45 were relativelylower. The specimen corresponding to 40 % recrystallization illustrates the transitionfrom the cold rolled to recrystallized texture. Theoretical calculations for single b.c.c.crystals based on the assumption of pencil glide slip in < 111 > directions have indicated rto be a strong function of a, depending on the orientation of the crystal [2]. In particular,those calculations showed that the values of r0, r45 and r90 were approximately 0, 1 and0 for (001)[1i0] orientation, 0.6, c, and 2 for (112)[1IO] orientation, and 2, 2.5 and 3 for(111)[1I0] orientation [22, 180]. These theoretical values in conjunction with the texturedata indicating the changes in the dominant orientations from (001)[1I0] and (112)[1i0]to (111)[1I0] and (554)[5] as recrystallization progresses, explain the observed changesin r vs. a shown in Fig. 6.19. The present observations agree reasonably well with theexperimental r vs. a data, reported for an Al-killed steel with a similar value ( =1.69) as in the present study [239].Previous studies on low-carbon steels have shown that high average strain ratio ()values were related to textures with strong {111} (7-fibre) and weak {001} (i9-fibre)Chapter 6. Characterization of Annealing Textures 239components [2, 22, 23, 163]. In particular, the ratios of the strengths of the {111} to{ 001} components have been shown to correlate well with the measured f values (see Fig.2.27) [163]. In the present study, f-values increased progressively during recrystallization,as shown in Table 6.2. This observation can be understood in terms of the continuouschanges in the-y (an increase, as shown in Fig. 6.13 (b)) and ‘9 (a decrease, as shown inFig. 6.14 (b)) fibres. An increasing density of {111} planes and a decreasing density of{001} planes (see for example Fig. 6.18), as indicated by the normal direction inverse polefigures, provide additional illustration of the textural changes that explain the increasingf-values. The same f-value obtained for the 15 and 40 % recrystallized specimens are dueto the averaging procedure. The r vs. a profiles shown in Fig. 6.19 clearly illustrate thedifferences between these two specimens, reflective of their respective textures (It shouldalso be noted that the z\r values corresponding to these two specimens are considerablydifferent). Grain growth following recrystallization (ASTM No. 9 - 10 to ASTM No. 8)has resulted in an increase in f value from 1.58 to 1.71. Such results have been reportedfor low-carbon steels [22, 23, 156], and can be understood in terms of the continuingchanges in the -y and 9 fibres during grain growth.The effect of heating rate on recrystallization texture is presented in terms of themajor fibres in Figs. 6.16 and 6.17; the resultant f-values could be found in Table 6.2.These results indicate that heating rate has very little effect on texture development andthe associated f-values. This is in agreement with other studies on I-F steels (see forexample Fig 2.29) [22, 23, 156, 172, 239]. In practice, an important advantage of I-Fsteels is due to the fact that the formation of the favourable recrystallization texturesdoes not depend on the heating rate and is not impaired by very short annealing times.The heating rates of 20.2, 1.88 and 0.025°C/s yielded f-values of 1.58, 1.71 and 1.50 inthat order, all specimens have the same grain size of ASTM No. 9 - 10. The higher f-valueobtained at 1.88°C/s can be attributed to the relatively strong presence of the -y-fibreChapter 6. Characterization of Annealing Textures 240(see Fig. 6.16 (b)). This is probably due to the slightly larger grain size observed in thiscase, although it was still within the range of ASTM No. 9 - 10. On the other hand, thelower i-value obtained at 0.025°C/s can be attributed to the relatively strong remnantsof the t9-fibre at 0.025°C/s (see Fig. 6.17 (b)). This is possibly due to some extremelysmall unrecrystallized areas that were not visible in the optical microscope. The normaldirection inverse pole figures also indicated the highest density of favourable { 111 } planesfor 1.88°C/s, whereas 0.025°C/s resulted in the highest density of unfavourable {001}planes. A relationship seems to exist between the intensity of (554)[25] and the heatingrate. Fig. 6.17 (a) shows that the intensity of (554)[5] increases steadily with adecreasing heating rate; the volume percentages shown in Table 6.1 also indicate thevalidity of this relationship. It should be noted that among all the fully recrystallizedspecimens, 0.025°C/s has resulted in the highest volume percentage of (554)[5] (23.4%) despite the fact that it also yielded the lowest volume percentage for (111)[1I0] (17.7%). These observations suggest that a lower heating rate or a longer annealing time ismarginally favourable in terms of the development of (554)[5], a texture componentwhich preferentially develops due to oriented growth.The values obtained in this study, i.e., the calculated ones in the range of 1.5 to 1.7or the measured ones in the range of 1.6 to 1.8, are relatively lower than the values of2, often reported for I-F steels [2, 22, 23, 196, 198, 239]. Although there can be severalreasons for such differences, the strong presence of (114)[1I0] in the annealed texture ispossibly one of them. This texture component, together with (001)[1I0], strongly developed during cold rolling. However, unlike (001)[1I0], considerable amounts of (114)[1i0jremained in the annealed texture (about 3 to 4 times in terms of the volume fraction, asshown in Table 6.1). The presence of both {001} and {114} components have been reported to be very deleterious to attaining high values [23]. Some past studies [172, 242]indicated coarse hot band grain size as a probable cause for the strong development ofChapter 6. Characterization of Annealing Textures 241(114)[1I0]. Such an observation is consistent with the present study with its relativelycoarse grain (ASTM No. 7 - 8) hot band.The relatively low values obtained in this study are also a result of the steel chemistryand other high temperature processing conditions. Previous calculations regarding excessTi (TiEx) and Nb (NbEX) in solid solution showed that 0.02 > TiEx > 0.01 and NbEx0.02. In addition, the present I-F steel has solid-solution strengthening elements of 0.011wt % P and 0.140 wt % Mn. There is no definite conclusion regarding the effects ofexcess Ti and/or Nb on ? values [7, 9, 15, 16, 149, 150, 204, 239]. The adverse effectof P on values is minimal [9, 20, 149, 204, 207, 208]. However, Mn in solid-solution isreported to significantly decrease values [20, 55, 204, 205, 206, 207], and hence anotherpossible explanation for the presently observed low values. The available informationregarding the preparation of I-F steel hot band indicates the use of a finishing deliverytemperature of around 890°C and a coiling temperature of less than 600°C. While thefinish rolling temperature is almost the same as the recommended temperature of slightlyabove Ar3, the coiling temperature is considerably lower than the suggested 700 to 800°Cto produce coarse precipitates [15, 16, 195, 202, 204, 209, 210, 211]. The microstructuralobservations obtained in this study also indicated the presence of fine-scale precipitates,and such precipitates retard the growth of {111}-oriented grains, resulting in reducedvalues.In summary, the evolution of crystallographic texture during cold rolling and annealing were characterized. Grain growth following recrystallization was shown to resultin a stronger/sharper texture. The effect of heating rate on the final recrystallizationtexture was determined to be insignificant. The measured textures were correlated toplastic anisotropy using the Taylor model of polycrystal deformation, and the resultingaverage strain ratio values were analysed in terms of the steel chemistry and processingconditions.Chapter 6. Characterization of Annealing Textures 242Table 6.1: Volume percentages of important texture components calculated from theODF data obtained for the hot band, the cold rolled sheet and annealed specimensProcessing/Microstructure Texture Components (vol. %)(001)[1I0J (112)[1i0] (114)[1I0]I(111)[1I0j (554)[5]Hot Band (ASTM No. 7-8) 2.4 12.6 12.1 11.2 11.0Cold Rolled (80 %) 10.1 15.5 27.3 11.6 11.220.2°C/s- 15 % recryst. 6.9 19.6 25.3 16.1 13.620.2°C/s- 40 % recryst. 6.0 14.3 18.9 16.9 17.720.2°C/s- 80 % recryst. 4.0 12.0 13.5 18.2 19.920.2°C/s- 100 % recryst. 3.1 12.4 11.7 20.1 20.2(ASTM No. 9-10)20.2°C/s - Grain Growth 3.0 12.5 10.4 22.8 23.1(ASTM_No._8)1.88°C/s- 100 % recryst. 3.0 12.4 10.7 20.7 22.9(ASTM No. 9-10)0.025°C/s- 100 % recryst. 3.7 13.0 13.1 17.7 23.4(ASTM_No._9-10)Chapter 6. Characterization of Annealing Textures 243Table 6.2: A summary of r at a = 0, 45 and 90°, and Ar predicted from the ODF dataobtained for the hot band, the cold rolled sheet and annealed specimensProcessing/Microstructure Predicted r values j Calculated Averagesa=00]a=450 a=90°ll ArHot Band (ASTM No. 7-8) 1.02 1.64 1.38 1.42 -0.44Cold Rolled (80 %) 0.49 1.19 0.84 0.92 -0.5220.2°C/s - 15 % recryst. 0.79 1.78 0.99 1.33 -0.8920.2°C/s - 40 % recryst. 1.24 1.39 1.30 1.33 -0.1220.2°C/s- 80 % recryst. 1.75 1.27 1.67 1.49 0.4420.2°C/s- 100 % recryst. 1.84 1.36 1.77 1.58 0.44(ASTM No. 9-10)20.2°C/s - Grain Growth 1.91 1.52 1.90 1.71 0.39(ASTM_No._8)1.88°C/s- 100 % recryst. 1.91 1.50 1.94 1.71 0.43(ASTM No. 9-10)0.025°C/s- 100 % recryst. 1.52 1.38 1.72 1.50 0.24(ASTM_No._9-10)Chapter 6. Characterization of Annealing Textures 2441.0 1.3 1.62.5 3.2 4.0 6,4.8 LO2.5 3.2L3 1.6 2.J4.0 . 6.4Figure 6.1: (a) Experimental and (b) recalculated (110) pole figures obtained for the 80% cold rolled I-F steel specimen.3(a)(b)Chapter 6. Characterization of Annealing Textures 245D UBC AS REC. (NEW?0 55/180/2.7/N EF& PAGE 180 1.00 1.30 1.60 200 2.50 3.20 4.00 9.00 640Figure 6.2: ODFs calculated for the I-F steel hot band (with the grain size of ASTMNo. 7 - 8) presented at constant ço sections; 2 = 450 section of the Euler space is alsoshown.Chapter 6. Characterization of Annealing Textures 246Figure 6.3: ODFs calculated for the 80 % cold rolled sheet presentedsections; Cp2 = 450 section of the Euler space is also shown.at constant Pi3ubc cold rolled 2mm osc 55/i80/2.&EF& PAGE 11 30 j 60 2 00 2 3 20 4 00 5 00 8 000 90 0 90 0 90 0 90uu- 1L57:cfI5:?f‘r \\5,/ • ‘, / 4’-, /--,-— I--— ,.—PHI—O—. PHIl— 5—. PHIl— 10- PHIl— 2590 PHIl 20 PHi — 25 PHIl— 30 PHIl 3500.--.‘-. . -----.b . a? - c22ZLZPHIl — 40 PHIl 45 PHIl . 50 PHIl 5500-PHIl — 60 PHIl 65 PHIl— 70 PHIl 7500.9( “—----.---PHIl— 80 PHIl — 85 PHIl — 90 PHI2 • 45Chapter 6. Characterization of Annealing Textures 247S USC 20.2C/S 670 C 2 MM OSC. 55/ISEFS PAGE 100 1.30 1.60 2.00 2 50 3.20 4.00 5.00 6.40 8.00Figure 6.4: ODFs showing constant y sections for the specimen quenched from 670°Cafter being heated at 20.2°C/s (‘-S.’ 15 % recrystallized); Y2 = 45° section of the Eulerspace is also shown.Chapter 6. Characterization of Annealing Textures 248PAGE4,00 500I6.40Figure 6.5: ODFs showing constant 1 sections for the specimen quenched from 720°Cafter being heated at 20.2°C/s (‘—‘ 40 % recrystallized); Y2 = 45° section of the Eulerspace is also shown.A UBC 20.2 c/s 720 C 2mm OSC. 55/IEF&.Ei0 1.00 1.30 1.60 2 0 2,50 3.20Chapter 6. Characterization of Annealing Textures 2494 UBC 20.2 c/s 760C 2mm QSC. 55/18&EF& PAGE 160 1.00 1.30 1.60 2.50 3.20 4.00 5 00 6.40Figure 6.6: ODFs showing constant y sections for the specimen quenched from 760°Cafter being heated at 20.2°C/s (‘-i 80 % recrystallized); 2 = section of the Eulerspace is also shown.Chapter 6. Characterization of Annealing Textures 250i UBC 20.2/800C 2mm osc. 55/180/2.&EF PAGEL30 160 200 3.20 4.00 5.00I8.00Figure 6.7: ODFs showing constant co sections for the specimen quenched from 800°Cafter being heated at 20.2°C/s (fully recrystallized with the grain size of ASTM No. 9 -10); c02 = 45° section of the Euler space is also shown.Chapter 6. Characterization of Annealing Textures 251Iz•:: : EdiE° PHIl— 0 PHIl — 5 PHIl— 10 PHIl — 15 -°°Thr(h.hHh49° PHIl — 20 PHIl— 25 PHIl— 30 PHIl — 35:PHIl 40 PHIl 45 PHIl — 50 PHIl 55or“-‘.wj*:a.90 PHIl — 60 PHIl 65 PHIl 70 PHIl 7500 \, \/ ‘90 PHI1 80 PHIl 85 PHIl— 90 PHI2 45Figure 6.8: ODFs showing constant y sections for the specimen quenched from 900°Cafter being heated at 20.2°C/s (fully recrystallized with the grain size of ASTM No. 8);= 45° section of the Euler space is also shown.0C UBC 20.2 c/s ooc 2MM OSC. 55/18EF PAGE1.00 140 2.00 :*B 4.00 56O 8.000 go oo 900 90252Chapter 6. Characterization of Annealing Textures7 UBC L88c/s 770C 2mm osc. 55/180EFLOO 1.30 1.60 2.00 25O 3.20 4.00PAGE 15.00 .4fl 8,00Figure 6.9: ODFs showing constant oj sections for the specimen quenched from 770°Cafter being heated at 1.88°C/s (fully recrystallized with the grain size of ASTM No. 9 -10); p2 45° section of the Euler space is also shown.Chapter 6. Characterization of Annealing Textures 2532 UBC 00248 700c 2mm osc. 55/180/&EF PAGE 1io 1.00 1,40 200 2e 4.00 5.60 8.00 ic 16.0Figure 6.10: ODFs showing constant y sections for the specimen quenched from 700°Cafter being heated at 0.025°C/s (fully recrystallized with the grain size of ASTM No. 910); P2 = 45° section of the Euler space is also shown.Chapter 6. Characterization of Annealing Textures 254Cc’-)0(a)bi>CC00Figure 6.11: Orientation density along the (a) a and (b)-y fibres for the as-received hotband and the 80 % cold rolled I-F steel specimens.d (degrees)40p1 (degrees)(b)tOCl)l)CCO0CO>-Cl)Cci0Chapter 6. Characterization of Annealing Textures 255(001)11101 (112)1111] (111)[112] (221)1114] (110)1001112Ti0>IiTD• Hot Band10+ Cold Rolled(degrees)(a)( 20 400 20 40 60 80(degrees)(b)Figure 6.12: Orientation density along the (a) e and (b) t9 fibres for the as-received hotband and the 80 % cold rolled I-F steel specimens.Chapter 6. Characterization of Annealing Textures 256>-‘C,)V0C)jV10(a)(111)11101 (II 1){ll] (111)[0l] (II l)[112112-8-0o0 2b 4b 6 8b(degrees)(b)Figure 6.13: Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolled specimensannealed at 20.2°C/s; the results are presented as orientation density along the (a) a and(b) y fibres.40d (degrees)<ill> IIND• Cold Rolled 40% Recryst. X 100% Recryst.+ 15 % Recryst. 80% Recryst. V Grain Growth-Chapter 6. Characterization of Annealing Textures 257>C0(a)CI).a)CCC0)0(b)Figure 6.14: Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolled specimensannealed at 20.2°C/s; the results are presented as orientation density along the (a) e and(b) 9 fibres.0 20 40 60 80(degrees)0 20 40 60 80q (degrees)Chapter 6. Characterization of Annealing Textures 258b1>(IDFigure 6.15: Development of annealing texture during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolled specimensannealed at 20.2°C/s; the results are presented as orientation density along the C-fibre.(ll0)[l 10] (112(1 10)[00l]<110>11 MD• Cold Rolled+ 15 % Recryst.c 40 % Recryst.80 % Recryst.X 100 % Recryst.V Grain Growtho 20 40 60 80(1 (degrees)Chapter 6. Characterization of Annealing Textures 259>C,)a)Ca)0(a)4->-JC’)Ca)C04—,Ca)0(b)Figure 6.16: Effect of heating rate on the annealing texture of fully recrystallized specimens with the grain size of ASTM No. 9 - 10; the results are presented as orientationdensity along the (a) a and (b) -y fibres.0 20 40 60 80(degrees)40c’1 (degrees)Chapter 6. Characterization of Annealing Textures40(degrees)(a)(OOl)[120J260be>-‘000(OO1)(IiO] (OOflfiiO]12 -____________<001> II ND- (recrystallized)10 -• 20.2°C/sbe- + 1.88 C/s0 0.025 °CIs> 8-(ID0ii)60001(degrees)(b)Figure 6.17: Effect of heating rate on the annealing texture of fully recrystallized specimens with the grain size of ASTM No. 9 - 10; the results are presented as orientationdensity along the (a) E and (b) 9 fibres.(OO1)[OiO] (OOI)[120]Chapter 6. Characterization of Annealing Textures 2611.0 1.3 1.62.5 3.2 4.0 6.41.0 1.32.5 3.2 4.0‘p1.65,: 6.4100(a)001 010100(b)Figure 6.18: Normal direction inverse pole figures calculated from the ODFs corresponding to (a) the 80 % cold rolled steel and (b) the fully recrystallized specimen with thegrain size of ASTM No. 9 - 10, annealed at 20.2°C/s.Chapter 6. Characterization of Annealing TexturesC.—I’Cl)26221.61.20.80.4Taylor/ODFPredictionsCold Rolled15 % Recryst.40 % Recryst.80 % Reciyst.100 % Reciyst.Grain Growth0 15 30 60 7545 90a (degrees)Figure 6.19: Development of plastic anisotropy during the progress of recrystallizationand grain growth (ASTM No. 9 - 10 to ASTM No. 8) for the cold rolled specimensannealed at 20.2°C/s; the results are presented as r (predicted) vs. (degrees).Chapter 7ConclusionsThe kinetics of the recovery and recrystallization processes operating during isothermal(500 to 760°C) and continuous (0.025, 1.88 and 20.2°C/s) heating annealing of a 80 %cold rolled, Ti-stabilized, Interstitial-Free steel were successfully characterized using the{ 220} x-ray peak resolution. While the x-ray ratio, R1, was used to monitor the recoveryprocess, the measurements of both the x-ray ratio, R1, and the valley intensity, ‘M, havebeen shown to lead to an identical kinetic analysis during recrystallization, as validatedusing quantitative metallography. An iterative procedure was adopted to separate thediffraction effects associated with the concurrent recovery and recrystallization processes.The concurrent recovery effects were found to be significant only during the early stagesof recrystallization.The isothermal recovery kinetics could be reasonably described using a semi-empiricallogarithmic equation. The kinetic characterization indicated that the apparent activationenergy for recovery, QR, increased from 173.1 kJ/mole at R1 = 0.6 (0 % recovery of Ri)to 312.1 kJ/mole at R1 = 0.15 (100 % recovery of R1). The I-F steel was also observed toundergo a considerable amount of recovery prior to recrystallization; recovery processescontributed to approximately 50 to 60 % of the total peak resolution.The isothermal recrystallization kinetics were adequately described using the JMAKequation with a time-exponent of n = 0.73 and the S-F equation with a time-exponentm = 1.17. The JMAK equation was found to be more suitable during the early stages ofrecrystallization (< 50 % recrystallized), whereas the S-F equation provided a better fit263Chapter 7. Conclusions 264during the later stages (> 70 % recrystallized). The JMAK- based kinetic characterizationyielded an apparent recrystallization activation energy, QR, of 501.7 kJ/mole, indicatinga severe retardation of recrystallization in I-F steels.A relatively novel approach involving the microstructural path concept was successfully applied to model the microstructural and kinetic aspects of recrystallization. Following this method, the isothermal recrystallization kinetics were characterized by theexperimentally determined microstructural path function, independent of the thermalpath, and an empirical kinetic function describing the interface-averaged growth rate,C, in terms of the growth-rate time-exponent na —0.58. The microstructural pathapproach being free from any assumption ragarding the nucleation and growth conditionsand being related to the evolution of microstructure, can be effectively used in modellingrecrystallization and should be preferred over the conventional JMAK/S-F approach.The isothermal recovery kinetics as described by the logarithmic equation and theisothermal recrystallization kinetics as characterized by the JMAK or the S-F or theempirical interface-averaged growth rate equations, have been successfully used in conjunction with the principle of additivity to describe continuous heating recovery and recrystallization kinetics at heating rates simulating both batch and continuous annealingprocessing. The Scheil additivity equation was found to overestimate the incubation timeduring continuous heating processes. Despite the longer Scheil-predicted start times, theadditivity procedure resulted in good kinetic predictions, particularly towards the laterpart of recrystallization after ‘- 30 % recrystallized.Microstructural observations during recrystallization, as obtained by quantitative optical metallography, indicated that the recrystallization event was heterogeneous. Preferential nucleation initiated at cold rolled grain boundaries and grain intersections. Thenucleation and growth of recrystallized grains were observed to be rapid in some deformed grains, and not in others. Most of the nuclei formed during the early stages ofChapter 7. Conclusions 265recrystallization, consistent with early site saturation.TEM examination of cold rolled and partially annealed specimens revealed that theheterogeneous cell structure developed during cold rolling. Well-defined subgrain formation occurred during the early stages of recovery. Recrystallized nuclei developed bysubgrain coalescence and the growth of recrystallized grains into the cold rolled matrixoccurred by the migration of high misorientation boundaries. SEM/EDX/WDX analysisrevealed that large precipitates of TiN and TiS ( 0.7 tm) acted as preferred nucleationsites and fine (0.1 to 0.3 tm) precipitates of TiS and possibly Ti4C2S were observed toimpede the boundary mobility.The crystallographic texture analysis by means of orientation distribution functionsindicated the presence of a weak partial a-fibre texture centered near (112)[1TO} in theI-F steel hot band. Cold rolling reinforced the hot band texture, resulting in a highlydeveloped partial a-fibre texture, extending from (001)[1I0] to (112)[1I0], with the highest intensity in the vicinity of (114)[1I0]. The progressive elimination of the cold rolledpartial a-fibre and the concomitant development of a strong7-fibre occurred during recrystallization. In particular, the texture of the fully recrystallized steel was characterizedby the presence of strong (554)[25] and (111)[1I0] components. Grain growth followingrecrystallization (ASTM No. 9 - 10 to ASTM No. 8) resulted in a strongly developed 7-fibre, with a corresponding increase in the Taylor predicted f value from 1.58 to 1.71. Nosignificant texture differences were found between the recrystallized specimens producedat heating rates simulating batch and continuous annealing.Bibliography[1] Leslie, W.C., The Physical Metallurgy of Steels, McGraw-Hill Book Co., New York,(1981), 1-67, 142-188.[2] Blickwede, D.J., Sheet Steel - Micrometallurgy by the Millions, Trans. ASM, vol.61, (1968), 653-679.[3] Elias, J.A., and Hook, R.E., Interstitial-Free Steels, in Proceedings of the 13thMechanical Working and Steel Processing Conference, ISS-AIME PubI., (1971),348-368.[4] Fekete, J.R., Strugala, D.C., and Yao, Z., Advanced Sheet Steels for AutomotiveApplications, JOM, vol. 44, (1992), 17-21.[5] Obara, T., Satoh, S., Nishida, M., and Irie, T., Control of Steel Chemistry forProducing Deep Drawing Cold Rolled Steel Sheets by Continuous Annealing, Scandinavian Journal of Metallurgy, vol. 13, (1984), 201-213.[6] Krauss, G., Wilshynsky, D.O., and Matlock, D.K., Processing and Properties ofInterstitial-Free Steels, in Interstitial-Free Steel Sheet Processing, Fabricationand Properties, Ed. Collins, L.E., and Baragar, D.L., CIM Publ., (1991), 1-14.[7J Takechi, H., Metallurgical Aspects on Interstitial Free Sheet Steel from IndustrialViewpoints, ISIJ International, vol. 34, No. 1, (1994), 1-8.[8] Comstock, G.F., Titanium in Iron and Steel, John Wiley and Sons Inc., New York,(1955), 30-47, 48-55, 163-201.266Bibliography 267[9] Irie, T., Satoh, S., Yasuda, A., and Hashimoto, 0., Development of Deep Drawableand Bake Hardenable High Strength Steel Sheet by Continuous Annealing of ExtraLow Carbon Steel with Nb or Ti, and P, in Metallurgy of Continuous-AnnealedSheet Steel, Ed. Bramfitt, B.L., and Mangonon, Jr., P.L., AIME Pubi., (1982),155-171.[10] Subramanian, S.V., Prikryl, M., Ulabhaje, A., and Balasubramanian, K., ThermoKinetic Analysis of Precipitation Behaviour of Ti-Stabilized Interstitial-Free Steel,in Interstitial-Free Steel Sheet: Processing, Fabrication and Properties, Ed. Collins,L.E., and Baragar, D.L., CIM Publ., (1991), 15-38.[11] Prikryl, M., Lin, Y.P., and Subramanian, S.V., The Identification of Titanium Sulphide and Carbosuiphide in Ultra-Low Carbon Steels, Scripta Met., vol. 24, (1990),375-380.[12] Hua, M., Garcia, C.I., and DeArdo, A.J., Multi-Phase Precipitates in Interstitial-Free Steels, Scripta Met., vol. 28, (1993), 973-978.[13] Goodenow, R.H., and Butcher, J.H., Yielding and Flow Characteristics of Low-Carbon Steel between Ambient and Liquid Nitrogen Temperatures, ASME Trans.,J. Basic Eng., 91D, (1969), 603-613.[14] DeMeo, L.J., O’Reilly, I.P., and Simanovic, Z., Development of Interstitial-FreeSteels at Dofasco, in Interstitial-Free Steel Sheet : Processing, Fabrication andProperties, Ed. Collins, L.E., and Baragar, D.L., CIM Publ., (1991), 145-156.[15] Satoh, S., Obara, T., Nishida, M., Irie, T., Effects of Alloying Elements and Hot-Rolling Conditions on the Mechanical Properties of Continuous-Annealed, Extra-Low- Carbon Steel Sheet, in Technology of Continuously Annealed Cold-Rolled SheetBibliography 268Steel, Ed. Pradhan, R., TMS-AIME Pubi., (1985), 151-166.[16] Goodman, S.R., Mould, P.R., and Siple, J.C., Effect of Composition and Processingon the Recrystallization Behaviour and Tensile Properties of Continuous AnnealedTitanium-Containing Interstitial-Free Steel Sheet, in Technology of ContinuouslyAnnealed Cold-Rolled Sheet Steel, Ed. Pradhan, R., TMS-AIME Publ., (1985),167-183.[17] Hook, R.E., and Nyo, H., Recrystallization of Deep-Drawing Columbium (Nb)Treated Interstitial-Free Sheet Steels, Met. Trans. A, Vol. 6A, (1975), 1443-1451.[18] Satoh, S., Obara, T., Nishida, M., Matsuno, N., Takasaki, J., and Satoh, H.,Development of Non-Aging Cold-Rolled Steel Sheets with Deep-Drawability by aContinuous Annealing Process, Kawasaki Steel Technical Report No. 8, (1983),1-10.[19] Mould, P.R., Methods for Producing High-Strength Cold-Rolled Steel Sheet, MetalsEngineering Quarterly, vol. 15, no. 13, (1975), 22-31.[20] Hosoya, Y., Urabe, T., Tanikawa, K., Tahara, K., and Nashimoto, A., Development of Super-Formable High-Strength Interstitial-Free Sheet Steel, in Interstitial-Free Steel Sheet : Processing, Fabrication and Properties, Ed. Collins, L.E., andBaragar, D.L., CIM Publ., (1991), 107-117.[21] Goodenow, R.H., and Held, J.F., Recrystallization of Low-Carbon TitaniumStabilized Steel, Met. Trans. A, Vol. 1, (1970), 2507-2515.[22] Mishra, S., and Darmann, C., Role and Control of Texture in Deep-Drawing Steels,Tnt. Met. Reviews, Vol. 27, No. 6, (1982), 307-320.Bibliography 269[23] Hutchinson, W.B., Development and Control of Annealing Textures in Low-CarbonSteels, mt. Met. Reviews, Vol. 29, No. 1, (1984), 25-42.[24] Mould, P.R., An Overview of Continuous-Annealing Technology for Steel SheetProducts, in Metallurgy of Continuous-Annealed Sheet Steel, Ed. Bramfitt, B.L.,and Mangonon, Jr., P.L., AIME Pubi., (1982), 3-33.[25] Obara, T., Sakata, K., Nishida, M., and Irie, T., Effects of Heat Cycle and CarbonContent on the Mechanical Properties of Continuous-Annealed Low Carbon SteelSheets, Kawasaki Steel Technical Report, No. 12, (1985), 25-35.[26] Gaskey, K.M., Hoffman, V.R., and Crosby, D.T., Design and Control of Inland’sNew Continuous Annealing Line, Iron and Steel Eng., vol. 62, (1985), 15-20.[27] Fukushima, T., Recent Technological Progress in High Speed Continuous Annealing,Trans. ISIJ, vol. 25, (1985), 278-293.[28] Pradhan, R., Developments in the Annealing of Sheet Steels, JOM, vol. 44, (1992),16.[29] Byrne, J.G., Recrystallization and Grain Growth , The Macmillan Co., New York,(1965), 13-36, 37-59, 60-92.[30] Cotterill, P., and Mould, P.R., Recrystallization and Grain Growth in Metals, Surrey University Press, London, (1976), 180-249.[31] Reed-Hill, R.E., Physical Metallurgy Principles, Van Nostrand Reinhold Co., NewYork, (1973), 267-325.[32] Gordon, P., Microcalorimetric Investigation of Recrystallization of Copper, Trans.AIME, J. of Metals, vol. 203, (1955), 1043-1052.Bibliography 270[33] Vandermeer, R.A., arid Gordon, P., The Influence of Recovery on Recrystallization in Aluminum, in Recovery and Recrystallization of Metals, Ed. Himmel, L.,Interscience Pubi., New York, (1963), 211-240.[34] Haessner, F., Calorimetric Investigation of Recovery and Recrystallization Phenomena in Metals, in Thermal Analysis in Metallurgy, Ed. Shull, R.D., and Joshi,A., TMS Pubi., (1992), 233-257.[35] Venturello, C., Antonione, C., and Bonaccorso, F., Influence of Small Amounts ofCarbon on Recovery and Recrystallization of High-Purity Iron, Trans. Met. Soc.AIME, vol. 227, (1963), 1433-1439.[36] Antonione, C., Della-Gatta, G., and Venturello, G., Influence of Small Amounts ofNitrogen on Recovery and Recrystallization of High-Purity Iron, Trans. Met. Soc.AIME, vol. 230, (1964), 700-706.[37] Leslie, W.C., Plecity, F.J., and Aul, F.W., The Recrystallization of Dilute AlphaIron-Molybdenum Solid Solutions, Trans. Met. Soc. AIME, vol. 221, (1961), 982-989.[38] Leslie, W.C., Plecity, F.J., and Michalak, J.T., Recrystallization of Iron and IronManganese Alloys, Trans. Met. Soc. AIME, vol. 221, (1961), 691-700.[39] Magee, K., Mukunthan, K., and Hawbolt, E.B., The Application of IsothermalRecrystallization Kinetics to Continuous Heating Processes, in Recrystallization’90,Ed. Chandra, T., TMS PubI., (1990), 393-398.[40] Michalak, J.T., and Paxton, H.W., Some Recovery Characteristics of Zone-MeltedIron, Trans. Met. Soc. AIME, vol. 221, (1961), 850-857.Bibliography 271[41] Sah, J.P., and Sellars, C.M., Effect of Deformation History on Static Recrystallization and Restoration in Ferritic Stainless Steel, in Hot Working and FormingProcesses, Ed. Sellars, C.M., and Davies, G.J., The Metals Soc. Pubi., (1979),62-66.[42] Hilliard, J.E., and Cahn, J.W., An Evaluation of Procedures in Quantitative Metallography for Volume-Fraction Analysis, Trans. Met. Soc. AIME, vol. 221, (1961),344-352.[43] Hillard, J.E., Applications of Quantitative Metallography in Recrystallisation Studies, in Recrystallization, grain growth and Texture, Ed. Margolin, H., ASM Pubi.,(1966), 267-286.[44] Pickering, F.B., The Basis of Quantitative Metallography, Inst. of MetallurgistsPuhl., London, (1975), 1-38.[45] Takamura, J., Takashima, T., and Omana, M., Lattice Defects in Deformed Low-carbon Steels and the Annealing Stage, Trans. ISIJ, vol. 9, (1969), 216-221.[46] Abe, H., and Suzuki, T., Thermoelectric Power versus Electrical Conductivity Plotfor Annealing Process in Low-Carbon Aluminium-Killed Steel, Trans. ISIJ, vol. 19,(1979), 689-693.[47] DiCello, J.A., and Cullity, B.D., Contactless Measurement of Recovery and Recrystallization in Steel, Met. Trans., vol. 3, (1972), 2703-2704.[48] Hawbolt, E.B., In Situ Measurement of Recrystallisation Kinetics and Applicationof the Data to Recrystallization During Continuous Heating, Report for N.R.C. ofCanada, Dept. of Metallurgical Eng., University of British Columbia, (1984).Bibliography 272[49] Cullity, B.D., Elements of X-Ray Diffraction, 2nd Edition, Addison-Wesley Publishing Co., Reading, Massachusetts, (1978), 107-145, 281-323.[50] Barrett, C.S., and Massaiski, T.B., Structute of Metals, McGraw-Hill Book Co.,New York, (1966), 447-465.[51] Warren, B.E., X-Ray Studies of Deformed Metals, Prog. in Met. Phys., vol. 8,(1959), 147-202.[52) Houska, C.R., The Use of Changes in X-Ray Diffraction Line Broadening to StudyRecovery Kinetics in Pure Cobalt, in Materials Science Research - vol. 2, Ed. Otte,H. M., and Locke, S.R., Plenum Press, New York, (1965), 111-119.[53] Ru, H., Annealing of Silicon-Iron Single Crystals, in Recovery and Recrystallizationof Metals, Ed. Himmel, L., Interscience Publ., New York, (1963), 311-378.[54] Mayo, W.E., Lo, C.F., Kamide, H., and Weissmann, S., X-Ray Determination ofRecovery Kinetics in Inconel Alloy 600, Scripta Met., vol. 20, (1986), 1405-1410.[55] Hu, H., and Goodman, S.R., Effect of Manganese on the Annealing Texture andStrain. Ratio of Low-Carbon Steels, Met. Trans., vol. 1, (1970), 3057-3064.[56] Magee, K., Mukunthan, K., and Hawbolt, E.B., Measurement of Recrystallization Kinetics using X-Ray Diffraction Peak Resolution, in Recrystallization’90, Ed.Chandra, T., TMS Publ., (1990), 363-368.[57] Magee, K., The Application of the Additivity Principle to Recrystallization, M.A.Sc.Thesis, Dept. of Metallurgical Eng., University of British Columbia, (1986).[58] Ono, S., Shimomura, T., Osawa, K., and Matsudo, K., Deep Drawability and Recrystallization Texture of Rephosphorized Al-killed High Strength Cold-rolled Steel,Bibliography 273Trans. ISIJ, vol. 22, (1982), 732-738.[59] Hansen, N., Leffers, T., and Kjems, J.K., Recrystallization Kinetics in CopperInvestigated by In Situ Texture Measurements by Neutron Diffraction, Acta metal!.,vol. 29, (1981), 1523-1533.[60] Hu, H., Rath, B.B., and Vandermeer, R.A., An Historical Perspective and Overviewof the Annealing Studies of Cold Worked Metals, in Recrystallization’90, Ed. Chandra, T., TMS Pub!., (1990), 3-16.[61] Li, J.C.M., Recovery Processes in Metals, in Recrystallization, Grain Growth andTextures, Ed. Margolin, H., ASM Pubi., (1966), 45-97.[62] Kuhiman, D., Z. Physik, vol. 124, (1948), 468.[63] Vandermeer, R.A., and Rath, B.B., Interface Migration during Recrystallization:The Role of Recovery and Stored Energy Gradients, Met. Trans. A, vol. 21A, (1990),1143-1149.[64] Friedel, J., Dislocations, Pergamon Press Ltd., Oxford, (1964), 241-274.[65] Kolmogorov, A.N., Izv. Akad. Nauk. USSR. Ser. Matemat., vol. 1, (1937), 355.[66] Johnson, W.A., and MehI, R.F., Reaction Kinetics in Processes of Nucleation andGrowth, AIME Trans., vol. 135, (1939), 416-442.[67] Avrami, M., Kinetics of Phase Change, J. Chem. Phys., vol. 7, (1939), 1103-1112;vol.8, (1940), 212-224; vol. 9, (1941), 177-184.[68] Vandermeer, R.A., Modelling Microstructural Evolution During Recrystallization,Scripta Met., Vol. 27, (1992), 1563-1568.Bibliography 274[69] Christian, J.W., The Theory of Transformations in Metals and Alloys., Pergamon.Press Ltd., Oxford, (1975), 1-20, 525-548.[70] Cahn, J.W., The Kinetics of Grain Boundary Nucleated Reactions, Acta. Met., vol.4, (1956), 449-459.[71] Michalak, J.T., and Hibbard, W.R., Effect of Rolling Procedure on the Kinetics ofRecrystallization of Cold-Rolled Iron, Trans. ASM, vol. 53, (1961), 331-347.[72] Rosen, A., Burton, M.S., and Smith, G.V., Recrystallization in High Purity Iron,Trans. Met. Soc. AIME, vol. 230, (1964), 205-215.[73] Anderson, W.A., and Mehi, R.F., Recrystallization of Aluminum in terms of theRate of Nucleation and the Rate of Growth, AIME Trans., vol. 161, (1945), 140-167.[74] Reiter, S.F., Recrystallization Kinetics of Low-Carbon Steel, AIME Trans., vol. 194,(1952), 972-979.[75] Vandermeer, R.A., and Rath, B.B., Modelling Recrystallization Kinetics in a Deformed Iron Single Crystal, Met. Trans. A, vol. 20A, (1989), 391-401.[76] Vandermeer, R.A., and Rath, B.B., Microstructural Modelling of Recrystallizationin Deformed Iron Single Crystals, Met. Trans. A, vol. 20A, (1989), 1933-1942.[77] Perryman, E.C.W., Recrystallization Characteristics of Super Purity Base Al-MgAlloys Containing 0-5 % Mg, AIME Trans., vol. 203, (1955), 369-378.[78] Dillamore, I.L., Smith, C.J.E., and Watson, T.W., Oriented Nucleation in the Formation of Annealing Textures in Iron, Met. Sci., vol. 1, (1967), 49-54.[79] Hutchinson, W.B., Development of Textures in Recrystallization, Met. Sci., vol. 8,(1974), 185-196.Bibliography 275[80] Vandermeer, R.A., and Gordon, P., Edge-Nucleated, Growth Controlled Recrystallization in Aluminum, Trans. Met. Soc. AIME, vol. 215, (1959), 577-588.[81] English, A.T., and Backofen, W.A., Recrystallization in Hot- Worked Silicon-Iron,Trans. Met. Soc. AIME, vol.230, (1964), 396-407.[82] Doherty, R.D., Nucleation of Recrystallization in Single Phase and DispersionHardened Polycrystalline Materials, in Recrystallization and Grain Growth ofMulti-Phase and Particle Containing Materials, Ed. Hansen, N., Jones, A.R., andLeffers, T., RISO Publ., (1980), 57-69.[83] Nes, E., and Hutchinson, W.B., Texture and Grain Size Control During Processingof Metals, in Materials Architecture, Ed. Bilde-Sorensen, J.B., Hansen, N., JuulJensen, D., Leffers, T., Lilholt, H., and Pedersen, O.B., RISO Pubi., (1989), 233-249.[84] Vandermeer, R.A., and Masumura, R.A., The Microstructural Path of Grain-Boundary-Nucleated Phase Transformations, Acta metall., Vol. 40, (1992), 877-886.[85] DeHoff, R.T., Microstructural Evolution During Recrystallization, in AnnealingProcesses-Recovery, Recrystallization and Grain Growth, Ed. Hansen, N., JuulJensen, D., Leffers, T., and Ralph, B., RISO Publ., (1986), 35-52.[86] Cahn, R.W., Recovery and Recrystallization, in Physical Metallurgy, Ed. Cahn,R.W., and Haasen, P., Elsevier Science Pubi., Amsterdam, (1983), 1595-1671.[87] Price, C.W., Comments on Kinetic Models for Recrystallization, Scripta Met., vol.19, (1985), 669-673.[88] Doherty, R.D., Rollett, A.R., and Srolovitz, D.J., Structural Evolution DuringRecrystallization, in Annealing Processes-Recovery, Recrystallization and GrainBibliography 276Growth, Ed. Hansen, N., Juul Jensen, D., Leffers, T., and Ralph, B., RISO Pubi.,(1986), 53-67.[89] Turnbull, D., Theory of Grain Boundary Migration Rates, AIME Trans., vol. 191,(1951), 661-665.[90] Speich, G.R., and Fisher, R.M., Recrystallization of a Rapidly Heated 325 % SiliconSteel, in Recrystallization, Grain Growth and Textures, Ed. Margolin, H., ASMPubi., (1966), 563-598.[91] Furu, T., Marthinsen, K., and Nes, E., Modelling Recrystallization, Mat. Sci. andTech., vol. 6, (1990), 1093-1102.[92] Cook, M., and Richards, T.L., Observations on the Rate and Mechanism of Recrystallization in Copper, J. Inst. Met., Vol. 73, (1947), 1.[93] Daaland, 0., Diploma Thesis, The Norwegian Institute of Technology, (1989).[94] Price, C.W., Comments on the Extent of Simultaneous Recovery During Recrystallization and its Effects on Recrystallization Kinetics, Scripta Met., vol. 23, (1989),1273-1276.[95] Hutchinson, B., Jonsson, S., and Ryde, L., On The Kinetics of Recrystallization inCold Worked Metals, Scripta Met., vol. 23, (1989), 671-676.[96] Rollett, A.D., Srolovitz, D.J., Doherty, R.D., and Anderson, M.P., Computer Simulation of Recrystallization in Non-Uniformly Deformed Metals, Acta metall., vol.37, (1989), 627-639.[97] Gokhale, A.M., and DeHoff, R.T., Estimation of Nucleation Rate and Growth RateBibliography 277from Time Dependence of Global Microstructural Properties during Phase Transformation, Met. Trans. A, vol. 16A, (1985), 559-564.[98] Vandermeer, R.A., and Rath, B.B., Modelling of Recrystallization, in MaterialsArchitecture, Ed. Bilde-Sorensen, J.B., Hansen, N., Juul Jensen, D., Leffers, T.,Lilholt, H., and Pedersen, O.B., RISO Publ., (1989), 589-599.[99] Vandermeer, R.A., and Rath, B.B., Kinetic Theory of Recrystallization, in Recrystallization’90, Ed. Chandra, T., TMS Pub!., (1990), 49-58.[100] Cahn, J.W., and Hagel, W., Theory of The Pearlite Reaction, in Decomposition ofAustenite by Diffusional Processes, Ed. Zackay, Z.D., and Aaronson, H.I., Inter-science, New York, (1960), 131-196.[101] Vandermeer, R.A., The Recrystallization Characteristics of Moderately DeformedAluminum, Met. Trans., vol. 1, (1970), 819-826.[102] Vandermeer, R.A., Masumura, R.A., and Rath, B.B., Microstructural Paths ofShape-Preserved Nucleation and Growth Transformations, Acta. Met., vol. 39,(1991), 383-389.[103] Rath, B.B., The Overall Kinetics of Isothermal Transformations, in Solid-SolidPhase Transformations, Ed. Aaronson, H.I., Laughlin, D.E., Sekerka, R.F., andWayman, C.M., TMS-AIME Publ., (1982), 1097-1103.[104] Cahn, J.W., The Significance of Average Mean Curvature and its Determinationby Quantitative Metallography, Trans. Met. Soc. AIME, vol. 239, (1967), 610-616.[105] Gokhale, A.M., Iswaran, C.V., and DeHoff, R.T., Application of MicrostructureModelling to the Kinetics of Recrystallization, Met. Trans. A, vol. hA, (1980),1377-1383.Bibliography 278[106] Price, C.W., Grain Impingement During Recrystallization, Scripta Met., vol. 19,(1985), 785-788.[107] Price, C.W., Simulations of Grain Impingement and Recrystallization Kinetics,Acta metall., vol. 35, (1987), 1377-1390.[108] Leffers, T., Modelling of Recrystallization Kinetics on Stereological Basis, in Annealing Processes-Recovery, Recrystallization and Grain Growth, Ed. Hansen, N.,Juul Jensen, D., Leffers, T., and Ralph, B., RISO Pub!., (1986), 427-436.[109] Furu, T., Marthinsen, K., Tundal, U., Ryum, N., and Nes, E., RecrystallizationKinetics as studied Experimenatally, Analytically and by Computer Simulation, inMaterials Architecture, Ed. Bilde-Sorensen, J.B., Hansen, N., Juul Jensen, D.,Leffers, T., Lilholt, H., and Pedersen, O.B., RISO Pubi., (1989), 343-350.[110] Anderson, M.P., Grest, G.S., and Srolovitz, D.J., The Microstructural Dynamics ofPrimary and Secondary Recrystallization, in Computer Simulation of Microstructural Evolution, Ed. Srolovitz, D.J., AIME Pub!., (1986), 77-93.[111] Ling, S., and Anderson, M.P., Monte Carlo Simulation of Grain Growth and Recrystallization in Polycrystalline Materials, JOM, vol. 44, (1992), 30-36.[112] Humphreys, F.J., Modelling Mechanisms and Microstructures of Recrystallization,Mat. Sci. and Tech., vol. 8, (1992), 135-143.[113] Price, C.W., Use of Computer Simulations to Analyze Limitations of Kinetic Models for Recrystallization, in Recrystallization’90, Ed. Chandra, T., TMS Pubi.,(1990), 789-794.[114] Cahn, J.W., Transformation Kinetics During Continuous Cooling, Acta metall.,vol. 4, (1956), 572-575.Bibliography 279[115] Kuban, M.B., Jayaraman, R., Hawbolt, E.B., and Brimacombe, J.K., An Assessment of the Additivity Principle in Predicting Continuous-Cooling Austeniteto-Pearlit e Transformation Kinetics Using Isothermal Transformation Data, Met.Trans. A, vol. 17A, (1986), 1493-1503.[116] Agarwal, P.K., and Brimacombe, J.K., Mathematical Model of Heat Flow andAustenite-Pearlite Transformation in Eutectoid Carbon Steel Rods for Wire, Met.Trans. B, vol. 12B, (1981), 121-133.[117] Hayes, J.W., Mathematical Models in Materials Science, M.Sc. Thesis, Mathematical Institute, University of Oxford, (1985).[118] Verdi, C., and Visintin, A., A Mathematical Model of the Austenite-Pearlite Transformation in Plain Carbon Steel Based on the Scheil’s Additivity Rule, Acta metall.,vol. 35, (1987), 2711-2717.[119] Leblond, J.B., and Devaux, J., A New Kinetic Model for Anisothermal MetallurgicalTransformations in Steels Including Effect of Austenite Grain Size, Acta metall.,vol. 32, (1984), 137-146.[120] Scheil, E., Anlaufzeit der Austenitumwandlung, Archiv fur das Eisenhuttenwesen,vol. 12, (1935), 565-567.[121] Hawbolt, E.B., Chau, B., and Brimacombe, J.K., Kinetics of Austenite-PearliteTransformation in Eutectoid Carbon Steel, Met. Trans. A, vol. 14A, (1983), 1803-1815.[122] Hawbolt, E.B., Chau, B., and Brimacombe, J.K., Kinetics of Austenite-Ferriteand Austenite-Pearlite Transformations in a 1025 Carbon Steel, Met. Trans. A,vol. 16A, (1985), 565-578.Bibliography 280[123] Pham, T.T., Mathematical Modelling of the Onset of Transformation from Austenite to Pearlite under Non-Continuous Cooling Conditions, M.A.Sc. Thesis, Dept.of Metals and Materials Eng., University of British Columbia, (1993).[124] Kirkaldy, J.S., and Sharma, R.C., A New Phenomenology for Steel IT and CCTCurves, Scripta Met., vol. 16, (1982), 1193-1198.[125] Wierszyllowski, l.A., The Effect of the Thermal Path to Reach Isothermal Temperature on Transformation Kinetics, Met. Trans. A, vol. 22A, (1991), 993-999.[126] Moore, P.T., Anisothermal Decomposition of Austenite in a Medium-Alloy Steel, J.of The Iron and Steel Inst., vol. 7, (1954), 305-311.[127] Campbell, P.C., Application of Microstructural Engineering to the Controlled Cooling of Steel Wire Rod, Ph. D. Thesis, Dept. of Metals and Materials Eng., Universityof British Columbia, (1989).[128] Mukunthan, K., and Hawbolt, E.B., Unpublished Research, Dept. of Metals andMaterials Eng., University of British Columbia, (1988).[129] Kamat, R.G., The Principle of Additivity and the Proeutectoid Ferrite Transformation, Ph. D. Thesis, Dept. of Metals and Materials Eng., University of BritishColumbia, (1990).[130] Leslie, W.C., Michalak, J.T., and Aul, F.W., The Annealing of Cold-Worked Iron,in Iron and Its Dilute Solid-Solutions, Ed. Spencer, C.W., and Werner, F.E., Interscience Pubi., New York, (1963), 119-216.[131] Cahn, R.W., Nucleation in Recrystallization, in Recrystallization of Metallic Materials, Ed. Haessner, F., Univ. of Stuttgart and Max-Planck-Inst., Stuttgart, (1970),43-79.Bibliography 281[132] Jones, A.R., and Hansen, N., Recovery Changes Leading to Nucleation of Recrystallization, in Recrystallization and Grain Growth of Multi-Phase and Particle Containing Materials, Ed. Hansen, N., Jones, A.R., and Leffers, T., RISO Pubi., (1980),13-25.[133] McQueen, H.J., and Jonas, J.J., Recovery and Recrystallization during High Temperature Deformation, in Treatise on Materials Science and Technology, vol. 6,Plastic Deformation of Materials, Ed. Arsenault, R.J., Academic Press, New York,(1975), 393-493.[134] Humphreys, F.J., Recrystallization Mechanisms in Two-Phase Alloys, Met. Sci.,vol. 13, (1979), 136-145.[135] Gawne, D.T., and Higgins, G.T., Associations Between Spherical Particles of TwoDissimilar Phases, J. Mat. Sd., vol. 6, (1971), 403-412.[136] Talbot, J., The Annealing Behaviour of High Purity Iron, in Recovery and Recrystallization of Metals, Ed. Himmel, L., Interscience Publ., New York, (1963),269-310.[137] Smith, C.J.E., and Dillamore, I.L., Subgrairi. Growth in High-Purity Iron, Met. Sci.,vol. 4, (1970), 161-167.[138] Goodenow, R.H., Recrystallization and Grain Structure in Rimmed and AluminumKilled Low-Carbon Steel, Trans. ASM, vol. 59, (1966), 804-823.[139] Davidson, A.P., and West, D.R.F., Structural and Textural Aspects of Deformation and Recrystallization of Low- Carbon Steels Containing Dispersions of Nb (CN),Met. Sci., vol. 13, (1979), 170-178.Bibliography 282[140] Aust, K.T., and Rutter, J.W., Grain Boundary Migration, in Recovery and Recrystallization of Metals, Ed. Himmel, L., Interscience Pubi., New York, (1963),131-169.[141] Hofmann, S., arid Haessner, F., Migration of High Angle Grain Boundaries, inRecrystallization of Metallic Materials, Ed. Haessner, F., Univ. of Stuttgart andMax-Planck-Inst., Stuttgart, (1970), 81-108.[142] Burke, J.E., and Turnbull, D., Recrystallization and Grain Growth, Prog. in Met.Phys., vol. 3, (1952), 220-292.[143] Abrahamson, E.P., and Blakeney, B.S., The Effect of Dilute Transition ElementAdditions on the Recrystallization of Iron, Trans. Met. Soc. AIME, vol. 218, (1960),1101-1104.[144] Lucke, K., and Detert, K., A Quantitative Theory of Grain Boundary Movementand Recrystallization in Metals in the Presence of Impurities, Acta metall., vol. 5,(1957), 628-637.[145] Rickett, R.L., Kahn, S.H., and Mackenzie, J.T., Recrystallization and Microstructure of Aluminum Killed Deep Drawing Steel, AIME Trans., vol. 185, (1949), 242-251.[146] Leslie, W.C., Rickett, R.L., Dotson, C.L., and Walton, C.S., Solution and Precipitation of Aluminum Nitride in Relation to the Structure of Low Carbon Steels,Trans. ASM, vol. 46, (1954), 1470-1499.[147] Michalak, J.T., and Schoone, R.D., Recrystallization and Texture Development ina Low-Carbon, Aluminum-Killed Steel, Trans. Met. Soc. AIME, vol. 242, (1968),1149-1160.Bibliography 283[148] Solter, R.L., and Beattie, C.W., Grain Structure of Aluminum-Killed Low-CarbonSteel Sheets, AIME Trans., vol. 191, (1951), 721-726.[149] Yoda, R., Tsukatani, I., Inoue, T., and Saito, T., Effect of Chemical Compositionon Recrystallization Behaviour and i-value in Ti-added Ultra Low Carbon SheetSteel, ISIJ International, vol. 34, No. 1, (1994), 70-76.[150] Hayakawa, H., Furuno, Y., Shibata, M., and Takahashi, N., Effect of Ti on Recrystallization Behaviour During Continuous Annealing of Very Low Carbon Steel,Trans. ISIJ, vol. 23, (1983), B-434.[151] Pradhan, R.R., Rapid Annealing of Cold-Rolled Rephosphorized Steels ContainingSi, Cb and V, in Metallurgy of Continuous-Annealed Sheet Steel, Ed. Bramfitt,B.L., and Mangonon, Jr., P.L., AIME PubI., (1982), 203-227.[152] Goodman, S.R., and Chaudhry, A.R., Recrystallization Behaviour and TensileProperties of Continuously Annealed High-Strength Cold-Rolled Steel Sheets Containing Columbium and Titanium, in Metallurgy of Continuous-Annealed SheetSteel, Ed. Bramfitt, B.L., and Mangonon, Jr., P.L., AIME Publ., (1982), 229-247.[153] Wilshynsky, D.O., Krauss, G., and Matlock, D.K., Recrystallization Behaviour ofInterstitial-Free Sheet Steels, in Interstitial-Free Steel Sheet : Processing, Fabrication and Properties, Ed. Collins, L.E., and Baragar, D.L., CIM Publ., (1991),69-79.[154] Hansen, S.S., Vandersande, J.B., and Cohen, M., Niobium Carbonitride Precipitation and Austenite Recrystallization in Hot-Rolled Microalloyed Steels, Met. Trans.A, vol. hA, (1980), 387-402.Bibliography 284[155] Porter, D.A., and Easterling, K.E., Phase Transformations in Metals and Alloys,Van Nostrand Reinhold Co., New York, (1981), 113-130.[156] Hatherly, M., and Hutchinson, W.B., An Introduction to Textures in Metals, TheInst. of Metallurgists Publ., London, (1979), 1-76.[157] Bunge, H.J., The Basic Concepts of Texture Investigation in Polycrystalline Materials, Steel Research, vol. 62, (1991), No. 12, 530-541.[158] Wenk, H.R., Measurement of Pole Figures, in Preferred Orientation in DeformedMetals and Rocks: An Introduction to Modern Texture Analysis, Ed. Wenk, H.R.,Academic Press Inc., New York, (1985), 11-47.[159] Schulz, L.G., J. Appi. Phys., vol. 20, (1949), 1030.[160] Takechi, H., Kato, H., and Nagashima, S., Rolling and Annealing Textures of Low-Carbon Steel Sheets, Trans. Met. Soc. AIME, vol. 242, (1968), 56-65.[161] Bunge, H.J., Physical Properties of Polycrystals, in Preferred Orientation in Deformed Metals and Rocks: An Introduction to Modern Texture Analysis, Ed. Wenk,H.R., Academic Press Inc., New York, (1985), 507-525.[162] Harris, G.B., X. Quantitative Measurement of Preferred Orientation in Rolled Uranium Bars, Phil. Mag., vol. 43, (1952), 113.[163] Held, J.F., The Relationship between R values and Structure Properties of SteelSheets, in Mechanical Working and Steel Processing IV (AIME), Ed. Edgecombe,D.A., Gordon and Breach Science Publ. Inc., New York, vol. 44, (1965), 3-38.[164] Ray, R.K., and Jonas, J.J., Transformation Textures in Steels, International Materials Reviews, vol. 35, (1990), 1-36.Bibliography 285[165] Bunge, H.J., Texture Analysis in Materials Science, Butterworth and Co. (Pubi.),London, (1982), 1-419.[166] Bunge, H.J., Representation of Preferred Orientations, in Preferred Orientation inDeformed Metals and Rocks: An Introduction to Modern Texture Analysis, Ed.Wenk, H.R., Academic Press Inc., New York, (1985), 73-108.[167] Bunge, H.J., and Esling, C., The Harmonic Method, in Preferred Orientation inDeformed Metals and Rocks: An Introduction to Modern Texture Analysis, Ed.Wenk, H.R., Academic Press Inc., New York, (1985), 109-122.[168] Bunge, H.J., Z. Metallkd., vol. 56, (1965), 872.[169] Roe, R.J., J. Appi. Phys., vol. 36, (1965), 2024, 2069.[170] Schlippenbach, U.V., and Lucke, K., Microstructure and Recrystallization TextureDevelopment in a Low-Carbon Steel, in Annealing Processes-Recovery, Recrystallization and Grain Growth, Ed. Hansen, N., Juul Jensen, D., Leffers, T., and Ralph,B., RISO Publ., (1986), 541-546.[171] Darmann, C., and Engl, B., On the Recrystallization Texture Development in LowCarbon Steel during Continuous Annealing, in Annealing Processes-Recovery, Recrystallization and Grain Growth, Ed. Hansen, N., Juul Jensen, D., Leffers, T.,and Ralph, B., RISO Publ., (1986), 279-284.[172] Bleck, W., Grobterlinden, R., Lotter, U., and Reip, C.P., Textures in Steel Sheets,Steel Research, vol. 62, (1991), No. 12, 580-586.[173] Kern, R., Lee, H.P., and Bunge, H.J., The Rolling Texture of Iron of DifferentPurities, Steel Research, vol. 62, (1991), No. 12, 563-571.Bibliography 286[174] Mondal, D.K., and Ray, R.K., Recrystallization Behaviour and Development ofTexture in afew Dual-Phase Steels, in Recrystallization’90, Ed. Chandra, T., TMSPubi., (1990), 795-800.[175] Backofen, W.A., Deformation Processing, Addison-Wesley Pubi. Co., Reading,Massachusetts, (1972), 1-87.[176] Mecking, H., Textures in Metals, in Preferred Orientation in Deformed Metals andRocks: An Introduction to Modern Texture Analysis, Ed. Wenk, H.R., AcademicPress Inc., New York, (1985), 267-306.[177] Dieter, G.E., Mechanical Metallurgy, McGraw-Hill Book Co., New York, (1986),651-678.[178] Whiteley, R.L., The Importance of Directionality in Drawing-Quality Sheet Steel,Trans. ASM, vol. 52, (1960), 154-169.[179] Wilson, D.V., Plastic Anisotropy in Sheet Steels, J. Inst. Metals., vol. 94, (1966),84-93.[180] Vieth, R.W., and Whiteley, R.L., IDDRG Colloq., Inst. of Sheet Metal Eng., London, (1964).[181] Schmid, E., Zn-normal stress law, in Proc. mt. Congr. Appi. Mech., Deift, (1924),342.[182] Sachs, G., Zur Ableitung einer Fliessbedingung, Z. Ver. Dtsch. Ing., vol. 72, (1928),734-736.[183] Taylor, G.I., Plastic Strain in Metals, J. Inst. Metals, vol. 62, (1938), 307-324.Bibliography 287[184] Bishop, J.F.W., and Hill, R., A Theory of Plastic Distortion of a PolycrystallineAggregate under Combined Stresses, Phil. Mag., vol. 42, (1951), 414-427.[185] Bishop, J.F.W., and Hill, R., A Theoretical Derivation of the Plastic Properties ofa Polycrystalline Face-Centered Metal, Phil. Mag., vol. 42, (1951), 1298-1307.[186] Hu, H., Cline, R.S., and Goodman, S.R., Deformation Textures of Metals, in Recrystallization, Grain Growth and Textures, Ed. Margolin, H., ASM PubI., (1966),295-367.[187] Dillamore, I.L., and Roberts, W.T., Preferred Orientation in Wrought and Annealed Metals, Metall. Reviews, vol. 10, No. 39, (1965), 271-380.[188] Heckler, A.J., and Granzow, W.G., Crystallite Orientation Distribution Analysisof the Cold Rolled and Recrystallized Textures in Low-Carbon Steels, Met. Trans.,vol. 1, (1970), 2089-2094.[189] Dillamore, I.L., and Katoh, H., A comparison of the Observed and Predicted Deformation Textures in Cubic Metals, Metal Science, vol. 8, No.1, (1974), 21-27.[190] Beck, P.A., and Hu, H., The Origin of Recrystallization Textures, in Recrystallization, Grain Growth and Textures, Ed. Margolin, H., ASM Publ., (1966), 393-433.[191] Hatherly, M., The Origin of Recrystallization Textures, in Recrystallization’90, Ed.Chandra, T., TMS Publ., (1990), 59-68.[192] Dunn, C.G., Cold-Rolled and Primary Recrystallization Textures in Cold-RolledSingle Crystals of Silicon Iron, Acta metall., vol. 2, (1954), 173-183.[193] Ushioda, K., Yoshinaga, N., and Akisue, 0., Influences of Mn on RecrystallizationBehaviour and Annealing Texture Formation in Ultralow-carbon and Low-carbonBibliography 288Steels, ISIJ International, vol. 34, No. 1, (1994), 85-91.[194] Girina, O.A., and Fonstein, N.M., Investigation of Microalloying Elements Influence on Structure Formation of Formable Low Carbon and Ultra Low Carbon Cold-Rolled Steels, in International Symposium on Low-Carbon Steels for the 90’s, Ed.Asfahani, R., and Tither, G., TMS PubI., (1993), 481-489.[195] Galvani, C., and Baragar, D., Effects of Hot Rolling Conditions on Texture andMechanical Properties of Hot Rolled and Annealed Ti- and Nb- Stabilized IF Steels,in Interstitial-Free Steel Sheet: Processing, Fabrication and Properties, Ed. Collins,L.E., and Baragar, D.L., CIM Pubi., (1991), 119-133.[196] Lotter, U., Mueschenborn, W., and Knorr, R., in Textures of Materials, vol. 2, Ed.Gottstein, G., and Lucke, K., Berlin, Springer-Verlag, (1978), 285.[197] Mould, P., and Gray, J.M., Plastic Anisotropy of Low-Carbon, Low-ManganeseSteels Containing Niobium, Met. Trans., vol. 3, (1972), 3121-3132.[198] Karlyn, D.A., Veith, R.W., and Forand, J.L, , in Mechanical Working and SteelProcessing VII, The Metall. Soc. of AIME Publ., New York, (1969), 127-140.[199] Gillanders, R., Dasarathy, C., and Hudd, R.C., in Texture and the Properties ofMaterials, Ed. Davies, G.J., et al., The Metals Society Publ., London, (1976),245-254.[200] Willis, D.J., and Hatherly, M., in Textures and the Properties of Materials, Ed.Davies et al., The Metals Society Publ., London, (1976), 48.[201] Abe, H., Suzuki, T., and Takagi, K., Effects of the Size and Morphology of Cementite Particles on the Annealing Textures in Low-Carbon Al-killed Steel, Trans. Ironand Steel Inst. of Japan, vol. 21, (1981), 100-108.Bibliography 289[202] Subramanian, S.V., Prikryl, M., Gaulin, RD., Clifford, D.D., Benincasa, S., andO’Reilly, I., Effect of Precipitate Size arid Dispersion on Lankford Values of Titanium Stabilized Interstitial-Free Steels, ISIJ International, vol. 34, No. 1, (1994),61-69.[203] Fujinaga, C., Tosaka, A., Kato, T., Kato, T., and Kuguminato, H., Effect of Production Conditions on the Mechanical Properties of Extra Low Carbon Steel Sheetfor Tin Mill Black Plate, ISIJ International, vol. 34, No. 1, (1994), 108-114.[204] Katoh, H., Takechi, H., Takahashi, N., and Abe, M., Cold-Rolled Steel SheetsProduced by Continuous Annealing, in Technology of Continuously Annealed Cold-Rolled Sheet Steel, Ed. Pradhan, R., TMS-AIME Pubi., (1985), 37-58.[205] Toda, K., Gondoh, H., Takeuchi, H., Abe, M., Uehara, N., and Komiya, K., Metallurgical Investigation on Continuous Annealing of Low- Carbon Capped-Steel Sheets,Trans. of Iron and Steel Inst. of Japan, vol. 15, (1975), 305-313.[206] Matsudo, K., Osawa, K., and Kurihara, K., Metallurgical Aspects of the Development of Continuous Annealing Technology at Nippon Kokan, in Technology ofContinuously Annealed Cold-Rolled Sheet Steel, Ed. Pradhan, R., TMS-AIMEPubl., (1985), 3-36.[207] Hu, H., in Textures of Materials, vol. 2, Ed. Gottstein, C., and Lucke, K., Berlin,Springer-Verlag, (1978), 3.[208] Hu, H., Effect of Manganese on Annealing Texture, Plastic Anisotropy and Mechanical Properties of Low-Carbon Steels Containing 0.067 % Phosphorous, Met.Trans. A, vol. 8A, (1977), 1567-1575.Bibliography 290[209] Morita, M., Sato, K., and Hosoya, Y., Factors Affecting Texture Formation of Cu-Precipitation Hardening Cold Rolled Steel Sheet, ISIJ International, vol. 34, No. 1,(1994), 92-98.[210] Brammar, I.S., Thomson, T.R., and Hobbs, R.M., J. Aust. Inst. Met., vol. 17,(1972), 147.[211] Hwang, Y.S., and Chen, H.C., Effect of Nb Content on Deep Drawability of Nb andTi-Added Extra Low Carbon Cold Rolled Sheet Steel, in International Symposiumon Low-Carbon Steels for the 90’s, Ed. Asfahani, R., and Tither, C., TMS Pubi.,(1993), 475-480.[212] Senuma, T., and Kawasaki, K., Texture Formation in Ti-bearing IF Steel Sheetsthroughout the Rolling and Annealing Processes in Terms of the Influence of HotRolling Conditions on Deep Drawability, ISIJ International, vol. 34, No. 1, (1994),51-60.[213] Ohashi, N., Irie, T., Satoh, S., Hashimoto, 0., and Takahashi, I., Development ofCold Rolled High Strength Steel Sheet with Excellent Deep Drawability, SAE PaperNo. 810027, (1981).[214] Whiteley, R.L., and Wise, D.E., in Flat Rolled Products III, Interscience Pubi.,New York, (1962), 47-63.[215] Evans, P.R.V., Bitcon, J.C., and Hughes, I.F., J. of Iron and Steel Inst., vol. 207,(1969), 331-339.[216] Smith, C.S., and Guttman, L., Measurement of Internal Boundaries in ThreeDimensional Structures by Random Sectioning, AIME Trans., vol. 197, (1953),81-87.Bibliography 291[217] Brarnmar, I.S., and Dewey, M.A.P., Specimen Preparation for Electron Metallography, Blackwell Scientific Pubi., Oxford, (1966), 22-81.[218] Thomas, 0., Transmission Electron Microscopy of Metals, John Wiley and Sons,Inc., New York, (1962), 133-186.[219] Saimoto, S., Kamat, R.G., Clarke, P., and Van Houtte, P., A Quantitative Methodto Examine Through Thickness Texture Variation, To be published in Textures andMicrostructures.[220] Wilshynsky-Dresler, D.O., Krauss, G., and Matlock, D.K., Recrystallization ofInterstitial-Free Steels, in Developments in the Annealing of Sheet Steels, Ed. Pradhan, R., and Gupta, I., TMS Publ., (1992), 189-218.[221] Perera, M., Saimoto, S., and Boyd, D., Precipitation and Microstructural Evolutionin Ferrite for a Ti-Nb I-F Steel, in Interstitial-Free Steel Sheet : Processing, Fabrication and Properties, Ed. Collins, L.E., and Baragar, D.L., CIM Pubi., (1991),55-64.[222] Hansen, N., Cold Deformation Microstructures, Materials Science and Technology,vol. 6, (1990), 1039-1047.[223] Hu, H., Direct Observations on the Annealing of a Si-Fe Crystal in the ElectronMicroscope, Trans. Met. Soc. AIME, vol. 224, (1962), 75-84.[224] White, E.W., and Johnson, Jr., G.G., X-ray Emission and Absorption Edge Wavelengths and Interchange Settings for LiF Geared Curved Crystal Spectrometers,Earth and Mineral Sciences Experiment Station, Special Pubi., No. 1-70, University Park, Pennsylvania, (1979), 1-168.Bibliography 292[225] Hua, M., Garcia, C.I., and DeArdo, A.J., Precipitation Studies in. Ti and Ti+NbStabilized Interstitial-Free Steels, in International Symposium on Low-CarbonSteels for the 90’s, Ed. Asfahani, R., and Tither, G., TMS Pubi., (1993), 445-451.[226] Yoshinaga, N., Ushioda, K., Akamatsu, S., and Akisue, 0., Precipitation Behaviourof Sulfides in Ti-added Ultra Low Carbon Steels in Austenite, ISIJ International,vol. 34, No. 1, (1994), 24-32.[227] Hinotani, S., Endo, J., Takayama, T., Mizui, N., and Inokuma, Y., Isolation andDetermination of Sulfides in Ti-bearing Ultra Low Carbon Steels, ISIJ International,vol. 34, No. 1, (1994), 17-23.[228] Kiessling, R., Non-Metallic Inclusions in Steel, Part V, The Inst. of Metals Pubi.,London, (1989), 97-141.[229] Massip, A., Meyer, L., and Stich, G., Stahl und Eisen, vol. 106, (1986), 115-121.[230] Pradhan, R., Effect of Nitride Formers (B, Zr, Ti) on the Mechanical Propertiesof Continuously Annealed Low-Carbon Steel Sheet, in Technology of ContinuouslyAnnealed Cold-Rolled Sheet Steel, Ed. Pradhan, R., TMS-AIME Publ., (1985),185-202.[231] Uhrus, L.O., Through-Hardening Steels for Ball Bearings - Effect of Inclusions onEndurance, in Clean Steel (Special Report 77), The Iron and Steel Inst. Publ.,London, (1963), 104-109.[232] Chone, J., Grinder, 0., and Hasseistrom, P., Surface Defects in Continuously CastStainless Steel, in Clean Steel, The Metals Society Publ., London, (1983), 385-415.[233] Pickering, F.B., The Constitution of Non-Metallic Inclusions in Steel, in Inclusions,Ed. Pickering, RB., The Inst. of Metallurgists Pubi., London, (1979), 47-72.Bibliography 293[234] Leach, J.C.C., Production of Clean Steel, in Production and Application of CleanSteels, The Iron and Steel Inst. Pubi., London, (1972), 105-114.[235] Brun, C., Patou, P., and Parniere, P., Influence of Phosphorous and Manganese onthe Recrystallization Texture Development During Continuous Annealing in Ti-IFSSheets, in Metallurgy of Continuous-Annealed Sheet Steel, Ed. BrarnFitt, B.L., andMangonon, Jr., P.L., AIME Pubi., (1982), 173-197.[236] Southwick, P.D., and Hiam, J.R., Continuous Annealing vs. Batch Annealing: TheEffect of Interstitials and Residual Elements on the Properties of Low Strength SteelSheet, in Inclusions and Residuals in Steels : Effects on Fabrication and ServiceBehaviour, Ed. Boyd, J.D., and Champion, C.S., CANMET Pubi., Ottawa, (1985),369-391.[237] Weiss, L.E., and Wenk, H.R., Symmetry of Pole Figures and Textures, in PreferredOrientation in Deformed Metals and Rocks: An Introduction to Modern TextureAnalysis, Ed. Wenk, H.R., Academic Press Inc., New York, (1985), 49-72.[238] van Houtte, P., Workshop on Quantitative Textural Analysis and its Application toMaterials• Processing, Queen’s University, (1988).[239] Hook, R.E., Heckler, A.J., and Elias, J.A., Texture in Deep Drawing Columbium(Nb)-Treated Interstitial-Free Steels, Met. Trans. A, vol. 6A, (1975), 1683-1692.[240] Holscher, M., Raabe, D., and Lucke, K., Rolling and Recrystallization Textures ofBCC Steels, Steel Research, vol. 62, (1991), No. 12, 567-575.[241] Darmann-Nowak, C., and Engl, B., Influence of Hot-Rolling Conditions on TextureDevelopment in Deep-Drawing Steels, Steel Research, vol. 62, (1991), No. 12, 576-579.Bibliography 294[242] Schlippenbach, U.V., Emren, F., and Lucke, K., Investigation of the Developmentof the Cold Rolling Texture in Deep Drawing Steels by ODF-Analysis, Acta metall.,vol. 34, NO. 7, (1986), 1289-1301.

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