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Austenite formation and grain refinement in C-Mn steels Azizi-Alizamini, Hamid 2010

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AUSTENITE FORAMTION AND GRAIN REFINEMENT IN C-Mn STEELS  by  HAMID AZIZI-ALIZAMINI B.Sc., Tehran University, Iran, 2001 M.Sc., Tehran University, Iran, 2004  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)  December 2010   © Hamid Azizi-Alizamini, 2010  ii  Abstract The present work deals with grain refinement and austenite formation in a plain C-Mn steel with 0.17C-0.74Mn (wt pct).  To improve the limited work hardening capability of ultrafine grained ferritic steels, new approaches were adopted to develop bimodal ferrite grain size distributions and ultrafine grained dual phase microstructures.  The first approach is based on deformation and annealing of a ferrite-martensite microstructure. Ultrafine grained dual phase steels were obtained through rapid heating of very fine ferrite-carbide aggregates into the intercritical annealing region where partial austenite formation takes place.  Hence, austenite formation was systematically investigated using a combination of microstructure characterization and detailed dilatometry analysis.  The effect of initial structure and heating rate on austenite formation was examined.  The resulting microstructure characteristics and mechanical properties of dual phase steels were also investigated.  A multi-phase field modelling approach was adopted to simulate austenite formation from a variety of initial structures including ferrite-spheroidized carbide aggregates, fully pearlitic and ferrite-pearlite structures. The results show that a bimodal distribution of ferrite grains negates the Lüdering effect, yet the improvement of work hardening rate remains marginal compared to fine grained ferrite structures.  Very fine grained initial structure and rapid heat treatment cycle are essential parameters to achieve ultrafine grained dual phase steels with improved mechanical properties in the steel employed in this study.  For austenite formation, dilatation data can be used to distinguish different stages of microstructure evolution iii  upon heating into the single austenite phase region including ferrite recrystallization, pearlite to austenite and ferrite to austenite transformation.  Heating rate has a pronounced effect on the size and morphology of austenite grains in the intercritical annealing region.  It is shown that phase field modelling is capable of predicting microstructural changes during austenite formation.  It is well suited to capture complex interaction between microstructure processes such as spheroidization, carbide dissolution and coarsening during austenite formation especially in fine grained structures where the length scale is comparable with carbon diffusion distance.          iv  Table of Contents Abstract ............................................................................................................................... ii  Table of Contents ............................................................................................................... iv  List of Tables .................................................................................................................... vii  List of Figures .................................................................................................................. viii  Chapter 1  Introduction ................................................................................................... 1  Chapter 2  Literature Review.......................................................................................... 4  2.1  Grain refinement in steels ................................................................................... 4  2.2  Innovative strategies ......................................................................................... 10  2.3  Austenite formation in plain low carbon steels ................................................. 15  2.3.1  Overview ..................................................................................................... 15  2.3.2  Austenite formation from pearlite ............................................................... 17  2.3.3  Austenite formation from ferrite-pearlite structures ................................... 24  2.3.4  Austenite formation from ferrite-spheroidized carbide aggregates ............ 26  2.4  Effect of heating rate on austenite formation .................................................... 27  2.5  Dilatometry evaluation of austenite formation ................................................. 30  2.6  Dual phase steels ............................................................................................... 32  2.6.1  An overview on dual phase steels ............................................................... 32  2.6.2  Processing of dual phase steels ................................................................... 34  2.6.3  Mechanical properties of dual phase steels ................................................. 34  2.6.4  Deformation behavior of dual phase steels ................................................. 37  2.6.5  Continuous yielding effect .......................................................................... 38  2.6.6  Ultrafine grained dual phase steels ............................................................. 39  2.7  Modelling of austenite formation from ferrite-carbide aggregates ................... 41  2.8  Multiphase field models .................................................................................... 45  2.8.1  Overview ..................................................................................................... 45  2.8.2  Phase field modelling of austenite formation ............................................. 47  Chapter 3  Scope and Objectives of the Thesis ............................................................ 49  Chapter 4  Methodology ............................................................................................... 51  4.1  Material ............................................................................................................. 51  4.2  Experimental approaches .................................................................................. 51  4.2.1  Processing routes ........................................................................................ 51  4.2.1.1  Development of bimodal ferrite grain size structure ........................... 51  4.2.1.2  Austenite formation ............................................................................. 53  4.2.1.3  Production of UFG dual phase steels .................................................. 54  4.2.2  Microstructure characterization .................................................................. 55  4.2.3  Tensile tests ................................................................................................. 59  Chapter 5  Bimodal Ferrite Grain Size Structures ........................................................ 60  5.1  Introduction ....................................................................................................... 60  5.2  Results and discussion ...................................................................................... 60  5.2.1  Initial structure ............................................................................................ 60  v  5.2.2  Development of bimodal ferrite grain size structure .................................. 61  5.2.3  Grain size measurements ............................................................................ 65  5.2.4  Mechanical properties ................................................................................. 68  5.3  Summary ........................................................................................................... 70  Chapter 6  Austenite Formation in Plain Low Carbon Steels....................................... 72  6.1  Introduction ....................................................................................................... 72  6.2  Results ............................................................................................................... 72  6.2.1  Initial structures .......................................................................................... 72  6.2.2  Dilation response and microstructural characteristics in the HR and CR materials .................................................................................................................... 73  6.3  Effect of heating rate on dilation response and microstructure evolution ........ 83  6.4  Cold rolled and recrystallized structures ........................................................... 92  6.5  Discussion ......................................................................................................... 95  6.6  Summary ......................................................................................................... 100  Chapter 7  UFG Dual Phase Structures ...................................................................... 102  7.1  Introduction ..................................................................................................... 102  7.2  Results ............................................................................................................. 102  7.2.1  Microstructure evolution ........................................................................... 102  7.2.1.1  Initial structures ................................................................................. 102  7.2.1.2  Benchmarking for selection of initial structure ................................. 107  7.2.1.3  Detailed examination of UFG ferrite-carbide aggregate ................... 112  7.2.1.4  Detailed examination of the UFG dual phase structure ..................... 112  7.3  Discussion ....................................................................................................... 115  7.4  Summary ......................................................................................................... 125  Chapter 8  Phase Field Modelling (PFM) of Austenite Formation ............................ 126  8.1  Introduction ..................................................................................................... 126  8.2  Methodology ................................................................................................... 126  8.3  Austenite formation from ferrite-spheroidized carbide aggregates ................ 130  8.4  Results and discussion .................................................................................... 130  8.4.1  Mode of phase transformation .................................................................. 130  8.4.2  Austenite formation from two carbide particles ....................................... 135  8.4.3  Austenite formation from a UFG structure ............................................... 138  8.5  Modelling of austenite formation from lamellar ferrite- carbide aggregates .. 145  8.6  Results and discussion .................................................................................... 145  8.6.1  Initial structures ........................................................................................ 145  8.6.2  Mode of phase transformation .................................................................. 147  8.6.3  Growth of austenite into pearlite ............................................................... 148  8.6.4  Effect of interlamellar spacing .................................................................. 151  8.6.5  Effect of interfacial diffusion .................................................................... 153  8.6.6  Austenite formation from ferrite-pearlite structure ................................... 155  8.7  Summary ......................................................................................................... 158  Chapter 9  Concluding Remarks ................................................................................. 160  vi  9.1  Grain refinement experiments......................................................................... 160  9.2  Austenite formation: experiments and modelling ........................................... 161  9.2.1  Experiments .............................................................................................. 161  9.2.2  Modelling .................................................................................................. 162  9.3  Future work ..................................................................................................... 163  References ....................................................................................................................... 166  Appendix A1 ................................................................................................................... 174               vii  List of Tables Table  2-1:  Synopsis of different techniques used to produce UFG structures in low carbon steels ...................................................................................................................... 14  Table  4-1:  Chemical composition of the steel used in this study in wt pct ..................... 51  Table  6-1:  Summary of the critical transformation temperatures (Ac1, Acθ and Ac3 in °C) at different heating rates ............................................................................................. 85  Table  6-2:  Comparison of austenite volume fraction measured using metallographic analysis and the lever-rule for the CR steel heated at 300°C/s ......................................... 88  Table  6-3:  Effect of heating rate on T0.5 in the HR and CR samples .............................. 88  Table  7-1:  Comparison of the effect of initial microstructure on the final dual phase structure........................................................................................................................... 109  Table  7-2:  Comparison of mechanical properties for different dual phase structures .. 111  Table  7-3:  Summary of mechanical properties for different dual phase structures ...... 121  Table  8-1:  Data for the linearized phase diagram (α: ferrite, θ: cementite, γ: austenite) ......................................................................................................................................... 129  Table  8-2:  Diffusion data for carbon [115] ................................................................... 130  Table  8-3:  Parameters used for the simulations (α: ferrite, θ: cementite, γ: austenite) . 130   Table A1-1:  Chemical composition of the IF steel in wt pct ........................................ 176          viii  List of Figures Figure  2-1:  Change in the yield strength as a function of grain size in a plain C-Mn-Si steel[7]. ................................................................................................................................. 5  Figure  2-2:  Scanning electron microscopy (SEM) micrograph of UFG ferrite-carbide achieved via warm rolling[21]. ............................................................................................. 8  Figure  2-3:  Tensile data for 0.13C-0.67Mn (wt pct) steel with different grain sizes[18]. 10  Figure  2-4:  (a) Effect of grain refinement on deterioration of uniform elongation (U. El.) and the concept of work hardening design[8] and (b) improving the balance between strength and ductility using new processing approaches. ................................................. 11  Figure  2-5:  (a) Microstructure of a graded steel with pearlitic hard core surrounded by a shell of ferrite and (b) true stress–true strain curves of the model materials and the CGMs. The open symbols indicate localization and the closed symbols represent the fracture. Fully ferrite structure was obtained using a very low carbon ARMCO steel[40]. 13  Figure  2-6:  Part of Fe-Fe3C phase diagram (adopted from Thermo-Calc). .................... 16  Figure  2-7:  Microstructure of a pearlitic structure in a 0.8C-0.25Mn steel (wt pct) with different microstructure hierarchies such as colonies and lamellae. ................................. 18  Figure  2-8:  Potential austenite nucleation sites in pearlite[60]. A type: the ferrite- cementite lamellae interfaces, B type: the interface between two pearlite colonies and C type: the triple junction of pearlite colonies. .................................................................... 19  Figure  2-9:  TTT diagram of austenitization for a pearlitic steel[58].  Ae1 is the equilibrium austenite formation start temperature. ........................................................... 21  Figure  2-10:  Effect of interlamellar spacing on the kinetics of austenite formation (adopted from Reference [58]). ......................................................................................... 22  Figure  2-11:  Different stages of austenite formation from ferrite-pearlite structures in a C-Mn steel[48] including pearlite dissolution and carbon and manganese diffusion- controlled austenite formation. ......................................................................................... 25  Figure  2-12:  Schematic of growth of austenite and carbide dissolution in a ferrite- carbide aggregate[68] (cem: cementite, γ: austenite). ......................................................... 27  ix  Figure  2-13:  Effect of heating rate on the martensite size and morphology in a Mn-Mo dual phase steel with 0.06 wt pct C, (a) CR steel, low heating rate (1ºC/s) and (b) CR steel, high heating rate (100ºC/s). ..................................................................................... 28  Figure  2-14:  An example of dilation-temperature data for a hot-rolled plain C-Mn steel. ‘S’ and ‘F’ stand for start and finish of austenite formation, respectively. ...................... 31  Figure  2-15:  Balance between the UTS and the total elongation for different steels, replotted from Reference [84]. .......................................................................................... 35  Figure  2-16:  Effect of tempering on tensile behavior of plain carbon dual phase steel (adopted from Reference [98]). ......................................................................................... 39  Figure  2-17:  True stress-true strain curves for UFG and CG dual phase steels[35]; fM: martensite volume fraction. .............................................................................................. 40  Figure  2-18:  Schematic of growth of austenite (grayish region) into ferrite and cementite in (a) cylindrical/spherical and (b) planar geometry (r0: initial interface between ferrite and cementite, ra and rb: austenite fronts into cementite and ferrite, respectively) with (c) schematic of their carbon concentration profile. ............................................................... 43  Figure  2-19:  (a) Representation of the microstructure and (b) change in the phase field parameter ( iφ ) along line AA ′ depicted in part (a). ........................................................... 46  Figure  4-1:  Schematic representation of thermomechanical process to develop bimodal ferrite grain size. ............................................................................................................... 52  Figure  4-2:  Schematic illustration for the dimension of the Gleeble test sample. .......... 54  Figure  4-3:  Thermomechanical processes employed to develop different initial structures. .......................................................................................................................... 55  Figure  4-4:  (a) Dual phase structure etched with LePera (Ferrite matrix: brown, martensite islands: white) and (b) after threshold adjustment in the Clemex software (Ferrite matrix: blue, martensite islands: red). .................................................................. 57  Figure  4-5:  Subsize tensile specimen according to the ASTM E8, dimensions are in ‘mm’. ................................................................................................................................. 59  Figure  5-1:  (a) Optical and (b) SEM micrographs of initial HR ferrite-pearlite structure. Pearlite is dark and ferrite is gray in color in the optical micrograph and F, P and C stand for ferrite, pearlite and cementite, respectively, in the SEM image. ................................ 61  x  Figure  5-2:  SEM micrograph of (a) initial dual phase microstructure, (b) dual phase microstructure after 50 pct cold reduction and (c) final structure after annealing at 525°С for 1200min.  ‘F’, ‘M’ and ‘Rex. M’ represent ferrite, martensite and recrystallized martensite, respectively..................................................................................................... 63  Figure  5-3:  SEM micrograph of deformed dual phase steel annealed at (a) 500ºC for 1440min and (b) 600 ºC for 30min. .................................................................................. 64  Figure  5-4:  (a) Grain size distribution, (b) grain size distribution for coarse grain size populations and (c) volume fraction of fine and coarse grain size classes. ...................... 66  Figure  5-5:  True stress-true strain curves for bimodal grain size structure (gray line) and a UFG structure (black line). ............................................................................................ 69  Figure  6-1:  Initial HR structure after 80 pct cold reduction. The inset show higher magnification image. RD and ND are rolling and normal directions, respectively (F: ferrite, P: pearlite). ............................................................................................................ 73  Figure  6-2:  Dilation curves and their first derivatives for the HR and CR steels during heating at 1°C/s. ................................................................................................................ 74  Figure  6-3:  Microstructure evolution of the CR structure quenched at (a) 510°C (point A in Figure  6-2) and (b) 670°C (point B in Figure  6-2) during heating at 1°C/s. ............ 76  Figure  6-4:  Microstructure of HR steel heated at 1°C/s to 735°C (a) and of CR steel heated at 1°C/s to 730°C (b), (c) and (d) (F:  ferrite, M: martensite, P: pearlite, C: cementite). ......................................................................................................................... 78  Figure  6-5:  (a) Microstructure of the CR steel heated at 1°C/s to reveal cementite particles inside martensite; arrows show carbide particles (F:  ferrite, M: martensite), (b) Auger spectra for carbide particles and martensite and (c) the differential Auger spectrum for the particle. .................................................................................................................. 79  Figure  6-6:  Microstructure of the CR steel continuously heated with 1°C/s heating rate followed by water quenching at (a) 740°C (the arrows inside the inset depict spheroidized carbide particles) and (b) 780°C (F:  ferrite, M: martensite). ........................................... 81  Figure  6-7:  Austenite fraction in the HR and CR steels as a function of temperature for continuous heating at 1°C/s and paraequilibrium (PE) austenite fraction. ....................... 82  Figure  6-8:  Dilation curves and their first derivatives for (a) HR and (b) CR steels during heating with different heating rates. ...................................................................... 84  xi  Figure  6-9:  Austenite fraction in (a) HR and (b) CR steels as a function of temperature for different heating rates and paraequilibrium (PE) austenite fraction. .......................... 87  Figure  6-10:  Microstructures of the HR steel continuously heated at (a) 1°C/s and (b) 300°C/s followed by water quenching from 750°C (F:  ferrite, M: martensite). .............. 89  Figure  6-11:  Microstructural evolution of the CR steel continuously heated at 300°C/s followed by water quenching from (a) 700°C, (b, c) 740°C and (d) 780°C (F:  ferrite, M: martensite, P: pearlite). ..................................................................................................... 90  Figure  6-12:  Revealing austenite grains in the CR samples heated at (a) 1°C/s and (b) 300°C/s to just above the corresponding Ac3 temperatures followed by water quenching. ........................................................................................................................................... 92  Figure  6-13:  Revealing cementite particles inside martensite islands in the CR sample heated at 300°C/s to 740°C. .............................................................................................. 92  Figure  6-14:  (a) Dilatation curves and their first derivatives for CR+REX samples (heated at 1°C/s heating rate up to 670°C followed by heating into austenite single phase region with different heating rates), (b) austenite fraction as a function of temperature for different heating rates, and paraequilibrium (PE) austenite fraction and (c) comparison of Ac1 temperatures at different heating rates for HR, CR and CR+REX samples. ............. 94  Figure  6-15:  Microstructure of the CR steel continuously heated at 900°C/s followed by water quenching from 710°C (F: ferrite, M: martensite, P: pearlite)................................ 97  Figure  7-1:  (a) Optical micrograph of as-quenched martensite structure, (b) bright field (BF) TEM image of lath martensite structure with the corresponding  selected area diffraction (SAD) pattern and (c) EBSD orientation map of as-quenched martensite together with superimposed boundary map. ................................................................... 104  Figure  7-2:  Initial microstructures developed for intercritical annealing treatment: (a) process (I), (b) process (II) and (c) process (III); processes are presented in Figure  4-3 . ......................................................................................................................................... 106  Figure  7-3:  Microstructural evolution after 10s annealing at 750°C for initial structures obtained from (a) process (I), (b) process (II) and (c) process (III). .............................. 108  Figure  7-4:  Volumetric ferrite grain size distribution for the dual phase microstructures obtained in (a) process (I), (b) process (II) and (c) process (III).  The horizontal, x, axis in all curves is in logarithmic scale. .................................................................................... 110  xii  Figure  7-5:  (a) EBSD grain boundary misorientation map for UFG ferrite-carbide aggregate and (b) grain boundary misorientation distribution with superimposed random distribution. ..................................................................................................................... 112  Figure  7-6:  (a) BF TEM images of UFG dual phase structure obtained by heating at 300°С/s and intercritically annealed at 750°C for 10s followed by water quenching and (b) higher magnification observation (M: martensite, F: ferrite) . ................................. 113  Figure  7-7:  EBSD results for UFG dual phase structure obtained by heating at 300°С/s followed by intercritical annealing at 750°С for 10s, (a) image quality map, (b) phase map (ferrite: white, martensite: black), (c) band contrast distribution and (d) ferrite grain boundary misorientation distribution with superimposed random distribution. ............. 114  Figure  7-8:  Microstructure evolution of intercritically annealed UFG ferrite-carbide aggregate at 750°С for 10s with (a) 1°С/s and (b) 50°С/s heating rate followed by water quenching. ....................................................................................................................... 116  Figure  7-9:  Microstructure evolution of intercritically annealed UFG dual phase structure at 750°С for (a) 1s and (b) 300s holding times followed by water quenching and (c) change in volume fraction of martensite at 750°С with paraequilibrium (PE) prediction of austenite fraction (M: martensite, F: ferrite). ............................................ 118  Figure  7-10:  Comparison for nominal stress-nominal strain curves between UFG ferrite- carbide aggregate and UFG dual phase structure with 17 pct martensite. ...................... 121  Figure  7-11:  (a) True stress-true strain curves together with (b) work hardening rate for different  dual phase  structures (fM: martensite volume fraction). ................................. 123  Figure  7-12:  Balance between UTS and uniform elongation for conventional CG and UFG dual phase steels. .................................................................................................... 124  Figure  8-1:  Schematic of linearized Fe-C phase diagram (α: ferrite, γ: austenite and θ: cementite). ....................................................................................................................... 128  Figure  8-2:  (a) Initial ferrite (red)- circular cementite (yellow) aggregate, (b,c) simulated growth of austenite (white) from cementite in ferrite (interfaces shown in blue), (d) evolution of normalized phase fraction using linearized phase diagram and Thermo- Calc coupled simulations and (e) carbon concentration profile along the dashed line in Figure  8-2b. ..................................................................................................................... 131  Figure  8-3:  (a) Effect of austenite interface mobility on the kinetics of austenite formation and (b) change in normalized volume fraction of austenite at 0.3s with the mobility of austenite interfaces. ...................................................................................... 133  xiii  Figure  8-4:  Comparison between diffusion-controlled growth of austenite in phase field model and analytical model. ........................................................................................... 135  Figure  8-5:  Evolution of an austenite grain (white) nucleated at the interface of ferrite (red) and cementite (yellow): (a-d) in the bulk and (e-h) at a ferrite grain boundary. ... 137  Figure  8-6:  Contour plot of carbon concentration in ferrite for the transformation stage shown in Figure  8-5b. Numbers on the graph show the carbon concentration (wt pct) of the corresponding contour.  The large and small black regions that are removed from the map represent austenite and cementite, respectively. ..................................................... 138  Figure  8-7:  Coarsening of austenite grains in a UFG ferrite-cementite aggregate at 750°C, (a) initial structure, (b) 0.02s, (c) 0.03s, (d) 3s, (e) 5s and (f) 9s (ferrite: red, cementite: yellow and austenite: white). ......................................................................... 140  Figure  8-8:  (a) Blown-up structure from the selected area in Figure  8-7d (ferrite in red and austenite in white and (b) carbon concentration profile in ferrite from point A to point B ............................................................................................................................. 141  Figure  8-9:  3D simulation of austenite growth in a fine grained ferrite-cementite aggregate in Fe-0.05 wt pct C at 750°C, (a) t=0.0s (initial ferrite-cementite aggregate, ferrite grains are chosen to be transparent, cementite particles are in black and austenite is in red), (b) t=0.05s, (c) t=3.0s and (d) t=5.0s. ................................................................ 143  Figure  8-10:  (a) Initial structure to simulate planar growth of austenite (b) initial 2D construction of pearlitic structure with λ=0.4μm and (c) initial ferrite-pearlite structure with 0.17 wt pct carbon and λ=0.5μm (ferrite: red, cementite: yellow, austenite: white and interfaces: blue. ............................................................................................................... 146  Figure  8-11:  Comparison between diffusion-controlled growth of austenite in phase field and analytical models[108]. ....................................................................................... 147  Figure  8-12:  Growth of austenite into pearlite at (a) 0.13s and at (b) 0.28s at 750°C (ferrite: red, cementite: yellow, austenite: white and interfaces: blue), and (c) carbide remnants in austenite, shown by arrows, after completion of pearlite to austenite transformation[62] and (d) experimental observation of growth of austenite (martensite at ambient temperature) into pearlite[62]. ............................................................................. 149  Figure  8-13:  Comparison of growth rate of austenite into pearlite in a 0.96C (wt pct) pearlitic steel. .................................................................................................................. 151  Figure  8-14:  Effect of temperature and interlamellar spacing (λ) on the kinetics of austenite formation in a 0.76C (wt pct) pearlitic steel. ................................................... 152  xiv  Figure  8-15:  Growth of austenite into pearlite at 750°C for 0.2s for different interlamellar spacing of (a) 0.4μm and (b) 1.0μm in an Fe-0.76C (wt pct) alloy (ferrite: red, cementite: yellow, austenite: white and interfaces: blue). ....................................... 153  Figure  8-16:  Effect of implementing interfacial diffusion on kinetics of austenite formation at 750°C (Dinterface / Dbulk = 10). ...................................................................... 154  Figure  8-17:  Microstructure evolution during isothermal holding of a ferrite-pearlite structure at 750°C for (a) 0.05s, (b) 0.11s, (c) 0.25s (ferrite: red, cementite: yellow, austenite: white and interfaces: blue) and (d) intercritically annealed DP600 steel at 790ºC[156]. ........................................................................................................................ 155  Figure  8-18:  Carbon concentration gradient at (a) 0.05s, (b) 0.25s and (c) 2.0s and (d) carbon concentration profiles along line AA presented in Figure  8-18c at different times. ......................................................................................................................................... 157  Figure  8-19:  Predicted normalized austenite fraction with time in an Fe-0.17C (wt pct) alloy at 750°C. ................................................................................................................ 158     Figure A1-1:  Dilatation curves for IF steel during heating-cooling-heating cycles. Cooling rate during rapid cooling was approximately 200°C/s. ..................................... 176        xv  Acknowledgements First of all, I thank God for His mercy and grace. I would like to take this opportunity to express my utmost gratitude towards my supervisors Dr. Matthias Militzer and Dr. Warren J. Poole for their continuous trust, support, and guidance throughout the course of this work.  I am forever indebted to them as my teachers.  My sincere thank goes to Dr. Chad Sinclair for the stimulating and fruitful discussions. I would like to thank all staff members at Department of Materials Engineering at UBC for their assistance on my research work.  My especial thanks to all colleagues and officemates for providing a friendly environment that I was always pleased to work in. Natural Sciences and Engineering Research Council of Canada (NSERC) is greatly acknowledged for financial support. The great sacrifice, wisdom and patience of my wife are very much appreciated. This work is a result of her love and encouragement.  I also thank my mom and dad for their love and understanding.   Thank you all. This thesis is dedicated to you!      1  Chapter 1 Introduction The application of steels as the major part of automotive and construction components together with recent concerns about energy efficiency and environmental impact has encouraged steel companies to develop advanced high strength steels (AHSSs)[1].  The recent trend in replacing steel components with lighter metals such as Al and Mg alloys has provided additional motivation to steel companies.  For example, the proposal for an ultra light steel body structure (ULSAB) illustrates the global need to advance both the design and material of choice for automotive applications.  ULSAB projects aim to replace conventional C-Mn and high strength low alloy (HSLA) steels by new generation of AHSSs.  These steel grades comprise dual phase (DP), transformation induced plasticity (TRIP) and complex phase (CP) steels with superior strength, formability and crashworthiness compared to existing steels. One of the main challenges for the automotive industry remains to be the development of these grades of steels at a competitive cost.  One way to fulfill this goal is to improve the properties via engineering the microstructure containing two or more phases like ferrite, bainite, martensite and retained austenite.  Grain refinement has been extensively studied over the past two decades to improve the properties of low carbon steels without addition of costly alloying elements[2,3,4].  Ultrafine grained (UFG) steels have become of interest as a new class of high strength steels which are particularly in demand for construction applications[5].  UFG structures in steels typically refer to microstructural constituents such as ferrite and martensite with sizes in the range of 0.5-3μm.  These structures offer high yield strength (YS) and toughness along with lower ductile to brittle transition temperature 2  (DBTT)[6,7] in comparison with their coarse grain counterparts.  Several approaches have been adopted to develop UFG structures in steels, however, there are three major challenges regarding UFG steels in an industrial perspective.  First, many of these approaches have been demonstrated only at the laboratory level.  Second, they are not appropriate for sheet products and third the limited uniform elongation, usually less than 5 pct in tension, makes UFG structures unfit for conventional forming operations. To tackle these problems, a number of strategies have been recently proposed in order to improve the work hardening rate of UFG materials.  Among them, introducing suitable carbide particles into the microstructure[8,9,10] may improve the work hardening rate of these materials.  Because this improvement is accompanied by an increase of carbon content in the steel, it is not considered to be a viable option for structural steels since the weldability will deteriorate with carbon addition.  Park et al.[11] have utilized the benefits of conventional dual phase steels (continuous yielding, low yield strength, adequate elongation and high yield ratio (yield to tensile strength ratio)) in order to develop UFG dual phase low carbon steels fabricated via equal channel angular pressing (ECAP).  Yet, the proposed processing approach remains industrially challenging.  Mukherjee et al.[12] have developed UFG dual phase steels through strain induced transformation (SIT) that is more industrial- adaptive.  However, there is a narrow window of temperature in which the SIT process can be operative.  Furthermore, introducing heterogeneous bimodal grain size structures appears to be a promising approach for developing fine-grained materials with an excellent strength-ductility balance[13].  Qualitatively, this effect can be explained by the fact that small grains usually offer high strength while the larger grains aid the work hardening and 3  fracture stress of the material.  It is the aim of the present work to develop new processing routes to address the aforementioned issues.  First, a novel technique is introduced to develop bimodal ferrite grain size distribution in low carbon steels.  Then, a new technique to form UFG dual phase steels using rapid heating of a UFG ferrite-carbide aggregate is presented.  Since austenite formation is a major step in processing of dual phase steels, this transformation is examined in detail upon rapid heating.  Using phase field modelling, austenite formation in carbon steels is described.  The model deals with austenite formation in ferrite-spheroidized carbide and ferrite-lamellar carbide aggregates.  This meso-scale model is capable of capturing the morphological complexity during austenite formation. This thesis is organized as follows:  Chapter 2 provides a brief review of the literature available on grain refinement in steels and new developments in processing of AHSS and more specifically in dual phase steels.  It also discusses austenite formation in steels and modelling approaches available to predict kinetics of austenite formation in steels.  In chapter 3, the objectives of this work are formulated.  In chapter 4, the effect of bimodal distribution of ferrite grains on mechanical properties is investigated.  In Chapter 5, the effect of heating rate on microstructure evolution of cold and hot-rolled C-Mn steels is presented.  Chapter 6 deals with processing and characterization of UFG dual phase steels. Chapter 7 is devoted to phase field modelling of austenite formation in Fe-C systems with different arrangements of ferrite and cementite.  Finally, a summary of the results is presented together with an outlook into the future work that can be concluded from the present study. 4  Chapter 2 Literature Review 2.1 Grain refinement in steels It is well known that mechanical properties of crystalline materials are dependent on their grain size.  The Hall-Petch[14,15] formula is a classic example of this dependency in which the yield or flow stress of polycrystalline materials is inversely related to the grain size. Figure  2-1 shows changes in the yield strength of a low carbon steel as a function of its grain size.  It can be seen that refinement of ferrite grains from 10µm to 0.5µm raises the yield strength by 400MPa without any aid of alloying elements[7].  This strength increase can be attributed to the significant population increase of grain boundaries per unit volume. Because of these effects, grain sizes in steels can be approximately divided into two rather distinct regimes: conventional and ultrafine grain size regimes.  Grain sizes in the range of 0.5μm to 3μm are in general considered as ‘ultrafine’ in steel-related literature. Beneficial effects of grain refinement in steels are not limited to the tensile strength. Nagai[7] has shown that in low carbon Mn-Si steels the DBTT, the temperature at which 50 pct of the fracture area is covered by brittle area, can be lowered by more than 100ºC with grain refinement.  Furthermore, it has been shown that the grain refinement will improve fatigue[16] and wear[17] properties of low carbon steels. Starting with the seminal contributions by Morrison[18], Grange[19] and Miller[20], grain refinement in low carbon steels has been extensively investigated during the past two decades. Several thermal/mechanical techniques have been employed to develop UFG structures in plain low carbon steels.  The main driving force for these efforts was to reduce 5  alloying elements in high strength structural steels.  These techniques can be classified into two major categories: severe plastic deformation (SPD) methods and thermomechanical controlled processes (TMCP)[3,4,21].  The former is based on applying large amount of accumulated strain (generally a true strain of more than 3).  A submicron grain size can be achieved with these methods.  The TMCP technique creates microstructures with fine grain sizes ranging typically from 1-5µm.  The amount of true strain required for these techniques is usually less than 3.   Figure  2-1:  Change in the yield strength as a function of grain size in a plain C-Mn-Si steel[7].  6  Typical SPD techniques include equal channel angular pressing (ECAP) and accumulative roll bonding (ARB). ECAP was developed to introduce severe plastic deformation into materials while the cross-sectional area remains unchanged.  Originally intended for non- ferrous alloys (e.g. Al and Mg alloys), this technique has also been applied to low carbon steels to generate UFG structures with grain sizes down to 0.2µm [22].  ARB is an intense plastic straining process in which two strips with the same thickness are subjected to simultaneous rolling in one pass to produce a sheet with the thickness of the initial strips via 50 pct cold reduction[23].  The process can be continued with cutting the sheet into two halves, stack them together and rolling again.  In this method a very high amount of strain can be accumulated in the materials while conserving a sheet geometry. Grain refinement strategies using thermomechanical processes can be differentiated into four approaches.  Conventional rolling in the single austenite phase region followed by subsequent austenite to ferrite transformation during accelerated cooling results in a ferrite grain size of 3-5µm in Nb-bearing microalloyed steels, but this industrially-adopted method is not effective for plain low carbon steels where a ferrite grain size limit of 10µm has been reported[24].  Strain induced transformation (SIT) of austenite to ferrite is a thermomechanical technique in which ferrite grain sizes of 1µm can be obtained rather independently of steel chemistry in simple plain low carbon steels as well as microalloyed steels with a small amount of strain[2].  In the SIT technique, accelerated cooling is combined with deformation of undercooled austenite that is carried out just above the austenite to ferrite transformation start temperature upon cooling, Ar3, of the undeformed material.  Strain induced ferrite formation together with possible dynamic recrystallization 7  (DRX) of ferrite are thought to be the main microstructure evolution characteristics of this method[2,25].  Deformation in the intercritical annealing region (ferrite+austenite) is another effective way to achieve UFG structures in steels[21].  Huang et al.[26] have shown that fine grained ferrite can be obtained through deformation in the intercritical annealing region. Coarse grained (CG) pro-eutectoid Widmannstätten ferrite transforms to a fine grained structure with a mixture of equiaxed and elongated ferrite.  Microstructural observations and the true stress-true strain curve characteristics support the occurrence of dynamic recrystallization of ferrite in this study[26]. Warm rolling of ferrite-pearlite microstructure below the austenite to ferrite transformation finish temperature upon cooling, Ar1, can result in considerable grain refinement in low carbon steels[27-28].  Song et al.[21] demonstrated in a systematic manner that dynamic recrystallization of ferrite together with the presence of fine pearlitic cementite that can be dissolved or fragmented into finer particles during large strain warm deformation are the main reasons for grain refinement in low carbon steels during warm rolling.  Figure  2-2 shows a typical microstructure obtained through warm rolling of ferrite[21].  Deformation and annealing of martensite is a simple thermomechanical method where a combination of deformation and annealing of the initial martensite structure can yield an ultrafine ferrite structure in low carbon steels[29].  Tsuji et al.[29] have shown that the effect of cold reduction followed by annealing of martensite in a 0.13C-0.37Mn (wt pct) steel can yield a UFG structure with submicron ferrite grain size.  Inherent fine structure of martensite, its high dislocation density which is similar to the that of heavily cold-worked microstructures, supersaturated solid solution and carbide precipitation combine to produce a fine grain 8  structure for deformed and annealed samples[30].  Lesch et al.[31] systematically showed that very fine ferrite microstructure can be obtained via rapid transformation annealing (RTA). Through rapid austenitization of a cold-rolled (CR) ferrite-pearlite structure just above the ferrite-pearlite to austenite transformation finish temperature upon heating, Ac3, and subsequent rapid cooling to ambient temperatures, they achieved grain sizes of less than 3μm in different low carbon steels.  1µm  Figure  2-2:  Scanning electron microscopy (SEM) micrograph of UFG ferrite-carbide achieved via warm rolling[21].  In spite of global efforts devoted to develop novel processing strategies to produce UFG ferrite-carbide microstructures in plain carbon steels to reduce and/or eliminate costly alloying additions, there remain several practical issues to be solved in order to industrialize these types of structures: 9  Most of these techniques are still at the laboratory level capable of producing samples barely enough to perform a subsize tensile test.  Only a few approaches such as dynamic recrystallization and strain induced ferrite transformation, deformation and annealing of martensitic structures and asymmetric rolling are emerging as possible routes to obtain UFG steel sheets suitable for automotive applications.  The first industrial data have been reported by Morimoto et al.[32] who employed asymmetric rolling to produce 2mm thick plain carbon steel strip with a ferrite grain size of 2-5μm.  Asymmetric conditions are introduced by making the velocities or diameters of the two work rolls different during rolling.  This feature results in nearly constant shear strain distribution through thickness that is different from symmetric rolling [33]. Beside practical challenges involved in production of large bulk UFG components, reduced elongation and consequently limited formability of UFG ferrite structures is severely hampering their potential applications.  For example, increasing the tensile strength by up to five times through ARB in IF steels reduces the total elongation to less than 3 pct[34]. Figure  2-3 shows nominal stress-elongation curves for a plain carbon steel with different grain sizes[18].  While the yield strength more than doubled via reducing the grain size from 30μm to 1.6μm, uniform elongation decreased fourfold as a result of grain refinement. Lüders strain is also extended such that it can potentially deteriorate the surface finish of the sheet products. 10  Elongation, pct N om in al  S tre ss , 1 00 0p si Figure  2-3:  Tensile data for 0.13C-0.67Mn (wt pct) steel with different grain sizes[18].  2.2 Innovative strategies To tackle these problems, several strategies have been proposed recently.  They can be mainly divided into two categories:  The first group of strategies is based on work hardening concepts, Figure  2-4a[8], thereby developing  high strength plain low carbon steels with sufficient ductility utilizing second phase constituents, either carbide particles or martensite islands, Figure  2-4b.  Ohmori et al.[8], Song et al.[9] and Zhao et al.[10]  introduced suitable carbide particles into the microstructure to improve the work hardening rate. Ohmori et al.[8] have shown that the work hardening rate of UFG plain carbon steels can be improved by increasing the carbon content up to 0.3 wt pct due to the increased fraction of carbides.  While there is some potential benefits of increasing the carbon content in a suitable fashion, this is not considered to be a viable option for structural steels since the 11  weldability will deteriorate with carbon addition.  Further, extensive Lüders banding still remains a drawback of this approach.  a  Figure  2-4:  (a) Effect of grain refinement on deterioration of uniform elongation (U. El.) and the concept of work hardening design[8] and (b) improving the balance between strength and ductility using new processing approaches.  Park et al.[35] translated the benefits of conventional dual phase steels such as continuous yielding, low yield strength, adequate elongation and low yield to tensile strength ratio (yield ratio) into a finer scale structure.  Via intercritical annealing of an ECAPed ferrite- pearlite structure, they developed low carbon UFG dual phase steels with improved properties.  Yet, the proposed processing approach remains practically challenging. Mukherjee et al.[36] introduced a more industrial-adaptive technique to develop UFG dual phase steels through deformation-induced ferrite transformation followed by rapid post- deformation cooling. 12  Introducing heterogeneity into structures was recently proposed as a possible strategy to bypass the limitations involved in conventional processing approaches.  Furthermore, introducing heterogeneous bimodal grain size structures appears to be a promising approach for developing fine grained materials with an excellent strength-ductility balance[37,38]. Zhao et al.[39] developed bimodal UFG ferrite-cementite microstructure through annealing of warm-rolled low carbon steel in ferrite.  They utilized heterogeneous distribution of cementite particles localized within the pearlite lamellae which spheroidized during rolling. Further, Hanamura et al.[6] have shown that UFG ferrite-cementite microstructure with bimodal distribution of ferrite grains has a larger impact toughness compared to conventional microstructures in a low carbon steel, including ferrite-pearlite, quenched and quench-tempered martensite. Compositionally graded materials (CGMs) have been long known for their heterogeneous structures.  Carburized steels are classical example of CGMs that are used for specific applications such as wear resistance on the contact surfaces.  However, application of the compositionally graded steels has recently been extended to address other properties such as plastic deformation, ductility and fracture[40-41].  This has created a new generation of materials that can be categorized as architectured materials[41].  For example, Lefevre- Schlick et al.[40] developed chemically graded steel strips via partial decarburization of a 1070 steel with initial pearlite/spheroidite structures.  The final microstructure after decarburizing was composed of a hard core of pearlite, or spheroidite, surrounded by a shell of coarse ferrite, Figure  2-5(a).  Figure  2-5(b) shows true stress-true strain curves for 13  different structures.  It is evident that the graded structures showed improved fracture strains while fracture stresses remained intact.  a 500µm  b True Strain T ru e S tr es s,  M P a  Figure 2-5:  (a) Microstructure of a graded steel with pearlitic hard core surrounded by a shell of ferrite and (b) true stress–true strain curves of the model materials and the CGMs. The open symbols indicate localization and the closed symbols represent the fracture. Fully ferrite structure was obtained using a very low carbon ARMCO steel [40] .  Table 2-1 presents a summary of available approaches to produce UFG plain carbon steels. It can be seen that further grain refinement in ferrite/ferrite-cementite structures increases the yield ratio as a sign of deteriorating the work hardening capacity.  For example, UFG structures with grain sizes of 1μm or below generally offer a yield ratio of approximately 0.9 or more.  However, UFG dual phase steels remain exceptions in this regard making them a promising candidate for the work hardening design.  Dual phase steels are a mixture of ferrite and martensite that are produced via intercritical annealing of ferrite-carbide aggregates followed by appropriate quenching to assure austenite to martensite 14  transformation upon cooling.  Austenite formation during intercritical annealing is a key step for the development of dual phase steels.  In the next section, austenite formation in steels will be briefly reviewed and available experimental and modelling approaches to characterize this transformation will be discussed in detail.  Table  2-1:  Synopsis of different techniques used to produce UFG structures in low carbon steels Approach Composition (wt pct) Average grain  size (μm) TS(a) (MPa) Elongation (pct)  Yield ratio ((L)YS(b)/TS)  Severe plastic deformation  ECAP  0.15C-0.25Si-1.1Mn[42] 0.15C-0.25Si-1.12Mn-0.06V[43]  0.3 0.2-0.3  ~ 945 ~ 955  ~ 10 (T. El.(c)) ~ 13 (T. El.)  ≥ 0.95 ARB Ti added-IF(d) steel[23] 0.42 870 ~ 2 (T. El.) ~ 1 Martensite straining 0.13C-0.37Mn-0.0043N[30] 0.18 870 8 (U. El. (e))-20 (T. El.) (with Lüdering) 0.9 Strain induced transformation (SIT) 0.06C-0.59Mn[44] Different C-Mn-Si steels[45] ~1 (strip surface) 510-676 15-33 (T. El.) (with extensive Lüdering)  ≥ 0.87  Warm rolling of ferrite- pearlite structure 0.22C-0.74Mn [21] 1.3 ~ 600 10 (U. El.)-20 (T. El.)  + Lüders strain  0.9  Rapid transformation annealing (RTA)  0.135C-1.17Mn and different HSLA steels[31] 2-3 607-648 14-15 (U. El.) 20-24 (T. El.) 0.75-0.84 Bimodal grain size structure 0.154C-0.3Si-1.5Mn[46] 500nm+5μm ~ 535 ~19 (U. El.)+Lüdering 0.84 UFG dual phase steel 0.15C-1.1Mn [11] 0.17C-1.63Mn[47] 1.4F(f)-1.3M(g) 1-2 (F and M) ~ 895 893 17.6(T. El.)-9.3(U. El.) 11.3(U. El.) 0.59 0.51 (a) Tensile strength; (b) (Lower) yield strength; (c) total elongation; (d) interstitial free; (e) uniform elongation; (f) ferrite; (g) martensite  15  2.3 Austenite formation in plain low carbon steels 2.3.1 Overview Austenite formation occurs during many industrial heat treatments of steels.  However, the importance of this phase transformation has been undervalued since austenite is not usually found in the microstructure of final steel products.  Further, it is challenging to characterize austenite microstructures that are present at high temperatures.  These limitations resulted in rather few studies of austenite formation as compared to austenite decomposition. Nevertheless, there is a significant body of work on austenite formation available in the literature[48,49,50,51,52].  However, with the development of advanced high strength steels such as dual phase, TRIP, quenched and partitioned (Q&P) as well as complex phase steels there has been renewed interest in studying austenite formation.  For example, intercritical annealing is an essential processing step for these steels when manufactured as CR and coated sheets, primarily for automotive applications.  Further, austenite formation is of major interest for microstructure evolution in the heat affected zone of welds. Microstructures from which austenite formation has been investigated include hot-rolled (HR) and CR ferrite-pearlite[48,51,53-54], ferrite-spheroidized carbide[51-52,55] and ferrite- martensite[56] structures.  Figure  2-6 illustrates part of an Fe-C phase diagram in which major phases like ferrite (α), austenite (γ) and cementite (θ) or combination of them are stable at different combinations of temperature and carbon content.  Austenite formation generally involves heating an aggregate of ferrite-cementite, either spheroidized or lamellar arrangement of cementite, into the two phase region (α+γ) or a single austenite (γ) region. Changing the carbon content or processing parameters such as austenitization temperature 16  and time and heating and cooling rates yield a variety of options in terms of volume fraction and distribution of phases as a result of austenite formation.  Carbon concentration, wt pct T  (º C )  Figure 2-6:  Part of Fe-Fe3C phase diagram (adopted from Thermo-Calc).  Addition of alloying elements such as Mn, Ni, Cr, Mo, etc. changes the phase boundaries adding degree of freedom for the heat treatment.  Arnold and McWilliam [57]  appear to have been the first to suggest that austenite formation is a nucleation and growth process. Since then, many studies have been conducted on austenite formation on steels with different alloying elements and initial structures for more than a century.  Roberts and Mehl [58]  systematically investigated the nucleation and growth of austenite in different pearlitic and hypo- /hyper- eutectoid steels.  They showed that both nucleation and growth of austenite 17  are structure-sensitive processes, i.e. the kinetics of nucleation and growth are affected by the structural features including interlamellar spacing and pearlite colony size in pearlitic steels and the size of carbide particles and ferrite grains in ferrite-spheroidized carbide structures.  2.3.2 Austenite formation from pearlite Pearlite is a product of the eutectoid reaction in steels in which austenite transforms into a lamellar ferrite and cementite structure.  A pearlitic steel with eutectoid composition, 0.76 wt pct carbon as shown in Figure  2-7, has several hierarchies in its structure.  It contains colonies of pearlite in which several nodules exist, see Figure  2-7.  Lamellae of ferrite and cementite with different orientations and spacings are located inside the nodules.  The difference in spacing in different areas may be partly due to difference in angles that the lamellae make with the plane of polish, and partly due to the fact that pearlite may have been formed in a range of temperatures.  Pearlite colony size and interlamellar spacing are the primary microstructure characteristics in pearlitic steels. Because of its lamellar nature, pearlite provides substantial interfacial boundaries.  The interfacial area per unit volume, Sv, is inversely related to interlamellar spacing[59] as shown in Equation  2-1. r v 4S λ=        Equation  2-1 18  where Sv is the interfacial area per unit volume and λr is the mean random interlamellar spacing.  In a pearlitic microstructure with an interlamellar spacing of 0.2μm, Sv will be 2×107 m2/m3.  A plain carbon steel with the carbon content lower than the eutectoid composition consists of a combination of pro-eutectoid ferrite and pearlite.  The higher the carbon content, the larger the pearlite fraction will be.  5µm Lamellae Colony interface  Figure  2-7:  Microstructure of a pearlitic structure in a 0.8C-0.25Mn steel (wt pct) with different microstructure hierarchies such as colonies and lamellae.  Nucleation of austenite in ferrite-carbide aggregates almost always takes place at the interface between ferrite and carbide because austenite can then be provided with carbon needed for further growth at the expense of carbide dissolution.  There are three different nucleation sites for austenite in pearlite as depicted in Figure  2-8, i.e. ferrite and cementite lamellae interfaces (type A), the interface between two pearlite colonies (type B) and triple 19  junctions where three pearlite colonies meet (type C)[60].  Although pearlite offers substantial A type nucleation sites, it is however energetically more favorable for austenite to nucleate at the C type nucleation sites[48]. After nucleation, austenite grows into the pearlitic structure to reach its equilibrium fraction.  This will be a full austenitic structure at above eutectoid temperature (TE) in pearlitic steels and above Ae3/Aecm temperatures (the equilibrium austenite formation finish temperatures) in hypo- /hyper- eutectoid steels, respectively.  In the intercritical annealing region, α+γ region for example as shown in Figure  2-6, the equilibrium austenite fraction can be estimated from the lever rule[61].   Figure  2-8:  Potential austenite nucleation sites in pearlite[60]. A type: the ferrite-cementite lamellae interfaces, B type: the interface between two pearlite colonies and C type: the triple junction of pearlite colonies.  20  The first step of austenite growth into pearlite consists of pearlite dissolution and growth of austenite into pearlite at a rate primarily controlled by bulk diffusion of carbon with a diffusion distance approximately equal to the interlamellar spacing of pearlite which is generally between 0.05-0.5μm.  Because of this very short diffusion distance, a rapid growth rate of austenite from pearlite is expected.  Diffusion distance of carbon in austenite is estimated to be approximately 1μm for 0.5s at 800°C1.  However, it is suggested that diffusion of substitutional alloying elements such as Mn may control the growth rate at lower austenitization temperatures[48] in C-Mn steels.  This may explain the three orders of magnitude increase in austenite growth rate from 1.1×10-7 cm/s to 2.0×10-4 cm/s when the temperature raises from 735°C to 770°C  in a plain C-Mn pearlitic steel[62]. The rate of austenite formation is faster than the rate of carbide dissolution that leaves behind carbide remnants undissolved inside austenite[58,62]. Finally, homogenization of interstitial/substitutional alloying elements takes place in the last stage of austenitization. These stages are summarized in a time-temperature-transformation (TTT) diagram shown in Figure  2-9.  Unlike austenite decomposition, the time necessary to start austenite formation decreases as the temperature rises above Ae1 (the equilibrium austenite formation start temperature).  This is because both the thermodynamic driving pressure and the atom mobility become larger at higher temperatures.  Heating rate is the other processing parameter that influences the kinetics and microstructure evolution during austenitization, details of which will be presented in the following sections.  [1] The diffusion distance, x, is estimated using x = (Dt)0.5 where D and t are the diffusion coefficient of carbon in austenite and time, respectively.  The diffusion coefficient, D, is 1.8×10-12 m2/s[50]. 21  Time, s Te m pe ra tu re , º C  Figure  2-9:  TTT diagram of austenitization for a pearlitic steel[58].  Ae1 is the equilibrium austenite formation start temperature.  Besides processing parameters, microstructure characteristics such as interlamellar spacing also influence austenite formation in pearlitic steels as shown in Figure  2-10[58].  It is clear that as the interlamellar spacing decreases, the growth rate of austenite increases.  Similar trends were reported by Caballero et al.[63] in a C-Mn pearlitic steel.  This increase in growth rate can be primarily related to the reduction of the diffusion distance for growing austenite to collect carbon as the spacing decreases. Speich et al.[62] adopted an analytical model to quantify the growth rate of austenite into pearlite, i.e. λ−π −−= γ γααγ γαγθ cD )CC( )CC(4 R&        Equation  2-2 22  where R& is the growth rate, λ is the interlamellar spacing, γcD is the carbon diffusion coefficient in austenite  and Cαγ represents the carbon equilibrium concentration in ferrite with austenite. Cγα and Cγθ are the carbon equilibrium concentration in austenite with ferrite and cementite, respectively.  Equation  2-2 clearly demonstrates that the growth rate in austenite is inversely related to the interlamellar spacing.  The effect of temperature on growth rate depends primarily on the diffusion coefficient with an Arrhenius relation with temperature.   Figure  2-10:  Effect of interlamellar spacing on the kinetics of austenite formation (adopted from Reference [58]).  Roόsz et al.[60] described nucleation and growth rates of austenite mathematically.  They correlated these rates to the characteristic parameters of the initial structure and processing parameters such as superheating such that: 23  ) T Q( 22P N e ])a[( AN Δ − λ= &        Equation  2-3 and ) T Q( i G eBR Δ − λ= &         Equation  2-4 where N& and R& are nucleation and growth rate respectively, A and B are constants, NQ and GQ are activation energies for nucleation and growth, TΔ is the superheating (T-Ac1), Pa is the edge length of a pearlite colony, λ is the interlamellar spacing, i=1 if the growth rate of austenite is controlled by volume diffusion of carbon, in accordance with Equation  2-2, and i=2 if the growth rate of austenite is controlled by boundary diffusion of substitutional alloying elements. In the case of austenite formation via continuous heating, Caballero et al.[63] reformulated Equation  2-3 to implement the effect of heating rate into the nucleation rate of austenite in a C-Si-Mn pearlitic steel: ) T Q ( 3 T c 5.0 6P N e)N()T()a(N Δ − λ= & &&       Equation  2-5 where T& is the heating rate and λ≈ 2Pc )a( 1N .  24  2.3.3 Austenite formation from ferrite-pearlite structures In ferrite-pearlite structures, it is widely reported that austenite nucleates inside pearlite colonies as well as at the interface of ferrite grains with pearlite colonies[51,54].  However, Navara et al.[64] have also shown that ferrite grain boundary nucleation can also take place without the presence of carbide particles. Savran et al.[65] have shown that both nucleation mechanisms are thermodynamically favorable.  In this scenario, the carbon needed for austenite growth will be supplied by higher carbon austenite grains formed in pearlite regions.  San Martín et al.[53] showed that the nucleation at ferrite grain boundaries can be a function of the heating rate, i.e. there is a critical heating rate beyond which ferrite grain boundary nucleation is not viable.  Using dilatometry data, Park et al.[66] have shown that in an ECAPed ferrite-pearlite structure, supersaturated ferrite grains in the vicinity of pearlite colonies will transform to austenite before pearlite colonies transformation. Speich et al.[48] specified three separate stages for growth of austenite in a ferrite-pearlite structure in a plain C-Mn steel.  It starts with a rapid pearlite to austenite transformation followed by relatively slower pro-eutectoid ferrite to austenite transformation.  The kinetics of this latter stage can be controlled either by carbon diffusion in austenite in a paraequilibrium condition where no Mn distribution is expected or by Mn diffusion in ferrite.  It is suggested that ferrite grain boundary diffusion of Mn can also be a rate controlling process at this stage.  As mentioned earlier, Mn diffusion-control stages are thought to be operative at lower temperatures compared to the carbon diffusion controlled stage.  Finally, compositional gradients will be homogenized in the third stage by the long- range diffusion of substitutional alloying elements.  Figure  2-11 summarizes different 25  stages of austenite formation from ferrite-pearlite structure in a 0.12C-1.5Mn (wt pct) steel. It can be seen that at temperatures just above the Ae1, very long intercritical annealing times are needed to reach equilibrium via a Mn diffusion-controlled reaction.  However, at temperatures near and above the Ae3, dissolution of pearlite is almost instantaneous (difficult to capture experimentally) and further growth of austenite into ferrite is controlled by carbon diffusion[48].  Time, s Te m pe ra tu re , º C Figure  2-11:  Different stages of austenite formation from ferrite-pearlite structures in a C- Mn steel[48] including pearlite dissolution and carbon and manganese diffusion-controlled austenite formation.  In the CR ferrite-pearlite structures the story is rather different.  Ferrite recrystallization and pearlite spheroidization are two additional microstructure changes that may happen before austenitization.  The sequence of these microstructure changes is strongly dependent on the 26  heating rate and steel chemistry[54,67].  Yang et al.[54] investigated the effect of initial cold reduction on the kinetics of austenite formation and its morphology.  They observed that recrystallization of deformed ferrite and spheroidization of pearlite lamellae taking place prior to austenite formation alters the distribution of austenite grains.  Austenite first forms at spheroidized particles sitting on unrecrystallized ferrite grain boundaries followed by intragranular formation on the carbide particles residing inside the recrystallized ferrite matrix.  2.3.4 Austenite formation from ferrite-spheroidized carbide aggregates Experimental observations revealed that nucleation of austenite takes place entirely at the interface between ferrite and carbides located at ferrite grain boundaries[51,68].  Austenite then tends to envelope the nearest carbides which do not themselves nucleate austenite. This process is schematically depicted in Figure  2-12 in which preferential growth along ferrite grain boundaries as effective diffusion paths is quite evident.  Carbide particles inside ferrite matrix will be dissolved at the expense of lengthening and thickening of austenite region.  Similar to the previous examples for austenite formation, complete carbide dissolution takes place after austenite formation followed by compositional homogeneity[55].  27   b a c d  Figure  2-12:  Schematic of growth of austenite and carbide dissolution in a ferrite-carbide aggregate[68] (cem: cementite, γ: austenite).  2.4 Effect of heating rate on austenite formation An increase in the heating rate shifts austenite formation start and finish temperatures, the Ac1 and Ac3 temperatures, to higher temperatures[69].  At the same time, heating rate can lead to microstructure changes in both HR and CR steels. The major microstructure change upon heating of hot-rolled steels is austenite formation. San Martín et al.[53] showed that there can be an overlap between the first two stages of austenite formation proposed by Speich et al.[48] at sufficiently low heating rates (e.g. 0.05°C/s) in a hot-rolled low carbon Nb microalloyed steel.  Savran et al.[65] also reported 28  that lamellar ferrite and cementite phases in pearlite colonies can either transform simultaneously or consecutively depending on heating rate. In the cold-rolled ferrite-pearlite structures, however, rapid heating results in an overlap between ferrite recrystallization, pearlite spheroidization and austenite formation.  This interaction directly affects the morphology of austenite and consequently mechanical properties of intercritically annealed multi-phase steels.  Huang et al.[67] systematically investigated the effect of heating rate on the microstructure of a Mo-alloyed dual phase steel.  They showed that an overlap between ferrite recrystallization and austenite formation with increasing the heating rate from 1°C/s to 100°C/s resulted in a morphological transition from a fine randomly distributed (almost equiaxed) to a banded (almost ellipsoid) structure of martensite as shown in Figure  2-13.  a 20µm  b 20µm  Figure  2-13:  Effect of heating rate on the martensite size and morphology in a Mn-Mo dual phase steel with 0.06 wt pct C, (a) CR steel, low heating rate (1ºC/s) and (b) CR steel, high heating rate (100ºC/s). 29  The extent of this overlap also depends upon the chemical composition of the steel and amount of cold reduction.  Petrov et al.[70] and Huang et al.[67] reported that an ultrafast heating rate, i.e. in excess of 1000°C/s, is needed to see the overlap in the C-Mn-Si TRIP steels used in their studies.  Kestens et al.[71] showed that this overlap is not viable even at 3000°C/s in an IF steel. An increase in heating rate can also result in grain refinement during austenitization[72]. Microstructure refinement as a result of an increase in cooling rate is well documented during austenite decomposition[73].  The refinement was related to an increase in nucleation rate driven by undercooling.  In the case of austenite formation, however, not only will the nucleation rate be increased by the superheating, but the rate of diffusion also rises simultaneously.  This combination accelerates the rate of austenite formation as the heating rate increases.  Andrade-Carozzoand and Jacques[72] have shown that the volume fraction of austenite increases from approximately 25-30 vol pct to 50 vol pct as the heating rate respectively changes from 0.5°C/s to 50°C/s in a Nb-bearing microalloyed steel intercritically annealed at 800°C.  Huang et al.[67] reported a similar trend in austenite fraction while the heating rate changes from 1°C/s to 100°C/s in a Mo-alloyed dual phase steel. Andrade-Carozzo and Jacques[72] also observed ferrite grain refinement from approximately 5μm to 1μm as a result of increase in heating rate.  30  2.5 Dilatometry evaluation of austenite formation Dilatometry is a classical approach to measure the volume fraction of transformation products in steels along with metallographic examination.  The approach is based on the fact that phase transformation in steels is accompanied by change in lattice structure that is recorded as a length change of the sample.  This length change can then be correlated to the change in specific volume.  For example, when austenite in pure iron transforms into ferrite, the volume expansion is about 1.6 pct[74]. Figure  2-14 shows a dilation-temperature diagram measured during heating of a ferrite- pearlite structure.  It can be seen that the diagram is composed of two linear portions. Lines, AA´ and BB´, represent thermal expansions of ferrite-pearlite and austenite structures, respectively.  Their slopes are the thermal expansion coefficients of the corresponding structures.  The dilation diagram deviates from linearity at point S giving a suitable estimate for the Ac1 temperature (austenite formation start temperature upon heating).  Similarly, it reaches point F that is an estimate for the Ac3 temperature.  Volume fraction, γV , of austenite between these two temperatures can be calculated as follows: BA OAVγ ′ ′=          Equation  2-6  31   Figure  2-14:  An example of dilation-temperature data for a hot-rolled plain C-Mn steel. ‘S’ and ‘F’ stand for start and finish of austenite formation, respectively.  Huang[75] proposed a similar approach to quantify austenite fraction during isothermal holding in the intercritical annealing region.  Using the dilation data, phase compositions and volume fraction of phases, it is possible to determine the kinetics of phase transformation[76].  Dilatometry analyses have been extensively employed to study kinetics of austenite formation and decomposition[67,76].  Huang[75] showed that dilatometry analyses can be applied to both processes of continuous heating and isothermal holding during austenitization.  Park et al.[66] utilized dilation data to distinguish different stages of austenite formation, for example pearlite to austenite and pro-eutectoid ferrite to austenite, in an undeformed and also ECAPed ferrite-pearlite structures. 32  The lattice parameter of austenite is a function of both temperature and carbon content[77]. At the early stages of austenite formation or at the late stages of austenite decomposition where austenite is enriched in carbon, the linear extrapolation of the dilation data can be misleading without taking into account the effect of carbon redistribution on the molar volume and thermal expansion coefficient of austenite.  Several corrections to the data analysis method have been proposed[76,78]. In the cold-rolled ferrite-pearlite structures, De Cock et al.[79] showed that ferrite recrystallization prior to phase transformation can be monitored using dilatometry data in low and ultra-low carbon steels.  The changes in the dilation data was primarily related to reduction in defect population upon heating.  2.6 Dual phase steels 2.6.1 An overview on dual phase steels Austenite formation is a critical processing step for developing a dual phase structure via intercritical annealing in CR steels.  Dual phase steels have a microstructure consisting of hard second phase particles (mostly martensite sometimes having small amounts of bainite and/or retained austenite) embedded in a ductile ferrite matrix. A large body of work has been devoted to develop dual phase steels in the 1970s.  However, use of dual phase steels was initially restricted to niche products, e.g. hot-rolled dual phase steels used in wheels. However a decade ago the increased demand from car makers for lighter, more fuel efficient yet safer vehicles has led to a renewed interest in dual phase steels.  Since then, 33  dual phase steels have been one of the most widely used grades of steels in the automotive applications.  Dual phase steels comprise 74 pct of the steels used for the body structure in the first design of the ULSAB project[80].  Dual phase steels are usually plain carbon steels containing 0.05-0.2 wt pct carbon and 0.2-2 wt pct manganese.  However, some additions of silicon, molybdenum, chromium and niobium may be added.  The purpose of these alloy additions are mainly to increase the hardenability, i.e. suppress formation of pearlite and encourage martensite formation, solid solution hardening and grain refinement.  Martensite is a metastable phase which is formed during rapid cooling of austenite from high temperatures.  Martensite is a supersaturated solid solution of carbon in ferrite with a crystal structure which is generally body-centered tetragonal (bct)[81].  As martensite is usually very hard, it is used in dual phase steels as reinforcement phase.  Since a small amount of bainite and/or retained austenite may exist within the martensite structure (depending on its chemical composition and processing parameters), the hard constituent in dual phase steels should be considered a second phase containing martensite with or without bainite and/or retained austenite.  Amongst the different alloying elements, carbon remains the most important addition through its effects on the volume fraction and strength of martensite.  Strength of martensite is mainly dependent upon its carbon content[82].  It also affects the amount of retained austenite by lowering the Ms temperature (martensite start temperature upon cooling)[83].  Dual phase steels used for automotive application usually contain 10-20 vol pct of martensite to provide the properties needed by the car makers.  34  2.6.2 Processing of dual phase steels Intercritical annealing is the major step for the processing of dual phase steels.  During this process, the steel (either hot- or cold-rolled) will be cooled/heated into intercritical (α+γ) region followed by quenching.  The industrial processes to develop dual phase steels can be summarized as follows, (i) As hot-rolled process that involves cooling from γ single phase to intercritical annealing region followed by appropriate rapid cooling and coiling to assure austenite to martensite transformation. (ii) Continuous annealed process for cold-rolled steels to heat ferrite-carbide aggregate into intercritical (α+γ) region before quenching. In this study the latter processing route is of interest where ferrite-carbide aggregates, either HR or CR, will be heated into the intercritical annealing region followed by quenching.  2.6.3 Mechanical properties of dual phase steels Dual phase steels offer unique mechanical properties features.  These features include: (i) High tensile strength (ii) Low yield ratio (iii) High initial work hardening (iv) No yield point (v) Appropriate elongation 35  A combination of proper mechanical properties and relatively easy processing makes dual phase steels the material of choice for the fabrication of complex shaped components that are particularly attractive for the automotive industries.  As can be observed in Figure 2-15, ferrite-martensite dual phase steels with tensile strength and total elongation in the range of 600-900MPa and 20-35 pct, respectively, exhibit a superior combination of strength and ductility when they are compared with other steels [84] .   Figure 2-15:  Balance between the UTS and the total elongation for different steels, replotted from Reference [84].  As a composite of hard martensite islands inside a ductile ferrite matrix, the mechanical properties of dual phase steels are a function of microstructure characteristics.  These characteristics include fraction, size, morphology and spatial distribution of ferrite and martensite.  Generally speaking, increasing the martensite fraction improves strength at the 36  expense of ductility[85].  At a fixed composition, the martensite fraction is a function of the intercritical annealing temperature.  Using the lever rule, fractions of ferrite and austenite can be estimated.  For example, using Figure  2-6 at 750°C in the intercritical (α+γ) region, ferrite and austenite fraction can be estimated in Fe-C system with nominal carbon content of C0 as follows: αγγα αγ γ − −= CC CC f 0         Equation  2-7 where the carbon concentrations for austenite and ferrite are γαC  and αγC , respectively. The volume fraction of ferrite, αf , is simply γ− f1 .  Higher intercritical temperature results in larger fraction of austenite with a lower carbon content.  For example, the carbon content of austenite decreases from 0.49 to 0.24 (wt pct) while the temperature raises from 770°C to 825°C in an Fe-C alloy[86].  Since carbon is the primary alloying element that determines the strength of martensite, it can be expected that a higher intercritical annealing temperature results in softer martensite. Size, shape and distribution of martensite islands are a function of the initial structure and processing parameters such as heating/cooling rate and annealing time and temperature. Using dedicated thermomechanical processes, Bag et al.[87] developed several morphologies of needle/blocky/banded martensite in a boron-containing dual phase steel.  Grange et al.[88] used a combination of suitable thermomechanical parameters and initial structures to achieve different morphologies of martensite (e.g. randomly distributed, fibrous) in dual phase steels and delineated the effects of martensite morphology and distribution on the 37  mechanical properties.  Huang et al.[67] also showed that the overlap between ferrite recrystallization and austenite formation results in a morphological transition from an equiaxed to a banded austenite in a Mo-alloyed dual phase steel.  All these geometrical transitions result in changes in mechanical behaviour[89].  2.6.4 Deformation behavior of dual phase steels During deformation of a dual phase steel, the ferrite matrix plastically deforms and transfers stress to the load-bearing martensite phase.  Although the hard martensite phase in dual phase steels usually remains elastic during deformation (at least in the uniform deformation regime), it may deform plastically under certain conditions.  Codeformation of ferrite and pearlite structures even at large strains has been well documented[90], however there are very few reports available on plastic deformation of martensite in dual phase steels[91-92]. Mazinani and Poole[89] demonstrated plastic deformation of martensite by measuring the average thickness of martensite islands with banded and equiaxed morphologies before and after deformation in a Mn-Mo dual phase steel.  According to their experimental results, martensite plasticity increases with an increase in the martensite content such that for the case of higher martensite content, almost no strain partitioning was found between the martensite and ferrite phases during deformation.  They also showed that the extend of martensite plasticity can be a function of its morphology since banded martensite has shown greater plasticity because of its load transfer capacity. 38  2.6.5 Continuous yielding effect It is known that a ferritic structure with or without carbide particles would show a discontinuous yielding effect[18,93,94], see Figure  2-3.  However, the yielding is continuous in ferrite-martensite dual phase steels in spite of the fact that yielding is controlled by the ferrite phase[95]. The continuous yielding of ferrite in dual phase steels can be attributed to the presence of internal stresses within the ferrite matrix as a consequence of strains associated with the martensite transformation and plastic incompatibility between the constituent phases[96]. Internal stresses can cause microyielding of the ferrite phase at regions around the martensite islands under relatively low stresses compared with the yield stress of the bulk phases that results in plastic flow of ferrite throughout the microstructure. The extend of continuous yielding can be altered via tempering of dual phase steels, a heat treatment process intended to make martensite softer and more ductile.  Several processes may happen during tempering including crystal change from bct to bcc, segregation of carbon atoms to the lattice defects, precipitation of carbides, recovery and recrystallization and transformation of retained austenite to ferrite-carbide aggregates[97], the extend of which is a function of tempering temperature and time.  Gündüz et al.[98] showed that tempering of dual phase plain carbon and microalloyed steels for 30min above 300°C results in the appearance of yield point phenomenon as depicted in Figure  2-16.  Similar observations were made elsewhere[86,99].  This trend in yielding behavior is associated with the relief of internal stresses in ferrite grains via restoration processes such as recovery and recrystallization during tempering. 39   Figure  2-16:  Effect of tempering on tensile behavior of plain carbon dual phase steel (adopted from Reference [98]).  2.6.6 Ultrafine grained dual phase steels UFG dual phase steels were first developed by Park et al.[35] in 2004.  They employed very fine ECAPed ferrite-pearlite microstructure as an initial structure for intercritical annealing. Figure  2-17 compares true stress-true strain curves for both coarse grained (CG) and UFG dual phase structures for a C-Mn steel.  Although different martensite fractions make it difficult to compare mechanical properties, it is clear that UFG dual phase steels offer higher strength at comparable ductility.  Park et al.[35] demonstrated that unlike ferrite- carbide aggregates, UFG ferrite-martensite structures maintain the characteristic properties of dual phase steels, especially a high initial work hardening rate.  They attributed the effect to martensite transformation-induced mobile dislocations in the ferrite matrix especially at 40  the vicinity of blocky martensite islands. Similar mechanical response from UFG dual phase steels was reported by Delincé et al.[100].   Figure  2-17:  True stress-true strain curves for UFG and CG dual phase steels[35]; fM: martensite volume fraction.  Calcagnotto et al.[47] showed that intercritical annealing of a low carbon steel with 1.63 wt pct Mn processed via large strain warm deformation can also lead to a UFG dual phase structure with improved properties.  But, applying the same technique to a leaner steel chemistry, i.e. 0.87 wt pct Mn, resulted in a relatively CG structure consisting of ferrite, martensite and pearlite.  Using high resolution electron backscatter diffraction (EBSD) technique, Calcagnotto et al.[47] showed that the population of dislocations in ferrite grains to accommodate the strain imposed by martensite transformation increases with decreasing ferrite grain size. Mukherjee et al.[36] successfully developed UFG dual phase structures through more industrial-adaptive techniques like SIT.  However, detailed assessment of 41  mechanical response using tensile tests is lacking in their study.  Overall, there are very limited numbers of studies devoted to the recently developed UFG dual phase structures[35,36,47,100,101,102].  2.7 Modelling of austenite formation from ferrite-carbide aggregates Microstructure modelling can greatly aid advancement of knowledge on the mechanisms of austenite formation and its morphological complexity.  However, modelling of austenite formation has been much less studied than austenite decomposition.  Details about recent developments on modelling of austenite formation can be found elsewhere[103]. In addition to the morphological complexity the generally non-additive character of this transformation constitutes a challenge to develop straightforward models using phenomenological approaches like the Johnson-Mehl-Avrami-Kolmogorov[104-105]  (JMAK) theory that is widely used to describe the austenite decomposition kinetics.  Roberts and Mehl[58] employed a nucleation and growth model to predict the kinetics of austenite formation.  Speich and Szirmae[62] explained the kinetics of isothermal austenite formation in Fe-C and Fe-C-Mn systems using the JMAK model, i.e.: )tRN 3 4exp(1f 3v & π−−=        Equation  2-8 where vf  is the austenite fraction, N is the number of nuclei per unit volume and R& is the growth rate.  In their approach, they assumed nucleation site saturation and a constant growth rate for austenite. 42  Several authors have used the JMAK type approaches to model austenitization of pearlite/ferrite-pearlite structures during isothermal holding or continuous heating[50,60,106- 107].  For example, Roόsz et al.[60] described isothermal austenite formation in a pearlitic steel with different interlamellar spacing using the JMAK model.  Caballero et al.[63] exploited the model to include the effect of heating rate on kinetics of austenite formation. They described the reaction during continuous heating with T& heating rate as fol1ows: )dTTRN )T(3 4exp(1x 33 T Ac 41 Δπ−−= ∫ &&&      Equation  2-9 where x is the austenite fraction upon heating form Ac1 to temperature T and N& and R& are the nucleation and growth rates defined in Equation  2-4 and Equation  2-5, respectively. The kinetics of austenite formation was also modelled analytically in ferrite-carbide aggregates.  Judd and Paxton[52] developed an analytical model to predict growth rate of an austenite rim around a carbide particle with spherical geometry and an initial diameter of 0r as shown in Figure  2-18a.  In their model, the growth rate is controlled by carbon diffusion in austenite.  The change in outer and inner diameter of austenite shell is as follows: ])Er)E1(r(Er)E1(r)[ CC CC ( ED2 1t 3/23b 3 0 2 b 2 0 C −+−−+− −= γαγθ αγγα γ   Equation  2-10 43  where t is time, γCD  is the diffusion coefficient of carbon in austenite, )CC/()CC(E γθθαγγα −−=  in which the concentrations ( γθθαγγα C,C,C,C ) are defined in Figure  2-6 and the inner radius is obtained from ]Er)E1(r[r 3b 3 0 3 a −+= . Akbay et al.[108] expanded the solution to the planar interface, see Figure  2-18b, to model lamellar pearlite to austenite transformation in Fe-C and Fe-C-X (X: substitutional alloying element) systems.  This will change Equation  2-10 to: ])rr)(E1)[( CC CC ( D2 1t 2b0 C −+− −= γαγθ αγγα γ  Equation  2-11  Akbay et al.[108] and Mancini et al.[109] also employed numerical finite difference method to model austenite formation from ferrite-carbide aggregates.  a  c  Figure  2-18:  Schematic of growth of austenite (grayish region) into ferrite and cementite in (a) cylindrical/spherical and (b) planar geometry (r0: initial interface between ferrite and cementite, ra and rb: austenite fronts into cementite and ferrite, respectively) with (c) schematic of their carbon concentration profile.  b 44  Speich et al.[62] introduced an analytical model to calculate growth rate of austenite nuclei in a fully pearlitic structure as explained in section 2.3.2. Gaude-Fugarolas and Bhadeshia[110] developed a diffusion controlled growth model to predict the progressive transformation of different phases in hypo-eutectoid steels (pro- eutectoid ferrite and pearlite) into austenite: ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ − −≈υ αγγα γαγθγ CC CC r DCint       Equation  2-12 where intυ is the velocity of the austenite interface, γαC , αγC and γθC are defined in Figure  2-6, γCD  is the diffusion coefficient of carbon in austenite and r is the diffusion distance in austenite.  They assumed once all the pearlite has been transformed into austenite, the austenite/ferrite interface keeps advancing into ferrite grains until all the material has been reaustenitised. Recent advances in computational materials science provide now a suite of modelling approaches that can be employed.  In particular, phase field models (PFMs) are a powerful tool to capture transformations with morphological complexity, e.g. the prediction of dendritic growth during solidification[111–112].  PFMs are phenomenological models that are formulated on the length scale of the microstructure, i.e. the so-called meso-scale. PFMs have been successfully employed to describe the austenite to ferrite transformation with simulations in 2D and 3D[113–114].  Some very initial PFM work has also been reported for austenite formation[115,116,117].  In the next section, a brief description of multiphase field model together with the application to austenite formation will be presented. 45  2.8 Multiphase field models 2.8.1 Overview In the phase field approach a phase field parameter is introduced to describe the free energy of the system. Microstructure evolution is described to minimize the free energy, F, using the Ginsburg-Landau equation, i.e.: δφ δ−=φ FM dt d         Equation  2-13 The factor δφ δ− F is the thermodynamic driving force, which drives the system towards the equilibrium and M is a frictional coefficient associated with dissipation during transformation. Steinbach et al. proposed an extension of the PFM approach by introducing the multi-phase field concept. The formulation of the multi-phase field model used here is based on the approach of Steinbach et al.[118].  In this approach, a polycrystalline system of N grains is described by a set of N order parameters )t,r(iφ , also represented by the vector ),...,,( N21 φφφ=φ r . Time evolution of order parameters )t,r(iφ  is obtained by minimizing the total free energy of the system, F , which is assumed to be a functional of the phase field vector ),...,,( N21 φφφ=φ r  and its gradient ),...,,( N21 φ∇φ∇φ∇=φ∇ r .  Here, each grain i is prescribed by its own phase field parameter iφ  [i=1,…,N].  Inside grain i, iφ  is equal to 1 while it is 0 outside the grain.  At the interface between two grains, i and j, there is a gradual change of the two corresponding phase field parameters from 0 to 1 with 1ji =φ+φ  or in a more generalized way 46  1)t,r( N i i =φ∑  holds at position r in the simulation domain with a total number of N grains, see Figure  2-19.  The interface thickness is taken to be the same for each pair of grains in contact, i.e. ηij=η.  a  Figure  2-19:  (a) Representation of the microstructure and (b) change in the phase field parameter ( iφ ) along line AA ′ depicted in part (a).  A solution for the differential equation presented in Equation  2-13 is given by Mecozzi [119].  The solution is presented as the rate of change in each phase field parameter with time which is given by pairwise interaction with all neighbouring grains[118]: ∑ ≠ ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ Δφφη π+φ−φη π+φ∇φ−φ∇φσμ=φ ji ijji ij ji2 ij 2 j 2 ii 2 jijij i G)]( 2 [ dt d  Equation  2-14 where ijμ is the interface mobility, ijσ is the interfacial energy, ijη is the interface thickness and ijGΔ is the driving pressure between grains i and j.  The phase field equations are b 47  coupled with the diffusion equations for carbon to describe phase transformations in the Fe–C systems. When neighbouring grains have the same phase, ijμ and ijσ are grain boundaries mobilities and energies, respectively.  In the case ijGΔ is zero and the driving pressure for the grain growth is given by the respective grain boundary energy times the curvature term (the term within square bracket in Equation  2-14).  2.8.2 Phase field modelling of austenite formation Thiessen et al.[120] employed phase field model to investigate austenite formation from ferrite-pearlite/martensite structures during welding process in the heat affected zone (HAZ).  However, to minimize computational cost they simplified pearlite as supersaturated ferrite with eutectoid carbon content and without resolving carbide lamellae. Thus, the model lacks detailed examination of microstructure complexity.  Using the same approach, Savran[117] modeled austenitization of medium carbon steels for continuous heating with different heating rates using the interfacial mobility as an adjustable parameter.  Savran[117] also attempted to resolve carbides in the lamellar structure; however, the physical parameters such as interfacial energies used for the model were unrealistic. For example, the value used for austenite-ferrite interfacial energy is 0.039 Jm-2 which is an order of magnitude smaller than typical ones used in the literature[121].  Further, Savran considered nucleation of austenite at the ferrite-cementite lamella interface (type A as shown in Figure  2-8) that is not observed experimentally[48].  Cordonier et al.[115] 48  investigated the effect of growth geometry on the austenite formation rate during intercritical annealing of ferrite-pearlite structure.  In their study, pearlite was considered to be already transformed to austenite at the onset of simulation.  Thus, resolving nano-size carbide particles remains one of the main challenges in studies devoted to austenite formation from ferrite-carbide aggregates.              49  Chapter 3 Scope and Objectives of the Thesis This study aims to examine new approaches to engineer microstructures of a plain low carbon steel with lean chemistry (0.17C-0.74Mn, wt pct) for improvement in mechanical properties.  To fulfill this goal, new processing techniques to develop bimodal ferrite grain size structures and ultrafine grained dual phase steels are introduced.  As an essential step for producing dual phase steel, a systematic study on austenite formation is conducted where the effect of initial structure and heating rate on microstructure evolution and dilation response is investigated. To accomplish this overall goal, the following sub-objectives are sought in this work: (i) One of the objectives of this study is to introduce a bimodal size distribution of ferrite grains in a low C-Mn steel.  The work aims at quantifying mechanical properties of these heterogeneous structures in comparison with UFG structures having a uniform distribution of ferrite grains. (ii) The work on developing UFG dual phase steels considers processing strategies that are suitable for sheet products.  The effect of initial structure and processing parameters on microstructure evolution and mechanical properties will be systematically studied.  Further, the work will examine the effect of initial structure and heating rate on dilation response and microstructural evolution during austenite formation in a systematic manner. (iii) Phase field model will be employed to predict microstructure evolution during intercritical from ferrite-carbide aggregates at intercritical annealing region.  Simulation 50  results will then be compared with experimental observations on austenitization of UFG ferrite-carbide aggregates.                  51  Chapter 4 Methodology 4.1 Material A plain low carbon steel received as industrially HR material was used for this study. The detailed chemical composition is presented in Table  4-1.  Table  4-1:  Chemical composition of the steel used in this study in wt pct Element Fe C Mn P S Si Al N wt pct Bal. 0.17 0.74 0.009 0.008 0.012 0.04 0.0047  Three different experimental strategies were adopted in this study.  These strategies were employed to investigate (i) the development of bimodal ferrite grain size structures, (ii) austenite formation and (iii) characteristics of UFG dual phase structures, the results of which will be presented in the next three chapters.  4.2 Experimental approaches 4.2.1 Processing routes 4.2.1.1 Development of bimodal ferrite grain size structure The thermomechanical treatment designed for producing a bimodal grain size structure is schematically summarized in Figure  4-1.  The samples were initially austenitized at 1000°С for 30min followed by rapid quenching into an ice brine solution (stage I in Figure  4-1). 52  The resulting martensite structure was then intercritically annealed in a salt bath at 740°С for 10min followed by direct quenching into an ice brine solution (stage II).  The resulting ferrite-martensite dual phase structure was cold rolled with 50 pct reduction using a laboratory rolling mill (roll diameter: 130mm) (stage III), then annealed between 500- 600°С for different times in an Ar atmosphere (step IV) before water quenching.  Except for the second stage, i.e. intercritical annealing, the process is similar to that of martensite straining to produce a UFG structure.  Details about the martensite straining process can be found elsewhere[29].   Figure  4-1:  Schematic representation of thermomechanical process to develop bimodal ferrite grain size.  53  4.2.1.2 Austenite formation Two sets of samples, both HR and CR, were used for austenite formation studies.  The HR steel was 80 pct cold-rolled, i.e. from 9.8mm to 1.8mm.  Test coupons of 10×60×1.8 mm were cut from the HR and CR sheets with the longitudinal direction of the test coupon being aligned with the rolling direction, Figure  4-2. A Gleeble 3500 thermomechanical simulator was employed for all heat treatments.  The temperature was controlled using a type K thermocouple spot-welded on the center of the sample.  Dilatometry tests were conducted under high vacuum (≈ 0.26 Pa (2.0×10-3 Torr)). Continuous heating tests were performed with heating rates ranging from 1°C/s to 900°C/s.  A dilatometer was attached to the center of the samples to measure the change in width during heating.  The volume fraction of austenite was determined via analyzing the dilatometric data using the lever-rule as explained in section 2-5.  To analyze the microstructure during heating, additional samples were then subjected to interrupted heating tests and water quenched.  The holding time before quenching was approximately 1s.  The cooling rate was approximately 1000°C/s to ensure complete austenite to martensite transformation upon quenching.  For these tests, the test chamber was back filled with inert Ar gas after a high vacuum had been achieved. 54  L=60mm Type K  thermocouple Φ = 5.16mm W =1 0m m 1.5 mm Longitudinal Figure  4-2:  Schematic illustration for the dimension of the Gleeble test sample.  4.2.1.3 Production of UFG dual phase steels In order to investigate the effect of initial structure on the final microstructure and properties of dual phase steels three different thermomechanical processes were designed. Figure  4-3 shows these processes schematically.  In process (I), Figure  4-3a, the initial HR ferrite-pearlite structure was first austenitized at 1000°C for 30min followed by ice brine quenching to assure a fully martensitic structure.  It was then 80 pct cold rolled with a laboratory rolling mill (roll diameter: 130mm).  In process (II), Figure  4-3b, a martensite structure was first annealed at 550°C for 2hrs and then 80 pct cold rolled. In process (III), Figure  4-3c, after annealing of martensite structure at 550°C for 1h followed by 80 pct cold rolling, an additional 75min annealing at 550°C was performed.  All tempering treatments were performed in a tube furnace with Ar controlled atmosphere.  The samples resulting from different processes were then rapidly heated into the intercritical annealing region at 300°C/s and held for 10s at 750°C followed by water quenching.  The effect of intercritical 55  processing parameters such as heating rate and holding time were systematically investigated.  All intercritical annealing treatments were done at 750°C.  Additional heating rates of 1°C/s and 50°C/s were used for comparison purposes and the holding time varied from 1-300s.  Test coupons of 93×12×0.7mm were machined from the cold rolled sheets with the longitudinal direction of the test coupon being aligned with the rolling direction. All controlled heating rate experiments were conducted in the Gleeble 3500 thermomechanical simulator.  The testing chamber was first put under high vacuum and then back filled with Ar.  The temperature was controlled using a type K thermocouple spot-welded on the center of the sample.  a  b  c  Figure 4-3:  Thermomechanical processes employed to develop different initial structures.  4.2.2 Microstructure characterization Microstructural analysis was carried out along the transverse direction (TD), i.e. the plane perpendicular to both the rolling and normal directions. 56  Microstructures were characterized using optical and electron microscopy.  A Hitachi S2300 SEM with a secondary electron detector and an energy-dispersive X-ray (EDX) system for chemical analysis was utilized. A Hitachi H-800 transmission electron microscope (TEM) operated at 200kV was employed for TEM observation.  For measuring the size of the cementite particles, a Hitachi S4700 field-emission SEM at 50k magnification was employed. Scanning Auger microscopy (SAM) was used for characterization of carbide particles using a Microlab 350 system (Thermo Electron Corp.) equipped with field emission source (10keV, 3.5nA) and hemispherical energy analyzer in a vacuum of 2×10-7 Pa.  A secondary electron detector attached to the equipment was used to select carbide particles. Electron backscatter diffraction (EBSD) analysis was performed using a Schottkey source field emission scanning electron microscope. The data analysis was performed with HKL Channel 5 software. Different sample preparation techniques and etchants were used to reveal microstructures metallographically: (i) For optical microscopy observations, samples were mounted and then mechanically grounded and polished, with the final polishing step using 1.0 micron silica solution. Polished samples were then etched in 2 pct Nital. (ii) LePera etching[122] was employed to reveal martensite and to measure the volume fraction of austenite (martensite at room temperature) from optical micrographs, Figure  4-4. 57  50µm a  50µm b  Figure  4-4:  (a) Dual phase structure etched with LePera (Ferrite matrix: brown, martensite islands: white) and (b) after threshold adjustment in the Clemex software (Ferrite matrix: blue, martensite islands: red).  (iii) In order to reveal prior austenite grain boundaries, the following procedure was followed: first as quenched samples were tempered in a tube furnace at 550°C for 15h in an Ar atmosphere followed by water quenching.  Then, an etching solution composed of aqueous picric acid with sodium dodecylbenzene, copper chloride and a few droplets of Triton X-100 as a surface active agent at a temperature range between 60°C and 80°C were used to reveal austenite grain boundaries.  Grain size measurements were based on the equivalent area diameter (EQAD) approach and at least 500 grains were analyzed using SEM.  The quantitative measurements were conducted using Clemex image analysis software. (iv) For SEM and EBSD analyses, samples were electropolished in 95 pct acetic acid and 5 pct perchloric acid solution.  Then, the samples etched with 2 pct Nital for SEM analyses. 58  (v) To reveal cementite particles inside martensite islands, two-step etching was employed.  After light etching with 2 pct Nital, deep etching using 4 pct Picral for 10-15s was performed[123].  These samples were also used for Auger measurements. (vi) For TEM observations, thin foils were prepared by twin-jet polishing technique using a mixture of 95 pct acetic acid and 5 pct perchloric acid at an applied potential of 40V at 20°C. The deformation of the pearlite/martensite phases ( .thick.pearlε and .thick.martε ) was measured through a series of thickness measurements of the pearlite colonies/martensite islands before and after rolling using Clemex image analyzer software.  At least 30 different images from different locations through the thickness were examined amounting to approximately 20,000 measurements in both as-received/as-quenched and as-rolled samples.  Having these measurements, the data was analyzed to calculate the average martensite/pearlite thickness using a weighted line length average: nt t n t t t t n n 1i 2 i n 1i i n i ∑∑ == ==        Equation  4-1 where n is the number of thickness measurement, ti is the measured thickness and nt is the average thickness ( n/)t(t n 1i i∑= = ).  The average level of strain in the martensite/pearlite phases was then measured using: ) t t ln( initial .def.thick =ε        Equation  4-2 59  where ititialt is the average initial thickness and .deft  is the average deformed thickness. Details of the procedure for the strain measurement can be found elsewhere[86].  4.2.3 Tensile tests To quantify mechanical properties, tensile tests were conducted on samples with a 40 mm gauge length at a nominal strain rate of 1×10-3s-1 using a MTS servo-hydraulic machine. For the dual phase structures intercritically annealed using the Gleeble 3500, smaller subsize tensile test samples with a 12.5mm gauge length as depicted in Figure  4-5 were prepared.  An extensometer was used to measure the axial elongation of the tensile sample. The reported tensile test experiment results are the average of at least two tensile tests.   Figure  4-5:  Subsize tensile specimen according to the ASTM E8, dimensions are in ‘mm’.     60  Chapter 5 Bimodal Ferrite Grain Size Structures  5.1 Introduction In this chapter a new method is proposed to create bimodal microstructures in low carbon steels.  The hypothesis for this work was developed from the observations that under suitable conditions, the martensite in ferrite-martensite dual phase steels co-deforms with the ferrite[89].  Thus, it was proposed that a bimodal grain size distribution could be produced by cold rolling of a ferrite-martensite dual phase steel and then annealing, i.e. the ferrite would recrystallize resulting in a conventional grain size and the deformed martensite would recrystallize to form UFG ferrite, details of which are presented in this chapter.  5.2 Results and discussion 5.2.1 Initial structure Figure  5-1 shows the initial HR ferrite-pearlite structure consisting of approximately 20 vol pct pearlite and 80 vol pct ferrite.  The HR microstructure is banded which can be related to the segregation of Mn.  EDAX analysis confirmed that concentration of Mn in ferrite region was close to the nominal value in the steel, however, it indicated segregation inside pearlite colonies with an average Mn content of approximately 1.0 wt pct and an average distance of 12μm between pearlite bands.  Figure  5-1b depicts SEM micrograph for the HR structure.  Ferrite grain size and pearlite interlamellar spacing are approximately 7μm and 61  240nm, respectively.  Individual cementite particles were also observed at ferrite grain boundaries (indicated by arrows in the inset in Figure  5-1b).    Figure  5-1:  (a) Optical and (b) SEM micrographs of initial HR ferrite-pearlite structure. Pearlite is dark and ferrite is gray in color in the optical micrograph and F, P and C stand for ferrite, pearlite and cementite, respectively, in the SEM image.  5.2.2 Development of bimodal ferrite grain size structure Figure  5-2a illustrates the dual phase structure produced by intercritical annealing of the initial HR structure at 740ºC and quenching; the structure consists of 60±1 pct ferrite and 100μm a 62  40±1 pct martensite measured using the Clemex image analysis software.  Ferrite grains were primarily equiaxed in morphology and ranged from 2µm to 6µm in size.  The martensite islands have an irregular shape varying from a lath type to a roughly equiaxed structure.  The carbon concentration in austenite after intercritical annealing was estimated to be 0.4 wt pct, using paraequilibrium (PE) calculation (note: paraequilibrium indicates constrained equilibrium without partitioning of substitutional alloying elements).  Figure  5-2b shows the dual phase structure after 50 pct cold reduction (equivalent strain of 0.8). Deformation of the ferrite matrix with martensite particles results in a heterogeneous distribution of the plastic strain.  The ferrite matrix is heavily deformed whereas plastic deformation of martensite occurs to a far lower extent.  Measurement of the change in the martensite islands’ thickness before and after deformation gives a strain level for martensite of .thick.martε =0.10 with a standard deviation of σ = 0.01.  This strain indicates that there is plastic deformation of martensite albeit at a level considerably below the applied rolling strain.  The deformed dual phase structure was then annealed between 500ºC-600ºC. Among the different annealing conditions, holding at 525°С for 1200min was found to offer an appropriate condition for developing a bimodal structure, Figure  5-2c.  Annealing at lower temperatures resulted in ferrite - tempered martensite structures while annealing at higher temperatures resulted in coarse ferrite-carbide aggregates, Figure  5-3.  63     Figure  5-2:  SEM micrograph of (a) initial dual phase microstructure, (b) dual phase microstructure after 50 pct cold reduction and (c) final structure after annealing at 525°С for 1200min.  ‘F’, ‘M’ and ‘Rex. M’ represent ferrite, martensite and recrystallized martensite, respectively.  64  After annealing the deformed structure at 525°С for 1200min it can be seen that both the ferrite and martensite recrystallize (Figure  5-2c).  Further, precipitation of iron carbide (Fe3C) occurs in the martensite regions during the annealing step.  As a result, a heterogeneous microstructure forms consisting of areas of fine grains with sizes of 2µm and smaller in a matrix of larger grains with sizes ranging from 3-15µm.  5µm  5µm  Figure  5-3:  SEM micrograph of deformed dual phase steel annealed at (a) 500ºC for 1440min and (b) 600 ºC for 30min. 65  5.2.3 Grain size measurements The grain size distribution obtained for this heterogeneous microstructure shown in Figure  5-2c is depicted in Figure  5-4.  Figure  5-4a shows the measured size distribution of the entire range of grain sizes (bar chart) together with a log-normal fit (solid line curve), i.e.[124]: ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ σ − πσ= 2 2 p 2 )}x/x{ln( exp 2x 1)x(f      Equation  5-1 where x is the grain diameter, σ is the standard deviation of natural logarithm of x and xp is the median grain size.  In the present case, a good fit to the distribution is obtained with σ = 0.55 and xp = 0.4µm.  At first sight, the log-normal fit appears to provide an adequate description of the grain size distribution. However, closer examination indicates that there is a clear tail of large grains which lie outside the log-normal distribution.  Because there are many more small grains in the distribution, these grains determine the apparent character of the grain size distribution.  In fact, if one removes the larger grains (>3µm), the population of the smaller grains can essentially be described by the same log-normal distribution (see dashed line in Figure  5-4a).  However, from a volumetric point of view, the large grains can not be neglected; for example one grain of 10µm diameter is of the same volume as 1000 grains of 1µm diameter.  Thus, in order to capture a statistically relevant representation for the distribution of larger grains, lower magnification observation is required. 66     Figure  5-4:  (a) Grain size distribution, (b) grain size distribution for coarse grain size populations and (c) volume fraction of fine and coarse grain size classes.  67  Using this approach, the larger ferrite grains were measured showing a log-normal distribution with a median grain size of 4.6µm and a standard deviation of σ = 0.56, Figure  5-4b.  Two different regimes of grain size, fine and coarse, can be distinguished from these separate measurements, although there is a small region of overlap for grains in the range of 1-3µm.  When considering mechanical behavior, the volume fraction of individual grain size classes is of primary importance.  Using the frequency distribution, i.e. here the log- normal distribution, f(x), volume fraction of grains with size x, fV, can be written as: ∫ = dx)x(fx )x(fxf 3 3 V       Equation  5-2 Figure  5-4c shows the volume fraction of grains for the microstructure shown in Figure  5-2c.  For simplicity, the analysis is based on the measured equivalent area diameter rather than the true volumetric diameter.  Further, the volume fraction of each class of grain size has been scaled based on the volume fraction of ferrite and martensite in the initial dual phase structure, i.e. 60 pct for the coarse grains and 40 pct for the fine grains. The key to understanding how these microstructures develop lies in a consideration of how the ferrite-martensite microstructure responds to this processing route.  During cold rolling, plastic deformation of martensite occurs.  Mazinani and Poole[89] have recently shown that martensite plasticity can be significant in low carbon steels, depending on the carbon concentration and morphology of the martensite phase.  This is important because in the absence of plastic deformation of the martensite phase (stage II in Figure  4-1), annealing produces tempered martensite and recrystallization does not occur at short times.  For 68  example, Speich and Leslie[125] have reported that recrystallization of martensite in 0.18 wt pct carbon steel occurs only after annealing for 96h at 600°С. In the present case, there is a complex interaction between recrystallization and precipitation that must be controlled to produce the final UFG structure in the martensite regions.  It is worth noting that  particle pinning is enhanced when interparticle spacing and grain size become comparable, as analyzed in more detail by Bréchet and Militzer[126]. Zhao et al.[39] have also shown that in a steel with 0.45 wt pct carbon, comparable with the carbon concentration of martensite in the dual phase structure, ferrite grains with less than 1µm in size will not coarsen even after 3000min annealing at 500°С.  On the other hand, the ferrite regions in the microstructure will deform greater than the average during cold rolling (i.e. since the martensite deforms less than average).  These regions subsequently recrystallize during annealing.  One may speculate because of relatively low number of recrystallization nuclei and the absence of Fe3C particles to pin grain boundaries in the ferrite regions, a relatively coarse grain structure is produced in these regions compared to the martensite regions. 5.2.4 Mechanical properties In order to examine the mechanical response of the bimodal structures, tensile tests were conducted.  The ultimate tensile strength (UTS) and uniform elongation of the annealed structure (Figure  5-2c) is 550MPa and 14 pct, respectively (gray line in Figure  5-5).  In comparison, cold rolling of a fully martensitic structure followed by annealing gives a UTS of 560MPa and a uniform elongation of 12 pct, i.e. quite similar results (black line in Figure  5-5).  However, the material with a bimodal grain distribution shows continuous yielding 69  whereas processing of a fully martensitic steel produced an undesirable Lüders strain of more than 5 pct.  One can speculate that the continuous yielding behavior of bimodal grain structures is similar to observations made for dual phase steels, i.e. the islands of UFG which have a relatively high strength may act in similar manner to martensite islands in the dual phase structures.  Thus, the optimum balance of strength and ductility in these composite type structures strongly depends on the morphology, volume fraction and distribution of martensite and ferrite in the dual phase steels and similarly fine and coarse grains in the bimodal structures.   Figure  5-5:  True stress-true strain curves for bimodal grain size structure (gray line) and a UFG structure (black line).  An advantage of the present approach is that through controlling the volume fraction, morphology and distribution[67] of ferrite and martensite in the initial dual phase structure it 70  is possible to develop a wide range of various bimodal grain size structures with different fractions of fine and coarse grains etc. The present processing route appears to be a very simple method which could be readily applied to the industrial production of sheet. Well established industrial processes, intercritical annealing of hot (or cold) rolled products followed by cold rolling and subsequent batch annealing could be used to produce these microstructures without the need for large strain processes such as equal channel angular extrusion or martensite rolling.  5.3 Summary In summary, a novel processing route for generating bimodal ferrite grain size structures in low carbon steels has been demonstrated.  The processing route is based on rolling and appropriate annealing of ferrite-martensite dual phase structures.  The concurrent recrystallization of ferrite and martensite combined with carbide precipitation in the martensitic regions are the main mechanisms by which this heterogeneous microstructure can be created.  Although the proposed method enhances mechanical properties, there is limited improvement of work hardening response compared to UFG ferritic structures. Dual phase steels have proven to be an appropriate candidate to tackle the problems related to UFG ferritic structures.  Further, it is shown that unlike ferrite-carbide aggregates, the work hardening rate in UFG dual phase steels is not deteriorated by grain refinement. Yet, providing a simple approach may open new avenues for developing structures with 71  improved balance between strength and ductility in UFG steels.  Since austenite formation is an essential step to produce dual phase structures, detailed examination of austenite formation from ferrite-carbide aggregate will be provided in the next chapter.              72  Chapter 6 Austenite Formation in Plain Low Carbon Steels 6.1 Introduction This chapter deals with austenite formation in plain low-carbon steels. This process is an essential step to develop dual phase steels.  Therefore, a detailed understanding of mechanisms of austenite formation can be utilized to advance dual phase steels.  In this section, the effect of initial structure and heating rate on microstructure evolution and dilation response during austenite formation in plain C-Mn steels will be studied.  6.2 Results 6.2.1 Initial structures Initial HR structure shown in Figure  5-1 was 80 pct cold rolled.  Figure  6-1 shows the CR structure, where alignment of ferrite grains and pearlite colonies in the rolling direction is evident. The higher magnification inset in the figure shows fragmentation and bending (arrows) of carbide plates. After 80 pct cold reduction, there was an inhomogeneous distribution of deformation in ferrite and pearlite.  Measurement of the average thickness of pearlite colonies before and after deformation showed that the amount of cold reduction is only 70 pct in pearlite, 01.02.1.thick.pearl ±=ε .  Both the HR and CR structures were used as initial structures to study austenite formation.  73   Figure  6-1:  Initial HR structure after 80 pct cold reduction. The inset show higher magnification image. RD and ND are rolling and normal directions, respectively (F: ferrite, P: pearlite).  6.2.2 Dilation response and microstructural characteristics in the HR and CR materials Figure  6-2 shows dilation curves for the HR and CR samples (black and gray lines, respectively) heated at 1°C/s into the single austenite phase region.   Using the first derivative of the dilation curves several evolution steps can be distinguished.  In region (1) lattice expansion in ferrite-pearlite structures in both HR and CR samples takes place upon heating.  Recovery of the deformed structure can also occur in the CR sample.  In region (2) deviation from linear thermal expansion can be seen in the CR sample while the dilation response in the HR steel remains unaffected.  Both of these two stages are prior to austenite 74  formation.  A sharp drop in the dilation curve is evident in both HR and CR samples in stage (3) that is related to the pearlite to austenite transformation.  Austenite formation continues in region (4) for both steels.  The dilation in this region can be related to the ferrite to austenite transformation.  Finally, in region (5), linear lattice expansion of austenite after completion of transformation is observed.  In detail these stages can be rationalized as follows:   Figure  6-2:  Dilation curves and their first derivatives for the HR and CR steels during heating at 1°C/s.  75  1) Thermal expansion of ferrite-pearlite structure In region (1), below ≈ 500°C, lattice expansion of ferrite-pearlite structure takes place in both HR and CR structures upon heating.  In the CR sample recovery of the deformed structure can proceed via rearrangement and annihilation of dislocations but this can not be observed with dilatometry.  The microstructural features of the CR steel remain unaffected, compare Figure  6-3a and Figure  6-1.  The measured linear thermal expansion coefficient of ferrite-pearlite structure is ≈ 16.0×10-6 °C-1 that is in good agreement with the available data in the literature[127]. 2) Recrystallization of ferrite in the CR sample In region (2), the linear thermal expansion continues in the HR sample, but it deviates from linearity in the CR steel.  This deviation starts at ≈ 500°C and reaches up to 0.1 pct at 650°C.  Microstructural observations, shown in Figure  6-3b, indicate that there are two major changes during this process: (i) recrystallization of deformed ferrite grains and (ii) spheroidization of cementite particles. The deviation from a linear coefficient of thermal expansion could arise from a number of mechanisms, i.e. i) volume change due to loss of dislocation density during recovery and recrystallization, ii) change in crystallographic texture, iii) dissolution/spheroidization of carbides and iv) relaxation of residual stresses from cold rolling.  Further examinations, presented in detail in the Appendix A1, revealed that ferrite recrystallization is the main mechanism responsible for the observed deviation.  76   Figure  6-3:  Microstructure evolution of the CR structure quenched at (a) 510°C (point A in Figure  6-2) and (b) 670°C (point B in Figure  6-2) during heating at 1°C/s.  3) Pearlite to austenite transformation The first stage of austenite formation in the HR and CR steel consists of pearlite to austenite transformation (stage (3)). The sharp drop in the first derivative of the dilation curve in Figure  6-2 indicates relatively fast phase transformation rate.  Closer observation reveals that the transformation started earlier in the CR samples.  The lower level of the first derivative curve for the CR sample in this stage suggests a slower transformation rate as compared to the HR sample.  Figure  6-4a shows martensite (formerly austenite at high temperature) sweeping lamellar pearlite colonies in the HR material.  There is almost no sign of spheroidization of cementite lamella inside pearlite colonies prior to austenitization. It has been reported that austenite mainly nucleates at ferrite-pearlite interfaces as well as the interface between pearlite colonies[62].  In addition, simultaneous nucleation of austenite at ferrite grain boundaries, especially at carbide particles, has also been reported at low heating rates[53]. 77  However, the situation is quite different in the CR steel.  Figure  6-4b represents early stages of austenite formation in the CR steel at 730°C. It can be seen that cementite lamellae were mostly spheroidized (≈ 90-95 pct) even though some small fraction of the lamellar structures are still preserved in the microstructure (shown by arrow P in Figure  6-4b). Closer examination of these latter regions reveals an interesting observation.  The bright field (BF) TEM image shown in Figure  6-4c provides an example for a ferrite recrystallization front moving into the deformed lamellar leaving behind rows of spheroidized carbides.  This provides evidence that this is one mechanism to produce spheroidized carbides which is not available in the undeformed case.  These carbides are clearly visible in Figure  6-4b and Figure  6-4d (indicated by arrow C). At the same time, deformed ferrite layers inside pearlite colonies recrystallize and form very fine equiaxed grains that are pinned by carbide particles, Figure  6-4d. Recrystallization is complete prior to austenite formation except for the small regions in the pearlite colonies (e.g. P in Figure  6-4b).  Nucleation and growth of austenite occur from the ferrite-spheroidized cementite aggregates. Growth of austenite continues until consumption of the aggregate is complete.   78    Figure  6-4:  (a) SEM micrograph of HR steel heated at 1°C/s to 735°C, (b,d) SEM images and (c) BF TEM micrograph of CR steel heated at 1°C/s to 730°C (F:  ferrite, M: martensite, P: pearlite, C: cementite).  Figure  6-5a shows the presence of particles inside martensite (austenite at high temperature) in the CR sample at 740°C.  The presence of the particles inside martensite after completion of pearlite to austenite transformation was also observed for the HR steel.  To confirm that these particles are carbides, Auger electron microscopy was used.  Prior to taking Auger spectra, surface contaminations were removed by sputtering with Ar ions.  Figure  6-5b provides an example of Auger electron spectra where the carbon content of the particle 79  there is a sharp increase in carbon content in the particle compared to the matrix.  Further analysis on the particles using differentiation spectrum, Figure  6-5c, compared with the reference data[128] indicates that the carbon is present in the form of a carbide that is most probably cementite.    Figure  6-5:  (a) Microstructure of the CR steel heated at 1°C/s to reveal cementite particles inside martensite; arrows show carbide particles (F:  ferrite, M: martensite), (b) Auger spectra for carbide particles and martensite and (c) the differential Auger spectrum for the particle.  c 80  Figure  6-6a shows the microstructure of the CR structure quenched from 740°C. It can be seen that further growth of austenite grains takes place at ferrite grain boundaries.  Closer examination using the inset reveals that undissolved carbide particles are mostly spheroidized inside the ferrite matrix.  The volume fraction of austenite at this temperature is 0.22 which is almost equivalent to the initial pearlite content in the steel.  The temperature at which the first contraction, due to pearlite to austenite transformation, finishes was defined as Acθ, as indicated in the derivative curve in Figure  6-2.  It was shown by San Martín et al.[53] that the Acθ temperature was a good metric to separate the pearlite to austenite and ferrite to austenite transformations at low heating rates, e.g. 0.05°C/s, but at higher heating rates, austenite formation at ferrite grain boundaries can also occur below the Acθ temperature[53]. 4) Ferrite to austenite transformation and final equilibrium A further increase in the austenite volume fraction occurs by austenite growth into proeutectoid ferrite grains, stage (4) in Figure  6-2.  Dissolution of carbide particles is completed during this stage and no carbide particles were evident at 760°C in ferrite or inside austenite. Figure  6-6b shows the ferrite-martensite dual phase structure resulting when quenching from 780°C in the CR sample.  Here, martensite islands are randomly distributed.  It can be seen that a necklace shape structure of these islands covers the majority of ferrite grain boundaries.  81    Figure  6-6:  Microstructure of the CR steel continuously heated with 1°C/s heating rate followed by water quenching at (a) 740°C (the arrows inside the inset depict spheroidized carbide particles) and (b) 780°C (F:  ferrite, M: martensite).  Volume fraction of austenite in both HR and CR structures calculated via the lever-rule using dilatometry curves together with metallographic measurements are presented in Figure  6-7.  In addition to the experimental results, the paraequilibrium (PE) austenite fraction calculated from Thermo-Calc using the FE-2000 database is shown for comparison. It is assumed that no Mn partitioning takes place during experimental heat treatments.  82   Figure  6-7:  Austenite fraction in the HR and CR steels as a function of temperature for continuous heating at 1°C/s and paraequilibrium (PE) austenite fraction.  It can be seen that the volume fraction obtained from dilatation data is in good agreement with the metallographic observations except at about 20 vol pct of austenite.  At this point, the dilation data underestimates the actual transformed fraction.  This point also coincides with complete pearlite to austenite transformation.  This discrepancy was also observed by Oh et al.[129] in the early stage of austenite formation experiments.  They attributed this to the redistribution of carbon atoms in austenite grains.  The carbon content in the austenite phase in the steel used in this study can reach up to ≈ 0.75 wt pct at the beginning of austenite formation based on paraequilibrium calculation.  The lattice parameter and thus the specific volume of austenite is a function of carbon content[127].  This effect was not considered in the simplified lever-rule calculations based on the linearized thermal 83  expansion of austenite with 0.17 wt pct carbon content.  However correction to take into account the carbon content of austenite using the approach proposed by Oh et al.[129] can be misleading in the present case because of the remnant carbide particles inside austenite, Figure  6-5a.  In their approach, Oh et al.[129] predicted lattice parameter of austenite as a function of its carbon content assuming complete dissolution of carbides within austenite. One would need to determine the volume fraction of cementite particles inside austenite grains and thereby estimate the actual carbon content of austenite. At the same time, 1s holding time before quenching can be sufficient to partially/entirely transform pearlite to austenite at the early stages of austenite formation. 5) Thermal expansion of austenite Further heating into the single austenite phase region, stage (5), consists of linear thermal expansion of austenite grains.  Both HR and CR materials expand linearly in single austenite phase region with a thermal expansion coefficient of ≈ 23.0×10-6 °C-1 that is in agreement with the reported data for low carbon austenite[127, 130]. 6.3 Effect of heating rate on dilation response and microstructure evolution In this section, the effect of heating rate on the dilation curves and microstructural evolution is studied.  Heating rates of 1°C/s, 10°C/s, 100°C/s, 300°C/s and 900°C/s were employed for the investigation.  For dilation experiments, all samples were heated into the single phase austenite region. Figure  6-8 shows dilation curves and their first derivatives for both HR and CR materials at different heating rates. 84  Table  6-1 summarizes the critical temperatures in both HR and CR samples at different heating rates.  Ae1 and Ae3 temperatures are 704°C and 823°C, respectively.  Effect of Mn segregation on the equilibrium temperatures remains marginal since it decreases Ae1 and Ae3 by 9°C and 7°C, respectively.  It is evident that raising the heating rate will increase the Ac1 temperature, the Ac3 temperature and the Acθ temperature in the HR material, Figure  6-8a. For example, the Ac1 and Ac3 temperatures increase from 730°C to 790°C and from 854°C to 927°C, respectively, when the heating rate is raised from 1°C/s to 900°C/s.   Figure  6-8:  Dilation curves and their first derivatives for (a) HR and (b) CR steels during heating with different heating rates.  85  Table  6-1:  Summary of the critical transformation temperatures (Ac1, Acθ and Ac3 in °C) at different heating rates  Heating rate, °C/s 1 10 100 900 HR sample Ac1 730 739 760 790 Acθ 763 778 792 812 Ac3 854 870 915 950 CR sample Ac1 719 720 724 734 Acθ 771 777 760 770 Ac3 852 854 887 910  However, the overall trend in the shape of dilation curves and their derivatives remain similar.  From the derivative of the dilation curves it can be seen that there are two distinct and perhaps overlapping stages, pearlite to austenite transformation with a relatively sharp slope followed by ferrite to austenite transformation for all the heating rates. Dilation curves for the CR structures however reveal two distinct and rather interesting observations in comparison with their HR counterparts, Figure  6-8b: First, it can be seen that increasing the heating rate from 1°C/s to 900°C/s resulted in disappearance of the deviation from linear thermal expansion before phase transformation. This effect is more pronounced in the derivative curves in which the cusp for 1°C/s at around 650°C is gradually shifting up towards the line representing the linear thermal expansion coefficient of the ferrite-pearlite structure (≈ 15.0×10-6 °C-1).  Secondly, as the heating rate increases there is a negligible change in the start temperature of austenite formation represented by the sharp drop in the derivative of dilation curves.  It can be seen that all these sharp drops collapse essentially onto the same line. A similar behavior is observed for the Acθ temperature.  However, the change in the Ac3 temperature is similar to 86  that observed for the HR material, i.e. the Ac3 temperature increases from about 852°C to 910°C when the heating rate ramps up from 1°C/s to 900°C/s. Figure  6-9 shows austenite fractions in both HR and CR steels as a function of temperature at different heating rates measured using dilatometry.  Prediction by paraequilibrium calculation is also included in the graphs.  It can be seen that increasing the heating rate increases both the Ac1 and Ac3 temperatures and shifts the transformation to higher temperatures in the HR steel.  Figure  6-9b also represents the lever-rule results for austenite fractions for different heating rates in the CR steel. Comparison between the lever-rule results and metallographic measurements for the 300°C/s heating rate is given in Table  6-2.  It is evident that the lever-rule analysis of dilation data for the early stages of austenite formation is unsatisfactory but there is a good agreement between the lever-rule calculation and metallographic measurements for austenite fractions above 0.2 at 300°C/s. Similar observations were made for 1°C/s heating rate.  Furthermore, the dilation measurements suggest that up to 20 vol pct austenite fraction the transformation is independent of heating rate.  However, beyond this point increasing the heating rates shifts the transformation gradually to higher temperatures. 87    Figure  6-9:  Austenite fraction in (a) HR and (b) CR steels as a function of temperature for different heating rates and paraequilibrium (PE) austenite fraction. 88  Table  6-2:  Comparison of austenite volume fraction measured using metallographic analysis and the lever-rule for the CR steel heated at 300°C/s Temperature, °C 720 760 780 800 830 Lever-rule 0.02 0.19 0.30 0.42 0.67 Metallography 0.14 0.26 0.30 0.38 0.70  Table  6-3 represents the temperature for the formation of 0.5 volume fraction of austenite (T0.5) for different heating rates for both HR and CR samples.  These data indicate a reduced temperature dependency of austenite fraction as a function of heating rate in the CR steel.  For example the shift in T0.5 when increasing the heating rate from 1°C/s to 900°C/s is 92°C in the HR steel while this shift is 33°C for the CR sample.  Table  6-3:  Effect of heating rate on T0.5 in the HR and CR samples Heating rate, °C/s 1 10 100 900 T0.5 (HR) 794 800 840 886 T0.5 (CR) 794 798 810 827  Figure  6-10 shows the microstructures for the HR steel heated at 1°C/s and 300°C/s to 750°C followed by water quenching.  It can be seen that increasing the heating rate has changed the morphology and distribution of austenite grains from a large blocky one to a network of fine austenite grains along ferrite grain boundaries.  89  Figure  6-10:  Microstructures of the HR steel continuously heated at (a) 1°C/s and (b) 300°C/s followed by water quenching from 750°C (F:  ferrite, M: martensite).  Figure  6-11 shows microstructural evolution of the CR structure heated at 300°C/s followed by immediate water quenching at 700°C, 740°C and 780°C, respectively.  There are several major differences between the microstructures of rapid heated samples in comparison with their low heating rate counterparts in the CR steel shown in Figure  6-6: 1) Figure  6-11a shows the microstructure at 700°C.  This temperature is just before the start of austenite formation, but, there are still regions in the ferrite structure which are not yet recrystallized. These regions are mostly distributed between closely spaced pearlite colonies, depicted by arrows.  Approximately 12 pct of ferrite remained unrecrystallized at this stage.  At the same time, the lamellar pattern of cementite particles in the pearlite colonies is almost unaffected and spheroidization of cementite lamellae in the pearlite colonies is at very early stages in contrast to the 1°C/s heating rate experiment.  90    Figure  6-11:  Microstructural evolution of the CR steel continuously heated at 300°C/s followed by water quenching from (a) 700°C, (b, c) 740°C and (d) 780°C (F:  ferrite, M: martensite, P: pearlite).  2) At 740°C, Figure  6-11b, it can be seen that elongated austenite grains are formed that are not observed during intercritical annealing at 1°C/s, Figure  6-6a.  Closer observation, Figure  6-11c, reveals that austenite formation starts at pearlite colonies and ferrite grain boundaries.  The latter nucleation sites are shown by arrows in Figure  6-11c. Austenite grains formed at ferrite grain boundaries are substantially smaller than those 91  formed at pearlite colonies elongated in the rolling direction. Figure  6-11d shows the microstructure at 780°C with 0.3 volume fraction martensite. It can again be seen that banded martensite islands are elongated in the rolling direction. This is in contrast to the random distribution observed for lower heating rates (see Figure  6-6b).  Similar to the sample quenched from 740°C, there are large numbers of isolated fine austenite grains distributed at the ferrite grain boundaries.  Unlike in the HR samples and the CR samples heated at 1°C/s, there is no network of austenite grains forming along ferrite grain boundaries. Further, measurements of austenite grain sizes on samples heated at 1°C/s and 300°C/s, respectively, to just above the Ac3 temperature followed by water quenching, revealed a grain size reduction from 11μm to 6μm as a result of increasing the heating rate, Figure  6-12. 3) Figure  6-13 shows the distribution of carbide particles inside martensite islands in the sample quenched from 740°C after heating at 300 °C/s.  It can be seen that the process of spheroidization of cementite lamella is almost complete.  There are just a few elongated particles remaining that are not yet spheroidized, indicated by arrows in Figure  6-13. Closer examination shows that the size of the carbide particles is finer than in the samples heated at 1°C/s to 740°C.  The average size for carbide particles decreases from 190nm to 130nm when increasing the heating rate from 1°C/s, Figure  6-5a, to 300°C/s, Figure  6-13.  92   Figure  6-12:  Revealing austenite grains in the CR samples heated at (a) 1°C/s and (b) 300°C/s to just above the corresponding Ac3 temperatures followed by water quenching.   Figure  6-13:  Revealing cementite particles inside martensite islands in the CR sample heated at 300°C/s to 740°C.  6.4 Cold rolled and recrystallized structures Starting with the CR structures, it was shown that the initial structure before austenite formation can be quite different depending on the heating rate, Figure  6-3b and Figure 93   6-11a, which makes it difficult to systematically compare the results. Thus, in a next step, all CR samples were heated to 670°C with 1°C/s heating rate, point B in Figure  6-2b, and then heated above the Ac3 temperature with different heating rates of 1°C/s, 10°C/s, 100°C/s and 900°C/s.  In this scenario, the initial structure will be a recrystallized ferrite matrix with partially spheroidized pearlite colonies, see Figure  6-3b; hereafter referred to as CR+REX structure.  Per definition, for heating at 1°C/s the CR+REX sample coincides with the CR one. Figure  6-14a shows the dilation curves and their first derivatives for the CR+REX samples. Unlike for the CR structures, Figure  6-9b, the shift in the Ac1 temperatures via increasing the heating rate is now evident.  Figure  6-14b represents the austenite fraction versus temperature at different heating rates for CR+REX structures.  With increasing the heating rate, the curves shift towards higher temperature, resembling the trend observed in the HR structures. This trend is summarized in Figure  6-14c in which the Ac1 temperature represented by a sharp drop in the derivative of the dilation curves is shown for the HR, CR and CR+REX samples. As discussed, the shift in the Ac1 temperature for the CR samples is just 15°C when increasing the heating rate by almost three orders of magnitude. In contrast, this shift is approximately 60°C for both HR and CR+REX samples confirming the importance of the overlap between recrystallization and austenite formation. The start temperatures for austenite formation in the CR+REX samples are about 10°C lower than those for the HR samples at all employed heating rates. 94   Figure  6-14:  (a) Dilatation curves and their first derivatives for CR+REX samples (heated at 1°C/s heating rate up to 670°C followed by heating into austenite single phase region with different heating rates), (b) austenite fraction as a function of temperature for different heating rates, and paraequilibrium (PE) austenite fraction and (c) comparison of Ac1 temperatures at different heating rates for HR, CR and CR+REX samples. 95  6.5 Discussion The observations made during high heating rate experiments can be explained in terms of the kinetics of the events such as recrystallization, spheroidization and austenite formation and their interactions.  In the HR steel, austenite formation is the main process while in the CR samples, spheroidization of cementite lamellae, recrystallization of deformed ferrite grains and austenite formation are the major events taking place during heating.  The heating rate dictates available time for these events and their interactions. In the HR samples, an increase in austenite formation start and finish temperatures, the Ac1 and Ac3 temperatures (Figure  6-8a), can then be understood in the aforementioned context. When increasing the heating rate there is less time available for austenite formation as a thermally activated process to take place which leads to a shift to higher transformation temperatures that is well documented in the literature[131].  This increase of the superheating for austenite formation results in an increased nucleation site density for austenite grains such that a finer network of austenite grains forms, Figure  6-10. In the CR steel, at low heating rates, e.g. 1°C/s, there is sufficient time for recrystallization of ferrite to take place before austenite formation starts.  This can be seen in Figure  6-3b in which fully recrystallized grains exist without any sign of austenite formation, i.e. presence of martensite at room temperature. In this scenario austenite forms at ferrite-cementite interfaces and then grows into ferrite grains.  Nucleation at ferrite grain boundaries as a competitive event results in formation of a network of austenite at higher temperatures. This trend suggest similarities between microstructural evolution during intercritical 96  annealing in both HR and CR samples heated at lower heating rate, e.g. 1°C/s, see Figure  6-6 and Figure  6-10. However, with increasing the heating rate in the CR steel, the possibility of having unrecrystallized ferrite grains at the beginning of austenite formation increases. The extent of this increase is proportional to the employed heating rate.  These unrecrystallized grains will then be suitable places for phase transformation[132].  Furthermore, fragmented pearlite lamella and/or spheroidized carbides provide an increased nucleation density as compared to HR samples.  Similar to the HR samples, increasing the heating rate in the CR samples delays austenite formation as a thermally activated process.  The balance of these effects leads to a similar dilation response independent of heating rate in the CR samples at the early stages of austenite formation, i.e. the Ac1 temperature is essentially independent of heating rate, Table  6-1.  Since there is not a network of austenite grains at ferrite grain boundaries, the dominant growth mechanism at high heating rates will be the one which requires short-range carbon redistribution, i.e. austenite nucleates at the interfaces of pearlite colonies that are elongated in the rolling direction, transforms these colonies and then grows laterally into the unrecrystallized ferrite grains that are mostly located between these colonies.  Growth of austenite grains nucleated at ferrite grain boundaries will then be hampered because of limited carbon supply.  In this scenario austenite grains will inherit the distribution of pearlite colonies elongated in the rolling direction, Figure  6-11d.   This leads to a transition from a random distribution of martensite islands for lower heating rates to a banded distribution for higher heating rates, compare Figure  6-6b and Figure  6-11d. 97  As shown in Figure  6-15, the formation of banded austenite structures from the pearlite colonies is particularly pronounced at the highest heating rate employed, i.e. 900°C/s.   Figure  6-15:  Microstructure of the CR steel continuously heated at 900°C/s followed by water quenching from 710°C (F: ferrite, M: martensite, P: pearlite).  Huang et al.[67] also observed a similar morphological shift in a Mo-alloyed dual phase steel in which increasing the heating rate from 1°C/s to 100°C/s resulted in banded structures. Their explanation for the transition was based on concurrent recrystallization of ferrite grains and austenite formation.  They speculated that recrystallization of ferrite grains during austenite formation encourages austenite grains to nucleate and grow on deformed pearlite colonies elongated in the rolling direction.  Further growth takes place via rapid lengthening and thickening of the austenite grains rather than nucleation on non-stationary ferrite grain boundaries.  However, at low heating rates, austenite has the possibility of 98  competitive formation on both ferrite grain boundaries as well as pearlite colonies leading to an equiaxed distribution of austenite grains.  They showed that in their steel approximately 90 pct of ferrite grains remained unrecrystallized at 100°C/s at the beginning of austenite formation while this volume fraction is much lower, ≈ 15 pct, in the steel used in this study even at 900°C/s because of the relatively lean steel chemistry.  Perhaps, heating rate of several thousands degree Celsius per second is needed to see a significant overlap of recrystallization and austenite formation in the present steel.  A morphological change via rapid heating was also reported by Grange et al.[88].  They achieved fibrous dual phase steels via heating of initially CR ferrite-pearlite/martensite structures. The kinetics of spheroidization of cementite lamella is mainly controlled by diffusion of carbon atoms.  Spheroidization of pearlite colonies can be essentially divided into fragmentation of carbide particles, rounding off the sharp edges and then growth of particles via Ostwald ripening and shape coarsening.  The fragmentation stage is essentially driven by instability of a cylindrical/platelet shape caused by capillarity-induced perturbation[133].  These stages can proceed simultaneously.  In the HR structure, the time available for the range of heating rates employed in this study is not sufficient for these processes to take place. Annealing times of the order of hours just below the eutectoid temperature are needed for complete spheroidization of cementite lamella in the HR steel[134].  But, in the CR samples the morphology of cementite lamellae has been modified by cold rolling.  Fragmentation and bending of cementite lamella as well as introducing crystal defects such as vacancies and dislocations into the ferrite grains and ferrite- cementite interfaces as fast diffusion paths stimulate the spheroidization process.  Thus, it is 99  likely to observe this process to take place in the CR samples.  At low heating rates, e.g. 1°C/s, sufficient time is available for almost complete spheroidization to occur before austenite formation.  Cementite particles can even coarsen to larger carbide particles during the process, while at high heating rates cementite lamellae remain fragmented without any further coarsening. This explains the finer distribution of carbide particles at 300°C/s as compared to 1°C/s. Austenite grain refinement in the CR samples via rapid heating can be related to an increase in austenite nucleation site density.  These nucleation sites include pearlite colonies and ferrite grain boundaries; see Figure  6-11b and Figure  6-11c.  Deformed pearlite colonies provide suitable nucleation sites for austenite grains.  Further, a rather large population of ferrite grain boundaries provides suitable sites for austenite nucleation. Simultaneously, rapid heating prevents extensive growth of austenite grains in the intercritical annealing region. Refinement of austenite grains via rapid heating was also reported by Andrade- Carozzo and Jacques[72].  Lesch et al.[31] employed this idea to develop an ultrafine grained ferrite structure via rapid transformation annealing in low carbon steels.  The process is essentially based on rapid heating of CR structures just above the Ac3 temperature followed by rapid cooling to room temperature. The relative independence of austenite fraction in the CR steel on heating rate in comparison with the HR counterpart, Figure  6-9, can be understood based on the initial structures prior to austenite formation in both materials. In the HR structure this initial structure remains unchanged.  Thus, increasing heating rate raises superheating until a network of austenite grains form at ferrite grain boundaries. In the CR sample, however, the 100  situation is different. Similarly, increasing the heating rate tends to increase the superheat but the initial structure prior to austenite formation will also be a function of heating rate. In ferrite, the initial structure changes from a fully recrystallized structure to a partially recrystallized one as the heating rate increases and in pearlite it delays the spheroidization of carbide particles.  Thus, nucleation and growth scenarios for austenite formation will change accordingly. The balance of these two effects will then affect the kinetics of austenite formation as a function of heating rate.  However, when first recrystallizing the CR sample, i.e. having the CR+REX structure, the similarity with the dilation response of the HR sample is restored, see Figure  6-14, as the initial structure in both materials mainly consists of recrystallized ferrite.  The slightly different transformation start temperatures, Figure  6-14c, may be attributable to partially spheroidized pearlite lamella in the CR+REX samples.  Since austenite nucleation commences at the interface of ferrite and cementite in the pearlite colonies, the broken lamellae provide more interfaces and consequently the possibility for austenite nucleation increases resulting in lower Ac1 temperatures in the CR+REX samples in comparison with their HR counterparts.  6.6 Summary Austenite formation in a HR and CR low C-Mn steel was systematically investigated using dilation experiments and microstructural characterization. A variety of scenarios can be rationalized to explain the overall rate of austenite formation considering the overlap 101  between austenite formation, recrystallization of ferrite-pearlite structure and spheroidization of Fe3C. The following can be concluded from this study: Different stages of microstructure evolution in both HR and CR structures can be predicted using the dilation data.  Increasing the heating rate shifts the austenite formation to higher temperatures in the HR sample and results in formation of a network of finer austenite grains.  Increasing the heating rate in the CR material however results in formation of a variety of initial structures ranging from fully recrystallized to partially recrystallized structures prior to austenite formation.  This transition can be monitored using the dilation data.  Further, the degree of spheroidization of carbide lamellae in pearlite colonies is reduced with increasing the heating rate.  As a result, a morphological shift is observed from randomly distributed to a banded structure of austenite.  It can be noted that the banded feature of austenite could in theory be controlled by the processing parameters such as the level of cold work and the heating rate.  Higher heating rate also resulted in austenite grain refinement in both HR and CR steels.  This finding was used for the development of UFG dual phase steels that is explained in more details in the next chapter.      102  Chapter 7 UFG Dual Phase Structures 7.1 Introduction In the previous chapter, it is shown that both the initial structure and the heating rate affect microstructure characteristics during austenite formation.  These two parameters change the scale and the arrangement of austenite grains.  Using this finding, this chapter aims at development of UFG dual phase structures in plain carbon steels with lean chemistry.  An appropriate combination of initial structure and processing parameters, heating rate and holding time, results in very fine grained dual phase steels with improved properties compared to conventional dual phase structures and bimodal ferrite grain size structures.  7.2 Results 7.2.1 Microstructure evolution 7.2.1.1 Initial structures During phase transformation, the geometrical length scale of the final products is greatly affected by the size of the parent phase. It is well established that starting with a finer austenite grain size will result in finer final products like ferrite[135-136], lath martensite[137- 138] and pearlite[139] after austenite decomposition.  This suggests that microstructural length scale of the initial structure can also be translated into the final dual phase microstructures using well designed intercritical annealing. 103  Martensite is intrinsically a fine scale structure with several levels of hierarchy in its microstructure[30].  Further, its highly dislocated fine structure with supersaturated carbon content provides all the necessary ingredients for further microstructure evolution such as precipitation and recrystallization.  Therefore the designed scenarios for developing initial structures depicted in Figure  4-3 all start with a fully martensitic structure.  For that, initial HR samples were austenitized at 1000ºC for 30min followed by rapid quenching using iced brine solution.  Figure  7-1a shows an optical micrograph of the as-quenched fully martensitic structure.  TEM observation showed that the lath martensite structure with lath width between 0.2-0.3μm, Figure  7-1b.  It is reported that the dislocation density is approximately 1014 m-2 in 0.18C (wt pct) steels with martensitic structure [140].  Figure  7-1c shows an EBSD orientation map of the as-quenched martensite.  The clean-up step involves in sequence of an 8-neighbour extrapolation, a 7-neighbour extrapolation and a 6-neighbour extrapolation.  The EBSD map also shows high angle (> 15º misorientation, black lines) boundaries. The EBSD map clearly reveals the presence of complicated and fine feature of lath martensite structure with different orientations (colors). The black solid lines show the boundaries with misorientation larger than 15° between adjacent objects.  Using the proposed approach by Ueji et al.[30], the mean grain size of lath martensite considering the boundaries with misorientation larger than 15° was measured.  The representative grain size of martensite was 4.3μm, and is comparable with the reported 3.2μm and 2.1μm grain size for lath martensite in 0.13[30] and 0.2[141] carbon (wt pct) steels, respectively. 104  The martensite structure was then subjected to different thermomechanical procedures to create three different initial structures as follow:  50µm a  1µm b  50µm c  Figure  7-1:  (a) Optical micrograph of as-quenched martensite structure, (b) bright field (BF) TEM image of lath martensite structure with the corresponding  selected area diffraction (SAD) pattern and (c) EBSD orientation map of as-quenched martensite together with superimposed boundary map.   105  (i) Deformed martensite:  Figure  7-2a shows an 80 pct cold-rolled martensite structure as initial structure for process (I).  Deformation features such as kinked lath structures and bent lamellae[30] can be seen in this micrograph.  Interstitial carbon atoms mainly reside at the lath boundaries as well as dislocations[97].  This microstructure is essentially a heavily dislocated supersaturated solid solution ferrite.  (ii) Deformed ferrite-carbide aggregate:  Tempering prior to cold rolling resulted in the presence of nano-size carbide particles in a ferrite matrix that can be seen in Figure  7-2b. This microstructure is the initial structure for process (II).  The major difference with the previous initial structure, i.e. deformed martensite, is the presence of carbide particles.  In this scenario, the deformed ferrite matrix is elongated in the rolling direction as can be seen in Figure  7-2b.  (iii) Equiaxed ferrite-carbide aggregate:  Further annealing of the deformed ferrite- carbide structure at 550°С for 75min resulted in a UFG ferrite-carbide aggregate with equiaxed ferrite grains (Figure  7-2c), initial structure for process (III).  Longer annealing time resulted in formation of larger grains in some areas that leads into inhomogeneous distribution of ferrite grain sizes.   106  a RD ND 3µm  b RD ND 3µm  RD ND c 3µm 500nm  Figure  7-2:  Initial microstructures developed for intercritical annealing treatment: (a) process (I), (b) process (II) and (c) process (III); processes are presented in Figure  4-3 .  A lower dislocation density and the equiaxed morphology of ferrite grains are the major differences between this structure and the deformed ferrite-carbide aggregate presented in Figure  7-2b.  The inset in Figure  7-2c shows the bimodal nature of size distribution of 107  nano-size carbide particles.  Larger particles with an approximate average size of ~150nm were mainly located at ferrite grain boundaries while smaller particles with an average size of ~50nm were distributed inside the grains.  The size of ferrite grains will be evaluated in the following sections. All these three initial structures were then subjected to similar heat treatment cycle into intercritical annealing region to benchmark the best option as an initial structure for developing UFG dual phase steels with improved properties, the results of which are presented in the following section.  7.2.1.2 Benchmarking for selection of initial structure Samples with the three microstructures shown in Figure  7-2 were then heated at 300°C/s to 750°C and held for 10s followed by water quenching.  Starting with initial structures obtained from the processes (I) and (II), i.e. deformed martensite and deformed ferrite- carbide aggregate, the typical resulting dual phase microstructures can be seen in Figure  7-3a and Figure  7-3b, respectively.  These microstructures consist of two distinct regions: UFG dual phase structure with uniform distribution of ferrite and martensite phases and relatively coarse ferrite grains elongated in the rolling direction. However, a homogeneous UFG dual phase microstructure was produced from the UFG ferrite-carbide aggregate developed in process (III), Figure  7-3c.  108  RD ND a 10µm RD ND b 10µm RD ND c 10µm  Figure  7-3:  Microstructural evolution after 10s annealing at 750°C for initial structures obtained from (a) process (I), (b) process (II) and (c) process (III).  Table  7-1 summarizes the characteristics of the microstructures.  It is evident that at comparable volume fraction of martensite, average sizes for ferrite grains and martensite islands are approximately equal.    109  Table  7-1:  Comparison of the effect of initial microstructure on the final dual phase structure Process Process (I) Process (II) Process (III) Heating rate, °С/s 300 300 300 Annealing condition 750°С-10s 750°С-10s 750°С-10s Martensite volume fraction 0.29 0.28 0.32 Martensite island size**, μm 1.2 1.6 1.2 Average ferrite grain size**, μm 1.4 1.3 1.2 ** The reported grain sizes are equivalent area diameter (EQAD).  Since the volume of the individual grains is of primary importance when considering mechanical and fracture behavior, the volumetric size distribution of the grains should be considered as shown in Figure  7-4.  Comparison between different distributions reveals an interesting observation. If one puts a ferrite grain size of 3μm as a boundary between fine and coarse grain size regimes, then the volume fraction of coarse grains in the microstructures developed in processes (I) and (II) is 0.7 and 0.6, respectively.  But, this value is only 0.32 in the UFG dual phase structure developed in the process (III).    110     Figure 7-4:  Volumetric ferrite grain size distribution for the dual phase microstructures obtained in (a) process (I), (b) process (II) and (c) process (III).  The horizontal, x, axis in all curves is in logarithmic scale. 111  These distributions have a profound effect on the corresponding mechanical properties as well as the fracture behavior as presented in Table  7-2. A better combination of strength and ductility is achieved in the dual phase structure obtained from process (III), i.e. when a complete UFG dual phase structure is attained.  The improvement can be clearly highlighted in the fracture behavior since strain to fracture is more than doubled in the UFG dual phase structure compared to the relatively coarser microstructure developed in the process (I).  The comparison between dual phase structures and bimodal ferrite grain size structure shown in Figure  5-2c reveals a better combination of properties in UFG dual phase structure compared to bimodal ferrite grain size structure.  Table  7-2:  Comparison of mechanical properties for different dual phase structures Process YS (1), MPa (0.2 pct offset) UTS (2), MPa U. El. (3), (pct) **Fracture strain,  εf  Process (I)  527  975  8.7  0.28 ± 0.02 Process (II) 559 975 8 0.5 + 0.01 Process (III) 625 980 11 0.62 ± 0.01 Bimodal ferrite grain size 455 550 14 0.34± 0.03  (1) YS: yield strength, (2) UTS: ultimate tensile strength, (3) U. El.: uniform elongation. ** Fracture strain, εf, was measured using εf = ln (A0/Af) where A0 and Af are the initial cross section area and area of fracture surface of the tensile test samples, respectively.  The fracture area, Af, was measured using SEM observation.  A combination of microstructural observations and mechanical properties assessments resulted in selection of the UFG ferrite-carbide aggregate obtained from process (III) as the initial structure for further investigation. 112  7.2.1.3 Detailed examination of UFG ferrite-carbide aggregate Figure  7-5a depicts an EBSD grain boundary misorientation map showing the ferrite grains of the UFG ferrite-carbide aggregate.  The gray and black solid lines represent the boundaries with misorientation between 2°-15° and larger than 15° between adjacent objects, respectively.  The misorientation diagram, Figure  7-5b, shows that approximately 80 pct of the existing boundaries are high angle grain boundaries (misorientation angle >15°) with an average ferrite grain size of approximately 0.7μm.   b  Figure  7-5:  (a) EBSD grain boundary misorientation map for UFG ferrite-carbide aggregate and (b) grain boundary misorientation distribution with superimposed random distribution.  7.2.1.4 Detailed examination of the UFG dual phase structure Figure  7-6 shows BF TEM micrographs of the UFG dual phase structure intercritically annealed at 750°С for 10s with the corresponding diffraction pattern.  Closer observation at a 113  higher magnification reveals dislocations in the ferrite grains especially adjacent to the martensite islands, Figure  7-6b, that is in agreement with observations made in by Son et al.[142] and Rigsbee et al.[143].  For further examination of misorientation observed in the TEM, EBSD analysis was performed.  a 2µm M F b M F 0.5µm Figure  7-6:  (a) BF TEM images of UFG dual phase structure obtained by heating at 300°С/s and intercritically annealed at 750°C for 10s followed by water quenching and (b) higher magnification observation (M: martensite, F: ferrite) .  Figure  7-7 shows the image quality and grain boundary misorientation maps.  Image quality indicates the sharpness of the Kikuchi pattern obtained from the diffraction of the incident electron beam. A deviation from the perfect crystalline structure will result in a diffused Kikuchi pattern with a low image quality and band contrast value.  Because martensite is inherently a more defect-containing structure as compared to ferrite, it is expected to have a lower image quality and band contrast. 114  5µm a  5µm b  c  Figure  7-7:  EBSD results for UFG dual phase structure obtained by heating at 300°С/s followed by intercritical annealing at 750°С for 10s, (a) image quality map, (b) phase map (ferrite: white, martensite: black), (c) band contrast distribution and (d) ferrite grain boundary misorientation distribution with superimposed random distribution.  Therefore, martensite islands can be distinguished from ferrite grains by their lower image quality and band contrast in dual phase structures.  The detailed procedure to distinguish ferrite from martensite is given by Mukherjee et al.[36].  The procedure consists of initial clean-up step followed by selections of objects based on a selected critical misorientation. Then objects will be classified based on their mean band contrast.  A critical mean band contrast (BCcritical) is determined such that objects having a mean band contrast above d 115  BCcritical are considered to be ferrite and the rest can be considered as martensite. Following the proposed procedure, a BCcritical of 55 was chosen to separate ferrite from martensite, Figure  7-7c.  The values below this boundary were removed from the map as black regions shown in Figure  7-7b. The volume fraction of these black regions, 0.32, is in agreement with the volume fraction of martensite measured using SEM micrographs presented in Table  7-1.  Grain boundary misorientation distribution shown in Figure  7-7d reveals that more than 85 pct of the ferrite grains are high angle grain boundaries with misorientation above 15°. The average size of these ferrite grains is approximately 2μm which is about twice the size obtained using SEM measurements.  Similar discrepancy between the EBSD and the SEM grain size measurements in plain carbon steel is also reported by Mukherjee et al.[36].  This is essentially related to the presence of subgrains with misorientation angles between 2° and 15° (Figure  7-7b).  These subgrains can be mistakenly interpreted as ‘grains’ in the SEM observation.  7.3 Discussion Results presented in the previous sections revealed that a fine aggregate of equiaxed ferrite grains with carbide particles is a microstructure of choice to develop UFG dual phase structures.  However, there are two aspects of the proposed thermomechanical treatment that should be addressed.  First, effect of heating rate should be further investigated to see the possibility of employing lower heating rates which would be easier for the industry to implement.  Secondly, the effect of holding time on microstructure evolution should be 116  addressed to have a wider window for the proposed intercritical annealing stage.  Figure  7-8 presents the effect of heating rate on microstructure evolution.  Two different sets of samples were heated to 750°С at 1°С/s and 50°С/s and then held for 10s before water quenching.  Figure  7-8a shows that at the lower heating rate, i.e. 1°С/s, substantial microstructure growth takes place upon heating and holding for 10s at 750°С.  Volume fraction of martensite is 0.18 in this case.  Average ferrite grain and martensite island sizes become 8μm and 5μm, respectively.  This ferrite grain size is approximately equal to the as- received condition.  At 50°С/s, localized growth of ferrite grains results in relatively coarse grained structure with patches of UFG ferrite-martensite structure, Figure  7-8b.  Here, volume fraction of martensite is 0.23. 10µm a RD ND 10µm b RD ND Figure  7-8:  Microstructure evolution of intercritically annealed UFG ferrite-carbide aggregate at 750°С for 10s with (a) 1°С/s and (b) 50°С/s heating rate followed by water quenching.  Figure  7-9a and Figure  7-9b show the effect of holding times of 1s and 300s on the microstructure features at 750°С, respectively.  Both samples were heated at 300°С/s.  With 117  increasing the holding time substructures inside ferrite grains are removed and cementite particles, shown by arrows in Figure  7-9a, are mostly dissolved at the expense of austenite formation (martensite at room temperature).  Figure  7-9c summarizes the effect of holding time on the volume fraction of martensite. The volume fraction of martensite increases with holding time and reaches the paraequilibrium prediction of 0.35 after 60s.  At the same time, the size of martensite islands rises from approximately 1μm to 2μm with annealing time.  Further, the volume fraction of ferrite grains larger than 3μm change from 32 pct to 46 pct as the holding time increases from 10s to 300s. These findings reveal that high heating rate and short holding time are essential to acquire uniform UFG dual phase structures.  Increasing the heating rate, equivalent to shorter ramping time, stimulates grain refinement in different ways as described below: At 1°C/s, substantial growth of ferrite grains upon heating results in coarser structures while at higher heating rates, i.e. 300°C/s, microstructural features of a UFG ferrite-carbide aggregate are mainly preserved prior to intercritical annealing.  These features consist of a high density of ferrite grain boundaries and the presence of a large population of carbide particles on these boundaries as shown in Figure  7-2c, both of which can be nucleation sites for austenite formation.   118  10µm a RD ND M  10µm b RD ND F M  c  Figure  7-9:  Microstructure evolution of intercritically annealed UFG dual phase structure at 750°С for (a) 1s and (b) 300s holding times followed by water quenching and (c) change in volume fraction of martensite at 750°С with paraequilibrium (PE) prediction of austenite fraction (M: martensite, F: ferrite). 119  Austenite preferentially nucleates at the interface between ferrite and cementite[48].  Thus, presence of carbide particles can potentially increase nucleation site density for austenite grains.  Judd and Paxton[52] showed that the nucleation rate can be three to eight times faster at ferrite grain boundaries compared to ferrite matrix.  At the same time, Kaluba et al.[144] have shown that increasing the heating rate above 200°C/s encourages austenite formation at ferrite grain boundaries.  These nucleation scenarios can be even more pronounced in the UFG ferrite-carbide aggregate.  Larger cementite particles at ferrite grain boundaries are not only suitable places for austenite nucleation, but these particles can also provide the carbon necessary for growth of austenite grains nucleated at ferrite grain boundaries.  Ferrite grain boundaries can essentially act as effective diffusion paths[145].  Unlike austenite decomposition upon cooling, the carbon diffusion rate increases in heating experiments. This combination accelerates nucleation and growth of austenite grains. The combination of the above mentioned factors on nucleation and growth of austenite grains can presumably explain an increase in volume fraction of austenite as the heating rate rises in agreement with the findings by Andrade-Carozzo and Jacques[72] and Huang et al.[67]. Microstructural growth during holding time is a consequence of both a curvature effect and diffusion distances.  While growth of ferrite grains is mainly controlled by curvature effect, it can be an overlap between the curvature effect and diffusion distance that results in coarsening type growth of austenite grains[146].  Details of coarsening of austenite grains during intercritical annealing of UFG ferrite-carbide aggregates will be presented in the next chapter. 120  It is suggested that austenite nuclei formed during intercritical annealing can stabilize the microstructure and impede ferrite grain growth as well[72]. This is even more effective when a UFG ferrite-carbide aggregate offers substantial nucleation sites for austenite.  This is possibly the reason behind relatively limited growth of ferrite grains even after 300s holding at 750°C, Figure  7-9b. Table  7-3 summarizes mechanical properties for different dual phase structures.  It can be seen that with increasing the heating rate from 50°C/s to 300°C/s, both the yield strength and the UTS increase at comparable ductility and yield ratio.  Similarly, with increasing holding time at 300°C/s heating rate, improvement in mechanical properties is evident as the volume fraction of martensite increases. Figure  7-10 presents a comparison of nominal stress- nominal strain curves between UFG ferrite-carbide aggregate shown in Figure  7-2c and UFG dual phase structure intercritically annealed for 1s at 750°С shown in Figure  7-9a.  In aggrement with previous studies conducted on UFG dual phase structures[11,47,100], the main charateristic mechanical properties of dual phase structures remain intact via grain refinement, however, this is not the case for the UFG ferrite-carbide aggregate.  Limited work hardening with approximately 10 pct Lüders strain resulted in a yield ratio of approximately ~1 in the UFG ferrite-carbide structure.  In contrast, the UFG dual phase structure showed typical characteristics of conventional dual phase steels such as continuous yielding with substaintial work hardening and relatively lower yield ratio.  121  Table  7-3:  Summary of mechanical properties for different dual phase structures Heating rate, holding time (°C/s, sec) Martensite fraction U. El. (pct) YS, MPa (0.2 pct offset) UTS, MPa Yield ratio (YS/UTS) 50, 10 0.23 11 533 880 0.6 300, 1 0.17 9 611 852 0.72 300, 5 - 7 594 877 0.68 300, 10 0.32 11 625 980 0.64 300, 30 - 12 611 930 0.66   Figure  7-10:  Comparison for nominal stress-nominal strain curves between UFG ferrite- carbide aggregate and UFG dual phase structure with 17 pct martensite.  Continuous yielding of dual phase steels can be primarily attributed to the presence of internal stresses within the ferrite matrix originated from the strains associated to the martensite transformation and plastic incompatibility between constituent phases[96].  The approximate volume expansion of 2.7 pct at the Ms (martensite start) temperature can be expected in the investigated steel quenched from 750ºC.  The measurement of volume 122  expansion is based on the equilibrium chemical composition of austenite at 750ºC, i.e. ~0.45C and 0.74Mn (wt pct) calculated using Thermo-Calc, and the approximate volume expansion for austenite-to-martensite transformation at the Ms temperature (324ºC here) presented by Magee and Davies[147] and Kung and Rayment[148].  Internal stresses cause microyielding of the ferrite matrix at regions around the martensite islands under relatively low applied stresses compared with the yield stress of the bulk ferrite. The initial work hardening rate of dual phase steels can be related to the mode of deformation in the constituent phases.  An estimate of the yield stress for the martensite with 0.45 wt pct carbon using the data reported by Leslie[82], ~1830MPa here, suggests that martensite islands may remain elastic when the dual phase structures yields. Further, higher martensite fractions and smaller island size result in an increase in work hardening rate in dual phase steels[85,149].  This may explain a decrease in yield ratio as the volume fraction of martensite increases upon holding at 750ºC at 300ºC/s experiments, see Table  7-3.  For example, the yield ratio decreases from 0.72 to 0.64 as the volume fraction of martensite increases from 0.17 to 0.32, respectively, while the size of the islands remains almost intact between 1-2µm. Figure  7-11 compares tensile stress-strain curves for different dual phase structures with the corresponding work hardening rate.  Different volume fractions of martensite and steel chemistry make it difficult to have an explicit comparison between the results.  However, it is evident that unlike ferrite-carbide aggregate, the work hardening rate has not been deteriorated as a result of grain refinement in dual phase structures. 123  Using high resolution EBSD, Calcagnotto et al. [150]  have recently shown that the population of dislocations in ferrite grains to accommodate the strain imposed by martensite transformation increases with decreasing ferrite grain size and the amount of ferrite interface covered with martensite.  Their estimation revealed that 1.9×10 14 m -2  dislocations exist in the ferrite in the vicinity of martensite islands in a UFG dual phase steel.   The balance between the uniform elongation and the UTS for different dual phase steels is summarized in Figure 7-12.  The open symbols represent conventional CG dual phase steels and the closed ones are the available data on UFG dual phase steels [11,47,89,100,143,151,152] . The results for UFG dual phase structures in this study are shown in circle.   Figure 7-11:  (a) True stress-true strain curves together with (b) work hardening rate for different  dual phase  structures (fM: martensite volume fraction). 124   Figure  7-12:  Balance between UTS and uniform elongation for conventional CG and UFG dual phase steels.  The results show that there can be an upper limit for the balance in CG dual phase steels depicted by the solid line.  However, the values for the UFG dual phase steels are mostly above this limit by up to 150MPa at comparable ductility, promising a new boundary that is shown by the dotted line.  Available data on UFG dual phase steels is so far restricted to the upper tail of the balance, i.e. elongation values below 15 pct since these studies were carried out on relatively large volume fraction of martensite and high carbon content steels. Carbon primarily controls the strength of martensite.  Using lower carbon content UFG dual phase steels or reducing martensite fraction may provide more data for UFG dual phase steels. 125  7.4 Summary This study aimed to produce and to characterize UFG dual phase structures in a plain low carbon steel with 0.17 wt pct carbon and 0.74 wt pct manganese.  The proposed thermomechanical technique is based on rapid heating and cooling of a UFG ferrite-carbide aggregate that is originally developed from an initial martensite structure.  It was shown that a rapid heating and cooling cycle is essential to guarantee UFG dual phase structures with optimum properties. This necessity is mainly to overcome undesired growth of ferrite grains and martensite islands.  Very short intercritical annealing treatment can be an advantage of this rather simple technique; however industrial implementation can be challenging with the existing production lines for steel sheets.  One way to tackle the problem is to add appropriate alloying addition such as Cr, Mo and Nb to stabilize an initial fine grained structure and to impede microstructure growth during the heat treatment cycle. Assessment of the mechanical properties reveals that UFG dual phase steels have the capacity to replace the conventional CG dual phase steels.  The main beneficial features of dual phase steels can be translated into finer scale structures.  Thus, UFG dual phase steels can be potentially material of choice for the automotive industries aimed for weight reduction while maintaining the performance intact.      126  Chapter 8 Phase Field Modelling (PFM) of Austenite Formation 8.1 Introduction In this chapter, PFM of austenite formation in Fe-C systems with two different sets of initial structures is studied.  These structures are in accordance with the experimental part of this study examined in the previous chapters.  First, austenite formation in a ferrite-spheroidized carbide structure will be investigated.  This part starts with simple examples of austenite formation from carbide in a ferrite matrix with and without neighbouring carbide particles. These simple examples will be compared with available analytical models to predict and to verify the mode of phase transformation.  Then, growth of austenite grains from UFG ferrite-carbide aggregates will be examined in order to shed light into microstructural observation made in the previous chapter. In the second part of this chapter, lamellar ferrite-carbide aggregates will be considered as an initial structure.  In this part austenite formation from fully pearlitic steels will be first examined and then growth rate of austenite from pearlite will be compared with experimental observation.  It will be followed by a qualitative investigation on austenite formation from ferrite-pearlite structures where experimental observations on microstructure evolution will be compared with simulation results. 8.2 Methodology Microstructure simulations were conducted with a multi-phase field approach using the commercially available code MICRESS (microstructure evolution simulation software)[153]. 127  The formulation of this PFM approach is based on the work of Steinbach et al.[118] (see section 2.10.1). An Fe-C system with a linearized phase diagram as depicted in Figure  8-1 is considered in this study.  It can be seen that the carbon content for the eutectoid reaction is 0.76 wt pct and the eutectoid temperature, TE, is set to be 723°C.  Two different scenarios were considered in the simulations: (i) Ferrite-spheroidized carbide aggregates as the initial structure (ii) Pearlite/ferrite-pearlite as the initial structures The driving pressure for austenite formation, ΔGij = Lij ΔTij, can be obtained from the linearized phase diagram shown in Figure  8-1 where ΔTij is the superheat and Lij is a proportionality factor which can be derived from Thermo-Calc[154].  The phases considered here are ferrite, austenite and cementite and there is only a driving pressure term provided grains i and j are different phases.  To verify the predictions made by linearized phase diagram, selective Thermo-Calc coupled simulations were carried out where thermodynamic data (phase boundaries and driving pressures) was directly derived from the software using the GES (Gibbs Energy System) file for the same steel chemistry.  In Figure  8-1, Cαθ and Cαγ represent the carbon equilibrium concentration in ferrite with cementite and austenite, respectively.  Cγα and Cγθ are the carbon equilibrium concentration in austenite with ferrite and cementite, respectively and Cθ is the carbon concentration of cementite.  Considering a carbon concentration of C1 in ferrite, as depicted in Figure  8-1, the superheat for this concentration at the austenite-ferrite interface, ΔTαγ , can be 128  calculated from T- T1 (C1) where T is the annealing temperature, 750°C here.  Table  8-1 provides information on carbon concentrations at 750°C and slopes of the different phase boundaries as well as the proportionality factors, ijL .   Figure  8-1:  Schematic of linearized Fe-C phase diagram (α: ferrite, γ: austenite and θ: cementite).  To resolve very fine carbide lamellae/particles, calculation domains were used with grid sizes in the range of 0.005-0.02μm.  Convergence of calculations with these grid spacings was confirmed by also performing calculations with half and double of the selected grid size.  The interface thickness is taken to have four nodes, i.e. it is four times the grid 129  spacing.  Cementite was treated as a stoichiometric phase with constant composition.  Table  8-2 represents the data for the carbon diffusion coefficients, )RT/Qexp(DD 0 −= , in ferrite and austenite. Table  8-3 summarizes interfacial energies and mobilities assumed in the simulations.  The mobilities for the austenite-ferrite and austenite-cementite interfaces are taken to be the same but their value is used as a variable.  Exact mobility values are not available from the literature and changing these values allows one to shift the transformation from interface- controlled for low mobilities to diffusion-controlled for sufficiently large mobilities. Sufficiently low mobilities are assumed for all other interfaces (ferrite-cementite interface and all the grain boundaries) to minimize their movement as this would not contribute to austenite formation. Periodic boundary conditions are assumed for all simulations in ferrite-spheroidized carbide aggregates.  But, both periodic/symmetrical boundary conditions were used for lamellar ferrite-carbide aggregates, details of which will be presented in the following sections.   Table  8-1:  Data for the linearized phase diagram (α: ferrite, θ: cementite, γ: austenite) Phase boundaries α/θ α/γ γ/α γ/θ Concentration (Cij, wt. %) at 750 °C 0.024 0.016 0.61 0.82 Slope (°C/wt pct) 5814.0 -9909.0 -154.0 353.0 Lij (J m-3) 0.18 -1.0 -1.0 -1.2     130  Table  8-2:  Diffusion data for carbon [115] Phase Ferrite Austenite D0 (m2  s-1) 2.2×10-4 0.15×10-4 Q (k J mol-1) 122.5 142.1  Table  8-3:  Parameters used for the simulations (α: ferrite, θ: cementite, γ: austenite) Interface α/α α/θ α/γ θ/γ γ/γ Interfacial energy, J m-2 [121] 0. 76 0.71 0.72 0.67 0.76 Mobility (×1014), m4 J-1 s-1 3.5 0.5 variable variable 0.05  8.3 Austenite formation from ferrite-spheroidized carbide aggregates 8.4 Results and discussion 8.4.1 Mode of phase transformation To analyze the mode of transformation, i.e. interface vs diffusion control, and to benchmark the PFM simulations a simple 2D scenario is considered with one cementite particle that acts as nucleation site for austenite.  The simulation results will then be compared with an analytical model for the same geometry. Figure  8-2 shows the progression of the austenite formation from the initial ferrite- cementite structure (see Figure  8-2a) when the mobility of austenite-cementite and austenite-ferrite interfaces is taken to be 10-10 m4 J-1 s-1.  Austenite nucleus was set to form at ferrite-cementite interface. 131    Figure  8-2:  (a) Initial ferrite (red)- circular cementite (yellow) aggregate, (b,c) simulated growth of austenite (white) from cementite in ferrite (interfaces shown in blue), (d) evolution of normalized phase fraction using linearized phase diagram and Thermo-Calc coupled simulations and (e) carbon concentration profile along the dashed line in Figure  8-2b.  At 750°C, austenite immediately nucleates at the interface and engulfs the cementite particle (Figure  8-2b). Austenite grows then until complete dissolution of cementite and reaching the equilibrium volume fraction (Figure  8-2c).  The change in the normalized volume fraction of austenite (volume fraction of austenite in units of its equilibrium volume fraction) with time is illustrated in Figure  8-2d.  The kinetics is also compared to a PFM simulation with direct coupling to Thermo-Calc to extract the driving pressures. 132  The comparison of these two simulation results shows an excellent agreement thereby confirming the validity of the simplified approach using a linearized phase diagram.  The carbon concentration profile along the dashed line in Figure  8-2b is shown in Figure  8-2e. Cementite has a constant stoichiometric composition of 6.69 wt pct of carbon, but there is a gradient in the carbon concentration in austenite and also in ferrite.  However, carbon concentration and gradients are essentially negligible in ferrite. Details of the austenite formation kinetics and the distribution of carbon in austenite are directly related to the mobility assumed for the austenite interfaces with ferrite and cementite.  Using the same simulation domain but employing different mobilities the role of the mobility values has been systematically investigated. Figure  8-3a shows the kinetics of austenite formation for different mobilities.  As a general trend, increasing the mobility accelerates the rate of austenite formation. To illustrate this trend further, Figure  8-3b shows the normalized fraction transformed after 0.3s of holding at 750°C.  Here, it can be seen that there are two limits for the kinetics of austenite formation as a function of mobility.  For sufficiently large mobilities, the fraction transformed becomes independent of mobility, i.e. the reaction is controlled by carbon diffusion.  Similarly, for sufficiently low mobilities, the fraction transformed remains negligible at 0.3s.  The transition between both limits displays a strong dependence of the fraction transformed on the assumed mobility value.  This region is indicative for the gradual shift from a diffusion-controlled to an interface-controlled transformation.  It can be seen that the upper and lower transition limits are about 10-12-10-11 m4 J-1 s-1 and 10-16-10-17 133  m 4 J -1 s -1 , respectively.  Thus, the results presented in Figure 8-2 depict a scenario of a diffusion-controlled austenite formation.    Figure 8-3:  (a) Effect of austenite interface mobility on the kinetics of austenite formation and (b) change in normalized volume fraction of austenite at 0.3s with the mobility of austenite interfaces.  134  To verify the accuracy of predicting the diffusion-controlled reaction with the phase field model approach, the results are compared with the analytical model proposed by Judd and Paxton[52] for diffusion-controlled growth of austenite from ferrite-carbide aggregate.  To solve the problem analytically, they made several simplified assumptions including carbon diffusion through austenite as the rate-controlling factor, constant concentration of carbon in ferrite, local equilibrium at all interfaces, steady state concentration gradient in austenite and no capillary effects.  Only the first assumption, i.e. carbon diffusion as the rate- controlling parameter, remains similar to that of phase field assumption.  Starting with a 2D cementite particle with the radius of r0 in the ferrite matrix (shown in Figure  2-18a), they assumed austenite, depicted as a grayish ring in Figure  2-18a, engulfs cementite immediately and grows into ferrite and cementite with radii rb and ra, respectively. Judd and Paxton[52] provided the solution for spherical geometry, Equation  2-10, and their approach was adapted to a cylindrical geometry to be consistent with the geometry of the above 2D PFM simulation, i.e. E/)]rln(Er2)ErErrln(Er)ErErrln(Er )ErErrln(r)rln(Er2)rln(r)[ CC CC ( D4 1t b 2 b 2 b 2 0 2 0 2 b 2 b 2 0 2 0 2 0 2 b 2 0 2 0 2 00 2 0 2 0 2 0 // // C −−++−+ −−+−+− −−= αγθγ γααγ γ    Equation  8-1 where t is time, γCD  is the diffusion coefficient of carbon in austenite, )CC/()CC(E /// θγθγααγ −−= and the inner radius is obtained from ]Er)E1(r[r 2b 2 0 2 a −+= .  The comparison between predictions by the phase field model (symbols, mobility for austenite interfaces: 5×10-10 m4 J-1 s-1) and the analytical model (solid lines) is shown in Figure  8-4.  There is an excellent agreement between the predictions 135  using these two approaches thereby confirming the validity of the employed phase field simulation approach.   Figure  8-4:  Comparison between diffusion-controlled growth of austenite in phase field model and analytical model.  8.4.2 Austenite formation from two carbide particles In the previous section, carbon diffusion-controlled growth of austenite in austenite was considered where austenite nucleation took place in all cementite particles.  In this section, however, austenite formation is considered when two cementite particles are placed in the ferrite matrix but nucleation of austenite does only occur at one of the two particles.  It is aimed at evaluating interaction of growing austenite grain with neighbouring cementite particles. Two cases are considered: (i) cementite particles are located in the bulk and (ii) cementite particles are located at a ferrite grain boundary.  In both cases, one austenite nucleus is 136  introduced at the interface of one of the cementite particles and the distance between these particles is 2.5μm.  No further austenite nucleation is permitted and the mobility of austenite interfaces is set to 10-12 m4 J-1 s-1.  When both cementite particles are inside the bulk of the ferrite grain (Figure  8-5a), austenite quickly envelopes the cementite particle and subsequently grows in an oval shape towards the dissolving second cementite particle (Figure  8-5b). Interestingly the second cementite particle dissolves quicker than the first particle where the nucleus had been placed (see Figure  8-5c).  This can be related to faster diffusion rate of carbon in the ferrite matrix.  However, starting with larger cementite particles the austenite grain would reach and envelope the second particle before its full dissolution.  Eventually, the shape of the austenite grain changes gradually towards that of a circle in the final stages of transformation (Figure  8-5d).  Similarly, in the second scenario, when the two cementite particles are at a ferrite grain boundary (Figure  8-5e), austenite grows towards the dissolving particle. But, in this case the austenite grain develops a needle shape feature along the ferrite grain boundary (Figure  8-5f).  The needle formation in this scenario is promoted by the reduction of free energy when locally eliminating a part of the grain boundary. It should be emphasized that fast diffusion along the grain boundary is not considered in this study.  Once the needle has reached the second cementite particle austenite envelopes this particle (Figure  8-5g).  Then further dissolution of both cementite particles takes place simultaneously inside the austenite grain.  Similar to the previous example, austenite gradually reshapes itself towards a circular geometry with time (Figure  8-5h).  137   Figure  8-5:  Evolution of an austenite grain (white) nucleated at the interface of ferrite (red) and cementite (yellow): (a-d) in the bulk and (e-h) at a ferrite grain boundary.  In the first case when the two particles are in the bulk any deviation from a circular shaped austenite grain can be traced back to effects of carbon diffusion from the dissolving second cementite particle. This situation is illustrated in Figure  8-6 where a contour plot of the carbon concentration in ferrite is shown for the transformation stage displayed in Figure  8-5b.  Austenite and cementite, in black, were extracted from the domain. The carbon concentration in ferrite increases from austenite towards the dissolving cementite particle that provides a source of carbon atoms to be incorporated into the growing austenite grain.  This scenario highlights a particular aspect of austenite formation in the Fe–C system that one can have at the austenite-ferrite interface also a net flux of 138  carbon atoms into the austenite grain as opposed to out of the austenite grain as is the case for circular austenite growth shown in Figure  8-2.   Figure  8-6:  Contour plot of carbon concentration in ferrite for the transformation stage shown in Figure  8-5b. Numbers on the graph show the carbon concentration (wt pct) of the corresponding contour.  The large and small black regions that are removed from the map represent austenite and cementite, respectively.  8.4.3 Austenite formation from a UFG structure It is shown that microstructure evolution during austenite formation is greatly affected by the nucleation scenario.  After having analyzed some idealized scenarios, the simulations are now extended to austenite formation from a typical UFG ferrite-carbide aggregate. 139  Figure  8-7a shows the 2D aggregate structure that is used as input for the simulations. Ferrite grains have an average size of about 0.5μm and the average size for cementite particles is about 0.1μm.  Cementite particles are located at ferrite grain boundaries including triple junctions.  The nucleation scenario is as following:  Austenite nucleation occurs on all cementite particles but nuclei are introduced in a sequential way with a rate of one nucleus in 0.005s.  This sequential nucleation scenario was used to investigate growth of closely spaced austenite grains with a distribution of grain sizes.  Mobility of austenite interfaces is set to 5×10-10 m4 J-1 s-1 such that the transformation is diffusion-controlled.  As illustrated in Figure  8-7b, the austenite grain that nucleates first grows into all dissolving cementite particles by developing needle-like features along ferrite grain boundaries, i.e. similar to what had been discussed above for the idealized case of two cementite particles at grain boundaries (see Figure  8-5f).  However, as soon as all the other nuclei have been formed the growth morphology reverses back to a more circular type of growth, as shown in Figure  8-7c. These shape changes are further promoted by the tendency of the austenite grains to minimize their interfacial area. Preferential grain boundary diffusion is also not considered here.  After complete dissolution of all cementite particles the average austenite grain size is about 0.3μm and austenite reaches its equilibrium volume fraction at this stage. In the next stages, Figure  8-7 d-f, the austenite fraction remains constant but larger austenite grains grow at the expense of smaller grains leaving one relatively large austenite grain of about 0.7μm in size in the calculation domain.  140    Figure  8-7:  Coarsening of austenite grains in a UFG ferrite-cementite aggregate at 750°C, (a) initial structure, (b) 0.02s, (c) 0.03s, (d) 3s, (e) 5s and (f) 9s (ferrite: red, cementite: yellow and austenite: white).  This is a classical coarsening process to reduce the interfacial energy of the system. Gradient of carbon content in ferrite in the vicinity of austenite grains plays an important role in this process.  Figure  8-8a gives the blown up structure from a selected area in Figure  8-7d.  The carbon concentration profile in ferrite in this area is presented in Figure  8-8b and confirms a gradient of carbon concentration in ferrite that leads to a carbon flux from point A, close to the dissolving grain, to point B, close to the growing grain.  141   Figure 8-8:  (a) Blown-up structure from the selected area in Figure 8-7d (ferrite in red and austenite in white and (b) carbon concentration profile in ferrite from point A to point B  To have a more realistic understanding of microstructural evolution during austenite formation from a UFG ferrite-cementite aggregate, 3D simulations have also been conducted for an Fe-0.05 wt pct carbon alloy at 750°C.  A cubic structure of ferrite grains with about 1μm grain size has been constructed with cementite particles located at different positions: one at a quadruple point, one at a triple line, one at a grain boundary face and one within the ferrite grain.  Figure 8-9a shows the initial structure which consists of ferrite grains (transparent with green interfaces), cementite particles (black) and one austenite nucleus (red) nearby the cementite particle located at the quadruple point. This austenite particle grows in a rather complex geometry towards all nearby particles and envelopes all cementite particles (Figure 8-9b).  The shell-type interface between austenite and all cementite particles is evident in Figure 8-9c.  Growth of austenite continues until complete dissolution of all cementite particles leaving an austenite grain inside the ferrite matrix 142  (Figure  8-9d).  The presented simulations indicate that a variety of growth scenarios can occur during austenite formation.  The details of these scenarios depend on the spacing between cementite particles and the nucleation sequence.  If all nuclei form at the same time a more circular (or spherical growth in 3D) is predicted.  However, when nucleation at a nearby cementite particle is delayed or does not occur there is a tendency for this particle to dissolve and to provide a source of carbon for the neighbouring growing austenite grain. The growth morphology in these cases is not equiaxed anymore and can range from oval shaped grains in the interior of ferrite grains to needle like features for austenite growth along ferrite grain boundaries (see Figure  8-5).  This behavior is related to carbon diffusion and Figure  8-6 depicts an example of a carbon gradient in ferrite with increasing concentrations from austenite to cementite.  This gradient is consistent with the Fe–C phase diagram (Figure  8-1) where Cαθ is larger than Cαγ at 750°C.  Since the austenite grain requires a sufficient level of carbon (Cγα) for further growth, it preferentially grows towards the dissolving carbide particle as a source of carbon. The capacity of the austenite grain to collect available carbon is magnified when its surface to volume ratio is increased, i.e. when developing an increasingly non-equiaxed shape. Depending on the relative speed of austenite growth vs dissolution of cementite it is possible that the growing austenite grain reaches the cementite particle before complete dissolution and austenite then envelopes the particle forming a double ring structure as shown in Figure  8-5g. 143   a b  c d Figure  8-9:  3D simulation of austenite growth in a fine grained ferrite-cementite aggregate in Fe-0.05 wt pct C at 750°C, (a) t=0.0s (initial ferrite-cementite aggregate, ferrite grains are chosen to be transparent, cementite particles are in black and austenite is in red), (b) t=0.05s, (c) t=3.0s and (d) t=5.0s. 144  After all carbide particles have been dissolved, austenite grains tend to change their shape back to equiaxed structures, i.e. circles in 2D simulations, to minimize the interfacial energy of the system.  These observations are consistent with experimental results by Estay et al.[68].  They reported asymmetrical growth of austenite in the vicinity of cementite particles.  They also observed the “enveloping stage” during austenitization of ferrite- carbide aggregates in a  C-Mn steel where austenite nucleated at grain boundary carbide tends to envelope large grain boundary carbides where no austenite nucleation had taken place. In addition to the shape changes of a single grain in the final stages, coarsening takes place whereby larger austenite particles consume smaller ones.  This is the same phenomenon as the coarsening of precipitates to minimize the total interfacial energy of the system.  It is controlled by the curvature driven gradient of solute concentration in the matrix containing the precipitates[145].  Austenite particles in Fe–C systems may be considered as a carbon- rich precipitate and Figure  8-7 gives an example of the carbon concentration that facilitates the coarsening process. This coarsening process is in particular important for UFG structures where austenite grains are rather fine and closely spaced in a ferrite matrix.  This aspect is of little relevance during intercritical annealing of conventional dual phase steel with a typical 10-20μm grain size.  The grain size and diffusion distance are simply too large to obtain any significant coarsening rates. However, for the processing of UFG dual phase steels coarsening of the fine austenite precipitates during intercritical annealing may provide a limit for the refinement that can be attained for dual phase structures. Intercritical treatments will have to be sufficiently short to minimize coarsening in order to maintain a 145  UFG dual phase structure.  For a diffusion controlled regime in Fe–C alloys the present simulations suggest that significant coarsening can occur within 5s at 750°C.  8.5 Modelling of austenite formation from lamellar ferrite- carbide aggregates 8.6 Results and discussion 8.6.1 Initial structures Simulations were carried out for three different scenarios of austenite formation.  Similar to the previous section, the validity of mobility selection to ensure diffusion-control reaction is first investigated.  For that, planar growth of austenite was simulated and the results are compared with an available analytical model.  A layer of austenite was incorporated at the interface between ferrite and cementite lamella in an Fe-0.17C (wt pct) alloy, Figure  8-10a. The results were then compared with available analytical model proposed by Akbay et al.[108].  Fully pearlitic and ferrite-pearlite structures were constructed as can be seen in Figure  8-10b and Figure  8-10c. Simulations were carried out for a 2D pearlitic structure with 0.96 wt pct carbon content and an interlamellar spacing (λ) of 0.4μm, Figure  8-10b. This calculation was carried out to mimic experimental observations on growth rate of austenite into pearlite in a pearlitic steel with 0.96 wt pct carbon[62].  Further, a pearlitic steel with 0.76 wt pct carbon is used for a parametric study of the effect of interlamellar spacing and potentially fast interfacial diffusion paths on the kinetics of austenite formation.  2D simulations were also conducted for the austenite formation from ferrite- pearlite structure in the Fe-0.17C (wt pct) system, Figure  8-10c.  Austenite nuclei were put 146  at the boundary between pearlite colonies in the pearlitic steel and at the interface between ferrite and pearlite in the ferrite-pearlite structure (Figure  8-10).  Growth of austenite was then simulated for selected isothermal and selected boundary conditions respectively. Black and gray lines at the borders of the micrographs present periodic and symmetrical boundary conditions, respectively.  In case of the pearlite-to-austenite transformation symmetrical boundary conditions were assumed whereas in the two other cases a mixture of periodic and symmetrical boundary conditions was adopted.  The grid spacing in these examples is 0.005 - 0.01µm.    0.5µm a 0.4µm b  0.5µm c  Figure  8-10:  (a) Initial structure to simulate planar growth of austenite (b) initial 2D construction of pearlitic structure with λ=0.4μm and (c) initial ferrite-pearlite structure with 0.17 wt pct carbon and λ=0.5μm (ferrite: red, cementite: yellow, austenite: white and interfaces: blue.  147  8.6.2 Mode of phase transformation To verify the diffusion-controlled mode of austenite formation, the results of growth of an austenite layer in an Fe-0.17C (wt pct) alloy, Figure  8-10a, were compared with the analytical model proposed for diffusion-controlled planar growth of austenite[108]. Assumptions made for this scenario are similar to those given for the cylindrical geometry presented in section 8.3.1.1.  In this case, mobility values for austenite interfaces, here 1×10-11 cm4 J-1 s-1, were chosen based on the results presented in Figure  8-3.  Carbon diffusion in austenite is the rate-controlling parameter.  Planar growth of austenite is schematically shown in Figure  2-18b.  The comparison between the phase field and the analytical models can be seen in Figure  8-11.  Further, the time necessary for complete dissolution of the cementite layer, i.e. ra=0, is 9.85s and 9.58s for the analytical and phase field models, respectively.  Excellent agreement between these two models proves the validity of phase field simulation.   Figure  8-11:  Comparison between diffusion-controlled growth of austenite in phase field and analytical models[108]. 148  8.6.3 Growth of austenite into pearlite Figure  8-12 shows simulated and experimental observed microstructure evolution during isothermal holding at 750°C of a pearlitic steel with 0.96 wt pct carbon and an interlamellar spacing of 0.4µm.  Growth of austenite into pearlite is accompanied by concurrent dissolution of carbide lamellae.  Remnants of carbide are predicted inside austenite in agreement with the experimental observations shown in Figure  8-12c[62].  Austenite has the tendency to grow faster along ferrite-cementite interfaces (shown by arrow in Figure  8-12a).  This path is prompted by the reduction in free energy when locally eliminating a part of the interfaces.  Further, dissolving carbides provide austenite with the carbon required for further growth (Cγα and Cγθ).  An experimentally observed pattern of austenite growth into pearlite in an Fe-0.96C (wt pct) alloy shown in Figure  8-12d reveals the step- like movement of austenite front into pearlite resembling simulation results.      149  0.4µm a  0.4µm b  20µm c  1µm d  Figure  8-12:  Growth of austenite into pearlite at (a) 0.13s and at (b) 0.28s at 750°C (ferrite: red, cementite: yellow, austenite: white and interfaces: blue), and (c) carbide remnants in austenite, shown by arrows, after completion of pearlite to austenite transformation[62] and (d) experimental observation of growth of austenite (martensite at ambient temperature) into pearlite[62].  To quantify the growth rate of austenite into pearlite the analytical model proposed by Speich et al.[62], Equation  2-2, was employed. 150  To measure the growth rate of austenite using phase field simulation results, the initial structure, shown in Fig. 2b, was approximated with an arrangement of circular austenite regions with radius R on a simple square lattice of edge L (4µm here). The volume fraction of austenite can then be calculated as: fv = π (R/L)2 when fv < 0.78, i.e. before the circular austenite regions impinge, and fv = π (R/L)2 – [(2R/L)2 cos-1(L/2R) – ((2R/L)2-1)1/2] when fv > 0.78.  Austenite growth rate, R& , is measured using Rt2 = Rt1 + R& Δt where Rt2 and Rt1 are the radii at two consecutive time steps. Figure  8-13 compares the average austenite growth rate between 5 and 95 pct transformation obtained with the analytical model, Equation  2-2 (lines), phase field simulations (circle symbols) and experimental observations (square symbols)[62].  Solid and dashed lines represent results from an analytical model assuming different thermodynamic data.  The analytical solution using the linearized phase diagram (shown in Figure  8-1) is presented by the solid line and that using the phase boundaries proposed by Wells et al. [155] is shown by the dashed line.  Simulation results, both the analytical and the phase field, are in good agreement with the experimental observations. In all cases, an increase in temperature from 750°C to 830°C raises the growth rate by almost two orders of magnitude.  151   Figure  8-13:  Comparison of growth rate of austenite into pearlite in a 0.96C (wt pct) pearlitic steel.  8.6.4 Effect of interlamellar spacing Figure  8-14 presents the simulated change in volume fraction of austenite with time at different temperatures and interlamellar spacing in a 0.76C (wt pct) pearlitic steel. It is evident, as expected, that raising the temperature increases austenite growth rate. Equation  2-2 reveals that the growth rate of austenite is inversely related to interlamellar spacing.  This is consistent with the phase field simulation.  Decreasing the interlamellar spacing from1.0μm to 0.4μm accelerates austenite formation, as shown in Figure  8-14. This can be attributed to the reduction of diffusion distance as the interlamellar spacing decreases. 152   Figure  8-14:  Effect of temperature and interlamellar spacing (λ) on the kinetics of austenite formation in a 0.76C (wt pct) pearlitic steel.  Figure  8-15 illustrates an example of the effect of interlamellar spacing on austenite formation for a similar processing time.  There are two major observations: first, thicker remnants of carbide lamellae remain undissolved in austenite as the spacing increases. Larger interlamellar spacing results in thicker cementite lamella.  Secondly, the evolution path of austenite growth remains smoother since there will be fewer interfaces available for austenite to divert into.  The effect of interlamellar spacing was experimentally investigated by Robert and Mehl[58] and Caballero et al.[63] for C-Mn pearlitic steels.  Their observations confirm the acceleration effect of decreased interlamellar spacing on austenite formation. For example, changing the spacing from 0.32μm to 0.12μm changes the volume fraction of transformed austenite from 0.42 to 0.84 in a 0.78C-0.62Mn (wt pct) pearlitic steel after 30s annealing at 732°C[58], see Figure  2-10. 153  0.4µm a  0.4µm b  Figure  8-15:  Growth of austenite into pearlite at 750°C for 0.2s for different interlamellar spacing of (a) 0.4μm and (b) 1.0μm in an Fe-0.76C (wt pct) alloy (ferrite: red, cementite: yellow, austenite: white and interfaces: blue).  8.6.5  Effect of interfacial diffusion Because of its lamellar nature, pearlite provides substantial interfacial boundaries that are potentially fast diffusion paths, in particular for substitutional alloying elements Interfacial area per unit volume, Sv, is inversely related to interlamellar spacing[59].   For an interlamellar spacing of 0.5μm, Sv will be approximately 1×107 m-1.  This highlights the potential importance of interfacial diffusion while dealing with diffusion-controlled phenomena in pearlite.  The diffusion equation implemented in the model is as follows: α+α−= interfacebulk D)1(DD       Equation  8-2 where α is a weighting factor that is defined as: fl jiφφη=α         Equation  8-3 154  where l (1nm here) is the actual thickness of the interface, η is the interface thickness in simulation (l/η is a normalized thickness), iφ  and jφ are the phase field parameters in the neighbouring grains i and j, respectively.  The factor f  is to guarantee that the profile for jiφφ is independent of ηat any position, x, at the interface.  Its value is related to the integral perpendicular to the interface contour (i.e. ∫ ψφφ1 0 ji d  where ψ is x/η).  The value for f is 8. Figure  8-16 shows the effect of interfacial diffusion on the kinetics of austenite formation at 750°C assuming Dinterface / Dbulk = 10.  Interface diffusion accelerates austenite formation, the extent of which depends upon the ratio between the bulk and interfacial diffusion.  For example, after 0.15s, the volume fraction of austenite is 0.67 and 0.45 with and without interfacial diffusion, respectively.   Figure  8-16:  Effect of implementing interfacial diffusion on kinetics of austenite formation at 750°C (Dinterface / Dbulk = 10). 155  8.6.6 Austenite formation from ferrite-pearlite structure Figure  8-17 shows austenite formation at 750°C for an initial ferrite-pearlite structure depicted in Figure  8-10b with 0.17 wt pct carbon and an interlamellar spacing of 0.5μm. Austenite nuclei are assumed to form at the interface between ferrite and the pearlite colony.  0.5µm a  0.5µm b 0.5µm c 5µm d Figure  8-17:  Microstructure evolution during isothermal holding of a ferrite-pearlite structure at 750°C for (a) 0.05s, (b) 0.11s, (c) 0.25s (ferrite: red, cementite: yellow, austenite: white and interfaces: blue) and (d) intercritically annealed DP600 steel at 790ºC[156].  Growing austenite first rapidly consumes pearlite and then grows much slower into ferrite to reach equilibrium. The austenite is predicted to grow preferentially along the cementite lamellae (Figure  8-17a).  Due to growth perpendicular to the cementite lamellae different 156  austenite grains impinge and a typical finger-type morphology of austenite results (Figure  8-17b).  The finger-type morphology was also observed experimentally during partial austenite formation in intercritically annealed 0.10C-1.86Mn-0.16Si-0.34Cr (wt pct) steel (DP600 steel)[156] shown in Figure  8-17d. shows experimental observation of finger-type features during partial austenite formation at intercritically annealed. Similar observation was also made by Savran et al.[65] during austenitization of continuously heated ferrite- pearlite structures.  Austenite then consumes pearlite completely and further growth takes place into ferrite, Figure  8-17c. Figure  8-18 depicts different stages of carbon distribution during austenite formation.  The process of redistribution of carbon throughout austenite can be clearly seen in Figure  8-18b and Figure  8-18c.  This process continues until the carbon content of austenite reaches the equilibrium concentration prescribed by the linearized phase diagram at 750°C, i.e. γαC . Figure  8-18d shows that carbon concentration profiles along line AA depicted in Figure  8-18c levels off at approximately 2.0s. 157  0.5µm a  0.5µm b  0.5µm cA A   Figure  8-18:  Carbon concentration gradient at (a) 0.05s, (b) 0.25s and (c) 2.0s and (d) carbon concentration profiles along line AA presented in Figure  8-18c at different times.  Figure  8-19 shows the kinetics of austenite formation from the ferrite-pearlite structure. Unlike austenite formation from fully pearlitic structures, see Figure  8-16 for example, it 158  clearly suggests two different stages of austenite formation.  These two stages include relatively fast pearlite to austenite transformation followed by slower pro-eutectoid ferrite to austenite transformation that is in agreement with experimental observations [48,65] .   Figure 8-19:  Predicted normalized austenite fraction with time in an Fe-0.17C (wt pct) alloy at 750°C.  8.7 Summary In ferrite-spheroidized carbide structures, the grain morphologies depend on the interplay between austenite nucleation at cementite particles and their dissolution. Coarsening plays an important role during intercritical annealing of UFG ferrite-carbide aggregates in Fe-C alloys.  Thus, it appears that addition of appropriate alloying elements as 159  solutes or precipitate formers may be useful to reduce interface mobilities and coarsening rates thereby stabilizing a UFG structure during intercritical annealing. In lamellar ferrite-carbide aggregates, it is shown that the growth rate is directly related to austenitization temperature as well as interlamellar spacing in pearlitic steels because of their effect on diffusion rate and diffusion distance in a diffusion-controlled regime of austenite growth, respectively.  In the ferrite-pearlite structure, austenite formation is composed of three distinct stages of relatively rapid pearlite to austenite transformation followed by proeutectoid ferrite to austenite transformation and final compositional homogenization in accordance with experimental observations.          160  Chapter 9 Concluding Remarks This work aims to present new developments in grain refinement in plain C-Mn steels. While bridging grain refinement and austenite formation through UFG dual phase structures, this study provides a detailed examination of the effect of initial structure and processing parameters on austenite formation.  The major findings of this work can be summarized as follows:  9.1 Grain refinement experiments Two novel techniques have been introduced to refine microstructure constituents in the studied steel.  First, an approach for development of bimodal ferrite grain size structures is analyzed.  This simple technique relies on co-deformation of ferrite and martensite followed by recrystallization.  It is shown that recrystallization of martensite is indeed accelerated by deformation.  Tailoring mechanical properties with changing the volume fraction of martensite thereby altering the fraction of fine grains is possible.  However, there are two concerns over the processing approach and the properties of the final products: (i) The approach is restricted to comparatively low level of carbon in martensite since higher carbon martensite may not co-deform resulting in decohesion at the interface of ferrite and martensite during cold rolling. (ii) The produced bimodal ferrite grain size structure shows limited improvement in mechanical properties compared to fine grained ferrite-carbide aggregates. 161  The second technique was devoted to development of UFG dual phase structures.  These structures reveal characteristic mechanical properties of conventional dual phase steels. Unlike ferrite-carbide aggregates, work hardening rate is not deteriorated as results of grain refinement in dual phase steels.  It is attributed to presence of internal stresses in ferrite matrix as a result of martensite formation. The proposed thermomechanical process is rather easy to implement industrially.  Equiaxed ultrafine ferrite-carbide aggregate is the structure of choice as initial structure for the process.  Rapid processing cycles are also needed to avoid growth of austenite grains that would results in a coarsened ferrite-martensite structure upon quenching.  9.2 Austenite formation: experiments and modelling In the present study, the effect of initial structure and heating rate on microstructure evolution and dilatometry response of plain C-Mn steels has been evaluated.  9.2.1 Experiments (i) The dilatometry experiments provide invaluable information about microstructure evolution during austenite formation.  The dilation response can, in the HR material, be subdivided into several stages: (i) thermal expansion of ferrite/pearlite structure, (ii) pearlite to austenite transformation, (iii) ferrite to austenite transformation and (iv) austenite thermal expansion.  Additionally, recrystallization of ferrite and spheroidization of pearlite can take 162  place in the CR sample.  Recrystallization of ferrite results in a change in the dilation response of the CR steel. (ii) The morphology of austenite grains can be modified using heating rate in both HR and CR materials.  In the HR steel, a transition from a large blocky one to a network of fine austenite grains along ferrite grain boundaries takes place with rising heating rate.  In the CR materials, however, a transition from randomly to banded distribution of austenite grains can be achieved as the heating rate increases.  The transition in the HR material is attributed to the higher nucleation site density for austenite and in the CR structure it has been explained in terms of interaction between recrystallization and austenite formation. (iii) Increasing the heating rate results in refinement of microstructural constituent in both HR and CR structures.  An approximately twofold decrease in austenite grain size has been observed as the heating rate increased from 1ºC/s to 300ºC/s.  9.2.2 Modelling Phase field modelling is very suitable to capture the morphological complexity of austenite formation that is enhanced due to the rather close spacing of cementite particles in the studied structures.  Here, the interaction between curvature effect and diffusion distance plays an important role in morphological changes during austenite formation.  Ferrite- spheroidized carbide, pearlite and ferrite-pearlite structures are chosen as initial structures for the study.  Carbon diffusion in austenite is the rate-controlling parameter in all simulations.  The main findings arising from this part of the work are as follows: 163  (i) In the ferrite-spheroidized carbide aggregate, austenite nucleates at the interface of ferrite and cementite.  Its morphology changes from a circular to an oval one (in 2D) depending on the nucleation scenario and the distance between neighbouring cementite particles. (ii) In UFG ferrite-carbide aggregate, closely spaced austenite grains coarsen resulting in relatively coarse ferrite-austenite structures. (iii) It is shown that the growth of austenite grains in pearlite is faster than carbide dissolution leaving behind remnants of carbide particles in austenite. (iv) Decreasing the interlamellar spacing accelerates austenite formation and changes the morphology of austenite in accordance with the experimental observations. (v) Different steps of austenite formation in ferrite-pearlite structures including fast pearlite to austenite followed by relatively slower ferrite to austenite transformation is predicted by the simulation results. (vi) Experimentally observed microstructure evolutions such as finger-type morphology and enveloping stage have been successfully captured using phase field modelling.  9.3 Future work To further enhance the present understanding, several suggestions can be made for further investigations as follow: 164  (i) The present study reveals a complex interaction between ferrite recrystallization, spheroidization of carbide lamellae and austenite formation upon heating of cold-rolled ferrite-pearlite structures.  Further work is required to thoroughly understand this interaction as a function of heating rate and steel chemistry. (ii) Industrial implementation of the suggested processing route to develop UFG dual phase structures is challenging because of (i) the high heating rate and (ii) the short holding time employed.  These restrictions are imposed because of relatively lean steel chemistry used in this study.  Applying the same method to industrially-relevant dual phase steel chemistries such as DP grades may result in more industrial-adaptive processing parameters. (iii) Current understanding of mechanical behaviour of recently developed UFG dual phase structures is limited to very few studies.  A systematic comparison of mechanical properties for conventional and UFG dual phase steels is also lacking. (iv) Phase field modelling of austenite formation is still in its infancy.  The present work is the first attempt to illustrate austenite formation in ferrite-cementite aggregates with suitable interfacial parameters; however more work is needed to provide more quantitative description of austenite formation.  Austenite formation under continuous heating processes, addition of alloying elements such as Mn and extending the model into 3D are yet to be accomplished for modelling austenite formation from ferrite-carbide aggregates. 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Heat Treat., 1971, vol. 13, pp. 20-22.     174  Appendix A1 To examine the effect of different factors on the deviation from linearity in the dilation curves observed before austenite formation, see section 6.1.2, additional investigations were carried out.  Cold rolling can introduce residual stresses that are concentrated on the surface of the samples[157]. Relieving residual stresses imposed by cold rolling can occur prior to austenite formation in the CR steel.  It can also contribute to the dimensional changes in the samples[158].  However, reduction of residual stresses via thinning the samples down to half- thickness by polishing shows no sign of change in the deviation.  Further, dilatometry of 80 pct CR pre-spheroidized samples (annealed for 24h at 690°C before cold rolling) revealed a dilation response similar to that of the CR sample.  Thus, spheroidization was then ruled out to contribute to dilation changes.  A 80 pct CR Ti-added IF steel with the chemical composition given in Table A1-1 was used to supplement the dilation study during heating for a case where no cementite is present, i.e. any effect from pearlite can be excluded.  The initial microstructure consists of elongated ferrite grains.  In order to examine ferrite to austenite transformation start temperature, a sample was heated into the single austenite phase region at 1°C/s and an Ac1 temperature of 920°C was measured.  As shown in Figure A1-1, a thermal cycle was then employed to investigate the dilation before phase transformation.  It includes a heating stage (solid black line), fast He quenching (gray line) and reheating stage of the sample (black dashed line).  The CR sample was heated first at 1°C/s to 850°C followed by rapid He quenching down to 200°C and immediate reheating at 1°C/s to 850°C.  The contraction in the dilation curve in the first heating path is evident in Figure A1-1 (similar to the CR low carbon steel in Figure  6-2).  The relative length change (ΔL/Lo) is approximately 0.11 pct which is similar to the CR low carbon steel, i.e. 0.1 pct. 175  However, in the next reheating stage the dilation curve shows no sign of contraction. Microstructural observations at 600°C and 850°C showed that the microstructure changed from the CR to a completely recrystallized one during the first heating stage.  Thus, reduction in dislocation density and texture changes from an alpha fiber to a gamma dominant texture[79] that occur during ferrite recrystallization remain as possible explanation for the deviation.  A reduction in specific volume of 0.37 pct for 80 pct cold- drawn steel wires during annealing and before austenite formation was reported by Gridnev et al.[159].  With an assumption of isotropic change in length during dilation, one can estimate ΔL/Lo through ΔL/Lo ≈ ΔV/3Vo for a small relative volume change in which ΔL is the length change, Lo is the initial length, ΔV is the volume change and Vo is the initial volume of the sample.  Thus, the value for ΔL/Lo concluded from the work by Gridnev et al.[155] is ≈ 0.12 pct which is in good agreement with the observations made in this study, i.e. 0.1 pct for the low carbon steel and 0.11 pct for the IF steel.  Gridnev et al.[159] attributed this observation to annihilation of point and line defects as well as microcracks. De Cock et al.[79] also showed that the reduction in dislocation density during recrystallization can account for the amount of dilation, ≈ 0.05 pct, observed during heating of 80 pct CR low and ultralow carbon steels before austenitization at 10°C/s.  Thus, it is concluded that the deviation from linear thermal expansion is related to recrystallization of the sample during heating and is consistent with the volume change due to a reduction in the average dislocation density.    176  Table A1-1:  Chemical composition of the IF steel in wt pct Element Fe C Mn P S Si Ti B N wt pct Bal. 0.0026 0.16 0.011 0.008 0.01 0.068 0.0005 0.003   Figure A1-1:  Dilatation curves for IF steel during heating-cooling-heating cycles. Cooling rate during rapid cooling was approximately 200°C/s. 

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