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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 DURING CONTINUOUS ANNEALING OF COLD ROLLED, TI-STABILIZED INTERSTITIAL-FREE STEEL By Kannappar Mukunthan B. Sc. (Materials Engineering) University of Moratuwa, 1983 M.A.Sc. (Metals and Materials Engineering) University of British Columbia, 1987  A THESIS SUBMJTTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES METALS AND MATERIALS ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  May 1994  ®  Kannappar Mukunthan, 1994  -  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Metals and Materials Engineering The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date:  A  ii/  Abstract  Interstitial-Free (I-F) steels are increasingly being used for press forming operations due to their markedly improved deep-drawability. Additional interest is due to the fact that the cold rolled I-F steels can be effectively heat treated in a continuous annealing line without the need for any accompanying overaging process. The objective of this study was to characterize the evolution of microstructure and crystallographic texture of a 80 % cold rolled, Ti-stabilized I-F steel during heating rates applicable to batch and continuous annealing processes. Isothermal recovery ki netics, as monitored by {220} x-ray peak resolution measurements, were described using a semi-empirical logarithmic equation. Isothermal recrystallization kinetics were deter mined by quantitative metallographic measurements and were characterized by both Johnson-Mehl-Avrami-Kolmogorov and Speich-Fisher relationships. The isothermal re crystallization kinetics were also described in terms of the experimentally determined microstructural path function and an empirical kinetic function relating the interfaceaveraged growth rate with recrystallization time. The additivity procedure was success fully employed in conjunction with the isothermal kinetic parameters to predict continu ous heating recovery and recrystallization kinetics at heating rates simulating batch and continuous annealing processing. Microstructural examination showed that the recrystallization event was heteroge neous and related to the cold rolled cell structure. The recrystallized nuclei, developed primarily by subgrain coalescence occurring during the later stages of recovery, grew into the cold rolled matrix by the migration of high misorientation boundaries. Large precip itates of TiN and TiS acting as preferred nucleation sites and fine precipitates impeding 11  the boundary mobility were also observed. The hot band texture with the moderate presence of (112)[1iO] yielded a strongly developed cold rolled texture extending from (OOi)[iIOj to (112)[1IO]. The recrystallization texture was characterized by the strong  presence of (554)[5] and (111)[1iO]. Grain growth following recrystallization strength ened the existing texture with an accompanying improvement in average strain ratio values. The effect of heating rate on the final recrystallization texture was found to be insignificant.  II’  Table of Contents  Abstract  ii  List of Tables  v  List of Figures  vi  Acknowledgement 1  2  vii  Introduction  1  1.1  Interstitial-Free Steels  1  1.2  Continuous Annealing Process  4  1.3  Scope and Objectives  5  Literature Review  9  2.1  Kinetic Models for Recovery and Recrystallization  9  2.1.1  Measurement of Recovery and Recrystallization Kinetics  9  2.1.2  Kinetics of Recovery Processes  15  2.1.3  Kinetic Models for Isothermal Recrystallization  18  2.1.4  Additivity and Continuous-Heating Kinetics  32  2.1.5  Annealing Phenomena in Low-Carbon Steels  42  Development of Texture during Cold Rolling and Annealing  57  2.2.1  Methods of Representation of Texture  58  2.2.2  Crystallographic Texture and Plastic Anisotropy  61  2.2.3  The Theoretical Mechanisms of Texture Development  63  2.2  iv  2.2.4 3  67  Experimental Procedure  86  3.1  Material  86  3.2  Cold Rolling Schedule  3.3  Kinetic Measurements  87  3.3.1  Apparatus  87  3.3.2  Diffraction Effects  88  3.3.3  Annealing Treatment  3.3.4  Quantitative Metallography  91  Electron Microscopic Observations  94  3.4.1  Gleeble Simulated Annealing Treatment  94  3.4.2  Thin Foil Preparation and TEM Investigations  95  3.4.3  SEM/EDX Analysis of Large Precipitates  96  3.4  3.5  4  Development and Control of Texture in I-F Steels  .  .  .  .  .  .  86  89  Texture Characterization  97  3.5.1  Specimen Preparation  97  3.5.2  Pole Figure Determination and ODF Calculations  98  Kinetic Characterization  105  4.1  Isothermal Recovery Kinetics  105  4.2  Recovery and Recrystallization during Isothermal Heating  111  4.3  Isothermal Recrystallization Kinetics  116  4.3.1  JMAK/S-F Analysis of Isothermal Recrystallization  116  4.3.2  Microstructural Path Concept in Recrystallization Modelling  4.3.3  Recrystallization Kinetics as related to Steel Chemistry and Pro cessing Conditions  4.4  .  .  122  130  Recovery and Recrystallization during Continuous Heating v  136  4.5 5  Continuous Heating Recrystallization Kinetics  140  Microstructural Examination of Structural Changes  190  5.1  Structural Changes during Cold Rolling and Annealing  190  5.2  Characterization of Large Precipitates  197  6  Characterization of Annealing Textures  224  7  Conclusions  263  Bibliography  266  vi  List of Tables  1.1  Typical chemical composition of I-F steel [6]  2.1  Characterization of isothermal recrystallization kinetics for a 89 % cold  7  rolled, rimmed low-carbon steel using the JMAK and the S-F equations [39]. 70 3.1  Steel composition provided by Stelco and that obtained from chemical analysis  99  4.1  Characterization of isothermal recovery kinetics  147  4.2  Characterization of isothermal recrystallization kinetics  147  4.3  Characterization of isothermal interface-averaged growth kinetics  148  4.4  Experimental and Scheil predicted recrystallization start times (and tem peratures) during continuous heating  6.1  148  Volume percentages of important texture components calculated from the ODF data obtained for the hot band, the cold rolled sheet and annealed specimens  6.2  A summary of r at a  242 =  0, 45 and 90°,  and Lr predicted from the ODF  data obtained for the hot band, the cold rolled sheet and annealed specimens243  vii  List of Figures  1.1  Comparison of schematic box- and continuous-annealing cycles along with the Fe-rich side of the Fe-Fe C equilibrium diagram [24] 3  8  1.2  Furnace sections of a continuous annealing line [26]  8  2.1  Effects of annealing temperature (200, 250, 300, 450°C for 1 hr) on the diffraction peak profiles of the {331} planes in a 90 % cold rolled 70-30 brass [49]  71  2.2  Schematic illustration of the X-ray peak resolution measurement [56, 57]  71  2.3  Comparison of the % peak resolution (in-situ) and microhardness mea surements obtained for a 89 % cold rolled, rimmed low-carbon steel during continuous heating [56]  2.4  72  Recrystallization behaviour of a 77 % cold rolled, Ti-stabilized extra-lowcarbon steel during the simulation of continuous annealing (soak time of 40 s at each temperature) [15]  2.5  72  Isothermal recovery kinetics in polycrystalline iron after 5 % prestrain at 0°C, showing fractional residual strain hardening vs. time [40]  2.6  73  Recovery of x-ray line broadening as measured by the residual line broad ening parameter (1-R) for isothermal treatments at 400, 500 and 600°C [53]  2.7  The graph of lnln[1/(1  73 —  X)] vs. ln(t) obtained by Rosen et al [72] for a  60 % deformed high-purity iron  74  viii  2.8  Fractional residual strain hardening curves obtained during isothermal an nealing of a) copper [92] and b) aluminum (arrows indicate onset of re crystallization) [93] as presented by Furu et al [91]  2.9  74  Interfacial area per unit volume plotted against the volume fraction re crystallized for a 60 % cold worked 3.25 % Si-steel [90]  75  2.10 Average boundary migration rates (0) during isothermal recrystallization of hot-worked 3.25 % Si-Fe [81]  75  2.11 Schematic representation of the additivity principle [69]  76  2.12 A schematic TTR diagram with proportionally distributed fractional re crystallization curves to illustrate the validity of the additivity rule.  .  .  77  2.13 Comparison of experimental and predicted continuous heating recrystal lization kinetics; the isothermal data characterized by both the JMAK and the S-F equations were used in the additivity calculations [39]  77  2.14 Schematic illustration of subgrain coalescence by subgrain rotation [53].  78  2.15 Schematic representation of nucleation by subgrain growth; boundaries thickly populated by dislocations (dots) have a high misorientation angle, and are the most likely to migrate [131]  78  2.16 The softening response of three iron alloys recrystallized at 595°C [38].  79  2.17 Effect of annealing time at 565°C on the longitudinal properties of a Ti stabilized I-F steel cold rolled between 50 and 88 % [21]  79  2.18 Time-temperature-recrystallization diagram for Ti-stabilized [21], rimmed and Al-killed steels after 50 % cold reduction [138]  80  2.19 Effect of excess titanium in solid solution and cold reduction on the re crystallization temperature (TF) for annealing soak times of 15 s [16].  ix  .  80  2.20 Relationship between the recrystallization start temperature, TR, and the amount of Nb in solid solution in ferrite; the points along the curve were obtained for coarsened precipitates and the open circles include the effect of precipitates as well as Nb in solid solution [17]  81  2.21 Recrystallization kinetic curves indicating sigmoidal-type behaviour, ob tained for a series of I-F steels, cold rolled 75 % and isothermally annealed at 650°C [153]  81  2.22 Partial (200) pole figures obtained for a rimmed steel (a) in the cold-rolled state and (b) after recrystallization; the ideal orientations {111} < 112 >, {111} < 110>, {100} <011 > and {211} <011 > are indicated [79].  .  82  2.23 Normal (ND), rolling (RD) and transverse (TD) direction inverse pole figures obtained for a 70 % cold rolled steel sheet [160]  82  2.24 Schematic description of crystal orientation by indices of crystal directions and by Euler angles ,  and  Y2  2.25 A three-dimensional view and a  [157) =  83  45° section of the Euler space showing  the locations of some important ideal orientations [164, 166]  83  2.26 Development of recrystallization texture during isothermal annealing (af ter 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]  84  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] 84 2.28 Comparison of the relative proportions of different textural components in rimmed, Al-killed, and Ti-stabilized interstitial-free as well as high strength steels [196]  85  x  2.29 Variation of  values with heating rate during annealing for a variety of  steels subjected to different high temperature processing conditions [23].. 3.1  85  (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 100  3.2  Schematic diagram illustrating the {220} x-ray peak resolution associated with annealing and the procedure for quantifying peak resolution  3.3  101  Summary of the isothermal (T-T.-R) and continuous heating (C-H-R) an nealing tests performed, together with the parameters measured  3.4  102  Comparison of fractional peak resolution, F, based on valley intensity,  ‘M,  as obtained from two different tests 3.5  103  Strip specimen thermocouple positions for determining the thermal gra dient; C.T. refers to control thermocouple; A, B and C are additional thermocouple positions  3.6  103  Illustration of the measurement of volume fraction recrystallized, X, and the interfacial area per unit volume, A, by quantitative metallography [90] 104  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, Magnification X 200)  4.1  104  Fractional peak resolution (F) calculated at 500°C based on in-situ mea surements of x-ray ratio (R ) and valley intensity (IM) 1  4.2  In-situ R 1 measurements obtained at 500°C, compared with the kinetic descriptions using Eq. 2.3 (ln R 1  4.3  149  =  K  —  kt) and Eq. 2.4 (R 1  =  b  —  a ln t)  150  (a) In-situ R 1 measurements at 500, 550, 600 and 625°C, together with the kinetic descriptions using Eq. 2.4, and (b) the same kinetic data when replotted on a logarithmic time scale xi  151  4.4  Time-Temperature-Recovery (T-T-Ry) diagram obtained using Eq. 2.4; experimental measurements corresponding to R 1  0.5 and 0.4 are also  shown 4.5  152  (a) Effect of inverse absolute temperature on the natural logarithm of the instantaneous rate of recovery calculated at constant R 1 values, and (b) the calculated activation energy for recovery,  Qm,,  as a function of the  extent of recovery, R 1 4.6  153  Temperature dependence of parameters b and a; isothermal recovery ki netics has been characterized by the logarithmic relationship, R 1  4.7  b  —  a In t 154  Effect of R 1 on in AR and -QR/R; recovery kinetics has been analysed in terms of the Arrhenius equation, 1 dR / dt  4.8  =  =  —AR exp —(QR/RT)  In-situ IM measurements at 500°C, compared with the kinetic curves ob tained using Eq. 2.3 (lnJM cx t) and Eq. 2.4 (IM cx int)  4.9  154  155  Rj measurements corresponding to the start of the isothermal hold and the onset of recrystallization, as obtained from the interrupted tests performed at 600, 625, 650 and 675°C  156  4.10 Fractional peak resolution, F, calculated at 625°C using interrupted R 1 values and in-situ IM measurements (obtained from two different tests); metallographically determined recrystallization start time is also indicated. 157 4.11 Isothermal 675°C R 1 measurements interpreted in terms of recovery (Eq. 2.4) based on the total area (RTA) or the unrecrystallized area (RUA), recrystallization (recovery 4.12 Isothermal 650°C  ‘M  -  ) and measured % recrystallized 1 R  158  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  xii  159  4.13 Comparison of the fractional peak resolution (F) calculated from inter rupted R 1 and in-situ  ‘M  measuremnts, and the fraction recrystallized  (X) determined from metallography at (a) 700 and (b) 720°C 4.14 The effect of isothermal annealing time on the intensity values, and  ‘b,  160 , ‘min 1 ‘K  as obtained from in-situ peak profile measurements at (a) 500 and  (b) 650°C  161  4.15 Metallographically determined isothermal recrystallization kinetics at 650°C 162 4.16 The JMAK [66, 67, 65] and the S-F [90] analysis of the isothermal data obtained at 650°C, indicating the best fit lines  162  4.17 Temperature dependence of the JMAK time-exponent, n, and the S-F time-exponent, m, as obtained from the best fit analysis; the average values of n (=0.73) and m (=1.17) are also indicated  163  4.18 Recrystallization measurements obtained at 650°C, compared with the ki netic descriptions using the JMAK and the S-F equations; the effects of using the original best fit parameters vs. the recalculated average param eters are also shown  163  4.19 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  164  4.20 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  165  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 descriptions using the JMAK and the S-F equations  xlii  166  4.22 Time-Temperature-Recrystallization (T-T-R) diagram obtained using the JMAK analysis; recrystallization start and finish times for the I-F steel under investigation, and for a Ti-stabilized [21] and a rimmed [57] lowcarbon steels are also shown  167  4.23 Temperature dependence of the recrystallization time corresponding to 10, 50 and 90 % recrystallization as obtained from the JMAK analysis.  .  .  168  4.24 Temperature dependence of the JMAK parameter, ln b, and the S-F pa rameter, in k; isothermal recrystallization kinetics has been characterized by the JMAK and the S-F equations with constant values of n (=0.73) and m (=1.17) 4.25 Recrystallization start time,  169 as a function of isothermal temperature  169  4.26 Typical microstructures of (a) the hot band with an equiaxed grain struc ture and (b) the 80 % cold-rolled sheet steel with a heavily banded struc ture along the rolling direction (Magnification X 200)  170  4.27 Photomicrographs showing the early stages of recrystallization obtained from specimens held at 700°C for (a) 2 s and (b) 4 s (Magnification X 200). 171 4.28 Photomicrographs showing the later stages of recrystallization obtained from specimens held at 700°C for (a) 12 s and (b) 30 s (Magnification X 200)  172  4.29 Typical microstructure of a fully recrystallized specimen, obtained after a 150 s hold at 700°C (Magnification X 200)  173  4.30 Photomicrographs at (a) Magnification X 400 and (b) Magnification X 1000, showing the initial stages of recrystallization obtained from a speci men held at 650°C for 32 s  174  xiv  4.31 Interfacial area per unit volume (A) vs. volume fraction recrystallized (X) obtained for all isothermal temperatures and heating rates; the best fit microstructural path description, A  =  2002 (X)° 44 (1  —  , is also 94 X)°  indicated  175  4.32 Temperature dependence of the interface-averaged growth rate time expo nent, riG, as obtained from the best fit analysis; the average  G  value of  -0.58 is also indicated 4.33 G  =  KG t (riG  =  176  -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  177  4.34 Effect of inverse absolute temperature on the natural logarithm of the instantaneous (interface-averaged) growth rate,  ,  calculated at constant  growth distances, dG  178  4.35 Temperature dependence of the growth parameter, KG; isothermal growth kinetics has been characterized by G  =  KG  t with a constant  G  value  of -0.58  179  4.36 The plot of the isothermal G values obtained at all test temperatures against time (both axes on logarithmic scale); the global best fit descrip tion line,  =  is  also indicated  180  4.37 Modelled X vs. t curves using the microstructural path approach, together with the experimental data points obtained at (a) 600, 625, 650 and 675°C and (b) 700, 720, 740 and 760°C  181  4.38 Schematic diagram illustrating the modelling procedure used in the pre diction of recovery and recrystallization kinetics during continuous heating. 182  xv  4.39 In-situ and interrupted R 1 measurements obtained at 0.025°C/s, compared with the additivity-predicted recovery kinetics (using ‘activation energy’ and ‘empirical’-type isothermal descriptions) and metallographic analysis of % recrystallized  183  4.40 Comparison of experimental (interrupted R ) and predicted continuous 1 heating recovery kinetics at 0.025, 1.88, 20.2 and 80°C/s  184  4.41 Interrupted R 1 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 R ) and measured 1 -  4.42 Temperature effect on (a) the values of (1min  -  Is), (‘Ka 1  -  % recrystallized 185  ib)  and R , and 1  (b) the 20 values of the J( peak and the valley  186  4.43 Comparison of experimental and predicted continuous heating recrystal lization kinetics at 0.025, 1.88 and 20.2°C/s; the predictions are based on the experimentally determined start times, t. expt’l  187  4.44 Comparison of the effect of t expt’l vs. t 9 Scheil on the JMAK equa tion based kinetic predictions at 0.025, 1.88 and 20.2°C/s; experimentally determined % recrystallized are also indicated  188  4.45 Comparison of the additivity predicted interface-averaged growth rates (G) with the the modelled (using dX/dt from the predicted recrystalliza tion kinetics and A from the derived microstructural path function) and estimated (using the experimental ‘X vs. t’ data and the experimental A values) G values at 0.025, 1.88 and 20.2°C/s 5.1  189  Bright-field transmission electron micrograph of the 80 % cold rolled I-F steel showing the highly dislocated cell structure  xvi  204  5.2  Microstructures illustrating the heterogeneous nature of the cold rolled cell structure; (a) a reasonably developed cell structure and (b) dense dislocation networks with much less developed cell structure  5.3  205  Subgrain structure development in a partially recovered specimen heated at 20.2°C/s up to 580°C; (a) small elongated subgrains and (b) relatively large subgrains  5.4  206  Well-defined subgrain structure formation in a specimen heated at 20.2°C/s up to 640° C; coalescence of subgrains is suggested by those boundaries in dicated by arrows  5.5  207  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  5.6  208  Microstructure indicating subgrain growth caused by both sub-boundary migration (indicated by arrow M) and coalescence (indicated by arrow C); the annealing treatment corresponds to quenching from 640°C after being heated at 20.2°C/s  5.7  209  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 the discontinuity in the boundary curvature.  5.8  .  210  Recrystallized grain nucleated in the interior of a matrix grain in a spec imen heated at 20.2°C/s up to 680°C; selected area diffraction patterns illustrate the orientation of the recrystallized grain A (zone axis type) with regard to the matrix subgrain area B (zone axis  xvii  <  <  111  111 >  >  type). 211  5.9  Recrystallized grain A (zone axis < 111 > type) bordering a cold rolled grain B (zone axis < 110 > type) in a specimen heated at 20.2°C/s up to 680°C; the pinning of one side of the boundary of the recrystallized grain by fine precipitates is also shown (arrows indicate the precipitates).  .  .  .  212  5.10 Photomicrographs obtained from a specimen heated at 20.2°C/s up to 740°C  (  50 % recrystallized), showing (a) recrystallized grains growing  into the cold rolled matrix and (b) fully recrystallized grains  213  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  214  5.12 Microstructure of the as-received hot band, showing random distribution of fine precipitates  215  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 precip itates (arrows indicate the discontinuities in the boundary curvature).  .  .  216  5.14 SEM micrograph and x-ray spectrum showing the presence of an angularshaped precipitate in the hot band (arrow indicates the precipitate); the x-ray spectrum is consistent with it being a TiS precipitate  217  5.15 SEM micrograph of the hot band showing the larger Ti/S-containing pre cipitate (appears near the centre) and the smaller precipitates (indicated by arrows); the associated x-ray spectrum obtained for a smaller precipi tate is consistent with it being Ti S 2 C 4  218  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  xviii  219  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  220  5.18 SEM micrograph obtained from the hot band and x-ray spectrum obtained from 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)  221  5.19 SEM micrograph obtained from the hot band and x-ray spectrum of the precipitate 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 lighter contrast outer layer indicated by arrow)  222  5.20 SEM micrograph and x-ray spectrum showing the presence of a P-containing precipitate in the hot band (arrow indicates the precipitate) 6.1  223  (a) Experimental and (b) recalculated (110) pole figures obtained for the 80 % cold rolled I-F steel specimen  6.2  244  ODFs calculated for the I-F steel hot band (with the grain size of ASTM No. 7  -  8) presented at constant ço sections; cp2  =  45° section of the Euler  space is also shown 6.3  ODFs calculated for the 80 % cold rolled sheet presented at constant y sections;  6.4  245  2 =  45° section of the Euler space is also shown  246  1 sections for the specimen quenched from 670°C ODFs showing constant cp after being heated at 20.2°C/s (‘-- 15 % recrystallized); of the Euler space is also shown  P2 =  45° section 247  xix  6.5  ODFs showing constant  ço  sections for the specimen quenched from 720°C  after being heated at 20.2°C/s  (‘-.‘  40 % recrystallized);  c02 =  45° section  of the Euler space is also shown 6.6  248  ODFs showing constant y sections for the specimen quenched from 760°C after being heated at 20.2°C/s (‘-. 80 % recrystallized); Cp2  =  45° section  of the Euler space is also shown 6.7  249  ODFs showing constant so sections for the specimen quenched from 800°C after being heated at 20.2°C/s (fully recrystallized with the grain size of ASTM No. 9  6.8  -  10);  Y2 =  45° section of the Euler space is also shown.  .  250  ODFs showing constant cc’ 1 sections for the specimen quenched from 900° C after being heated at 20.2°C/s (fully recrystallized with the grain size of ASTM No. 8); cp2  6.9  =  45° section of the Euler space is also shown  ODFs showing constant  coi  251  sections for the specimen quenched from 770° C  after being heated at 1.88°C/s (fully recrystallized with the grain size of ASTM No. 9  -  10);  Y2  45° section of the Euler space is also shown.  .  252  6.10 ODFs showing constant p sections for the specimen quenched from 700°C after being heated at 0.025°C/s (fully recrystallized with the grain size of ASTM No. 9  -  10);  c°2  45° section of the Euler space is also shown.  6.11 Orientation density along the (a)  .  and (b) y fibres for the as-received hot  band and the 80 % cold rolled I-F steel specimens 6.12 Orientation density along the (a)  253  E  and (b)  9 t  254  fibres for the as-received hot  band and the 80 % cold rolled I-F steel specimens  255  6.13 Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9  -  10 to ASTM No. 8) for the cold rolled  specimens annealed at 20.2°C/s; the results are presented as orientation density along the (a) a and (b)  fibres xx  256  6.14 Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9  10 to ASTM No. 8) for the cold rolled  -  specimens annealed at 20.2°C/s; the results are presented as orientation density along the (a)  E  and (b) ‘9 fibres  257  6.15 Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9  -  10 to ASTM No. 8) for the cold rolled  specimens annealed at 20.2°C/s; the results are presented as orientation density along the c-fibre  258  6.16 Effect of heating rate on the annealing texture of fully recrystallized spec imens with the grain size of ASTM No. 9  -  10; the results are presented  as orientation density along the (a) a and (b) -y fibres  259  6.17 Effect of heating rate on the annealing texture of fully recrystallized spec imens with the grain size of ASTM No. 9 as orientation density along the (a)  E  -  10; the results are presented  and (b) i9 fibres  260  6.18 Normal direction inverse pole figures calculated from the ODFs corre sponding to (a) the 80 % cold rolled steel and (b) the fully recrystallized specimen with the grain size of ASTM No. 9  -  10, annealed at 20.2°C/s  261  6.19 Development of plastic anisotropy during the progress of recrystallization and grain growth (ASTM No. 9  -  10 to ASTM No. 8) for the cold rolled  specimens annealed at 20.2°C/s; the results are presented as r (predicted) vs. a (degrees)  262  xxi  Acknowledgement  I 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 also extended to Professor R.G. Butters (Retired), Mr. Serge Milaire and Ms. Mary Mager for their help regarding the experimental aspects of this work.  Financial assistance  provided by Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. All of the texture measurements of this work were performed in Queen’s University and 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. Rajeev Kamat for taking the initiative and all the other necessary steps to successfully carry out the texture measurements. Various aspects of this research work were greatly enhanced by the input provided by several researchers of the Metals and Materials Engineering department. In particular, the assistance provided by Dr. R.B. Mahapatra regarding modelling, Dr.  F. Saint  Antonin regarding transmission electron microscopy and Dr. Fidel Reyes-Carmona re garding precipitate characterization is gratefully acknowledged. A special note of thanks to 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 sincerely appreciated. In particular, the constant encouragement, help and moral support provided by 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 friends of British Columbia for making my stay in UBC/Vancouver pleasant and rewarding. xxii  The debt I owe to my parents cannot be described in words. It is their love and sacrifices that made my education possible and it is to them this thesis is dedicated.  xxiii  Chapter 1  Introduction  1.1  Interstitial-Free Steels  Low-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, properties such as strength, good formability, attractive surface finish, and easy weldability. One of the most important requirements for many applications involving sheet steel is good formability. In place of the conventional low-carbon (typically has 0.06 wt % C and 0.005 wt % N) sheet steel, further reduction of carbon content to levels of approximately 0.005 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 forming operations such as deep-drawing [1, 2]. The annealed sheet steel with very low C and N contents has been produced com mercially since the early 1970’s [3]. This constitutes one of the most recent steps in the evolution of formable, cold rolled and annealed sheet steels. Vacuum-degassing and rig orous 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 processing steps are now commonly applied at a reasonable cost and have led to the commercial production of interstitial-free (I-F) steels [3, 4, 5, 6, 7]. Interstitial-free or fully stabilized steel sheet is produced from aluminum-killed steel with extremely low amounts of carbon and nitrogen, treated with one or more of Ti,  1  Chapter 1. Introduction  2  Nb; the typical composition ranges of the elements present in I-F steels are shown in Table 1.1 [6]. Stochiometrically sufficient amounts of Ti and Nb are added to remove C and N completely from the solid solution by forming stable carbides, nitrides, and carbonitride precipitates. Titanium added to low-carbon steel combines with N, S and C in that order, primarily in the temperature range of 1400  -  900°C, while Niobium almost  exclusively combines with the residual C at lower temperatures [4, 6, 8, 9, 10]. Various studies on I-F steels dealing with the thermo-kinetic analysis of precipitation as well as the physical and chemical characterization of different precipitates have been reported [6, 10, 11, 12]. In addition, the Ar 3 temperatures of I-F steels are considerably higher than those of conventional low-carbon steels, and because of this increased range of ferrite stability, the temperatures used for finish hot rolling and for annealing after cold rolling are significantly higher for I-F steels [6]. The elimination of interstitial elements from the iron matrix has a number of benefits for the product, particularly the removal of inhomogeneous deformation associated with strain aging, decreased yield stress values (140  -  180 MPa), significant reduction in the  yield strength dependence on grain size, good ductility (40  -  50 % elongation), and  markedly improved drawability (high ‘average plastic strain ratio’ values) [6, 8, 13]. This allows the steel user to produce more complex shapes with fewer forming steps and lower rejection levels. In deep-drawn oil pan applications, scrap levels were reported to be reduced from 5 % to I % with the replacement of conventional low-carbon steel with 1-F steel [14]. However, the manufacturing cost of I-F steel is high and the surface quality may 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 processing conditions and properties.  Excess Ti and Nb levels in solid-solution (above what is  needed for stabilizing interstitials) is reported to considerably retard the recrystallization kinetics in I-F steels [16, 17]. Nb-precipitates, being finer than Ti-precipitates, are more  Chapter 1. Introduction  3  effective in retarding the growth of new grains, resulting in a fine-grained, recrystallized microstructure [4, 18]. To make up for the loss of strength associated with reducing the carbon content, P, Si and Mn are the most commonly used alloying elements in I-F steels to impart solid-solution strengthening. In particular, phosphorus additions strengthen Ti-stabilized I-F steels very effectively without a significant concurrent drop in deep-drawability [9, 19, 20]. In addition to steel chemistry, processing factors have a major influence on the final properties of the I-F steels. All of the stabilizing precipitation takes place during the high temperature processing, and the precipitates are in place prior to cold rolling and an nealing. Coarse and widely spaced precipitates allow rapid growth of new grains, thereby helping to achieve stronger textures favouring deep-drawability. Lower reheat tempera tures (1000  -  1100°C), finish rolling temperature values just above Ar 3  higher coiling temperatures (700  -  (‘-‘  900°C) and  800°C) are reported to be beneficial for Ti-stabilized  I-F steels [4, 6, 15, 16]. In general, however, Ti-steels are less sensitive to the lower temperature finish rolling and coiling of the processing schedules due to the presence of a stable precipitate distributions in these steels [4, 6]. Coiling temperature control can be quite significant for Nb-steels because this process can occur in the temperature range of Nb(C,N) precipitation [4, 6]. The degree of deep-drawability is primarily related to the type of recrystallization texture formed. Consequently, cold rolling and annealing, two processing parameters markedly 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 compared to other low-carbon steel [21].  Cold reduction of approximate’y 90 % and annealing  temperatures as high as 800° C (independent of the heating rate) are reported to produce favourable textures in I-F steels for deep-drawing applications [4, 6, 14, 22, 23].  In  comparison, Al-killed low-carbon steels are usually cold rolled about 70 %, and annealed  Chapter 1. Introduction  by slowly heating at  1.2  —  4  0.01°C/s to a temperature of  ‘—.‘  700°C [22, 23].  Continuous Annealing Process  During the cold rolling of steel sheet, the plasticity of the material is exhausted, resulting in limited formability and increased hardness. For the sheet to be used in subsequent forming operations, the ductility must be restored through a heat treatment which results in recrystallization. Two processes are employed by the steel industry to accomplish this task, batch annealing (BA) and continuous annealing (CA). Batch annealing involves heating tight-wound sheet steel coils in a gas fired furnace with a controlled atmosphere. A typical representation of the annealing cycle experienced during batch annealing is shown in Fig. 1.1 (a) [24]. The heating rates are approximately 30°C/hr, the soak temperature around 700°C and the entire process taking several days to complete. Modern CA lines combine several processes including electrolytic cleaning, annealing, overaging and sometimes temper rolling [24, 25, 26, 27]. Sections of annealing and aging furnaces of a continuous annealing line are shown in Fig. 1.2 [26]. Radiant tubes fired by natural gas are used for heating. Heating rates of 10 40°C/s, soak temperature of around -  800°C, cooling rates of 20  -  200°C/s and an overaging temperature of approximately  350°C are commonly employed to anneal low-carbon steels; the time taken for the total cycle is only 4 8 -  mm. as indicated in Fig. 1.1 (c) [24]. The short heating time minimizes  detrimental carbide coarsening, allowing higher annealing temperatures to be employed to promote recrystallization [24]. When carbon-steels are subjected to BA, nearly all the carbide will precipitate during the slow cooling cycle. However, the rapid cooling during CA inhibits the complete precipitation of carbide from ferrite, making subsequent overaging necessary. Despite  Chapter 1. Introduction  5  overaging, more carbon is retained in solid solution during CA than in BA, and, as a result, even Al-killed continuously annealed steels show some aging effects [24]. This explains why traditionally BA was preferred over CA in producing the highly formable carbon-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 due to the absence of free carbon for subsequent precipitation. With I-F steels, the overaging process (as an essential component of a continuous annealing line for low-carbon sheet steels) can be completely eliminated; this makes CA a much more attractive process than BA. In fact, almost all of the cold-rolled I-F steel sheet produced today is continuously annealed before being subjected to press-forming operations [7]. Hot-dip galvanized (HDG) sheet has major use in automotive applications (e.g., door inners). Most of it is currently produced from cold-rolled, Al-killed low-carbon steel by employing annealing, hot-dip galvanizing, and overaging processes. However, annealing and galvanizing of the I-F steel can be completed in a single continuous operation to produce 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 HDG applications. As a result, manufacturers of HDG sheet using I-F steels are reported to have significantly increased the production of I-F steel for deep-drawing applications [14, 28].  1.3  Scope and Objectives  The relationship between microstructure and mechanical properties and the control of microstructure by solid state processing have been important topics of extensive research  Chapter 1. Introduction  6  in physical metallurgy. However, most of this work has resulted in a qualitative link ing of product properties with processing parameters. The current emphasis is focussed on obtaining quantitative product-processing knowledge through the use of knowledge based computer models, describing microstructure evolution during industrial process ing. 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 with powers of prediction are now needed to improve process control. This new generation of models must incorporate both microstructure and texture development, to predict the mechanical properties of the processed product. The emerging field of “microstruc tural engineering” has as its goal the development of models to quantitatively predict the properties of a metal product as a function of its composition and thermo-mechanical his tory. Fundamental to microstructural engineering is the development of a mathematical model that links mechanical properties to processing parameters through the evolution of microstructure. In the present study, the microstructural engineering approach will be applied to de velop a model describing the continuous annealing of a heavily cold rolled, Ti-stabilized I-F steel with emphasis on kinetic modelling of recovery and recrystallization during continuous heating, associated microstructure and texture evolution, and development of plastic anisotropy. To accomplish this task, the recrystallization kinetics will be measured and modelled over an appropriate range of isothermal temperatures and during selected continuous heating cycles applicable to industrial annealing processes. The evolution of crystallographic texture during simulated continuous annealing will be characterized quantitatively using orientation distribution functions. Scanning and transmission elec tron microscopy will also be employed to improve the understanding of the microstruc tural mechanisms responsible for recovery and recrystallization.  Chapter 1. Introduction  7  Table 1.1: Typical chemical composition of I-F steel [6] Element C N S Si Mn P Al Ti Nb  Weight Percentage 0.002 0.008 0.001 0.005 0.004 0.010 0.010 0.030 0.100 0.340 0.010 0.020 0.030 0.070 0.010 0.110 0.005 0.040 -  -  -  -  -  -  -  -  -  Chapter 1. Introduction  8  (a)  (b)  (c)  Fe-FeC EQUILIBRIUM DIAGRAM  BOX ANNEALING  ‘  I  ‘  CONTINUOUS ANNEALING -r  High Temo  800  1 A TEMP,  600  4, Rapid CooIng  I y +  TEM P 400  Overaging  .  oc  C 3 Fe 200  0  1  2  3  TIME,days  I  I  I  .01  .02  M3  C,wt%  0 .04  2  4  6  8  TIME, mm  Figure 1.1: Comparison of schematic box- and continuous-annealing cycles along with the Fe-rich side of the Fe-Fe C equilibrium diagram [24]. 3  —  ANNEALING FURNACE  —AGEING FURNACE—  Figure 1.2: Furnace sections of a continuous annealing line [26].  Chapter 2  Literature Review  2.1  Kinetic Models for Recovery and Recrystallization  During the plastic deformation of a metal, energy will be stored in the material due to the introduction of defects such as dislocations and their associated strain energy. This stored energy provides the driving force for the two relaxation processes occurring during annealing; recovery and recrystallization.  During recovery, some annihilation  and rearrangement of point defects and dislocations takes place, and these processes aid the formation of recrystallized nuclei. During recrystallization, new relatively strain-free grains nucleate, and grow by the migration of high-angle grain boundaries until the entire cold-worked matrix is consumed. Grain growth can take place at high temperatures following recrystallization, with the decrease in the total surface energy of the grain boundaries being the driving force [29, 30]. 2.1.1  Measurement of Recovery and Recrystallization Kinetics  The techniques used for quantifying the effects of an annealing treatment generally involve either a direct measurement of the release of stored energy (calorimetric techniques) or the recrystallization event (quantitative metallography), or the measurement of a change in some mechanical or physical property of the alloy associated with the progress of annealing.  9  Chapter 2. Literature Review  10  Most of the recrystallization studies are based on measurements made at room tem perature (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, and x-ray diffraction monitoring are a few measurement procedures that permit in-situ mea surement of the annealing effects. 2.1.1.1  Microcalorimetry  Calorimetric techniques have been used to measure the heat evolved during isothermal and anisothermal annealing [31]; the observations have been interpreted in terms of a combined recovery and recrystallization process [32, 33, 34]. Important information con cerning the nature of the annealing mechanisms and the imperfections involved can be obtained thorough this approach. In particular, calorimetric studies have been found to be very useful in quantifying the effects of competing recovery processes on recrys tallization, as a function of temperature and degree of deformation [32, 33]. However, correlating the calorimetric observations to the fraction recrystallized may not be a triv ial task. This will be further complicated if additional phase transitions, such as the dissolution or the precipitation of a second phase, occur during recrystallization [34]. 2.1.1.2  Hardness Measurements and Tensile Testing  Micro and macro hardness measurements have been used extensively to measure the progress of recrystallization due to their ease of use and significance in industrial appli cations. Recovery seems to play a major role in the softening response of high purity iron [35, 36] and dilute solid solutions of a-iron [37, 38]. However, the observed hardness changes in some low-carbon [38, 39] and I-F [15, 17] steels have been attributed almost en tirely to recrystallization. Microhardness evaluation methods have been used to monitor  Chapter 2. Literature Review  11  recrystallization of thin specimens. Due to the locallized nature of these microhardness indentations, 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 steels are yield strength [16, 21], percent elongation [21] and the ratio of tensile strength to yield strength (TS/YS) [17]. The changes in yield stress values of iron-based alloys, depending on the chemical composition, have been found to be related to either recovery [40] or recrystallization [41], or a combination of both [17, 21]. However, the softening response in an I-F steel, reflected by the TS/YS ratio, is reported to be due almost entirely to recrystallization [17]. 2.1.1.3  Quantitative Metallography  In quantitative metallography, the fraction of recrystallized grains is measured. Despite being tedious and prone to error of judgement, this method gives the most appropriate data for developing a kinetic equation describing recrystallization in terms of nucleation and growth parameters. Microhardness impressions are sometimes made to distinguish between the recrystallized and unrecrystallized regions [32]. Precise microstructural mea surements are always necessary to validate the recrystallization measurements obtained from 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 in terms of efficiency for a given experimental error [42, 43, 44]. 2.1.1.4  Measurement of Electrical Resistivity and Magnetic Permeability  Changes in electrical resistivity [45, 46] and magnetic permeability [47, 48] have also been used to monitor the progress of annealing. Although these methods can be readily adopted as in-situ techniques, they have been shown to be most effective in monitoring only the recovery stages [46, 47].  Chapter 2. Literature Review  2.1.1.5  12  X-Ray Techniques  When a metal is plastically deformed by rolling, slip occurs in each grain and the grains become flattened and elongated in the direction of rolling. However, contacts among grains are retained during deformation, and because of this constraint, a plastically de formed grain will usually also have regions of its lattice left in an elastically bent or twisted condition. These residual microstresses, the associated non-uniform strain and the corresponding range of crystallographic plane spacings in the deformed grain struc ture are all characteristics of the cold-worked state [49, 50]. The x-ray line position of the diffracted peaks from different crystallographic planes can be determined from Bragg’s law, sinO 0 A=2d  (2.1)  where A is the wavelength of the x-ray beam, 0 is the incident angle the beam makes with the crystal plane under consideration (2 0 is the angle of diffraction), and d 0 is the unstrained lattice spacing of the diffracting plane. For a cold rolled metal, the well-defined K, /iç 2 peaks corresponding to the spacing , will be replaced by a number of smaller, more diffuse peaks corresponding to the 0 d range of spacings in the deformed lattice; combining these peaks, a broadened diffraction peak is obtained [49, 50, 51, 52]. In addition to non-uniform lattice strain, small coherent crystallites (fragmented grains) and stacking faults have also been identified by Fourier analysis 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 strain is 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 70-30 brass is shown in Fig. 2.1 [49]. A broad diffraction peak for the {331} planes is obtained after cold work. The effect of annealing at increasing temperatures causes recovery and  Chapter 2. Literature Review  13  recrystallization processes to occur. Recovery, which dominates the lower temperature re sponse, involves partial stress relief and causes the broad x-ray peak to sharpen and partly resolve. During recrystallization, new grains form and residual stresses are eliminated, with sharper resolution occurring as recrystallization proceeds. Although, diffractometry provides a means of monitoring the effects of recovery and recrystallization, it is much less sensitive to the growth processes that occur following the completion of recrystallization [49]. Any kinetic study of recovery and/or recrystallization requires the quantitative char acterization of the degree of peak resolution using x-ray diffraction procedures. The pa rameters 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,  2 peaks ‘ç  and the intensity of any one peak [15, 48, 49, 53, 55, 56, 57]. In x-ray studies of re crystallization 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 sharpening parameter’, R [56, 57], R  = (Iiç 1 (‘K  where  —  1mm)  —  (2.2)  Ib)  is the intensity of the J(, peak, ‘mm is the intensity of the valley, and  ib  is  the background intensity, as indicated schematically in Fig. 2.2. Other researchers have used a ‘residual line broadening parameter’, (1-R), to quantify peak resolution in their investigations [15, 53, 55]. The fractional annealing effects could be estimated using the peak 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 re crystallization. Fig. 2.3 shows some results where both in-situ fractional peak resolution and interrupted microhardness measurements were used to characterize the progress of  Chapter 2. Literature Review  14  annealing 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 not be determined, both the hardness and the peak resolution profiles change rapidly in the same time interval, indicating that these two measurement procedures are effective in monitoring different stages of recrystallization. Although x-ray diffraction peak broadening measurements provide a means of in-situ monitoring of annealing (recovery and recrystallization) processes, no clear distinction between the effects of recovery and recrystallization processes are obtained. In low-carbon steels, the observed peak resolution prior to the onset of recrystallization, has been found to vary from 20 % [15, 47, 48, 56] to 70 % [15, 55] of the total peak resolution, depending on the alloy content, heat-treatment conditions and the particular diffraction peak being monitored. Although an inflection point in the peak resolution response corresponding to the onset of recrystallization has some times been observed [48, 55], no general procedure has been reported for separating the two effects using x-ray procedures. In cold-rolled metals, recrystallization is normally accompanied by a change in tex ture. Such a change can also be used as a measure of the degree of recrystallization as the intensity of the diffracted signal from a given texture component is proportional to the amount of material with this texture. Fig. 2.4 shows the results of an investigation where hardness, fraction of residual line broadening (fractional change in (1-R)), and integrated pole intensity have been measured on a 77 % cold rolled, Ti-stabilized extra-low-carbon steel subjected to continuous heating-quenching procedure [15]. The integrated pole in tensity of some selected diffraction peaks seem to provide a reasonable measure of the degree of recrystallization. Precipitation during recrystallization [58] and grain growth following it [15] can also influence the integrated intensity measurements, and may have to be considered in interpreting the experimental observations. This method has the po tential to be used for in-situ investigations, as was demonstrated in a recent study where  Chapter 2. Literature Review  15  the textural evolution was monitored in-situ using neutron diffraction and the measured intensity values were interpreted in terms of a sigmoidal-type recrystallization kinetics  [591. 2.1.2  Kinetics of Recovery Processes  The rate of recovery of a property from its cold-worked state depends on the instantaneous value of that property and results in kinetics exhibiting a continuously decreasing rate of change with increasing time, without any initial incubation period. This response is markedly different from the sigmoidal property change usually obtained for nucleation and growth processes, such as recrystallization. Two different expressions have been used in the past to describe the kinetcs of the recovery processes during isothermal annealing. The first equation, based on the asslimp tion that the rate of decay of a property is proportional to its instantaneous value, can be expressed as [29], lnx=K—kt  (2.3)  where x is the instantaneous value of some property measured at time t, and K and k are 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 experimental constants 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 of the initial flow stress in a 5 % prestrained, polycrystalline iron. The parameter used to measure the extent of recovery was the fractional residual strain hardening, defined  Chapter 2. Literature Review  16  as the ratio of the difference in flow stress values between partly-annealed and fullyannealed iron to the difference in flow stress between pre-strained and fully-annealed iron. Fig. 2.5 shows the results of this study, where fractional residual strain hardening was plotted against time for the temperature range 300 to 500°C. These curves are typical of a recovery process, in that they show a rapid initial decrease with the rate of change decreasing with increasing time. When the same data were plotted on a logarithmic time scale, 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 single crystals by monitoring the sharpening of the (002) reflection. The results obtained at 400, 500 and 600°C for a (001)[110] crystal are shown in Fig. 2.6 as the residual line broadening parameter (1-R) vs. log (time). These results support the proposal that the isothermal recovery and the associated peak resolution in iron can be described well by Eq. 2.4. In Hu’s study, recovery processes were responsible for the sharpening of the broadened peak, from (1-R) of 0.55 to 0.15 as indicated in Fig. 2.6; the (1-R) value of 0.35 was considered to correspond to approximately 50 % recovery. Although most kinetic recovery models are based on the measurement of specific property changes, several researchers have included the details of specific microstruc tural processes. Li [61] modelled recovery in terms of the kinetics of the annihilation of dislocation dipoles (pairs of parallel dislocations of opposite signs) through a statistical treatment. With some simplifying assumptions, he derived a second-order kinetic rela tionship of the form, dp/dt cx  —  , where p is the dilocation density. The integration of 2 p  this, with the additional assumption that the stored energy, E, was proportional to the dislocation density, p, led to the kinetic relationship dE/dt cx  —  2 [61]. Vandermeer t  and Gordon [33] monitored recovery in cold worked aluminum in terms of the two distinct stages of stored energy release that were observed. The first energy release, with a rate  Chapter 2. Literature Review  17  proportional to t , was attributed to the reduction and rearrangement of dislocations in 1 subgrains. The second stored energy release, observed at 139°C with a rate proportional to 2 t 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), the rate of recovery increases with increasing temperature. By assuming Arrhenius rate be haviour, 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 the studies indicate an activation energy that increases as recovery proceeds [40, 62]; a con stant activation energy corresponding to the recovery process has also been reported in a few studies [52, 54]. In general, a combination of simultaneous microstructural mechanisms have been found to operate during the recovery process. The increase in the activation energy during recovery can be rationallized in terms of a change in the dominant recovery mech anism [29]. It has been suggested [62], that the activation energy is a function of x, the instantaneous value of the recovering property. Such an activation energy would have the form, dx (Qo—Bx” --=—A exp RT  )  (2.5)  where Qo, A and B are experimental constants for a given recovery study, R is the gas constant 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 varies linearly with the recovering property [29]. Vandermeer and Rath [63] in their recovery studies on iron single crystals used an equation of the same form as Eq. 2.5, dP_ —  -  (  —  r)  exp -  Q B 0 (PPr) RT  (.)  Chapter 2. Literature Review  18  where P is the instantaneous value of the stored energy, Pr is the remnant stored energy which is unrecoverable after long annealing times. They used this equation to analyse the flow stress measurements made by Michalak and Paxton [40] during recovery, based on the assumption that the flow stress is proportional to the square root of both the dislocation density and the stored energy [64]. An increase in the activation energy with the progress of recovery is consistent with recovery processes initially occurring at severely deformed regions, where mechanisms with a relatively low activation energy can easily operate. Activation energy values of 91.9 and 281.7 kJ/mole, corresponding to the start and the end of recovery, were reported from flow stress measurements on 5 % prestrained polycrystalline iron [40]. Based on these values, it was suggested that simple vacancy migration was rate controlling at the start, 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/mole at 50 % recovery has been reported for 80 % cold rolled silicon-iron single crystals based on peak resolution measurements [53]. 2.1.3  Kinetic Models for Isothermal Recrystallization  The evolution of microstructure during recrystallization can be described phenomenolog ically as a nucleation and growth process. New strain-free grains emerge from the cold worked microstructure (nucleation) surrounded by high angle grain boundaries which migrate (growth) until the cold worked matrix is consumed. 2.1.3.1  JMAK Equation  -  Theoritical Development  Mathematical treatment of the kinetics of nucleation and growth processes must compen sate for the impingement effects of the new, growing grains with one another. Kolmogorov [65], Johnson and Mehl [66] and Avrami [67] (JMAK) incorporated grain impingement  Chapter 2. Literature Review  19  through an abstract consideration, where the new grains were assumed to grow unim peded through one another and to continue to nucleate in already-transformed as well as untransformed regions. The totality of this volume transformed, referred to as the extended volume, could be related to the kinetic laws of growth without considering the geometric problem of impingement. For a random distribution of the new phase, the real volume 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 by the JMAK method. The modelling process is implemented by calculating the extended volume fraction transformed in terms of the nucleation and growth parameters. The following general case is used as an illustration [68]. If NT is the nucleation rate, i.e. the number of new grains appearing per unit volume of material during the time increment between r and T+dT,  and v(t  for time (t  —  —  T)  T)  is the volume of a new grain nucleated at r and growing unimpinged  (t is the overall reaction time), then  dXex = Nv(t  —  T)dT  (2.8)  This ideallization assumes that all new grains have the same geometry and each one grows independently of the others. For a shape preserved growth of spheroidal shaped grains, v(t  —  where a is the grain radius after time (t  r) = Ka 3 —  -r) and K is a shape factor, which is  (2.9) for  spherical grains. Finally, a may be related to an interface migration rate, 0, and the growth time, t’, by the equation,  a=jGdt’  (2.10)  Chapter 2. Literature Review  20  Equations 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, a growth rate, a geometrical factor and the reaction time. In the most general case, NT and G, which are scalar and vector quantities respec tively, may vary both spatially and with time. If G is assumed to be isotropic and time independent, and NT is treated either as a constant or as a sharply decreasing function of time (a case where the preferred nucleation sites are quickly exhausted), then for a random spatial distribution of nucleation sites, the JMAK theory predicts the following simple relationship [67], X  =  1  —  exp(—bt’)  (2.11)  where X is the volume fraction transformed in time t and n (referred to as the JMAK exponent) and b are constants. For three dimensional growth, n is equal to 3 in the limiting case of early site sat uration [67], and equal to 4 when NT is treated as a constant [66, 67]; for a general decreasing nucleation rate, the value of n will be between 3 and 4. This general expres sion remains valid for two- and one- dimesional growth with appropriate n values. The JMAK exponent, ri, is dependent on the time variation of nucleation and growth rates and the dimensionality of the growth fronts [69, 70], and is some times independent of temperature [69]. The constant, b, represents the relative magnitude of the nucleation and growth rates and is often a strong function of temperature [69]. 2.1.3.2  JMAK Equation  -  Application to Recrystallization  The JMAK equation has been used extensively to model the kinetics of phase transfor mations, including recrystallization in metals. However, in some of the reported studies,  Chapter 2. Literature Review  21  the observed recrystallization kinetic behaviour could not be adequately described us ing the JMAK equation. Primarily two types of failure have been observed. First, the time-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 theory would predict 3 < n <4 for such cases. Second, there are a number of studies where the kinetic data, when plotted as In ln[1/(1  —  X)] vs. ln(t) (the JMAK theory format), show  a 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 % deformed high-purity iron. These discrepencies suggest that one or more of the assumptions involved in the development of the JMAK equation are not being met. Most of the metallographic observations indicate that the assumption of a random distribution of nucleation sites is not valid; in reality, randomness has been observed only in a very few cases, such as in a lightly deformed metal [73, 74] and in some single crystal studies [75, 76]. It is common to observe a high density of nuclei only in certain grains of the cold rolled metal [72, 77], as a result of the non-uniform distribution of stored energy between grains of different orientations [78, 79]. Further non-uniformity is due to the presence of preferential 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 JMAK analysis through analytical means. Cahn [70] considered grain boundary nucleated pro cesses, and demonstrated the possibility of n varying between 1 to 3 depending on the nature 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 kinetic  Chapter 2. Literature Review  22  equations; the low experimental n values result from the fact that the nuclei are clus tered 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 equa tion  =  (1  —  2 (as opposed to the random nucleation assumed in Eq. 2.7) to X)  appropriately reduce the real volume fraction recrystallized. The assumption of a constant growth rate (G) in the JMAK analysis, has come under considerable scrutiny in the modelling of recrystallization. G, usually obtained by measuring 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 experiments suggest a constant growth rate [73, 74, 77, 80, 86], while a decreasing growth rate has also been 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 the expected 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 driving force and mobility, may be reduced considerably due to a decrease in either one of the terms [89]. The dynamic interactions of moving grain boundaries with dissolved solute atoms and the associated effects on their mobility may partly explain some of the ob served decrease in growth rate [68, 81]. However, the observed reduction in interface migration rate with increasing recrystallization is thought to be based on the reducing driving force. This can be attributed to on going recovery effects or the non-uniform dis tribution of stored energy or a combination of both. No single explanation here satisfied all researchers. Another proposed explanation for the retardation of interface migration rate considers growth to be highly anisotropic or the dimensionality of growth to be less than three [60, 76].  Chapter 2. Literature Review  23  Concurrent recovery in the unrecrystallized regions reduces the growth rate by de creasing 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 energy alloys, as clearly illustrated by Furu et al. [91] in their examination of the low stacking fault copper and high stacking fault aluminum; the softening curves presented by them for pure copper [92] and for pure aluminum [93] are shown in Fig. 2.8. It is obvious that in the case of aluminum, a substantial portion of the stored energy evolution occurs during recovery, whereas no recovery effects are visible for copper. Price [94] presented strong arguments in favour of the recovery effects, based on the observed linear JMAK behaviour when recovery was absent as in pure copper [32, 61]. However, the recovery processes are generally rapid at recrystallization temperatures, and consequently, they may not exhibit the necessary temperature/time dependence to provide a complete ex planation for the decreasing interface migration rate, particularly towards the end of recrystallization [63, 75, 85]. The second major explanation for the decreasing interface migration rate is the non uniform 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, would be expected to grow along a driving force gradient with a progressively decreasing growth rate. Rollett et al. [96], by neglecting recovery effects and considering such a distribution of stored energy in the simulation of recrystallization, could obtain a negative deviation from the linear JMAK behaviour. Additional evidence was provided by the calorimetric studies of Hutchinson et al. [95], who showed that a given fraction of recrystallization in pure copper was associated with a greater amount of stored energy evolution during the early stages than during the later stages, even though the stored energy release caused by recovery was negligbly small. They also rationallized the low n exponents in terms of this non-linearity. Vandermeer and Rath [63] used the combined recovery effects and stored  Chapter 2. Literature Review  24  energy gradients to explain their observed non-linear growth in iron single crystals. There are few reported analytical treatments where a varying growth rate has been incorporated into a JMAK-type equation. Furu et al. [91] have presented one such study in which the recovery effects were accounted for by, =  [1 +  (t/Ti)],  0  b < 1  (2.12)  where r 1 is a temperature dependent relaxation time parameter, and the special case b  0 corresponds to a constant growth rate 0  =  G. If it is assumed that the variation  in 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 dominant recovery mechanism [91]. If the growth rate given by Eq. 2.12 is incorporated into the JMAK derivation procedure for spherically shaped grains, that will lead to, =1- exp where r 2  =  {4  [(1  ‘6)]  (—)  3(1—b)  }  (2.13)  3 is a relaxation time parameter for recrystallization. Eq. 2.13 / 1 (NG)  corresponds to a limiting case where r,/r 2 << 1. Furu et al. [91] successfully modelled the recovery and recrystallization in aluminum using equations 2.12 and 2.13 respectively, by selecting the appropriate values for r , 6 and r,/r 1 . They also rationalized a low ri 2 value in terms of the slowing down of the growth rate. Vandermeer and Rath [63] followed a 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 usually a sound one, and not expected to contribute towards any observed failure in recrystal lization 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 effectively  Chapter 2. Literature Review  25  instantaneous [33, 37, 38, 75, 80, 81]. However, a constant and an increasing nucle ation rates were also reported in a few studies, particularly when the metal was lightly deformed (eg., 5  -  10  %)  [73, 74, 77].  The inadequacies of the JMAK equation in describing the recrystallization kinetics and some of the analytical treatments to address this problem were highlighted in this discussion. However, it should be emphasized that the JMAK equation was employed in a vast majority of the reported recrystallization kinetic studies. In many of these cases, a reasonably good fit to the experimental kinetic data was provided by the JMAK equation, despite the resulting JMAK exponents being considerably different from those predicted by the theory. This successful curve-fitting by the JMAK equation is primarily due to the fact that recrystallization, like other nucleation and growth processes, exhibits a sigmoidal kinetic behaviour, a form described well by the JMAK equation. 2.1.3.3  Improved Models  -  Microstructural Path Concept  Traditionally, many kinetic studies focussed only on the variation of volume fraction re crystallized (X) with time (t), and such data could be readily analysed using the JMAK equation. However, such an approach invokes the apparent anomaly of using only volu metric terms to model a surface reaction. It has also been shown that useful information related to modelling can be inferred from additional microstructural properties; interfa cial 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 from quantitative metallography. Experimental determination of the nucleation rate  (NT)  is  a complicated task. However, a mathematical procedure using Laplace transform tech niques 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 a  Chapter 2. Literature Review  26  set 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 de velopment is adopted for areal terms (instead of volumetric terms), then the following complementary 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 in recrystallization modelling; this can be estimated throughout the transformation by using the Cahn-Hagel [100] formulation, 4 AG=  (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 and other geometrical considerations, but is independent of the kinetics [81, 90, 101]. The path function, being dependent on the number of nuclei, is usually affected by the amount of deformation [81]. However, a study on aluminum [101] has shown the path function to be independent of the impurity content, despite the observed reduction in growth rate by three orders of magnitude. Under simplifying JMAK assumptions, both X and Aex will have t’-type time dependence, 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.  27  Chapter 2. Literature Review  2.7 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-empirical path 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 develop a microstructural model using a microstructural path function (eg., Eqs. 2.17, 2.18) in conjunction with one kinetic function (eg., Eqs. 2.11, 2.15). The use of the path function is an advantage when time dependent complications such as competing recovery effects are present; these factors manifest themselves in the kinetic functions, but do not affect the path function [102]. The approach outlined above forms the basis for developing a comprehensive model of recrystallization. However, determining the appropriate kinetic function through ana litical means remains a formidable task. An alternative approach would be to find an empirical kinetic function. As an example, for deformed iron single crystals, Vandermeer and 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 Aex were obtained using Eqs. 2.7 and 2.14 from the experimentally determined X and A. It was 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 that can be readily employed for modelling purposes.  Chapter 2. Literature Review  2.1.3.4  S-F Equation  -  28  An Empirical Approach  The model developed by Speich and Fisher [90] was based on two different empirical relations. The first, a parabolic equation, was obtained from the metallographic mea surements 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 that work [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 the initial 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 surfacecontrolled growth (Eq. 2.16) [100], this will lead to the Speich and Fisher (S-F) equation for isothermal recrystallization [90],  (1  =  kt m  where k is a function of temperature and m(= KAKG) is a constant.  (2.21) It should be  emphasized here that the empirical equations 2.19 and 2.20 are quantitative descriptions of a microstructural path function and a kinetic function, respectively. Speich and Fisher [90] stressed the validity of Eq. 2.19 within the experimental range X  =  0.02 to 0.95. Cahn [104] showed stereologically that this equation was not rigorously  correct at either extreme of X. However, Eq. 2.19 is a simple expression that compensates  Chapter 2. Literature Review  29  reasonably well for grain impingement during recrystallization. In addition, nucleation is implicit in this model, unlike the JMAK theory, where the nucleation parameters have to be explicitly specified. It has been shown that 0 is a function of time for 3.25 % Si-steel, but independent of temperature [81, 90]. Both Speich and Fisher [90] and Li [61] rationalised the inverse time dependence, based on concurrent recovery occurring at a rate proportional to t . 2 The temperature independence, although apparently incompatible with the view that interface migration is a thermally activated procees, was explained by invoking the same activation energy for the interface-averaged boundary migration rate (0) and the later stages 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 in the dimensionality of growth during recrystallization. In deformed iron single crystals, Vandermeer and Rath [75] obtained approximately the same t 038 dependence for both G and 0 at all isothermal temperatures. They attributed these observations to the non-uniform distribution of stored energy in the deformed matrix. The stronger t 1 time dependence observed by Speich and Fisher [90] was thought to be due to a greater non-uniformity of stored energy expected in polycrystalline materials [75, 76]. Speich and Fisher [90] initially obtained a kinetic equation by combining a constant G with Eq. 2.19, and showed that for a silicon steel, the resulting expression overestimated X during the later stages of recrystallization. Price [87] demonstrated similar effects in 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 dependence of  .  Based on these observations, Price [87] suggested the S-F equation to be an  improvement 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-F equations, and the results, shown in Table 2.1, indicate that both equations describe the  Chapter 2. Literature Review  30  data reasonably well with comparable correlation coefficients, the poorest fit being at the low 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 empirical equation (Eq. 2.19) provide reasonable compensation for grain impingement. Based on the analysis by Price, the major limitation of the JMAK equation is its assumption of linear growth, while that of the S-F relation is its empiricism. The fact that relations identical 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  —  2 [85]) X)  further emphasizes the empirical nature of the S-F equation. 2.1.3.5  Microstructural Evolution  -  Computer Simulations  An essential prerequisite for the estimation of the final mechanical properties is the prediction of the microstructure that results from a deformation and annealing treatment. The spatial inhomogenity of the nucleation and growth processes makes this a difficult problem to be treated analytically. However, computer simulations based on the JMAK approach [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 analysed from two-dimensional sections. The nucleation and growth conditions and rates can be set 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 stored energy to the lattice sites of each grain in the mapped microstructure. Recrystallization nuclei with zero stored energy are then introduced, and the boundary motion is simulated  Chapter 2. Literature Review  31  according to the standard Monte Carlo procedure. A model based on a network of grains or subgrains, with the capability to simulate recovery and recrystallization, has also been reported [112]. An equation describing the motion of a boundary is solved for each boundary, which is then moved accordingly, and the process repeated. The recrystallization kinetics obtained from those models were analysed in terms of the JMAK equation, and the grain size distributions were compared with those obtained experimentally. The predicted grain size distribution, in general, did not coincide well with 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 applied to recrystallization. Furu et al.  [911, based on a JMAK-type simulation, showed the  possibility of a transition from three to one dimensional growth (with the associated decrease in n value) during transformation when nucleation was restricted to certain parallel planes. A JMAK-based simulation by Leffers [108] showed that both random nucleation combined with a decreasing growth rate (proportional to t° ) and non95 random nucleation combined with a constant growth rate, could produce an  ii  value  of around 0.8. Doherty et al. [88], using Monte Carlo simulation of two-dimensional recrystallization, obtained n values in the range of 0.4 to 1.1 by allowing a grain to grain variation in the stored energy; under these conditions, the JMAK impingement correction factor (1  —  X) (Eq. 2.7) has been shown to seriously underestimate the real  impingement effects [96]. These, and other results obtained from such simulations have improved the understanding of the physical processes involved in recrystallization and thus aid in refining the existing analytical models [113].  Chapter 2. Literature Review  2.1.4  32  Additivity and Continuous-Heating Kinetics  Determination of the kinetics of recrystallization at a number of different tempera tures, allows one to draw a complete isothermal recrystallization diagram. This TimeTemperature-Recrystallization (T-T-R) diagram gives the relation between the temper ature and the time for any fixed fractional amount of recrystallization.  However, in  industrial practice, the kinetic behaviour of an assembly at constant temperature is fre quently of less importance than its behaviour during continuous heating. 2.1.4.1  The Concept of Additivity  The kinetics of phase transformations under non-isothermal conditions has not been extensively studied using fundamental kinetic equations. Part of the difficulty is that both the nucleation rate and the growth rate are time-dependent parameters under such conditions. One approach to this problem which has been successful is the assumption that the transformation is additive. For the application of the ‘additivity principle’, it is necessary that the transformation behaviour depends only on the state of the assembly and not on the thermal path by which it is reached. For this to be valid, the instantaneous transformation rate has to be a function solely of the amount already transformed and the temperature [69], i.e., =  2.1.4.2  f(X, T)  (2.22)  Proportional Consumption and the Additivity Rule  Christian [69] illustrated additivity by considering a simple non-isothermal reaction com bining two isothermal treatments, as shown in Fig. 2.11. The transformation is consid ered to occur initially at temperature T , for time t, with the kinetic law X 1 to X  =  =  (t) (up 1 f  X ) 1 , and is then continued at a second temperature T 2 (after rapidly heated from  Chapter 2. Literature Review  33  ), with the kinetic law X 2 1 to T T  =  (t), until the total amount transformed is Xa. If 2 f  the transformation is additive, it will continue at T 2 as if the fraction transformed, X , 1 had been transformed at T ; the time corresponding to that, i.e., t 2 2 in Fig. 2.11, is called the ‘virtual time’. If  tal  and  2 ta  are the times taken to transform Xa at temperatures T 1  and T 2 respectively, and if the following equation, termed ‘proportional consumption’, is assumed, 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 of time to reach this stage isothermally until the sum reaches unity. This concept can be generalized into the following ‘additivity rule’, t  L  dt = 1 ta(T)  (2.25)  where ta(T) is the time to transform Xa isothermally at temperature T, and t and tx are the start time and the time to transform Xa respectively, under non-isothermal con ditions. Thus, by using the ‘general rate equation’ (Eq. 2.22) for applying the ‘additivity principle’, and assuming ‘proportional consumption’ (Eq. 2.23) is valid, the ‘additivity rule’ (Eq. 2.25) is obtained. In this derivation of the additivity rule, certain restrictions have been imposed on the isothermal transformation behaviour through the assumption of proportional consump tion. Proportional consumption, as given by Eq. 2.23, implies that a certain fraction of the total reaction time (eg., 10  %)  always corresponds to the same fixed percentage  34  Chapter 2. Literature Review  of the transformation event (eg., 6  %),  irrespective of the isothermal reaction tempera  ture. In a T-T-T or T-T-R diagram, this requires that the curves representing fractional transformation be distributed in a proportional manner within the curves corresponding to 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 an elegant manner. In this illustration, the continuous heating path is considered to consists of several isothermal steps, the first being time step, dt, at temperature T . If the time 1 to transform Xa at T 1 is ta(Ti), then the fractional time consumed will be dt/ta(Ti). , the reaction, if additive, will continue as 2 For the next time step, dt, at temperature T given by the isothermal line at T . Now, if the virtual time at temperature T 2 2 is dt* (the time to produce X 1 at T ), as indicated in Fig. 2.12, then according to proportional 2 consumption, dt*  dt ) = ta(Ti) 2 ta(T  (2.26)  Hence, the addition of the fractional time consumptions corresponding to the first two time steps will be, dt a  dt 1  a  —  (dt*+dt) a  2  2  Summing the fractional increments to T gives, di ia(T)  ta(Tn) 1 ta(Tn) —.  —  228  This illustrates the validity of the additivity rule given by Eq. 2.25 for continuous heating conditions. 2.1.4.3  Isokinetic Transformations  Christian [69] showed that the additivity rule, in the form of Eq. 2.25, can be proven analytically, only if the transformation can be described by a ‘separable rate equation’,  Chapter 2. Literature Review  35  i.e., in a factorized form, dx h(T) dtg(X)  229  where, the rate of transformation is a separable function of temperature, T, and fraction transformed, 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] defined reactions of this kind as ‘isokinetic’, where transformation at different isothermal tem peratures would take the same course, except for the time scale. It should be noted that Avrami [67] originally described isokinetic conditions using a constant nucleation rate (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 be further illustrated by comparing the isothermal reaction rates (given by Eq. 2.29) at two different temperatures, T 1 and T , for any given X, 2 (dX/dt)T 1 2 (dx/dt)T  -  h(T ) 1 ) 2 h(T  2 1 (.3)  This equation suggests that the ratio of the isothermal reaction rates depends only on the temperatures 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 requirements given by Eq. 2.22 and Eq. 2.29. Clearly, neither this kind of isokinetic behaviour nor the associated additivity rule can be inferred from Eq. 2.22 alone. To examine if proportional consumption is attainable for any isokinetic reaction using the JMAK equation (Eq. 2.11), x  =  1  —  exp(—bt”), requires rearranging of the JMAK  equation to obtain the transformation time, t, [ln(1_X)]* =  (2.32)  Chapter 2. Literature Review  36  Differentiating the JMAK equation with respect to time and combining with Eq. 2.32 gives, dx  di  —  ‘  (  2 33  ]n_1/n  [  1 1-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 previously reported [115]. The validity of the additivity rule (Eq. 2.25) for this condition has also been illustrated [116]. To illustrate proportional consumption for the case corresponding to Fig. 2.11, let the JMAK parameters n , b 1 1 describe the isothermal event at temperature T , and 1  , 2 ii  2 b  at temperature T . For the notations given in Fig. 2.11 it can be shown, using Eq. 2.32, 2 (ti/ta,)i  —  )T (12/1a 2  —  ln(1 ln(1  —  —  ) 1 X  (-)  ( 234)  Xa)  Now, if n is a constant, \  = 1 aJ’p  (2.35) \  a2J7’2  This shows the validity of proportional consumption for a constant n.  Under these  conditions, the ratio of the isothermal reaction rates for a given X can be calculated from Eq. 2.33, 1  ’ 1 (b  1 (dX/dt)T 2 (dx/dt)T  (2.36)  =  When b is solely a function of temperature, and n is a constant, this satisfies the isoki netic condition expressed by Eq. 2.31. All these illustrations remain valid when the S-F Equation (Eq. 2.21), X/(1  — X)  =  , is used to describe the isothermal recrys m kt  tallization kinetics with a constant m and temperature dependent k. These derivations illustrate that certain transformations are isokinetic, and for those isokinetic reactions, the proportional consumption and hence, the additivity rule (Eq. 2.25) are valid.  37  Chapter 2. Literature Review  2.1.4.4  Kinetic Calculations for a General Transformation  The 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 time consumed, dt/ta(T), is calculated, • the calculated fractions are added until the sum reaches the appropriate fraction transformed or unity (in the case of fractional time). When proportional consumption is valid, it can be seen from Fig. 2.12 that both these Xa and d/ta(T) = 1.  sums reach the total at the same instant, i.e., >ZdX(T)  This is not the case for any general non-isokinetic type transformation. As an illus tration, a case with an increasing JMAK exponent, n, with temperature is considered, ; such kinetic behaviour has been reported for recrystallization 1 2 > T 2 > n i.e., n 1 for T on a rimmed low-carbon steel [57]. Now, from Eq. 2.34, the following relationship can , 1 be derived since Xa > X (2.37)  > \ta2IT  ‘\taiJj  , to 1 This equation suggests the fractional time consumption at a lower temperature, T . This results, when applied 2 be equivalent to a larger fraction at a higher temperature, T to Fig. 2.12 as in Eq. 2.27 will give, dt \  +  a1i)  dt fm \  ) 2 tal  (dt*+dt)  (2.38)  ) 2 tal  Now, when the summation is performed in the usual manner, either of the following combinations will be possible, EdX(T) = Xa,  ta(T)  <1  or  1(T)  =  1, dX(T) > Xa  (2.39)  Chapter 2. Literature Review  38  These calculations illustrate the difficulties associated with the modelling process if the transformation is not an isokinetic one. 2.1.4.5  A Summary on the Various Conditions of Additivity  There is some confusion regarding the terminology and the different conditions available to describe additivity. The different additivity descriptions and their inter-relationships have also been studied from the mathematical point of view [117, 118, 119]. Based on those studies, and from the discussion in this section, it can be concluded that there are basically three different conditions that have to be met to assume a transformation is additive: 1. the ‘general rate equation’ given by Eq. 2.22 (this is the basic requirement for the application of the ‘additivity principle’), 2. the ‘separable rate equation’ given by Eq. 2.29 (‘isokinetic condition’ and ‘propor tional 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 con ditions. 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 condition 3 [117]. On the other hand, condition 1 will not lead to conditions 2 or 3 without the additional assumption of isokinetic condition or proportional consumption. Hence, there are really only two types of additivity conditions. The former one, given by condition 1, can be used for a broad range of situations whereas, the later one, given by either condition 2 or condition 3, is valid only for the isokinetic-type transformations [117, 119].  39  Chapter 2. Literature Review  When the JMAK equation describes the isothermal event, isokinetic transformations re quire  ii  to be a constant and b to be solely a function of temperature [115, 116, 118], and  these restrictions will lead to a single additivity model since all three conditions are the same. 2.1.4.6  Scheil Equation for Incubation and Its Applications  Scheil [120] originally proposed an equation similar to Eq. 2.25 to determine the incu bation period during a non-isothermal event. He assumed that the time spent at a par ticular 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 of transformation 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 proportional consumption 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 con siderably longer start times than were actually observed. Recently an attempt [123] was made to address this problem in austenite-to-pearlite transformation by incorporating ideal isothermal incubation times into Scheil predictions. These ideal start times, corre sponding to an infinite cooling rate rather than an experimental one, could be calculated either from experimental CCT curves through an inverse additivity procedure [124] or based on isothermal experiments performed with two different initial cooling rates [125]. Although this approach marginally improved the predictions, it is thought that the most serious problem with the Scheil equation is its assumption of proportional consumption,  Chapter 2. Literature Review  40  as was illustrated by Moore [126] in an early work on austenite decomposition. Moore [126] conducted stepped isothermal experiments at two different temperatures with known incubation times, and observed the start of the reaction microscopically. The sum of the fractional incubation times corresponding to the start of transformation was invariably less than unity during austenite-to-ferrite transformation. He explained this by suggesting the non-equivalence between a given percentage of the incubation period spent at different temperatures, and correlated these effects to the smaller critical size of the ferrite nuclei at lower temperatures. During a step-down experiment, an unstable nucleus at a higher temperature might become a stable one at a lower temperature, suggesting disproportionately larger effects of early nucleation on later nucleation at a different temperature. He also interpreted the experimentally determined incubation period as a composite of two separate processes, a period of nucleation, followed by a period of growth which extends beyond the completion of incubation. Although Moore suggested these effects to be minimal during continuous cooling, his study clearly indicates that incubation may not be an additive process. 2.1.4.7  Application of Additivity for Transformation Kinetics  The principle of additivity has been successfully applied to predict the kinetics of austenite ferrite 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 was employed to describe only the transformation event (excluding incubation), the JMAK time-exponent, n, showed little dependence on temperature and therefore described as a mean ñ value, and b was a strong function of temperature, thus satisfying the isoki netic requirement. Good agreement between the additivity predictions and the exper imental measurements during continuous cooling were reported under those conditions [115, 121, 122].  Chapter 2. Literature Review  41  The same approach was successful in describing the recrystallization kinetics of a cold rolled, rimmed, low-carbon steel continuously heated at a rate simulating batch annealing [39, 57, 128]. A comparison of the predicted and experimental kinetics are shown in Fig. 2.13. Fig. 2.13 also compares the effectiveness of the JMAK and the S-F equations in describing the continuous heating recrystallization kinetics. The good agreement obtained for both approaches supports the experimental validity of applying the additivity principle to describe non-isothermal recrystallization. 2.1.4.8  Criteria for the Validity of Additivity  In general, a reaction involving two different time-temperature dependent parameters corresponding to nucleation and growth, will not be additive. However, if the reaction is controlled by a single time-temperature parameter, it is then isokinetic (as indicated by Eq. 2.30) and will be additive. Avrami [67] demonstrated the validity of additivity when the nucleation rate, N , is proportional to the growth rate, G, over a range of tempera 7 tures. Cahn [114] introduced a less restrictive additivity requirement based on ‘early site saturation’, where nucleation sites are rapidly exhausted and the subsequent transforma tion kinetics are dominated by growth, a temperature dependent parameter. Based on experimental measurements on the pearlite transformation, Kuban et al. [115] proposed that ‘effective site saturation’, an even less stringent condition, would also satisfy the additivity requirement. This condition proposed that the added volume associated with the incremental growth of the large, early nucleated sites dominate the later stages of the transformation kinetics. Recently the principle of additivity was tested by Kamat [129] by examining the proeutectoid ferrite transformation under step-quenching conditions, where the ferrite growth is controlled by long range diffusion processes. Early site saturation was observed at all temperatures during the transformation. The use of the JMAK equation (as an  42  Chapter 2. Literature Review  empirical equation to describe the sigmoidal transformation kinetics), in conjunction with the additivity principle was successful in describing the non-isothermal transformation kinetics. The validity of applying the additivity principle to describe non-isothermal recrystal lization 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 been reported to be instantaneous [33, 37, 38, 75, 80, 81], thereby satisfying the early site saturation condition. For this condition, additive behaviour would be expected. 2.1.5 2.1.5.1  Annealing Phenomena in Low-Carbon Steels Structural Changes during Cold-Rolling and Annealing  When a cold-worked metal is held at any homologous temperature, TH, above  ‘S-’  0.1, some  recovery 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, the energy input will be sufficient to overcome the activation energy requirements for other recovery mechanisms, such as the motion and rearrangement of dislocations [86]. In metals of high stacking fault energy such as iron, the initial structure that forms after heavy deformation (60  -  80  % cold work) consists of cells whose walls are tangled  dislocation arrays of very high density, with some dislocations in the cell interiors. These metals, in pure form, when heated to a sufficient temperature, undergo a considerable amount 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 forms during deformation, and the reduced tendency for dislocations to cross-slip leads to the formation of planar dislocation arrays with a high strain energy.  This constitutes a  strong driving force for recrystallization, so that recrystallization is likely to proceed  Chapter 2. Literature Review  43  before recovery progresses significantly [86]. Emphasizing the iron-base alloys, initial recovery results in the tangled dislocations in the cell walls rearranging themselves into lower energy configuration, and the interior dislocations migrating towards the cell walls. Dislocations are also reduced in number due to a variety of annihilation processes. The cell walls become more clearly defined with greater misorientation and eventually form subgrains of about the same size as the initial cells. These subgrains remain at about the same size until quite late in the recovery pro cess when they may begin to grow [29]. Hu [53] attributed the observed subgrain growth to ‘subgrain coalescence’, based on transmission electron microscopic observations of 80 % cold-rolled silicon-iron single crystals. The coalescence process, shown schematically in Fig. 2.14, involves a gradual moving of dislocations out of the subgrainboundary be tween two cells, to the boundaries surrounding them, and a rotation of the subgrain itself into the same orientation as its neighbouring subgrain. This mechanism requires lattice diffusion, and consequently a moderately high temperature is needed. Misorientation increases during the coalescence process, and a cluster of coalesced subgrains eventually becomes 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 sug gested that a small region of high dislocation density, and therefore of high strain gradient and substantial local misorientation, turns into a small strain-free cell by a process of dislocation climb and rearrangement. Polygonized domains or subgrains thus formed at relatively high temperatures, are dislocation boundaries of high mobility (misorientation of 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 large subgrairi, a highly misoriented subgrain, even if it is not larger than the average size, can also grow freely at the expense of its neighbours. A growing subgrain with an increasing  Chapter 2. Literature Review  44  misorientation angle eventually becomes a nucleus for recrystallization. There is considerable debate as to whether the initial growth of subgrains occurs by subgrain 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 subgrain coalescence and low angle boundary migration, no single process being dominant. Exper imental observations support the occurrence of both these processes during recovery of iron based alloys [30]. Cahn [131] suggested that the later stages of growth of a nucleus formed by either mechanism would be due to the migration of boundaries with increased misorientation. In some lightly deformed metals, nuclei formation has been attributed to straininduced boundary migration or grain boundary bulging. When the strain is low, the dislocation density varies from grain to grain. As a result, a short segment of an ex isting high angle boundary anchored by the substructure in one grain may bulge out into a region of higher density to produce a roughly spherical volume (relatively free of dislocations) 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 vacancies to solute atoms, and also reduce the stacking fault energy permitting dislocations to extend into partials, making climb and cross-slip more difficult. These effects render network nodes more resistant to unpinning [133]. Solute atoms also reduce sub-boundary mobility, causing further retardation of recovery. When the diffuse cell walls formed during deformation are broader than the interparticle spacing, the particles can stabilize networks of subboundary dislocations, and hence interfere with the conversion of the cell structure into well-defined subgrains. In addition, small particles retard subgrain growth rate by Zener pinning of migrating low angle boundaries and by hindering coalescence through the inhibition of boundary to boundary dislocation transfer [132].  Chapter 2. Literature Review  45  Recrystallized grains nucleate preferentially in a region where residual damage due to plastic deformation is greatest. This observation is usually explained in terms of a localized high dislocation density and a substantial local lattice curvature. Cahn [131] suggested the existance of substantial local lattice misorientation to be a necessary pre condition for nucleation of recrystallized grains. A high density of nuclei observed at deformed grain boundaries, deformation bands and coarse particles can be explained in this 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 deformation bands; 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 were observed, and consequently no recrystallization occurred even at a temperature as high as 800°C [53]. Second phase particles influence the formation of recrystallization nuclei by altering the density and distribution of dislocations in the metal matrix [134]. If the particles are harder than the matrix, the matrix immediately adjacent to the particles will be deformed to a greater extent.  Large particles give rise to an increased local lattice  misorientation, and hence will be favoured nucleation sites. A critical particle size of 0.74 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 formation of joint deformation zones. Other investigations on steels have also indicated that large particles 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 % cold reduction. For commercially pure iron, cold rolling produced a cell structure, with the cell wall thickness varying widely up to 1 m. Recovery occurred at high temperatures with an overall reduction in dislocation density. In particular, the tangled dislocation  Chapter 2. Literature Review  46  walls became thinner and more sharply defined, although no significant change in the relative misorientation was observed. A general growth of cells up to approximately 5 was reported after 2 h at 550°C, and recrystallization proceeded within the recovered structure. However, for the highly pure zone-refined iron, the cells formed after cold rolling were much coarser, and the misorientation across the cell walls was of the order of 2 to 3°. The nuclei for recrystallization were observed to grow directly from the coldworked cells at lower temperatures (‘-.. 350°C), without going through any significant structural changes prior to the onset of recrystallization. Dillamore and co-workers [78, 137] studied annealing of 70 % deformed high purity iron and Al-killed steel by TEM observations. They demonstrated an increasing level of stored 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 misorientation were associated with an increased stored energy level. For high purity iron, subgrain structures in {111} < 110 > and {110} < 110 > oriented grains coarsened more rapidly than in either {0O1} < 110 > or {113} <  110  >  oriented grains. A higher growth rate was  attributed to higher stored energy and to a wider initial subgrain size distribution. Other researchers have observed more complex deformation patterns and associated smaller, more elongated deformation cell structures with larger mean boundary misorientations near grain boundary regions, when compared to grain interior [132]. The effects of cold rolling and annealing on the microstructure in rimmed and Al killed steels were examined by Goodenow [138]. The cold rolled cell structure within an individual grain appeared to be uniform and arranged in one of two distinct groups; one consisted of small, elongated cells of 0.5 to 1 tm arranged in parallel rows and the other contained large cells of 1 to 2 tm arranged randomly. Some grains appeared to con tain both groups separated by a transition zone. Depending on the initial cell structure, two different groups of subgrains were observed after initial recovery. With continued  Chapter 2. Literature Review  47  annealing, the larger subgrains appeared to grow by a slow sub-boundary migration pro cess. However, the small subgrains were observed to merge with one another, primarily through a coalescence process. It was these small subgrains that eventually grew by ad ditional coalescence and boundary migration to form the nuclei. In addition, coalescence seemed to occur more readily at the relatively finer cell structure observed along grain boundaries and was responsible for most of the nucleation of recrystallized grains [138]. The structural changes associated with recovery and recrystallization in cold rolled Ti-stabilized [21] and Nb-stabilized [17] I-F steels have been investigated by TEM obser vations. The general observations were similar to those reported for rimmed and Al-killed steels, i.e., elongated dislocation cell structures formed as a result of cold rolling; dislo cation densities decreased and subgrains formed during recovery; continued subgrain formation, coalescence and growth eventually lead to nucleation. For Ti-stabilized steels, coalescence and growth of subgrains at prior grain boundaries was reportedly the main source of recrystallization nuclei [21]. Davidson and West [139], in a study on 80 % cold-rolled low-carbon Nb-microalloyed steels, observed retardation of cell formation and refinement of cell size caused by the distributions of small Nb(C,N) particles. They also noted these effects to be grain ori entation sensitive. In grains with {100} planes oriented parallel to the rolling plane, cell formation was restricted more severely than in {111} oriented grains. A tendency for nucleation to be biased towards grain boundaries has been observed and attributed to the suppression of general nucleation by particles [139]. Recrystallization is considered to commence when the outermost boundary of a grown subgrain 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]. Growth into the deformed material then occurs by the migration of the high-angle boundary. The driving force for migration is provided by the reduction in dislocation density, typically  Chapter 2. Literature Review  from  ‘-  2 to m 6 10’  ‘—i  48  , between the interior of a recrystallized nucleus and the 2 10’°m  surrounding cold worked metal [29]. The driving force continuously decreases during annealing due to recovery effects in the unrecrystallized matrix and also due to the fact that grains initially nucleate in the areas of highest stored energy. The mobility of a boundary, as well as the driving force, strongly influences the kinetics of boundary migration. In particular, the misorientation across the boundary, and in some cases the orientation of the boundary itself, significantly influence the rate of migration [140, 141].  The kinetics of grain boundary migration in the absence of  impurities has been adequately described by considering the transfer of single atoms across the boundary to be the elementary process involved [140]. Small amounts of solutes 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 of small particles on the migrating grain boundaries [132]. 2.1.5.2  Recovery and Recrystallization in Iron and Its Solid-Solutions  Polycrystalline zone-melted iron has been shown to recover relatively easily with an acti vation energy increasing from 91.9 to 281.7 kJ/mole; these activation energies correlate to vacancy migration and self-diffusion in iron, respectively [40]. However, solute atoms and fine precipitate particles in alloy systems, reduce the relative ease with which recovery occurs. Pure iron displayed much more softening (reduction in hardness) during recrystalliza tion than could be attributed to recrystallization alone, due to the concurrent recovery processes [35]. A few ppm of interstitial impurities, carbon [35] and nitrogen [36], when added to pure iron, showed a strong effect in reducing recovery; these effects were more evident for nitrogen than for carbon. For example, at 400°C, recovery processes occurring prior to the onset of recrystallization caused more than 50 % of the total softening in  Chapter 2. Literature Review  49  pure 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 display similar retardation effects on recovery. Fig. 2.16 [38] shows the effects of increased Mn on percentage softening during isothermal recrystallization. The combined effect of alloying additions in amounts typical of low carbon steel (0.52 Mn, 0.06 C, 0.005 Al) is also shown in Fig. 2.16, indicating that % softening and % recrystallization are approximately equal. These observations suggest that the extent of recovery is considerably reduced with in creased alloying additions and that the recovery effects are less important in low-carbon steel. The recrystallization characteristics of high-purity iron after 60  % cold working were  investigated by Rosen et al. [72] in the temperature range of 517 to 632° C. They observed the formation of nuclei only at certain boundaries of deformed grains; consequently re crystallization was rapid for those grains, but very slow for others. These stable deformed grains were eventually consumed by an extremely slow growth process from the surround ing grains. They observed a decreasing isothermal growth rate, and associated it with the very coarse grain size of the stable grains. Leslie et al. [38] observed recrystallization in iron to be a growth controlled process, with substantial nucleation occurring at zero time. They attributed the measured decreasing isothermal growth rates to the reduction in driving force resulting from concurrent recovery. The JMAK equation has been shown to describe the kinetic measurements only at the beginning of recrystallization, as can be seen in Fig. 2.7 [72]. Two distinct stages could be seen in Fig. 2.7; the first was growth-controlled, and the second was attributed to the lack of initial nucleation. The recrystallization 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 recrystallized after 2 h at 350°C whereas commercially pure Armco iron completely recrystallized after  Chapter 2. Literature Review  50  2 h at 600°C [136]. Such anomalous disparities in the recrystallization kinetics, often ex hibited by iron, were speculated to be due to the strong interaction between some trace elements (eg., P, As, Sb, Sn) and the boundaries or sub-boundaries [37, 38] Recrystallization kinetics have been characterized either in terms of separate nucle ation and growth activation energies, QN and  QG,  or an overall recrystallization activa  tion energy, QR [142]. Typically, an Arrhenius-type relationship is assumed, Rate where  tR  =  =  AR exp  (  (2.41)  RT)  is the time required for a constant fraction of the specimen to recrystallize, K  is a constant, T is absolute temperature, R is the gas constant, AR is a pre-exponential constant, and QR is recrystallization activation energy. Rosen et al. [72] reported a constant QR value of 335.9 kJ/mole for pure iron at temperatures above 590°C, which then increased with a decreasing temperature. They attributed this change to the rapid reduction in recrystallization rate observed towards completion. a  QG  They also reported  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 increasing  temperature, and reported that QR could vary between 125.3 and 367.7 kJ/mole for zone-melted iron. Their studies on dilute binary solid solutions of iron indicated the non existence of any simple relationship between temperature, solute content and activation energy; the effect of solute content on growth rate was observed to change the pre exponential constant, rather than affect the activation energy. Small amounts of carbon added to high purity iron were reported to cause only a slight reduction in the recrystallization rate [35]. This, in contrast with the stronger effects of substitutional solutes, was partly explained in terms of the high mobility of the interstitials. It was further speculated that any reduction in grain boundary  mobility  caused by carbon would be compensated for by the greater stored energy in the system,  Chapter 2. Literature Review  51  due to the reduced recovery [35]. Similar conclusions were made regarding the nitogen additions, except for its stronger retarding effect on recrystallization [36]. The alloying additions to iron usually have a strong inhibiting effect on the growth of 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 additions up to 0.04 at. % [37] have been shown to considerably reduce the rate of grain growth during recrystallization. The effect of Mo was reported to be much more pronounced than that of Mn. Recrystallization in these dilute iron solid solutions was characterized primarily as a growth-controlled process, with a decreasing isothermal growth rate and with 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. Titanium and niobium in solid solution were also reported to strongly retard recrystallization in iron-based alloys [130, 143]. Several mechanisms have been put forward to explain the retarding effect of solute atoms on grain boundary mobility. Lucke and Detert [144] assumed an elastic interaction between grain boundaries and solute atoms which tends to increase the concentration of the solute along grain boundaries. Except at very low solute concentrations or at high temperatures, the mobility of the boundary is assumed to be controlled by the rate of dif fusion of the accompanying solute atoms. This may also explain the previously described ineffectiveness of the highly mobile C and N in reducing the rate of grain boundary mi gration. Leslie et al. [37] proposed that the growth of recrystallized grains is inhibited by clustering of solute atoms at imperfections (ahead of the migrating boundary) in the Un recrystallized matrix. Abrahamson and Blakeney [143] considered the electronic effects, and noted a correlation between the rate of change of recrystallization temperature with atomic percent solute and the electron configuration (the number of d-shell electrons) of  Chapter 2. Literature Review  52  the solute element. In a study by Leslie et al. [38], a low-carbon steel was found to recrystallize consid erably faster than high-purity iron. They attributed the rapid recrystallization in the steel to the increased number of nucleation sites caused by a smaller initial grain size, the presence of large, hard second phase particles (Fe C, inclusions) and the increased 3 driving force due to highly reduced recovery effects. They suggested that these effects could outweigh any decrease in the growth rate caused by the larger amounts of solutes in the commercial steel. A study on rimmed low-carbon steel [39, 56] revealed negligi ble changes in hardness and x-ray peak resolution due to the recovery effects occurring during recrystallization, and the steel recrystallized relatively easily in the temperature range of 480 to 560°C with a sigmoidal-shaped kinetic response. The JMAK equation with a time-exponent of 0.68 described the kinetics reasonably well as indicated in Table 2.1 [39]. Aluminum-killed low-carbon steels were reported to recrystallize much more slowly than rimmed steels, and their kinetic response is often not characterized by a sigmoidal type relationship. In particular, recrystallization at low isothermal temperatures was observed to be severely retarded [138]. It was also reported that Al-killed steels sometimes display an initial period of recrystallization, followed by a levelling off period of very slow kinetics, and then followed by rapid recrystallization [145]. The slower annealing behaviour and the associated texture development in Al-killed steels were attributed to pre-precipitation clustering of aluminum and nitrogen at subgrain boundary sites developed by prior cold working [138, 146, 147]. This clustering has been shown to inhibit nucleation by preventing subgrain growth and consequently retard recrystallization [147]. Some slowing down of recrystallization was also attributed to the impeding effect of precipititates on the mobility of high angle grain boundaries [148].  Chapter 2. Literature Review  2.1.5.3  53  Recovery and Recrystallization Kinetics in I-F Steels  The matrix of an I-F steel is interstitial-free iron, and consequently these alloys may undergo considerable amount of recovery, comparable to that of pure iron. However, the recovery 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. The presence of a fine precipitate distribution may additionally retard the recovery effects in I-F steels. No quantitative studies characterizing the recovery processes occurring in I-F steels during recrystallization were found in the published literature.  However, several in  vestigations have indicated that a considerable amount of recovery occurs prior to the onset of recrystallization. Fig. 2.17 [21] shows the effect of isothermal annealing on the yield strength and the % elongation of a cold rolled, Ti-stabilized, I-F steel. The tensile properties recovered linearly with the logarithm of time until the onset of recrys tallization; recovery alone contributed to approximately 50  % of the reduction in yield  strength. This recovery response is similar to that reported for pure iron [36, 40]. The residual line broadening measurements obtained by Satoh et al. [15] on unstabilized and Ti-stabilized (see Fig. 2.4) extra-low-carbon steels indicated that considerable recovery could 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 residual line broadening measuments for unstabilized and Ti-stabilized extra-low-carbon steels [15] indicated that Ti additions decrease the extent of recovery. Tensile strength and yield strength of a Nb-stabilized I-F steel decreased by about 15 % before the commence ment of recrystallization, while no such recovery effects were visible in terms of the ratio of tensile strength to yield strength or the hardness measurements [17]. I-F steels are known to recrystallize in a very sluggish manner. The major retarding  Chapter 2. Literature Review  54  effect is caused by the type and amount of excessive stabilizing elements in the iron matrix and the size and distribution of the associated precipititates. Fig. 2.18 shows isothermal Time-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 those obtained for rimmed and Al-killed steels [138]. The retarded recrystallization apparent in 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. Another study by Yoda et al. [149] showed that the half-recrystallization temperature was more closely 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-stabilized extra-low-carbon steels also indicated the retardation of recrystallization caused by Ti additions. Goodman et al. [16] simulated continuous annealing cycles with many different Tistabilized steels, and measured the recrystallization temperature, TF, i.e., the necessary soak temperature (soak time of 15 s) for the completion of recrystallization. They at tributed the high measured TF values to both the excess Ti content and the TiC precip itate distribution. They also found a relationship between TF and the excess titanium in solid solution, as shown in Fig. 2.19. Hayakawa et al. [150] also estabilished a similar strong relationship between the recrystallization temperature and the excess Ti content. In addition, several other continuous annealing simulation studies on low-carbon steels indicated 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 Nb treated I-F steels by softening response and microscopy. The initiation of recrystallization was observed at the free surfaces, and these layers thickened with increasing temperature or time. This observation was explained in terms of the surfaces, having an increased dislocation mobility, being the preferred nucleation sites when recrystallization is severely  Chapter 2. Literature Review  55  retarded. The recrystallization start temperature, TR, increased markedly with increasing levels of Nb in solid solution, as shown in Fig. 2.20 [17]. The values of TR shown as open circles on the left hand side include the effects of precipitates as well as Nb in solid solution. The values shown along the curve on the right hand side were obtained after the effects of precipitates were minimized by sufficiently coarsening them prior to cold reduction; 0.5 h at 870°C increased the average diameter of the NbC precipititates from approximately 5 to 40 nm. These data, being representative of the effect of Nb in solid solution, indicate its dominance over precipitates in retarding recrystallization. The same study 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, due to the size and density of the precipitate distribution [17]. Wilshynsky et al. [153] studied the recrystallization of I-F steels stabilized with Ti and/or Nb, and compared the kinetics obtained with those for an unstabilized, Al-killed steel. The unstabilized steel recrystallized the most rapidly, followed by Ti-stabilized and Nb-stabilized steels in that order. The sigmoidal-shaped kinetic curves obtained for one testing condition are shown in Fig. 2.21 [153]. They observed the formation of the newly recrystallizing grains only along certain cold-worked boundaries, as was reported previously for pure iron [72]. Large Ti-rich precipitates, of the order of 1 1 um in diameter, were observed to act as preferred nucleation sites in the Ti-steels. Despite this, the recrystallization kinetics were more sluggish in Ti-steels than in unstabilized steels. 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 fine Nb(C,N) precipitates, as well as Nb in solution [153]. This study, together with another similar 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  56  Except for the few observations reported by Wilshynsky et al. [153], little information has been published concerning the nature of the nucleation and the growth processes that control the overall kinetics of recrystallization in I-F steels. However, similarities in the general recrystallization response between I-F steels and other dilute solid-solutions of iron would be expected. The retarding effect of precipitates on recrystallization was treated by Hansen et al. [154} in the following manner. The force of recrystallization, FR, which is the force per unit area related to the reduction of strain energy, or the reduction of dislocations generated by the cold work, was given by, FR =  where  t  ()  (zip)  (2.42)  is shear modulus, b is burger’s vector, and /p is the change in dislocation density  between the cold worked and recrystallized grains. The restraining force on boundary migration per unit area of spherical particles could be written as, =  where  f is  (2.43)  volume fraction of particles, ‘y is interfacial energy per unit area of boundary  and 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 and  recrystallized grains [155]. Boundaries will be pinned only when F is greater than FR. The observation that precipitates impede grain boundary motion in one instance, but not in another [153], can be explained in terms of the changes in FR and/or F. The large number of discontinuities observed in the grain boundaries of a partially recrystallized Nb-steel [153] indicate that the boundary motion has been significantly impeded; this can be correlated to a high value of F caused by a high density of fine precipitates, as given by Eq. 2.43.  Chapter 2. Literature Review  57  The precipitates in I-F steels are randomly scattered, and consequently do not appear to exert any significant influence on grain morphology [17, 21, 153]. Goodman et al. [16] obtained recrystallized microstructures consisting of equiaxed ferrite grains, with grain sizes 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 in certain directions, resulting in the observed blocky grain morphology. Goodenow and Held [21] observed the hot rolled structure of a Ti-stabilized I-F steel to be equiaxed (grain size of ASTM No. 9  -  10), with numerous fine Ti(C,N) particles  smaller than 0.1 1 um, uniformly scattered through the grains. A few large particles, thought to be Ti sulfide and oxide, were also present. They reported that the size and distribution of precipitates were the same for both the initial hot rolled and the final fully recrystallized specimens. Unlike in Al-killed steels, sigmoidal-shaped isothermal recrystallization kinetic curves were obtained for all test temperatures between 450 and 900°C, giving additional indication for the absence of precipitation or dissolution in this temperature 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 precipitates reportedly present after hot rolling and coiling, survived cold rolling and remained stable during annealing [153]. Hook and Nyo [17] observed Nb-stabilized steels to recrystallize in the 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 the hardness measurements after long holding times (3600 s) at temperatures above 700°C [17].  Chapter 2. Literature Review  2.2  58  Development of Texture during Cold Rolling and Annealing  Deformation textures have their origins in the crystallographic nature of the deformation processes of slip and twinning. During the slip process, the crystal lattice rotates as a result of the shape change and the geometrical constraints of its surroundings. The restricted number of slip systems available produces rotations towards a limited number of end points and consequently a deformation texture is produced. During recrystallization, new grains with different orientations are nucleated and grow at the expense of the cold worked matrix; these processes lead to an overall texture modification. The mechanical behaviour of single crystals is anisotropic, and therefore preferred orientations have a significant effect on the properties of materials. In a strongly textured sheet metal, the yield stress varies with direction in the plane of the sheet as well as across the sheet thickness; such effects are critically important during non-uniform flow encountered in deep-drawing operations [156]. 2.2.1  Methods of Representation of Texture  Texture can be defined as the orientation distribution of all crystallites in an assembly of grains [157]. Traditionally, preferred orientations are described by means of pole fig ures. Pole figures are stereographic projections which show the distribution of particular crystallographic directions and are readily determined using techniques employing the principles of x-ray diffraction. The Schulz reflection method [49, 156, 158, 159] is com monly used for determining textures in sheet metals; the peripheral areas of the pole figure are not determined in this method due to some defocussing effects. In the Schulz reflection method, the normal to the diffracting planes {hkl} remains fixed in space while the specimen is rotated through a wide range of angles, and whenever a crystal becomes appropriately oriented, a diffracted intensity is measured; the total diffracted intensity  Chapter 2. Literature Review  59  at 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 steel in 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 parallel to the sheet surface, and the < 112 > directions in that plane lie parallel to the rolling direction). For deformation processes of higher symmetry that require only one axis to be speci fied (e.g., cold drawing), a satisfactory description of the texture can also be given by an inverse pole figure [49, 156]. An inverse pole figure uses a crystallographic unit trangle as a reference frame with contour lines to show the frequency with which the various directions in the crystal coincide with the specimen axis under consideration. In the case of sheet specimens, inverse pole figures are determined for normal (ND), rolling (RD) and transverse (TD) directions; three such inverse pole figures obtained for a 70 % cold rolled steel are shown in Fig. 2.23 [160]. Inverse pole figures are of great interest as related to the uniaxial properties (properties that depend only on one crystal direction) of a textured material; in this case, the inverse pole figure is the weighting function needed in order to calculate the mean values of the single crystal properties [161]. In particular, ND inverse pole figures can be determined easily for a sheet metal by the usual difFractometry method [49, 156, 158, 162]. These integrated intensity measurements have been found to be useful in correlating the texture evolution and the associated changes in plastic anisotropy [15, 21, 55, 163]. Although pole figures and inverse pole figures provide a useful description of the tex ture 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, a pole figure (or inverse pole figure) specifies only two independent variables [49, 156, 164].  Chapter 2. Literature Review  60  This difficulty has been overcome by the use of the orientation distribution function (ODF), which describes the frequency of occurence of particular orientations in a threedimensional orientation space. This space is defined by three Euler angles which consti tute a set of three consecutive rotations that must be given to each crystallite in order to bring its crystallographic axes into coincidence with the specimen axes. The description of crystal orientation by indices of crystal directions and by Euler angles p, q and  S02  are schematically shown in Fig. 2.24 [157]. The complete ODF consists of the sets of rotations pertaining to all the crystallites in the specimen. The fundamental relationship between pole figure and ODF is based on the fact that the diffraction process does not see a rotation of the crystallites about the normal direction to the reflecting lattice plane. As a result, a pole figure is an integral over the ODF and consequently, ODFs are calculated by a method called ‘pole figure inversion’. Mathematical methods have been developed by Bunge [165, 166, 167, 168] and Roe [169] that allow ODFs to be calculated from the numerical data obtained from several pole figures. According to the analysis (‘series expansion’ or ‘harmonic method’) presented by Bunge [165], an ODF may be expressed as a series of generalized spherical harmonics, 00  f(cp1,q,co2)  +1  +1  ’(q5) 2 m 1 exp(imç 1 ) C F exp(in )  =  (2.44)  1rO m=—1 ,=—.1  p m n() are certain generalisations of the as where C are the series coefficients and 1 sociated Legendre functions. It is the C-coefficients, C, that are calculated from the experimentally determined partial pole figures [165]. For cubic/orthorhombic crystal/specimen symmetry, a three-dimensional orientation volume may be defined by using three orthogonal axes for y, q and the Euler angles ranging from 0 to  900.  2  with each of  Any point in this space corresponds to a single  orientation (hIcl)[uvw] and the density at that point is the strength of the texture com ponent in multiples of random units. A three-dimensional view and a  45° section of  Chapter 2. Literature Review  61  the Euler space, indicating the locations of some important ideal orientations are shown in Fig. 2.25 [164, 166]. Regions of higher and lower orientation density are separated by contour surfaces, and the results are usually presented as a series of parallel sections (constant cp 1 sections for b.c.c. metals) through this space. Since the ODF image in the Eulerian space is not very descriptive, the ODF information is sometimes presented as orientation densities along selected fibres. Fig. 2.26 shows an example where the devel opment of recrystallization texture during isothermal annealing (700°C) of a 90 % cold rolled 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 texture development to cold rolling and annealing parameters [170, 171, 172, 173, 174]. 2.2.2  Crystallographic Texture and Plastic Anisotropy  An important requirement for many applications involving sheet steel is good deep drawability. Drawability is the capacity to achieve maximum plastic flow in the plane of the sheet and maximum resistance to flow in a direction perpendicular to the sheet; this condition reflects the normal anisotropy of the sheet. In addition, the plastic flow in the plane of the sheet varies along different directions, and such planar anisotropy leads to the formation of ears during drawing operations. In phenomenological plasticity theory, the anisotropic plastic behaviour is described by the anisotropic yield locus [161, 175, 176]. In practice, however, the anisotropy of plastic flow is often correlated to the Lankford parameter ‘r’ [2, 22, 23, 156, 163], which  is 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]. Since  anisotropy has been observed not to change significantly with straining, r is usually determined from the measurements of true finite strains. Typically, the measurements are made from a standard tensile specimen strained to approximately 15 % elongation;  Chapter 2. Literature Review  62  conventionally, it is the width (em) and length ( ) strains that are measured due to the 1 difficulty of determining the thickness strain  (Et)  accurately in a thin sheet [156]. Thus,  based on the volume constancy during plastic deformation, r=—=  —E  In rolled products, r values are usually measured in the rolling direction (ro), at 45° from the rolling direction (r ) and in the transverse direction 9 45 (r o ). The average strain ratio, i (or  rm),  commonly defined as, =  0 + 45 (r 2r + rgo)  (2.46)  is a good characterization of the average anisotropy of the sheet. While  is a conve  nient measure of the normal anisotropy, the extent of planar anisotropy is related to the parameter, r, defined as, (ro The good correlation between high  i  —  90 r +)  (2.47)  values and good deep-drawability has been clearly  demonstrated [175, 177, 178, 179]. It has been suggested that the ideal deep-drawing steel 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 anisotropic flow properties of single crystals and the nature of the existing crystal orientation. Theo retical calculations for single b.c.c. crystals, based on the assumption of pencil glide slip in < 111 > directions, have indicated  to be strongly dependent on crystal orientation  [2]. It was also reported based on similar calculations that the values of r , r 0 45 and r 90 were 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 observa tions 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]. In  Chapter 2. Literature Review  63  particular, the ratio of the strengths of the {111} and {OO1} texture components has been shown to correlate well with the measured f values, and an experimental verification of this relationship is shown in Fig. 2.27 [163]. It is also possible to calculate the anisotropic flow properties such as r values by incorporating texture in the form of an ODF into a theoretical model of polycrystal deformation. The early theories that described the deformation behaviour of single and polycrystalline solids were due to Schmid [181] and Sachs [182]. These theories led to the Taylor [183] model of plastic flow where the plastic strain was assumed to be the same for all grains of the aggregate and also equal to the macroscopic strain; this was considered to be achieved by permitting the simultaneous activation of five slip systems. The model also assumed a selection rule for the slip systems based on the principle of minimizing the internally dissipated deformation work. Another model, proposed by Bishop and Hill [184, 185], using maximum work principle also yielded the same solutions as the Taylor model. 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 the tensile loading direction of the test specimen) by incorporating the texture in the form of ODF into the Taylor model of polycrystal deformation [161, 165]. 2.2.3  The Theoretical Mechanisms of Texture Development  During cold rolling, the texture of b.c.c. metals becomes progressively stronger and sharper with increasing deformation, but the main components that develop are almost independent of material and processing variables [186, 187]. For these metals, it is slip and the associated lattice rotations (towards the ideal orientations) that are responsible for the development of the deformation texture, and the most appropriate deformation mode corresponds to pencil glide on {hkl} < 111 > systems [186, 187]. It has been estab lished that the cold rolled texture of steels comprised of two major orientation spreads  Chapter 2. Literature Review  64  [23, 160, 188]. One of these is an almost complete fibre texture with {111} planes parallel to the sheet ( -fibre) and the directions 7  <  110  >, <  112> and  rolling direction, and the other is a partial fibre texture with direction (a-fibre), encompassing the orientations {001} {111}  <  110  >.  <  < <  110  123 110 >,  >  aligned with the  >  along the rolling  {112}  <  110  >  and  The Taylor-Bishop-Hill theory has been extensively used in the predic  tion of rolling textures; this is accomplished by calculating the orientation path during deformation of arrays of crystals with an initially random distribution of orientations [176, 189]. In general, the calculated results were in good qualitative agreement with the measured textures [156, 176]. Recovery processes in general are reported to have no significant effect on cold rolled textures. Recrystallization processes on the other hand involve local reorientation and thus cause textural changes [22, 23, 187, 190]. The orientation dependence of the deforma tion structures (and hence the internal stored energy) are generally responsible for biasing the recrystallization process in favour of certain texture components. In particular, for a 70 % 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 coarser and less misoriented in {001} family. Nucleation by subgrain growth mechanisms occurs most rapidly within the grains having the greatest stored energy [72, 77, 78, 79]; the nucleation process is also aided by a high local dislocation density and by the presence of a sharp lattice curvature [33, 80, 81, 82, 83, 156]. These observations suggest that nuclei are formed in specific orientations (‘oriented nucleation’), and that the resulting annealing texture is characterized by the orientation of these nuclei. Another common observation is that the recrystallization texture is related to the deformation texture by rotations around specific axes, e.g., rotations of 25 to 30° around  <  110  >  direction in  b.c.c. single crystals. Experiments have also indicated that grain boundaries with such misorientations have high mobility [22, 23, 187, 190]. This concept suggests that the  Chapter 2. Literature Review  65  nuclei with certain orientations grow rapidly (‘oriented growth’), and that these nuclei determine the resulting annealing texture. The suitability of one theory over the other continues 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 oriented nucleation is generally the favoured mechanism [156]. Grain growth, occuring after the completion 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 expense of small ones during grain growth and that the grain size distribution for grains of strong texture 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] consist of two major components which are approximately {111} < 110 > and {554} < 225 > (‘—‘  6° apart from {111} < 112 >). A comparison of the annealed textures with the  cold 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 it in the partial fibre texture; the other relates to the redistribution of intensity in the fibre texture with {111} planes parallel to the sheet [156]. The texture development during annealing is sometimes monitored through the measurement of integrated pole intensities. 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 relatively negligible [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 1.0  -  values of around  1.3, and are characterized by a weak texture, while Al-killed steels yield higher  values (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  values  Chapter 2. Literature Review  66  (1.6 2.0) than Al-killed steels, and are characterized by a sharper {111}-type texture (in -  particular the {554}  <  225  >  orientation) [21, 22, 23, 156]. Fig. 2.28 shows a comparison  of the relative proportions of different textural components in rimmed, Al-killed, and Tistabilized interstitial-free as well as high strength steels [196]. The texture modification in Al-killed steels is usually attributed to the precipitation or 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 re tardation of recrystallization, particularly by inhibiting the nucleation event. Although the 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 tilt the balance more in favour of {111} orientations [23]. However, strict process control is usually necessary to get the best possible effects. For example, a high soaking tem perature  (‘-.‘  1200°C) and rapid cooling from the hot rolling temperature to the coiling  temperature are considered essential to keep Al in solid solution. In addition, a very slow heating rate (i.e., batch annealing) should be employed during recrystallization to encourage the clustering of Al and N in the deformed structure prior to the onset of recrystallization [23, 138, 146, 156]. The mechanism by which the annealing textures of I-F steels are developed is not properly understood [22, 23, 156]. Most researchers [22, 23, 197, 198] have taken the view that textures are controlled by the already existing carbonitride particles, which interfere with the nucleation and growth of recrystallized grains (e.g., inhibition of nucleation of all orientations, 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]. Some  authors suggest the strong presence of the {112}  <  110  >  component in the I-F steel hot  band (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  67  199, 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, the absence of the damaging effects of the interstitials C and N is considered to be the most important factor [23]. This suggestion is based on the observation that higher dissolved C 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 generally suggested that the inhibition of subgrain-growth nucleation of {111} oriented grains is significantly lessened by the absence of the interstitials [23].  It should be indicated  however that such a view does not rule out the influence of the carbonitride particles; in particular, if these are too finely dispersed they may inhibit the growth of recrystallizing grains, with detrimental effects to the final texture, and thus the need for relatively coarse-scale precipitation [23, 202]. 2.2.4  Development and Control of Texture in I-F Steels  Industrial control of  values of steel sheets depends on the control of the development of  a suitable texture, and this in turn means a careful control of steel composition and other metallurgical processing parameters [22, 23, 156]. In general, reductions in the amounts of oxygen (0.04 to 0.002 wt  %)  %),  sulphur (0.01 to 0.001 wt  and nitrogen (0.007 to 0.001 wt  %)  %),  carbon (0.15 to 0.0005  present in low-carbon steels have been reported  to result in progressively increasing f values [22, 23, 149]. These observations clearly indicate the benefits of using killed and stabilized steels for deep-drawing applications. Numerous investigations have shown that by adding stochiometrically sufficient amounts of Ti and/or Nb to combine with all of the interstitial C and N, significant improvements in 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 effects of excess Ti and/or Nb in solid solution (i.e., after stabilizing the interstitials) on  Chapter 2. Literature Review  68  values; the reported studies indicate all three possibilities, i.e., increasing or decreasing or having no effect at all [7, 9, 15, 16, 149, 150, 204]. The presence of the solid-solution strengthening elements Mn and P in low-carbon steels is usually detrimental to deep drawability. In particular,  values have been reported to decrease steadily as the Mn  content was increased from 0.02 to 0.5 wt  % [20, 55, 204, 205, 206, 207]. In the case of  P, the adverse effects were reported to be minimal; even an increase in F value has been reported 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 of  the hot-rolling, cold-rolling and annealing conditions.  In I-F steels, all of the stabi  lizing precipitation takes place during high temperature processing, and the process ing conditions leading to the formation of coarse and widely spaced precipitates are desirable 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 texture evolution and -  values are briefly summarized here. Lower reheat temperatures (1000  1100°C) are considered beneficial since they prevent complete dissolution Ti and Nb  precipitates, allowing them to coarsen. Finishing below Ar 3 to reduce -  f  (.-‘-‘  900°C) has been shown  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. Some  of the recent studies on Ti and Nb stabilized I-F steels indicate that carefully controlled finish rolling in a-region can also lead to improved deep drawability [149, 203, 212]. In general, controlling the processing conditions are much more important in the case of Nb-stabilized steels than in the case of Ti-stabilized steels because of the relatively low precipitation temperatures of the Nb-compounds [4, 6, 15, 213]. Obtaining high  values is also dependent on optimizing the cold rolling and annealing  conditions. For rimmed and Al-killed steels, the optimum amount of cold reduction was reported to be around 70 to 80 % [22, 210, 214]. It has been pointed out that above 75  %  Chapter 2. Literature Review  69  cold reduction the value falls off despite the continiously increasing {111} components in the 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} components  were reported to be present to a lesser extent and the highest  values were obtained for  reductions of around 90 % [210, 215]. In contrast to Al-killed steels, the  values obtained  for I-F steels are not very sensitive to the annealing conditions [22, 23, 156]. The annealing studies performed on Ti and/or Nb stabilized I-F steels indicate that in general higher annealing temperatures promote increased  values; this is primarily due to the larger  grain 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 range of 850 to 900° C to produce high  values [2, 9, 14, 20]. Fig. 2.29 summarizes the results  from several investigations showing the effects of heating rate during annealing on values of different grades of steels [23]; when compared to Al-killed steels, the effects of heating rate on  values were negligible in Ti-stabilized I-F steels.  Chapter 2. Literature Review  Temp.  70  Avrarni. Equation  C  (i in  440 460 480 490 500 520 540 560  —  —  —  —  —  —  —  —  =  Speich and Fisher  0 L  b  2 R  9.93 8.81 7.56 6.64 6.21 5.17 4.32 3.24  0.88 0.96 0.96 0.88 0.95 0.98 0.92 0.77  (=  .92)  ink  2 R  —12.64 —11.21 9.59 8.20 7.69 6.34 5.24 3.58  0.88 0.96 0.92 0.74 0.93 0.93 0.87 0.64  —  —  —  —  —  —  Table 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].  Chapter 2. Literature Review  71  Figure 2.1: Effects of annealing temperature (200, 250, 300, 450°C for 1 hr) on the diffraction peak profiles of the {331} planes in a 90 % cold roIled 70-30 brass [49].  —i  o  Figure 2.2: Schematic illustration of the x-ray peak resolution measurement [56, 57].  Chapter 2. Literature Review  72  • E  8  RSI OO2C/  x  a  L_z’ — a  Figure 2.3: Comparison of the % peak resolution (in-situ) and microhardness measure ments obtained for a 89 % cold rolled, rimmed low-carbon steel during continuous heating [56].  C..  100 U)  C.,  z  C.)  Za:  z <z  DC.)  05  CflO C.)  A x,Id-,oHd ANNEALING TEMPJC  Figure 2.4: Recrystallization behaviour of a 77 % cold rolled, Ti-stabilized ex tra-low-carbon steel during the simulation of continuous annealing (soak time of 40 s at each temperature) [15].  Chapter 2. Literature Review  73  2!: U:: (1) -J  4— (-)  0  0  50  100  150  250 200 TIME MINUTES  300  350  400  450  —  Figure 2.5: Isothermal recovery kinetics in polycrystalline iron after 5 % prestrain at 0°C, showing fractional residual strain hardening vs. time [40].  55 ° ro 50  -  045!  040: 035 0301 £00C 025’ or  020: 0I5 010! 10’  102 ANNEAEING TIME. MINUTES  Figure 2.6: 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].  Chapter 2. Literature Review  74  o:  ccItzo1on Tm (Mnoes)  Figure 2.7: The graph of in in[1/(1 % deformed high-purity iron.  —  X)] vs. ln(t) obtained by Rosen et a! [72] for a 60  C  C  a  a  T(tl{ h1  a  C  a  Figure 2.8: Fractional residual strain hardening curves obtained during isothermal an nealing of a) copper [92] and b) aluminum (arrows indicate onset of recrystallization) [93] as presented by Furu et a! [91].  Chapter 2. Literature Review  75  -r  x Figure 2.9: Interfacial area per unit volume plotted against the volume fraction recrys tallized for a 60 % cold worked 3.25 % Si-steel [90].  0  E .  +  0  • o x V  T Sn 812 812 812 750  046 045 030 023 03S 8025 -1  I0 I  tO  102 Time (sec)  Figure 2.10: Average boundary migration rates (G) during isothermal recrystallization of hot-worked 3.25 % Si-Fe [81].  76  Chapter 2. Literature Review  Tme  Figure 2.11: Schematic representation of the additivity principle [69].  Chapter 2. Literature Review  0.0  C)  z  TO  77  3 X  0.99  -  I  C)  C)  H  Time Figure 2.12: A schematic TTR diagram with proportionally distributed fractional recrys tallization curves to illustrate the validity of the additivity rule.  09  3D 07  06 0 <3  0.3  C C  0.3  L 0.2 0i  6  20  22  2.  76  27  30  32  3.6  36  Time (s)  Figure 2.13: Comparison of experimental and predicted continuous heating recrystalliza tion kinetics; the isothermal data characterized by both the JMAK and the S-F equations were used in the additivity calculations [39].  Chapter 2. Literature Review  THE ORIGINAL SU8GRAIN 8EFORE COALESCENCE  78  STRUCTURE  (c) THE SUOGRAiN STRUCTURE AFTER COALESCENCE  JUST  ONE SURGRAIN IS UNDERGOING ROTATION  THE FINAL  SU8GRAIN  A  STRUCTURE  AFTER SOME SU88OUNDARY MiGRATION  Figure 2.14: Schematic illustration of subgrain coalescence by subgrain rotation [53].  Figure 2.15: Schematic representation of nucleation by subgrain growth; boundaries thickly populated by dislocations (dots) have a high misorientation angle, and are the most likely to migrate [131].  Chapter 2. Literature Review  79  z 0 <I)  0/  40 60 RECRYSTALLiZED  Figure 2.16: The softening response of three iron alloys recrystallized at 595°C [38].  1050-F  E  4  • 88% duton — 105. Redooon 050%  Rodof.on  90ji 800  70 8gionng Of 6Gb 17.5  15.0 12.5 0  10.0 7.5  0  5.0  -  -  -  -  -  -  2.5 0.1  10  10  1(30  1000  TIUC AT TEMP(RATURE. MIN  Figure 2.17: Effect of annealing time at 565°C on the longitudinal properties of a Ti-stabilized I-F steel cold rolled between 50 and 88 % [21].  Chapter 2. Literature Review  80  ‘yr 9-  a I-  TiME AT TEMPERA TtJRE. MIN.  Figure 2.18: Time-temperature-recrystallization diagram for Ti-stabilized [21], rimmed and Al-killed steels after 50 % cold reduction [138].  1460 D  1360  a:  D  YOU  a: 1260  coto f(OUCT ION C.  >-  6O  a: 0  I-  • 60P(HC(N  o  1200  7Pf4CN1  a:  1160  000  010  021]  (XC( S TI 1ANU.d  Figure 2.19: Effect of excess titanium in solid solution and cold reduction on the recrys tallization temperature (TF) for annealing soak times of 15 s [16].  81  Chapter 2. Literature Review  975  1275 950  14 C  12  122  100 U  0  i17  a  -  900 1150  ii2  -  —  3 0 7:3 0 28 0  hOC  875 23PA  3C 0  .04  .08 WT PCT  I 22  I 16  .20  .24  Nb  Figure 2.20: Relationship between the recrystallization start temperature, TR, and the amount of Nb in solid solution in ferrite; the points along the curve were obtained for coarsened precipitates and the open circles include the effect of precipitates as well as Nb in solid solution [17].  100  C 0, > U C,  C 10°  101  102  flm  10  (ieconds)  Figure 2.21: Recrystallization kinetic curves indicating sigmoidal-type behaviour, ob tained for a series of I-F steels, cold rolled 75 % and isothermally annealed at 650°C [153].  Chapter 2. Literature Review  82  0  (a)  (b)  Figure 2.22: Partial (200) pole figures obtained for a rimmed steel (a) in the cold-rolled state and (b) after recrystallization; the ideal orientations {111} < 112 >, {111} < 110 >, {100} <011 > and {211} <011 > are indicated [79].  111  100  110  Figure 2.23: Normal (ND), rolling (RD) and transverse (TD) direction inverse pole figures obtained for a 70 % cold rolled steel sheet [160].  Chapter 2. Literature Review  83  NO  Figure 2.24: Schematic description of crystal orientation by indices of crystal directions and by Euler angles ço, q and Y2 [157].  n  (001)11101 I  / 10 4 0  /  13  30  %0  40  40  10  80  I  —  (114)11101’  —  (114)1Oill,  30  (112)1110)’ ‘ (223)1110)  50  3111)11211 ,-‘  —  ioioi  80  1  90  —  i0( t0I  tuG)  p  (i211  (332]  —  (0211  1223)  (132)  11)3  .  102I  50  11221  (111)  4  (110)100!)  60  12311  110)  1121]  (1321  1011)  (332)  70  40  70  p  (1313  (554)15) (332)11131  ‘  —  (445))1)0)’/  60  l01I (l121  (111)11121  <1I1> 3 ND  —  50  A  30  (113)1li)  40  L0  .  1113)  il  —  ‘I  30 •  _L5 2 tf(  10  4,  •‘  20  (0011)110)  23  20  •.  10  (11311332)  20  10  110112301 11201 1330)  TDU<110>  3  0  RDII<1I0>  11131  —(2211  11103 (3313  70  80  (123)11(23  p  10231  133)  1i3]  .  (2321  (1221 1233)  1103  (3123 11231  (0131  80 ‘0  [1101 13313  1(110)1110)  l22111323 )111  (22311112)  (i3)  (110)  (001  45° section of the Euler space showing Figure 2.25: A three-dimensional view and a the locations of some important ideal orientations [164, 166]. =  Chapter 2. Literature Review  84  1t2,  y_ 16 14  14  CR -—--—2 S -——3 S •  —  60  —las  90  Figure 2.26: 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 >j RD) and (b) y (< 111 >11 ND) fibres [170]. 28r— 24 0 I  20  a: a:  :  16  a: <3  12  a: >  08 04  :-  C 01  10  10.0 tNTENSTY 1111: NTENSTY (001  1000  10000  Figure 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  85  3.6  Il1l l 1 {ooij <110>  3.2 2.8 -j  (iii) <110>  24  UI  cr2.0,  (ii2} <110>  {‘1 <225>  Figure 2.28: Comparison of the relative proportions of different textural components in rimmed, Al-killed, and Ti-stabilized interstitial-free as well as high strength steels [196].  2.0  J. Typcct  08% T seeI cii (Oinç tempercitures  TypcnI  —  b3x-onnea1n0  Onhnucxjs  onneouin,  1.8  1.6  Ai-+Iled steel  -  colng temperoture Ce  11.  -  12  Pinemcig Sleel low cotrno teopecoIre -  1.0 0.1  1  10  100  1000  HEATING PATE  Figure 2.29: Variation of i values with heating rate during annealing for a variety of steels subjected to different high temperature processing conditions [23].  Chapter 3  Experimental Procedure  This chapter describes the techniques and procedures used during the course of this investigation. They can be broadly categorized into the following processes: cold rolling and annealing; kinetic characterization by diffraction effects; quantitative metallography; electron microscopic observations of structural changes, and quantitative characterization of texture evolution.  3.1  Material  The material used in this study was a Ti-rich, Nb-lean Interstitial-Free (I-F) steel; its chemical composition, as provided by Stelco, and that obtained from a laboratory chem ical analysis, are shown in Table 3.1. This is one of the commercially produced DeepDrawing 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 Ar 3 temperature of less than  3.2  (  890°C) and over, and a coiling  600°C.  Cold Rolling Schedule  The 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 to  86  Chapter 3. Experimental Procedure  87  0.58 mm corresponds to an overall reduction of 80 %, as commonly used in industrial practice. Cold rolling was performed only in one direction, between clean, dry rolls, without reversal.  3.3  Kinetic Measurements  Isothermal annealing experiments were performed with the objective of characterizing the isothermal recovery and recrystallization kinetics over an appropriate range of tem peratures. The annealing kinetics during selected continuous heating rates simulating batch and continuous annealing processes were also determined.  3.3.1  Apparatus  The isothermal and continuous heating annealing experiments were performed in a ‘Philips PW 1158’ high temperature, x-ray diffraction camera. The original camera was modified to incorporate two grooved quartz tracks for supporting the steel strip. Strip specimens of 155 mm x 13.5 mm x 0.58 mm, sheared from the cold rolled steel sheet, were resis tively heated using a 60 Hz power supply capable of delivering up to 500 A. The current to 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 ther mocouple were spot welded at the centre of the bottom strip surface, directly beneath the focal point of the x-ray beam. A thermocouple-instrumented strip sample in place in the open hot x-ray camera is shown in Fig. 3.1. All the experiments were performed in a He + 10 % by vol. H 2 environment, by maintaining a continuous flow of the mixed gas at the rate of 200 c.c. per minute. The chamber was first evacuated before introducing the 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  88  Diffraction Effects  3.3.2  Initial experiments were performed with the objectives of establishing the operating pa rameters 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, /Ka 2 doublet. FeKc, radi ation and the {220} diffraction peak were selected for the experiments. The peak profile was 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 are shown in Fig. 3.2. The degree of peak resolution of the Ka,/K 2 doublet has been described quantitatively in terms of: (i) the x-ray ratio, R 1 (also referred to as ‘residual line broadening parameter’ [15, 53, 55]), = ‘mm  ‘Ka,  where  , ‘mm 01 ‘K  and  ‘b  —  ‘b  (3.1)  —  are the intensities of the K 1 peak, the valley between the K,  and Ka , and the background, respectively; 2 (ii) the valley intensity,  ‘M,  = where  ‘mmn  ‘mm  —  ‘b  (3.2)  and I, are the intensities of the valley and the background, respectively.  The fractional annealing effects, i.e., the volume fraction recovered and/or recrystal lized, were estimated using the ‘fractional peak resolution’, F, defined in terms of the measured parameter, F, (3.3)  Chapter 3. Experimental Procedure  89  where F, P and P correspond to the initial, an intermediate and the final measured values of the parameter P during the annealing treatment. P could be either R 1 or IM, as indicated in Fig. 3.2. The initial and the final measurements correspond to the cold rolled and the fully recrystallized states, respectively. 3.3.3  Annealing Treatment  Isothermal 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 isothermal temperature; a higher heating rate could not be employed due to the necessity to keep the initial overshoot of temperature associated with the thermal inertia at  10°C. Con  tinuous heating experiments were conducted at 0.025, 1.88 and 20.2°C/s; the slowest and the fastest heating rates are typical of batch and continuous annealing processes, respec tively. The specimens were rapidly cooled to room temperature after various stages of isothermal or continuous heating annealing by shutting off the power and cooling the specimen under the flow of the gas mixture. Initial cooling rates as high as 45°C/s (at 800° 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 sampies prepared from interrupted heating-quenching procedure. The interrupted heatingquenching procedure was also employed to measure peak profiles on specimens heated at 0.025, 1.88 and 20.2°C/s. In addition, in-situ peak profiles were obtained during isother mal testing at 500, 550, 600 and 625°C and during continuous heating at 0.025°C/s; the time corresponding to the in-situ peak profile was recorded as being that at which the valley intensity measurement was made. The time required to obtain the peak profile, i.e., to scan from the  peak to the  valley between the Kcj and Ka 2 peaks, was approximately 24 s. This was a prohibitively  Chapter 3. Experimental Procedure  90  long time, and restricted the use of the in-situ method to low reaction rates (i.e., isother mal 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 required to overcome this problem. Partly to address this difficulty, and also to simplify the mea surement procedure, experiments were performed to determine if the magnitude of the minimum point in the valley,  ‘mm  (or IM), is sufficient to describe the resolution of the  peak profile. This method of monitoring only the valley was employed at all isothermal temperatures in the range of 500 to 760°C. However, the x-ray peak shift (and hence the shift in the valley position) with temperature and the necessity to compensate for this shift by manually adjusting the x-ray detector, allowed this method to be used only at the very slow heating rate of 0.025°C/s. Fig. 3.3 lists the isothermal and continuous heating annealing tests performed, together with the measurements made on each test. The effect of temperature on the positions (20) of the Kai /K 2 valley and the Kai /Kcw 2 peaks, and on the values of R 1 and  ‘M  were also investigated by obtaining the peak  profiles of a fully recrystallized specimen at different temperatures. A number of isothermal recrystallization tests were performed using the diffractome ter to examine the reproducibility of the x-ray data. R 1 values in the range of 0.60 to 0.15, obtained both during in-situ monitoring and from interrupted tests, were reason ably reproducible. For example, the R 1 values obtained from three different specimens produced by rapid cooling to room temperature after holding for 300 s at 650°C were 0.27, 0.30, and 0.32, indicating reproducibility within + 10 %. The reproducibility of the IM data was tested more rigorously, because when IM was the monitored parameter, a single test was sufficient to characterize the kinetics at any isothermal temperature. To ensure reproducibility, every isothermal test performed between 600 and 760° C by valley monitoring, was repeated at least once. From the results, it was evident that no single  ‘M  value could be assigned to reflect the state of  Chapter 3. Experimental Procedure  annealing of the metal; the values of  91  ‘min b t  and consequently  ‘M  (in arbitrary units)  corresponding to the same state of annealing were observed to vary considerably from test to test, some times as much as by 20 %. However, the proportional change in  ‘M  caused  by annealing, i.e., the fractional peak resolution (F), was reproducible. An example of this is shown in Fig. 3.4, where F values obtained from two different tests are plotted as a function of time at 650°C, indicating good reproducibility. To determine the temperature variation with position in the resistance heated strip specimens, four thermocouples were welded onto a typical specimen, at the positions indicated in Fig. 3.5. The specimen was held isothermally at temperatures over the range of 600 to 800°C, and the difference between the set-temperature maintained at the midpoint by the controlling thermocouple, and that of the three measuring thermocouples (A, B and C), were then determined. The largest temperature differences, measured at the highest set-temperature of 800°C, were 10, 30 and 15°C at positions A, B and C respectively. The larger thermal gradient, measured along the width direction (as indicated by the temperature differences at A and B), is thought to be due to the tapered heating ends (see Fig. 3.1 (a)) or the quartz specimen holders. As a consequence, the area covered by the x-ray beam was reduced by employing modified (non-standard) slit arrangements. With this beam configuration, only position A fell within the area exposed to x-rays, making each x-ray scan essentially at constant temperature, within 10°C. 3.3.4  Quantitative Metallography  Small rectangular specimens, 10 mm long, were cut along the length of the 13.5 mm wide strip in such a way that the midpoint of the specimen was the same as the original thermocouple location. The specimens were set in cold-mount, and then ground and polished using 120, 180, 320, and 600 grit grinding paper, and 5, 1 and 0.06 um alumina powder. The microstructures of the polished specimens were revealed using an etchant  Chapter 3. Experimental Procedure  92  prepared from 100 ml H 0, 5 gm picric acid and 2-3 ml teepol (wetting agent), and etching 2 by swabbing at 80°C. The optimum etching time was determined to be approximately 120 s. The best etching results were obtained when the specimen was washed and dried after a 60 s etch and then followed by another 60 s etch. The midpoint of the specimens was examined using an optical microscope to estimate the times corresponding to the start  (‘—i  1  %)  and the finish (.—‘ 99  %)  of recrystallization. For quantifying the degree of  recrystallization on partially recrystallized specimens, photomicrographs were obtained using a ‘Unitron MR2-11’ metallographic microscope at a magnification of 200 for the coarser recrystallized grains and 400 for the finer recrystallized grains (i.e., near the start of recrystallization). Selected partially recrystallized specimens were also observed at a magnification of 1000 to provide additional microstructural detail on the nucleation and the growth processes involved during recrystallization in I-F steels. The photomicrographs were analysed according to standard quantitative metallo graphic techniques applicable to recrystallization. The volume fraction recrystallized, X, and the interfacial area per unit volume between the recrystallized grains and the cold worked 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 inter sections that fall on recrystallized grains. Similarly, following the analysis of Smith and Guttman [216], A was determined as follows, A=—  (3.5)  where n’ is the number of intersections of the grid line and the boundary between recrys tallized and unrecrystallized regions, and L is the total length of grid line. No attempt was  made to measure the growth rate or the nucleation rate.  Chapter 3. Experimental Procedure  93  The grain size of the as-received and other fully recrystallized specimens was deter mined using the mean linear intercept (m.l.i.) method, which defines it as the average chord length intersected by the grains on a random straight line in the planar polished and etched section [44]. Efforts were made to reduce any systematic bias or errors into the counting proce dure. The grid spacing relative to the scale of the structure is the most critical item in determining the accuracy of the analysis. While an increased number of points counted will reduce the statistical errors, it has also been suggested that to improve the efficiency and to minimize the sampling error for a given number of points counted, the average number of points falling in any one area of the phase to be measured should not greatly exceed unity [43]. This condition has been met during the counting procedure by using two 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 the micrographs corresponding to the early stages of recrystallization). With the objective of further reducing the experimental error, at least four different optical micrographs were obtained 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 was used for the kinetic calculations. During the diffraction studies of the sheet specimen, it is primarily a thin layer be neath the surface that contributes to the total diffracted intensity. The thickness of this layer could be estimated by considering the ratios of the diffracted intensities from different depths [49]; for the {220} diffraction peak of an iron specimen under FeK radia tion, this thickness was estimated to be approximately 60tm. During the metallographic studies, a typical grinding and polishing operation was estimated to remove about 100 urn of material from the surface. Microstructural variation through the thickness of the  Chapter 3. Experimental Procedure  94  sheet was also investigated by sectioning a number of partially recrystallized sheet spec imens through the thickness of the beam/thermocouple location. The typical uniform, through-microstructure shown in Fig. 3.7, was obtained from a specimen produced by rapid cooling from 750°C after being heated at 20.2°C/s. The negligble through-thickness variation in microstructure observed in these specimens supports the assumption that the kinetic measurements obtained from diffraction effects and metallography are compara ble.  3.4  Electron Microscopic Observations  The major aim of this part of the investigation is to study the microstructural evo lution during annealing of heavily cold-rolled I-F steel by transmission and scanning electron microscopy (TEM and SEM). In particular, the influence of the precipitates on the microstructural evolution was examined during a heating rate simulating the contin uous annealing process. In addition, a brief examination of the orientation relationships among subgrains and the nature of the precipitate distributions was conducted. Large precipitates were also examined for identification using an energy dispersive x-ray (EDX) microanalyser. 3.4.1  Gleeble Simulated Annealing Treatment  Cold rolled strip specimens of 100 mm x 30 mm annealed in the ‘Cleeble 1500’ thermo mechanical simulator were used for TEM analysis. As with the hot x-ray camera, the sheet samples were resistively heated in a specimen chamber evacuated and back-filled with inert Ar gas. The specimen temperature was controlled and monitored using a 0.25 mm diameter, extrinsic chromel-alumel thermocouple spot welded to the surface of the strip at its midpoint. Rapid cooling of the specimens after various stages of annealing  Chapter 3. Experimental Procedure  95  was accomplished by shutting off the power and cooling the specimens in the inert Ar atmosphere. For a specimen cooled from 800°C, an initial cooling rate of 31.6°C/s was obtained using this procedure. Thermal gradients in the longitudinal and transverse directions were determined using additional thermocouples welded in different positions of a typical specimen. The differ ence between the set-temperature of 800° C, maintained at the midpoint by the controlling thermocouple, 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 across the width, indicating shallow thermal gradients along the transverse direction. However, considerable thermal gradients were observed along the longitudinal direction, and con sequently the working length had to be restricted to 3 mm from the midpoint, this being the distance corresponding to a difference of 10°C from the midpoint set-temperature of 800°C. Different cold-rolled specimens heated at 20.2°C/s were rapidly cooled from the tem peratures of 580, 640, 680, 740 and 800°C. These specimens were used to study the microstructural changes associated with the recovery and recrystallization processes. In addition, a single specimen heated at 0.025°C/s was cooled from 700° C to produce a fully recrystallized microstructure, typical of that formed by the batch annealing process. 3.4.2  Thin Foil Preparation and TEM Investigations  Thin foils for TEM investigations were prepared [217, 218] from the hot rolled, cold rolled and annealed specimens. Discs 3 mm in diameter were cut along the width (through the midpoint) of the annealed and cold rolled strips using electro discharge machining. These 0.58 mm (580 jim) thick discs were mounted to a ‘Gatan’ disc grinder and mechanically thinned in small increments of 50 jim. Wet grinding was done alternatively from both surfaces until a final thickness of approximately 80  -  90 jim was achieved with a surface  Chapter 3. Experimental Procedure  96  finish of 600 grit. The thicker hot rolled (as-received) material was machined first (equal reduction from both surfaces) to a thickness of  ‘-  0.58 mm before the discs were cut, prior  to the same grinding operation. The ground discs were then electropolished to perforation in a ‘Struers Tenupol-2’ jet polishing unit with an electrolyte of 5 % perchloric acid and 95 % glacial acetic acid (by volume) at a polishing current of 60  -  80 mA (potential of  60 V) at room temperature [217, 218]. The thin foils thus produced were examined in a ‘Hitachi H-800’ scanning transmission electron microscope operated at an accelerating voltage of 200 kV. In addition to the images obtained in the magnification range of 4 k to 40 k, a limited number of diffraction patterns and Kikuchi patterns were also obtained with the objective of studying the orientation relationships among subgrains. 3.4.3  SEM/EDX Analysis of Large Precipitates  Selected specimens of as-received hot band and partially and fully recrystallized steels that were observed under the light microscope were also examined using an SEM. The annealed specimens chosen corresponded to the steels produced by rapidly cooling from 660, 730 and 800°C, after continuously heating the cold rolled steel at 20.2°C/s. The specimens 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 5570’ 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 10 k, were used to study the relationship of the particles to the nucleation and growth processes. The precipitates larger than 0.1 4 um in diameter were examined with a ‘Kevex 8000’ microanalyser using energy dispersive x-ray (EDX) spectroscopy. A ‘Microspec’ wavelength dispersive x-ray (WDX) microanalyser was also employed on a limited number of samples to facilitate the complete chemical identification of some of the particles that were larger than 1 im in diameter.  Chapter 3. Experimental Procedure  3.5  97  Texture Characterization  The primary objective of this part of the research was to quantitatively characterize the evolution of crystallographic texture during cold rolling and subsequent annealing operations. The effects of heating rate and grain growth on the resultant texture were also briefly examined. 3.5.1  Specimen Preparation  The annealing of the 100 mm x 30 mm cold-rolled strips were performed in a ‘Glee ble 1500’ thermomechanical simulator as described previously.  Interrupted heating-  quenching procedure was adopted to produce specimens reflective of different stages of recrystallization. Different cold-rolled specimens heated at 20.2°C/s were quenched in the Ar atmosphere from temperatures of 670, 720, 760, 800 and 900°C, and two other specimens 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-rolled strip was also characterized. Small rectangular specimens of 16 mm long (in rolling direction) x 12 mm wide were cut from the center of the annealed strips, with the center of the long axis coinciding with the midpoints of the strips. For cold-rolled and annealed sheet steels, some differences in texture through the thickness of the sheet, particularly between the surface and the mid plane had been reported [163, 186], and consequently all current texture measurements were made on the mid-plane of the specimens. Cold rolled and annealed specimens were ground and polished to reduce the thickness to half its original value of 0.58 mm. The thicker, 2.92 mm hot band was machined first before being ground to remove its half thickness. All of the prepared specimens were then lightly etched in 2 % Nital.  Chapter 3. Experimental Procedure  3.5.2  98  Pole Figure Determination and ODF Calculations  Partial {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 were generated 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 through 360°. During the measurement, the specimen is oscillated in its own plane in order to expose 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 because of the high temperature gradients observed along the longitudinal direction during the annealing treatment. Orientation distribution functions (ODFs) corresponding to each specimen were calculated from the four partial pole figures using the method developed by Bunge [165]. The ODF data was used to calculate the volume fractions of important texture components using  =  values for average strain ratio  16.5° Gaussian distributions [166, 219]. In addition, the  ()  were estimated by incorporating texture data into the  Taylor model of polycrystal deformation [161, 165]; the predictions were compared to the experimentally determined  values provided by Stelco.  99  Chapter 3. Experimental Procedure  Table 3.1: Steel composition provided by Stelco and that obtained from chemical analysis Element C N S P Mn Al Ti+Nb  Nominal (wt %) Max. 0.0028 Max. 0.003 Max. 0.010 Max. 0.15 0.10 0.03 0.06 Ti-rich, Nb-lean ( Ti: 0.03 -  )  Actual (wt %) n/a 0.00118 0.003 0.011 0.140 0.060 Ti : 0.03, Nb : 0.02  Chapter 3. Experimental Procedure  100  (a)  (b) Figure 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.  Chapter 3. Experimental Procedure  101  PEAK RESOLUTION DURING ANNEALING  A AA  FULLY ANNEALED  PARTIALLY ANNEALED  AS COLD ROLLED  {220} DIFFRACTION PEAK  Parameters Measured X-Ray Ratio (  1 R  Valley Intensity  ) 1 R  Im.fllb  IM  (IM)  LmnIb  =  IKaIb  Fractional Peak Resolution (F) ) 1 —(R ) 1 F(R  = —  (RI)finaj  (IM)jnjtjai  F(IM)  —  (IM)t  =  (IM)jnjtjal  —  (IM)fjnJ  Figure 3.2: Schematic diagram illustrating the {220} x-ray peak resolution associated with annealing and the procedure for quantifying peak resolution.  Chapter 3. Experimental Procedure  102  KINETIC MEASUREMENTS ROLLING:  2.92 mm  I  5 passes 0.58 mm  80 % reduction  X-RAY:  Fe Karadiation;  Monitoring (220) Peak.  Annealing Treatment: T-T-R Test Temperatures (°C)  Parameters Measured  500, 550  1 (in-situ) IM(ifl-situ), R  600, 625  1 (in-situ), R 1 (interrupted) IM(in-situ), R  650, 675, 700, 720, 740, 760  1 (interrupted) Iii(in-situ). R  Heating Rate (b/s)  Parameters Measured  0.025  1 (interrupted) 1 (in-situ),R IM(in-situ), R  1 .88, 20.2  1 (interrupted) R  METALLOGRAPHY:  3.3:  (Initial Heating Rate: 80 °CIs)  On selected specimens from interrupted tests.  Summary of the isothermal (T-T-R) and continuous heating ing tests performed, together with the parameters measured. Figure  (C-H-R)  anneal  Chapter 3. Experimental Procedure  103  1  ‘-  0.8  0 4-I  0.4 cI  C U 1-.  0  Time (s) Figure 3.4: Comparison of fractional peak resolution, F, based on valley intensity, as obtained from two different tests.  ‘M,  LENGTH  \  C  A2.5  C.T.  CIL —“—H——-——•• 10.0  —  B  CIL  L  DIMENSIONS IN  mml  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.  Chapter 3. Experimental Procedure  7 -  104  Recrystaflized  1ntertacat  1  ractior  Area  Ej  Figure 3.6: Illustration of the measurement of volume fraction recrystallized, X, and the interfacial area per unit volume, A, by quantitative metallography [90].  Figure 3.7: Through-thickness microstructural variation of a partially recrystallized spec imen produced by rapid cooling from 750°C after being heated at 20.2°C/s, Magnification X 200).  Chapter 4  Kinetic Characterization  This chapter deals with the kinetic characterization of the recovery and the recrystal lization processes operating during isothermal and continuous heating annealing cycles. The recovery process was monitored primarily through the measurement of x-ray ratio ), while the fraction recrystallized determined by quantitative metallography was used 1 (R in the analysis of recrystallization. Isothermal recovery, as described by a logarithmic type equation, and isothermal recrystallization, as characterized by the JMAK and the S-F equations are presented. In addition, the microstructural path approach was also employed in the kinetic analysis of recrystallization. Finally, the recovery and the re crystallization kinetics during continuous heating were predicted using the principle of additivity, and validated through appropriate experimental measurements.  4.1  Isothermal Recovery Kinetics  Metallographic examination of samples rapidly cooled after progressive stages of isother mal annealing established the following • At 500 and 550°C, the observed peak resolution was related solely to recovery processes, • 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 later stages, 105  106  Chapter 4. Kinetic Characterization  • At 700, 720, 740 and 760° C, recrystallization commenced during the heating to the test temperature, and consequently the observed peak resolution was due to the concurrent recovery and recrystallization processes, although recrystallization was the dominant cause. The fractional peak resolution (F) calculated at 500°C using both the in-situ x-ray ratio (R ) and the in-situ valley intensity 1  (Lw) are shown in Fig. 4.1, indicating that  the recovery kinetics can be reasonably quantified using either parameter; analysis of the measurements made at 550°C also resulted in the same conclusion. In the present work, only the in-situ R 1 measurements were used in the detailed kinetic analysis of the recovery process. The suitability of the semi-empirical equations 2.3 (in R 1 b  —  =  K  —  kt) and 2.4 (R 1  =  a in t) [29] for describing the isothermal recovery kinetics was tested first. Fig. 4.2  shows the in-situ R 1 measurements obtained at 500°C, together with the curves calculated using Eq. 2.3 and Eq. 2.4. Similar recovery measurements were also made at 550° C and preceding recrystallization at 600 and 625°C; very short recrystallization start times (e.g., 15 s at 650°C) precluded any in-situ R 1 measurements corresponding to recovery at 650 or 675°C. Isothermal recovery data obtained at each temperature have been analysed in similar manner to those at 500°C, the results being summarized in Table 4.1. The high correlation coefficients (R ) clearly indicate that the recovery kinetics in I-F steels 2 can be adequately described by the logarithmic relationship, Eq. 2.4. This is consistent with the previously reported annealing studies on iron, where the recovery kinetics were quantified by the measurement of initial flow stress [40] and x-ray peak resolution [53]. Fig. 4.3 (a) shows the in-situ R 1 measurements at 500, 550, 600 and 625°C, together with 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  107  This is a markedly different kinetic response from the sigmoidal property change usually exhibited by recrystallization. The validity of Eq. 2.4 in describing the recovery kinetics can be additionally demonstrated by replotting the same data on a logarithmic time scale, as shown in Fig. 4.3 (b). Fig. 4.4 shows the Time-Temperature-Recovery (T-T-Ry) diagram obtained by cal culating the time required for R 1 to be equal to 0.5, 0.4, 0.3 and 0.15, using Eq. 2.4; several measured values for R 1  =  0.5 and 0.4 are also shown. The R 1 values can be  converted to % recovery using the maximum possible change in R , from 0.6 to 0.15, ob 1 served in the present study. It should be emphasized, however, that all of the isothermal 1 measurements that could be attributed only to the recovery processes were within R the range of 0.56 to 0.34 depending on the test temperature, and the development of the T-T-Ry diagram at lower R 1 values is totally dependent upon the extrapolation of the modelled expressions outside the experimental range. In practice, recrystallization was observed to commence at R 1  0.34, making further R 1 measurements corresponding to  recovery impossible. The kinetics of the thermally activated recovery process was analysed by assuming Arrhenius rate behaviour given by, 1 dR =  —Ar,  --  where AR is a pre-exponential constant,  (Qiy’\  exp  (4.1)  —  QRy  is the recovery activation energy, R is the  gas constant and T is absolute temperature. The analysis was carried out by plotting the /dt 1 natural logarithm of the instantaneous rate of recovery (in —dR  =  in aft), at fixed  fractions of recovery (at constant R 1 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 the recovery activation energy, QR at R 1 values of 0.6, 0.45, 0.3 and 0.15, the results being  108  Chapter 4. Kinetic Characterization  shown graphically in Fig. 4.5 (b). The apparent activation energy, to increase from 173.1 kJ/mole at R 1  =  0.6 to 312.1 kJ/mole at R 1  has been found =  0.15.  The recovery of heavily deformed iron based alloys has been reported to occur by annihilation of point defects, rearrangement, migration and eventual annihilation of dis locations and finally the formation and growth of subgrains (described in detail in section 2.1.5). The increasing activation energy with increasing % recovery, suggests a change in the dominant recovery mechanism as recovery proceeds. An increasing activation energy with the progress of recovery is also consistent with recovery processes occurring initially at severely deformed regions, where the stored energy is a maximum, and therefore the required activation energy is a minimum. Such an activation energy would be a function of 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 com parable to the activation energy values of 91.9 to 281.7 kJ/mole, reported by Michalak and Paxton [40] from flow stress measurements made on lightly deformed polycrystalline iron; they correlated the lower and the upper limits of the reported activation energy val ues to simple vacancy migration and self-diffusion, respectively [29]. The values obtained in the present work are higher than those reported by Michalak and Paxton, particularly during the early recovery stages, even though the amount of deformation was 80 the present study and only 5  -  % in  15 % in the Michalak and Paxton study. The activation  energy values obtained in the present study are also higher than the activation energy value of 126.2 kJ/mole at 50 % recovery, reported for 80 % cold rolled silicon-iron single crystals based on line broadening measurements [53]. The presence of the excess solute Ti and Nb in solid solution and the fine stabilizing precipitates of Ti and Nb carbides have 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 is  109  Chapter 4. Kinetic Characterization  comparable to the reported activation energy for self-diffusion in iron  (‘-‘  275 kJ/mole  [29]). The prediction of recovery kinetics during continuous heating requires the character ization of recovery kinetics over a wide range of isothermal temperatures. Fig. 4.6 shows ) of 0.99 were 2 plots of b and a vs. T. Linear relationships with correlation coefficients (R obtained for both cases, with corresponding equations, b  =  0.95  (4.2)  0.00072 T  —  and a  =  0.0072  —  (4.3)  0.000027 T  dt and 1/T (K—’), shown in Fig. 4.5 (a), —dR / The linear relationship between ln 1 indicates that the intercept, in AR, and the gradient, -QR/R, as obtained from Eq. 4.1, , 1 are dependent on R . Both the parameters in AR and -QR,,/R were plotted against R 1 the graphs being shown in Fig. 4.7, with the following appropriate equations, in AR  23.6  —  (4.4)  1 0.075 R  and —  =  (4.5)  1 —43137.1 + 37182.2 R  This method can also be used to characterize the recovery kinetics during isothermal and continuous heating processes. In-situ valley intensity (IM) measurements made at 500 and 550°C, and prior to the onset of recrystallization at 600, 625 and 650° C were also analysed for characterizing the recovery kinetics. Fig. 4.8 shows the IM measurements obtained at 500°C, together with the modelled curves using Eq. 2.3 (In ‘M  CX  t) and Eq. 2.4 (IM  CX  in t). This, along with  the analysis of the data obtained at other temperatures, showed that the  ‘M  variation  Chapter 4. Kinetic Characterization  with time can also be described adequately (R 2  110  0.95) using Eq. 2.4 and consequently  provided a simpler method of monitoring the isothermal recovery kinetics. However, the difficulty of comparing the intensity values obtained at different test temperatures precluded the use of this method in the calculation of recovery activation energy. Fig. 4.9 shows the R 1 measurements corresponding to both the start of the isothermal treatment (once the test temperature is reached) and the approximate commencement of the recrystallization event (determined from metallography), as obtained from the interrupted heating-quenching tests performed at 600, 625, 650 and 675°C. These results, when compared to the maximum R 1 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 R 1 values are caused by recovery alone; this includes the recovery effects occurring during heating to the test temperature and the isothermal recovery effects prior to the onset of recrystallization. The lower R 1 values corresponding to the start of the isothermal treatment obtained at higher test temperatures indicate the higher amount of recovery the steel underwent during heating to the test temperature. On the other hand, recrystallization commenced within a short isothermal hold time, and consequently the R 1 values corresponding to the onset of recrystallization were higher at higher test temperatures. The difference between these R 1 values at each test temperature, shown in Fig. 4.9, indicates the recovery effects associated with the isothermal hold and shows that recovery is more significant at lower isothermal temperatures. At higher temperatures, recrystallization commences after a short hold time, thereby reducing the recovery effects on peak resolution. It is clear from the present study that the I-F steel under investigation undergoes a considerable amount of recovery prior to the onset of recrystallization, in agreement with data reported previously for Ti-stabilized [15, 21] and Nb-stabilized steels [17]. This suggests that the absence of C and N in the matrix of the I-F steel is more effective in promoting recovery than is the presence of Ti and Nb in solid solution and as precipitates  Chapter 4. Kinetic Characterization  111  in hindering the recovery processes. In summary, the isothermal recovery kinetics as monitored by in-situ R 1 measure ments have been described using a semi-empirical logarithmic type equation. The kinetic characterization indicated the recovery activation energy to be a function of the state of recovery, an observation attributed to the change in the dominant recovery mechanism, as recovery proceeds. The calculated activation energy values were moderately higher than those reported for pure iron. This was explained in terms of the possible retardation of recovery caused by the presence of the excess Ti/Nb in solid solution and the fine sta bilizing precipitates of Ti and Nb carbides. This I-F steel has been observed to undergo a considerable amount of recovery prior to recrystallization, an observation attributed primarily to its interstitial-free iron matrix.  4.2  Recovery and Recrystallization during Isothermal Heating  At temperatures > 600°C, concurrent recovery and recrystallization processes contribute to the observed x-ray peak resolution. This is true for the later part of the isothermal tests at 600, 625, 650 and 675°C, and for the entire annealing time at 700, 720, 740 and 760°C. The combined recovery and recrystallization kinetics were monitored using interrupted R 1 and in-situ IM measurements at all test temperatures. In addition, in-situ 1 measurements were also made at 600, 625 and 650°C. Fractional peak resolution, F, R calculated at every isothermal temperature, was found to vary with time in a similar manner irrespective of the parameter used in the estimation of F. Fig. 4.10 presents the results obtained for the F values as a function of annealing time at 625° C, using both the interrupted R 1 values and the in-situ  ‘M  measurements (obtained from two  different tests); the metallographically determined recrystallization start time of 240 s is also indicated. These results indicate that the combined recovery and recrystallization  Chapter 4. Kinetic Characterization  112  kinetics can be quantified through the measurement of either R 1 or The determination of recrystallization kinetics from these x-ray measurements re quires that a procedure be developed to separate the effects of recovery and recrystal lization on peak resolution. The contribution of recovery to the measured R 1 values, as quantified using Eq. 2.4, was subtracted from the measured total change to yield the recrystallization kinetics. Fig. 4.11 shows a typical example where the isothermal R 1 (interrupted) data of 675°C is analysed to give the percentage recrystallized. The effect of recovery during recrystallization is shown by extrapolating the recovery kinetics into the recrystallization zone (RTA) and reducing the magnitude of the recovery effect by the increasing area recrystallized (RUA). The estimation of the unrecrystallized area for the recovery correction has been accomplished through an iterative procedure. The initial estimation of the fraction recrystallized was made by neglecting the concurrent recovery effects, i.e., by attributing all of the R 1 change to recrystallization. The resulting unre crystallized fraction thus estimated was considered to undergo recovery (instead of the whole area) and the R 1 values corresponding to recovery were modified accordingly. The difference between these newly calculated R 1 values and the experimental R 1 values were then used in the estimation of the new fraction recrystallized. These calculations were repeated until the difference between two subsequent estimations of fractions recrystal lized 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 % recrystallized obtained through this procedure, was compared with the metallographic measurements, as shown in Fig. 4.11. The reasonable agreement validates the separation procedure adopted in the present study. Fig. 4.12 presents the results of a similar analysis applied to the in-situ  ‘M  measurements obtained at 650°C.  At temperatures of 700°C and above, x-ray measurements could be directly corre lated to recrystallization, due to the rapid recrystallization rates and reduced recovery  113  Chapter 4. Kinetic Characterization  effects. 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) calculated from interrupted R 1 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 values as influenced by the recovery or recrystallization or a combination of both through the x-ray peak resolution measurements of either R 1 or  ‘M•  To test this approach, a series of  in-situ x-ray peak profiles obtained at selected isothermal temperatures, were analysed to 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 dominant peak,  , 1 ‘K  1 and Ka the valley between the K 2 peaks,  ‘mm,  and the background,  ‘b,  at  500 and 650°C respectively. The intensity of the Ka 2 peak was always in the range of 60 -  70 % of the intensity of the Kai peak. At 500° C, recovery effects were solely responsible  for the peak resolution, while at 650°C, recrystallization was the dominant structural change. In the present work, the degree of peak resolution associated with the progressive elimination of non-uniform lattice strain has been characterized primarily through the x-ray ratio, R 1 (Note: the contribution to broadening from the relatively coarse parti 1 value was cle size involved in the present study is considered to be negligble). The R then correlated to the fractional annealing effects through the fractional peak resolution factor, F. The interpretation of F values in terms of recovery and recrystallization was carried out with the aid of confirmatory microstructural measurements, in particular the metallographically determined recrystallization start time. The fractional peak resolu 1 within the minimum tion, F, as defined by Eq. 3.3, is in fact the ratio of change of R 1 values. A similar approach has been used in previous and the maximum measured R  114  Chapter 4. Kinetic Characterization  recovery 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 of F. During recovery, a progressive reduction in  ‘mn,  as well as a small increase in  has been observed, as shown in Fig. 4.14 (a). This will lead to a faster rate of decrease in R 1 than in  ‘M  1 and However, Figs. 4.2 and 4.8 indicate that both R  1 logarithmic-type recovery equation (R  =  —  a in t and  ‘M =  ) 1 observation explains the same time variation of F (i.e., F(R  =  bM  —  aM  ‘M  obey the  in t), and this  F(IM) obtained during  recovery. When recrystallization was the dominant cause for peak resolution, the intensity, 1 remained relatively constant, as shown in Fig. 4.14 (b). In addition, since R 1 (R  =  values generally vary between 0.45 to 0.15 during recrystallization, the  larger variation in  ‘mm  1 shown in Fig. 4.14 (b), will have a stronger influence on R  than the smaller variation in Iiç . These observations provide the necessary explanation 1 1 and for the same ratio of change (F) obtained with R addition, the observation that  ‘M  during recrystallization. In  and I remain unchanged during recrystallization,  1 will be approximately equal to that of suggests that the rate of change of R  ‘M  during  recrystallization. In general, the intensity measurements were observed to be influenced by several factors such as the temperature and the surface conditions of the specimens.  More  importantly, the development of prefered crystallographic texture and the corresponding change in the number of planes participating in diffraction, can have a major influence in the absolute intensity measurements such as  However, in the case of x-ray ratio,  , this being the ratio of two different intensities, the influence of these parameters may 1 R not be significant; this will be demonstrated in a later section relating to the influence of temperature. 1 measurements are more suitable The preceding arguments clearly indicate that R  115  Chapter 4. Kinetic Characterization  than  ‘M  for the detailed kinetic analysis. However, the major advantage with the  ‘M  measurement is that it allows the complete kinetic characterization of annealing effects at any isothermal temperature to be accomplished by monitoring a single 20 (valley) position 1 measurements. Previous and the background; no 20 scan is required, as it is for R recrystallization studies on heavily cold rolled low-carbon steels using integrated pole intensity 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 and the annealing conditions [21, 163]. In particular, recent recrystallization studies on Tistabilized extra-low-carbon steels showed the integrated pole intensity of the {11O} planes to remain unchanged during the entire annealing period (see Fig. 2.4) [15, 193]. The texture 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 be  presented in a later chapter), thereby validating the IM measurements in characterizing the recrystallization kinetics. In summary, the {220} x-ray peak resolution, a parameter primarily related to the non-uniform lattice strain, can be successfully employed to characterize the kinetics of 1 and the recovery and the recrystallization processes. In particular, both R  ‘M  mea  surements have been shown to lead to identical kinetic analyses during the time when recrystallization dominates. These observations were explained in terms of the relative constancy of the number of {220} planes that are parallel to the rolling plane during recrystallization. An iterative procedure was adopted in conjunction with confirmatory microstructural measurements to separate the diffraction effects associated with the con current recovery and recrystallization processes; the concurrent recovery effects were found to be significant only during the early stages of recrystallization.  116  Chapter 4. Kinetic Characterization  Isothermal Recrystallization Kinetics  4.3  For the isothermal annealing treatments performed at 600, 625, 650, 675, 700, 720, 740 and 760°C, quantitative metallography was carried out on samples rapidly cooled after progressive stages of annealing. Polished and etched specimens were examined using an optical microscope to estimate the times corresponding to the onset completion  99  %)  (‘-.-‘  1%) and the  of recrystallization. Only partial recrystallization was studied at  600 and 625° C due to the long recrystallization times involved, and consequently no re crystallization end time was determined at these temperatures. Similarly, only partial recrystallization could be obtained at 700, 720, 740 and 760°C because recrystallization initiated 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 of establishing an exact start time, an estimated start time range (any value within this range is referred to as t) corresponding to the onset of recrystallization was initially established at 600, 625, 650 and 675°C. At every isothermal temperature, however, pho tomicrographs were obtained from the partially recrystallized specimens, and were used to estimate the volume fraction recrystallized, by the point counting grid method [42]. 4.3.1  JMAK/S-F Analysis of Isothermal Recrystallization  Fig. 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 point on 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 the measurements observed during the evaluation of all specimens. The recrystallization kinetics at each isothermal temperature was characterized in terms of the JMAK equation (Eq. 2.11) [65, 66, 67]. Using least square analysis, the  Chapter 4. Kinetic Characterization  117  best fitting line was determined for a plot of lnln(1/1  —  X) vs. ln(t  —  test),  correlation coefficient (R ) was recorded. The value of the estimated start time, 2  and its test,  was  then varied by a small time increment, and the best fitting line determined once again. This procedure was repeated and the best correlation (max.  ) was obtained, the 2 R  associated t being taken as the recrystallization start time, t. The kinetic parameters n and ln b resulting from the analysis, in combination with the computed t , were used 9 to 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 of ln(X/1  —  X) vs. ln(t  —  ), with the previously established recrystallization start time, 8 t  . Fig. 4.16 shows a comparison of the JMAK and the S-F kinetic characterization of 5 t the isothermal recrystallization data obtained at 650°C. The results of the JMAK and S-F kinetic characterization of the isothermal recrystal lization for test temperatures 600 to 760°C, are summarized in Table 4.2. It is apparent that the time-exponents n (JMAK) and m (S-F) remain relatively constant over the test temperatures, while the parameters in b and ln k, being reflective of the temperaturedependence of the nucleation and the growth equations, are strongly dependent on tem perature. 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 for  the JMAK analysis implies that the nucleation conditions and the growth dimensional ity are similar over the temperature range examined, a condition corroborated by the metallographic observations. In addition, a constant n value is required if the reaction is assumed to be additive (discussed in section 2.1.4). In the present work, the isother mal 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 recalculated at each test temperature, and in combination with  and  ñi,  were used to characterize  Chapter 4. Kinetic Characterization  118  the isothermal recrystallization kinetics. Fig. 4.18 shows the experimentally determined isothermal recrystallization kinetics obtained at 650°C, and those characterized by the best fitting and constant average time-exponent analyses using the JMAK and the S-F equations. The constant average time-exponent characterization of both equations gave a good fit and were used for subsequent continuous heating calculations. The isothermal recrystallization results obtained at 600, 625, 650, 675, 700, 720, 740 and 760°C, together with 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 obtained by calculating the time required for 1, 50 and 99 % recrystallization using the JMAK anal ysis and includes the calculated recrystallization start time, t, the metallographically determined recrystallization completion times for the present study and those reported for a Ti-stabilized [21] and a rimmed [57] low-carbon steels. Recrystallization kinetics have also been characterized in terms of an overall recrys tallization activation energy, QR, by assuming an Arrhenius-type rate behaviour in the form 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 JMAK analysis, and the QR value was estimated by plotting ln(1/tR) vs. 1/T (K’), as shown in Fig. 4.23. The linear relationship (R 2  =  0.99) obtained between ln(1/tR) and 1/T  data supports the validity of the Arrhenius relationship in describing the recrystalliza tion kinetics. The parallel lines corresponding to 10, 50 and 90 % indicate an activation energy of 501.7 kJ/mole for the entire recrystallization event. A similar analysis using the S-F equation gave a QR value of 493.9 kJ/mole. The prediction of recrystallization kinetics during continuous heating using the addi tivity principle [121, 122, 128] requires mathematical expressions describing the tempera ture dependence of the kinetic parameters, ln b and ln k for the JMAK and S-F equations,  Chapter 4. Kinetic Characterization  119  respectively. Fig. 4.24 shows the plots of in b and in k vs. T (°C). Linear relationships with correlation coefficients (R ) of 0.99 were obtained for both cases, with corresponding 2 equations, ln b  =  0.049 T  ink  =  0.077 T  —  36.6  (4.6)  56.9  (4.7)  and —  Similarly, the prediction of recrystallization start time during continuous heating us ing the Scheil equation (Eq. 2.40) [120] requires the characterization of the isothermal start time, t, as a function of temperature. Fig. 4.25 shows the in tS vs. T (°C) ex perimental results obtained for the low temperature recrystallization experiments where recrystallization was initiated during isothermal annealing. Linear relationship (R 2  =  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 illustrating the 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 heavily cold worked banded structure of the 80 % cold-rolled sheet, respectively. The average grain 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 from specimens held at 700°C for 2, 4, 12 and 30 s, respectively. These microstructures, corre sponding to approximately 15, 30, 60 and 80 % recrystallization, illustrate the progress of 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 recrystallized  120  Chapter 4. Kinetic Characterization  specimen 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 x  400 and (b) obtained at x 1000 show two different microstructures corresponding to the initial stages (.-.-‘ 6  %)  of recrystallization obtained from a specimen annealed for 32 s at  650°C. These microstructures confirm that the recrystallization event is heterogeneous, pref erential nucleation initiating at cold-rolled grain boundaries and grain intersections as can be seen in Figs. 4.27 (a), (b), and Figs. 4.30 (a), (b). The same figures also indicate that 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 mea sure 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, recrystallization is predominantly controlled by growth processes. Similar microstructural observations have been previously reported from recrystal lization studies on high-purity iron and its dilute solid solutions [37, 38, 72, 81]. The present observations are also in general agreement with the microstructural changes re ported 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 nucleation assumption of the JMAK theory. In reality, the nuclei are clustered on planes rather than randomly distributed in volume, and the associated increase in the impingement during the early stages of recrystallization is grossly underestimated by Eq. 2.7, as provided in the random nucleation JMAK treatment [68, 85, 96]. This is thought to be the major reason for obtaining the low value of apprximately 0.7 (Table 4.2) for the JMAK time exponent, n, in this study. Isothermal kinetics with such low JMAK time-exponents have been widely reported from recrystallization studies on iron and its alloys [38, 39, 71, 72].  Chapter 4. Kinetic Characterization  121  Another type of failure that has been observed with the JMAK analysis of recrys tallization is the negative deviation from the expected linearity between in ln(1/1 vs. in(t  —  —  X)  ) [33, 72, 87]. Such effects are visibie in Figs. 4.19 (a) and (b), particu 3 t  larly at 650, 675 and 700°C. The same effect can also be seen in the X vs. t graphs in Fig. 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, these effects 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 during recrystallization is a possible explanation for this observation of negative deviation from the linearity, as has already been suggested by other researchers [33, 37, 38, 72, 75]. A decreasing growth rate during isothermal recrystallization has been explained pri marily in terms of a reducing driving force (for growth), caused either by concurrent recov ery 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 show the effects of recovery during recrystallization, by extrapolating the recovery kinetics into the recrystallization zone. It is clear from these figures that the recovery effects become negligibly small during the final 50 % of recrystallization, consistent with their rate pro gressing inversely proportional to time. This observation suggests that the non-uniform distribution of stored energy (or growth along a driving force gradient) is the probable cause for any reduction in growth rate that might have occurred during recrystallization of the present steel. Price [87, 106, 107] recognized the deficiency of the JMAK equation as related to its assumption of constant growth rate, and suggested the S-F equation with a decreasing interface-averaged boundary migration rate (G) as a better alternative. When the present isothermal 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 be  Chapter 4. Kinetic Characterization  122  seen 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 a function of time, also reveals that the S-F equation is more suitable in describing the later 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 descriptions of the experimental data as indicated by Figs. 4.19 through 4.21. The comparable corre lation coefficients resulting from the regression analysis using either equation, as shown in Table 4.2, are due to the fact that the JMAK and the S-F equations describe different stages of the recrystallization event particularly well. The microstructural observations as related to the heterogeneous nature of recrystallization suggest the need to adopt an empirical approach with physical significance to better describe the kinetics of isothermal recrystallization. 4.3.2  Microstructural Path Concept in Recrystallization Modelling  The second approach used in the present study to model the microstructural and ki netic aspects of recrystallization involves the microstructural path concept. The path of microstructural change is the sequence of the microstructural states through which the system passes during a process [85]. The instantaneous state of the system undergoing microstructural evolution during the process of recrystallization is frequently described experimentally in terms of the stereological properties, X, the volume fraction recrys tallized, and A, the interfacial area per unit volume separating the recrystallized grains from the deformed matrix. In the present study, the photomicrographs obtained from the partially recrystallized specimens were used to estimate the interfacial area per unit volume (A) according to Eq. 3.5 [216]. Fig. 4.31 shows the resulting A vs. X data obtained for all isothermal temperatures and heating rates. The existance of a single  123  Chapter 4. Kinetic Characterization  microstructural path function independent of the thermal path is obvious. Because of the 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, giving A  =  2002 (X)° 44 (1  2 which has a correlation coefficient of R  =  —  (4.9)  94 X)°-  0.98.  In the microstructural path approach, the kinetic function is usually described by the 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 Cahn Hagel formulation (Eq. 2.16), i.e.,  =  A C [100]. In the present study, each isothermal  temperature or heating rate was treated separately to calculate the C values. The X vs. t data obtained for each annealing condition was subjected to curve-fitting, using a 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 corresponding to each annealing test. For each isothermal test, the relationship between  and t was  described 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 correspond  ing to each isothermal temperature were obtained through a linear regression analysis of in C vs. ln(t  —  t) (t 8 is the calculated recrystallization start time), performed sepa  rately for each isothermal temperature. The results are summarized in Table 4.3. It is apparent that the growth rate time-exponent,  G,  remains relatively a constant over the  test 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 the  Chapter 4. Kinetic Characterization  124  average riG value of -0.58. In explaining this observation,  G  is expected to be a function  of the growth dimensionality. Since comparable equiaxed grains are obtained at each temperature, the nG value remains a constant, comparable to that of the temperatureindependent JMAK time-exponent. In addition, a temperature-independent  G,  also  satisfies 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 char acterized in terms of the average  G  value of -0.58. Using this value, the appropriate  log Ka values were recalculated at each test temperature, and in combination with the riG value of -0.58, were used to characterize the isothermal recrystallization kinetics. The resulting 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 and 760°C. It should be emphasized that the experimental points in these graphs are specific growth rates calculated from experimental measurements and not primary data points. The interface-averaged growth kinetics have also been characterized in terms of a growth activation energy, QG, by assuming an Arrhenius-type rate behaviour of the form G cx exp(—QG/RT). The activation energy calculations were made at different temperatures, but at constant degree of recrystallization. A parameter, called ‘interface averaged growth distance’, dG, was used to fix the state of the reaction (in an analogous manner to fraction recrystallized, X), and defined as follows, dG=JGdt=  ‘ t+’ (riG + 1)  (4.11)  By substituting the total recrystallization times obtained at the isothermal tempera tures into Eq. 4.11, the total (interface-averaged) growth distance corresponding to the  Chapter 4. Kinetic Characterization  125  complete recrystallization event was estimated to be about 0.0024 cm  (‘S-’  24  t  m). Conse  quently, 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 plot  ting ln G vs. 1/T (K—’), as shown in Fig. 4.34. The linear relationship (R 2  =  0.99)  obtained between ln G and l/T indicates the validity of the Arrhenius relationship in describing the growth kinetics. The common slope obtained for each growth distance gave an activation energy of 544.9 kJ/mole for the entire recrystallization event. The prediction of the growth kinetics during continuous heating using the additivity principle requires a mathematical expression describing the temperature dependence of the 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 present work, as shown in Fig. 4.31, and the associated microstructural path function, as given by Eq. 4.9, are asymmetric in nature. A increases rapidly during the early stages of recrystallization, remains close to the maximum when the % recrystallized is in the range of 25 to 45 %, and decreases steadily thereafter. The initial rapid rise in A with an increasing X can be rationalized in terms of the early site saturation type nucleation and the 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, occurs roughly in the form of pancake shaped manner as shown in Figs. 4.28 (a) and (b); this provides the rationale for the slowly decaying A during the later stages. To the author’s knowledge, there is no reported study of the microstructural path function for a heavily deformed polycrystalline low-carbon steel. However, the present microstructural observations are in general agreement with the A vs. X data reported  126  Chapter 4. Kinetic Characterization  for a deformed iron single crystal [75, 102], and with some of the other recent theoretical and 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 function described by Eq. 2.19, as incorporated into the S-F model [90], are considerably different from 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. X  relationship, may not adequately describe recrystallization with early site saturation type nucleation. The kinetic relationship obtained in the present study between the interface-averaged growth rate (G) and the recrystallization time, as shown in Figs. 4.33 (a) and (b), is similar to the results reported by Vandermeer and Rath [75] for a deformed iron single 0 at all isothermal tempera crystal. They obtained a relationship in the form of C cx t tures, and rationalized this behaviour in terms of a nonuniform stored energy distribution 058 time dependence ob or growth along a stored energy gradient [75]. The stronger t tained in the present work can be easily explained in terms of the greater non-uniform distribution 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 into the S-F model [90] is considerably different, with a stronger growth time dependence,  Oo  , apparently independent of temperature. 1 t  ), but apparently 1 The quantitative understanding of a strongly time dependent (cx t temperature independent, migration rate (C) continues to be a controversial issue. En glish and Backofen [81] observed this behaviour with the exception of short times, as shown in Fig. 2.10, and attributed it to the time dependence of the extent of solute segregation to subboundaries in the unrecrystallized material. Speich and Fisher [90] re ported the growth equation,  0  4 8.5x10  to describe the growth rates at all isothermal  127  Chapter 4. Kinetic Characterization  temperatures. They explained this by invoking the same activation energy for both the boundary migration and the later stages of recovery. Gokhale et al. [105] reinterpreted the same data in terms of the reduction in the dimensionality of growth during recrystal lization. Vandermeer and Rath [76] suggested that highly anisotropic three-dimensional growth could also produce the same result, without the need for invoking competing recovery. The anisotropy was postulated to be due to an orientation effect on boundary mobility. 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 mi gration rates during the later stages of recrystallization. On the other hand, in view of the fact that the recrystallized grains did not change shape during growth (i.e., isotropic growth), the change in growth dimensionality or any other anisotropic effects cannot be significant. In the present study, isothermal G vs. t data was analysed separately at each tem perature. For comparison purposes only, the data from all test temperatures was plotted on a single graph, as indicated in Fig. 4.36. The best fitting line obtained from a lin ear regression is shown in Fig. 4.36. The equation corresponding to this line, with a correlation coefficient of 0.95, is given by, =  4 3.8 x10  (4.13)  This temperature independent equation is remarkably close to the one reported by Speich and Fisher [90]. Some resemblance can also be seen with the graph reported by English and Backofen [81] (see Fig. 2.10) in terms of the deviation from the linearity at short recrystallization times. A closer examination of the regression line, particularly at low temperatures, indicates that the data obtained at a single temperature have a slightly different gradient than that corresponding to the global fit. However, the global regression line does a reasonable job in relating X vs. t. It should be noted that when the isothermal  Chapter 4. Kinetic Characterization  128  data were subjected to the regression analysis, one temperature at a time, all of the timeexponents (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 time exponent of -1. This observation provides an additional explanation to the previously reported strongly time-dependent growth. However, it should be emphasized that though the G values obtained from the global regression line or Eq. 4.13 may not be very different from the actual calculated ones, the relationship among the points corresponding to a single temperature or the associated time-exponent is significantly different in the global representation. The interface-averaged growth rate, G, was measured in the present study throughout the recrystallization event using the procedure described previously. The local growth rate, G, usually obtained by measuring the time variation of the largest intercept-free dis tance on the microstructure, is limited to X < 0.20, due to the impingement effects. Such measurements require several specimens corresponding to the initial stages of recrystal lization, 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 obtained between  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° ) and 40  oc t° ). 38  They also obtained approximately the same activation energy for both 0 and G, although the pre-exponential constants are slightly different. These arguments suggest the general time-dependence of 0 and G to be approximately the same. In addition, for an early site saturation type nucleation, one can reasonably expect the same G and G values before impingement. In the present results shown in Fig. 4.33 (a) and (b), the first two points 58 at each isothermal temperature, which usually corresponds to X < 0.20, obey the t° relationship reasonably well. The 0 values corresponding to these points are expected 58 relationship for 0 vs. t. to be comparable to the G values, suggesting a similar t°  129  Chapter 4. Kinetic Characterization  Combining the microstructural path function, Eq. 4.9, and the isothermal interfaceaveraged growth kinetic function, Eq. 4.10, obtained in the present study using the Cahn-Hagel formulation (Eq. 2.16), the following relationship is obtained,  Ix 44 . 0 where  (KG)T  dX 94 (1 X)O.  2002  (KG)T Jt_0.58dt  (4.14)  is the value of KG for a given temperature, T, and can be obtained using  Eq. 4.12. Unlike the S-F equation development [90], this integration will not lead to a simple analytical expression to relate to X and t. However, Eq. 4.14 can be numerically integrated to yield the fraction recrystallized at any isothermal temperature as a function of 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 isothermal recrystallization kinetics. The existence of a single microstructural path function independent of the thermal path implies that the total number of nuclei is more or less fixed, i.e., the number of recrystallization centers does not vary markedly with temperature. This is in agreement with 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 constant for a particular grain size, inclusion distribution and degree of cold work. The same argument also suggests the recrystallized grain size to be independent of the thermal path and to be a measure only of the density of nuclei. In the present study, irrespective of the annealing treatment performed, the recrystallized grain sizes were found to be in the range of ASTM No. 9- 10; this corresponds to a mean linear intercept of 12 m [44]. The interface-averaged growth distance, as defined by Eq. 4.11, is related to the recrystallized grain structure. The appropriate time required in Eq. 4.11 to obtain the growth distance that corresponds to the final recrystallized grain size is not known, although the use of an average time at which impingement occurs around most of each grain, has been  Chapter 4. Kinetic Characterization  130  suggested [90]. However, it suffices to mention here that the growth distance obtained by substituting the total recrystallization time obtained at different isothermal temperatures was approximately 24  t  m. This is of the same order of magnitude as the average grain  size of a fully recrystallized microstructure. In summary, modelling recrystallization kinetics is a difficult task due to the het erogenity introduced during the original deformation processes and the subsequent non homogeneous nucleation of recrystallized grains and time-dependent growth rate. Ad ditional complication results from the concurrent recovery processes which compete for the same stored energy. Due to these factors, recrystallization as a process is very re sistant to generalizations and simplifying assumptions. In the present work, the basic JMAK assumptions of random nucleation and constant growth rate have been shown to be invalid. The microstructural path and the kinetic functions incorporated into the S-F model have also been shown to be inappropriate. In light of this, the usefulness of the JMAK and the S-F equations can be attributed more to their curve-fitting ability than to their fundamental significance. However, it should be emphasized that these two expressions still provide a simple empirical relationship for adequately describing the isothermal recrystallization kinetics. The major advantage with the microstructural path approach used in the present study is the absence of any assumption regarding the nucleation 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 Process ing Conditions  The T-T-R diagram shown in Fig. 4.22 clearly supports the reported observations that the recrystallization kinetics of I-F steel are severely retarded, when compared to that of rimmed steel [57] and also slower than the recrystallization kinetics of Al-killed steel  Chapter 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, suggesting the similarity of the site-saturation type nucleation and growth dimensionality in both of these steels (both steels were subjected to similar amount of cold work). Severe retarda tion of recrystallization in I-F steels is usually attributed to the reduction in the interface migration rate caused by the excess Ti/Nb in solid-solution and by the fine stabilizing precipitates of Ti and Nb [15, 16, 17, 21, 150, 153]. The recrystallization kinetics reported by Goodenow [21] for the Ti-stabilized low-carbon steel are similar to those obtained in the present work (Fig. 4.22). However, the onset of recrystallization occurs later in the work by Goodenow, probably due to the lower amount of cold reduction (50  % as opposed  to 80 % in the present study). In addition, the progress of recrystallization in the present study was considerably slower. The hot band grain size of the steel used in the current work is considerably larger (ASTM No. 7 9  -  -  8) than that used by Goodenow (ASTM No.  10); this is expected to result in a lower nuclei density and slower recrystallization  kinetics. As indicated in Fig. 4.23, the recrystallization kinetics in the present work has been characterized in terms of a single activation energy, QR, of 501.7 kJ/mole. QR values of 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 activation energy at lower temperatures and towards the end of recrystallization, and explained this behaviour in terms of a rapid reduction in the recrystallization rate observed towards completion. 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 the end of the recrystallization event.  However, this change is not as sharp as the one  reported by Rosen et al., and the recrystallization kinetics in the present work clearly  Chapter 4. Kinetic Characterization  132  followed the usual sigmoidal behaviour to completion. While both of the previously described studies dealt with cold deformations of 50 to 60 %, an 80 % cold reduction was 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 of large particles may yet be another source for a high nuclei density (electron microscopic observations supporting particle induced nucleation will be presented in the next chapter). Such increased nucleation might have prevented the occurrence of the extremely slow growth process in the current study.  Sigmoidal-type, kinetic behaviour without any  sharp discontinuities has also been reported for Ti and/or Nb-stabilized I-F steels after 50 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 constant QR  value of 407.5 kJ/mole. It is obvious that the measured QR value of 501.7 kJ/mole obtained is considerably  higher than the QR values of around 360 kJ/mole and 407.5 kJ/mole reported for high purity iron and rimmed low-carbon steel, respectively and is also much higher than 275 kJ/mole reported for self-diffusion in iron [29]. The higher QR value reported for the rimmed steel, when compared to pure iron, can be explained in terms of the reduced interface 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 also been shown to strongly inhibit the growth of the newly recrystallized grains. In particu lar, Ti and Nb in solid solution are reported to have a very strong influence in retarding recrystallization in iron-based alloys [130, 143]. Additional retardation can be due to the pinning of migrating boundaries by the numerous fine (< 0.1k m in diameter) precip itates of Ti and Nb [154, 155], as discussed in section 2.1.5. The electron microscopic observations obtained in the present study, illustrating the effect of fine precipitates on boundary migration, will be presented in the next chapter. There are several reported  Chapter 4. Kinetic Characterization  133  studies on I-F steels that demonstrate the effects of these two parameters on retarding recrystallization [15, 16, 17, 21, 150, 153] and such strong retardation of the recrystal lization kinetics is clearly reflected in the high activation energy value obtained in the present 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 for the I-F steel with those reported for high purity iron, indicates that the difference caused by solute additions is much more significant in the case of recrystallization. This obser vation is probably due to the fact that the rate of recrystallization depends on boundary migration over considerable distances, a process severely retarded by excess solutes and fine precipitates. It should also be indicated that the QR value of 501.7 kJ/mole obtained for recrystallization and the  Qcj  value of 544.9 kJ/mole obtained for interface-averaged  growth are similar. This observation provides additional support to the suggestion that recrystallization 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 process ing, and the amount of Ti remaining in solid-solution,  TiEX,  can be estimated according  to [4, 6] (all amounts are in weight percentages), TiEx  =  TiTOTAL  —  4C  —  3.42N  —  (4.15)  1.55  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  —  (4.16)  7.75C  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 0.02, is attributed to Ti alone, then, according to Eq. 4.9,  TiEx  =  0.03 and  NbTOTAL  =  0.01. Similarly, if all of  134  Chapter 4. Kinetic Characterization  the carbide precipitation is due to Nb alone, then, NbEx  0, and corresponding TiEX  0.02. 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 > 0.01 and NbEx <0.02.  TiEX  The excess amounts of Ti and Nb in solid solution have been reported to have a stronger retarding effect on recrystallization than the amount present as precipitates. Correlations have been reported between recrystallization temperatures and TiEX or NbEx (see Figs. 2.19 and 2.20) [15, 16, 17, 21, 149, 150]. The present I-F steel has  very low amounts of TiEx and NbEX; steels with 10 times higher TiEX and NbEX have been studied for recrystallization.  Based on these arguments, the present steel  should recrystallize with relative ease, within the family of I-F steels, and the measured recrystallization temperatures are in general agreement with the reported literature in this regard. An exact comparison is difficult, since factors such as size and distribution of precipitates and hot band grain size will also have to be considered. In addition, the amounts of carbon (0.0028 wt  %)  and nitrogen (0.00118 wt  %)  in the base steel used in  this study is extremely low (compared with the typical I-F steel compositions given in Table 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 thermody namic and kinetic parameters of the precipitation reactions and the high temperature processing conditions [4, 6, 10, 15, 161. Lower reheat temperatures (1000 3 ish rolling temperature values just above Ar  (‘--‘  -  1100°C), fin  900°C) and higher coiling temperatures  (700 800°C) are reported to be beneficial for Ti-stabilized I-F steels [4, 6, 15, 16]. These -  conditions have been reported to result in coarse and widely spaced precipitates, allowing rapid growth of new grains with favourable textures. The available information regarding the hot band used in this study indicates a finishing rolling temperature of around 890° C  Chapter 4. Kinetic Characterization  135  and a coiling temperature of less than 600°C. These processing conditions, particularly the lower coiling temperature, could have resulted in a relatively finer precipitate struc ture, causing significant retardation of recrystallization kinetics. The relatively large (‘— 1 m) precipitates of TiN and TiS have been reported to be effective in causing particle induced nucleation of recrystallization in Ti-stabilized I-F steels [153]. In the present study, 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, may explain 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 ASTM No. 9  -  10. The equiaxed recrystallized grain structure obtained for the present I-F steel  indicates that the presence of the randomly scattered fine precipitates has no significant influence on the resulting grain morphology. This observation is in agreement with most of the reported literature on I-Fstee1s [16, 17, 21, 153], with the exception of a study on a Nb-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 a Nb-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 with other low-carbon steels, has been demonstrated through the development of a T-T-R diagram and the measurement of high activation energies. These observations were at tributed to the reduced interface migration rates caused by the excess Ti/Nb in solid solution and the presence of fine stabilizing precipitates of carbides/carbo-sulfides of Ti and Nb. The observed recrystallization kinetics and the microstructural changes were also analysed in terms of the steel chemistry and the high temperature processing conditions.  Chapter 4. Kinetic Characterization  4.4  136  Recovery and Recrystallization during Continuous Heating  Continuous heating annealing tests have been conducted at heating rates of 0.025, 1.88 and 20.2°C/s. The slowest heating rate of 0.025°C/s (89.4°C/h) and the fastest heating rate 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 re covery and recrystallization kinetics during continuous heating. The continuous heating cycle was described by assuming it to be made up of a series of isothermal steps. The kinetic 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-F equation (Eq. 2.21), were performed at each isothermal step. The amount of recovery 1 value), and/or the percentage recrystallized calculated (as indicated by the change in R at each time step, were summed to predict the continuous heating kinetics. As indicated in the isothermal recovery section, two different descriptions were used to characterize the temperature dependence of the isothermal recovery kinetic parameters to be used to predict continuous heating recovery. One involved Eq. 2.4, and Eqns. 4.2 /dt, to temperature 1 and 4.3 and the other relates the instantaneous rate of recovery, —dR 1 (Eqns. through the recovery activation energy, which in turn, is a linear function of R 4.1, 4.4 and 4.5). 1 measurements obtained at 0.025°C/s, Fig. 4.39 shows the in-situ and interrupted R together with the recovery kinetic predictions and the metallographically determined recrystallization start and finish temperatures. As can be seen, the recovery portion of the annealing curve has been successfully predicted and no difference appears between the predictions based on the activation energy approach or that using the empirical relationships, Eqns. 4.2 and 4.3. For this reason, only the activation energy approach was used in subsequent recovery predictions. The recovery curve is extrapolated into  137  Chapter 4. Kinetic Characterization  1 values the recrystallization zone, but, as shown, the agreement between the measured R (without any recovery correction) and the metallographically determined recrystallization kinetics indicates that recrystallization dominates. The validity of additivity for the recovery process was further tested using the in terrupted R 1 measurements obtained at 0.025, 1.88, 20.2 and 80°C/s, as indicated in Fig. 4.40. The reasonable agreement obtained between the predicted and the experi mental R 1 values for a wide range of heating rates clearly demonstrates the usefulness of the additivity principle in predicting the recovery kinetics during continuous heating processes. 1 (interrupted) vs. T Fig. 4.41 emphasizes the recrystallization portion of the R (°C) data obtained at 20.2°C/s. The procedure adopted during the isothermal analysis to separate the concurrent recovery and recrystalliztion effects with appropriate area 1 corrections (see Figs. 4.11 and 4.12), was applied as related to the experimental R values and the predicted recovery kinetics (RTA). The % recrystallized obtained through this procedure is in reasonable agreement with the metallographic measurements. 1 value of 0.47 The start of recrystallization at 20.2°C/s corresponds to a higher R as opposed to 0.36 at 0.025°C/s (see Fig. 4.39). As a result, more recovery effects can be expected at 20.2°C/s during the early stages of recrystallization. This explains the 1 values and % recrystallized at 20.2°C/s once good correlation obtained between the R 1 measurements; whereas, at the recovery effects were removed from the experimental R 0.025°C/s, the agreement was good even without any recovery corrections. /K diffraction peaks, the 1 Ka The effect of temperature on the intensity of the 2 2 valley and the background, and on the 20 positions of the peaks and the valley Kai/Ka were also investigated. This was accomplished by obtaining the peak profiles of a fully recrystallized specimen heated to different test temperatures through a step-heating pro cedure. Fig. 4.42 (a) and (b) show the effect of temperature on (imin  -  Ib), (IK. 1  -  Ib)  138  Chapter 4. Kinetic Characterization  and R , and on the 219 values of the Kci peak and the valley, respectively. 1 Increased thermal vibration of the atoms, as the result of an increase in temperature, is known to decrease the intensities of the diffraction lines and to slightly increase the back ground intensity. The former has been explained in terms of the atoms lying no longer on mathematical planes but rather in platelike regions of ill-defined thickness, while the later is attributed to general coherent scattering in all directions (temperature-diffuse scattering) [49, 50]. The experimental observations during the current investigation also revealed similar temperature effects on intensity values. The general mathematical treat ment of this problem involves the modification of the atomic scattering factor using a temperature dependent term [49, 50]. However, in the present study, only a very simple treatment is used to illustrate the effect of temperature on intensity and consequently on . A linear regression was performed between the measured intensity 1 the x-ray ratio, R values of (‘mm  -  Is), (iK,  -  Ib)  and temperature (°C) yielding, ‘mm  —  ‘b  = 7.2  —  0.0046 T  (4.17)  0.03 T  (4.18)  and IK,  —  ‘b  = 47.3  —  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 temperature1 value of 0.15, as indicated in Fig. 4.42 (a). independent R At high temperatures, the unit cell expands, causing changes in plane spacings and 2 therefore in the 20 positions of the diffraction lines [49]. Linear relationships with R = 0.99 were obtained between the (20)° values corresponding to the Ka, peak and the valley, and temperature (°C), as shown in Fig. 4.42 (b). The equation relating the (2&)° 1 peak to the temperature (°C) is, value of the K (20)° = 145.9  —  0.0052 T  (4.19)  Chapter 4. Kinetic Characterization  139  In the present study, in-situ x-ray measurements were made oniy at the slowest heating rate of 0.025°C/s and were correlated well with the kinetics of recovery and recrystal lization. If in-situ R 1 measurements are to be obtained during high heating rates, the process must be fully automated to follow the shift of the {220} peak with temperature, based on Eq. 4.19. Such R 1 measurements may be directly correlated to the degree of annealing since Rj values were shown to be independent of temperature. As in the case of isothermal studies, in-situ measurements will be considerably easier if only the valley and the background intensities are monitored. However, unlike in isothermal analysis, IM measurements during continuous heating will be influenced by both the degree of  annealing 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 recovery  and recrystallization processes. In a few isothermal and continuous heating tests, both in-situ and interrupted R 1 measurements were made to monitor the annealing process. The heating rate of 0.025°C/s is one such case, and both the in-situ and the interrupted R 1 measurements made at this heating rate are shown in Fig. 4.39. The apparent agreement between these two sets of values supports the general assumption that no significant annealing occurred during the rapid cooling  (- 45°C/s)  to room temperature. In addition, Fig. 4.39 clearly indicates  the effectiveness of the x-ray peak resolution measurements in determining the kinetics of the recovery and recrystallization processes. The designated recrystallization start and finish temperatures shown in this figure were obtained from metallography. The recrystallization start point is also characterized by a change in the gradient,  .  This  transition is particularly clear in this case, since it occurs at a low R 1 value of 0.36, where the concurrent recovery effects are expected to be low. At the recrystallization finish point, no further decrease in R 1 was observed. This observation, together with similar findings from previous investigators [49, 57], indicates that grain growth has no  Chapter 4. Kinetic Characterization  140  significant effect on peak resolution. In summary, the usefulness of the additivity principle in predicting the recovery ki netics during continuous heating processes has been demonstrated. The experimental R 1 measurements have been interpreted in terms of the predicted recovery and recrystalliza tion. The procedure adopted during the isothermal analysis to separate the concurrent recovery and recrystallization effects on peak resolution has been successfully employed to interprete the interrupted R 1 measurements obtained at 20.2°C/s. The temperature effect on the intensity values and 20 positions of the Ka, peak and the Ka, /K 2 val ley has been analysed. The temperature independence of the x-ray ratio, R , has been 1 demonstrated.  4.5  Continuous Heating Recrystallization Kinetics  For heating rates of 0.025, 1.88 and 20.2°C/s, quantitative metallography was performed on samples rapidly cooled after progressive stages of annealing. The specimens were directly observed in an optical microscope to estimate the time corresponding to the onset 3 expt’l) and completion of recrystallization. In addition, photomicrographs obtained (t  from the partially recrystallized specimens, were used to quantify the volume fraction recrystallized (X) and the interfacial area per unit volume separating the recrystallized grains from the unrecrystallized matrix (A). The continuous heating recrystallization kinetics were predicted using the experimen tally determined start time (t 3 expt’l), the isothermal recrystallization kinetic parameters (JMAK and S-F), and the principle of additivity. As indicated in Fig. 4.38, at each time step after the onset of recrystallization, i.e., after t expt’l, the fraction recrystallized was calculated based on the isothermal recrystallization kinetics at the temperature of the particular isothermal step, and the fraction of the recrystallized material already present.  Chapter 4. Kinetic Characterization  141  This process was continued until all the cold worked matrix had been consumed. The isothermal 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 was adopted based on the Scheil equation [120] to estimate the continuous heating ‘recrystal lization start time’ (t 5 Scheil), as defined by the fractional consumption of the isothermal incubation time determined from Eq. 4.8. The additivity procedure was used in the prediction of continuous heating recrystal lization kinetics at 0.025, 1.88 and 20.2°C/s, the predicted and experimental results are compared in Fig. 4.43. Reasonable agreement is apparent for all three heating rates, indi cating that recrystallization is experimentally additive. A comparable level of agreement is obtained irrespective of whether the isothermal recrystallization was characterized by the JMAK or the S-F equation. However, a careful examination of the comparison shows that the predictions using the JMAK equation are better in the early stages of recrystal lization, while the S-F equation predicted a better fit to the later stages. This observation is 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 any additivity-based kinetic prediction would be expected to behave accordingly. The Scheil equation was used to estimate continuous heating recrystallization start times (t 8 Scheil) at 0.025, 1.88 and 20.2°C/s. The results, in combination with the experimentally determined recrystallization start times (t 3 expt’l), are shown in Table 4.4.  The temperatures corresponding to the start times, referred to as “T expt’l”  and “T Scheil” are also indicated. The Scheil equation consistently overestimates the incubation time associated with the onset of recrystallization; the extent of overestimation is higher at higher heating rates. The continuous heating recrystallization kinetics were also calculated at 0.025, 1.88  Chapter 4. Kinetic Characterization  142  and 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 predictions for all three heating rates compared with the experimental % recrystallized. The pre dictions based on t 51 Scheil are virtually identical with the t 9 expt’l-based predictions after approximately 30  % recrystallization. Despite the higher start times predicted by  the Scheil equation, the increased recrystallization rate associated with a higher start temperature seems to have quickly compensated for the difference. The corresponding analysis with the S-F equation-based predictions exhibited similar behaviour. The additivity procedure was also employed in the prediction of the continuous heat ing interface-averaged growth rates (G) at 0.025, 1.88 and 20.2°C/s. The predictions were based on the isothermal characterization of the growth kinetics as provided by the temperature-independent growth rate time-exponent,  flu,  (= -0.58) and the temperature-  dependent parameter, KG, (Eq. 4.12). The primary isothermal equation used in this modelling exercise was Eq. 4.11, i.e., dG  = (n)  j(nc+l)  With this equation, the steps  involved in the continuous heating recrystallization model were converted to predict the growth kinetics. The fraction recrystallized, X, was replaced by the interface-averaged growth distance, dG, and the final growth rates were calculated from the predicted dG values using the equation, ZIG  (4.20)  where dG is the additional growth distance corresponding to the time step, Lit. These calculations were continued until the experimentally determined recrystallization finish time was reached. In addition, growth rates during continuous heating were also calculated using the experimental X vs. t data and the experimental A values; a JMAK-type equation was  Chapter 4. Kinetic Characterization  143  found to be useful for curve-fitting and for the calculation of dX/dt. Another mod elling procedure was also used to calculate the G values during continuous heating. In this method, dX/dt was calculated from the JMAK equation based additivity predicted recrystallization kinetics, as given in Fig. 4.43 and the A values were obtained from the experimentally determined microstructural path function, Eq. 4.9. Fig. 4.45 com pares the additivity predicted G values with (i) the modelled 0 values obtained using dX/dt from the predicted recrystallization kinetics and A from the derived microstruc tural path function and (ii) the estimated 0 values using the experimental X vs. t data and the experimental A values. The results presented in this graph clearly indicate that the interface-averaged growth rate, 0, during continuous heating can be succesfully pre dicted using the isothermal growth kinetics and the principle of additivity. It can also be seen from Fig. 4.45 that the 0 values increase during the progress of recrystallization due to the increased thermal activation, despite the fact that the driving force for growth steadily decreases. To test the validity of the isokinetic concept [114] for recrystallization, as characterized by its growth kinetics, the Cahn-Hagel formulation, Eq.  2.16, and the growth rate  equation, Eq. 4.10, can be writen as, =  A KG  (4.21)  tnG  Substituting the time, t, calculated from Eq. 4.11 into Eq. 4.21, and rearranging gives, dX  ——  — —  A  11  1 .J’G+ UG  17 1kG  I  /  1  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 will  satisfy Cahn’s [114] isokinetic condition expressed by Eq. 2.29. In the present study,  Chapter 4. Kinetic Characterization  144  the 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 de scribed by the temperature-independent JMAK, S-F and growth rate time-exponents, can be considered to be an isokinetic-type transformation. Such isokinetic transforma tions satisfy all of the additivity conditions and lead to a single additivity model (see section 2.1.4 [114, 115, 116, 118]). Hence, there are no ambiguities in the current mod elling exercise to predict the recrystallization kinetics during continuous heating, and the good agreement obtained between the predicted and the experimental recrystallization kinetics for a wide range of heating rates (covering 3 orders of magnitude) clearly indi cates that recrystallization in the present I-F steel is experimentally additive. A previous recrystallization study on the rimmed low-carbon steel resulted in the same conclusion [39]. The validity of additivity for phase transformations involving nucleation and growth processes has been tested in considerable detail; ‘early site saturation’ [114] and ‘effec tive site saturation’ [115] are two different criteria resulting from those studies. All of these studies point to the fact that a reaction will be additive if the transformation is dominated by a single temperature dependent process  -  ‘growth’. The microstructures  obtained during the present study, conducted over a wide range of isothermal temper atures and continuous heating rates, indicated that nucleation substantially occurred during the early stages of recrystallization, suggesting the validity of early site satura tion. Similar observations have often been reported from recrystallization studies on heavily deformed metals [33, 37, 38, 75, 80, 81]. The early site saturation type nucleation makes recrystallization primarily a growth-controlled process, a sufficient condition to explain the experimentally demonstrated validity of additivity in the present study. The fact that a single activation energy (QR  =  501.7 kJ/mole) was obtained for  Chapter 4. Kinetic Characterization  145  recrystallization is consistent with the additivity criterian of the dominance of the same process (or mechanism) throughout the transformation; this also implies recrystallization to be isokinetic [114]. This argument would suggest that the recovery process, with its increasing activation energy, QR, from 173.1 kJ/mole at R 1 1 R  =  =  0.6 to 312.1 kJ/mole at  0.15, is not additive. However, the additivity procedure could be used successfully  to predict the recovery kinetics during continuous heating, as shown in Fig. 4.40. This is probably due to the fact that all of the predicted R 1 values were within the narrow range of 0.58 to 0.36, and the corresponding change in  Qm,  values, i.e., from 179.3 to  247.2 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], with its inherent assumption of proportional consumption of isothermal incubation, to over estimate the continuous heating recrystallization start time. This observation suggests incubation to be a non-additive event. This may be the case if no single mechanism dom inates throughout the incubation period. Recovery takes place during incubation, and leads to the formation of recrystallized nuclei. A range of different mechanisms operate during recovery. This was reflected in the increasing activation energy for recovery as ob tained in the present work, providing indirect evidence that incubation is a non-additive event. Moore [126j observed similar non-additive behaviour from stepped isothermal tests performed during the austenite-ferrite transformation. He explained those observations by suggesting the non-equivalence between a given percentage of the incubation period spent at different isothermal temperatures, and correlated these effects to the smaller crit ical size of the ferrite nuclei at lower temperatures. This non-proportional consumption of isothermal incubation time, may also explain the presently observed overestimation of incubation time during continuous heating. Despite the higher Scheil-predicted start  Chapter 4. Kinetic Characterization  146  times, the additivity procedure resulted in good kinetic predictions, particularly towards the (more significant) later part of recrystallization. These results clearly demonstrate the usefuliness of the Scheil equation in kinetic modelling, as it eliminates the necessity to experimentally determine the recrystallization start time for any heating rate. In summary, the isothermal recrystallization kinetics as characterized by the JMAK and the S-F equations, have been successfully used in conjunction with the principle of additivity to predict the recrystallization kinetics during continuous heating. A similar procedure was adopted to predict the interface-averaged growth rates at different heating rates. These observations have been rationallized in terms of the early site saturation type nucleation and the isokinetic nature of the subsequent growth.  The additivity  procedure also led to useful recovery predictions. This was explained in terms of the activation energy for recovery not changing significantly within the narrow test range. Despite overestimating the non-isothermal incubation times, the usefulness of the Scheil equation in recrystallization modelling has been demonstrated.  Chapter 4. Kinetic Characterization  147  Table 4.1: Characterization of isothermal recovery kinetics Temp. °C 500 550 600 625  In R 1 K -0.780 -0.838 -0.738 -0.804  K kt k x 10—6 x i0 x iO x i0  =  8.4 1.3 3.4 9.1  =  —  2 R 0.71 0.70 0.89 0.83  b 0.587 0.558 0.517 0.499  b  a In t a 2 R 0.020 0.95 0.022 0.96 0.023 0.99 0.024 0.96 —  Table 4.2: Characterization of isothermal recrystallization kinetics Temp. °C 600 625 650 675 700 720 740 760  JMAK_Equation 1?2 n lnb 0.65 -6.63 0.96 0.74 -6.31 0.95 0.68 -4.34 0.98 0.62 -3.09 0.95 0.71 -1.89 0.98 0.79 -1.52 0.97 0.90 -0.65 0.99 0.76 0.34 0.99  S-F m 0.84 0.95 0.99 0.93 1.07 1.28 1.64 1.68  Equation ink 2 R -7.96 0.92 -7.58 0.91 -5.41 0.99 -3.75 0.99 -2.03 0.97 -1.68 0.97 -0.50 0.97 1.21 0.98  Chapter 4. Kinetic Characterization  148  Table 4.3: Characterization of isothermal interface-averaged growth kinetics Temp. (°C) 600 625 650 675 700 720 740 760  G  log KG  2 R  -0.56 -0.48 -0.61 -0.68 -0.59 -0.53 -0.48 -0.67  -5.35 -5.28 -4.48 -4.15 -3.87 -3.75 -3.41 -3.19  0.97 0.97 0.96 0.93 0.96 0.91 0.91 0.97  Table 4.4: Experimental and Scheil predicted recrystallization start times (and temper atures) during continuous heating Heating Rate °C/s 0.025 1.88 20.2  Experimental (s) T 5 (°C) 23680 600 331 630 31.3 640  Scheil Predictions (s) T 3 (°C) 24080 610 349 664 34.0 694  Chapter 4. Kinetic Characterization  149  1—  500°C  -  (Recovery Only) 0.8 C •_  -  a  1 (in-situ) R  +  ‘M  a a-+  -  (in-situ)  0.6  ++  l)  a I  0.4 O  a  0.2  a  +  + +  o  a  b1’ Time (s)  Figure 4.1: Fractional peak resolution (F) calculated at 500°C based on in-situ measure ments of x-ray ratio (R ) and valley intensity (IM). 1  Chapter 4. Kinetic Characterization  150  0.6  0.54  6  0.48  0.42  0.36  0.3 0  20 (Thousands)  10  30  40  Time (s)  Figure 4.2: In—situ R 1 measurements obtained at 500°C, compared with the kinetic de scriptions using Eq. 2.3 (in R 1 = K kt) and Eq. 2.4 (R 1 = 6 a in t). —  —  Chapter 4. Kinetic Characterization  151  0.6  0.5  0.4 ci  x 0.3  0.2 0  10  20 (Thousands)  30  40  Time (s) (a) 0.6  0.5  C  0.4 >-‘  x 0.3  0.2  Tirrie (s)  (b) Figure 4.3: (a) In-situ R 1 measurements at 500, 550, 600 and 625°C, together with the kinetic descriptions using Eq. 2.4, and (b) the same kinetic data when replotted on a logarithmic time scale.  Chapter 4. Kinetic Characterization  152  650  600  = 1 R 550  500  Time-Temp.-Recovery •  Predicted (Eq. 2.4) Expt’l 1 (R 0.5) + Expt’l (R = = 0.4) 1  450 101  7 ib  ib’ Time (s)  Figure 4.4: Time-Temperature-Recovery (T-T-Ry) diagram obtained using Eq. 2.4; ex perimental measurements corresponding to R 1 = 0.5 and 0.4 are also shown.  Chapter 4. Kinetic Characterization 70  5  153  7O0  626O0  50i  5Q0 t  -  0  -  IsothermalRecovery 0.45 0.30 0.15  +  —3J  —  I  I  0.96  I  1.04  I  I  I  I  1.12  1.2  1.28  l0 / 3 T (°K ) 1  350  0  300  -  b I—  250  -  0 0  0  200  150  —  0.1  0.2  0.3  I  I  0.4  0.5  0.6  0.7  X-Ray Ratio, R 1  Figure 4.5: (a) Effect of inverse absolute temperature on the natural logarithm of the instantaneous rate of recovery calculated at constant R 1 values, and (b) the calculated  activation energy for recovery,  as a function of the extent of recovery, R . 1  Chapter 4. Kinetic Characterization  154  0.64  0.028  0.6  0.026  0.56 0.024 -  0.52 0.022 0.48  0.44  -  • 0.02 -  0.4  0.018  400  500  600  Temperature  700  800  (t)  Figure 4.6: Temperature dependence of parameters b and a; isothermal recovery kinetics has been characterized by the logarithmic relationship, R 1 = b a in t. —  23.61  -20  23.6 -QR/R  in Ap.  -25  23.59  H  o,O -30 23.58  ‘  zc. CM  -35 23.57  23.56  C  0.1  0.2  I  I  0.3  0.4  I  0.5  0.6  --40 0.7  X-Ray Ratio, R 1 Figure 4.7: Effect of R 1 on in AR and -QR/R; recovery kinetics has been analysed in terms of the Arrhenius equation, dR /dt = —ARk exp —(QR/RT). 1  Chapter 4. Kinetic Characterization  155  25 C/D -‘S  >  23 1  cc  >  ‘S  21  (I)  Q  20  =  19 18 0  10  20 (Thousands)  30  40  Time (s)  Figure 48: In-situ ‘M measurements at 500° C, compared with the kinetic curves obtained using Eq. 2.3 (lnIM x t) and Eq. 2.4 (IM x int).  Chapter 4. Kinetic Characterization  156  0.60  0.45’ C  .-  + + +  0.30  1 (interrupted) R • +  • 0.15  -  580  I  I  600  620  640  Isothermal start Recrystallization start (metallography) 660  680  700  Isothermal Test Temperature (°C)  Figure 4.9: R 1 measurements corresponding to the start of the isothermal hold and the onset of recrystallization, as obtained from the interrupted tests performed at 600, 625, 650 and 675°C.  Chapter 4. Kinetic CharacteriEation  157  e:stal1iZti ‘—‘  C  cFJ I)  a  R (interrupted) 1 Test 1  +  ‘M  0.8  -  I—  (in-situ) Test 2 -  0.6-  +  0.4  o  1  .— ,4.1  0  ‘a I +1’ UI  + +  02  a  a  I  Recryst. start  +  0100  i’o’  ib 2 Time (s)  4 io  Figure 4.10: Fractional peak resolution, F, calculated at 625°C using interrupted R 1 val ues and in-situ ‘M measurements (obtained from two different tests); metallographically determined recrystallization start time is also indicated.  Chapter 4. Kinetic Characterization  0.5  158  Recryst. start based on 1 Recovery nrecrystallized I(RUA) area ]  0.4  Recovery 0 —4  0.3 a  -  -  100  1 (interrupted) R % Recrystallized (metallography)  0.1  I La]  1 (interrupted) RUA R  675 02-  ased o total I(RTA)  -  1 (intemipted) R  -  75 CD  C)  -50 (ID -  - 25 ——  0 100  10’  102  3 io  4 io  0  N  a  Time (s)  Figure 4.11: Isothermal 675°C R 1 measurements interpreted in terms of recovery (Eq. 2.4) based on the total area (RTA) or the unrecrystallized area (RUA), recrystallization (recovery R ) and measured % recrystallized. 1 -  Chapter 4. Kinetic Characterization  159  20  16  12 100 .  1-4  75  8  50  CD C) (ID  4 25  4-.  N  CD  0  Time (s)  Figure 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. -  Chapter 4. Kinetic Characterization  160  0.8  0.8  C  0  Cl)  C)  C  0.6  0.6 C) C Cl:  0.4  0.4  0.2  0.2  Ce  0 C) Ce  0  ><  0  Time (s)  (a) .  -  0.8  I  !  0.8  +  C  :i  C Cl)  Ce  Ce  C C C-) Ce  720C 0.2  0  1 (interrupted) R M (in-Situ) 1 o Metallography  +  100  .  0.2  0 102  Time (s) (b) Figure 4.13: Comparison of the fractional peak resolution (F) calculated from interrupted 1 and in-situ ‘M measuremnts, and the fraction recrystallized (X) determined from R metallography at (a) 700 and (b) 720° C.  Chapter 4. Kinetic Characterization  161  70  CD  1 Ce I  60  50  Ce  >-  40  Cd,  30  20 20 (Thousands)  Time (s) (a) 70 aa.a a a a. • —S  aa a a a  U  •a a. a  a a a  60-  650°C >  (Recryst. start  50-  =  a  ‘KAiphal  +  ‘nun  15 s)  40-+ ++  + + +  —  30 -  200  +  ++++ +  ++  +++++  + +  2 (Thousands)  3  + ++  ++  4  Time (s) (b) Figure 4.14: The effect of isothermal annealing time on the intensity values, ‘Ku,, ‘mm and ‘b, as obtained from in-situ peak profile measurements at (a) 500 and (b) 650°C.  Chapter 4.  Kinetic Characterization  162  a a a  ><  0.8  a  N Ce  0.6  > 0  04 C  a  -  0  0.2 a  0  lOl  102  Time (s) Figure 4.15: 650°C.  Metallographically determined isothermal recrystallization kinetics at  4  4  650°C 3  a  Experimental (JMAK) Experimental (S-F) JMAK (best fit) ----S-F (best fit)  +  +  2-  -  +  1--  0 C  3  - - - -  2  +  --  a  +  —l -2  -2  -3  -3  -4  -4 2  4  6  In  8  ) 1 (t—t  Figure 4.16: The JMAK [66, 67, 65] and the S-F [90] analysis of the isothermal data obtained at 650°C, indicating the best fit lines.  Chapter 4. Kinetic Characterization  163  4  A  Isothermal Recrystallization •  n-bestfit m-bestfit n average ----rn-average  3  +  —  -  -  2-  2 *  +  +  1  + +  I  I  580  •  I  I  620  +  +  I  -1  -.  •  •  •  I  I  660  I  I  —  I  I  700  I  I  740  i  780  Temperature (k) Figure 4.17: Temperature dependence of the JMAK time-exponent, n, and the S-F time-exponent, m, as obtained from the best fit analysis; the average values of n (=0.73) and m (=1.17) are also indicated.  650t ><  0.8  Experimental —JMAK (best fit) —JMAK (average) S-F(bestfit) S-F (average) -  —  N  0.6  1:  2/ I  101  3 i0  10  Time (s) Figure 4.18: Recrystallization measurements obtained at 650°C, compared with the ki netic descriptions using the JMAK and the S-F equations; the effects of using the original best fit parameters vs. the recalculated average parameters are also shown.  Chapter 4. Kinetic Characterization  2  164  JMAK a +  625C  °  650 D 9 675  0-  -2  -3  -  I  -  1  3  5  7  9  11  in (t—L,)  (a) 2  I  0  —1  -2  -3 -1  -  1  3  5  In (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.  Chapter 4. Kinetic Characterization  165  4  2  0  -2  -4 1  3  5  7  In  9  (t-t)  (a) 4  2  0  -2  -4  In  (t-t)  (b) Figure 4.20: 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.  Chapter 4.  Kinetic Characterization  ><  166  0.8  ‘D N  (I)  > C-)  0.4 0 C)  0.2 [1  0  Time (s) (a)  0  0.8  N  C,)  >  06  0  0 0 0  0.4  0.2 10’  102  Time (s) (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 descriptions using the JMAK and the S-F equations.  Chapter 4. Kinetic Characterization  720  167  -  T-T-R N  UOU  N  +  N  -  (,  N.  N.  -  N? + N N N. ‘N  N  640 -  Predicted (JMAK) + Start/Finish Ti-stabilized (Present Work) o Start/Finish Ti-stabilized (Goodenow) Start/Finish Rimmed (Magee) -  N  600560 1%  -  520  50%  99%  -  480101  I  10  3 i0  Time (s)  Figure 4.22: Time-Temperature-Recrystallization (T-T-R) diagram obtained using the JMAK analysis; recrystallization start and finish times for the I-F steel under investiga tion, and for a Ti-stabilized [21] and a rimmed [57] low-carbon steels are also shown.  Chap Ler 4. Kinetic Characterization  -  168  7qot  760°C  5  6q0°C  650°C  0 (ID .—  ;  -5-  Isothermal —  -10  Recrystallization (JMAK)  -  •  10  + 0  90%J  -150.96  QR(kJ/mole) 501.7 1.00  1.04  1.08  1.12  iO f 3 f (K’)  Figure 4.23: Temperature dependence of the recrystallization time corresponding to 10, 50 and 90 % recrystallization as obtained from the JMAK analysis.  Chapter 4. Kinetic Characterization  169  2 0 -2 -4 -D  -6 -8 -10 -12 580  620  660  700  740  780  Temperature (°C) Figure 4.24: Temperature dependence of the JMAK parameter, in b, and the S-F param eter, in k; isothermal recrystallization kinetics has been characterized by the JMAK and the S-F equations with constant values of n (=0.73) and m (=1.17).  8  6 B  4  2  580  600  620  640  660  680  Temperature (°C) Figure 4.25: Recrystallization start time, t, as a function of isothermal temperature.  Chapter 4. Kinetic Characterization  170  (a)  (b) Figure 4.26: 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).  171  Chapter 4. Kinetic Characterization  (b) Figure 4.27: Photomicrographs showing the early stages of recrystallization obtained from specimens held at 700° C for (a) 2 s and (b) 4 s (Magnification X 200).  Chapter 4. Kinetic Characterization  172  (b) Figure 4.28: Photomicrographs showing the later stages of recrystallization obtained from specimens held at 700°C for (a) 12 s and (b) 30 s (Magnification X 200).  Chapter 4. Kinetic Characterization  173  Figure 4.29: Typical microstructure of a fully recrystallized specimen, obtained after a 150 s hold at 700°C (Magnification X 200).  Chapter 4. Kinetic Characterization  174  ..  .  (b) Figure 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 32 s.  Chapter 4. Kinetic Characterization  1000  175  -  x  (-)  j j  :: ::  x  x  -  x  Ix Ix  1+  t+  Microstructural Path Function +  x  0.’2  ÷  600, 625 650, 675Z 700, 7209 740, 760 0.025, 1.88, 20.2CC/s Best Fit ‘  04  x x  0.6  0.8  1  Fraction 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 microstructural , is also indicated. 94 44 (1 X)° path description, A 2002 (X)° —  Chapter 4. Kinetic Characterization  176  0C  -05 C  -10  -1.5  Isothermal Growth  -  (interface averaged) • •  nG-bestfit nG average -  -2580  I  620  660  I  700  740  780  Temperature (°C)  Figure 4.32: Temperature dependence of the interface-averaged growth rate time expo nent, riG, as obtained from the best fit analysis; the average G value of -0.58 is also indicated.  Chapter 4. Kinetic Characterization  177  Isothermal Growth (interface averaged) • 600°C + 625°C ° 650°C 675°C  0,  E  ci  t,) Ce  0  7 io-  io°  10  4 1o  102  Time (s)  (a)  N  0,  E C)  0  ID 0 C2  10  0  isothermal Growth  p CD  +  (interface averaged)  io  • 700°C + 720°C ° 740°C 760°C -  10-I  10  Time (s) (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.  Chapter 4. Kinetic Characterization  760°C I  5  (I)  178  650°C I  700°C  600°C I  +  I  C.)  .-  -10•  +  +  C  Isothermal Growth -15  Ic  -  +  (interface averaged) Growth Dist.  • 0.0005 ci1 + 0.OOlOcmI  0.OOl5cmF 0.0020 cm]  -200.96  QG  (kJ/mole) 544.9 I  I  1.00  +  1.04  1.08  1.12  ) 1 iO (K  Figure 4.34: Effect of inverse absolute temperature on the natural logarithm of the in stantaneous (interface-averaged) growth rate, G, calculated at constant growth distances, dG.  Chapter 4. Kinetic Characterization  179  1  1  5 io_  -  6 iO  I  I  580  620  I  660  I  I  700  I  I  740  780  Temperature (°C)  Figure 4.35: Temperature dependence of the growth parameter, KG; isothermal growth kinetics has been characterized by G = KG jlzG with a constant T G value of -0.58. 1  Chapter 4. Kinetic Characterization  180  -9  10  ci)  0  S  +  0  + ++ +  +  1 06  + * + + I U.  Isothermal  II  • ÷  1  1010 101  •  600, 625 650, 6759, 700, 720Z 740, 760Z Best Fit 101  1  Time (s)  Figure 4.36: The plot of the isothermal G values obtained at all test temperatures against time (both axes on logarithmic scale); the global best fit description line, G 3.810 also indicated.  Chapter 4. Kinetic Characterization  ><  181  0.8  0 C) N  .E v)  0.6  > 0 C)  0.4 0 0 ci  çs..  0.2  0 106  Time (s) (a)  -  0.8  C) N ci ci  0.6 C). C 0 0 ccl  OA  0.2  Time (s) (b) Figure 4.37: Modelled X vs. t curves using the microstructural path approach, together with the experimental data points obtained at (a) 600, 625, 650 and 675°C and (b) 700, 720, 740 and 760°C.  182  Chapter 4. Kinetic Characterization  Recrystallization ) 11 JMAK —-X = 1 exp(-bt m S-F —-(XIl-X)=kt -  H  Recovery =  b a ln -  t  Time  Figure 4.38: Schematic diagram illustrating the modelling procedure used in the predic tion of recovery and recrystallization kinetics during continuous heating.  183  Chapter 4. Kinetic Characterization  0.6  0.5 Recovery  C  0.4  Recryst.  start  .  -o 0.025 °CIs  0.3  • o  0.2  -  -  -  0.1  R (in-situ) 1 1 (interrupted) R Predicted Recovery (activation energy) Predicted Recovery (empirical) % Recrystallized (metallography) I  300  I  400  -25 Recovery and Recrystallization  .cJ  -75 N CD  -100 Q Recryst. finish  I  —  500  ——-——J——  600  I  700  Temperature (°C)  Figure 4.39: In-situ and interrupted R 1 measurements obtained at O.025°C/s, compared with the additivity-predicted recovery kinetics (using ‘activation energy’ and ‘empiri cal’-type isothermal descriptions) and metallographic analysis of % recrystallized.  184  Chapter 4. Kinetic Characterization  0.6  0.5  -  -  C  .-  0.4  -  Continuous Heating Recovery • 0.025 °C/s 0 1.88 C/s + 20.2 °C/s 80 °C/s Prediction  +  .  —  0.3  —  400  I  I  440  480  I  I  520  I  I  560  I  I  I  600  640  680  I  Temperature (°C)  ) and predicted continuous 1 Figure 4.40: Comparison of experimental (interrupted R heating recovery kinetics at 0.025, 1.88, 20.2 and 80°C/s.  185  Chapter 4. Kinetic Characterization  0.5 based o Recovery unrecrystallized (RUA) area L  start  0.4  -  Rcovery  0.3  20.2 °CIs  0.2  R (interrupted) 1 % Recrystallized (metallography)  C .-  ‘based O1 total (RTA) L area]  I  a a RUA RTA  -  -  1 (intemipted) R  -100  1 (intemipted) R  -7c ‘-‘  CD C) ‘1  0.1 -25 0  I  620  I  I  660  1  I  700  740  780  820  -0 860  Temperature (°C) 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 H ) and measured % recrystallized. 1 -  N CD c1  Chapter 4. Kinetic Characterization  186  50  2  0.6 0.5  40  C C  ct  1  0.4  30  -p  )<  V.3  20 —  C  02  -  10 0.I 0  0  400  Temperature  (b)  (a) 147 Cl)  a)  a)  144 Cl)  C  C-  143  a)  >  142  a)  141  Temperature  (t)  (b) Figure 4.42: Temperature effect on (a) the values of (b) the 20 values of the Ka, peak and the valley.  (Jmn  -  1J,  (j*01  -  16)  and B , and 1  Chapter 4. Kinetic Characterization  187  1  580  620  660  700  740  780  820  Temperature (°C) Figure 4.43: Comparison of experimental and predicted continuous heating recrystalliza tion kinetics at 0.025, 1.88 and 20.2°C/s; the predictions are based on the experimentally determined start times, t expt’l.  Chapter 4. Kinetic Characterization  188  1  ntinuous Heatin [zatiOn o 0.025 UCIs 1.88 °CIs 20.2 °C/s expt’l) 81 —JMAK (t JMAK (tSchei1 -  580  620  660  700  740  780  820  Temperature (Z)  Figure 4.44: Comparison of the effect of t. expt’l vs. t Scheil on the JMAK equa tion based kinetic predictions at 0.025, 1.88 and 20.2°C/s; experimentally determined % recrystallized are also indicated.  Chapter 4. Kinetic Characterization  189  1 02  If)  10_  ‘  0  6 io  1 08 600  640  680  720  760  800  Temperature (°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 A from the derived microstructural path function) and estimated (using the experimental vs. 1’ data and the experimental A values) G values at 0.025, 1.88 and 20.2°C/s.  Chapter 5  Microstructural Examination of Structural Changes  The major aim of this part of the research work is to study the microstructural changes during annealing of heavily cold-rolled I-F steel by transmission and scanning electron microscopy (TEM and SEM). In particular, the influence of the precipitates on these structural changes was examined during a heating rate simulating that of the continuous annealing process. In addition, the orientation relationships among subgrains and the na ture of the precipitate distributions were briefly studied. The composition of precipitates larger than 0.1 jim in diameter were also examined with a scanning energy dispersive x-ray (EDX) microanalyser.  5.1  Structural Changes during Cold Rolling and Annealing  The annealing treatments performed correspond to either a heating rate of 20.2°C/s (simulating continuous annealing) after which the specimens were rapidly cooled from peak 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 heated to 700° C. Thin foils produced from the as-received hot band, the cold rolled steel and the annealed sheet specimens were examined in a STEM operated at 200 kV to study the microstructural changes associated with the recovery and the recrystallization processes. Diffraction patterns and Kikuchi patterns were also obtained to determine the orientation relationships among siibgrains. The heavily cold-rolled interstitial-free steel specimens exhibited a poorly defined, 190  Chapter 5. Microstructural Examination of Structural Changes  191  non-homogeneous cell structure, as shown in Fig. 5.1. The heterogeneous nature of the observed 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 cell structure. The cells contain a relatively small number of dislocations, separated from one another by highly deformed cell boundaries; the cell boundaries contain the greater fraction of the dislocations introduced by cold rolling. Fig. 5.2 (a) indicates that the cells can take different sizes and geometric shapes, varying from relatively large equiaxed to small elongated cells. For the approximately equiaxed cells, the cell size varied between 0.3 to 0.8 jim, while the thickness of the cell walls was typically in the range of 0.2 to 0.4  Figs. 5.3 (a) and (b) were obtained from a specimen quenched from 580°C after being heated at 20.2°C/s. These micrographs correspond to a partly recovered state as the metallographically determined recrystallization start temperature was 640°C and provide evidence of an overall reduction in the dislocation density during the early phase of recovery caused by a variety of annihilation processes. In particular, dislocations can annihilate by glide and climb within grains, in addition to migrating to cell walls. The tangled dislocations in the cell walls rearrange themselves, and, as a result, a reasonably well defined cell structure evolves, as shown in Figs. 5.3 (a) and (b). These microstruc tures are characterized by a considerably lower dislocation density in the cell interior and more sharply defined (thin) cell boundaries. The subgrains thus formed are approx imately of the same size and shape as the initial cells; the relatively smaller elongated subgrains and the larger ones can be seen in Figs. 5.3 (a) and (b), respectively. With additional recovery, continued subgrain formation and subgrain growth take place. These processes eventually lead to the formation of recrystallized nuclei as seen in Figs. 5.4 through 5.7 for specimens heated at 20.2°C/s up to 640°C. Figs. 5.4 (a) and  Chapter 5. Microstructural Examination of Structural Changes  192  (b) show the well-defined subgrain structure developed with continued recovery. These figures also suggest that the early growth of subgrains occurs largely by coalescence, i.e., by eliminating the boundaries between them. The probable positions of eliminated boundaries are indicated by arrows, based on shape considerations and/or by identifying the visible residual dislocations from the coalesced boundaries. Fig. 5.5 shows another example of subgrain coalescence, together with the Kikuchi patterns corresponding to both of the subgrains. The estimated misorientation of 0.6° (equal to the displacement between the corresponding lines divided by the camera length of 0.8 m) provides ad ditional evidence for the possible occurrence of the coalescence process. In addition to coalescence, sub-boundary migration also contributes to the growth process. Fig. 5.6 shows an example where both sub-boundary migration (as suggested by the curvature of the boundary) and coalescence seem responsible for subgrain growth. Precipitates influ ence 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 nucleation  process (note the preferential formation of dislocation-free subgrains around the precip itate). Fig. 5.7 (b), on the other hand, suggests the retarding effect of fine precipitates on sub-boundary migration; this can be inferred from the sharp discontinuity observed along the curvature of the boundary. Continued subgrain growth by coalescence and sub-boundary migration leads to the formation of recrystallized nuclei. The subsequent growth of these nuclei into the cold rolled matrix takes place by the migration of boundaries with relatively high misorienta tion. Figs. 5.8 and 5.9 show two such examples together with the corresponding diffrac tion patterns; these microstructures were obtained from a specimen quenched from 680°C after being heated at 20.2°C/s. Fig. 5.8 indicates that the orientation of the recrystallized nucleus 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 comparing  Chapter 5. Microstructural Examination of Structural Changes  193  the two diffraction patterns. Fig. 5.9 shows an example where a fully developed recrys tallized grain with {111} orientation borders with a {110} oriented cold rolled grain; this figure also suggests that one side of the boundary of the recrystallized grain has been pinned by fine precipitates. The following microstructures were obtained from a specimen produced by rapidly cooling 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 growing into the cold rolled matrix, while Fig. 5.10 (b) corresponds to the fully recrystallized region of the specimen. Figs. 5.11(a) and (b) show microstructures typical of fully recrystallized material obtained 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 rolling and annealing processes. The presence of a moderate number of dislocations in the fully recrystallized microstructures is thought to be due to the stabilizing effect of precipitates on dislocations. The limitations of thin foil work, in particular the possibility of foil damage from foil flexing, should also be considered in interpreting these observations. The surface of several lightly etched specimens was examined using the SEM to obtain additional evidence regarding the effects of precipitates on the nucleation and growth processes. Fig. 5.13 was obtained from a specimen heated up to 800°C at 20.2°C/s, and this corresponds to the fully recrystallized state. The discontinuous boundary curvature observed in this figure suggests that the grain boundary migration has been impeded by fine precipitates, most of which are not visible at this magnification. The overall microstructural changes observed in the present study are in general agree ment with those reported for high purity iron [136j, rimmed and Al-killed steels [138] and  Chapter 5. Microstructural Examination of Structural Changes  194  I-F steels [17, 21], and consequently, only a brief discussion of these observations are pre sented here. The development of the cell structure during cold deformation is usually explained in terms of plastic strain accomodation by multislip and energy minimization of dislocation clusters [222]. The observed heterogeneities in the cold rolled microstruc ture, as illustrated in Figs. 5.1 and 5.2, are consistent with the previous recrystallization studies on high purity iron and low-carbon steels [78, 132, 137, 138, 139], and are usually attributed to the dependence of the amount of stored energy on grain orientation. The reasonably well-developed cells, formed in certain grains of the cold rolled matrix, evolve into recrystallized nuclei, as illustrated in Figs. 5.3, 5.4 and 5.8. This explains the ob served heterogeneous nucleation behaviour during the kinetic characterization (see Figs. 4.27 and 4.30); in addition, such observations attribute the origin of the recrystallization heterogeneity to the cold rolling operation itself. The typical cell sizes of 0.3 to 0.8 tm observed in the present study are smaller than the 0.5 to 2 1 um reported for the rimmed and 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 result in retardation of cell formation and refinement of cell size [132, 139]; this may also explain the small cell size observed in the present study. The microstructural observations illustrated in Figs. 5.4, 5.5 and 5.6 indicate that the early growth of subgrains occurs primarily by subgrain coalescence; some growth by sub-boundary migration also occurs, as indicated in Fig. 5.6. These observations provide stronger support for the subgrain coalescence model proposed by Hu [53, 223] than for the sub-boundary migration concept of Cahn [131]. Coalescence was observed among different types of subgrains, although it seemed to be more common among the relatively small elongated subgrains, as previously indicated by Goodenow [138]. The coalescence process, shown schematically in Fig. 2.14, involves a gradual moving of dislocations out of the boundary between the subgrains to the boundaries surrounding  Chapter 5. Microstructural Examination of Structural Changes  195  them, and a rotation of the subgrain itself into the same orientation as its neighbouring subgrain. The example shown in Fig. 5.5 and the corresponding small misorientation of 0.6° between the subgrains, suggests the occurrence of subgrain coalescence by such a mechanism. Hu [53, 223] suggested that the angular misfit of the boundary around the rotated subgrain may increase, and that a cluster of coalescenced subgrains would have higher-angle boundaries in addition to being large; the recrystallized nucleus thus formed could grow into the cold rolled matrix by high angle boundary migration. A limited attempt was made to determine the orientation of the recrystallized nuclei with respect to the surrounding cold rolled matrix. The example shown in Fig. 5.8 indicates 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 similar relationship has been previously reported by Goodenow [138] based on an annealing study 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 show that the later stages of growth of the recrystallized grains take place by the migration of boundaries with relatively high misorientation. They also give some indication about the textural changes associated with recrystallization, a subject to be dealt with in more detail 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 re  ported previously for a Ti-stabilized I-F steel [153], and are usually explained in terms of a localized high dislocation density and substantial local lattice distortion in the sur rounding matrix [82, 131). A distribution of fine precipitates, on the other hand, has been reported to retard sub-boundary/boundary migration during recrystallization of I-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  196  5.7 (b) and 5.13 suggest that some precipitates are more effective in impeding boundary migration than others. Such observations are usually explained in terms of the complex interactions between the migrating boundaries and precipitates, i.e., by considering fac tors such as the particle radius, the interfacial energy per unit area of the boundary and the change in dislocation density across the migrating boundary (a detailed treatment provided by Hansen et al. [154] is given in section 2.1.5). Fully recrystallized microstructures shown in Fig. 5.11 and the microstructure of the hot band given by Fig. 5.12 suggest that the precipitates do not undergo any significant changes during cold rolling and annealing operations. This seems to be the case irrespec tive 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 reported research on I-F steels [21, 153] and can be rationallized in terms of the low annealing temperatures (maximum of 800°C) compared to the precipitation temperatures for most of 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 scat tered randomly. A random distribution of precipitates will not significantly influence the 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 cold rolling was examined and shown to lead to well-defined subgrain formation during the early stages of recovery. The subgrain growth, occurring primarily by subgrain coales cence, led to the formation of the recystallized nucleus which grew into the recovered matrix by the migration of high misorientation boundaries. Large precipitates  (..  0.7  tim) acting as preferred nucleation sites and fine precipitates impeding the boundary mobility were illustrated. The microstructures obtained from the hot band and the fully  Chapter 5. Microstructural Examination of Structural Changes  197  recrystallized steel suggest that the precipitates remain unchanged during cold rolling and annealing operations.  5.2  Characterization of Large Precipitates  The as-received hot band and a fully recrystallized steel produced by heating up to 800° C at 20.2°C/s were examined using an SEM operated at 20 kV. The specimens, ground and polished (up to 1  diamond paste) by conventional metallographic techniques,  were lightly etched with 2 % nital to facilitate the observation of the precipitates. The precipitates larger than 0.1 itm in diameter were analysed using EDX spectroscopy; WDX spectroscopy was employed in a limited number of cases to confirm the microchemistry of certain precipitates. More than 200 different particles were analysed from the hot band and the fully recrystallized steel specimens. The observations indicate that the precipitates have the same composition, and consequently, only the results obtained from the hot band are presented. The most common precipitates observed during this study were the sulfides of ti tanium. Fig. 5.14 is an SEM micrograph of the hot band showing an angular shaped precipitate 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 standardless analysis indicating an atomic ratio of 1. This suggests that the observed precipitate is TiS (Note: the Fe peak corresponds to the iron matrix surrounding the precipitate). In addition, regular shaped precipitates of TiS in the size range 0.3 to 0.8 m were also ob served. 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 obtained for these smaller precipitates, shown in the same figure, indicates the Ti/S atomic ratio to be approximately 2, suggesting that these precipitates are Ti . It should also be S 2 C 4  Chapter 5. Microstructural Examination of Structural Changes  198  emphasized that often the Ti/S atomic ratio obtained from the relatively large (0.3 to 0.8 m) precipitates was found to vary between 1 and 2, suggesting the possible coexistance of TiS and Ti S in the same particle. S-rich, Mn-containing, regular-shaped precip 2 C 4 itates were also observed on a few occasions, a 0.8 m diameter example being shown in Fig. 5.16 with its x-ray spectrum. The x-ray peaks shown in this figure suggests this precipitate to be of the type (Ti,Mn)S. In addition to sulfides and carbo-sulfides, a second type of Ti-rich precipitate usually larger 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 characteristic angular shape of this precipitate suggests it to be titanium nitride. The WDX dot maps obtained 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 is consistent with the precipitate being TiN; the analysis for N was not carried out due to the fact that both Ti and N have overlapping peaks. Some other noticeable features regarding the observed larger particles ( 1 urn) are indicated in Fig. 5.18, where the coexistance of two different types of precipitates is suggested. The x-ray spectrum obtained from the different regions in the particle indicate that Ti-rich precipitates form on the already existing Al-rich particle. Because these particles were too small to be clearly resolved in a WDX analysis, the true identity of these phases was not established. However, some confirmatory WDX point analysis indicated the base particle to be alumina, and the characteristic angular shapes suggest the newly formed precipitates to be titanium nitride. In certain cases, an Al-rich core (probably Al ), a surrounding Ti-rich precipitate (probably TiN) and a third layer 3 0 2 of precipitate (the lighter contrast outer layer indicated by arrow) were observed, as shown 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 a  Chapter 5. Microstructural Examination of Structural Changes  199  carbo-sulfide of Ti. It should also be noted that in certain instances S-containing outer layer of precipitate was observed directly around the Al-rich core without the second Ti-rich layer. During this study, evidence of the presence of P-containing precipitates was 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 with alumina. The characterization of fine precipitates can best be accomplished by studying carbon extraction replicas in a TEM. This method allows one to study precipitates as small as a few nm. In addition, the interference of the matrix in the analysis of the microchemistry can be avoided. In the present study, however, the precipitates were observed in an SEM and the analysis was done primarily through EDX. The effective magnification that could be employed was in the range of x 2k to x 10k, and consequently the smallest precipitate that could be studied was of 0.1 sum. Almost all the particles studied were within the size range of 0.1 to 2 ,um, and because of this, the observed x-ray spectrum invariably had a peak corresponding to the iron matrix (the volume of the material interacting with the electron 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 known information regarding the characteristic shapes were also used in the identification. The WDX spectroscopy was employed in a limited manner primarily to identify the presence of C, N and 0. However, obtaining proper dot maps was found to be difficult with these small particles (‘ 1 jim); this is mainly due to the fact that even a small movement of the specimen (instability caused by heating effects due to the high beam current, tilt of the specimen etc.) becomes critical at the high magnifications necessary for proper resolution. Because of these difficulties, some WDX analyses were done by point analysis, where the peak/background ratio of the element of interest was measured in the precipitate and in the matrix, and the comparison of these values indicated the relative presence of C, N or  Chapter 5. Mjcrostructural Examination of Structural Changes  200  0 in the particle. In addition, since Ti and N have overlapping peaks (the ) values for N K and Ti L 1 are 31.59 and 31.36  A,  respectively [224]), the presence of a TiN precipitate  was confirmed by verifying the absence of C and 0. As illustrated in this chapter, the progress of recrystallization in an I-F steel is in fluenced by the size and distribution of the precipitates. Coarse and widely spaced pre cipitates allow rapid growth of new grains with favourable orientation, thereby helping to achieve stronger textures favoring deep-drawability. In addition, all of the stabilizing precipitation takes place during the high temperature processing (primarily in the tem perature range of 1400 to 900°C [4, 6, 8, 10]), and the precipitates therefore undergo no noticeable changes during the cold rolling and annealing operations. Thus, it is impor tant to control the size and distribution of the precipitates and the grain size in the hot band in order to achieve good deep drawability. The precipitate size ranges observed for TiN, TiS and Ti S during this study are in general agreement with those reported 2 C 4 for other Ti-stabilized I-F steels [10, 11, 12, 225]. The present method of analysis was restricted to precipitates that are larger than 100 nm, and because of this, other possible precipitates, such as TiC and NbC with size ranges of 10 to 40 nm [10, 14, 221] could not be observed. In addition, the reported presence of Ti S as small as 50 nm [10, 12] 2 C 4 could not be confirmed. The precipitation sequence of a typical Ti-stabilized I-F steel is reported to be TiN, TiS, Ti S and TiC [4, 10]; the present observations indicate that 2 C 4 the size of the precipitates decreased in the same order. The present study mainly deals with sulfides and carbo-sulfides of Ti, as shown in Figs. 5.14, 5.15 and 5.16. Previous studies on I-F steels have also indicated the formation of TiS with different morphologies [10, 11, 226], as observed in the present study (see Figs. 5.14 and 5.15). A direct transformation from TiS to Ti S has been reported 2 C 4 to 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 high  Chapter 5. Microstructural Examination of Structural Changes  201  temperatures (‘- 1200°C) as coarse carbo-sulfides rather than as fine carbides at relatively lower temperatures  (‘-‘.‘  900°C). In addition, it was also reported that TiS and Ti S 2 C 4  phases often coexist as composite particles [12, 225, 226, 227]. The present observation that the Ti/S atomic ratio was occasionally found to lie between 1 and 2 is consistent with 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 inclusions has been reported in previous studies on steels [228]. The presence of only a very few Mn-rich precipitates indicates that the stabilization of S must have occurred primarily by Ti. It has generally been reported that when Ti*/Mn  0.125, the precipitation of  MnS could be suppressed, where Ti* refers to that amount of Ti available after forming TiN at high temperatures [229]. Such a condition is easily met in the present steel which has the appropriate Ti*/Mn ratio of 0.206; this might explain the noticeable absence of MnS in this steel. On the other hand, this observation suggests the bulk of the Mn to be present in the solid solution. Mn in solid solution is beneficial in terms of solidsolution 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 high temperatures  (-...  1400°C) [4, 6, 10, 15, 227, 230]. TiN particles were usually observed  to be larger than 1 jim in size [10] and were observed to assume a characteristically angular shaped morphology [231, 232]. The present observations of TiN, as shown in Figs. 5.17, 5.18 and 5.19, are consistent with those studies. TiN has been observed either 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 shows an example where in addition to the Al-rich core and the surrounding Ti-rich precipitate,  Chapter 5. Mjcrostructural Examination of Structural Changes  202  a third layer of Ti/S containing precipitate (either TiS or Ti ) was also observed; S 2 C 4 the presence of similar three-layered particles, i.e., alumina core, TiN precipitate and the surrounding layer of TiS, has been reported for a Ti-stabilized stainless steel [232]. It should also be noted that an existing particle may act as a preferential nucleation site for the later formation of a precipitate as was observed in the present study. The presence of alumina inclusions in the steel can be attributed to the fact that the base steel is an Al-killed steel containing 0.060 wt % Al. Alumina inclusions have been reported to remain in steels from the primary deoxidation process [233, 234]. The relatively small (2 to 5 im) isolated alumina particles observed in this study are probably the secondary inclusions that precipitate from the steel during cooling and solidification, i.e., the result of 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 element since it imparts solid-solution strengthening without significantly reducing the deep drawability [4, 6, 9, 235, 236]; the steel used in the present study has a P content of 0.011 wt %. Some previous studies indicate that precipitates of (Ti,Fe)P (titanium-iron phosphide) with sizes ranging from 0.1 to 1 m, form during the high temperature pro cessing [9, 235]. These precipitates have been reported to reduce both the tensile strength and deep-drawability [235]. In the present study, however, the P-rich precipitates have been observed only in a very few occasions, and always together with a large Al-rich particle (probably alumina), as shown in Fig. 5.20. This observation suggests that the bulk of the phosphorous remains in solid solution, a necessary condition to achieve the beneficial 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 was coiled at a relatively low temperature of around 600° C which may explain the present observation of the low amount of P-rich precipitates. The finest precipitates present in I-F steel are usually Ti and Nb carbides (10 to 40  Chapter 5. Microstructural Examination of Structural Changes  203  nm) [10, 14, 221], and these have been usually observed as individual particles (from independent nucleation and growth). However, some epitaxial growth of TiC on Ti S 2 C 4  has also been reported [225]. None of these particles were observed in the present study due to the method of analysis, and hence, no detailed discussions of these precipitates are presented. It is worth noting that no Nb-rich precipitate was observed, despite the presence of 0.02 wt % Nb. This is thought to be due to the fact that except for the possible stabilization 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, is desirable. One way to achieve this distribution is by facilitating the high temperature removal of C by promoting the direct transformation from TiS to Ti S [10]. 2 C 4 In summary, precipitates larger than 0.1 ,um, i.e., the nitrides, sulfides and carbo sulfides of Ti, were characterized. It was shown that the existing alumina particles act as nucleation sites for the precipitation of Ti-compounds. Only a few Mn and P rich precipitates were observed, which suggests the possibility that the bulk of these elements remain 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 direct transformation from TiS to Ti , was discussed. S 2 C 4  Chapter 5. Microstructural Examination of Structural Changes  204  Figure 5.1: Bright-field transmission electron micrograph of the 80 % cold rolled I-F steel showing the highly dislocated cell structure.  Chapter 5. Microstructural Examination of Structural Changes  205  0.5tm II (a)  0.5tm (b) Figure 5.2: Microstructures illustrating the heterogeneous nature of the cold rolled cell structure; (a) a reasonably developed cell structure and (b) dense dislocation networks with much less developed cell structure.  Chapter 5. Microstructural Examination of Structural Changes  206  (a)  (b) Figure 5.3: Subgrain structure development in a partially recovered specimen heated at 20.2°C/s up to 580°C; (a) small elongated subgrains and (b) relatively large subgrains.  Chapter 5. Mjcrostructural Examination of Structural Changes  207  (a)  (b) Figure 5.4: We11-defined subgrain structure formation in a specimen heated at 20.2°C/s up to 640°C; coalescence of subgrains is suggested by those boundaries indicated by arrows.  Chapter 5. Microstructural Examination of Structural Changes  A  208  B  Figure 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 bound ary); Kikuchi lines corresponding to the subgrains A and B are also given.  Chapter 5. Microstructural Examination of Structural Changes  209  O5jim  H  Figure 5.6: Microstructure indicating subgrain growth caused by both sub-boundary migration (indicated by arrow M) and coalescence (indicated by arrow C); the annealing treatment corresponds to quenching from 640°C after being heated at 20.2°C/s.  Chapter 5. Microstructural Examination of Structural Changes  210  (a)  p  0.5,um  (b) Figure 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 the discontinuity in the boundary curvature.  Chapter 5. Microstructural Examination of Structural Changes  211  Figure 5.8: 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 patterns illustrate the orienta tion of the recrystallized grain A (zone axis < 111 > type) with regard to the matrix subgrain area B (zone axis < 111 > type).  212  Chapter 5. Microstructural Examination of Structural Changes  V  I  0.5 im  Figure 5.9: Recrystallized grain A (zone axis < 111 > type) bordering a cold rolled grain B (zone axis < 110 > type) in a specimen heated at 20.2°C/s up to 680°C; the pinning of one side of the boundary of the recrystallized grain by fine precipitates is also shown (arrows indicate the precipitates).  Chapter 5. Microstructural Examination of Structural Changes  213  (a)  (b) Figure 5.10: Photomicrographs obtained from a specimen heated at 20.2°C/s up to 740°C (.-- 50 % recrystallized), showing (a) recrystallized grains growing into the cold rolled matrix and (b) fully recrystallized grains.  Chapter 5. Microstructural Examination of Structural Changes  214  (a)  (b) Figure 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.  Chapter 5. Microstructural Examination of Structural Changes  215  Figure 5.12: Microstructure of the as-received hot band, showing random distribution of fine precipitates.  Chapter 5. Microstructural Examination of Structural Changes  216  Figure 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 (arrows indicate the discontinuities in the boundary curvature).  Chapter 5. Microstructural Examination of Structural Changes  r  r  217  P  Ti  S  Fel  A :::::.jfl 4...  4 0.320  Rane=  L1.aLi  Energy  Figure 5.14: SEM micrograph and x-ray spectrum showing the presence of an angu lar-shaped precipitate in the hot band (arrow indicates the precipitate); the x-ray spec trum is consistent with it being a TiS precipitate.  Chapter 5. Microstructural Examination of Structural Changes  1  218  2725  Fel  -‘I  j 4—  0. 000  Rariie  10. 130  Energy  Figure 5.15: SEM micrograph of the hot band showing the larger Ti/S-containing pre cipitate (appears near the centre) and the smaller precipitates (indicated by arrows); the associated x-ray spectrum obtained for a smaller precipitate is consistent with it being 4C2 Ti . S  Chapter 5. Microstructural Examination of Structural Changes  027234 20KV  219  X2:O’KI0ufl Fe  I  S  J Mn 6  i  I il  -  4—  O.[1[  5nqr=  Energy  Figure 5.16: SEM micrograph and x-ray spectrum showing the presence of a regu lar-shaped precipitate in the hot band (arrow indicates the precipitate); the x-ray spec trum suggests this to be of the type (Ti,Mn)S.  Chapter 5. Microstructural Examination of Structural Changes  Ti  220  .:Fe  L. 4—  C.32O  Rane=  1C..?C 1eV  Energy  1O.2.E11  —  Figure 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.  Chapter 5. Microstructural Examination of Structural Changes  221  £  Ac::.  Al  ::.:::....  .:::::  ....  .  .  Ti),  v:.:...  .  *  Fe  I iama LL Al  :.  Fe .  4—  2. 160  Rnge=  2, 10.230 keV  Energy  :.t..  :  10.’C  —,  4—  0.160  Pange=  10.230 6eV  Energy  12230  Figure 5.18: SEM micrograph obtained from the hot band and x-ray spectrum obtained from 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).  —  Chapter 5. Microstructural Examination of Structural Changes  222  Fe  Ii -  ‘I  tSr  .tcc.  4—  0,480  Panqe=  10.23C.’ keV  Energy  Figure 5.19: SEM micrograph obtained from the hot band and x-ray spectrum of the precipitate 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 lighter contrast outer layer indicated by arrow).  Chapter 5. Microstructural Examination of Structural Changes  Fe  :••  • :••  .•  .  Ti  223  .  .  ..  .  Al  1$ r  4—  LI. 3.20  Panye=  1.1]. 233 [eV  Energy  Figure 5.20: SEM micrograph and x-ray spectrum showing the presence of a P-containing precipitate in the hot band (arrow indicates the precipitate).  Chapter 6  Characterization of Annealing Textures  The primary objective of this part of the research work is to characterize the evolution of crystallographic texture by means of orientation distribution functions (ODFs) dur ing cold rolling and annealing processes. The basis for the comparison of texture in this study is primarily three-fold. First, the texture development from the as-received hot band to the 80 % cold rolled state was studied. Then, the progressive development of recrystallization texture  (‘—‘  15, 40, 80 and 100 % recrystallized) and the additional  changes caused by grain growth (ASTM No. 9  -  10 to ASTM No. 8) were monitored for  the specimens annealed at 20.2°C/s. Finally, the effect of heating rate on texture devel opment 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 heating  rates of 20.2, 1.88 and 0.025°C/s. In addition, the values for the strain ratio  ()  were  estimated by incorporating the texture data into the Taylor model of plastic flow, and the predictions were verified against the mechanical measurements. Nine different specimens were subjected to the texture analysis; they correspond to the 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) of the specimens. Most of the continuous heating annealing treatments were performed at 20.2°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 correspond to approximately 15, 40 and 80 % recrystallized, respectively. The specimen produced by 224  Chapter 6.  Characterization of Annealing Textures  225  rapidly cooling from 800°C corresponds to complete recrystallization with an estimated average grain size of ASTM No. 9  -  10. The specimen cooled from 900° C underwent  considerable grain growth after completion of recrystallization and resulted in an average grain size corresponding to ASTM No. 8. Two other cold rolled specimens heated at 1.88 and 0.025°C/s were quenched from 770 and 700°C, respectively; these two specimens correspond to the fully recrystallized state without any grain growth. The average grain size of these specimens was estimated to be in the range of ASTM No. 9  -  10. It should  be noted that the heating rates of 20.2 and 0.025°C/s are typical of a continuous and a batch annealing process, respectively. Partial (110), (200), (211) and (310) pole figures (measured up to 80° from the cen tre of the pole figure) were determined for each of the prepared specimen on a texture goniometer using Cu K radiation. The experimental pole figures were scrutinized for symmetry aspects [165, 237], and the intensity values confirmed the orthorhombic sym metry of all the pole figures. Orientation distribution functions (ODFs) were calculated from the partial pole figures using the series expansion method (lmar = 22) developed by 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 indica tion of the quality of the measurements and the absence of significant errors in the ODF calculations [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 and recalculated (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 presented now. Figs. 6.2 and 6.3 were obtained for the as-received hot band and the 80 % cold-rolled steel, respectively. Figs. 6.4, 6.5, 6.6, 6.7 and 6.8 correspond to the annealing treatments in which the 80 % cold rolled sheets were heated at 20.2°C/s to peak temperatures of 670, 720, 760, 800 and 900°C and rapidly cooled, in that order. Fig. 6.9 corresponds  Chapter 6.  Characterization of Annealing Textures  226  to the specimen heated at 1.88°C/s to 770°C. Fig. 6.10 was obtained for the specimen quenched from 700°C after being heated at 0.025°C/s. The microstructural state of each specimen is indicated in the appropriate figure caption. The three-dimensional ODFs are presented at constant y sections, i.e., cpi sections, =  Y2  coi =  0 to 90° in increments of 5°. For the constant  is given by the horizontal axes, while the vertical axes indicate q . The 5  S°2  45° section, which contains most of the important orientations, is also shown at the  end of each figure; for this section, ço 1 is given by the horizontal axis, while the vertical axis indicates q. The analysis of the ODF results shown in Fig. 6.2 suggests that no highly developed texture is present in the hot band. Fig. 6.3 indicates the formation of a reasonably developed texture during cold rolling; this texture is represented by an extended-tube in orientation 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 the tube-shaped density distribution remains approximately the same. However, a general sharpening 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 a redistribution of density within the ‘tube’. In particular, the positions (i.e.,  2  and  values) 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 two  black dotted curves and their intersection point in each y section indicate the three-fold symmetry elements in the Euler space for cubic/orthorhombic crystal/sample symmetry; the intersection points in all y sections correspond to the 7-fibre where The shift towards  { 111 }-type  111  >11  ND.  orientations with increasing % recrystallization is shown  in Fig. 6.5, which corresponds to a the maximum intensities in all  <  40 % recrystallized microstructure; in this case  sections approach near {111}-type components. With  continued recrystallization, a general sharpening and strengthening of this texture occurs  Chapter 6. Characterization of Annealing Textures  227  without any other significant changes; see for example, Figs. 6.6 and 6.7 that correspond to 80 and 100 % recrystallized microstructures, respectively. A similar trend continues with grain growth following the completion of recrystallization, as can be seen by com paring Fig. 6.8 (ASTM No. 8) with Figs. 6.9 and 6.10 (both ASTM No. 9  -  10); these  three fully recrystallized microstructures were obtained at heating rates of 20.2, 1.88 and 0.025°C/s, respectively. All of the ODFs obtained from the fully recrystallized mi crostructures (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 to that of the cold rolled steel. The development of textures during cold rolling and annealing is most conveniently studied by expressing the orientation densities along selected fibres (see Fig. 2.26 for example). <  111  >11  In the present study, the development of fibres < 110 > RD (a-fibre), 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 hot and cold rolling textures as well as for recrystallization textures. For deep-drawing steels, the course of the pole density in the 7 -fibre characterizes the recrystallization texture and these components are highly desirable for good deep-drawability. The e-fibre is presented since it contains the important (554)[5] texture component. The t9-fibre marks the undesired components of the deep-drawing texture. The C-fibre development is of some interest in this particular study since the {220} peak resolution was used in characterizing the kinetics of the recovery and recrystallization processes. The development of all five fibres (a, 7, E, t9 and In the case of  and  C) 9 t  were analysed, and all the significant changes are presented here.  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 this study for all the cases. In addition, all of the fibres are plotted with the same maximum orientation density scale of twelve times random to illustrate the relative significance of  Chapter 6. Characterization of Annealing Textures  228  different texture components. Figs. 6.11 (a), (b) and Figs. 6.12 (a), (b) show the orientation density f(g) along the a, -y, e and ?9 fibres for both the as-received hot band and the 80 % cold-rolled I-F steel 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 still far from a random texture. One observes the presence of a weak partial a-fibre texture extending 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 complete -fibre and a weak E-fibre in between (111)[112] to (110) [001] with a high strength value 7 of 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 presence of a strong partial a-fibre texture extending from (001)[1i0] to (112)[1i0], with strength values 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 (from three to five times random) during cold rolling. The 7-fibre remained almost the same at about two to three times random during cold rolling. There is a general development of E and ‘0 fibres during cold rolling. In particular, the strong development of (001)[1I0]-type components 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 could be observed. The development of annealing texture from the cold rolled texture during the progress of 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){1IOj  Chapter 6. Characterization of Annealing Textures  229  (from two times random to ten times random) could be observed during annealing; the plots corresponding to 15 and 40 % recrystallized microstructures indicate the transition between the cold rolled and recrystallized textures. There is a consistent increase in the complete 7-fibre from about two to three times random to about ten times random during annealing. The  and 9 fibres also indicate a continuous reduction in the spread around  the (001)[1I0J-type texture components during annealing. In the case of t9-fibre, most of the other components are reduced to below random level during annealing. The e fibre indicates the strong development of (554){5J (from two times random to ten times random); while (111)[112] was relatively stronger initially, (554)[5] was more dominant towards the end of recrystallization. Annealing causes some additional reduction in the already weak C-fibre components. However, these changes are very small when compared to the changes in other fibres, and in particular, the changes in the C-fibre components are 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 recrystallization texture (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 orientation density f(g) along the a, 7,  6,  9 and  C  fibres, in that order.  In general, the effect  of heating rate on the final recrystallization texture appears to be small. The a-fibre indicates the strength of (111){1I0] to be the minimum (about six times random) for the specimen produced at 0.025°C/s, while the other two heating rates resulted in almost the 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 the same orientation density of about seven times random; overall however, 1.88°C/s seems to have resulted in stronger {111}-type components. In the case of 6-fibre, the strength of (554)[5j increased steadily with a decreasing heating rate, from about seven times  Chapter 6.  Characterization of Annealing Textures  230  random at 20.2°C/s to about ten times random at 0.025°C/s. Although the ‘0-fibre was reduced almost to the random level during annealing, the remnants of {001}-type components were relatively strong for the specimen annealed at 0.025°C/s. The volume fractions of important texture components were also estimated from the C-coefficients of the ODFs, and the calculations were based on ideal orientations with a spread described by  =  16.5° Gaussian distributions [166]. Although the absolute  values of the calculated volume fractions are questionable, they have been used in relative terms as supporting evidence in texture studies [219]. The texture analysis presented so 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 percentages of these texture components, calculated for all nine test specimens are presented in Table 6.1. 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 the standard 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 small amounts 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 the volume fractions are dependent on the orientation density of the considered component, the assumed spread of model function and the multiplicity factor corresponding to the texture component [238]. The relatively low values obtained for the volume fraction of (001)[1I0], despite the observed high orientation density (compare with (112)[1I0] for example, in the the cold rolled a-fibre shown in Fig. 6.11 (a) and also in Table 6.1), is primarily 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 Table 6.1 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 on  Chapter 6.  Characterization of Annealing Textures  231  the annealing texture. Normal direction (ND) inverse pole figures indicate the density of different crystal lographic planes that are parallel to the sheet, and consequently they provide a simpler (though not complete) method of monitoring texture development. In particular, the densities of different principal planes that are parallel to the rolling plane have been found to be useful in correlating the texture evolution to the associated changes in plas tic anisotropy [15, 21, 55, 163, 193]. While ND inverse pole figures can be determined easily for a sheet metal using diffractometry [49, 156, 158, 162], they can also be cal culated from the ODFs [165, 166]. In the present study, ND inverse pole figures were calculated using the ODF data for all nine specimens, and Figs. 6.18 (a) and (b) show two such examples corresponding to the 80 % cold rolled steel and the fully recrystallized specimen with the grain size ASTM No. 9  -  10 annealed at 20.2°C/s. The general con  clusions that could be made from the inverse pole figures were similar to those already presented in this section. Of particular interest are the following observations as related to 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 random after 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 number of {110} planes decreased slightly from 1.3 times random to less than 0.8 times random. • For the specimens annealed at 20.2°C/s, the density of {l11} planes increased steadily from 2.5 times random for the cold rolled to 8 times random for the an nealed 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 0.8  Chapter 6.  Characterization of Annealing Textures  232  times random during annealing. Among the three different heating rates that were employed to produce fully re crystallized specimens (grain size of ASTM No.  9  -  10), 1.88°C/s yielded the  highest 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 ap proximately the same density of {111} planes (6.4 times random) although the specimen heated at 0.025°C/s had a relatively higher number of {001} planes (1 times 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 the hot band, where it was 1.3 times random. Finally, the anisotropic flow properties, in particular the strain ratio, r, was predicted by incorporating the measured texture in the form of ODF into the Taylor model of poiy crystal deformation [161, 165]. The Taylor factor (or M-factor) calculations were carried out for simple tensile deformation by assuming glide along (110)[111j and (112)[111] slip systems. 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 loading direction of the test specimen. Fig. 6.19, a plot of r vs. a, for specimens annealed at 20.2°C/s, illustrates the development of plastic anisotropy from the cold rolled texture during the progress of recrystallization growth (ASTM No. 9  -  15, 40, 80 and 100 % recrystallized) and grain  10 to ASTM No. 8). The plot corresponding to the 40 %  recrystallized microstructure indicates the transition between the cold rolled and the re crystallized states. The r values corresponding to 0, 45 and 90° were also used to estimate the average properties, f and r, based on Eqs. 2.46 and 2.47. Table 6.2 summarises the predicted r values at a nine test specimens.  =  0, 45 and 90° and the calculated averages  i  and r for all  Chapter 6. Characterization of Annealing Textures  233  The strain ratio (r) values were not experimentally determined during the present in vestigation. However, some of the plant trial information obtained from ‘Stelco’ regarding I-F steel annealing cycles and mechanical properties is used for validation purposes. The reported  values for the 80 % cold rolled I-F steel subjected to various annealing cycles  were within the range of 1.6 to 1.8. The measured steel temperatures during a typical continuous annealing cycle indicated a heating rate of 46.6°C/s up to the peak temper ature of 845°C, a hold of 16s at the peak temperature and final cooling at the rate of 7.4°C/s. The I-F steel subjected to this annealing cycle resulted in a microstructure with an average grain size of 25.5 jim and a  value of 1.69. For another case with a fairly  similar temperature profile, the measured properties were an average grain size of 15.1 jim and a  value of 1.68. These values are in good agreement with the predicted values  in the present study. In particular, the 9  -  values of 1.58 for the grain size of ASTM No.  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 the final 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 usually observed for the hot-rolled strips of Al-killed and other low-carbon steels, finish-rolled at temperatures of  950° C [172, 239, 240]. This is primarily a consequence of the austenite  to ferrite transformation from a completely recrystallized austenite. Ti/Nb-stabilized and other microalloyed low-carbon steels, however, develop moderately strong hot band textures [172, 239, 240, 241]. These textures are attributed to the retarding effects of the alloying elements on austenite recrystallization, and the consequent transformation of the highly textured austenite into ferrite. The major components of the deformation texture of austenite are {110} < 112 > and {112} < 111 > which give rise, respectively, to {332} < 113 > and {113} < 110 > orientations in ferrite. The recrystallization texture  Chapter 6.  Characterization of Annealing Textures  234  of 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), in particular (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 deformed austenite. These observations and the presence of the moderately strong complete 7fibre, are consistent with most of the hot band textures reported from similar studies on I-F steels [164, 172, 239, 240, 241]. The cold rolled texture obtained in this study consists of a strongly developed partial a-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 closer to (112)[1i0] (or near (114)[1I0]) rather than near (111)[1I0] (volume fractions shown in Table 6.1 indicate this clearly). This observation indicates that cold rolling reinforces the 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 and other 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 regard is the hot band grain size. The effect of hot band grain size on cold rolled texture development, though not inves tigated in depth, has been demonstrated in a few studies [170, 172, 242]. A comparitive study conducted by Bleck et al. [172] on Al-killed steels with two different hot band grain sizes (obtained from different areas of the same strip) indicated that the hot band texture  Chapter 6. Characterization of Annealing Textures  235  of the coarse grain size material was relatively stronger; after about 90 % cold rolling, the coarse grain hot band (when compared to the fine grain one) resulted in a texture which constitutes a relatively stronger partial a-fibre (about 2 times stronger for (114)[1i0]), and a considerably weaker -7 fibre (half as strong). The hot band grain size of the present steel (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]), and consequently this difference might have been another contributory factor for the observed strong 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 small increase in the 7 -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 size or not, the a-fibre, in particular the components near (112)[1i0J and (114)[1i0], strongly develop 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 any low-carbon ferritic steels [22, 23, 156, 170, 171, 172, 239, 240, 241]. The rolling texture exhibiting high orientation densities along the a-fibre, in particular the strong compo nents stretching from (001)[iIOj to (112)[1I0], continuously decrease to near random level during recrystallization. On the other hand, the recrystallization texture, typically characterized by the orientation of the 7-fibre, especially the (111)[iIo] and (111)[112] components increase throughout recrystallization. The development of the 7-fibre dur ing recrystallization is explained by oriented nucleation of the { 111 }-orientations caused by 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 is also attributed to oriented growth from the strong (112) [110] component of the cold rolled matrix, and such growth is because of the favourable orientation relationship between these two components (35° around the  <  110  >  transverse direction which is close to the  Chapter 6.  Characterization of Annealing Textures  236  ideal 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 progres sive manner throughout recrystallization, and such an observation can be understood in terms of the steady consumption of the cold rolled matrix by differently oriented nu clei. In particular, the a and -y fibres corresponding to the  15 and 40 % recrystallized  specimens indicate the magnitude of the change to be significant during the early stages of recrystallization. This observation seems to disagree with two other studies on lowcarbon steels where the changes in the texture during the early stages of recrystallization was 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 the commencement of recrystallization, and the overall changes in the  -fibre components  during recrystallization were small (an increase of about 50 % or less). In the present study, however, all of the -fibre components increased by a magnitude of about 3 to 4 times during recrystallization. In particular, the cold rolled and consequently all of the new grains with  -fibre was relatively weak  { 111 }-orientation  would have contributed  to a significant change in texture. In addition, the microstructural observations of the present study indicated that the initial nucleation preferentially occurred along grain boundaries. Such nuclei and their consequent growth into the differently oriented ad jacent 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 % recrystallized specimen (see Fig. 6.13 (a)) is the apparant strengthening of the (112)[1I0] component during the early stages of recrystallization. Such an increase can also be seen from the volume fractions indicated in Table 6.1. A similar increase in the (112)[1I0] compo nent during the early stages of recrystallization was also reported by other researchers [170, 171]. Those researchers suggested a strain-induced boundary migration nucleation  Chapter 6. Characterization of Annealing Textures  237  process favouring the lower energy orientations such as (112)[1I0] as a possible explana tion. While such a factor may also explain the present observations, a thorough study will be required to clarify the matter further. The e-fibre shown in Fig. 6.14 (a) indicates the strong development of the spread around (111)[112] during recrystallization. These components are usually enhanced by oriented 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 of the (112)[1IO] in the cold rolled steels, the spread around (111)[112] is usually stronger than the spread around (111)[1I0] [239, 240, 241]. It should be noted that in the case of Al-killed and other low-carbon steels, (111)[1I0] is often the strongest component of the annealing texture [172, 239, 241]. In addition, the spread was reported to be centered on (554)[5] rather than (111)[112j, due to a more matching growth relationship of the former [22, 23, 189, 196, 239]. The present observations indicate (554)[5] to be the strongest component after about 40 % recrystallization, i.e., after growth has become dominant. Such observations are consistent with other reported texture studies on I-F steels [22, 23, 196, 239, 241]. The C-fibre components, shown in Fig.  6.15, undergo very small changes during  recrystallization. Additionally, the normal direction inverse pole figures indicated the density 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 (see for example, Fig. 2.4). These observations provide supporting evidence for using the {220} peak resolution, particularly the corresponding valley intensity, in characterizing the kinetics of recrystallization, as conducted in the present study. The elimination of the partial a-fibre and the development of the y-fibre continued during grain growth after the completion of recrystallization. In particular, the 7 -fibre exhibited a significant increase during grain growth (ASTM No. 9  -  10 to ASTM No 8).  Chapter 6. Characterization of Annealing Textures  238  Obviously the grains with {111} orientation have grown selectively at the expense of the differently oriented grains. Similar observations have been reported previously based on texture studies on low-carbon and I-F steels [22, 23, 79, 171]. The development of plastic anisotropy (r-value) as related to the texture evolution during recrystallization is shown in Table 6.2 and Fig. 6.19. It is important to note that these r-values were not determined experimentally; they were calculated from the measured textures. Fig. 6.19 clearly illustrates the change in the nature of the r vs. a (a is the angle to the rolling direction) relationship during the progress of recrystallization. The cold rolled and the 15 % recrystallized specimens exhibit high r 45 values, but the values for r 90 were relatively low. The recrystallized specimens, i.e., the ones 0 and r corresponding to 80 and 100 % recrystallized microstructures and the one with additional grain growth, exhibit high r values in general, although the values for r 45 were relatively lower. The specimen corresponding to 40  % recrystallization illustrates the transition  from 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 r to be a strong function of a, depending on the orientation of the crystal [2]. In particular, , r 0 45 and r 90 were approximately 0, 1 and those calculations showed that the values of r 0 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 texture  data 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 changes in r vs. a shown in Fig. 6.19. The present observations agree reasonably well with the experimental 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  ()  -fibre) and weak {001} (i9-fibre) 7 values were related to textures with strong {111} (  Chapter 6. Characterization of Annealing Textures  239  components [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 continuous changes in the -y (an increase, as shown in Fig. 6.13 (b)) and ‘9 (a decrease, as shown in Fig. 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 pole figures, provide additional illustration of the textural changes that explain the increasing f-values. The same f-value obtained for the 15 and 40 % recrystallized specimens are due to the averaging procedure. The r vs. a profiles shown in Fig. 6.19 clearly illustrate the differences between these two specimens, reflective of their respective textures (It should also be noted that the z\r values corresponding to these two specimens are considerably different). 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 reported for low-carbon steels [22, 23, 156], and can be understood in terms of the continuing changes in the -y and 9 fibres during grain growth. The effect of heating rate on recrystallization texture is presented in terms of the major 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 and the associated f-values. This is in agreement with other studies on I-F steels (see for example Fig 2.29) [22, 23, 156, 172, 239]. In practice, an important advantage of I-F steels is due to the fact that the formation of the favourable recrystallization textures does 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 in that order, all specimens have the same grain size of ASTM No. 9 10. The higher f-value -  obtained at 1.88°C/s can be attributed to the relatively strong presence of the -y-fibre  Chapter 6. Characterization of Annealing Textures  240  (see Fig. 6.16 (b)). This is probably due to the slightly larger grain size observed in this case, although it was still within the range of ASTM No. 9  -  10. On the other hand, the  lower i-value obtained at 0.025°C/s can be attributed to the relatively strong remnants of the t9-fibre at 0.025°C/s (see Fig. 6.17 (b)). This is possibly due to some extremely small unrecrystallized areas that were not visible in the optical microscope. The normal direction inverse pole figures also indicated the highest density of favourable { 111 } planes for 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 heating rate.  Fig.  6.17 (a) shows that the intensity of (554)[5] increases steadily with a  decreasing heating rate; the volume percentages shown in Table 6.1 also indicate the validity of this relationship. It should be noted that among all the fully recrystallized specimens, 0.025°C/s has resulted in the highest volume percentage of (554)[5] (23.4  %) despite the fact that %). These observations  it also yielded the lowest volume percentage for (111)[1I0] (17.7  suggest that a lower heating rate or a longer annealing time is  marginally favourable in terms of the development of (554)[5], a texture component which preferentially develops due to oriented growth. The  values obtained in this study, i.e., the calculated ones in the range of 1.5 to 1.7  or the measured ones in the range of 1.6 to 1.8, are relatively lower than the values of 2, often reported for I-F steels [2, 22, 23, 196, 198, 239]. Although there can be several reasons for such differences, the strong presence of (114)[1I0] in the annealed texture is possibly one of them. This texture component, together with (001)[1I0], strongly devel oped during cold rolling. However, unlike (001)[1I0], considerable amounts of (114)[1i0j remained in the annealed texture (about 3 to 4 times in terms of the volume fraction, as shown in Table 6.1). The presence of both {001} and {114} components have been re ported 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 of  Chapter 6.  Characterization of Annealing Textures  241  (114)[1I0]. Such an observation is consistent with the present study with its relatively coarse grain (ASTM No. 7  -  8) hot band.  The relatively low values obtained in this study are also a result of the steel chemistry and other high temperature processing conditions. Previous calculations regarding excess Ti (TiEx) and Nb (NbEX) in solid solution showed that 0.02 > TiEx > 0.01 and NbEx 0.02. In addition, the present I-F steel has solid-solution strengthening elements of 0.011 wt  % P and 0.140 wt % Mn. There is no definite conclusion regarding the effects of  excess Ti and/or Nb on of P on  ?  values [7, 9, 15, 16, 149, 150, 204, 239]. The adverse effect  values is minimal [9, 20, 149, 204, 207, 208]. However, Mn in solid-solution is  reported to significantly decrease  values [20, 55, 204, 205, 206, 207], and hence another  possible explanation for the presently observed low  values. The available information  regarding the preparation of I-F steel hot band indicates the use of a finishing delivery temperature of around 890°C and a coiling temperature of less than 600°C. While the finish rolling temperature is almost the same as the recommended temperature of slightly above Ar , the coiling temperature is considerably lower than the suggested 700 to 800°C 3 to produce coarse precipitates [15, 16, 195, 202, 204, 209, 210, 211]. The microstructural observations obtained in this study also indicated the presence of fine-scale precipitates, and such precipitates retard the growth of {111}-oriented grains, resulting in reduced values. In summary, the evolution of crystallographic texture during cold rolling and an nealing were characterized. Grain growth following recrystallization was shown to result in a stronger/sharper texture. The effect of heating rate on the final recrystallization texture was determined to be insignificant. The measured textures were correlated to plastic anisotropy using the Taylor model of polycrystal deformation, and the resulting average strain ratio values were analysed in terms of the steel chemistry and processing conditions.  Characterization of Annealing Textures  Chapter 6.  242  Table 6.1: Volume percentages of important texture components calculated from the ODF data obtained for the hot band, the cold rolled sheet and annealed specimens Processing/Microstructure  Hot Band (ASTM No. 7-8) Cold Rolled (80 %) 20.2°C/s 15 % recryst. 20.2°C/s 40 % recryst. 20.2°C/s 80 % recryst. 20.2°C/s 100 % recryst. (ASTM No. 9-10) 20.2°C/s Grain Growth (ASTM_No._8) 1.88°C/s 100 % recryst. (ASTM No. 9-10) 0.025°C/s 100 % recryst. (ASTM_No._9-10) -  -  -  -  -  -  -  Texture Components (vol. (001)[1I0J 2.4 10.1 6.9 6.0 4.0 3.1  (112)[1i0] 12.6 15.5 19.6 14.3 12.0 12.4  (114)[1I0] 12.1 27.3 25.3 18.9 13.5 11.7  3.0  12.5  3.0 3.7  %)  (111)[1I0j 11.2 11.6 16.1 16.9 18.2 20.1  (554)[5] 11.0 11.2 13.6 17.7 19.9 20.2  10.4  22.8  23.1  12.4  10.7  20.7  22.9  13.0  13.1  17.7  23.4  I  Chapter 6. Characterization of Annealing Textures  243  Table 6.2: A summary of r at a = 0, 45 and 90°, and Ar predicted from the ODF data obtained for the hot band, the cold rolled sheet and annealed specimens Processing/Microstructure  Predicted r values  Hot Band (ASTM No. 7-8) Cold Rolled (80 %) 20.2°C/s 15 % recryst. 20.2°C/s 40 % recryst. 20.2°C/s 80 % recryst. 20.2°C/s 100 % recryst. (ASTM No. 9-10) 20.2°C/s Grain Growth (ASTM_No._8) 1.88°C/s 100 % recryst. (ASTM No. 9-10) 0.025°C/s 100 % recryst. (ASTM_No._9-10) -  -  -  -  -  -  -  j  1.02 0.49 0.79 1.24 1.75 1.84  1.64 1.19 1.78 1.39 1.27 1.36  1.38 0.84 0.99 1.30 1.67 1.77  Calculated Averages Ar 1.42 -0.44 0.92 -0.52 1.33 -0.89 1.33 -0.12 1.49 0.44 1.58 0.44  1.91  1.52  1.90  1.71  0.39  1.91  1.50  1.94  1.71  0.43  1.52  1.38  1.72  1.50  0.24  a=00]a=450  a=90°ll  Chapter 6. Characterization of Annealing Textures  2.5  1.0  1.3  3.2  4.0  244  1.6  6,4 3  (a)  .8  LO  L3  2.5  3.2  4.0  1.6 .  2.J  6.4  (b) Figure 6.1: (a) Experimental and (b) recalculated (110) pole figures obtained for the 80 % cold rolled I-F steel specimen.  Chapter 6. Characterization of Annealing Textures  D UBC AS REC. (NEW?0 55/180/2.7/N EF& 80 1.00 1.30 1.60 200 2.50 3.20  245  4.00  PAGE 9.00  1 640  Figure 6.2: ODFs calculated for the I-F steel hot band (with the grain size of ASTM No. 7 8) presented at constant ço sections; 2 = 450 section of the Euler space is also shown. -  Characterization of Annealing Textures  Chapter 6.  246  3ubc cold rolled 2mm osc 55/i80/2.&EF& 1 30 j 60 2 00 2 3 20 4 00 0  90 0  uu  PAGE  90 0  90 0  — PHI—  /  PHIl  4’  ,  I—.  20  PHIl—  PHi  5  PHIl  —.  25  —  —  PHIl  —  /  -,  —  -  O  90  /  ‘,  •  57:  5 : ?f  cfI  \\5  ,  90  1L  -  ‘r  1 8 00  5 00  10  -  30  -  ,.  —  -  -  PHIl—  25  PHIl  35  00 .--  .  b  ‘ .  -  -.  a?  .  -  c  -.  -  9 2 2ZLZ PHIl  —  40  PHIl  45  PHIl  50  PHIl  55  —  70  PHIl  75  —  “ 90  .  00 -  PHIl  —  60  PHIl  PHIl  —  80  PHIl  00  65  PHIl  85  PHIl  .  9(  —  —----.---  PHI2  •  45  Figure 6.3: ODFs calculated for the 80 % cold rolled sheet presented at constant Pi sections; Cp2 = 450 section of the Euler space is also shown.  247  Chapter 6. Characterization of Annealing Textures  S USC 20.2C/S 670 C 2 MM OSC. 55/ISEFS 00 1.30 1.60 2.00 2 50 3.20 4.00  5.00  PAGE 6.40  1 8.00  Figure 6.4: ODFs showing constant y sections for the specimen quenched from 670°C 15 % recrystallized); Y2 = 45° section of the Euler after being heated at 20.2°C/s space is also shown. (‘-S.’  Chapter 6. Characterization of Annealing Textures  A UBC 20.2 c/s 720 C 2mm OSC. 55/IEF& .Ei0 1.00 1.30 1.60 2 0 2,50 3.20  248  PAGE 4,00  500  I  6.40  Figure 6.5: ODFs showing constant 1 sections for the specimen quenched from 720°C after being heated at 20.2°C/s (‘—‘ 40 % recrystallized); Y2 = 45° section of the Euler space is also shown.  Chapter 6. Characterization of Annealing Textures  4 UBC 20.2 c/s 760C 2mm QSC. 55/18& EF& 60 1.00 1.30 1.60 2.50 3.20  249  4.00  PAGE 5 00  1 6.40  Figure 6.6: ODFs showing constant y sections for the specimen quenched from 760°C after being heated at 20.2°C/s section of the Euler 80 % recrystallized); 2 = space is also shown. (‘-i  Chapter 6.  Characterization of Annealing Textures  i UBC 20.2/800C 2mm osc. 55/180/2.&EF 3.20 4.00 L30 160 200  250  PAGE 5.00  I 8.00  Figure 6.7: ODFs showing constant co sections for the specimen quenched from 800°C after 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  c/s ooc  C UBC 20.2  1.00  2MM OSC. 55/18EF 2.00 :*B 4.00 56O  140  0  oo  go 0  Iz•::  °  PHIl  —  251  0  900  : PHIl  —  5  PAGE  8.00  PHIl  10  —  90  EdiEPHIl  —  15  ° T r(h. hHh ° h 4 9°  PHIl  —  20  PHIl  —  25  PHIl  —  30  PHIl  PHIl  —  50  PHIl  55  PHIl  75  PHI2  45  —  35  : or  PHIl  40  .  90  00  90  wj PHIl —  60  PHIl  45  *:a. PHIl  65  \,  PHI1  80  PHIl  “-‘  70  PHIl  \/  85  PHIl  —  ‘  90  Figure 6.8: ODFs showing constant y sections for the specimen quenched from 900°C after 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.  Chapter 6. Characterization of Annealing Textures  7 UBC L88c/s 770C 2mm osc. 55/180EF LOO 1.30 1.60 2.00 25O 3.20 4.00  252  5.00  PAGE .4fl  1 8,00  Figure 6.9: ODFs showing constant oj sections for the specimen quenched from 770°C after being heated at 1.88°C/s (fully recrystallized with the grain size of ASTM No. 9 2 45° section of the Euler space is also shown. 10); p  -  Chapter 6. Characterization of Annealing Textures  2 UBC 00248 700c 2mm osc. 55/180/&EF io 1.00 1,40 200 2e 4.00 5.60  253  PAGE 1 8.00 ic 16.0  Figure 6.10: ODFs showing constant y sections for the specimen quenched from 700°C after being heated at 0.025°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  254  C  c’-)  0  d (degrees) (a)  bi  >  C C 0  0  40  1 (degrees) p (b) Figure 6.11: Orientation density along the (a) a and (b) -y fibres for the as-received hot band and the 80 % cold rolled I-F steel specimens.  Chapter 6.  Characterization of Annealing Textures  (001)11101  (111)[112]  (112)1111]  255  (110)10011  (221)1114]  12  Ti0>IiTD •  10  +  Hot Band Cold Rolled  tO  Cl)  l)  C CO  0  20  (  40  (degrees)  (a)  CO >Cl)  C ci  0  0  20  40  80  60  (degrees)  (b) Figure 6.12: Orientation density along the (a) e and (b) band and the 80 % cold rolled I-F steel specimens.  9 t  fibres for the as-received hot  Chapter 6. Characterization of Annealing Textures  256  >-‘ C,)  V 0 C)j  V 1  0  40  d (degrees) (a) (111)11101  (II l)[1121  (111)[0l]  (II 1){ll]  12-  80  <ill> IIND • Cold Rolled + 15 % Recryst.  o 0  40% Recryst. 80% Recryst.  X V  100% Recryst. Grain Growth  4b (degrees)  2b  6  8b  (b) Figure 6.13: Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9 10 to ASTM No. 8) for the cold rolled specimens annealed at 20.2°C/s; the results are presented as orientation density along the (a) a and (b) y fibres. -  Chapter 6. Characterization of Annealing Textures  257  >  C  0  0  40  20  60  80  60  80  (degrees) (a)  CI)  .a) C C C 0)  0  0  40  20  q (degrees) (b) Figure 6.14: Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9 10 to ASTM No. 8) for the cold rolled specimens annealed at 20.2°C/s; the results are presented as orientation density along the (a) e and (b) 9 fibres. -  Chapter 6.  Characterization of Annealing Textures  (ll0)[l 10]  258  (1  (1 10)[00l]  12  <110>11 MD • +  b1  c  >  X  V  Cold Rolled 15 % Recryst. 40 % Recryst. 80 % Recryst. 100 % Recryst. Grain Growth  (ID  o  20  40 1 (  60  80  (degrees)  Figure 6.15: Development of annealing texture during the progress of recrystallization and grain growth (ASTM No. 9 10 to ASTM No. 8) for the cold rolled specimens annealed at 20.2°C/s; the results are presented as orientation density along the C-fibre. -  Chapter 6. Characterization of Annealing Textures  259  > C,)  a) C  a)  0  0  20  40  60  80  (degrees) (a)  4-  >  -J  C’)  C  a) C 0  4—,  C  a)  0  40 1 c’  (degrees) (b)  Figure 6.16: Effect of heating rate on the annealing texture of fully recrystallized spec imens with the grain size of ASTM No. 9 10; the results are presented as orientation density along the (a) a and (b) -y fibres. -  Chapter 6. Characterization of Annealing Textures  260  be >-‘  0 0  0  40  (degrees) (a) (OO1)(IiO]  12  (OOl)[120J  (OO1)[OiO]  10  <001> II ND -  •  -  + 0  >  (OOflfiiO]  (recrystallized)  -  be  (OOI)[120]  -  8-  20.2°C/s 1.88 C/s 0.025 °CIs  (ID  0 ii)  6 0  0 0 1  (degrees) (b) Figure 6.17: Effect of heating rate on the annealing texture of fully recrystallized spec imens with the grain size of ASTM No. 9 10; the results are presented as orientation density along the (a) E and (b) 9 fibres. -  Chapter 6. Characterization of Annealing Textures  1.0  1.3  2.5 3.2  261  1.6  4.0 5,:  6.4  ‘p  100  (a) 1.3 1.6 2.5 3.2 4.0 6.4 1.0  001  010  100  (b) Figure 6.18: Normal direction inverse pole figures calculated from the ODFs correspond ing to (a) the 80 % cold rolled steel and (b) the fully recrystallized specimen with the grain size of ASTM No. 9 10, annealed at 20.2°C/s. -  Chapter 6. Characterization of Annealing Textures  262  2  1.6 C  1.2 .—  Taylor/ODF Predictions  I’  Cl)  Cold Rolled 15 % Recryst. 40 % Recryst.  0.8  80 % Reciyst. 100 % Reciyst.  Grain Growth  0.4 0  30  15  45  60  75  90  a (degrees) Figure 6.19: Development of plastic anisotropy during the progress of recrystallization and grain growth (ASTM No. 9 10 to ASTM No. 8) for the cold rolled specimens (degrees). annealed at 20.2°C/s; the results are presented as r (predicted) vs. -  Chapter 7  Conclusions  The 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, R , was used to monitor the recovery 1  process, the measurements of both the x-ray ratio, R , and the valley intensity, 1  ‘M,  have  been shown to lead to an identical kinetic analysis during recrystallization, as validated using quantitative metallography. An iterative procedure was adopted to separate the diffraction effects associated with the concurrent recovery and recrystallization processes. The concurrent recovery effects were found to be significant only during the early stages of recrystallization. The isothermal recovery kinetics could be reasonably described using a semi-empirical logarithmic equation. The kinetic characterization indicated that the apparent activation energy for recovery, QR, increased from 173.1 kJ/mole at R 1 to 312.1 kJ/mole at R 1  =  =  0.6 (0 % recovery of Ri)  0.15 (100 % recovery of R ). The I-F steel was also observed to 1  undergo a considerable amount of recovery prior to recrystallization; recovery processes contributed to approximately 50 to 60 % of the total peak resolution. The isothermal recrystallization kinetics were adequately described using the JMAK equation with a time-exponent of n m  =  =  0.73 and the S-F equation with a time-exponent  1.17. The JMAK equation was found to be more suitable during the early stages of  recrystallization (< 50 % recrystallized), whereas the S-F equation provided a better fit 263  Chapter 7.  Conclusions  264  during the later stages (> 70 % recrystallized). The JMAK- based kinetic characterization yielded an apparent recrystallization activation energy, QR, of 501.7 kJ/mole, indicating a severe retardation of recrystallization in I-F steels. A relatively novel approach involving the microstructural path concept was success fully applied to model the microstructural and kinetic aspects of recrystallization. Fol lowing this method, the isothermal recrystallization kinetics were characterized by the experimentally determined microstructural path function, independent of the thermal path, 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 path  approach being free from any assumption ragarding the nucleation and growth conditions and being related to the evolution of microstructure, can be effectively used in modelling recrystallization and should be preferred over the conventional JMAK/S-F approach. The isothermal recovery kinetics as described by the logarithmic equation and the isothermal recrystallization kinetics as characterized by the JMAK or the S-F or the empirical interface-averaged growth rate equations, have been successfully used in con junction with the principle of additivity to describe continuous heating recovery and re crystallization kinetics at heating rates simulating both batch and continuous annealing processing. The Scheil additivity equation was found to overestimate the incubation time during continuous heating processes. Despite the longer Scheil-predicted start times, the additivity procedure resulted in good kinetic predictions, particularly towards the later part of recrystallization after  ‘-  30 % recrystallized.  Microstructural observations during recrystallization, as obtained by quantitative op tical metallography, indicated that the recrystallization event was heterogeneous. Pref erential nucleation initiated at cold rolled grain boundaries and grain intersections. The nucleation and growth of recrystallized grains were observed to be rapid in some de formed grains, and not in others. Most of the nuclei formed during the early stages of  Chapter 7. Conclusions  265  recrystallization, consistent with early site saturation. TEM examination of cold rolled and partially annealed specimens revealed that the heterogeneous cell structure developed during cold rolling. Well-defined subgrain for mation occurred during the early stages of recovery. Recrystallized nuclei developed by subgrain coalescence and the growth of recrystallized grains into the cold rolled matrix occurred by the migration of high misorientation boundaries. SEM/EDX/WDX analysis revealed that large precipitates of TiN and TiS  (  0.7 tm) acted as preferred nucleation  sites and fine (0.1 to 0.3 tm) precipitates of TiS and possibly Ti S were observed to 2 C 4 impede the boundary mobility. The crystallographic texture analysis by means of orientation distribution functions indicated the presence of a weak partial a-fibre texture centered near (112)[1TO} in the I-F steel hot band. Cold rolling reinforced the hot band texture, resulting in a highly developed partial a-fibre texture, extending from (001)[1I0] to (112)[1I0], with the high est intensity in the vicinity of (114)[1I0]. The progressive elimination of the cold rolled partial a-fibre and the concomitant development of a strong 7 -fibre occurred during re crystallization. In particular, the texture of the fully recrystallized steel was characterized by the presence of strong (554)[25] and (111)[1I0] components. Grain growth following recrystallization (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. No significant texture differences were found between the recrystallized specimens produced at 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 13th Mechanical 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 Automotive Applications, JOM, vol. 44, (1992), 17-21. [5] Obara, T., Satoh, S., Nishida, M., and Irie, T., Control of Steel Chemistry for Producing Deep Drawing Cold Rolled Steel Sheets by Continuous Annealing, Scan dinavian Journal of Metallurgy, vol. 13, (1984), 201-213. 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