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Microstructure evolution during intercritical annealing of a Mn-Cr dual-phase steel Kulakov, Mykola 2013

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Microstructure Evolution during Intercritical Annealing of a Mn-Cr Dual-Phase Steel by Mykola Kulakov B.Sc., Donetsk National Technical University, 2005 M.Sc., Clemson University, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Materials Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) July 2013 c© Mykola Kulakov 2013 Abstract A model was developed to describe the microstructure evolution during in- tercritical annealing of a low-carbon steel suitable for industrial production of dual-phase steels (DP600 grade) on a hot-dip galvanizing line. The mi- crostructure evolution model consists of individual submodels for recrystal- lization, austenite formation in a fully recrystallized material and austen- ite decomposition after partial austenization. These submodels were devel- oped using the Johnson-Mehl-Avrami-Kolmogorov approach and the addi- tivity principle. The model parameters were obtained based on the results of systematic experiments addressing the effects of initial microstructures and processing conditions on the microstructure evolution in the course of in- tercritical annealing. The initial microstructures included 50 pct cold-rolled ferrite-pearlite, ferrite-bainite-pearlite and martensite. If heating to an in- tercritical temperature was sufficiently slow, recrystallization was completed before austenite formation, otherwise austenite formed in a partially recrys- tallized microstructure. The recrystallization-austenite formation interaction accelerated austenization in all three starting microstructures by providing additional nucleation sites and enhancing growth rates; this complex process could not be accounted for with the current modelling approach. A variety of austenite morphologies was produced by using different initial microstruc- ii Abstract tures and/or by means of the interaction of recrystallization and austenite formation. Following the complete intercritical annealing cycle, the final mi- crostructure was composed of ferrite, bainite and martensite; the latter two components inherited the distribution and morphology of those for inter- critical austenite. The microstructure evolution model was validated using simulated industrial thermal paths for intercritical annealing. Laser ultrason- ics was employed for in-situ monitoring of phase transformations to facilitate the validation of the microstructure evolution model. iii Preface This thesis is based on the original work conducted at Materials Engineering Department, The University of British Columbia. I was the lead investi- gator, responsible for designing experiments, data collection, analysis and interpretation, modelling and writing this manuscript. My supervisors, Dr. Matthias Militzer and Dr. Warren Poole, were involved in all stages of the project, provided guidance and assisted with the manuscript composition. A version of Chapter 5 was published in: M. Kulakov, W. J. Poole and M. Militzer, “The effect of the initial microstructure on recrystallization and austenite formation in a DP600 Steel,” Metallurgical and Materials Transac- tions A, vol. 44, pp. 3564-3576, 2013. Section 7.1 was published in the conference proceedings: M. Militzer, T. Garcin, M. Kulakov and W. J. Poole, “Laser ultrasonics for in-situ moni- toring of microstructure evolution in steels,” in Baosteel Biennial Academic Conference, Shanghai, China, June 4-6, 2013. A part of section 7.2 was published in the conference proceedings: M. Militzer, W. J. Poole, T. Garcin, M. Kulakov and B. Zhu, “Microstructure engineering of dual-phase steels,” in New Developments in AHSS, Vail, Col- orado, June 23-27, 2013. iv Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Austenite formation and decomposition . . . . . . . . . . . . 13 2.3.1 General considerations . . . . . . . . . . . . . . . . . . 13 2.3.2 Nucleation of austenite . . . . . . . . . . . . . . . . . 15 v Table of Contents 2.3.3 Growth of austenite and ferrite . . . . . . . . . . . . . 17 2.3.4 Austenite formation in a partially recrystallized mi- crostructure . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.5 Bainite formation . . . . . . . . . . . . . . . . . . . . 26 2.3.6 Martensite . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4 Mechanical properties . . . . . . . . . . . . . . . . . . . . . . 32 2.4.1 General considerations . . . . . . . . . . . . . . . . . . 32 2.4.2 Microstructure-property relationships . . . . . . . . . 34 2.5 Modelling microstructure evolution during intercritical anneal- ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5.1 General approaches in modelling of materials engineer- ing problems . . . . . . . . . . . . . . . . . . . . . . . 36 2.5.2 JMAK model and its applicability to intercritical an- nealing . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.5.3 Analytical models . . . . . . . . . . . . . . . . . . . . 43 2.5.4 Meso-scale models . . . . . . . . . . . . . . . . . . . . 46 3 Scope and objectives . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Materials and experimental methodology . . . . . . . . . . . 52 4.1 Material and initial microstructures . . . . . . . . . . . . . . 52 4.2 Experimental methodology . . . . . . . . . . . . . . . . . . . 56 4.2.1 Samples geometry and annealing conditions . . . . . . 56 4.2.2 Recrystallization . . . . . . . . . . . . . . . . . . . . . 59 4.2.3 Austenite formation . . . . . . . . . . . . . . . . . . . 62 4.2.4 Austenite decomposition after intercritical annealing . 64 vi Table of Contents 4.2.5 Laser ultrasonics . . . . . . . . . . . . . . . . . . . . . 65 4.2.6 Mechanical properties . . . . . . . . . . . . . . . . . . 68 4.3 Modelling methodology . . . . . . . . . . . . . . . . . . . . . 69 5 Recrystallization, austenite formation and their interaction 70 5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1.1 Experimental results . . . . . . . . . . . . . . . . . . . 70 5.1.2 Recrystallization and austenite formation models . . . 86 5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6 Austenite decomposition after intercritical annealing . . . . 102 6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.1.1 Experimental results . . . . . . . . . . . . . . . . . . . 102 6.1.2 Austenite decomposition model . . . . . . . . . . . . . 110 6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7 Application of microstructure evolution model to continuous annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.1 Laser ultrasonics as a tool for in-situ monitoring of microstruc- ture evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.2 Application of microstructure evolution model . . . . . . . . . 128 7.3 Mechanical properties . . . . . . . . . . . . . . . . . . . . . . 137 8 Summary and suggestions for future work . . . . . . . . . . 142 8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8.2 Suggestions for future work . . . . . . . . . . . . . . . . . . . 145 vii Table of Contents Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 viii List of Tables 4.1 Key alloying elements in the investigated steel (wt. pct). . . . 53 5.1 Austenite grain sizes (µm) after complete austenization. . . . 84 5.2 Recrystallization model parameters. . . . . . . . . . . . . . . . 87 5.3 Nuclei density and stored energy for recrystallization. . . . . . 96 5.4 Ranking of initial microstructures based on recrystallization rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.1 Results of stereological analysis of six ferrite-austenite mi- crostructures for austenite decomposition experiments. . . . . 105 6.2 Austenite decomposition model parameters. . . . . . . . . . . 113 7.1 Summary of equations and parameters for model describing microstructure evolution during intercritical annealing (recrys- tallization is completed before austenite formation). . . . . . 130 7.2 Temperatures for recrystallization completion and austenite formation during laboratory simulations of industrial inter- critical annealing of different initial microstructures. . . . . . . 133 ix List of Tables 7.3 Temperatures for recrystallization completion and austenite formation during laboratory simulation of industrial intercrit- ical annealing of different durations for ferrite-bainite-pearlite initial microstructure. . . . . . . . . . . . . . . . . . . . . . . 135 7.4 Tensile test results. . . . . . . . . . . . . . . . . . . . . . . . 140 x List of Figures 1.1 Comparison of HSLA and AHS steels. . . . . . . . . . . . . . . 3 1.2 Microstructure evolution during intercritical annealing. . . . . 5 2.1 Nucleation during recrystallization in 0.03C-0.19Mn (wt. pct) steel after 4 s at 6000C (electron backscatter diffraction image quality map). . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Effect of manganese concentration on recrystallization kinetics in Fe-Mn alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Schematics of (a) Fe-C phase diagram, effects of (b) austenite- and (c) ferrite- stabilizing elements on phase diagram. . . . . 14 2.4 Time-temperature-transformation diagrams for austenite for- mation and decomposition. . . . . . . . . . . . . . . . . . . . . 14 2.5 Austenite nucleation and geometry of subsequent growth in (a, d) spheroidite, (b, e) ferrite-pearlite and (c, f) martensite. 16 2.6 Schematics of iron-rich corner of ternary iron-carbon-M (austenite- stabilizing element) phase diagram at intercritical temperature under (a) full equilibrium, (b) paraequilibrium. . . . . . . . . 19 xi List of Figures 2.7 Schematics of austenite-stabilizing element concentration pro- files at ferrite-austenite interface under (a) local equilibrium partitioning, (b) local equilibrium nonpartitioning, (c) parae- quilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.8 Schematics of cyclic phase transformation experiments: (a) thermal cycle, (b) corresponding dilation as a function of tem- perature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.9 Carbon concentration profiles at ferrite-austenite interface for diffusional and mixed-mode (a) austenite growth and (b) fer- rite growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.10 Solute drag concept: (a) solutes-interface interaction, (b) so- lute concentration profiles and (c) solute drag pressure for dif- ferent interface velocities. . . . . . . . . . . . . . . . . . . . . 24 2.11 Schematics of various bainite morphologies: (a) nodular, (b) columnar, (c) upper, (d) lower, (e) grain boundary allotri- omorphic, (f) inverse. . . . . . . . . . . . . . . . . . . . . . . . 28 2.12 Temperature-carbon concentration map for various bainite mor- phologies in steels containing 2 wt. pct manganese. . . . . . . 29 2.13 Summary of displacive theory of bainite formation. . . . . . . 31 2.14 Dependence of yield and tensile strengths on martensite con- tent for wide range of steels. . . . . . . . . . . . . . . . . . . . 34 2.15 General stages in building model for materials-engineering prob- lem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 xii List of Figures 2.16 Softening and recrystallization kinetics of 0.08C-1.34Mn-0.03Nb steel (major alloying elements in wt. pct) during annealing at 900 0C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.17 Microstructure of dual-phase steel as predicted by cellular au- tomata model describing entire microstructure evolution dur- ing intercritical annealing. . . . . . . . . . . . . . . . . . . . . 48 4.1 Initial microstructures before (a, b, c) and after 50pct cold- rolling (d, e, f): (a, d) furnace cooled (ferrite-pearlite), (b, e) as-received (ferrite-bainite-pearlite), (c, f) water-quenched (martensite). . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 Temperature distribution in the center of 10x60x1.8mm sheet sample after prolonged annealing at 625 0C. . . . . . . . . . . 58 4.3 Geometry of tensile specimens (thick solid lines) and corre- sponding Gleeble samples (thin dashed lines). . . . . . . . . . 60 4.4 Partially recrystallized martensite initial microstructure after annealing at 650 0C for 60 s. . . . . . . . . . . . . . . . . . . . 61 4.5 (a) Schematics of laser ultrasonics system setup, (b) example of raw signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.1 Recrystallization experiments. . . . . . . . . . . . . . . . . . . 71 5.2 Hardness evolution during annealing at 650 0C. . . . . . . . . 72 5.3 Recrystallization kinetics at 650 0C. . . . . . . . . . . . . . . . 73 5.4 Recrystallization kinetics during continuous heating at 1 0C/s. 74 5.5 Fully recrystallized microstructures after annealing at 600 0C. 75 5.6 Austenite formation experiments. . . . . . . . . . . . . . . . . 76 xiii List of Figures 5.7 Austenite formation kinetics during continuous heating of ferrite- bainite-pearlite initial microstructure at 1 0C/s, five identical tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.8 Austenite formation kinetics during continuous heating: (a) in ferrite-pearlite-bainite, (b) temperature-heating rate map for 50 pct austenization. . . . . . . . . . . . . . . . . . . . . . . . 79 5.9 Austenite formation kinetics at 770 0C after heating at (a) 1 0C/s and (b) 100 0C/s. . . . . . . . . . . . . . . . . . . . . . . 80 5.10 Early stages of austenite formation in ferrite-bainite-pearlite during continuous heating to 740 0C at (a) 1, (b) 10, (c) 100 0C/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.11 Austenite morphology after continuous heating to 760 0C at (a, b, c) 1 and (d, e, f) 100 0C/s in (a, d) ferrite-pearlite, (b, e) ferrite-bainite-pearlite, (c, f) martensite . . . . . . . . . . . 83 5.12 Austenite formation kinetics during step-heating experiments (a) in ferrite-bainite-pearlite initial microstructure, (b) temperature- heating rate austenization map. . . . . . . . . . . . . . . . . . 85 5.13 Temperature-heating rate recrystallization-austenite formation map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.14 Comparison of relative softening estimated using hardness changes and recrystallized percentage quantified through metallographic measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1 50 pct ferrite - 50 pct austenite microstructures after intercrit- ical annealing at 770 0C. . . . . . . . . . . . . . . . . . . . . . 103 6.2 Austenite decomposition experiments. . . . . . . . . . . . . . . 104 xiv List of Figures 6.3 Kinetics of austenite decomposition after intercritical anneal- ing of recrystallized ferrite-pearlite initial microstructure: (a) cooling from 770 0C to 465 0C, (b) 180 s holding at 465 0C. . 106 6.4 Effect of microstructure after intercritical annealing on kinet- ics of austenite decomposition: (a) cooling from 770 0C to 465 0C at 30 0C/s, (b) subsequent 465 0C holding for 180 s. . . . . 108 6.5 Final microstructures after intercritical annealing at 770 0C followed by cooling at 3 0C/s and 465 0C hold for 180 s. . . . . 111 6.6 Analysis of final microstructures obtained by decomposition of austenite formed after recrystallization completion (solid lines) or in unrecrystallized material (dashed lines) for (a) ferrite- pearlite, (b) ferrite-bainite-pearlite and (c) martensite initial microstructures. . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.7 Adopted geometries of ferrite growth in recrystallized/ un- recrystallized and partially austenized ferrite-bainite-pearlite initial microstructure: (a) shrinking austenite shell, (b) shrink- ing spherical austenite particles. . . . . . . . . . . . . . . . . . 115 6.8 (a) Evolution of austenite content and (b) corresponding changes in ferrite-austenite velocity during cooling at 3 0C/s of recrys- tallized and unrecrystallized ferrite-bainite-pearlite initial mi- crostructure after partial austenization. . . . . . . . . . . . . . 118 6.9 Schematics of carbon redistribution leading to formation of martensite rim around bainite. . . . . . . . . . . . . . . . . . . 120 xv List of Figures 7.1 Recrystallization progress and changes in laser ultrasonic ve- locity during two sequential isothermal anneals of ferrite-bainite- pearlite initial microstructure at 625 0C. . . . . . . . . . . . . 122 7.2 Recrystallization, austenite formation and changes in laser ul- trasonic velocity during (a) 1 and (b) 10 0C/s continuous heat- ing of ferrite-bainite-pearlite initial microstructure. . . . . . . 125 7.3 (a) Intercritical annealing cycle and (b) corresponding evolu- tion of austenite content and changes in ultrasonic velocity. . 127 7.4 Flow chart for model describing microstructure evolution dur- ing intercritical annealing. . . . . . . . . . . . . . . . . . . . . 129 7.5 (a) Industrial intercritical annealing cycle, (b) effect of initial microstructure on on phase transformations. . . . . . . . . . 132 7.6 Comparison of microstructures obtained by laboratory simu- lation of industrial intercritical annealing process of different initial microstructures and model predictions. . . . . . . . . . 133 7.7 Effect of line speed on phase transformations during labora- tory simulation of industrial intercritical annealing of ferrite- bainite-pearlite initial microstructure. . . . . . . . . . . . . . . 135 7.8 Comparison of microstructures obtained by laboratory sim- ulation of industrial intercritical annealing of ferrite-bainite- pearlite initial microstructure at different line speeds and model predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.9 Microstructure of intercritically annealed samples tested in tension (ferrite-bainite-pearlite initial microstructure). . . . . . 138 7.10 Tensile test results. . . . . . . . . . . . . . . . . . . . . . . . . 139 xvi List of Symbols 95CI 95 pct confidence interval As austenite formation start temperature ( fγ feqγ =0.05) b rate parameter in the JMAK equation b0 preexponential factor in the Arrhenius expression for rate parameter b Bs bainite start temperature c magnitude of the Burger’s vector cα/γ carbon concentration at ferrite-austenite interface( cα/γ )eq equilibrium carbon concentration at ferrite-austenite interface cγ carbon concentration in austenite far from ferrite-austenite interface d average particle size of hard phase in two-phase microstructure dα ferrite grain size after recrystallization completion DγC carbon diffusion coefficient in austenite E bulk modulus f volume fraction of hard phase in two-phase microstructure xvii List of Symbols fB volume fraction of bainite fmaxB maximum volume fraction of bainite that can be formed during 465 0C anneal fprec volume fraction of precipitates fREX recrystallized volume fraction fα volume fraction of ferrite fγ volume fraction of austenite f eqγ equilibrium volume fraction of austenite fγ(t = 0) austenite volume fraction at the beginning of 465 0C anneal( f ?γ )EX extended austenite volume fraction G shear modulus of iron GN critical driving pressure for bainite nucleation h sample thickness H Vickers hardness of partially recrystallized material H0 Vickers hardness of as-deformed material H(10s) Vickers hardness after 10 s of isothermal annealing HRex Vickers hardness of fully recrystallized material k number of analyzed images L carbon diffusion distance in austenite M grain boundary mobility M0 preexponential factor in the Arrhenius expression for grain boundary mobility Ms martensite start temperature n exponential factor in the JMAK equation xviii List of Symbols N density of nuclei for recrystallization p (X) arbitrary function of fraction transformed P stored energy PDeformation energy stored during cold-rolling PL number of intercepts between test line and ferrite-austenite interface PTransformation energy stored during phase transformations prior to cold-rolling PZener pinning (Zener) pressure by precipitates on grain boundary q heating rate Q effective activation energy in the Arrhenius expression for rate parameter b QMob activation energy in the Arrhenius expression for grain boundary mobility r average radius of precipitates R gas constant Rα radius of recrystallized ferrite grains prior to austenite formation Rγ distance from center of prior ferrite grain to ferrite-austenite interface (shrinking austenite shell) R?γ radius of shrinking spherical austenite particle s precipitate-matrix interface energy S softening t reaction time xix List of Symbols t50 annealing time required for fREX=0.5 T temperature u (T ) arbitrary function of temperature U (β) shape factor in expression for activation barrier for austenite nucleation V growth rate of nuclei during recrystallization Vα/γ velocity of ferrite-austenite interface VLUS velocity of ultrasonic wave W standard deviation X fraction transformed dX/dt transformation rate z dimensionless parameter in expression for Zener pressure α ferrite γ austenite ∆gV chemical driving pressure for austenite nucleation ∆G? activation energy for austenite nucleation ∆tLUS time necessary for ultrasonic wave to travel through sample thickness twice ∆ρdisl decrease in dislocation density during recrystallization ∆σY decrease in yield strength during recrystallization ε true strain Θ cementite λ dimensionless parameter in expression for 95 pct confidence interval xx List of Symbols ρ density ρα/γ area of ferrite-austenite interface per volume( ρ?α/γ )EX extended ferrite-austenite interface area per volume σ true stress dσ/dε strain hardening rate xxi Acknowledgments I would like to thank my both supervisors, Dr. Matthias Militzer and Dr. Warren Poole, for their insightful guidance and inexhaustible patience. I hope to be able to carry their adherence to high standards throughout my future career. The contribution of my departmental committee members, Dr. Tom Troczynski and Dr. Akram Alfantazi, is acknowledged with gratitude. I am also grateful to my university examiners, Dr. Chad Sinclair and Dr. Yusuf Altintas, and my external examiner, Dr. Bruno DeCooman, for their critical feedback. I want to thank Dr. Fateh Fazeli and Dr. Thomas Garcin for their assistance with dilatometry and laser ultrasonics tests. The cooperation of the mashine shop team, Mr. Ross Mcleod, Mr. Carl Ng and Mr. David Torok, is greatly appreciated. I want to acknowledge the help and support of the former and current Microstructure Engineering group members, whose names I do not want to list here for I may overlook someone undeservingly. Last but not least, I want to thank Angela, who appeared in my life in the dusk of the Ph.D. program and made it so much brighter. xxii Chapter 1 Introduction In 1909 an article entitled “American Automotive Steel” appeared in The New York Times [1]. Henry Souther, the author, while discussing trends in steelmaking for the automotive applications in the USA and Europe, stated that “The secret of the use of steel is to put the right steel in the right place”. Taking into account that in the early 20th century most of the cars were made of plain carbon steels, the recognition of the potential of steels for achieving different mechanical properties and application in various car components depending on their service conditions is visionary. Since then steels have been constantly improved. In the 1960’s high-strength low-alloy (HSLA) steels were developed, which had high strength despite their low-carbon con- tent [2]. The improvements in mechanical properties were achieved by grain refinement, precipitation and shape control of nonmetallic inclusions. Follow- ing the energy crisis in the 1970’s and dramatic increase in fuel prices, steel makers were challenged to improve the strength-ductility combination even further to lower vehicle weight and, thus, fuel consumption. As a result dual phase (DP) steels with a ferrite-martensite microstructure were introduced. Unlike HSLA steels, the strengthening effect in DP structures is achieved by the addition of hard martensite, while the inhomogeneous plastic deformation and the necessity to maintain the integrity of the material are responsible 1 Chapter 1. Introduction for high strain hardening rates and high ductility. Three major international conferences in 1979 and 1981 were held on the progress in DP steel develop- ment [3–5]. In the beginning hot-rolled DP steels had a niche application for manufacturing light-weight wheels in Europe and Japan. However, DP steels did not find widespread use until the early 2000’s. In 1994 thirty five major steel companies founded the Ultra-Light Steel Auto Body project to design a light, safe and fuel-efficient vehicle using high strength steels. In the 2001 conceptual design developed utilizing steel grades yet to be commercialized, DP steels accounted for about 74 pct by weight of the body in white [6]. DP steel belongs to the first generation of advanced high strength (AHS) steels, which also includes complex-phase (CP) and transformation-induced plasticity (TRIP) steels. All of them possess higher elongation for a given tensile strength compared to that of their predecessors, i.e. the HSLA steels, as shown in Fig. 1.1. At present, DP steels having excellent crash-worthiness are routinely used for manufacturing various car components. Typical alloying elements are manganese and molybdenum. However, due to the recent steep increase in molybdenum pricing, steel producers prefer to replace it with a higher concentration of manganese, silicon and chromium. Current research is fo- cused on the microstructure-property optimization. This includes reduction of nominal carbon content, refinement of ferrite grains and martensite parti- cles, and precipitation strengthening of the ferrite component by small addi- tions of carbide-forming elements, all of these aiming to improve weldability, strength and formability. 2 Chapter 1. Introduction Figure 1.1: Comparison of HSLA and AHS steels (replotted from [7] with permission). There are two methods to obtain the dual-phase structure. After hot- rolling, during cooling on the run-out table, a controlled amount of ferrite is formed, the remaining austenite is then converted into martensite by coiling near room temperature. Alternatively, cold-rolled steel is heated to an inter- critical temperature to achieve a certain austenite content and then cooled to form the ferrite-martensite structure. Automotive applications require sheets to be coated, therefore, intercritical annealing is frequently combined with the coating process in a hot-dip galvanizing line. The thermal cycle for intercritical annealing on a continuous hot-dip gal- vanizing line is schematically depicted in Fig. 1.2. Recrystallization is the first physical process to take place in a cold-rolled material upon heating to the intercritical temperature region. As soon as the austenite formation start temperature is reached, austenite nucleates and grows until the end of 3 Chapter 1. Introduction the isothermal holding. A ferrite-austenite mixture exists before the cool- ing stage. Upon cooling first to the molten zinc bath temperature (∼465 0C), part of austenite transforms back into ferrite. During the time spent in the molten zinc, bath bainite may form. The remaining austenite trans- forms into martensite during the final quench to room temperature. The final microstructure of steel that has undergone such a thermal treatment, therefore, despite the term “dual-phase”, may contain, in addition to ferrite and martensite, bainite as well. Slight variations in chemical composition between different heats and cooling conditions on the run-out table may re- sult in different microstructures being subjected to intercritical annealing. Phase transformations during intercritical annealing and, therefore, the final microstructure may be affected by the differences in initial microstructures. Intercritically annealed steels are very sensitive to the processing conditions. Therefore, models describing microstructure evolution are crucial for process design, optimization and control. In the present study, the effects of various initial microstructures and pro- cessing conditions on microstructure evolution during intercritical annealing were studied for a 0.11C-1.86-0.34Cr-0.16Si (wt. pct) steel, which is suit- able for industrial production of DP600 grade (600 refers to tensile strength in MPa). A phenomenological model describing the microstructure evolu- tion was developed and validated with laboratory simulations of intercritical annealing cycles. 4 Chapter 1. Introduction Figure 1.2: Microstructure evolution during intercritical annealing. 5 Chapter 2 Literature review 2.1 Introduction The mechanisms and factors affecting different metallurgical processes, i.e. recrystallization, austenite formation and austenite decomposition, taking place during intercritical annealing are first reviewed in this chapter with emphasis on low-carbon low-alloy steels. Deformation characteristics of dual- phase steels are then discussed. The latter part of the chapter is devoted to general approaches for modelling metallurgical processes and models appli- cable to the description of the microstructure evolution during intercritical annealing. 2.2 Recrystallization During cold-rolling about 99 pct of the applied energy is dissipated in form of heat and only the remaining 1 pct is retained in the microstructure. This 1 pct of energy is stored mainly in form of dislocations and increased grain boundary area. Depending on grain orientations and integrity requirements, not only individual grains but also areas inside of a single grain accumulate different stored energy during plastic deformation. As a consequence, the 6 2.2. Recrystallization stored energy is inhomogeneously distributed in a deformed metal. The stored energy provides the driving pressure for competing restora- tion processes including recovery and recrystallization. Recovery lowers the total energy of a system through annihilation and rearrangement of disloca- tions into low-energy structures and motion of low-angle grain boundaries. During the initial stages elastic stress fields of dislocations having opposite signs act to bring them together, this resulting in dislocation annihilation. Individual randomly distributed dislocations can rearrange themselves into regular arrays or low-angle grain boundaries thereby lowering the free energy of the system through a process known as polygonization. Finally, subgrains may coarsen by migration of the low-angle grain boundaries or rotation and coalescence. In general, for pure metals the extent of recovery is propor- tional to their stacking fault energy [8]. However, solutes are known to be capable of both accelerating or retarding recovery. In the case of low-carbon steels, recovery accounts for only a small decrease in the stored energy [9] and accompanying microstructural changes are subtle. Recrystallization involves creation and motion of high-angle grain bound- aries. Generally, recrystallization is similar to a solid state phase transfor- mation proceeding through nucleation and growth [8]. However, the driving pressure for recrystallization is one or two orders of magnitude smaller than those typically encountered in phase transformations. As a consequence, the critical nucleus has a size on the order of several microns and the initiation of recrystallization can not be explained by classical nucleation theory. In gen- eral, nuclei for recrystallization either preexist or develop during the recovery stage, e.g. by abnormal subgrain growth [10]. A successful nucleus also has 7 2.2. Recrystallization to be sufficiently large in order to outgrow its neighboring grains. Nuclei for recrystallization are nonuniformly distributed in the deformed material and develop in areas with high stored energy such as grain boundaries, shear bands etc. Texture of a cold-rolled material plays an important role in nucleation. The two major texture components in cold-rolled steels are the so-called α− (< 110 > parallel to the rolling direction) and γ− fibers (< 111 > parallel to the normal direction) [11]. Grains belonging to the α− fiber are characterized by a relatively low stored energy and have a substructure composed of equiaxed cells with less than 3 0 misorientation [12]. On the other hand, elongated subgrains with misorientations of up to 10 0 are found in grains belonging to the γ− fiber having higher levels of stored energy. Upon subsequent annealing nuclei for recrystallization form preferentially within the γ− fiber, this leading to strengthening of the γ− fiber as a result of recrystallization [9,13,14]. Fig. 2.1 shows an electron backscatter diffraction image quality map for 84 pct cold-rolled 0.03C-0.19Mn-0.13Al (wt. pct) steel in the early stages of recrystallization. In a first approximation, gray intensity in this figure is proportional to the stored energy. Recrystallization nuclei (light small regions) develop in the darker areas corresponding to the γ− fiber that has a high stored energy. Moreover, the microstructure before cold-rolling also has an effect on recrystallization. For a low-carbon steel having either ferritic or bainitic microstructures, different textures developed after cold-rolling and upon subsequent annealing [15]. 8 2.2. Recrystallization Figure 2.1: Nucleation during recrystallization in 0.03C-0.19Mn (wt. pct) steel after 4 s at 6000C (electron backscatter diffraction image quality map) (Reprinted from [9] with permission from Elsevier). 9 2.2. Recrystallization Growth of a recrystallizing grain is an interface-controlled process. The velocity of the recrystallization front can, therefore, be expressed as: V = M · P (2.1) where M is the effective mobility of the interface and P is the driving pres- sure. Among many factors that influence the mobility of high-angle grain bound- aries, the most important ones are chemical composition, temperature, ori- entation and boundary plane. Temperature-dependence of the interface mo- bility is typically described using the Arrhenius equation: M = M0 · exp ( −QMob R · T ) (2.2) where M0 is the preexponential factor and QMob is the activation energy. The driving pressure for recrystallization is the energy retained after plas- tic deformation. Nonuniform strain energy distribution forces different re- gions of the deformed microstructure to recrystallize at different rates. As a result, the average growth rate decreases in the course of recrystallization. This can be illustrated by differences in the growth rates within the α and γ− fibers. In 84 pct cold-rolled 0.03C-0.19Mn-0.13Al steel, nuclei form in the γ− fiber as discussed above and 70 pct of recrystallization is completed in 50 s during annealing at 600 0C [9]. However, an additional 5000 s is needed for recrystallization of the remaining 30 pct of the microstructure corresponding to the α− fiber. In most low-carbon steels the effect of texture on recrystal- lization is less pronounced; typically, only one stage in the recrystallization 10 2.2. Recrystallization Figure 2.2: Effect of manganese concentration on recrystallization kinetics in Fe-Mn alloys (Reprinted from [20] with permission of The Minerals, Metals & Materials Society). kinetics can be distinguished [16–18]. Solutes tend to segregate at grain boundaries and exert a retarding pres- sure on a moving boundary. This solute-boundary interaction is called solute drag [19]. The effect of manganese content on recrystallization kinetics is il- lustrated in Fig. 2.2: recrystallization kinetics becomes sluggish as the solute concentration increases [20]. The role of solute drag decreases with increasing temperature and grain boundary velocity. The presence of second-phase particles of different sizes can either hinder or promote recrystallization. A population of fine particles (diameters < 1 µm) exert a pinning force on a boundary, i.e. the Zener pressure [21], which 11 2.2. Recrystallization has to be overcome for the boundary to move: PZener = z · s · fprec r (2.3) where z is a dimensionless parameter to account for the geometry of the particle-grain boundary interaction and the distribution of particle sizes [22, 23], s is the matrix-precipitate interface energy, fprec and r are the volume fraction and average radius of precipitates. In cold-deformed Al-killed steels, recrystallization competes with con- current precipitation of aluminum nitrides; this interaction leads to three possible scenarios [13, 24]. At lower temperatures or during slow heating, precipitation takes place first. These precipitates slow down restoration pro- cesses in the γ−fiber and completely suppress recrystallization development in the α−fiber. Thus-annealed materials have strong γ−fiber texture com- ponent, excellent deep drawability and the characteristic “pan-caked” grain morphology. At intermediate temperatures or heating rates, recrystallization is interrupted by precipitation of AlN. At higher temperatures or fast heat- ing, recrystallization is completed before precipitation. In this case, the steel has weak γ−fiber texture component and inferior formability. Similar effects of preexisting precipitates on recrystallization in intersti- tial free (IF) steels were found as well [25]. At low fprec/r values (see Eq. 2.3), recrystallization is somewhat retarded but still accompanied by the desired strengthening of the γ−fiber texture component. Strong pinning, partial completion of recrystallization and weakening of the γ−fiber texture com- ponent are found for high fprec/r values. At intermediate levels of fprec/r, the precipitate-boundary interactions lead to a two-stage recrystallization. 12 2.3. Austenite formation and decomposition During deformation of a material containing large nondeformable par- ticles (diameters > 1µm ), regions of high strain develop around them to maintain compatibility across the matrix-particle interface. Preferential nu- cleation takes place in these regions upon annealing. Particle stimulated nucleation accelerates recrystallization and increases the randomness of re- crystallization texture [26]. 2.3 Austenite formation and decomposition 2.3.1 General considerations As can be seen from the schematic iron-carbon phase-diagram in Fig. 2.3(a), carbon solubility drastically differs in various phases and major carbon re- distribution is needed for austenite formation and decomposition. Moreover, addition of austenite- or ferrite-stabilizing elements shifts the ferrite-austenite two-phase regions either to lower or higher temperatures, respectively, and modifies the phase diagram further by creating a three-phase region, Fig. 2.3(b, c). Alloying elements may also drastically affect the phase transfor- mation kinetics through solute drag. Two phases, i.e. ferrite and cementite, are involved in the austenite formation process, while during cooling austen- ite alone serves as a parent phase for the two new phases. The dependencies of the driving pressure for transformations and diffusion coefficients as a func- tion of temperature are different as well. In the case of austenite formation, both the driving pressure, ∆G, and carbon diffusivity, D, increase with tem- perature such that the austenite formation rate continuously increases as a function of temperature as schematically shown in Fig. 2.4. During cooling, 13 2.3. Austenite formation and decomposition the driving pressure increases, while the rate of carbon diffusion decreases. The interplay of these two factors results in the characteristic C-curve of the time-temperature-transformation diagram, Fig. 2.4. The nose of the curve corresponds to the highest rate of the austenite decomposition. Figure 2.3: Schematics of (a) Fe-C phase diagram, effects of (b) austenite- and (c) ferrite- stabilizing elements on phase diagram. Figure 2.4: Time-temperature-transformation diagrams for austenite forma- tion and decomposition (Reprinted from [27] with permission from Maney). 14 2.3. Austenite formation and decomposition 2.3.2 Nucleation of austenite Austenization proceeds through nucleation and growth, both of them are structure-sensitive. The variety of possible structures that can be subjected to the austenization treatment can be classified in the following way: • A relatively uniform distribution of carbides dispersed in ferrite grains. These structures can be formed through prolonged heat treatments of initial fully pearlitic, bainitic or martensitic materials. • Ferrite-pearlite structures. The latter component often has banded morphology due to the segregation of alloying elements during solidifi- cation. • Bainite or martensite having a fine plate- or lath-like ferrite structure with either carbides (forming during tempering in the case of marten- site) or retained austenite particles. Successful nucleation of austenite requires an ample source of carbon, as can be seen from the iron-carbon phase diagram in Fig. 2.3. Considering austenite formation in ferrite with a dispersion of carbides, austenite nu- cleates preferentially only at those carbide particles which are located at ferrite grain boundaries, Fig. 2.5(a), where the energy barrier for the nu- cleation process is the lowest [28–31]. Moreover, austenite nuclei maintain Kurdjumov-Sachs (KS) relationship (the close packed planes of face-centered- and body-centered-cubic lattices are parallel) with one of the parent ferrite grains [30]. Austenite quickly forms a shell around the carbide particle. Fur- ther transformation proceeds via carbon diffusion that results in movement of the ferrite-austenite and austenite-carbide interfaces in opposite directions. 15 2.3. Austenite formation and decomposition Figure 2.5: Austenite nucleation and geometry of subsequent growth in (a, d) spheroidite, (b, e) ferrite-pearlite and (c, f) martensite. 16 2.3. Austenite formation and decomposition In the case of ferrite-pearlite microstructures, austenite nucleates at the interfaces between ferrite grains and pearlite colonies or the boundaries of the colonies [28, 31–37], Fig. 2.5(b). Austenite then grows into the pearlite interior. Pearlitic ferrite is consumed faster than the cementite lamellas and their remnants are often found even after the completion of austenite for- mation [28, 37]. The refinement of pearlitic structure characterized by the interlamellar spacing results in higher density of nuclei and faster austenite formation rates [28, 38]. During slow heating ferrite grain boundaries also may serve as nucleation sites for austenite [36]. When martensite is heated to intercritical temperature, rapid tempering first takes place [39], that results in carbide precipitation. Therefore, bainite and tempered martensite have essentially very similar structures: a rela- tively uniform distribution of cementites dispersed in the fine ferrite matrix. Austenite nucleates at carbides located on the prior austenite grain bound- aries or lath/plate boundaries in martensite [30, 33, 34, 39–41], Fig. 2.5(c). Nucleation rates are the highest for these structures. 2.3.3 Growth of austenite and ferrite The consumption of carbon-rich regions is followed by a relatively slow austen- ite - to - ferrite transformation, Fig. 2.5(d-f). At the end of holding in the intercritical region, a mixture of ferrite and austenite exists. Upon cooling austenite becomes unstable and transforms partially back into ferrite. No boundary between the old and new ferrite was detected using optical and transmission electron microscopy [42, 43]. Moreover, there was no change in texture during the formation of new ferrite [44] and no misorientation be- 17 2.3. Austenite formation and decomposition tween the two kinds of ferrite was observed [45, 46]. More recently, in-situ observations of ferrite growth using hot stage confocal microscopy showed clear evidence, that no nucleation was needed for the formation of new fer- rite [47]. The newly formed ferrite is called epitaxial ferrite. Therefore, the mechanisms of austenite and ferrite growth are similar: either of them grows simply by the advancement or retraction of the ferrite-austenite interface away from or towards the center of austenite islands. Factors affecting the interface movement are discussed in this section. A schematic section of Fe-C-M phase diagram is shown in Fig. 2.6 (M can be any austenite-stabilizing element and similar ideas can be applied to ferrite-stabilizers). Solubility of both carbon and M are very different in austenite and ferrite under full equilibrium as indicated by the tie-lines in Fig. 2.6(a). For the conditions of local equilibrium at the ferrite-austenite interface, the growth of both austenite and ferrite must satisfy the mass balance for the diffusional fluxes of carbon and M across the interface. A hypothetical concentration profile of substitutional austenite-stabilizing ele- ments at the interface is shown in Fig. 2.7(a). These conditions are termed as local equilibrium-partitioning (LE-P) and result in a relatively slow growth controlled by diffusion of M [48]. The area within the two-phase region below the LE-P/NP transition line, 2.6(a), corresponds to compositions at which austenite may grow without partitioning of M, i.e. local equilibrium nonpartitioning (LE-NP) conditions. The only diffusing element in this case is carbon, while a steep gradient of M, the so-called spike, is maintained over a short distance in front of the ferrite- austenite interface. The new phase forms with a nominal concentration of 18 2.3. Austenite formation and decomposition substitutional solutes. Therefore, the spike is negative in ferrite in the case of austenite formation and positive in austenite during ferrite growth for austenite-stabilizing elements as shown in Fig. 2.7(b). Another possible transformation mode is paraequilibrium (PE), Fig. 2.6(b). This is a constrained equilibrium when the concentration of substitutional elements remains constant in ferrite and austenite, while carbon diffuses until equal chemical potentials are achieved in austenite and ferrite, Fig. 2.7(c). These three transformation modes are not uniquely defined as seen, for example, from the overlapping concentration regions for LE-NP and PE con- ditions in Fig. 2.6. The transformation mode can not be easily predicted and is typically determined by comparison experimentally measured interface velocity to the predictions of the three theories, see e.g. [49]. Figure 2.6: Schematics of iron-rich corner of ternary iron-carbon-M (austenite-stabilizing element) phase diagram at intercritical temperature under (a) full equilibrium, (b) paraequilibrium. 19 2.3. Austenite formation and decomposition Figure 2.7: Schematics of austenite-stabilizing element concentration profiles at ferrite-austenite interface under (a) local equilibrium partitioning, (b) local equilibrium nonpartitioning, (c) paraequilibrium. Recently, a series of papers on the so-called cyclic phase transforma- tions was published [50–53]. A steel sample with a chemical composition of 0.17Mn-0.023C (wt. pct) was cycled between temperatures T 1 and T 2 in the intercritical region, Fig. 2.8(a). Austenite formed during heating and ferrite grew upon cooling. The main advantage of this technique is the absence of nucleation during either austenite or ferrite formation. The sample dilation during the first cycle is schematically shown in Fig. 2.8(b). In the beginning of heating to the T 2 temperature, the sample expanded linearly, points a− b, i.e. no phase transformation took place. This was termed as a stagnant stage. Further heating resulted in a nonlinear contraction corresponding to austenite formation, points b − c, i.e. normal transformation. During the first part of the cooling, austenite continued to form, points c− d. This was 20 2.3. Austenite formation and decomposition called an inverse transformation. Another stagnant stage, points d − e, fol- lowed by normal austenite-to-ferrite transformation, points e− f , took place upon further cooling. The same transformation stages were observed during the subsequent cycles. Assuming paraequilibrium, simulations of the ferrite- austenite interface migration failed to predict the stagnant stages. However, a good qualitative agreement between the dilation results and simulations under local equilibrium conditions was obtained. The stagnant and inverse stages were attributed to the behavior of alloying elements. Normal austen- ite or ferrite growth took place under LE-NP conditions during heating or cooling, respectively. The inverse stage was due to not reaching equilibrium phase contents during prior heating or cooling, transformation took place in LE-P mode in this case. The formation of a manganese-rich rim around austenite particle was often reported [32,33,54], this confirming a possibility for manganese to partition during austenite formation. The reversion of the interface concentration from LE-P to LE-NP, i.e. from the concentration profile shown in Fig. 2.7(a) to the one in Fig. 2.7(b), was required for fur- ther normal growth of austenite or ferrite. The stagnant stage was caused by the necessity for the ferrite-austenite interface to pass a region enriched with austenite-stabilizing elements (ferrite growth) or the solutes-depleted area (austenite growth) [55]. The length of the stagnant stage depends on the distribution of substitutional alloying elements in ferrite and austenite, nominal concentration of solutes and their partitioning coefficients [53]. 21 2.3. Austenite formation and decomposition Figure 2.8: Schematics of cyclic phase transformation experiments: (a) ther- mal cycle, (b) corresponding dilation as a function of temperature. The mobility of the ferrite-austenite interface is not infinitely large, as it was implicitly assumed in the prior discussion. For a simple Fe-C binary system, if austenite growth is controlled by the slower carbon diffusion in austenite and the net flux across the ferrite-austenite interface is equal to zero, the interface migration rate is then coupled with the diffusion flux of carbon, Fig. 2.9(a). However, when the ferrite-austenite interface mobility is sufficiently low, the carbon net flux is not equal to zero and a nonequi- librium carbon concentration, cα/γ, develops at the interface. The difference in the actual, cα/γ, and equilibrium, ( cα/γ )eq , concentrations provides a local driving pressure for the interface migration. This transformation mechanism is called mixed-mode possessing characteristics of both long-range diffusion- and interface-controlled transformations [56]. The sign of the carbon con- centration gradient formed in austenite during ferrite growth is opposite to the one developed during austenite formation, see Fig. 2.9. 22 2.3. Austenite formation and decomposition Figure 2.9: Carbon concentration profiles at ferrite-austenite interface for diffusional and mixed-mode (a) austenite growth and (b) ferrite growth. In multicomponent systems there is an interaction between the ferrite- austenite interface and substitutional elements. As a result, the concentra- tion of solutes at the interface differs from that far from it: The interfacial concentration can be either lower or higher depending on the sign of the po- tential well [19, 57], see e.g. Fig. 2.10(a). For a stationary ferrite-austenite interface, the solute concentration within the interface is asymmetric due to the chemical potential difference between ferrite and austenite, curve a in Fig. 2.10(b); however, solutes exert equal and oppositely directed forces on the interface, point a in Fig. 2.10(c) [58]. For an interface moving at a con- stant velocity, more solutes are left behind it, curve b in Fig. 2.10(b), and the interface experiences a non-zero dragging force from solutes, point b in Fig. 2.10(c). At high velocities solute drag pressure becomes negligible as the in- terface breaks away from its solutes, curve c and point c in Fig. 2.10(b) and (c). Solute drag may be responsible for the lowering of the ferrite-austenite mobility and the development of non-equilibrium carbon concentrations as shown schematically in Fig. 2.9. 23 2.3. Austenite formation and decomposition Figure 2.10: Solute drag concept: (a) solutes-interface interaction, (b) so- lute concentration profiles and (c) solute drag pressure for different interface velocities. 24 2.3. Austenite formation and decomposition 2.3.4 Austenite formation in a partially recrystallized microstructure Addition of alloying elements aiming to delay pearlite and bainite formation from austenite may slow down kinetics of recrystallization prior to austen- ite formation. Moreover, modern continuous annealing lines permit heating rates in excess of 50 0C/s. Fast heating will delay recrystallization to higher temperatures. Therefore, it is possible that by the time austenite forma- tion is initiated, recrystallization is not yet completed and there will be an interaction between the two processes. Incomplete recrystallization is known to accelerate austenite formation irrespective of initial microstructure [18, 37, 40, 59]. Unrecrystallized regions provide additional sites for the nucleation of austenite [60, 61]. In addition, austenite morphology is affected by incomplete recrystallization. For exam- ple, when a hot-rolled ferrite-pearlite structure was intercritically annealed, austenite formed in the prior pearlite bands and along ferrite grain bound- aries [18, 62]. However, predominantly banded austenite was formed, when the same ferrite-pearlite but cold-rolled material was heated quickly to post- pone recrystallization to the intercritical temperature range. The transition from acicular to granular austenite morphology was also reported for austen- ite formed in as-quenched or cold-rolled martensite [40,41]. The as-quenched martensite did not recrystallize and the fine lath structure leading to the development of the acicular morphology was preserved up to temperatures at which austenite formed. Whereas after deformation, recrystallization be- came possible; different austenite morphologies developed depending on the degree of recrystallization completion prior to austenite formation. 25 2.3. Austenite formation and decomposition Recrystallization itself is significantly affected by concurrent austenite for- mation [63]. During intercritical annealing of a cold-rolled bainitic structure, it was found that austenite nucleated at the boundaries between recrystal- lized and unrecrystallized grains, as well as in unrecrystallized regions. At a low austenite content, recrystallization proceeded rapidly. As austenite con- tent increased, recrystallization was retarded presumably due to the pinning effect by the austenite particles located at the boundaries of unrecrystallized grains. Prolonged annealing leading to the austenite coarsening resulted in unpinning of the boundaries and the resumption of recrystallization. 2.3.5 Bainite formation Bainite is perhaps the most controversial subject in physical metallurgy of steels. Bainite was discovered in 1912 and disputes on the mechanisms of its formation did not abate for the last hundred years (for a recent account on the early history of bainite see [64]). This is in part due to the fact that bainite being a product of austenite decomposition forms at temperatures although lower than those for ferrite or pearlite transformation, but still well above martensite start temperature. Therefore, it is difficult to study the structure of bainite-austenite interface or their orientation relationship as they are dis- torted, when any remaining austenite is transformed into martensite. There are two contradicting theories of bainite formation. One of them considers bainite as a diffusional product and another one - as a displacive product. Proponents of the diffusional model reject bainite definitions based on the surface relief and the incomplete transformation phenomenon as they can not be applied to all conditions when bainite formation is observed [65]. Instead, 26 2.3. Austenite formation and decomposition they propose a generalized definition: bainite is a “product of nonlamellar, noncooperative mode of eutectoid decomposition” [65, 66]. This definition covers a wide range of bainite morphologies shown in Fig. 2.11. For low- carbon low-alloy steels bainite is a mixture of ferrite and carbides. The ferrite component has a plate shape with carbides located either only at the plate boundaries, upper bainite, or with both inter- and intra-plate carbides, lower bainite, see Figs. 2.11(c, d) and 2.12 (note that manganese concentration of 2 pct in steels used for the construction of the temperature-carbon map in Fig. 2.12 is typical for dual-phase steels). Bainite formation starts by ferrite nucleation. The growth of ferrite is controlled by carbon diffusion in austenite. Accumulation of carbon rejected from the growing ferrite leads to carbide precipitation. The growth rates of the ferrite and carbide components are different and this causes the development of characteristic nonlamellar structure in bainite. Further transformation involves sympathetic nucleation of ferrite. According to the displacive theory [68], bainite starts to form when the maximum driving pressure reaches a critical value, GN , J/mol, for temper- atures, T , varying between 400 and 620 0C [69]: GN = 3.637 · T − 2540 (2.4) To achieve the maximum in the driving pressure, carbon content in the nu- cleus has to be lowered substantially from the carbon concentration in the parent austenite. Nucleation of the ferrite sub-unit is, therefore, a diffusional process. The expression shown in Eq. 2.4 is referred to as a universal nu- cleation function, as it defines the nucleation conditions for bainite in “any” 27 2.3. Austenite formation and decomposition Figure 2.11: Schematics of bainite morphologies: (a) nodular, (b) colum- nar, (c) upper, (d) lower, (e) grain boundary allotriomorphic, (f) inverse (Reprinted from [66] with permission of The Japan Institute of Metals and Materials). 28 2.3. Austenite formation and decomposition Figure 2.12: Temperature-carbon concentration map for various bainite mor- phologies in in steels containing 2 wt. pct manganese [67] (Reproduced with kind permission from Springer Science+Business Media B.V.). 29 2.3. Austenite formation and decomposition steel [68]. Further growth takes place via displacive mechanism without car- bon diffusion below the T0 temperature (for a given carbon content, ferrite and austenite free energies are equal at the T0 temperature). The undercool- ing below the T0 temperature has to be sufficient to compensate an energy barrier of 400 J/mol for the diffusionless growth. The growth of sub-unit is halted when the austenite-ferrite volume mismatch can not be accommo- dated any further by plastic deformation of austenite. Nucleation of another subunit then happens as shown in Fig. 2.13. Subunits are grouped into sheaves in bainite. The growth rate of sheave is slower than of individual sub-unit and limited by the nucleation process. Carbon trapped in ferrite es- capes into austenite, this causing carbide precipitation between the sub-units and the development of upper bainite. At lower temperatures, carbon diffu- sion becomes progressively slower and additional carbide precipitation occurs from supersaturated ferrite. The presence of intra-sub-unit precipitates is a characteristic feature of lower bainite. Both theories agree in that substitutional elements affect bainite forma- tion but do not partition. The effect of carbon and several substitutional elements (in wt. pct) on the bainite start temperature is described empiri- cally by [71]: Bs( 0C) = 830− 270 · C − 90 ·Mn− 83 ·Mo− 70 · Cr − 37 ·Ni (2.5) All of these elements shift bainite formation to lower temperatures. Another common alloying element in dual-phase steels, silicon, was reported to have the same effect [72]. 30 2.3. Austenite formation and decomposition Figure 2.13: Summary of displacive theory of bainite formation (Reproduced from [70] by permission of the Royal Society). 2.3.6 Martensite Upon cooling to room temperature, bainite ceases to form, the transforma- tion of austenite into martensite is initiated. Martensite is composed of a single phase having body-centered tetragonal crystal structure. It is super- saturated with carbon causing the tetragonal distortion of the body-centered cubic lattice of ferrite. On a micro-scale martensite in low-carbon steels con- sists of individual laths with high dislocation density. Martensite is formed by a displacive mechanism involving cooperative movement of individual atoms. Martensite formation proceeds through nucleation and growth. The latter occurs at a rate approaching the speed of sound. The amount of martensite formed is determined by the undercooling below the martensite start temper- ature rather than transformation time [73]. The martensite transformation 31 2.4. Mechanical properties start temperature is a function of chemical composition (in wt. pct) [74]: Ms( 0C) = 539− 423 ·C − 30.4 ·Mn− 7.5 ·Mo− 12.1 ·Cr− 17.7 ·Ni (2.6) In a partially austenized microstructure, the effective concentration of carbon is determined by the volume fraction of austenite. For a typical DP600 steel, martensite volume fraction in the final microstructure is ∼20 pct, the rest being composed of ferrite. The major alloying elements are carbon (∼0.1 wt. pct) and manganese (∼2.0 wt. pct). Assuming that all carbon is stored in austenite prior to martensite formation, the martensite start temperature is equal to ∼270 0C according to Eq. 2.6. An undercooling of 215 0C below the martensite start temperature is necessary for complete martensite transformation [71]. Therefore, during processing of a typical DP600 steel, recall Fig. 1.2, austenite remaining after holding in the molten zinc bath is expected to transform fully into martensite during the final quench to room temperature. 2.4 Mechanical properties 2.4.1 General considerations The change from ferrite-pearlite to ferrite-martensite microstructure leads to lower yield strength, higher strength and strain hardening rates, and im- proved ductility. These deformation characteristics are typical for all ferrite- martensite steels. 32 2.4. Mechanical properties When a dual-phase steel is subjected to an external load, both ferrite and martensite components deform elastically first. Upon further loading, softer ferrite yields in a continuous manner. A volume expansion of 2-4 pct accom- panying the austenite-to-martensite transformation causes ferrite adjacent to austenite to deform plastically and leads to the development of residual stresses. The transformation-induced dislocations within the deformed fer- rite regions are quickly pinned by carbon atoms (Cottrell atmospheres) and do not contribute to the continuous yielding which is caused primarily by the residual stresses [75]. Yielding becomes continuous when 3-10 pct of martensite is present [75,76]. In the early stages of deformation, only ferrite deforms plastically, while martensite still remains in the elastic regime. Macroscopic strain in this case is partitioned between ferrite and martensite. Higher dislocation density in the vicinity of martensite is maintained at all times during deformation to en- sure the material integrity [77]. The formation of geometrically-necessary in addition to statistically-stored dislocations increases strain hardening rates. The enhanced strain hardening delays fulfillment of the Considère condition for strain localization and results in superior uniform elongations in dual- phase steels as compared with ferrite-pearlite steels. Martensite structure and strength are mainly determined by its carbon content [78]. Therefore, a low-carbon martensite may codeform together with ferrite and contribute to the strain hardening in the later stages of deformation [79–81]. Both brittle and ductile fractures of dual-phase steels have been reported [81–83]. Separated martensite particles deforming plastically together with ferrite promote ductile fracture, while an interconnected network of marten- 33 2.4. Mechanical properties Figure 2.14: Dependence of yield and tensile strengths on martensite content for wide range of steels [84] (Reproduced with kind permission from Springer Science+Business Media B.V.). site experiencing only elastic deformation leads to brittle fracture. Cracks nucleate at the ferrite-martensite interface or inside of the martensite islands. 2.4.2 Microstructure-property relationships Martensite volume fraction, its size, morphology and distribution, as well as ferrite characteristics, all affect mechanical behavior of dual-phase steels. Typically, yield and tensile stresses increase, while ductility decreases, as martensite volume fraction is raised [75, 80, 84–86], see Figs. 1.1 and 2.14. However, nonmonotonic relationships have been reported as well [82]. According to Ashby’s deformation theory for plastically inhomogeneous materials, when the generation of geometrically necessary dislocations pre- vails, the work hardening rate, dσ/dε, is proportional to the content of hard 34 2.4. Mechanical properties phase, f , and inversely proportional to its particle size, d [87]: dσ dε ∼ √ f d (2.7) Work hardening of dual-phase steels having different contents and sizes of martensite particles was found to obey this relationship at low strains [75,86]. For a given martensite content, the rate of work hardening is higher in steel containing finer martensite particles. Based on Eshelby’s theory of elastic stress fields of an ellipsoidal inclu- sion in an infinite matrix [88], Weng developed a model to estimate stress- strain relations for dual-phase steels when both components could deform plastically [89]. Using this approach, Maziani and Poole evaluated effects of martensite morphology on the deformation characteristics of ferrite-martensite steels [80]. Elongated shape of martensite was found to favor its plastic de- formation. Detailed analysis of the stress partitioning revealed that stresses in martensite were ∼2.5 times higher than in ferrite for a steel with spherical martensite particles, while the elliptical ones resulted in the stress ratio of ∼3.5. Plastic deformation of martensite suppressed void formation at the ferrite-martensite interface and led to an increase in total elongation. How- ever, uniform elongation was higher in dual-phase steels containing spherical martensite islands. Uniform distribution of martensite was reported to de- lay fracture, while the mid-thickness martensite band promoting accelerated void growth should be avoided [83]. The refinement of martensite particle size is also known to increase total elongation. The structure of ferrite in dual-phase steels also affects their mechanical properties. Unlike conventional ferrite-pearlite steels [90], refinement of fer- 35 2.5. Modelling microstructure evolution during intercritical annealing rite grains in dual-phase steels improves strength without significant losses in ductility [81, 84, 91–94]. In a steel containing 30 pct of martensite and ferrite with grain sizes ranging between 1.2 and 12.4 µm, lower grain sizes resulted in an increase of yield and tensile strengths, while maintaining their ratio constant [81]. Finer ferrite grains also promoted plastic deformation of martensite. Higher contents of a relatively soft epitaxial ferrite containing lesser amounts of austenite-stabilizing elements were also reported to improve ductility without affecting strength of dual-phase steels [92]. Although the low-temperature isothermal holding that may lead to bai- nite formation associated with hot-dip galvanizing is an essential step for the production of all dual-phase steels, information on the effect of bainite on mechanical properties is scarce. The addition of bainite to the dual-phase structure increases its yield strength but lowers tensile strength; however, ductility and formability both improve [76,95,96]. 2.5 Modelling microstructure evolution during intercritical annealing 2.5.1 General approaches in modelling of materials engineering problems Despite the abundance of different modelling approaches in materials engi- neering, there is surprisingly little information on general modelling strategies in the literature. About twenty years ago, Ashby [97] summarized all essen- tial stages in building a model for a materials-engineering-related problem in 36 2.5. Modelling microstructure evolution during intercritical annealing a simple flow chart shown in Fig. 2.15. Following a thorough understanding of a problem and physical processes involved, the author emphasized the im- portance of targeting specific precision of the model and selecting modelling tools accordingly. Empirical models can be used only for a process description for a limited range of parameters confirmed experimentally; while physical models do not have this limitation and can even predict process features not captured experimentally. In the process of the model development, the evo- lution of material behavior with time, multiple operating processes, coupling different segments of the model and spatial variations should all be taken into account. The internal state variable method was advocated to link one or more internal state variables (e.g. volume fraction, grain size etc.) to ex- ternal influences (e.g. stress, temperature etc.) through a set of constitutive equations. Applicability of this general method to a wide range of material problems including solidification, phase transformations and grain growth during casting, hot forming and welding has been demonstrated in [98]. Val- idation of the model is a vital step required before its use, Fig. 2.15. “The ultimate usefulness of the model depends” on effective visualization, e.g. con- struction of mechanisms map [97]. The last word in the paper is “iterate”: the model improvement never ends. 37 2.5. Modelling microstructure evolution during intercritical annealing Figure 2.15: General stages in building model for materials-engineering prob- lem (Reprinted from [97] with permission from Maney). 38 2.5. Modelling microstructure evolution during intercritical annealing 2.5.2 JMAK model and its applicability to intercritical annealing In 1937-1939 a model describing the kinetics of phase transformations involv- ing nucleation and growth was developed independently by Kolmogorov [99], Johnson and Mehl [100], and Avrami [101] (for a recent account on the his- tory and legacy of the model see [102]). A very simple expression linking volume fraction of the new phase, X, and the reaction time, t, has been derived (i.e. an internal state variable model with one variable): X = 1− exp (−b · tn) (2.8) where b is the rate parameter and n is the exponential factor. This equation is now known as JMAK named after its four authors. Or as recently suggested by Hillert to add one more M to the JMAK abbreviation to acknowledge the input of Mirkin who introduced Kolmogorov to the problem of nucleation and growth in phase transformations [103]. The JMAK model is one of the most influential concepts in physical metallurgy. It even crossed the boundaries of the discipline and found applications in physics, chemistry and biology. For example, in chemistry this equation is usually referred to as Avrami-Erofeev [104]. According to the Web of Knowledge, Avrami’s original paper has been cited nearly six thousand times as of late 2012. In the development of the model, the following simplifications were made: • random nucleation; • constant nucleation and growth rates (at least until impingement). 39 2.5. Modelling microstructure evolution during intercritical annealing For these idealized nucleation conditions and three-dimensional growth ge- ometry, the exponent, n, in Eq. 2.8 is equal to 4. For the site satura- tion nucleation, the exponent is equal to the dimensionality of growth [105]. In diffusion-controlled transformations, the magnitude of the exponent is lower for given nucleation conditions and growth geometry, compared with interface-controlled reactions. Nucleation and growth in real processes usu- ally do not obey the ideal conditions. The rate parameter, b, and the expo- nent, n, are typically obtained by fitting the JMAK equation to experimental results. Nucleation and growth rates, and, therefore, the rate parameter are all temperature dependent. The JMAK model can also be applied under non- isothermal conditions assuming additivity, which, however, is only fulfilled for isokinetic reactions. For a reaction to be isokinetic, the transformation rate, dX/dt, has to be a product of separable functions of the fraction transformed, p (X), and temperature, u (T ) [106,107]: dX dt = p (X) · u (T ) (2.9) Upon differentiation the JMAK equation takes the following form: dX dt = { n · (1−X) · [ ln ( 1 1−X )]n−1/n} · b1/n (2.10) If n is a constant, the expression enclosed in braces in Eq. 2.10 is a function of only the fraction transformed, X, and b is temperature dependent. Therefore, such a reaction satisfies the condition for being additive, i.e. Eq. 2.9. From a physical point of view, a reaction is additive if its kinetics is 40 2.5. Modelling microstructure evolution during intercritical annealing determined by either nucleation or growth, or their ratio remains constant in the course of transformation. The JMAK model is potentially capable of describing all phase transfor- mations during intercritical annealing. It was successfully applied to model recrystallization for a range of low-carbon steels [16,18,20]. However, for IF steels the JMAK exponent n was found to be a function of temperature [17]; in this case recrystallization was not additive. As for austenite formation, it was reported for a molybdenum-containing DP steel that during continuous heating at different rates, austenite changed its growth morphology [18]. Moreover, faster heating also led to the recrys- tallization - austenite formation interaction (recall Section 2.3.4). All of this suggest a non-additive character of austenite formation. Nevertheless, there is an example of successful application of the JMAK model to austenite for- mation during heating and heating-holding tests for three steels with carbon varying from 0.08 to 0.4 (wt. pct) and ∼0.5 wt. pct of manganese [108]. Models describing austenite decomposition after partial austenization are of relevance to intercritical annealing. However, they received less attention by far compared to models for cooling on a run-out table after hot rolling, i.e. austenite decomposition from a fully austenitic state. The latter class of models is thus reviewed here. Both sequential or simultaneous formation of different transformation products during austenite decomposition was con- sidered, see e.g. [109, 110]. Typically, ferrite growth was reported to be an additive process with the exponent n close to unity for cooling rates encoun- tered during industrial processing [109, 111–114]. The controversy on bai- nite formation mechanisms makes consideration of bainite additivity difficult. 41 2.5. Modelling microstructure evolution during intercritical annealing From the point of view of the diffusional theory, bainite formation involves a multitude of phenomena including ferrite nucleation - growth and cementite precipitation. It is hard to envision conditions under which time-dependence of all of these processes could be described using Eq. 2.9. If bainite is viewed as a product of displacive reaction, its kinetics is defined by the repetitive nucleation process requiring diffusion. Additivity principle can be potentially applied to this nucleation-limited transformation. For a hypereutectoid high- chromium steel, bainite formation was described using the JMAK equation for both isothermal and continuous cooling experiments experiments [115]. More recently, the JMAK model was applied to the bainite formation occur- ring during the run-out table cooling of a niobium-molybdenum low-carbon complex-phase steel [114]. However, for a wide range of plain carbon and low- alloy steels, the exponent n and activation energy were reported to change with temperature [116–119]; the condition for additivity was not fulfilled in these cases. A phenomenological model describing the microstructure evolution during intercritical annealing of TRIP steels was previously developed [120]. The starting microstructure prior to the annealing was hot-rolled ferrite-pearlite and, therefore, recrystallization was not considered. Austenite formation was described using the JMAK model. Upon cooling it was assumed that austenite did not transform into ferrite. The only austenite decomposition product was bainite formed during a low temperature isothermal holding; the JMAK model was applied to the bainite formation as well. Evidently, this model does not consider all the physical phenomena taking place during processing of DP steels through intercritical annealing. 42 2.5. Modelling microstructure evolution during intercritical annealing 2.5.3 Analytical models Following hot deformation of a niobium microalloyed steel, nonmonotonic changes in softening and incomplete recrystallization were observed, see Fig. 2.16. Clearly, the JMAK equation could not be applied in this case. An ana- lytical model was developed to account for the interaction between concurrent precipitation, recovery and recrystallization. Precipitation was modelled as a two-stage process (nucleation-growth and growth-coarsening), the effect of precipitation on flow stress was then evaluated. The dislocation density was translated into strength using the Taylor relationship, a separate model was employed to describe softening due to recovery. Recrystallization was mod- elled by assuming site-saturation conditions, expressing the growth rate in terms of time-dependent boundary mobility and driving pressure and using the JMAK formalism to link extended and real fractions transformed. The effect of niobium remaining in solid-solution on the boundary mobility, i.e. solute drag, was described as well. Precipitation affected recovery by pinning the dislocation nodes and reduced the net driving pressure for recrystalliza- tion by exerting the Zener pinning pressure on grain boundaries. The com- petition between recovery and recrystallization both consuming the stored energy was also accounted for. The softening plateau, see Fig. 2.16, before the onset of recrystallization was attributed to the recovery-precipitation in- teraction, each of these processes had an opposite effect on strength. The recrystallization halt at a later stage of annealing took place, when the stored energy was equal to the pinning pressure. Judd and Paxton were among the first to model analytically austenite for- mation during intercritical annealing [123]. Austenite was assumed to form 43 2.5. Modelling microstructure evolution during intercritical annealing Figure 2.16: Softening and recrystallization kinetics of 0.08C-1.34Mn-0.03Nb steel (major alloying elements in wt. pct) during annealing at 900 0C (Mod- elling results replotted from [121], experimental data - from [122] with per- mission from Elsevier). 44 2.5. Modelling microstructure evolution during intercritical annealing instantaneously a shell at the ferrite-cementite interface, as schematically shown in Fig. 2.5(a); the nucleation rate was measured experimentally. The rate of the ferrite-austenite and austenite-cementite interfaces advancement in opposite directions was calculated based on the mass balance of carbon diffusional fluxes across the interfaces. For simple binary iron-carbon sys- tems, the model accurately captured the austenite formation kinetics. The rate of austenite growth was limited in this case by the carbon diffusivity in austenite. However, for alloys containing 0.5 wt. pct. of manganese, the model overestimated the rate of austenite growth. This problem arises due to order of magnitude differences in diffusivity of carbon and substitutional ele- ments and their mutual effect on thermodynamics. Wycliffe et al. considered diffusion of both carbon and manganese during austenite formation in Fe-C- Mn systems with ferrite-pearlite initial microstructure [124]. Austenization was modelled from a preexisting ferrite-austenite mixture, i.e. austenite nu- cleation and pearlite dissolution were omitted. In the beginning the carbon diffusivity in austenite controlled the rate of its growth. After this relatively quick stage, transformation proceeded at a much slower rate with manganese partitioning between austenite and ferrite. Prolonged annealing was needed for equilibrium concentrations of manganese in ferrite and austenite to be established. Similarly to austenite formation, the growth of ferrite upon cooling for plain carbon steels can be described using diffusional models assuming lo- cal equilibrium, where the carbon diffusivity in austenite limits the rate of transformation [112, 125]. In interstitial-free Fe-M alloys, ferrite formation is modelled as an interface-controlled reaction [126]. When both long-range 45 2.5. Modelling microstructure evolution during intercritical annealing diffusion of carbon and the interface reaction determine the rate of ferrite growth in Fe-C-M systems, mixed-mode models are employed to describe the kinetics of austenite-to-ferrite transformation [127]. Recently, a mixed- mode model also considering the solute drag effect was developed by Fazeli and Militzer [58]. Site-saturation conditions for the ferrite nucleation were assumed and only the growth was considered. Paraequilibrium conditions were adopted, i.e. long-range diffusion of only carbon was considered. There were four fitting parameters having a clear physical meaning to describe temperature dependence of the interface mobility and the interface-solutes interaction. The model yielded accurate predictions of the ferrite formation kinetics for several AHS steels. Typically, in analytical models the nucleation stage of any transformation is either simplified to a site-saturation process or omitted. Assumptions for the geometry of growth have to be made as well. These requirements limit applicability of analytical models. 2.5.4 Meso-scale models In the last two decades, advancements in computer technology stimulated rapid development of meso-scale models in materials engineering. Unlike all the previously discussed modelling approaches that describe only kinet- ics of metallurgical processes, meso-scale models are capable of visualizing microstructures. Cellular automata and phase-field among others belong to this emerging class of models. In a cellular automaton model, the entire microstructure is discretized into a series of cells. Each cell is assigned a state variable, e.g. crystal struc- 46 2.5. Modelling microstructure evolution during intercritical annealing ture, concentration, orientation etc, which changes abruptly between areas possessing different state variables, i.e. sharp interface approach. To describe microstructure evolution, a set of probabilistic or deterministic laws is then applied to the interfacial cells, the interior cells remain unaffected, thereby reducing computational costs of this modelling approach. A comprehen- sive model describing the entire microstructure evolution during intercritical annealing of a cold-rolled ferrite-pearlite 0.1C-1.5Mn (wt. pct) steel was de- veloped recently using a three-dimensional cellular automaton method [128]. Even though a separate recrystallization model was included, the interac- tion between recrystallization and austenite formation was not considered: irrespective of fraction recrystallized at the austenite formation tempera- ture, austenite nuclei were assigned only to pearlite colonies. The growth of austenite was simplified to an interface-controlled reaction. Austenite decom- position into ferrite upon cooling was described using a mixed-mode model assuming paraequilibrium conditions. Any remaining austenite at the end of intercritical annealing was assumed to transform into martensite. The model predicted the evolution of microconstituents content in the course of anneal- ing. Another output of the model was three-dimensional representation of the final microstructure, i.e. size, distribution and morphology of ferrite and martensite, as shown in Fig. 2.17. In phase-field models, a discretized space is also described with a set of phase-field parameters related to crystal structure, orientation etc. A diffuse interface approach is employed, i.e. phase-field variables change grad- ually within the interface thickness. Complex microstructure morphologies can be simulated using phase-field models. Microstructure evolution is gov- 47 2.5. Modelling microstructure evolution during intercritical annealing Figure 2.17: Microstructure of dual-phase steel as predicted by cellular au- tomata model describing entire microstructure evolution during intercritical annealing (ferrite - blue, austenite - orange) (Reprinted from [128] with per- mission from Elsevier). 48 2.5. Modelling microstructure evolution during intercritical annealing erned by the minimization of the total free energy of the system. Individual models were developed to describe recrystallization, austenite formation and decomposition in different steels, for a recent overview see [129]. The most relevant phase-field simulations to intercritical annealing were performed for the welding process of dual-phase steel with a ferrite-martensite initial mi- crostructure [130]. The formation of austenite and ferrite was considered for a thermal cycle consisting of heating to intercritical temperature and cooling. Austenite nucleation rate was calculated using classical nucleation theory and integrated into a two-dimensional phase-field model, which was also coupled to the diffusion equation for carbon. The growth of austenite during heat- ing and ferrite upon cooling was modelled as a mixed-mode transformation under paraequilibrium conditions. The description of phase transformations kinetics was in good agreement with experimental measurements. Moreover, the microstructure evolution was visualized and the existence of nonuniform carbon distribution in austenite and ferrite was predicted. Despite the physical realism of meso-scale models, they require a priori knowledge of many difficult-to-measure parameters, e.g. nucleation rates, interface mobilities etc. Moreover, the complexity and high computational costs make them not suitable for a fast-paced manufacturing environment. 49 Chapter 3 Scope and objectives The primary goal of the present study is to develop a model describing mi- crostructure evolution during processing of a DP600 steel (0.11C-1.86Mn- 0.34Cr-0.16Si, wt. pct) through intercritical annealing on a typical hot dip galvanizing line (HDGL). Following Ashby’s recommendations for a materi- als engineering-related model development [97], recall Fig. 2.15, a general strategy for designing the microstructure evolution model is outlined in this chapter. 1. The microstructure evolution model has to be applicable to processing conditions encountered on a typical HDGL: heating and cooling rates of up to 100 0C/s, several minutes long holding at an intercritical temperature and in the molten zinc bath. 2. The thermal path for intercritical annealing is one of the inputs for the model. Another input is the initial microstructure. Various microstruc- tures, e.g. ferrite-pearlite, bainite or martensite, may be obtained dur- ing steel processing prior to intercritical annealing, the type of initial mi- crostructure may influence the microstructure evolution during the anneal- ing. Volume fractions of microconstituents in the final microstructure have dominant effect on mechanical properties and they are the desired outputs of the model. 50 Chapter 3. Scope and objectives 3. Microstructure evolution during intercritical annealing involves recrystal- lization, austenite formation and austenite decomposition. As described in Chapter 2, kinetics of these metallurgical phenomena depends on a number of material-specific parameters and is not known a priori. These parameters will be determined in dedicated laboratory experiments. 4. Similar to industry practice [131], a variation of ±5 pct for tensile strength of the final DP600 product is taken as a target range of properties, i.e. between 600 and 660 MPa. Based on the mechanical properties data for a wide range of steels shown in Fig. 2.14, this variation translates into an acceptable range of martensite content of 19 to 23 pct, i.e. 21±2 pct or ±10 pct relative accuracy. This will be adopted as the desired accuracy of the model predictions. 5. Individual models for recrystallization, austenite formation and austenite decomposition will be constructed first. This set of models will then be coupled and applied to the complete intercritical annealing cycle. Priority in the choice of modelling tools will be given to robust and computationally inexpensive models suitable for a fast-paced industrial environment. 7. The model will be designed to be run on a single computer and provide a quick estimate of the effect of processing parameters on microconstituents content in the final microstructure after intercritical annealing. 8. The model will be validated using simulations of industrial thermal paths for intercritical annealing. 51 Chapter 4 Materials and experimental methodology 4.1 Material and initial microstructures Chemical composition of the investigated steel is shown in Table 4.1. The in- dustrially processed steel was supplied by ArcelorMittal Dofasco Inc. (Hamil- ton, ON, Canada) from the same heat in form of 3.6 mm thick hot-rolled and 1.8 mm thick 50 pct cold-rolled sheets. The latter was used as one of three starting microstructures, while the hot-rolled material was reaustenized in a box furnace at 900 0C for 1800 s, then either furnace-cooled or water- quenched to produce two additional starting microstructures. Subsequently, these materials were cold-rolled in a single stand laboratory mill having 150 mm diameter rolls. The cold-rolling schedule consisted of ten passes with 5 pct reduction per pass to obtain a total reduction of 50 pct as in the industri- ally cold-rolled sheets. The ratio of the mean sample thickness to the length of the sample-roll contact was always below unity during laboratory rolling to achieve homogeneous strain distribution through the sample thickness [132] similar to that commonly obtained in industrially cold-rolled sheets. 52 4.1. Material and initial microstructures Table 4.1: Key alloying elements in the investigated steel (wt. pct). C Mn Cr Si 0.105 1.858 0.340 0.157 Microstructures obtained before and after cold-rolling were revealed by etching with 2 pct Nital and then examined using optical (Nikon Epiphot 300) and scanning electron microscopes (Hitachi 3000 or Zeiss Sigma). Volume fractions of microconstituents were measured on at least fifteen secondary electron images using the point counting method (ASTM E562-11). Vickers microhardness measurements were conducted at 1 kg load and 15 s dwell time; an average of five hardness measurements is reported. The average equivalent area diameter of ferrite grains before cold-rolling was determined on at least 500 grains according to ASTM E1382-97 using the grain area measurement technique. Microstructures of the three materials before and after cold-rolling are shown in Fig. 4.1 and can be described as follows: 1. After reaustenizing at 900 0C for 1800 s and slow furnace cooling of the as-received hot-rolled material, its microstructure consisted of 85 pct of ferrite and 15 pct of pearlite (F-P), Fig. 4.1(a). The average ferrite grain size in the as-heat-treated condition was 11 µm. Pearlite bands were parallel to the rolling direction with an average band spacing of 14 µm after 50 pct cold-rolling, Fig. 4.1(d). The pearlite band thickness characterized using the intercept method with the test lines being aligned perpendicular to the bands was equal to 5.6 and 3.4 µm before and after cold-rolling, respectively. The relative change in pearlite bands thickness of 40 pct reduction is less than the macroscopic 53 4.1. Material and initial microstructures strain of 50 pct. The strain partitioning is a common feature observed during cold-rolling of ferrite-pearlite structures [133]. After the heat treatment the hardness was equal to 135 HV and it increased by 93 HV to 228 HV after cold-rolling. 2. The microstructure of the as-received material consisted of 5 pct of pearlite with the rest being either ferrite or bainite (F-B-P), Fig. 4.1(b). No attempt was made to differentiate the latter two phases due to their similar appearance in the micrographs. Grain size of the ferrite/bainite constituents prior to cold-rolling was equal to 3.0 µm. The hardness was 189 and 272 HV before and after cold-rolling, respectively, this corresponding to a 83 HV gain in hardness due to cold-rolling, Fig. 4.1(e). 3. After reaustenizing at 900 0C for 1800 s and water quenching of the as- received hot-rolled material, a martensitic microstructure was formed, Fig. 4.1(c), with a hardness of 378 HV. This hardness falls into the range of 340-380 HV expected for martensite with 0.1 wt. pct carbon [134] suggesting that this third starting microstructure can indeed be considered as lath martensite (M). The martensite hardness increased by 63HV to 444 HV in the course of cold-rolling, Fig. 4.1(f). Hereafter the initial microstructures will be designated by their abbrevia- tions, i.e. F-P, F-B-P and M. 54 4.1. Material and initial microstructures Figure 4.1: Initial microstructures before (a, b, c) and after 50pct cold-rolling (d, e, f): (a, d) furnace cooled (ferrite-pearlite), (b, e) as-received (ferrite- bainite-pearlite), (c, f) water-quenched (martensite) (P: pearlite, F: ferrite). 55 4.2. Experimental methodology The three starting microstructures have different grain sizes and different distributions of carbon. The F-P and M materials are the bounding cases, i.e. for F-P carbon is clustered in pearlite bands and for M, carbon is uniformly distributed, while the F-B-P initial microstructure represents an intermedi- ate case in terms of carbon distribution. These three materials cover the full spectrum of structures which could be potentially used for cold-rolling and subsequent annealing. The 50 pct cold-rolled samples were used for recrystal- lization, austenite formation and decomposition experiments in the present study. 4.2 Experimental methodology 4.2.1 Samples geometry and annealing conditions Further heat treatments of the three initial materials were conducted under a high vacuum of ≈0.26 Pa using the Gleeble 3500 thermomechanical simulator (Dynamic Systems Inc., Poestenkill, NY) equipped with a dilatometer. From the as-cold-rolled materials, 10x60x1.8 mm sheet samples were machined with the longitudinal axis coinciding with the rolling direction. Temperature was controlled through a K-type thermocouple spot welded at the centre of each sample. One test series, i.e. heating-holding transformation tests at 770 0C with 100 0C/s heating rate, was conducted using the Bähr 805A/D dilatometer (TA Instruments, Hüllhorst, Germany) and 10x5x1 mm sheet samples having the longitudinal axis aligned with the transverse direction. Equal amounts were ground off both sides to reduce the sheet thickness from 1.8 to 1 mm. The dimensional changes in the course of phase transformations 56 4.2. Experimental methodology were measured using a dilatometer along either transverse (Gleeble tests) or longitudinal axis (Bähr experiments) with respect to the same rolling direction. The following thermal paths were employed in the present study: • isothermal tests at subcritical temperatures • continuous heating experiments • heating-holding at intercritical temperature • cooling tests after partial austenization • simulations of the complete intercritical annealing cycle. Temperature distribution is not uniform during the Gleeble tests. Temper- ature gradients steepen with annealing time until a steady state is reached. An example of temperature distribution evaluated by employing multiple thermocouples for a 10x60x1.8 mm sheet sample (this type of samples was primarily used in this study) after prolonged annealing at 625 0C is shown in Fig. 4.2. Within ±3 mm from the sample center, temperature varies only by 5 0C. The microstructure analysis of the heat treated samples was limited to this narrow region. Tensile properties of the as-received material in the hot-rolled (3.6 mm thick) and 50 pct cold-rolled (1.8 mm thick) conditions were determined us- ing 24 mm gauge specimens (subsize sheet type ASTM E8M-04) shown in Fig. 4.3(a). To extend the region with uniform temperature distribution to the gauge length of tensile specimens, 50x200 mm Gleeble samples were 57 4.2. Experimental methodology Figure 4.2: Temperature distribution in the center of 10x60x1.8mm sheet sample after prolonged annealing at 625 0C. 58 4.2. Experimental methodology used to simulate the industrial processing route for the 50 pct cold-rolled as- received material. Two tensile specimens having 24 mm gauge length were then machined from the center of the heat treated sample as shown in Fig. 4.3(b). The effect of martensite morphology on tensile properties was stud- ied using 8 mm gauge length specimens machined from the center of 12x93 mm Gleeble samples after different heat treatments of the 50 pct cold-rolled as-received material, Fig 4.3(c). Any surface defects were removed from the tensile specimens by grinding off ∼0.25 mm from each side thereby reduc- ing thickness from 1.8 to 1.3 mm. Machining alters the sample subsurface which is commonly referred to as white etching layer due to its featureless appearance in light optical micrographs. The white etching layer is heav- ily deformed and it also experiences rapid heating/cooling in the process of machining. In steels the machining-affected zone typically does not exceed 10-20 µm [135, 136]. In the present study, the white etching layer comprises at most 2-3 pct of the sample thickness and is considered to have negligible effect on the results of tensile tests. 4.2.2 Recrystallization Partially recrystallized samples were helium-quenched with cooling rates of ∼100 0C/s. Their microstructure was examined using optical and scanning electron microscopes after etching with 2 pct Nital. The point counting method was employed to determine recrystallized volume fraction based on the analysis of at least fifteen secondary electron images. An example of the point counting measuremtns is shown in Fig. 4.4. 59 4.2. Experimental methodology Figure 4.3: Geometry of tensile specimens (thick solid lines) and correspond- ing Gleeble samples (thin dashed lines). 60 4.2. Experimental methodology Figure 4.4: Partially recrystallized martensite initial microstructure after an- nealing at 650 0C for 60 s (recrystallized areas are marked with blue circles). The discrimination between recrystallized and unrecrystallized areas was based on the following criteria: • shape: recrystallizing grains had a more equiaxed shape as opposed to the elongated grain structure after 50 pct cold-rolling with the average aspect ratio of 1:4 • substructure: recrystallizing grains had a clean interior free of substruc- ture. Multiple repetitions of identical heat treatments and samples analysis by a number of different metallographers would be needed to evaluate the actual accuracy of the point counting method. As recommended by the ASTM stan- dard, 95 pct confidence interval (CI) was used instead to estimate accuracy 61 4.2. Experimental methodology of these measurements: 95CI = λ ·W√ k − 1 (4.1) where λ is a constant equal to 2.145 for k = 15 analyzed images, σ is the standard deviation for the 15 measurements. 95 pct confidence interval includes contributions from both the heterogeneity of microconstituents distribution and the absolute error of these measure- ments, e.g. because of the subjectivity in discrimination recrystallized and unrecrystallized areas. Therefore, 95 pct confidence interval was a rather conservative estimate of the accuracy for the stereological measurements. Softening during recrystallization was monitored via Vickers microhard- ness measurements. The grain area measurement technique was used to eval- uate average equivalent area diameter of ferrite grains after recrystallization completion in the same manner as described before. 4.2.3 Austenite formation The progress of austenite formation was monitored in-situ based on dimen- sional changes of the sample recorded using a dilatometer. At least two identical tests were conducted for each condition to verify their repeatability. Furthermore, two criteria were used to make sure that the dilation measure- ments were valid. First, thermal expansion coefficients had to be within ±5 pct of those reported in the literature [137,138]: 15.5− 16.6 · 10−6 0C−1 (for the subcritical temperature range of 500 to 700 0C) and 24.8 · 10−6 0C−1 (for 0.1 wt. pct of carbon) for ferrite and austenite, respectively. Contraction 62 4.2. Experimental methodology due to the complete ferrite-to-austenite transformation also had to exceed by not more than 10 pct the ideal value of ∼40 µm evaluated using the lat- tice parameters [137] for the initial sample width/length of 10 mm. Austenite volume fractions were calculated from the dilatometer data using the lever rule (ASTM A1033-10) assuming linear thermal expansion of ferrite within the intercritical temperature range. To validate these results and gain a deeper insight into the austenite formation mechanisms, partially austenized samples were water-quenched at cooling rates of ≈1000 0C/s to convert all intercritical austenite into martensite at room temperature. The martensite content was determined using the automatic image analysis (ASTM E1245- 03) of optical micrographs after etching with LePera’s reagent [139]. The freshness of this etchant was found to be crucial for achieving high contrast between martensite and the rest of the microstructure. The martensite mor- phology and distribution were investigated with scanning electron microscopy on samples etched with 2 pct Nital. Fully austenized samples were water- quenched right after the completion of austenite formation to determine the austenite grain size. For these fully martensitic samples, the prior austenite grain boundaries were revealed by etching at 90 0C for 75 s in a saturated water based solution of picric acid, 1.3 g of sodium dodecylbenzene sulfonate and 1 ml of concentrated hydrochloric acid per 100 ml solution. The average equivalent diameter of austenite grains was measured. 63 4.2. Experimental methodology 4.2.4 Austenite decomposition after intercritical annealing Austenite decomposition was studied for microstructures composed of ∼50 pct austenite and ∼50 pct ferrite. In addition to the austenite content mea- surements described before, density of the ferrite-austenite interface was also evaluated to characterize microstructures existing right before cooling more thoroughly. The number of intercepts, PL, between the test line and the martensite-ferrite interface was counted on three secondary electron micro- graphs. The measurements were carried out using the test lines oriented parallel to the rolling and normal directions. The interface area per unit volume, ρα/γ, was then calculated according to [140]: ρα/γ = 2 · PL (4.2) After cooling to room temperature, bainite and martensite volume frac- tions were measured using the point counting method on at least fifteen sec- ondary electron micrographs after etching with 2 pct Nital. Accuracy of these measurements was estimated using the 95 pct confidence interval, Equation 4.1. For cooling after partial austenization, extremely low helium pressure was sufficient to reach cooling rates of up to 50 0C/s; such a low helium flow was also essential to avoid perturbations in dilation. Austenite decomposi- tion kinetics was determined from the dilation signal recorded during cooling and 465 0C holding using the lever rule allowing austenite content to change between ∼50 pct and martensite volume fraction in the final microstructure. Epitaxial ferrite content, i.e. ferrite formed during cooling, was estimated 64 4.2. Experimental methodology indirectly as a difference between the amount of intercritical austenite, i.e. ∼50 pct, and the sum of martensite and bainite volume fractions at room temperature. 4.2.5 Laser ultrasonics Ultrasonics is a routinely used tool for nondestructive testing of materials. However, it requires a contact between the sample and transducer. A non- contact variation of this technique employing lasers for the generation of ultrasonic waves and their detection has been developed more recently [141]. The characteristics of ultrasonic waves are affected by the structure of the test piece. The velocity of ultrasonic wave propagation depends on the material density and elastic modulus, and is, thus, sensitive to the crystal structure and texture changes. The reduction in amplitude of ultrasonic waves, i.e. at- tenuation, is caused by scattering and absorption phenomena. Grain size, dis- location density and porosity are the main factors affecting attenuation. Fer- rite recovery [142], recrystallization of ferrite and austenite [143,144], austen- ite grain growth [145–147], austenite formation and decomposition [148–150] have been studied to date with the aid of laser ultrasonics. This technique can be also employed during industrial processing [141,151]. Laser ultrasonics was employed for a limited number of experimental con- ditions to evaluate its applicability for in-situ monitoring of various physical processes taking place during intercritical annealing and to aid rapid valida- tion of the microstructure evolution model. Laser ultrasonics for metallurgy (LUMet) system was attached directly to the Gleeble machine as schemat- ically shown in Fig. 4.5(a). All conditions were identical to those for the 65 4.2. Experimental methodology phase transformation experiments employing the Gleeble simulator as de- scribed above. A neodymium-doped yttrium aluminum garnet (Nd: YAG) laser operating at a wavelength of 532 nm for 5 ns is used to generate ultra- sonic waves in a sample by localized heating just beneath the surface (nonde- structive thermoelastic mechanism) or by ablation/vaporization [141]. After traveling through the sample thickness, the ultrasonic waves bounce at the back wall and return to the original surface where they are registered with another Nd: YAG laser having 1064 nm wavelength and pulse duration of 50 µs. The same wave travels back and forth within the sample; the wave ampli- tude gradually decreases due to the interaction with the material. Multiple echos are thus detected for each generation pulse as shown in Fig. 4.5(b). A phase shift or frequency change between the original wave of the detection laser and the one reflected by the sample are analyzed using a photorefractive interferometer [152]. A cylinder with a base diameter of ∼2 mm is sampled by the laser, Fig. 4.5(a). The maximum rate of pulse generation is limited to 50 Hz. Every time the laser strikes the sample surface, it evaporates some of the material. As a rule of thumb, the total number of generated pulses should not be greater than ∼1000 to avoid excessive surface damage. Velocity and attenuation of different types of ultrasonic waves can be measured. In the present study, the analysis was limited to the velocity measurements of compressive waves. Their velocity was calculated simply as a ratio of twice the sample thickness, 2 ·h, to the time between two successive echos, ∆tLUS: VLUS = 2 · h ∆tLUS (4.3) 66 4.2. Experimental methodology Figure 4.5: (a) Schematics of laser ultrasonics system setup, (b) example of raw signal. 67 4.2. Experimental methodology To aid accurate velocity measurements, the effect of thermal expansion on sample thickness was taken into account (thermal expansion coefficients were taken from [138]). The time delay, ∆tLUS, between the second and third echos was determined with an accuracy of ∼1 ns by the cross-correlation method. 4.2.6 Mechanical properties Tensile tests were conducted using the MTS system (MTS Systems Corpora- tion, Eden Prairie, MN) at a nominal strain rate of 0.002 s−1. The 12.5 mm INSTRON extensometer (travel distance ±5 mm) was used to record axial elongation during the tests and the load applied to the tensile specimens was measured using a 25 kN load cell. At least two tensile tests were conducted to verify their reproducibility for each sample type. Engineering and true stresses and strains were calculated; the reported values were average results of the two tests. For a tensile test to be valid, the measured elastic modulus had to be within ±5 pct of the nominal value of ∼210 GPa for iron or a low carbon steel [153]. Yield strength was considered as the intercept between engineering stress-strain curve and the elastic portion of the curve offset by 0.2 pct. To aid comparison of tensile tests conducted using specimens with different gauge lengths, post-uniform deformation was not considered in the present study. The onset of necking and the corresponding uniform strain and ultimate strength were determined based on the Considère condition: σTrue = d (σTrue) d (εTrue) (4.4) 68 4.3. Modelling methodology where σTrue and εTrue are true stress and strain, respectively. 4.3 Modelling methodology The Johnson-Mehl-Avrami-Kolmogorov equation was selected to model phase transformations during intercritical annealing. Individual models for recrys- tallization, austenite formation and austenite decomposition with one inter- nal state variable, being recrystallized volume fraction or austenite content, were constructed first. Kinetics of non-isothermal transformations was de- scribed using the JMAK equation in differential form, see Eq. 2.10, and adopting the additivity principle. The set of models was then integrated for the complete microstructure evolution description. The entire microstruc- ture evolution model was implemented in MATLAB. For a non-isothermal thermal treatment, numerical integration was conducted using a time step of 0.01 s. Further refinement of the time increment did not affect the results of calculations. The model was validated for the industrial thermal paths using laser ultrasonics, dilatometry and metallography. 69 Chapter 5 Recrystallization, austenite formation and their interaction1 5.1 Results 5.1.1 Experimental results Recrystallization Recrystallization in all starting microstructures was studied during isother- mal holds at 600, 625 and 650 0C; heating rate to the holding temperature was equal to 50 0C/s, as indicated in Fig. 5.1. Recrystallization kinetics was also measured during continuous heating tests at 1 0C/s. Hardness of F-P and F-B-P decreased gradually in the course of isother- mal annealing, while M softened in two stages, Fig. 5.2. The first, rapid softening stage, took place in less than 10 s, where the microstructure did not show any evidence of recrystallization. The second stage led to a more gradual hardness decrease. For long annealing times after which recrystal- lization was complete, a hardness of 145HV was measured for all the initial 1A version of this chapter was published in: M. Kulakov, W. J. Poole, M. Militzer, “The effect of the initial microstructure on recrystallization and austenite formation in a DP600 Steel,” Metallurgical and Materials Transactions A, vol. 44, pp. 3564-3576, 2013. 70 5.1. Results Figure 5.1: Recrystallization experiments. microstructures. Fig. 5.3 shows metallographically measured recrystallized percentage as a function of holding time at 650 0C. The F-B-P initial mi- crostructure had the highest rate of recrystallization, the F-P material re- quired the longest times for recrystallization to be completed, while M re- crystallized at intermediate rates. Similar trends were observed for 600 and 625 0C holding temperatures, as well as for recrystallization during continu- ous heating at 1 0C/s, as shown in Fig. 5.4. After recrystallization, all the microstructures consisted of various arrays of carbide particles in a ferrite ma- trix, Fig. 5.5. For the F-P starting material, pearlite partially spheroidized in the course of annealing and clusters of cementite particles in the recrystal- lized microstructure inherited the distribution and morphology of the former pearlite bands, as can be observed in Fig. 5.5(a). Relatively coarse carbide particles were either clustered or arranged into linear arrays in the fully re- crystallized state resulting from the F-B-P initial structure, see Fig. 5.5(b). The clusters were formed presumably at the former bainite or pearlite, while the linear arrays could be inherited from the grain boundary carbides in the 71 5.1. Results Figure 5.2: Hardness evolution during annealing at 650 0C. cold-deformed structure. A finer and more homogeneous distribution of car- bides was found after recrystallization of the M initial structure, Fig. 5.5(c). The ferrite grain size after recrystallization completion was found to be inde- pendent of the annealing temperature and equal to 7.6 (7.2-8.3), 5.1 (4.9-5.3) and 6.5 (5.9-7) µm for F-P, F-B-P and M, respectively (the ranges of grain sizes after annealing at different temperatures are noted in parentheses). It is noteworthy that recrystallization in F-B-P and M led to a coarser grain size, while in F-P the final grain size is lower than the one before recrystallization. 72 5.1. Results Figure 5.3: Recrystallization kinetics at 650 0C. (Symbols correspond to experimental results, lines are the JMAK model fit) 73 5.1. Results Figure 5.4: Recrystallization kinetics during continuous heating at 1 0C/s. (Symbols correspond to experimental results, lines are the JMAK models). 74 5.1. Results Figure 5.5: Fully recrystallized microstructures after annealing at 600 0C: (a) ferrite-pearlite after 4020 s, (b) ferrite-bainite-pearlite after 3000 s, (c) martensite after 3000 s. (P: intact pearlite, SP: spheroidized pearlite) 75 5.1. Results Figure 5.6: Austenite formation experiments. Austenite formation Austenite formation was studied during continuous heating at 1, 10 and 100 0C/s and heating-holding tests with 1200 s long holding at 770 0C after heating either at 1 or 100 0C/s as shown schematically in Fig. 5.6. The third group of austenite formation tests involved heating at 1 0C/s to a subcritical temperature of 720 0C and then switching heating rate either to 10 or 100 0C/s. Lever rule analysis of dilation data was routinely used in this study for in- situ austenite content measurements. Accuracy of this method was evaluated based on the repeatability of continuous heating experiments at 1 0C/s using the F-B-P initial microstructure, Fig. 5.7. The lever rule analysis assumes nominal concentration of carbon in austenite at all stages of the transforma- tion, while in reality austenite carbon concentration in austenite gradually decreases thereby increasing thermal expansion coefficient of austenite. As a result of this, the lever rule analysis systematically underestimates austenite 76 5.1. Results Figure 5.7: Austenite formation kinetics during continuous heating of ferrite- bainite-pearlite initial microstructure at 1 0C/s, five identical tests. content in the beginning of austenite formation, but yields more accurate re- sults in the later stages [154]. A scatter of ∼7 pct in austenite content after five identical tests was observed at ∼60 pct; this translates into a relative accuracy of ∼10 pct (or ±5 pct) for the austenite content estimates using the lever rule method. Austenite volume percentage as a function of temperature for the F-B-P initial microstructure is shown in Fig. 5.8(a) for continuous heating rates of 1, 10, and 100 0C/s. Ortho- and para-equilibrium austenite content is also shown as calculated with Thermo-Calc using the FE-2000 database (Thermo- Calc Software, Stockholm, Sweden). The austenite fraction as a function of 77 5.1. Results temperature appears to be rather independent of heating rate even though in none of the cases equilibrium is reached at any given temperature. Thus, the austenite formation rates increase with heating rate and this acceleration of austenite formation scales in a first approximation with heating rate. There is even a slight tendency that higher heating rates can lower the transfor- mation temperatures. Similar trends were observed for the other two initial microstructures: Temperatures needed to achieve 50 pct of austenite during continuous heating were similar for all heating rates and in some cases (M and F-B-P) appeared to be lower by about 10 0C for higher heating rates, Fig. 5.8(b). Further, the austenite formation start temperature is for all continuous heating cases approximately 730 0C, e.g. Fig. 5.8(a). During holding at 770 0C after slow heating at 1 0C/s, the rate of austen- ite formation was similar irrespective of initial microstructure, Fig. 5.9(a). As shown in Fig. 5.9(b), the rate of austenite formation was accelerated in all three starting microstructures when the heating rate to the intercrit- ical temperature was increased from 1 to 1000C/s. After heating at a rate of 1000C/s, the austenite volume fraction approached the paraequilibrium austenite content after 1200 s long holding. During heating at 1 0C/s, recrystallization was completed below 720 0C for all three starting microstructures (see Fig. 5.5), i.e. before austenite formation starts. This was confirmed by direct metallographic observations of the early stages of austenite formation in F-B-P, Fig. 5.10(a). Austenite nucleated at the boundaries of recrystallized ferrite grains in this case. A faster heating rate of 10 0C/s shifted recrystallization completion into the intercritical temperature region and resulted in concurrent recrystallization 78 5.1. Results Figure 5.8: Austenite formation kinetics during continuous heating: (a) in ferrite-pearlite-bainite, (b) temperature-heating rate map for 50 pct aust- enization. 79 5.1. Results Figure 5.9: Austenite formation kinetics at 770 0C after heating at (a) 1 0C/s and (b) 100 0C/s. 80 5.1. Results and austenite formation. Unrecrystallized regions were found to provide ad- ditional nucleation sites for austenite, Fig. 5.10(b). During heating at 100 0C/s austenite formation was found to initiate before the onset of recrys- tallization. As a result, a dense and relatively uniform distribution of fine martensite particles (i.e. intercritical austenite) was formed in the unrecrys- tallized ferrite matrix, as shown in Fig. 5.10(c). Different starting microstructures and different scenarios for the interac- tion between ferrite recrystallization and austenite formation resulted in a variety of austenite morphologies and distributions. Fig. 5.11 shows intercrit- ical austenite (martensite upon quenching) formed after continuous heating to 760 0C from either recrystallized (1 0C/s heating rate) or unrecrystallized structures (100 0C/s heating rate). For the fully recrystallized F-P material, both pearlite bands and boundaries of recrystallized ferrite grains provided nucleation sites for austenite, as illustrated in Fig. 5.11(a), while predomi- nantly banded austenite was found when austenite formed in unrecrystallized F-P, Fig. 5.11(d). The morphology and distribution of austenite formed in F-B-P and M was similar. After recrystallization was completed, austenite appeared along ferrite grain boundaries and formed a continuous boundary network, Fig. 5.11(b, c). In unrecrystallized F-B-P and M, a uniform dis- tribution of fine nearly equiaxed austenite particles was formed, Fig. 5.11(e, f). The resulting austenite grain size decreased with increasing heating rate, Table 5.1; faster heating enhanced austenite nucleation rates and reduced time available for the grain coarsening. To provide a comparison basis for analyzing the effect of incomplete re- crystallization on austenite formation, step-heating experiments, see Fig. 5.6, 81 5.1. Results Figure 5.10: Early stages of austenite formation in ferrite-bainite-pearlite during continuous heating to 740 0C at (a) 1, (b) 10, (c) 100 0C/s. (M: martensite, NF: unrecrystallized ferrite) 82 5.1. Results Figure 5.11: Austenite morphology after continuous heating to 760 0C at (a, b, c) 1 and (d, e, f) 100 0C/s in (a, d) ferrite-pearlite, (b, e) ferrite-bainite- pearlite, (c, f) martensite (M: martensite, F: ferrite). 83 5.1. Results Table 5.1: Austenite grain sizes (µm) after complete austenization. Initial microstructure Continuous heating, 0C/s Step heating, 0C/s 1 10 100 1-10 1-100 Ferrite-Pearlite 9.2 5.8 5.5 7.1 5.4 Ferrite-Bainite- Pearlite 6.8 4.2 3.4 6.8 6.2 Martensite 8.3 6.3 3.5 6.4 5.4 were conducted. First, samples were heated slowly at 1 0C/s to 720 0C, which is ∼10 0C lower than the austenite formation start temperature, to provide sufficient time for recrystallization to be completed and then heating rate was increased to either 10 or 100 0C/s. As an example, Fig. 5.12(a) shows the effect of heating rate on the austenite formation kinetics in the fully re- crystallized the F-B-P starting microstructure. In contrast to the continuous heating experiments, Fig. 5.8(a), the transformation curves were shifted to higher temperatures as heating rate increased. An increase in heating rate from 1 to 100 0C /s raised the transformation start temperature by ∼40 0C. Interestingly, the austenite formation rates as measured by the temperature required to reach an austenite fraction of 10, 50 and 90 pct were very similar for all three starting microstructures, see Fig. 5.12(b). The final austenite grain size was found to decrease with increasing heating rate, but the magni- tude of this decrease was, in general, lower for the step-heating than for the continuous heating experiments, Table 5.1. 84 5.1. Results Figure 5.12: Austenite formation kinetics during the step-heating experi- ments (a) in ferrite-bainite-pearlite initial microstructure, (b) temperature- heating rate austenization map (dashed lines are trend-lines). 85 5.1. Results 5.1.2 Recrystallization and austenite formation models Recrystallization model The JMAK equation, see Eqs. 2.8 and 2.10, and the additivity principle [106, 107], were employed to model recrystallization. Temperature dependence of the parameter b was expressed using the Arrhenius relationship: b = b0 · exp (−Q/R·T) (5.1) where b0 is the preexponential factor, Q is the effective activation energy, R and T have their usual meaning. Based on the isothermal recrystallization kinetics at 600, 625 and 650 0C, separate sets of the fitting parameters were obtained for the three start- ing microstructures, Table 5.2. The model parameters were found rather insensitive to the experimental errors and unique for each of the initial mi- crostructures. The quality of the fit for recrystallization tests conducted at 650 0C is shown in Fig. 5.3. For continuous heating experiments at 1 0C/s, the model predictions for the F-P and M initial microstructures are in close agreement with the experimentally measured recrystallization kinetics, Fig. 5.4. However, in the case of the F-B-P material, the model overestimates recrystallization rates in the initial stages of the process. The experimen- tal and modelling results are within ±7 0C at all times and the models are, thus, considered as a good representation of the recrystallization process for all initial microstructures. The overall conformity of the experimental and modelling results suggests the additive nature of the recrystallization process. 86 5.1. Results Table 5.2: Recrystallization model parameters. Initial microstructure n b0, s −n Q, kJ/mol Q/n, kJ/mol Ferrite-Pearlite 1.7±0.1 (1.1 · 1029) · 10±2 581±40 342±24 Ferrite-Bainite- Pearlite 1.4±0.1 (2.3 · 1027) · 10±2 531±30 379±21 Martensite 2.5±0.1 (1.3 · 1052) · 10±4 1011±50 404±20 The recrystallization models were subsequently applied to predict tempera- tures of recrystallization start and finish (here considered as 10 and 90 pct of recrystallization, respectively) for continuous heating at rates between 0.1 and 100 0C/s to create a temperature-heating rate recrystallization-austenite formation map as seen in Fig. 5.13. As heating rate increases completion of recrystallization is postponed to higher temperatures. The rate of recrys- tallization is fastest in F-B-P and slowest in F-P, while M recrystallizes at intermediate rates. The intercept of the austenite formation start temper- ature of 730 0C during continuous heating and temperatures required for recrystallization to be completed gives a critical heating rate below which austenite will form from a fully recrystallized microstructure. For heating rates above this critical value, recrystallization and austenite formation will, at least partially, take place simultaneously. The critical heating rate is 3 0C/s for F-P and 7 0C/s for F-B-P and M. The aforementioned agreement between experimental and modeling results within the margin of±7 0C trans- lates into ∼20 pct relative accuracy in determination of the critical heating rates in Fig. 5.13. 87 5.1. Results Figure 5.13: Temperature-heating rate recrystallization-austenite formation map. 88 5.1. Results Austenite formation model Austenite formation is a complex multistage process involving austenite nu- cleation, dissolution of individual carbide particles or pearlite colonies and ferrite-to-austenite transformation. Moreover, the potential interaction of re- crystallization and austenite formation adds further complexity as discussed above. In the present study a single model was developed to describe austen- ite formation for all initial microstructures after the completion of recrystal- lization. The model was based on the JMAK equation and the additivity principle. Actual austenite volume fractions were normalized by the orthoe- quilibrium austenite content, Eq. 5.2, for the intercritical temperature region of 690 to 812 0C, i.e. f eqγ = 25.78− 0.07405 · T + 5.36 · 10−5 · T 2 (5.2) where T is temperature,0C. Austenite formation start temperature ( fγ feqγ =0.05) as a function of heating rate, q, was expressed using a power function: As = 735 · q0.012 (5.3) The following model parameters were deduced from the results of the step-heating experiments using Rios’s method [155]: n = 0.4 ± 0.05, b0 = (3.6 · 1018) · 10±1 s−n, Q = 386 ± 15 kJ/mol. The JMAK model fit is in excellent agreement with the results of the step-heating experiments at 10 and 100 0C/s, Fig. 5.12(a), while for heating at 1 0C/s the model gives good predictions for the first 50 pct transformed, but then overestimates 89 5.2. Discussion austenite content for higher fractions. However, it is worth noting that for intercritical annealing, the initial portion of austenite formation (i.e. up to 50 pct) is primarily of interest. Taking into account the aforementioned relative accuracy of ±5 pct for the austenite content measurements relying on dilation, the model provides good description of the austenite formation kinetics during holding at 770 0C after 1 0C/s heating for all three starting microstructures, Fig. 5.9(a). 5.2 Discussion For ideal site-saturated nucleation and constant growth conditions, the ex- ponent n in the JMAK model is equal to 3. The exponents found in this study for recrystallization of the F-P and F-B-P initial microstructures are equal to 1.4 and 1.7 respectively, Table 5.2, and close to the values typically obtained for recrystallization of cold-deformed iron and steels [16, 18, 20]. The difference in the ideal and measured exponents is because the simpli- fying assumptions of the JMAK model (homogeneous nuclei distribution, site saturation or constant nucleation rate, constant and isotropic growth rate) are not fulfilled during recrystallization due to the time- and/or spa- tial dependence of the nucleation and growth rates, see e.g. [9]. However, the exponent for M is the highest among the three microstructures studied here and approaches the ideal value of 3; this indicates a more homogeneous structure of M compared to the other two initial microstructures. The Q/n ratio representing, in a first approximation, the average activation energy for the migration of high-angle grain boundaries, Table 5.2, was found to 90 5.2. Discussion be nearly constant for the three starting microstructures with the average of 375 kJ/mol being similar to 330kJ/mol found for another DP 600 steel (Fe-0.06C-1.86Mn-0.16Mo) [18]. The following simple physical model is proposed to explain the observed recrystallization rates in different starting microstructures. Recrystallization proceeds through a nucleation and growth. Assuming the site saturation nu- cleation conditions and three-dimensional growth, the recrystallized volume fraction is equal to: X = 1− exp (−N · (V · t)3) (5.4) where N is the nuclei density and V is the growth rate. Since annealing temperatures in isothermal recrystallization experiments are comparatively low (≤6500C), no substantial ferrite grain coarsening is expected such that the nuclei density can be assumed to be equal to: N = ( pi · (dα)3 6 )−1 (5.5) where dα is the average ferrite grain size after recrystallization completion. Growth rate of a recrystallizing grain is equal to the product of grain boundary mobility, M , and driving pressure, P , Eq. 2.1. The mobility of high angle grain boundaries is assumed here to be the same for all three ini- tial microstructures. The driving pressure for recrystallization is the energy stored in form of dislocations having two sources: dislocations formed during phase transformations prior to cold-rolling (relevant only to highly deformed structures, e.g. bainite or martensite), PTransformation, and dislocations stored 91 5.2. Discussion in the course of cold-rolling, PDeformation: P = PTransformation + PDeformation (5.6) To estimate the driving pressure, a relative softening during annealing for all three initial microstructures was considered: S = H0 −H H0 −HRex (5.7) where H0, H, HRex is the microhardness of as-deformed, partially recrystal- lized and fully recrystallized material, respectively. For the F-B-P initial microstructure the relative softening was in a close agreement with the recrystallization percentage as shown in Fig. 5.14. There- fore, the total hardness change in the course of annealing can be assumed to be due to the dislocation density decrease, ∆ρdisl, neglecting all other pos- sible factors affecting hardness, e.g. grain size, solid solution strengthening, inherent difference in hardness of different microconstituents etc.: P ≈ 0.5 ·G · c2 ·∆ρdisl (5.8) where G is the shear modulus of iron, equal to 83 GPa at room temperature [153]; c is the magnitude of the Burger vector. The dislocation density decrease is related to the yield strength change, ∆σY : ∆σY ≈ 0.5 ·G · c · √ ∆ρdisl (5.9) 92 5.2. Discussion Figure 5.14: Comparison of relative softening estimated using hardness changes and recrystallized percentage quantified through metallographic measurements. 93 5.2. Discussion In a first approximation, the yield strength change (in MPa) is equal to one third of the Vickers hardness drop (in MPa): ∆σY ≈ H0 −HRex 3 (5.10) It is noteworthy that a material is subjected to a strain of∼8 pct in the course of hardness testing (Tabor’s relation). Therefore, for a cold-rolled material possessing limited ability to strain-harden, hardness will provide an accurate estimate of yield strength. While hardness will overestimate yield strength for a fully recrystallized material; as a result Eq. 5.10 will underestimate the yield strength change. However, in the present study relative magnitudes of the yield strength change for different initial microstructures are of primary interest and the aforementioned artifact is neglected. Combining Eqs. 5.8-5.10, the stored energy is proportional to the square of the hardness change (in MPa) for the F-B-P initial microstructure: P ≈ 2 · (H0 −HRex) 2 9 ·G (5.11) Only a fraction of the softening for the F-P and M initial microstructures can be attributed to recrystallization, as other processes also lowering hard- ness took place in these materials, Fig. 5.14. In F-P the additional softening mechanism is pearlite spheroidization. Cold-deformation leads to the frag- mentation of cementite lamellas thereby promoting the spheroidization of pearlite upon subsequent annealing [37, 60]. Even in the fully recrystallized microstructure of F-P, unspheroidized areas can still be found, as shown in Fig. 5.5(a). Spheroidization took place concurrently with recrystallization 94 5.2. Discussion and, therefore, it is rather challenging to discriminate their individual effects on hardness changes. However, for 0.1C (wt. pct) plain carbon steel com- plete spheroidization of fine pearlite leads to ∼20 HV hardness decrease [156], while the total softening for the F-P initial microstructure after isothermal annealing was 82 HV. Therefore, the hardness changes are primarily due to recrystallization and Eq. 5.11 can still be applied for an order of magni- tude estimate of the stored energy for F-P. Finally, turning to the case of M, during cold-deformation of a low-carbon martensite, laths are replaced with dislocation cell structures [157, 158]. Upon subsequent annealing the hardness of M dropped by ∼150 HV within the first 10 s without any evi- dence of recrystallization, Fig. 5.2. This initial softening was thus ascribed to martensite tempering. Greater annealing times resulted in a gradual hard- ness decrease through recrystallization of the tempered M. Typically, high temperature anneals, such as those used for the recrystallization experiments in the present study, lead to extremely rapid tempering. For instance, Caron and Krauss [159] found in 0.2C (wt. pct) martensite a hardness drop of 50 pct due to carbide precipitation after 0.26 s long heat treatment at 650 0C. Thus, tempering was assumed to take place first, followed by recrystalliza- tion for the M initial microstructure. Hardness achieved after the first 10 s of annealing, H(10s), is assumed to be the initial hardness for the estimates of the stored energy to separate this from the tempering effect: P ≈ 2 · (H(10s)−HRex) 2 9 ·G (5.12) Based on the above arguments, the estimated values for the nuclei density and stored energy are summarized in Table 5.3. They are the lowest for 95 5.2. Discussion Table 5.3: Nuclei density and stored energy for recrystallization. Initial microstructure Nuclei density, 10−15 ·m−3(Eq. 5.5) Stored energy, MPa (Eq. 5.11, 5.12) Ferrite-Pearlite 4.4 1.8 Ferrite-Bainite- Pearlite 14.4 4.2 Martensite 7.0 5.3 the F-P initial microstructure. The M microstructure possessed the highest stored energy, while the highest number of nuclei formed during the F-B-P recrystallization. The average nuclei density and stored energy representing an average microstructure compartment were used to estimate ratios of characteristic times required for 50 pct recrystallization, t50, for F-P and F-B-P initial microstructures using Eqs. 2.1, 5.4, 5.5, 5.11: t50 ∝ dα (H0 −HRex)2 (5.13) Whereas for M the characteristic time t50 was evaluated according to: t50 ∝ dα (H(10s)−HRex)2 (5.14) The obtained ratios of annealing times needed to reach 50 pct of re- crystallization for different initial microstructures, Table 5.4, replicate the experimentally observed trends suggesting similar recrystallization rates for the F-B-P and M initial microstructures, and longer times required for the F- P recrystallization. Moreover, the ratios of times for 50 pct recrystallization are similar to those calculated using the JMAK models. 96 5.2. Discussion Table 5.4: Ranking of initial microstructures based on recrystallization rates. Ratio of initial microstructures Ratios of times for 50pct recrystallization Based on hardness change and grain size (Eqs. 5.13, 5.14) Models (T = 7000C) M/FBP 1.0 1.3 M/FP 0.3 0.4 FBP/FP 0.3 0.3 To rationalize the observed trends for austenite formation, nucleation and growth also need to be considered. Two conditions must be met for the nucle- ation to take place. First of all, according to the iron-carbon phase diagram, carbon solubility in austenite is much higher than in ferrite, and austenite nuclei will form at carbon-rich sites. Secondly, classical nucleation theory predicts preferred nucleation at high-energy nonequilibrium defects, which lower the activation barrier for nucleation, i.e. heterogeneous nucleation. For a distribution of cementite in a ferrite matrix, such as fully recrystallized F-B-P and M, Fig. 5.5(b, c), both conditions are met for cementite particles located at ferrite grain boundaries as observed experimentally, Fig. 5.10(a). In the fully recrystallized F-P, preferable nucleation sites for austenite are ferrite-pearlite interfaces at the beginning of the transformation, while fer- rite grain boundaries become active nucleation sites at later transformation stages, this being observed in as-quenched samples with different contents of martensite, i.e. austenite at an intercritical temperature, e.g. Fig. 5.11(a). Assuming that the density of austenite grains after the transformation com- pletion provides some indication of the trends in the nuclei density at the 97 5.2. Discussion beginning of the transformation, more nuclei were formed during faster heat- ing in the step-heating experiments, Table 5.1. Nucleation and growth are competing phenomena. Higher heating rates lead to less growth of nuclei at any given temperature and promote additional nucleation at higher super- heating. As shown in Fig. 5.13, for continuous heating experiments at a rate above the critical value, austenite forms in a partially recrystallized microstructure. Considering that during continuous heating at 1 and 100 0C/s, austenite forms within the same temperature range of 730-850 0C and taking into ac- count the hundredfold difference in time available for the transformation, e.g. Fig. 5.8(a), the rate of austenite formation in unrecrystallized material is accelerated by one hundred times. Comparison of austenite formation ki- netics during the continuous and step-heating experiments reveals that the presence of unrecrystallized regions lowers the transformation start temper- atures during heating at 10 and 100 0C/s for all initial microstructures by approximately 20 and 40 0C, respectively, e.g. compare Figs. 5.8(a) and 5.12(a). The austenite formation-recrystallization interaction also affects the austenite nuclei distribution and density as can be seen in Figs. 5.10 and 5.11. Employing the final austenite grain size as a measure of the nuclei density, i.e. similarly to Eq. 5.5, as much as six times more nuclei were formed during the continuous heating than during the step-heating experi- ments for a given heating rate, see Table 5.1. These observations are consis- tent with previous studies on the recrystallization-austenite formation inter- action where preferential nucleation of austenite in unrecrystallized regions was reported [37,60,61,63]. 98 5.2. Discussion The higher austenite nuclei densities in partially recrystallized microstruc- tures can be explained with the aid of the classical nucleation theory. The activation barrier for nucleation, ∆G?, is lowered by increasing the driving pressure for austenite formation, ∆gV , by the magnitude of the stored energy, P , otherwise released in the course of recrystallization: ∆G? ∝ U (β) (∆gV + P ) 2 (5.15) where U (β) is the shape factor (0 < U < 1) that is related to the benefits of heterogeneous nucleation sites in lowering the activation barrier. For instance, at the austenite formation temperature of 730 0C, the chemical driving pressure for the nucleation is equal to 82 MPa under orthoequilibrium conditions based on the Thermo-Calc calculations, while the stored energy varies between 1.7 MPa for the F-P initial microstructure and 5.3 MPa for M, Table 5.3. An additional contribution of 5 MPa is equivalent to a 10 0C temperature drop for the same magnitude of the driving pressure of 82 MPa for the nucleation. Local variations in the stored energy could even magnify this effect of the stored energy on austenite nucleation. Moreover, the quality of nucleation sites as quantified by the shape factor in Eq. 5.15 may also be improved in deformed material thereby lowering the energy barrier for the nucleation even further. Combination of the lower activation energy for nucleation and the higher density of potential nucleation sites increases the nucleation rate in partially recrystallized or unrecrystallized material. However, the enhancement of nucleation rate by the aforementioned fac- tor of six alone can not account for the observed hundred-fold increase in the transformation rate, i.e. the growth rate changed dramatically as well. 99 5.2. Discussion Considering again the case of austenite formation during continuous heating at 1 or 100 0C/s between 730 and 850 0C, Fig. 5.8(a), the ratio of the final austenite grain sizes was approximately equal to two, see Table 5.1. Taking into account the hundredfold difference in time available for the transforma- tion, the average velocity of austenite-ferrite interface during the fast heating is estimated to be accelerated by at least 50 times. Further, austenite grain coarsening may have taken place and its extent will be more pronounced during slow heating. Then, the growth rate increase might be even greater than 50 times. One possible explanation for the fast austenite growth in non- recrystallized microstructures may be related to the presence of fast diffusion paths for substitutional alloying elements in the deformed ferrite. The en- hanced diffusion of austenite stabilizing elements such as manganese toward the ferrite-austenite interface may accelerate austenite formation. The fast growth rate could be even further amplified by reduced solute drag [19,57,58]. Solutes exert lower pressures on a boundary moving rapidly, this leading to its apparent mobility increase. Another consequence of the fast austenite formation during rapid continu- ous heating is a potentially inhomogeneous carbon distribution after complete austenization. For heating at a constant rate, the carbon diffusion distance can be estimated from: L = √ DγC · T2 − T1 q (5.16) where T1 = 730 and T2 = 850 0C are the temperatures for start and finish of austenite formation during heating at a rate q, i.e. 1 or 100 0C/s, respectively, DγC is the average carbon diffusion coefficient in austenite for this temperature 100 5.2. Discussion range [160]. The carbon diffusion distance in austenite decreases from 14 to 1.4 µm when heating rate is increased from 1 to 100 0C/s, i.e. the diffusion distance in the latter case is smaller than the radius of the austenite grain, Table 5.1. The through-thickness manganese distribution is not uniform in the in- dustrially produced steel sheets as evidenced by the banded structure of pearlite in F-P, Fig. 4.1(a). The variation in manganese content is typi- cally inherited from casting and remains unaffected by the laboratory re- austenitization heat treatment at 900 0C for 1800 s in the present study, as much higher soaking times and temperatures would have to be employed for the homogenization treatment [161]. The nonuniform distribution of man- ganese leads to pearlite banding in F-P, whereas, there are no obvious signs of banding in the other two initial microstructures (F-B-P, M). Intercritical annealing of the F-P initial microstructure leads to the development of the banded austenite structure, Fig. 5.11(a, d). Primarily because of its higher carbon concentration, pearlite serves as a preferential site for austenite nu- cleation and growth. In the F-B-P and M materials carbon is more uniformly distributed and manganese segregation, in the present case, does not have any major effect on austenite nucleation and morphology. 101 Chapter 6 Austenite decomposition after intercritical annealing 6.1 Results 6.1.1 Experimental results In the previous chapter it was demonstrated, that different morphology, size and distribution of ferrite and austenite in intercritically annealed samples could be achieved by heat treating different initial microstructures or em- ploying the recrystallization-austenite interaction. Six ferrite-austenite mi- crostructures formed after different holdings at 770 0C were used for the austenite decomposition experiments, see Fig. 6.1. The thermal paths im- itated intercritical annealing on a hot-dip galvanizing line and involved in- tercritical annealing at 770 0C, cooling at 3, 10 and 30 0C/s and 180 s long holding at 465 0C, as schematically shown in Fig. 6.2. Results of the stereological analysis for the aforementioned six microstruc- tures, Fig. 6.1, are summarized in Table 6.1. All of the microstructures con- tained ∼50 pct of austenite. Holding times at 770 0C to reach this austen- ite content varied between 70 and 1000 s; shorter times were needed when 102 6.1. Results Figure 6.1: 50 pct ferrite - 50 pct austenite microstructures after intercritical annealing at 770 0C: (a, b, c) austenite formed after recrystallization com- pletion (1 0C/s heating), (d, e, f) austenite formed in unrecrystallized mi- crostructure (100 0C/s heating); (a, d) ferrite-pearlite, (b, e) ferrite-bainite- pearlite, (c, f) martensite initial microstructures prior to intercritical anneal- ing. 103 6.1. Results Figure 6.2: Austenite decomposition experiments. austenite formed in unrecrystallized microstructures. The ferrite-austenite interface area per unit volume was about two times higher for unrecrystal- lized F-B-P and M than for the other four materials. The effect of cooling rate on austenite decomposition kinetics during con- tinuous cooling and holding at 465 0C, as an example, is shown in Fig. 6.3 for the ferrite-austenite microstructure developed in recrystallized F-P mate- rial, i.e. Fig. 6.1(a). In the beginning of cooling, austenite content remained unchanged. A certain undercooling was necessary to initiate the austenite-to- ferrite transformation. The magnitude of the required undercooling increased with cooling rate. At higher temperatures austenite transformed into ferrite, while bainite was formed at lower temperatures. As cooling rate increased, the transformation curves were shifted to lower temperatures, Fig. 6.3(a). The more austenite was present at the beginning of the 465 0C holding, the higher bainite volume fraction was formed during the hold, Fig. 6.3(b). The process of bainite formation was largely completed in the first 40 s of the holding. 104 6.1. Results Table 6.1: Results of stereological analysis of six ferrite-austenite microstruc- tures for austenite decomposition experiments. Initial microstructure Austenite formation conditions Austenite content, pct Ferrite-austenite interface area per unit volume, m2/m3 · 10−6 Austenite formed after recrystallization completion Ferrite- pearlite 1 0C/s - 770 0C - 1000 s 46 ± 3.5 0.35± 0.10 Ferrite- bainite- pearlite 1 0C/s - 770 0C - 600 s 47± 2.7 0.53± 0.09 Martensite 1 0C/s - 770 0C - 600 s 44± 4.0 0.41± 0.08 Austenite formed in unrecrystallized microstructure Ferrite- pearlite 100 0C/s - 770 0C - 300 s 48± 3.0 0.43± 0.14 Ferrite- bainite- pearlite 100 0C/s - 770 0C - 90 s 50± 4.5 0.99± 0.20 Martensite 100 0C/s - 770 0C - 70 s 49± 3.1 0.96± 0.17 105 6.1. Results Figure 6.3: Kinetics of austenite decomposition after intercritical annealing of recrystallized ferrite-pearlite initial microstructure: (a) cooling from 770 0C to 465 0C, (b) 180 s holding at 465 0C. 106 6.1. Results The effect of the six types of ferrite-austenite microstructures on austen- ite decomposition kinetics is shown in Fig. 6.4 for cooling at 30 0C/s. Taking into account the relative accuracy of ±5 pct for austenite content measure- ments employing dilatometer, the six curves can be grouped into two classes with either slower or faster ferrite formation rates, Fig. 6.4(a). Austenite decomposed slower for the microstructures shown in Fig. 6.1(a-d) which had a relatively low ferrite-austenite interface area, Table 6.1. On the other hand, the fine scale of the microstructures developed in unrecrystallized F-B-P or M materials, Fig. 6.1(e, f) and Table 6.1, facilitated the ferrite formation process. During the 465 0C hold a somewhat different trend was observed: unrecrystallized microstructures were more resilient against bainite forma- tion, Fig. 6.4(b). Three microstructural components were found after complete intercritical annealing cycle: ferrite, bainite and martensite, Fig. 6.5. Ferrite can be fur- ther classified into two types: ferrite that is not transformed into austenite during intercritical annealing will be referred to as intercritical ferrite; and the one formed during cooling - epitaxial ferrite as no nucleation is involved in its formation [42–47]. According to the temperature - carbon concentra- tion map identifying different types of bainite for ternary steels containing 2 wt. pct of Mn [67], i.e. similar to the chemical composition of the inves- tigated steel in the present study, see Fig. 2.12 and Table 4.1, the holding temperature of 465 0C lies on the boundary between regions for upper and lower bainites. Therefore, both types of bainite are expected to be present in the final microstructure. Bainite and martensite had the distribution and morphology inherited from austenite, e.g. compare Figs. 6.1 and 6.5. Higher 107 6.1. Results Figure 6.4: Effect of microstructure after intercritical annealing on kinetics of austenite decomposition: (a) cooling from 770 0C to 465 0C at 30 0C/s, (b) subsequent 465 0C holding for 180 s. (Note: open symbols correspond to austenite formed after recrystallization completion, solid symbols - austenite formed in unrecrystallized microstructure) 108 6.1. Results magnification was needed to discriminate them as indicated by the inserts in Fig. 6.5. Bainite was nearly always surrounded by a rim of marten- site, this suggesting that the interior of the austenite particles was a more suitable nucleation site for bainite than the vicinity of the ferrite-austenite interface. The fine structure of the unrecrystallized F-B-P and M materials was retained through the entire annealing cycle as illustrated in Figs. 6.5(f, e). In the present study it was challenging to distinguish bainite from ferrite during the microstructure analysis. Based on fifteen micrographs of recrys- tallized M after intercritical annealing with 3 0C/s cooling, see Fig. 6.5(c), average volume fraction of areas, where bainite was readily distinguishable, was equal to 10 pct and 6 pct for the areas where discriminating bainite from ferrite was ambiguous. Therefore, bainite content can in this case be anywhere between 10 and 16 pct. These lower and upper estimates of bainite content translated into a relative accuracy of ±20 pct. For the four partially austenized microstructures with slower rates of epi- taxial ferrite growth upon cooling, volume fraction of epitaxial ferrite was found to be relatively independent of cooling rate, the cumulative content of bainite and martensite on average was equal to ∼30 pct as can be seen in Fig. 6.6. Bainite content increased slightly at the expense of martensite as cooling rate was raised. For the F-P initial microstructure, there was no significant effect of forming austenite in either recrystallized or unrecrystal- lized materials on the microconstituents content in the final microstructure (compare solid and dashed contours in Fig. 6.6(a)). However, for F-B-P and M the recrystallization-austenite formation interaction affected the final 109 6.1. Results microstructures by causing a greater fraction of austenite to be transformed into ferrite rather than bainite, see Figs 6.6(b) and (c); the cumulative con- tent of bainite and martensite in this case was equal to ∼25 pct for all cooling rates. 6.1.2 Austenite decomposition model The austenite decomposition kinetics was described using the JMAK model and the additivity principle, Eqs. 2.8 and 2.10. Two sets of the model parameters were obtained as summarized in Table 6.2, for the slower and faster austenite decomposition observed experimentally, see e.g. Fig. 6.4. The range of parameters provides the description of austenite decomposi- tion kinetics within the accuracy of experimental measurements. Ferrite and bainite transformations were assumed to take place sequentially. Based on the experimental observations, bainite formation was initiated when the re- maining austenite content reached ∼25-30 pct. Then the amount of bainite formed during cooling was equal only to ∼5-10 pct, e.g. see Fig. 6.3(a), i.e. comparable to the measurement accuracy of the overall bainite content. Fer- rite was thus the dominant austenite decomposition product during cooling. Both ferrite and bainite formation during cooling were described using the same model. The exponent n of ∼1 was typically reported in the previously developed models employing the JMAK equation for ferrite formation from fully austenized states, see e.g. [109, 111]. However, in the present model describing ferrite formation in partially austenized microstructure, the ex- ponent of 0.05 or 0.1, see Table 6.2, was found to replicate the continuous cooling transformations empirically including the stagnation in austenite con- 110 6.1. Results Figure 6.5: Final microstructures after intercritical annealing at 770 0C fol- lowed by cooling at 3 0C/s and 465 0C hold for 180 s: (a, b, c) austen- ite formed after recrystallization completion, (d, e, f) austenite formed in unrecrystallized microstructure; (a, d) ferrite-pearlite, (b, e) ferrite-bainite- pearlite, (c, f) martensite initial microstructures prior to intercritical anneal- ing. (Note: F - ferrite, B - bainite, M - martensite) 111 6.1. Results Figure 6.6: Analysis of final microstructures obtained by decomposition of austenite formed after recrystallization completion (solid lines) or in unre- crystallized material (dashed lines) for (a) ferrite-pearlite, (b) ferrite-bainite- pearlite and (c) martensite initial microstructures. 112 6.1. Results Table 6.2: Austenite decomposition model parameters. Slower austenite decomposition Faster austenite decomposition Austenite decomposition during cooling (epitaxial ferrite and bainite) n = 0.1± 0.02 n = 0.05± 0.02 b = (0.82± 0.07) + 0.003 · T − 0.44 · 10−5 · T 2 b = − (1.9± 0.08) + 0.0133 · T − 1.33 · 10−5 · T 2 Bainite starts to form when fγ = 0.3± 0.03 fγ = 0.25± 0.02 Bainite formation during 465 0C holding n = 1± 0.05 b = 0.3 · fγ(t = 0)− (0.04± 0.01) fmaxB = 2 · fγ(t = 0)− (0.32± 0.02) n = 1± 0.05 b = 0.6 · fγ(t = 0)− (0.1± 0.01) fmaxB = 2 · fγ(t = 0)− (0.34± 0.02) tent in the beginning of cooling. Temperature dependence of the parameter b was described using a second order polynomial rather than the Arrhenius re- lationship. To ensure that the model could adequately describe the cessation of the bainite formation process during the 465 0C hold, see e.g. Figs. 6.3(b) and 6.4(b), bainite fractions, fB, were normalized over the maximum amount of bainite, fmaxB , that could form during the holding, fB/fmaxB , see Table 6.2. The fmaxB parameter was proportional to the volume fraction of austenite at the beginning of the holding, fγ(t = 0). Any remaining austenite at the end of the 465 0C hold was assumed to transform fully into martensite during the final cooling to room temperature. Examples illustrating the quality of the model fit to the experimental data are shown in Figs. 6.3 and 6.4. The model somewhat underestimated austenite volume fraction in the beginning of cooling, however, by the end of the 465 0C holding, the model output always reached the actual austenite content due to limiting the total fraction transformed at this temperature to fmaxB . 113 6.2. Discussion 6.2 Discussion For every austenite decomposition experiment conducted in the present study, in the beginning of cooling there was a temperature range when austenite content remained unchanged, see e.g. Figs. 6.3(a) and 6.4(a). This temper- ature range is referred to as a stagnant stage in the literature [47,50–52,55]. As discussed in Chapter 2, upon cooling the ferrite-austenite interface has to pass the manganese-rich region formed during prior austenite growth. This creates obstructions for the interface movement, as austenite is more stable within this region in comparison with its interior possessing nominal concen- tration of manganese. Ferrite formation in the unrecrystallized and partially austenized F-B-P and M initial microstructures was substantially faster than in the other four ferrite-austenite microstructures, Fig. 6.4(a). These two materials had finer structure and a large ferrite-austenite interface area, recall Figs. 6.1(e, f) and Table 6.1. To verify if factors, other than the fineness, affected the transfor- mation rate, velocities of the ferrite-austenite interface were evaluated based on the experimentally measured kinetics of austenite decomposition and ge- ometrical assumptions. Ferrite formation during cooling in the recrystallized and unrecrystallized F-B-P material after partial austenization, Figs. 6.1(b, e), was considered. In the former case, geometry of the ferrite growth was simplified to a shrinking spherical shell of austenite occupying the prior fer- rite grain boundaries, Fig. 6.7(a). Austenite volume fraction can then be 114 6.2. Discussion Figure 6.7: Adopted geometries of ferrite growth in recrystal- lized/unrecrystallized and partially austenized ferrite-bainite-pearlite initial microstructure: (a) shrinking austenite shell, (b) shrinking spherical austen- ite particles. (Red arrows indicate dirrection of ferrite-austenite interface movement) written in the following way: fγ = 4pi/3 ( R3α −R3γ ) 4pi/3 ·R3α (6.1) where Rα is a radius of the prior ferrite grains (before austenite formation) and Rγ is the distance from the center of the prior ferrite grain to the ferrite- austenite interface, see Fig. 6.7(a) for an illustration. Similarly, the ferrite-austenite interface area per unit volume is equal to: ρα/γ = 4pi ·R2γ 4pi/3 ·R3α (6.2) Radius of the prior ferrite grain, Rα, calculated using initial values for ρα/γ and fγ from Table 6.1, and Eqs. 6.1-6.2, is equal to 3.8 µm. This value is approximately equal to the average recrystallized ferrite grain radius of 2.6 µm reported in the previous chapter if the factor of 1.2 is taken into account 115 6.2. Discussion for the conversion from equivalent area to equivalent volume radius [162]. Velocity of the ferrite-austenite interface as a function of temperature can be calculated using the experimentally measured changes in austenite volume fraction, 4fγ: Vα/γ ≈ R 3 α 3R2γ · 4fγ4t (6.3) where 4t is time step (in seconds) and Rγ(0) = 3.1µm corresponds to the the initial austenite content of 47 pct, Table 6.1. After partial austenization of the unrecrystallized F-B-P initial microstruc- ture, a relatively uniform distribution of nearly equiaxed and occasionally im- pinging austenite particles was formed, see Fig. 6.1(e). This microstructure was simplified to initially overlapping spherical austenite particles that were shrinking during ferrite formation upon cooling as schematically shown in Fig. 6.7(b). Therefore, extended austenite volume fraction, ( f ?γ )EX , [99–101] and extended ferrite-austenite interface area per volume, ( ρ?α/γ )EX , [163] need to be introduced: f ?γ = 1− exp ( − (f ?γ )EX) (6.4) ρ?α/γ = ( ρ?α/γ )EX ( 1− f ?γ ) (6.5) Alternatively, the extended ferrite-austenite interface area per volume can 116 6.2. Discussion be expressed as: ( ρ?α/γ )EX = 4pi · (R?γ)2 4pi/3 · (R?γ)3 · ( f ?γ )EX (6.6) where R?γ is the radius of the shrinking austenite particle as shown in Fig. 6.7(b). For initial values of f ?γ and ρ ? α/γ reported in Table 6.1, the austenite particle radius is equal to 1.1 µm which is in a good qualitative agreement with the microstructure shown in Fig. 6.1(e). The ferrite-austenite interface velocity can then be calculated using the following expression: V ?α/γ = 1 ρ?α/γ · 4fγ4t (6.7) The ferrite-austenite interface velocity was calculated for cooling at 3 0C/s and temperature range of 770-550 0C where epitaxial ferrite was ex- pected to be the only product of austenite decomposition, Fig. 6.8. The velocities for the two considered cases were essentially equal and the faster ferrite formation in unrecrystallized and partially austenized F-B-P and M materials can be attributed primarily to the more extensive transformation front. The velocity reaches the maximum at ∼660 0C, this peak is simi- lar to the “nose” commonly observed for the ferrite formation curve on the time-temperature-transformation diagram. Even for the shortest intercritical annealing time of 70 s at 770 0C em- ployed to produce one of the six microstructures for the austenite decom- position experiments, see Table 6.1, carbon diffusion distance in austenite is ∼8 µm (diffusion coefficient taken from [160]) which is greater than half 117 6.2. Discussion Figure 6.8: (a) Evolution of austenite content and (b) corresponding changes in ferrite-austenite velocity during cooling at 3 0C/s of recrystallized and un- recrystallized ferrite-bainite-pearlite initial microstructure after partial aust- enization. 118 6.2. Discussion width of the austenite regions shown in Fig. 6.1. Therefore, a uniform car- bon concentration is established before cooling, as schematically shown in Fig. 6.9(a). During the epitaxial growth of ferrite, carbon is rejected into austenite; a gradient in carbon concentration is thus created, Fig. 6.9(b). As soon as conditions necessary for bainite formation are achieved, it forms in the interior of the austenite particles, where carbon concentration is lower and austenite thermodynamically is less stable, see Fig. 6.9(c). Depending on the width of the manganese-rich region discussed previously (which is determined by the transition between the growth of austenite without and with partitioning of austenite stabilizers), it may also contribute to the sta- bilization of the outer austenite areas. During cooling to room temperature, any remaining austenite is transformed into martensite surrounding bainite. This leads to a particular arrangement of microconstituents after complete intercritical annealing cycle, see e.g. Fig. 6.5. Moreover, faster cooling leads to steeper carbon gradients (carbon diffusion distance in austenite is ∼4 and 1.3 µm during cooling between 770 and 465 0C at 3 and 30 0C/s , respec- tively). Greater fraction of austenite is then transformed into bainite after faster cooling during the 465 0C hold as observed experimentally, see e.g. Fig. 6.3(b). 119 6.2. Discussion Figure 6.9: Schematics of carbon redistribution leading to formation of martensite rim around bainite: (a) after holding at intercritical temperature, (b) after cooling to bainite start temperature, (c) at room temperature. 120 Chapter 7 Application of microstructure evolution model to continuous annealing 7.1 Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution2 Laser ultrasonics for metallurgy (LUMet) system permits in-situ characteri- zation of materials in the course of thermomechanical processing. This tech- nique is remote, nondestructive and probes the bulk of sample. Various metallurgical phenomena can be studied using laser ultrasonics more rapidly than conventional methods, this can facilitate the development and valida- tion of metallurgical process models. In this section applicability of laser ultrasonics is evaluated for the monitoring of the microstructure evolution during intercritical annealing. Isothermal recrystallization during annealing of F-B-P at 625 0C was 2This section was published in the conference proceedings: M. Militzer, T. Garcin, M. Kulakov and W. J. Poole, “Laser ultrasonics for in-situ monitoring of microstructure evolution in steels,” in Baosteel Biennial Academic Conference, Shanghai, China, June 4-6, 2013. 121 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution Figure 7.1: Recrystallization progress and changes in laser ultrasonic veloc- ity during two sequential isothermal anneals of ferrite-bainite-pearlite initial microstructure at 625 0C. monitored first using laser ultrasonics. The evolution of ultrasonic velocity along with the recrystallization progress is shown in Fig. 7.1. Relatively small changes in velocity were observed in the initial stages of annealing. While during the second half of recrystallization, the ultrasonic velocity in- creased by ∼110 m/s and reached a constant value in the fully recrystallized material. The constancy of the velocity during annealing after the same fully recrystallized sample was reheated again to 625 0C, further confirms that the velocity changes are associated with recrystallization, see Fig. 7.1. The speed of sound in any medium is related to its bulk modulus, E, and 122 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution density, ρ (Newton-Laplace equation): VLUS = √ E ρ (7.1) In a polycrystalline material, the bulk modulus is affected by the texture due to the elastic anisotropy. Therefore, in a first approximation, the ve- locity changes in the present case may reflect the evolution of texture. Re- crystallization is accompanied by the changes in texture: Typically, for low- carbon steels the strengthening of the γ− fiber component is reported, see e.g. [9, 13, 14]. Grains belonging to the high stored energy γ− fiber recrys- tallize faster compared to those of the α− fiber. When recrystallization is confined to the γ− fiber, the orientation distribution may remain unchanged; this provides a hypothetical explanation of the relative constancy of the ultra- sonic velocity during the first ∼40 pct of recrystallization. Further velocity increase may be attributed to the consumption of the α− fiber by recrystalliz- ing grains developed in the γ− fiber. Similar conclusions were made based on the calculations of the ultrasonic velocity using experimentally measured tex- ture at different stages of recrystallization for an interstitial-free steel [144]. Laser ultrasonics was also employed to monitor phase transformations during continuous heating, when, in addition to recrystallization, austenite formation took place. The changes in ultrasonic velocity, the progress of re- crystallization and austenite formation during heating at 1 0C/s are shown in Fig. 7.2(a). For temperatures below ∼670 0C, the velocity decreased nonlinearly in the course of heating due to the nonlinear temperature de- pendence of magnetic ordering and elastic constants [164]. The ultrasonic velocity started to increase at ∼670 0C when ∼40 pct of recrystallization 123 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution was reached. Following recrystallization completion at 700 0C, the veloc- ity resumed to decrease upon further heating. Austenite formation did not cause significant changes in the velocity due to similar rates of the ultrasonic waves propagation in ferrite and austenite. The inflection at ∼745 0C was attributed to the ferromagnetic-paramagnetic transformation, i.e. the Curie temperature, as also reported for other low alloy steels [149, 150]. Above ∼830 0C the ultrasonic velocity was a linear function of temperature in the single phase austenitic region. The change in the velocity slope correlated well with the completion of austenite formation. During continuous heating at 10 0C/s, the velocity decreased monoton- ically up to the Curie temperature of ∼745 0C as shown in Fig. 7.2(b). According to metallographic observations, austenite started to form in a par- tially recrystallized microstructure. The absence of the velocity increase cor- responding to recrystallization also indicated the recrystallization-austenite formation interaction. The velocity variations in the intercritical region were different from that during 1 0C/s heating when austenite formed in a fully recrystallized microstructure. The ultrasonic velocity remained nearly con- stant between ∼745 0C and 785 0C and decreased slightly in the last stages of austenite formation. At higher temperatures, a linear decrease of the velocity was observed that is consistent with the behavior in single phase austenite. However, the completion of austenite formation was not as readily detectable as for the 1 0C/s heating case discussed above. The evolution of austenite content and the corresponding changes in the ultrasonic velocity during the complete intercritical annealing cycle is shown in Fig. 7.3. As shown above for continuous heating at 1 0C/s, the observed 124 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution Figure 7.2: Recrystallization, austenite formation and changes in laser ul- trasonic velocity during (a) 1 and (b) 10 0C/s continuous heating of ferrite- bainite-pearlite initial microstructure. 125 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution local velocity maximum was indicative of the recrystallization completion at ∼700 0C. The subsequent increase in austenite content from ∼15 to 50 pct during intercritical annealing at 770 0C did not affect the velocity having similar magnitudes in ferrite and austenite above the Curie temperature. During cooling from 770 to 465 0C (between ∼1350 and 1450 s in Fig. 7.3), when austenite content decreased from ∼50 to 20 pct due to the formation of epitaxial ferrite and bainite, ultrasonic velocity showed a nonlinear increase that was consistent with the presence of ferrite in the structure. Bainite formation during holding at 465 0C led to a gradual increase in the velocity by ∼40 m/s, as at this temperature the velocities of the ultrasonic wave propagation in ferrite and austenite were substantially different. In summary, the velocity of the ultrasonic compressive waves is sensitive to the later stages of recrystallization presumably when strong changes in texture occur. The ultrasonic velocity can be employed to measure time or temperature for the recrystallization completion. The absence of the charac- teristic velocity increase upon heating to intercritical temperature also indi- cates incomplete recrystallization prior to austenite formation. The progress of austenization can not be quantified using this particular signal due to the similarity of the velocities in ferrite and austenite at intercritical tempera- tures. However, when recrystallization is completed before austenite forma- tion, temperature for the completion of austenization can be estimated based on the change in the slope of the velocity as a function of temperature. The ultrasonic velocity can be used for the measurements of austenite decompo- sition kinetics provided it takes place below the Curie temperature, where the ultrasound velocities in austenite and ferrite are sufficiently different. 126 7.1. Laser ultrasonics as a tool for in-situ monitoring of microstructure evolution Figure 7.3: (a) Intercritical annealing cycle and (b) corresponding evolution of austenite content and changes in ultrasonic velocity. 127 7.2. Application of microstructure evolution model 7.2 Application of microstructure evolution model3 The model developed in the present study is essentially semiempirical and represents a rather pragmatic approach to the problem of the microstructure evolution during intercritical annealing. The flowchart for the integrated mi- crostructure evolution model is shown in Fig. 7.4. Initial microstructure and thermal path for intercritical annealing are the model inputs. The recrystal- lization completion temperature is predicted by the model and compared to the austenite formation temperature. If recrystallization is completed before austenite forms, the model proceeds to the next segment. If recrystallization and austenization overlap, microstructure for austenite formation becomes a function of the degree of recrystallization completion. This complex process is not accounted for; the present model is limited to lower heating rates, which are typical for hot-dip galvanizing lines but not necessarily for modern continuous anealing lines. Austenite content prior to cooling predicted by the austenite formation model is used as an input for the austenite decom- position model. The formation of epitaxial ferrite and bainite during cooling and holding in the molten zinc bath at 465 0C is described by the austenite decomposition model. Any remaining austenite at the end of the isothermal holding at 465 0C is assumed to transform fully into martensite. Volume fractions of intercritical and epitaxial ferrite, bainite and martensite are the outputs. Table 7.1 summarizes equations and parameters for the model. 3A part of this section was published in the conference proceedings: M. Militzer, W. J. Poole, T. Garcin, M. Kulakov and B. Zhu, “Microstructure engineering of dual-phase steels,” in New Developments in AHSS, Vail, Colorado, June 23-27, 2013. 128 7.2. Application of microstructure evolution model Figure 7.4: Flow chart for model describing microstructure evolution during intercritical annealing. 129 7.2. A p p lication of m icrostru ctu re evolu tion m o d el Table 7.1: Summary of equations and parameters for model describing microstructure evolution during intercritical annealing (recrystallization is completed before austenite formation). Metallurgical phenomenon Equations and parameters dfREX dt = { n · (1− fREX) · [ ln ( 1 1−fREX )]n−1/n} · b1/n b = b0 · exp (−Q/R·T) Recrystallization Ferrite-Pealite: n = 1.7 b0 = 1.1 · 1029 s−1.7 Q = 581 kJ/mol Ferrite-Bainite-Pealite: n = 1.4 b0 = 2.3 · 1027 s−1.4 Q = 531 kJ/mol Martensite: n = 2.5 b0 = 1.3 · 1052 s−2.5 Q = 1011 kJ/mol As = 735 · q0.012 ( fγfeqγ = 0.05) Austenite formation f eqγ = 25.78− 0.07405 · T + 5.36 · 10−5 · T 2 (for T=690 to 812 0C) (after recrystallization completion) d(fγ/feqγ ) dt = { n · (1− fγ/feqγ ) · [ ln ( 1 1−fγ/feqγ )]n−1/n} · b1/n b = b0 · exp (−Q/R·T) n = 0.4 b0 = 3.6 · 1018 s−0.4 Q = 386 kJ/mol Austenite decomposition dfα dt = { n · (1− fα) · [ ln ( 1 1−fα )]n−1/n} · b1/n (ferrite and bainite formation during cooling) Bainite starts to form when fγ = 0.3 n = 0.1 b = 0.82 + 0.003 · T − 0.44 · 10−5 · T 2 s−0.1 (T in 0C) Austenite decomposition fB = (1− exp(−b · tn)) · fmaxB (bainite formation during holding in molten zinc bath) fmaxB = 2 · fγ(t = 0)− 0.32 n = 1 b = 0.3 · fγ(t = 0)− 0.04 s−1130 7.2. Application of microstructure evolution model The microstructure evolution model was validated with laboratory simu- lations of industrial intercritical annealing cycle typically employed by Arcelor- Mittal Dofasco for the investigated DP600 steel. The effect of the initial mi- crostructure on the microstructure evolution was studied for the processing route shown in Fig. 7.5(a) (total anealing time ∼380 s). The corresponding microstructural changes were monitored in-situ using dilatometry and laser ultrasonics. Temperatures for the completion of recrystallization were mea- sured using laser ultrasonics as it was described in the previous section. The measured and predicted temperatures for the recrystallization completion were in a good agreement and below the austenite formation temperature for all initial microstructure as shown in Table 7.2. Austenite volume fraction at any stage of the intercritical annealing was essentially independent of the initial microstructure, Fig. 7.5(b). The austenite formation model captured the evolution of austenite content before cooling. Kinetics of the subsequent austenite decomposition was predicted accurately using the output of the austenite formation model as illustrated in Fig. 7.5(b). Fig. 7.6 shows mi- croconstituents content in the final microstructure obtained from experiments and predicted by the model. The final microstructure was composed among others of ∼11 and ∼55 pct of martensite and intercritical ferrite, respectively, for any initial microstructure; their contents were accurately predicted by the model as shown in Fig. 7.6. Somewhat less accurate predictions were ob- tained for the remainder of the microstructure. Epitaxial ferrite and bainite contents measured experimentally for different initial microstructures varied between 18 to 24 pct and 9 to 17 pct, respectively; and the corresponding model predictions were 18 and 12 pct. 131 7.2. Application of microstructure evolution model Figure 7.5: (a) Industrial intercritical annealing cycle, (b) effect of initial microstructure on on phase transformations. 132 7.2. Application of microstructure evolution model Table 7.2: Temperatures for recrystallization completion and austenite for- mation during laboratory simulations of industrial intercritical annealing of different initial microstructures. Initial microstructure Recrystallization completion temperature, 0C Austenite formation temperature Laser ultrasonics Model (99 pct) (5 pct - experiment),0C Ferrite-Pearlite 726 733 756 Ferrite-Bainite- Pearlite 725 712 750 Martensite 714 705 747 Figure 7.6: Comparison of microstructures obtained by laboratory simulation of industrial intercritical annealing process of different initial microstructures and model predictions. 133 7.2. Application of microstructure evolution model The performance of the microstructure evolution model was also evalu- ated for the industrial thermal path, see Fig. 7.5(a), with intercritical an- nealing time scaled by a factor of 0.5, 1 or 2 while maintaining the peak temperatures constant, i.e. total annealing time was equal to 190, 380 and 760 s, to replicate annealing of sheets with different thicknesses or line speeds. The as-received 50 pct cold-rolled material (the F-B-P initial microstructure) was employed for these simulations. Upon heating to the intercritical tem- perature, recrystallization was completed before austenite formation for all annealing times, as shown in Table 7.3. The maximum austenite content reached in the course of intercritical annealing increased from ∼41 to 46 pct as the intercritical annealing time was raised from 190 to 760 s, Fig. 7.7. The model accurately described the evolution of austenite content for the 380 and 760 s long anneals. Although the model underestimated austenite content in the beginning but yielded accurate predictions by the end of 190 s long annealing; as a consequence of this, content of intercritical ferrite in the final microstructure was overestimated, Fig. 7.8. Volume fractions of dif- ferent microconstituents in the final microstructure after 380 and 760 s long anneals were in a good agreement with the model predictions. The model also captured the experimentally observed trend of decreasing intercritical ferrite and martensite contents at the expense of epitaxial ferrite and bainite for longer anneals. Microstructure evolution during intercritical annealing can be described using the developed model for all initial microstructures after recrystalliza- tion completion. In particular, after the complete intercritical annealing cycle, martensite content having dominant effect on mechanical properties 134 7.2. Application of microstructure evolution model Table 7.3: Temperatures for recrystallization completion and austenite for- mation during laboratory simulation of industrial intercritical annealing of different durations for ferrite-bainite-pearlite initial microstructure. Intercritical annealing time, s Recrystallization completion temperature, 0C Austenite formation temperature Laser ultrasonics Model (99 pct) (5 pct - experiment),0C 190 s 731 727 757 380 s 725 712 750 760 s 706 698 751 Figure 7.7: Effect of line speed on phase transformations during laboratory simulation of industrial intercritical annealing of ferrite-bainite-pearlite ini- tial microstructure. 135 7.2. Application of microstructure evolution model Figure 7.8: Comparison of microstructures obtained by laboratory simula- tion of industrial intercritical annealing of ferrite-bainite-pearlite initial mi- crostructure at different line speeds and model predictions. 136 7.3. Mechanical properties is predicted with the desired relative accuracy of ±10 pct (recall Scope and objectives Chapter 3). The model also yields reliable predictions of ferrite and bainite content after rather longer anneals, i.e. lower heating/cooling rates. 7.3 Mechanical properties A survey of achievable mechanical properties for the investigated steel be- fore and after intercritical annealing is presented in this section. Changes in mechanical properties during the final stages of DP600 steel processing were evaluated first. Tensile properties were measured for the as-received hot-rolled and 50 pct cold-rolled materials, i.e. the F-B-P initial microstruc- ture, Figs 4.1(b) and (d). F-B-P subjected to the laboratory simulations of the industrial intercritical annealing, see Fig. 7.5(a), was also tested in tension; the final microstructure and mechanical properties are shown in Fig. 7.9(a), Fig. 7.10 and Table 7.4. Finally, specimens with “true” dual-phase ferrite-martensite structure were tested as well: the effect of the scale of fer- rite/martensite components on tensile properties was evaluated for samples possessing martensite content of 20-25 pct, see Figs. 7.9(b) and (c), and Table 7.4. Utilizing thermal paths explored in Chapters 5 and 6, the coarse grained structure developed following recrystallization completion during heat treat- ment of F-B-P (1 0C - 770 0C - 600 s - 3 0C/s - 550 0C - Water quench), while the fine ferrite-martensite microstructure resulted from the unrecrystallized material (100 0C/s - 770 0C - 90 s - 3 0C/s - 550 0C - Water quench). 137 7.3. Mechanical properties Figure 7.9: Microstructure of intercritically annealed samples tested in ten- sion (ferrite-bainite-pearlite initial microstructure): (a) laboratory simula- tion of industrial intercritical annealing, (b) coarse ferrite-martensite, (c) fine ferrite-martensite. (Note: B - bainite, M - martensite) 138 7.3. Mechanical properties Figure 7.10: Tensile test results (portion of curve before strain localization is only shown) . 139 7.3. Mechanical properties Table 7.4: Tensile test results. In comparison to the hot-rolled state, yield and tensile strengths in- creased significantly after cold-rolling to 50 pct, while the ability deform plastically decreased drastically, see Fig. 7.10 and Table 7.4. After all inter- critical anneals, deformability was restored and the ratio of yield to tensile strengths was lowered substantially. The discontinuous yielding observed in the hot-rolled condition also disappeared. These changes in deformation characteristics are typical for intercritically annealed steels and have been well documented in the literature [75, 84–86]. It is noteworthy, that similar tensile strengths were achieved in the 50 pct cold-rolled as-received and the fine grained ferrite-martensite materials, however, the latter had about eight times higher uniform elongation; this once again illustrates the advantages of the composite structure of dual-phase steels. 140 7.3. Mechanical properties After simulations of the industrial intercritical annealing cycle, the re- sulting uniform elongation and tensile strength were at the level required for the commercial DP600 product [131]; however, yield strength was ∼50 MPa lower as the industrially processed material underwent temper rolling with 1-2 pct reduction to improve the surface finish after galvanizing. Ferrite- martensite structures possessed higher tensile strength but lower uniform elongation than the specimens intercritically annealed using the industrial thermal path; these observations are in accord with the previous studies [76, 95, 96]. In spite of ∼5 pct reduction in martensite content, the refine- ment of ferrite/martensite components led to 5-10 pct increase in yield and tensile strengths at the expense of uniform elongation. During deformation of a ferrite-martensite steel, softer ferrite yields first. Strengthening of the ferrite component via grain refinement, therefore, leads to an increase in yield strength. The refinement of ferrite grains and martensite particles also increases the rates of strain hardening and results in higher levels of tensile strength [81,84,93,94]. 141 Chapter 8 Summary and suggestions for future work 8.1 Summary A microstructure evolution model was developed to describe all physical phe- nomena (recrystallization, austenite formation and austenite decomposition after partial austenization) taking place during intercritical annealing of a DP600 steel (0.11C-1.86Mn-0.34Cr-0.16Si, wt. pct). The model was de- signed to be applicable to the processing conditions on a typical industrial hot-dip galvanizing line. Three initial 50 pct cold-rolled microstructures in- cluding ferrite-pearlite, ferrite-bainite-pearlite and martensite (which are re- ferred to as F-P, F-B-P and M, respectively), were employed in this study. These materials covered the full range of possible inputs for cold-rolling and subsequent annealing. The effects of processing parameters and initial mi- crostructures on the subsequent phase transformations were determined in systematic experiments. In particular, the effect of incomplete recrystalliza- tion on austenite formation and decomposition was studied in detail. Using this experimental data, the microstructure evolution model was constructed and validated. The main experimental findings, modelling results and their 142 8.1. Summary implications are summarized below: • Recrystallization in F-B-P and M was faster than in F-P, as the former two materials had finer structures and higher stored energies. • If the material was heated slowly to intercritical temperature, recrys- tallization was completed prior to austenite formation. The austenite formation kinetics after recrystallization completion was relatively in- dependent of the initial microstructure. • When heating rate exceeded a critical value, austenite formed in a partially recrystallized microstructure. Incomplete recrystallization ac- celerated austenite formation rate and altered its morphology; both austenite nucleation and growth rates were accelerated. Shorter hold- ing times at an intercritical temperature would be needed to reach a desired austenite content in this case. • Austenite morphology and distribution can be controlled by variation of either the initial microstructure and/or employing different degrees of recrystallization completion before the start of austenite formation. • The ferrite-austenite interface area after partial austenization deter- mined the rate of ferrite growth upon cooling. After the complete intercritical annealing cycle, cumulative content of bainite and marten- site was equal to ∼25-30 pct irrespective of cooling conditions. • Laser ultrasonics proved to be an attractive tool complementing more traditional methods, i.e. metallography and dilatometry, for the mon- itoring of the microstructure evolution during intercritical annealing. 143 8.1. Summary Time or temperature for the recrystallization completion was accu- rately measured using the velocity of ultrasonic waves propagation, which were presumably sensitive to the texture changes. Due to the similarity of the velocities in ferrite and austenite, this particular sig- nal was insensitive to the changes in austenite content at intercritical temperatures. When austenite decomposition took place at sufficiently low temperatures, e.g. molten zinc bath temperature of 465 0C, the ki- netics of austenite-to-bainite transformation could be monitored based on the velocity changes. • Individual models for recrystallization, austenite formation and austen- ite decomposition after partial austenization were based on the Johnson- Mehl-Avrami-Kolmogorov (JMAK) equation and the additivity princi- ple. The model parameters were obtained by fitting the JMAK equa- tion to experimental data. • The critical heating rate to avoid the recrystallization-austenite forma- tion interaction, as predicted by the recrystallization models, was equal to 3 0C/s for F-P, and 7 0C/s for F-B-P and M. Austenite formation was modelled only for fully recrystallized materials. Upon heating at a rate above the critical value, recrystallization and austenite formation occurred concurrently. This complex process could not be adequately described with the current modelling approach. However, the process of austenite decomposition after intercritical annealing was successfully modelled in either recrystallized or unrecrystallized microstructures. • The integrated microstructure evolution model was validated for the in- 144 8.2. Suggestions for future work dustrial intercritical annealing conditions for different initial microstruc- tures, and simulated line speeds or sheet thicknesses. Recrystallization was completed before austenite formation in all considered cases as pre- dicted by the recrystallization models and confirmed with laser ultra- sonics. The austenite formation model provided an accurate description of austenite formation for all fully recrystallized materials. The evo- lution of austenite content during cooling was accurately described by the austenite decomposition model. Contents of intercritical ferrite and martensite in the final microstructure were in a good agreement with those observed experimentally. However, predictions for the remainder of the microstructure shared between epitaxial ferrite and bainite were less reliable, this being inherited from a relatively low accuracy of the bainite content measurements. • The developed model is, in essence, semi-empirical. It should be em- ployed only for the experimentally verified range of processing param- eters. 8.2 Suggestions for future work The following extensions of the present study are suggested: • One important aspect of recrystallization, i.e. texture evolution, was not addressed in the present study. In the case of austenite formation from an unrecrystallized microstructure, the effect of the initial ferrite texture retention through the entire intercritical annealing cycle should be evaluated as well. 145 8.2. Suggestions for future work • From a practical point of view, the effect of size, morphology and dis- tribution of different microconstituents in the final microstructure after intercritical annealing on mechanical properties needs to be character- ized using formability rather than tensile tests. • Accurate and robust methods requiring as little of the operator’s sub- jective interpretation as possible need to be developed for the quanti- tative microstructure analysis. For example, imaging in back-scattered electron mode sensitive to grain orientation and electron back-scattered diffraction are promising tools for the characterization of complex mi- crostructures in steels [44,165,166]. The proposed microstructure evolution model can be improved if bainite content in the final microstructure after the complete intercritical anneal- ing cycle is measured more accurately. Ferrite and bainite formation during cooling can then be described properly using two separate models. Moreover, an extension for the austenite formation model needs to be developed to ac- count for the recrystallization-austenite formation interaction, which may be encountered during rapid processing of dual-phase steels. The complexity of the concurrent metallurgical phenomena can not be captured with the JMAK equation. A different, more physically-realistic modelling approach is needed for accurate description of the processes taking place simultaneously during intercritical annealing. The variety of possible distributions and morpholo- gies of microconstituents has to be addressed as well. These challenges can be met by using a meso-scale model, e.g. a phase-field approach. However, such a model would come at a price of higher computational costs. From the point of view of experiments, measurements of a single parameter characterizing 146 8.2. Suggestions for future work the entire material, i.e. volume fraction transformed, will not be sufficient anymore. The balance between experimental efforts, computational costs, desired outputs and prediction accuracy should be carefully considered. 147 Bibliography [1] H. Souther, “American automobile steel,” The New York Times, January 17 1909. [2] M. S. Rashid, “High-strength, low-alloy steels,” Science, vol. 208, pp. 862–869, 1980. [3] R. A. Kot and J. W. Morris, eds., Structure and Properties of Dual Phase Steels, AIME, New York, 1979. [4] A. T. Davenport, ed., Formable HSLA and Dual Phase Steels, AIME, New York, 1979. [5] R. A. Kot and B. L. Bramfitt, eds., Fundamentals of dual-phase steels, AIME, New York, 1981. [6] “Ultralight steel auto body - advanced vehicle concepts - engineering report,” Steel Market Development Institute, Washington, DC, www.autosteel.org, 2002. [7] O. Kwon, K. Lee, G. Kim, and K.-G. Chin, “New trends in advanced high strength steel developments for automotive application,” Materials Science Forum, vol. 638- 642, pp. 136–141, 2010. [8] F. J. Humphreys and M. Hatherly, Recrystallization and Related Annealing Phe- nomena. Elsevier, New York, 2nd ed., 2004, pp. 169-267. [9] M. Oyarzabal, A. M. de Guerenu, and I. Gutierrez, “Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel,” Materials Science and Engineering: A, vol. 485, pp. 200 – 209, 2008. [10] E. A. Holm, M. A. Miodownik, and A. D. Rollett, “On abnormal subgrain growth and the origin of recrystallization nuclei,” Acta Materialia, vol. 51, no. 9, pp. 2701– 2716, 2003. 148 Bibliography [11] W. B. Hutchinson, “Deformation microstructures and textures in steels,” Philosoph- ical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 357, pp. 1471–1485, 1999. [12] R. L. Every and M. Hatherly, “Oriented nucleation in low-carbon steels,” Texture, vol. 1, pp. 183–194, 1974. [13] W. B. Hutchinson, “Development and control of annealing textures in low-carbon steels,” International Metals Reviews, vol. 29, no. 1, pp. 25–42, 1984. [14] R. K. Ray, J. J. Jonas, and R. E. Hook, “Cold rolling and annealing textures in low carbon and extra low carbon steels,” International Materials Reviews, vol. 39, no. 4, pp. 129–172, 1994. [15] W. Xu and M. Ferry, “Recrystallisation textures in cold rolled low carbon steel containing ferritic and bainitic microstructures,” Materials Science and Technology, vol. 26, pp. 1159–1172, 2010. [16] K. Mukunthan and E. Hawbolt, “Modeling recovery and recrystallization kinetics in cold-rolled Ti-Nb stabilized interstitial-free steel,” Metallurgical and Materials Transactions A, vol. 27, pp. 3410–3423, 1996. [17] W. Ye, R. L. Gall, and G. Saindrenan, “A study of the recrystallization of an IF steel by kinetics models,” Materials Science and Engineering: A, vol. 332, pp. 41 – 46, 2002. [18] J. Huang, W. J. Poole, and M. Militzer, “Austenite formation during intercritical annealing,” Metallurgical and Materials Transactions A, vol. 35, pp. 3363–3375, 2004. [19] J. W. Cahn, “The impurity-drag effect in grain boundary motion,” Acta Metallur- gica, vol. 10, pp. 789–798, 1962. [20] W. C. Leslie, F. J. Plecity, and J. T. Michalak, “Recrystallization of iron and iron- manganese alloys,” Transactions of the Metallurgical Society of AIME, vol. 221, pp. 691–700, 1961. 149 Bibliography [21] C. Zener as quoted by C. S. Smith, “Grains, phases, and interfaces: An interpreta- tion of microstructure,” Transactions of AIME, vol. 175, pp. 15–51, 1948. [22] P. A. Manohar, M. Ferry, and T. Chandra, “Five decades of the zener equation,” ISIJ International, vol. 38, no. 9, pp. 913–924, 1998. [23] G. Couturier, R. Doherty, C. Maurice, and R. Fortunier, “3D finite element simula- tion of the inhibition of normal grain growth by particles,” Acta Materialia, vol. 53, no. 4, pp. 977 – 989, 2005. [24] E. Kozeschnik, V. Pletenev, N. Zolotorevsky, and B. Buchmayr, “Aluminum nitride precipitation and texture development in batch-annealed bake-hardening steel,” Metallurgical and Materials Transactions A, vol. 30, pp. 1663–1673, 1999. [25] D. Raabe and L. Hantcherli, “2D cellular automaton simulation of the recrystalliza- tion texture of an if sheet steel under consideration of zener pinning,” Computational Materials Science, vol. 34, pp. 299–313, 2005. [26] T. D. Cock, C. Capdevila, F. Caballero, and C. G. de Andrés, “Global recrystallisa- tion model of low carbon sheet steels with different cementite contents,” Materials Science and Engineering: A, vol. 519, pp. 9–18, 2009. [27] L. Gavard, H. K. D. H. Bhadeshia, D. J. C. MacKay, and S. Suzuki, “Bayesian neural network model for austenite formation in steels,” Materials Science and Technology, vol. 12, pp. 453–463, 1996. [28] G. A. Roberts and R. F. Mehl, “The mechanism and the rate of formation of austen- ite from ferrite-cementite aggregates,” Transactions of ASM, vol. 31, pp. 613–650, 1943. [29] G. R. Speich and A. Szirmae, “Formation of austenite from ferrite and ferrite-carbide aggregates,” Transactions of AIME, vol. 245, pp. 1063–1074, 1969. [30] N. Law and D. Edmonds, “The formation of austenite in a low-alloy steel,” Metal- lurgical and Materials Transactions A, vol. 11, pp. 33–46, 1980. [31] C. Garcia and A. Deardo, “Formation of austenite in 1.5 pct Mn steels,” Metallur- gical and Materials Transactions A, vol. 12, pp. 521–530, 1981. 150 Bibliography [32] G. Speich, V. Demarest, and R. Miller, “Formation of austenite during intercritical annealing of dual-phase steels,” Metallurgical and Materials Transactions A, vol. 12, pp. 1419–1428, 1981. [33] X.-L. Cai, A. Garratt-Reed, and W. Owen, “The development of some dual-phase steel structures from different starting microstructures,” Metallurgical and Materials Transactions A, vol. 16, pp. 543–557, 1985. [34] J. Yi, I. Kim, and H. Choi, “Austenitization during intercritical annealing of an Fe-C-Si-Mn dual-phase steel,” Metallurgical and Materials Transactions A, vol. 16, pp. 1237–1245, 1985. [35] V. I. Savran, Y. Van Leeuwen, D. N. Hanlon, C. Kwakernaak, W. G. Sloof, and J. Sietsma, “Microstructural features of austenite formation in C35 and C45 alloys,” Metallurgical and Materials Transactions A, vol. 38, pp. 946–955, 2007. [36] V. Savran, S. Offerman, and J. Sietsma, “Austenite nucleation and growth observed on the level of individual grains by three-dimensional X-ray diffraction microscopy,” Metallurgical and Materials Transactions A, vol. 41, pp. 583–591, 2010. [37] H. Azizi-Alizamini, M. Militzer, and W. J. Poole, “Austenite formation in plain low- carbon steels,” Metallurgical and Materials Transactions A, vol. 42, pp. 1544–1557, 2011. [38] F. Caballero, C. Capdevila, and C. de Andres, “Influence of pearlite morphology and heating rate on the kinetics of continuously heated austenite formation in a eutectoid steel,” Metallurgical and Materials Transactions A, vol. 32, pp. 1283–1291, 2001. [39] R. A. Grange, “The rapid heat treatment of steel,” Metallurgical Transactions, vol. 2, pp. 65–78, 1971. [40] M. Tokizane, N. Matsumura, K. Tsuzaki, T. Maki, and I. Tamura, “Recrystallization and formation of austenite in deformed lath martensitic structure of low carbon steels,” Metallurgical and Materials Transactions A, vol. 13, pp. 1379–1388, 1982. 151 Bibliography [41] N. Nakada, Y. Arakawa, K.-S. Park, T. Tsuchiyama, and S. Takaki, “Dual phase structure formed by partial reversion of cold-deformed martensite,” Materials Sci- ence and Engineering: A, vol. 553, pp. 128 – 133, 2012. [42] R. D. Lawson, D. K. Matlock, and G. Krauss, “An etching technique for microalloyed dual-phase steels,” Metallography, vol. 13, no. 1, pp. 71 – 87, 1980. [43] M. Geib, D. K. Matlock, and G. Krauss, “The effect of intercritical annealing tem- perature on the structure of niobium microalloyed dualphase steel,” Metallurgical and Materials Transactions A, vol. 11, pp. 1683–1689, 1980. [44] S. Zaefferer, J. Ohlert, and W. Bleck, “A study of microstructure, transformation mechanisms and correlation between microstructure and mechanical properties of a low alloyed trip steel,” Acta Materialia, vol. 52, no. 9, pp. 2765 – 2778, 2004. [45] M. J. Santofimia, L. Zhao, and J. Sietsma, “Microstructural evolution of a low- carbon steel during application of quenching and partitioning heat treatments after partial austenitization,” Metallurgical and Materials Transactions A, vol. 40, pp. 46– 57, 2009. [46] M. J. Santofimia, C. Kwakernaak, W. G. Sloof, L. Zhao, and J. Sietsma, “Experi- mental study of the distribution of alloying elements after the formation of epitax- ial ferrite upon cooling in a low-carbon steel,” Materials Characterization, vol. 61, no. 10, pp. 937–942, 2010. [47] H. Chen, E. Gamsjäger, S. Schider, H. Khanbareh, and S. van der Zwaag, “In situ observation of austenite-ferrite interface migration in a lean Mn steel during cyclic partial phase transformations,” Acta Materialia, vol. 61, pp. 2414–2424, 2013. [48] A. Van der Ven and L. Delaey, “Models for precipitate growth during the gamma - alpha + gamma transformation in Fe-C and Fe-C-M alloys,” Progress in Materials Science, vol. 40, no. 3, pp. 181–264, 1996. [49] H. S. Zurob, C. R. Hutchinson, A. Béché, G. R. Purdy, and Y. J. M. Bréchet, “A transition from local equilibrium to paraequilibrium kinetics for ferrite growth in Fe- C-Mn: A possible role of interfacial segregation,” Acta Materialia, vol. 56, no. 10, pp. 2203–2211, 2008. 152 Bibliography [50] H. Chen and S. van der Zwaag, “Application of the cyclic phase transformation concept for investigating growth kinetics of solid-state partitioning phase transfor- mations,” Computational Materials Science, vol. 49, no. 4, pp. 801–813, 2010. [51] H. Chen, B. Appolaire, and S. van der Zwaag, “Application of cyclic partial phase transformations for identifying kinetic transitions during solid-state phase transfor- mations: Experiments and modeling,” Acta Materialia, vol. 59, no. 17, pp. 6751 – 6760, 2011. [52] H. Chen and S. van der Zwaag, “Indirect evidence for the existence of the Mn parti- tioning spike during the austenite to ferrite transformation,” Philosophical Magazine Letters, vol. 92, no. 2, pp. 86–92, 2012. [53] H. Chen, M. Gouné, and S. van der Zwaag, “Analysis of the stagnant stage in diffusional phase transformations starting from austenite-ferrite mixtures,” Compu- tational Materials Science, vol. 55, no. 0, pp. 34 – 43, 2012. [54] Y. Toji, T. Yamashita, K. Nakajima, K. Okuda, H. Matsuda, K. Hasegawa, and K. Seto, “Effect of mn partitioning during intercritical annealing on following gamma-to-alpha transformation and resultant mechanical properties of cold-rolled dual phase steels,” ISIJ International, vol. 51, no. 5, pp. 818–825, 2011. [55] H. Chen, W. Xu, M. Goune, and S. van der Zwaag, “Application of the stagnant stage concept for monitoring Mn partitioning at the austenite-ferrite interface in the intercritical region for Fe-Mn-C alloys,” Philosophical Magazine Letters, vol. 92, pp. 547–555, 2012. [56] J. Sietsma and S. van der Zwaag, “A concise model for mixed-mode phase trans- formations in the solid state,” Acta Materialia, vol. 52, no. 14, pp. 4143 – 4152, 2004. [57] G. R. Purdy and Y. J. M. Bréchet, “A solute drag treatment of the effects of alloying elements on the rate of the proeutectoid ferrite transformation in steels,” Acta Metallurgica et Materialia, vol. 43, pp. 3763 – 3774, 1995. 153 Bibliography [58] F. Fazeli and M. Militzer, “Application of solute drag theory to model ferrite for- mation in multiphase steels,” Metallurgical and Materials Transactions A, vol. 36, pp. 1395–1405, 2005. [59] R. Mohanty, O. Girina, and N. Fonstein, “Effect of heating rate on the austenite formation in low-carbon high-strength steels annealed in the intercritical region,” Metallurgical and Materials Transactions A, vol. 42, pp. 3680–3690, 2011. [60] D. Yang, E. Brown, D. Matlock, and G. Krauss, “Ferrite recrystallization and austenite formation in cold-rolled intercritically annealed steel,” Metallurgical and Materials Transactions A, vol. 16, pp. 1385–1392, 1985. [61] V. Andrade-Carozzo and P. J. Jacques, “Interaction between recrystallization and phase transformations during annealing of cold-rolled Nb-added TRIP-aided steel,” Materials Science Forum, vol. 539-543, pp. 4649–4654, 2007. [62] A. Karmakar, M. Ghosh, and D. Chakrabarti, “Cold-rolling and inter-critical anneal- ing of low-carbon steel: Effect of initial microstructure and heating-rate,” Materials Science and Engineering: A, vol. 564, pp. 389 – 399, 2013. [63] T. Ogawa, N. Maruyama, N. Sugiura, and N. Yoshinaga, “Incomplete recrystal- lization and subsequent microstructural evolution during intercritical annealing in cold-rolled low carbon steels,” ISIJ International, vol. 50, no. 3, pp. 469–475, 2010. [64] M. Hillert and A. Borgenstam, “Centennial of the diffusionless paradigm of bainite,” Metallurgical and Materials Transactions A, vol. 43, pp. 4487–4495, 2012. [65] H. Aaronson, W. Reynolds, G. Shiflet, and G. Spanos, “Bainite viewed three different ways,” Metallurgical and Materials Transactions A, vol. 21, pp. 1343–1380, 1990. [66] W. T. Reynolds, H. I. Aaronson, and G. Spanos, “A summary of the present dif- fusionist views on bainite,” Materials Transactions, The Japan Institute of Metals, vol. 32, pp. 737–746, 1991. [67] G. Spanos, H. Fang, D. Sarma, and H. Aaronson, “Influence of carbon concentra- tion and reaction temperature upon bainite morphology in Fe-C-2 pct Mn alloys,” Metallurgical and Materials Transactions A, vol. 21, pp. 1391–1411, 1990. 154 Bibliography [68] H. K. D. K. Bhadeshia, Bainite in Steels. The Institute of Materials, London, UK, 2nd edition ed., 2001, pp. 129-188, 225-236. [69] A. Ali and H. K. D. H. Bhadeshia, “Nucleation of Widmanstätten ferrite,” Materials Science and Technology, vol. 6, pp. 781–784, 1990. [70] H. Matsuda and H. K. D. H. Bhadeshia, “Kinetics of the bainite transformation,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 460, pp. 1707–1722, 2004. [71] W. Steven and A. G. Haynes, “The temperature of formation of martensite and bainite in low-alloy steel,” The Journal of the Iron and Steel Institute, vol. 183, pp. 349–359, 1956. [72] J. Wang, P. J. van der Wolk, and S. van der Zwaag, “On the influence of alloy- ing elements on the bainite reaction in low alloy steels during continuous cooling,” Journal of Materials Science, vol. 35, pp. 4393–4404, 2000. [73] D. Koistinen and R. Marburger, “A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels,” Acta Metallurgica, vol. 7, pp. 59–60, 1959. [74] K. Andrews, “Empirical formulae for the calculation of some transformation tem- peratures,” Journal of the Iron and Steel Institute, vol. 203, pp. 721–727, 1965. [75] N. K. Balliger and T. Gladman, “Work hardening of dual-phase steels,” Metal Sci- ence, vol. 15, no. 3, pp. 95–108, 1981. [76] M. Sudo, M. Higashi, H. Hori, T. Iwai, S. Kambe, and Z. Shibata, “Effects of mi- crostructures on the mechanical properties of multi-phase sheet steels,” Transactions of the Iron and Steel Institute of Japan, vol. 21, no. 11, pp. 820–827, 1981. [77] D. Korzekwa, D. K. Matlock, and G. Krauss, “Dislocation substructure as a function of strain in a dual-phase steel,” Metallurgical and Materials Transactions A, vol. 15, pp. 1221–1228, 1984. 155 Bibliography [78] G. Krauss, “Deformation and fracture in martensitic carbon steels tempered at low temperatures,” Metallurgical and Materials Transactions B, vol. 32, pp. 205–221, 2001. [79] Y. Su and J. Gurland, “Strain partition, uniform elongation and fracture strain in dual-phase steels,” Materials Science and Engineering, vol. 95, pp. 151 – 165, 1987. [80] M. Mazinani and W. J. Poole, “Effect of martensite plasticity on the deformation behavior of a low-carbon dual-phase steel,” Metallurgical and Materials Transactions A, vol. 38, pp. 328–339, 2007. [81] M. Calcagnotto, Y. Adachi, D. Ponge, and D. Raabe, “Deformation and fracture mechanisms in fine- and ultrafine-grained ferrite/martensite dual-phase steels and the effect of aging,” Acta Materialia, vol. 59, no. 2, pp. 658 – 670, 2011. [82] A. Bag, K. Ray, and E. Dwarakadasa, “Influence of martensite content and mor- phology on tensile and impact properties of high-martensite dual-phase steels,” Met- allurgical and Materials Transactions A, vol. 30, pp. 1193–1202, 1999. [83] G. Avramovic-Cingara, Y. Ososkov, M. K. Jain, and D. S. Wilkinson, “Effect of martensite distribution on damage behaviour in DP600 dual phase steels,” Materials Science and Engineering: A, vol. 516, pp. 7 – 16, 2009. [84] R. Davies, “Influence of martensite composition and content on the properties of dual phase steels,” Metallurgical and Materials Transactions A, vol. 9, pp. 671–679, 1978. [85] M. S. Rashid, “Dual phase steels,” Annual Review of Materials Science, vol. 11, no. 1, pp. 245–266, 1981. [86] C. A. N. Lanzillotto and F. B. Pickering, “Structure-property relationships in dual- phase steels,” Metal Science, vol. 16, no. 8, pp. 371–382, 1982. [87] M. F. Ashby, “The deformation of plastically non-homogeneous materials,” Philo- sophical Magazine, vol. 21, pp. 399–424, 1970. 156 Bibliography [88] J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion, and related problems,” Proceedings of the Royal Society of London. Series A. Mathemat- ical and Physical Sciences, vol. 241, pp. 376 – 396, 1957. [89] G. Weng, “The overall elastoplastic stress-strain relations of dual-phase metals,” Journal of the Mechanics and Physics of Solids, vol. 38, pp. 419 – 441, 1990. [90] R. Song, D. Ponge, D. Raabe, J. G. Speer, and D. K. Matlock, “Overview of pro- cessing, microstructure and mechanical properties of ultrafine grained BCC steels,” Materials Science and Engineering: A, vol. 441, pp. 1–17, 2006. [91] C. Peng-Heng and A. Preban, “The effect of ferrite grain size and martensite volume fraction on the tensile properties of dual phase steel,” Acta Metallurgica, vol. 33, pp. 897 – 903, 1985. [92] M. Erdogan and R. Priestner, “Effect of epitaxial ferrite on yielding and plastic flow in dual phase steel in tension and compression,” Materials Science and Technology, vol. 15, no. 11, pp. 1273–1284, 1999. [93] Y. I. Son, Y. K. Lee, K.-T. Park, C. S. Lee, and D. H. Shin, “Ultrafine grained ferrite-martensite dual phase steels fabricated via equal channel angular pressing: Microstructure and tensile properties,” Acta Materialia, vol. 53, no. 11, pp. 3125 – 3134, 2005. [94] M. Delincé, Y. Bréchet, J. D. Embury, M. G. D. Geers, P. J. Jacques, and T. Par- doen, “Structure-property optimization of ultrafine-grained dual-phase steels using a microstructure-based strain hardening model,” Acta Materialia, vol. 55, pp. 2337 – 2350, 2007. [95] M. Sudo and T. Iwai, “Deformation behavior and mechanical properties of ferrite- bainite-martensite (triphase) steel,” Transactions of the Iron and Steel Institute of Japan, vol. 23, no. 4, pp. 294–302, 1983. [96] B. Y. Choi, G. Krauss, and D. K. Matlock, “Bainite formation and deformation behavior in an intercritically annealed Fe-1.0Mn-0.09C steel,” Scripta Metallurgica, vol. 22, pp. 1575 – 1580, 1988. 157 Bibliography [97] M. F. Ashby, “Physical modelling of materials problems,” Materials Science and Technology, vol. 8, no. 2, pp. 102–111, 1992. [98] A. Grong and H. R. Shercliff, “Microstructural modelling in metals processing,” Progress in Materials Science, vol. 47, pp. 163 – 282, 2002. [99] A. Kolmogorov, “A note on statistical theory of crystallization,” Izvestiya Akademii Nauk USSR, Seriya Mathematica, vol. 1, pp. 355–359, 1937. [100] W. A. Johnson and R. F. Mehl, “Reaction kinetics in processes of nucleation and growth,” Transactions of AIME, vol. 135, pp. 416–458, 1939. [101] M. Avrami, “Kinetics of phase change. I general theory,” The Journal of Chemical Physics, vol. 7, pp. 1103–1112, 1939. [102] K. Barmak, “A commentary on: Reaction kinetics in processes of nucleation and growth,” Metallurgical and Materials Transactions A, vol. 41, pp. 2711–2775, 2010. [103] M. Hillert, “Discussion of: A commentary on reaction kinetics in processes of nucle- ation and growth,” Metallurgical and Materials Transactions A, vol. 42, pp. 3241– 3241, 2011. [104] B. V. Erofeev, “Generalized equation of chemical kinetics and its application for solid state reactions.,” Doklady Akademii Nauk USSR, vol. 52, pp. 512–519, 1946. [105] J. W. Christian, The theory of transformations in metals and alloys. Pergamon Press, Oxford, UK, 2002, pp. 538-546. [106] J. W. Cahn, “Transformation kinetics during continuous cooling,” Acta Metallurgica, vol. 4, pp. 572 – 575, 1956. [107] M. Lusk and H.-J. Jou, “On the rule of additivity in phase transformation kinetics,” Metallurgical and Materials Transactions A, vol. 28, pp. 287–291, 1997. [108] S. K. Nath, S. Ray, V. N. S. Mathur, and M. L. Kapoor, “Non-isothermal austeni- tisation kinetics and theoretical determination of intercritical annealing time for dual-phase steels,” ISIJ International, vol. 34, no. 2, pp. 191–197, 1994. 158 Bibliography [109] M. Militzer, E. B. Hawbolt, and T. R. Meadowcroft, “Microstructural model for hot strip rolling of high-strength low-alloy steels,” Metallurgical and Materials Transac- tions A, vol. 31, pp. 1247–1259, 2000. [110] S. J. Jones and H. K. D. H. Bhadeshia, “Kinetics of the simultaneous decomposition of austenite into several transformation products,” Acta Materialia, vol. 45, pp. 2911 – 2920, 1997. [111] P. C. Campbell, E. B. Hawbolt, and J. K. Brimacombe, “Microstructural engineering applied to the controlled cooling of steel wire rod: Part II. Microstructural evolu- tion and mechanical properties correlations,” Metallurgical Transactions A, vol. 22, pp. 2779–2790, 1991. [112] R. G. Kamat, E. B. Hawbolt, L. C. Brown, and J. K. Brimacombe, “The principle of additivity and the proeutectoid ferrite transformation,” Metallurgical Transactions A, vol. 23, pp. 2469–2480, 1992. [113] D. Liu, F. Fazeli, M. Militzer, and W. J. Poole, “A microstructure evolution model for hot rolling of a Mo-TRIP steel,” Metallurgical and Materials Transactions A, vol. 38, pp. 894–909, 2007. [114] S. Sarkar and M. Militzer, “Microstructure evolution model for hot strip rolling of Nb-Mo microalloyed complex phase steel,” Materials Science and Technology, vol. 25, pp. 1134–1146, 2009. [115] M. Umemoto, K. Horiuchi, and I. Tamura, “Transformation kinetics of bainite dur- ing isothermal holding and continuous cooling,” Transactions of the Iron and Steel Institute of Japan, vol. 22, pp. 854–861, 1982. [116] S. V. Radcliffe and E. C. Rollason, “The kinetics of the formation of bainite in high-putiry iron-carbon alloys,” Journal of The Iron and Steel Institute, vol. 191, pp. 56–65, 1959. [117] J. S. White and W. S. Owen, “Kinetic features of upper and lower bainite formation in a plain carbon and a 3pctNi-Cr steel,” Journal of The Iron and Steel Institute, vol. 195, pp. 79–82, 1960. 159 Bibliography [118] M. J. Hawkins and J. Barford, “Experimental kinetics of bainite formation,” Journal of The Iron and Steel Institute, vol. 210, pp. 97–105, 1972. [119] H. Okamoto and M. Oka, “Lower bainite with midrib in hypereutectoid steels,” Metallurgical Transactions A, vol. 17, pp. 1113–1120, 1986. [120] M. De Meyer, J. Mahieu, and B. C. De Cooman, “Empirical microstructure predic- tion method for combined intercritical annealing and bainitic transformation of trip steel,” Materials Science and Technology, vol. 18, pp. 1121–1132, 2002. [121] H. S. Zurob, C. R. Hutchinson, Y. J. M. Bréchet, and G. Purdy, “Modeling recrys- tallization of microalloyed austenite: effect of coupling recovery, precipitation and recrystallization,” Acta Materialia, vol. 50, no. 12, pp. 3077 – 3094, 2002. [122] K. B. Kang, O. Kwon, W. B. Lee, and C. G. Park, “Effect of precipitation on the recrystallization behavior of a Nb containing steel,” Scripta Materialia, vol. 36, pp. 1303 – 1308, 1997. [123] R. R. Judd and H. W. Paxton, “Kinetics of austenite formation from a spheroidized ferrite-carbide aggregate,” Transactions of the Metallurgical Society of AIME, vol. 242, pp. 206–214, 1968. [124] P. A. Wycliffe, G. R. Purdy, and J. D. Embury, “Growth of austenite in the inter- critical annealing of Fe-C-Mn dual phase steels,” Canadian Metallurgical Quarterly, vol. 20, no. 3, pp. 339–350, 1981. [125] R. A. Vandermeer, “Modeling diffusional growth during austenite decomposition to ferrite in polycrystalline Fe-C alloys,” Acta Metallurgica et Materialia, vol. 38, pp. 2461 – 2470, 1990. [126] G. P. Krielaart and S. van der Zwaag, “Kinetics of austenite-to-ferrite phase trans- formation in Fe-Mn alloys containing low manganese,” Materials Science and Tech- nology, vol. 14, pp. 10–18, 1998. [127] T. A. Kop, Y. van Leeuwen, J. Sietsma, and S. van der Zwaag, “Modelling the austenite to ferrite phase transformation in low carbon steels in terms of the interface mobility,” ISIJ International, vol. 40, pp. 713–718, 2000. 160 Bibliography [128] C. Bos, M. G. Mecozzi, and J. Sietsma, “A microstructure model for recrystallisation and phase transformation during the dual-phase steel annealing cycle,” Computa- tional Materials Science, vol. 48, pp. 692 – 699, 2010. [129] M. Militzer, “Phase field modeling of microstructure evolution in steels,” Current Opinion in Solid State and Materials Science, vol. 15, pp. 106 – 115, 2011. [130] R. G. Thiessen, J. Sietsma, T. A. Palmer, J. W. Elmer, and I. M. Richard- son, “Phase-field modelling and synchrotron validation of phase transformations in martensitic dual-phase steel,” Acta Materialia, vol. 55, pp. 601 – 614, 2007. [131] Private communication with Jeff Gao, research engineer at ArcelorMittal Dofasco Inc., Hamilton, ON, Canada, 2013. [132] W. F. Hosford and R. M. Caddell, Metal Forming: Mechanics and Metallurgy. Cam- bridge University Press, New York, NY, 2007, pp. 163-164. [133] T. Gladman, “Deformation and recrystallisation of steels,” Materials Science and Technology, vol. 6, pp. 1131–1138, 1990. [134] G. Krauss, Steels - Processing, Structure and Performance. ASM International, Materials Park, OH, 2nd ed., 2005, pp. 299. [135] J. Barry and G. Byrne, “Tem study on the surface white layer in two turned hardened steels,” Materials Science and Engineering: A, vol. 325, pp. 356–364, 2002. [136] A. Ramesh, S. N. Melkote, L. F. Allard, L. Riester, and T. R. Watkins, “Analysis of white layers formed in hard turning of aisi 52100 steel,” Materials Science and Engineering: A, vol. 390, pp. 88–97, 2005. [137] M. Onink, C. M. Brakman, F. D. Tichelaar, E. J. Mittemeijer, S. van der Zwaag, J. H. Root, and N. B. Konyer, “The lattice parameters of austenite and ferrite in Fe- C alloys as functions of carbon concentration and temperature,” Scripta Metallurgica et Materialia, vol. 29, no. 8, pp. 1011 – 1016, 1993. [138] X.-G. Lu, M. Selleby, and B. Sundman, “Assessments of molar volume and thermal expansion for selected BCC, FCC and HCP metallic elements,” Calphad, vol. 29, no. 1, pp. 68 – 89, 2005. 161 Bibliography [139] F. S. LePera, “Improved etching technique to emphasize martensite and bainite in high-strength dual-phase steel,” Journal of Metals, vol. 32, pp. 38–39, 1980. [140] E. E. Underwood, Quantitative stereology. Addison-Wesley, Reading, MA, 1970, pp. 30-37. [141] J.-P. Monchalin, “Laser-ultrasonics: From the laboratory to industry,” AIP Confer- ence Proceedings, vol. 700, pp. 3–31, 2004. [142] A. Smith, S. E. Kruger, J. Sietsma, and S. van der Zwaag, “Laser-ultrasonic monitor- ing of ferrite recovery in ultra low carbon steel,” Materials Science and Engineering: A, vol. 458, pp. 391–401, 2007. [143] S. E. Kruger, A. Moreau, M. Militzer, and T. Biggs, “In-situ, laser-ultrasonic monitoring of the recrystallization of aluminum alloys,” Materials Science Forum, vol. 426-432, pp. 483–488, 2003. [144] B. Hutchinson, E. Lindh-Ulmgren, and L. Carlson, “Application of laser-ultrasonics to studies of recrystallisation and grain growth in metals,” in 1st International Symposium on Laser Ultrasonics: Science, Technology and Applications, Montreal, Canada, July 16-18, 2008. [145] M. Dubois, M. Militzer, A. Moreau, and J. F. Bussière, “A new technique for the quantitative real-time monitoring of austenite grain growth in steel,” Scripta Mate- rialia, vol. 42, pp. 867 – 874, 2000. [146] S. Sarkar, A. Moreau, M. Militzer, and W. J. Poole, “Evolution of austenite recrys- tallization and grain growth using laser ultrasonics,” Metallurgical and Materials Transactions A, vol. 39, pp. 897–907, 2008. [147] M. Maalekian, R. Radis, M. Militzer, A. Moreau, and W. J. Poole, “In situ mea- surement and modelling of austenite grain growth in a Ti/Nb microalloyed steel,” Acta Materialia, vol. 60, pp. 1015 – 1026, 2012. [148] M. Dubois, A. Moreau, M. Militzer, and J. F. Bussière, “Laser-ultrasonic monitoring of phase transformations in steels,” Scripta Materialia, vol. 39, pp. 735 – 741, 1998. 162 Bibliography [149] M. Dubois, A. Moreau, and J. F. Bussière, “Ultrasonic velocity measurements during phase transformations in steels using laser ultrasonics,” Journal of Applied Physics, vol. 89, pp. 6487–6495, 2001. [150] S. E. Kruger and E. B. Damm, “Monitoring austenite decomposition by ultrasonic velocity,” Materials Science and Engineering: A, vol. 425, pp. 238 – 243, 2006. [151] A. Hedin, E. Lindh-Ulmgren, M. Borg, B. Hutchinson, and L. Carlson, “Laser- ultrasonics for microstructure characterisation on-line in steel processing,” in 1st International Symposium on Laser Ultrasonics: Science, Technology and Applica- tions, Montreal, Canada, July 16-18, 2008. [152] R. K. Ing and J.-P. Monchalin, “Broadband optical detection of ultrasound by two- wave mixing in a photorefractive crystal,” Applied Physics Letters, vol. 59, pp. 3233– 3235, 1991. [153] ASM International Handbook Committee, ed., ASM Handbook, Volume 01 - Proper- ties and Selection: Irons, Steels, and High-Performance Alloys. ASM International, Materials Park, OH, 1990, pp. 617-652. [154] T. Kop, J. Sietsma, and S. van der Zwaag, “Dilatometric analysis of phase transfor- mations in hypo-eutectoid steels,” Journal of Materials Science, vol. 36, pp. 519–526, 2001. [155] P. R. Rios, “Relationship between non-isothermal transformation curves and isother- mal and non-isothermal kinetics,” Acta Materialia, vol. 53, pp. 4893 – 4901, 2005. [156] W. D. Callister and D. G. Rethwisch, Materials Science and Engineering: an Intro- duction. John Wiley and Sons, New York, NY, 2007, pp. 137, 341. [157] T. Swarr and G. Krauss, “The effect of structure on the deformation of as-quenched and tempered martensite in an Fe-0.2 pct C alloy,” Metallurgical Transactions A, vol. 7, pp. 41–48, 1976. [158] S. Takaki, S. Iizuka, K. Tomimura, and Y. Tokunaga, “Influence of cold working on recovery and recrystallization of lath martensite in 0.2 pct C steel,” Materials Transactions, The Japan Institute of Metals, vol. 33, pp. 577–584, 1992. 163 Bibliography [159] R. N. Caron and G. Krauss, “The tempering of Fe-C lath martensite,” Metallurgical Transactions, vol. 3, pp. 2381–2389, 1972. [160] E. A. Brandes and G. B. Brook, Smithells Metals Reference Book. Elsevier, New York, 7th ed., 1998, pp. 13-19. [161] J. D. Verhoeven, Steel Metallurgy for the Non-Metallurgist. ASM International, Materials Park, OH, 2007, pp. 210. [162] A. K. Giumelli, M. Militzer, and E. B. Hawbolt, “Analysis of the austenite grain size distribution in plain carbon steels,” ISIJ International, vol. 39, pp. 271–280, 1999. [163] A. M. Gokhale and R. T. Dehoff, “Estimation of nucleation rate and growth rate from time dependence of global microstructural properties during phase transfor- mations,” Metallurgical Transactions A, vol. 16, pp. 559–564, 1985. [164] D. J. Dever, “Temperature dependence of the elastic constants in alpha-iron single crystals: relationship to spin order and diffusion anomalies,” Journal of Applied Physics, vol. 43, pp. 3293–3301, 1972. [165] A. F. Gourgues, H. M. Flower, and T. C. Lindley, “Electron backscattering diffrac- tion study of acicular ferrite, bainite, and martensite steel microstructures,” Mate- rials Science and Technology, vol. 16, pp. 26–40, 2000. [166] K. Zhu, D. Barbier, and T. Iung, “Characterization and quantification methods of complex BCC matrix microstructures in advanced high strength steels,” Journal of Materials Science, vol. 48, pp. 413–423, 2013. 164

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