Design of bainite. in steels from homogeneous and inhomogeneous microstructures using physical approaches. (Bainite Design) EUR EN

Transcription

1 Design of bainite in steels from homogeneous and inhomogeneous microstructures using physical approaches (Bainite Design) Research and Innovation EUR EN

2 EUROPEAN COMMISSION Directorate-General for Research and Innovation Directorate G Industrial Technologies Unit G.5 Research Fund for Coal and Steel rtd-steel-coal@ec.europa.eu RTD-PUBLICATIONS@ec.europa.eu Contact: RFCS Publications European Commission B-1049 Brussels

3 European Commission Research Fund for Coal and Steel Design of bainite in steels from homogeneous and inhomogeneous microstructures using physical approaches (Bainite Design) G. Paul, Dr. R. Großterlinden ThyssenKrupp Steel Europe AG Duisburg, GERMANY Dr. J. Aldazabal, O. Garcia Centro de Estudios e Investigaciones Tecnicas de Guipuzcoa-Asociacion San Sebastian, SPAIN H. H. Dickert Rheinisch-Westfaehlische Technische Hochschule Aachen Aachen, GERMANY Dr. A. I. Katsamas, Dr. E. Kamoutsi, Prof. G.N. Haidemenopoulos Panepistimo Thessalias University of Thessaly Volos, GREECE Dr. T. Hebesberger, K. Satzinger Voest Alpine Stahl GMBH Linz, AUSTRIA Grant Agreement RFSR-CT July 2007 to 30 June 2010 Final report Directorate-General for Research and Innovation 2013 EUR EN

4 LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information. The views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect the views of the European Commission. Europe Direct is a service to help you find answers to your questions about the European Union Freephone number (*): (*) Certain mobile telephone operators do not allow access to numbers or these calls may be billed. More information on the European Union is available on the Internet ( Cataloguing data can be found at the end of this publication. Luxembourg: Publications Office of the European Union, 2013 ISBN doi: /64860 European Union, 2013 Reproduction is authorised provided the source is acknowledged. Printed in Luxembourg Printed on white chlorine-free paper

5 CONTENT Page Final SUMMARY 11 1 Objectives of the Project 11 2 Comparison of initially planned activities and work accomplished WP1: Literature Study WP 2: Material Supply WP 3: Bainite Design for Homogeneous Austenite WP 4: Bainite Design for Heterogeneous Structures with Inhomogeneous C Distribution in Austenite WP 5: Validation and Conclusions 15 3 Description of Activities and Discussion 15 4 Conclusions 17 5 Exploitation and impact of the research results 18 APPENDIX I: WP APPENDICES 21 1 WP1: Literature Study Retrieval of Existing Model Approaches and Experimental Data Existing models 21 TK-StripCam Available data for the bainite start temperature Experimental data of bainite transformation kinetics Existing data Application of existing modelling approaches to experimental data Structure of the model code Application of the model Evaluating of existing Approaches Assessment of controlling mechanisms 34 2 WP 2: Material Supply Definition of materials Laboratory and industrial production and distribution 38 3 WP 3: Bainite Design for Homogeneous Austenite 39 3

6 3.1 Experimental Bainitic Transformation Kinetics from Deformed Austenite Microstructural Characterization Thermodynamic + DICTRA Calculations Model Development Finite Differences Model Interfacial energies Interfacial Energies Model Implementation Influence of Si and Al on PE cementite Cellular Automaton Model 77 4 WP4: Bainite Design for Heterogeneous Structures with Inhomogeneous Carbon Distribution in Austenite Cold Strip Characterization Experimental RWTH-Aachen SE-AG VOESTALPINE 96 Results of bainitic transformation after incomplete austenitization for steel Microstructural Characterization Characterization of the chemical composition of austenite after intercritical annealing Chemical composition of carbides Microstructural characterisation Thermodynamic and DICTRA Calculations Model Development Finite Differences Model Cellular Automaton Model WP 5: Validation and Conclusions Parametric Analysis / Field of Application Finite Differences Model Cellular Automaton Model Validation Against Untrained Data Experimental Simulation results Calculation of Examples for which Older Models from Literature Failed Application Cases Guide Lines References 158 4

7 LIST OF TABLES Table 1: Table 2: Table 3: Table 4: Table 5: Table 6: Table 7: Table 8: Table 9: Table 10: Table 11: Table 12: Table 13: Table 14: Table 15: Table 16: Table 17: Table 18: Table 19: Table 20: Table 21: Table 22: Table 23: Table 24: Table 25: Table 26: Table 27: Table 28: Table 29: Table 30: Table 31: Table 32: Table 33: Table 34: Table 35: Table 36: Table 37: Table 38: Table 39: Table 40: Table 41: Table 42: Table 43: Table 44: Summary of most worth-noting, published models for bainite kinetics...22 Validation ranges for the B s -Temperature models of different authors...24 Summary of literature sources reporting experimental data of bainitic transformation kinetics...25 Materials selected for laboratory investigations...38 Annealing cycles for the four alloys with higher carbon content...39 The phase fractions after the different annealing cycles of DP-Al_high C...40 The phase fractions after the different annealing cycles of DP-Si_high C...41 The phase fractions after the different annealing cycles of DP-Si_high C, Mo, Cr...42 The phase fractions after the different annealing cycles of of DP-Si_high C, Cr...43 Phase fractions for steel 10 annealed at 850ºC for different holding temperatures...55 Phase fractions for steel 12 annealed at 850ºC for different holding temperatures...55 Phase fractions for steel 13 annealed at 850ºC for different holding temperatures...55 Phase fractions for steel 10 annealed at 850ºC for different holding temperatures...56 Phase fractions for steel 12 annealed at 850ºC for different cooling rates...56 Phase fractions for steel 13 annealed at 850ºC for different cooling rates...56 Calculated thermodynamic driving-forces for the nucleation of product phases in paraequilibrium with the corresponding parent phase for selected steel grades...62 Enthalpy values H [kj/mol] for different Carbides from Literature...77 Weights assigned to different types of neighbours...78 Chemical composition of steels 12 and 13 in weight percent...82 Steel 12 annealed at 850ºC. Simulation results for isothermal holding transformations...89 Steel 13 annealed at 850ºC. Simulation results for isothermal holding transformations...89 Steel 12 annealed at 850ºC. Simulation results for continuous cooling transformation...90 Steel 13 annealed at 850ºC. Simulation results for continuous cooling transformations...90 Annealing cycles for the three alloys having a higher carbon content...93 Chemical composition of the DP-steel and annealing cycles...95 Microstructural characterisation of the samples after quenching...96 Grades of austenitization calculated out of isothermal data...98 Grades of austenitization calculated out of helium-cooled measurements...99 Calculated grades of austenitization out of x-ray diffraction measurements Calculated grades of austenitization from image analysis Transformed phase amounts of steel 12 after annealing at 750 C for 60s Transformed phase amounts of steel 12 after annealing at 775 C and 60s Transformed phase amount of steel 12 after annealing at 800 C for 60s Grades of austenitization of investigated materials Phase fractions for steel 12 annealed at 775ºC for different holding temperatures Phase fractions for steel 12 annealed at 750ºC for different holding temperatures Phase fractions for steel 12 annealed at 800ºC for different cooling rates Phase fractions for steel 13 annealed at 800ºC for different cooling rates Calculated vol. fraction and chemical composition of austenite in TRIP-Si steel, after intercritical annealing at various temperatures Calculated vol. fraction and chemical composition of austenite in TRIP-Al steel, after intercritical annealing at various temperatures Steel 12 annealed at 750ºC. Simulation results for isothermal holding transformations Steel 12 annealed at 800ºC. Simulation results for continuous cooling transformations Steel 13 annealed at 800ºC. Simulation results for continuous cooling transformations Chemical composition of reference CP-steel grade and of five composition variants (in % mass)

8 LIST OF FIGURES Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11: Figure 12: Figure 13: Figure 14: Figure 15: Figure 16: Continuous cooling transformation for a carbon steel (top), dilatation signal for one of the cooling cycles of a TRIP steel (bottom)...26 Heating cycles for investigation with complete austenitization incl. simulation limits...27 Schematic procedure of calculating the transformed phase amounts...27 Overview of the transformed phase amounts of steel 13 (left) and steel 14 (right)...28 Calculated transformation curves during isothermal soaking of steel 13 (upper line of figures) and steel 14 (lower line of figures) at different soaking temperatures (300 C, 450 C, 550 C)...28 Comparison between results of Azuma et al. [1] and of this project...32 An example of the effect of nucleation-site density of bainitic ferrite on transformation kinetics...33 An example of the effect of ferrite/austenite interfacial energy on transformation kinetics...33 Interdependence between C-content of austenite and vol. fractions of the phases during the bainitic transformation...34 Dilatation curves for transformation from homogenous austenite for DP-Al_high C at different holding temperatures...40 Dilatation curves for transformation from homogenous austenite for DP-Si_high C at different holding temperatures...41 Dilatation curves for transformation from homogenous austenite for DP-Si_high C, Mo, Cr at different holding temperatures...42 Dilatation curves for transformation from homogenous austenite for DP-Si_high C, Cr at different holding temperatures...43 Isothermal bainitic transformation from homogenous austenite for DP-Al_high C at different soaking temperatures...44 Influence of chromium on the isothermal bainitic transformation from homogenous austenite at two different soaking temperatures...44 Influence of molybdenum on the isothermal bainitic transformation from homogenous austenite at three different soaking temperatures...45 Figure 17: Dilatation signal for steel 5 during cooling with an intermediate isothermal holding ( C) from 5 min. austenitisation at 850 C (left) respective 1250 C (right)...45 Figure 18: Figure 19: Figure 20: Figure 21: Kinetics of isothermal (300 to 500 C) transformation of steel 5 during 1800s after quenching from 850 C (left) respective 1250 C (right)...46 Dilatation signal for steel 2 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right)...46 Dilatation signal for steel 3 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right)...47 Dilatation signal for steel 4 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right)...47 Figure 22: Influence of the austenitisation conditions during the isothermal transformation ( C) of steel 2. Above: 5min at 1250 C (solid) respective 5min at 1150 C (dashed) austenitisation, Below: 1250 C austenitisation for 5 min (solid) and 30 min (dashed)...48 Figure 23: Figure 24: Figure 25: Figure 26: Figure 27: Figure 28: Overview of the transformed phase amounts of steel 10 (left) and steel 11 (right)...49 Overview of the transformed phase amounts of steel 12 (left) and steel 2 (right)...49 Transformation curves calculated from measured data during isothermal soaking of steel 10 at different soaking temperatures (300 C, 450 C, 550 C)...50 Transformation curves calculated from measured data during isothermal soaking of steel 11 at different soaking temperatures (300 C, 450 C, 550 C)...50 Transformation curves calculated from measured data during isothermal soaking of steel 12 at different soaking temperatures (300 C, 450 C, 550 C)...50 Transformation curves calculated from measured data during isothermal soaking of steel 2 at different soaking temperatures (300 C, 450 C, 550 C)...51 Figure 29: Experimental time-temperature cycle (a) and the corresponding isothermal dilatation curves at 400 C (b), 450 C (c) and 500 C (d)...52 Figure 30: Figure 31: Figure 32: Figure 33: Figure 34: Transformation kinetics at 400 C of DPW 600 after different degrees of deformation...53 The microstructure in the samples of DPW600 after annealing with the cycle in Figure 2 with applying an isothermal holding temperature of 400 C...53 Annealing cycle for DP-Al high C for stepwise quenching...54 Annealing cycle for DP-Al high C...57 EBSD maps for a DP-Al high C sample quenched from 350 C

9 Figure 35: Figure 36: Figure 37: Figure 38: Figure 39: Figure 40: Figure 41: Figure 42: Calculated driving-forces for the nucleation of bainitic ferrite in paraequilibrium with austenite for steel CP...63 Calculated driving-forces for the nucleation of cementite in paraequilibrium with austenite for steel CP...63 Calculated ferrite/austenite paraequilibrium phase-boundaries for steels CP and TRIP-Si...64 Flow chart of the SE-AG implementation of the bainite model...65 Calculated driving forces for ferrite nucleation from austenite for Steel 12 (VA-DP 2.2Mn 0.8Cr)...66 Calculated interfacial energy σ α/γ as a function of carbon content and temperature for DP-Si...67 Calculated interfacial energy σ γ/cem as a function of carbon content and temperature for DP-Si...67 Calculated interfacial energy σ α/cem as a function of carbon content and temperature for DP-Si...68 Figure 43: Figure 44: Figure 45: Figure 46: Figure 47: Figure 48: Figure 49: Figure 50: Figure 51: Influence of Chromium on the calculated interfacial energies σ α/γ (a-c), σ γ/cem (d-f) and σ α/cem (g-i) as a function of carbon content and temperature for VA-DP+2.2Mn+0.3Cr, VA-DP+2.2Mn+0.5Cr and VA-DP+2.2Mn+0.8Cr...69 Influence of Manganese on the calculated interfacial energies σ α/γ (a-c), σ γ/cem (d-f) and σ α/cem (g-i) as a function of carbon content and temperature for VA-DP+1,8Mn+0,8Cr, VA-DP+2,0Mn+0,8Cr and VA-DP+2,2Mn+0,8Cr...71 Influence of Molybdenum on the calculated interfacial energies σ α/γ (a-b), σ γ/cem (c-d) and σ α/cem (e-f) as a function of carbon content and temperature for DP-Si-Cr+highC-noMo and DP-Si-Cr+highC...72 Calculated interfacial energies σ α/γ (a-b), σ γ/cem (c-d) and σ α/cem (e-f) as a function of carbon content and temperature for TRIP-Si and TRIP-Al...73 Comparison of the bcc-fcc interfacial energies for Steel2, DP-Si obtained by RWTH and SE-AG...75 Comparison of the ferrite phase fraction in DP-Al at 550 C and the corresponding mixing enthalpy for calculations with MatCalc (RWTH) and ThermoCalc (SE-AG)...76 Modelling approach flowchart...78 The Moore neighbourhood definition domain...78 Modelled microstructural carbon concentration map and distribution...79 Figure 52: Isothermal transformation kinetics for each transformation product at 350ºC holding temperature. Steel Figure 53: Comparison between LOM and microstructure obtained by the model at 350ºC. Steel Figure 54: Isothermal transformation kinetics for 400ºC and 450ºC. Steel Figure 55: a. 400ºC holding temperature transformation microstructure obtained by LOM. b. Modelled microstructure 400ºC. c. 450ºC microstructure obtained by LOM. d. Modelled microstructure 450ºC. Steel Figure 56: Isothermal transformation kinetics for 500ºC. Steel Figure 57: Isothermal transformation kinetics. a. 350ºC holding temperature. b. 400ºC. c. 450ºC. d. 500ºC. Steel Figure 58: a. Microstructure obtained by LOM 350ºC. b. Microstructure obtained by simulation 350ºC. c. Microstructure obtained by LOM 450ºC. Microstructure obtained by the model 450ºC. Steel Figure 59: Figure 60: Figure 61: Figure 62: Figure 63: Figure 64: Figure 65: Figure 66: Figure 67: Figure 68: Figure 69: Figure 70: Figure 71: a. Transformation kinetics at 60K/s. b. Transformation kinetics at 40K/s. c. Transformation kinetics at 20K/s. d. Transformation kinetics at 10K/s. Steel a. Microstructure obtained by LOM 60K/s. b. Modelled microstructure 60K/s. c. Microstructure obtained by LOM 5K/s. d. Modelled microstructure 5K/s. Steel a. Transformation kinetics at 60Ks. b. Transformation kinetics at 40Ks. c. Transformation kinetics at 20Ks. d. Transformation kinetics at 10Ks. Steel a. Microstructure obtained by LOM 60 K/s. b. Modelled microstructure 60 K/s. c. Microstructure obtained by LOM 5 K/s. d. Modelled microstructure 5 K/s. Steel a: Grain structure in steel 4 (cold rolled state), b: homogeneous distribution of main elements in the cold rolled state of steel Microstructures in materials TRIP-Al (steel 3) and DP-Al (steel 1) quenched out of the intercritical region...91 Microprobe analysis of the Trip-Al steel, sampled from industrial production...92 Microprobe analysis of the DP-Al steel, sampled from industrial production...92 Isothermal bainitic transformation after intercritical annealing for 60 s at 850 C of aluminium alloyed TRIP steel at different soaking temperatures...93 Transformation during continuous cooling of steel 3, TRIP Al, from 1300 C...94 Continuous cooling transformation-diagram for steel 3 (TRIP, Al) after 10 s at 1300 C...94 Influence of time on the transformation during continuous cooling steel 3, TRIP Al, from 1300 C...95 Dilatation signal during the isothermal part of the cycle

10 Figure 72: Figure 73: Figure 74: Figure 75: Figure 76: Figure 77: Figure 78: Figure 79: Figure 80: Figure 81: Figure 82: Figure 83: Figure 84: Figure 85: Figure 86: Figure 87: Figure 88: Figure 89: Figure 90: Figure 91: Figure 92: Figure 93: Figure 94: Description of using the "Law of Lever"...97 Procedure of calculating the grades of austenitization (T AN = 750 C)...97 Procedure for calculating the grades of austenitization for helium-cooled samples...98 Micrographs of helium - cooled samples etched with Le Pera...99 Intensity spectra resulting of different annealing temperatures Segmentations of the microstructures for calculating the grades of austenitization Compared grades of austenitization calculated with different methods Overview of transformed phase amounts of steel 12 after annealing at 750 C for 60s Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 750 C for 60s Overview of transformed phase amounts of steel 12 after annealing at 775 C for 60s Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 775 C for 60s Overview of transformed phase amounts of steel 12 after annealing at 800 C for 60s Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 800 C for 60s Time dependent phase transformation curves of steel 12 after annealing at 750 C for 60s and different soaking temperatures Time dependent phase transformation curves of steel 12 after annealing at 775 C for 60s and different soaking temperatures Time dependent phase transformation curves of steel 12 after annealing at 800 C for 60s and different soaking temperatures Heating cycles for dilatometric investigations with complete and incomplete austenitization Time dependent phase transformation curves of steel 12 after annealing at 800 C for 60s and different cooling conditions Time dependent phase transformation curves of steel 12 after annealing at 825 C for 60s and different cooling conditions Time dependent phase transformation curves of steel 13 after annealing at 800 C for 60s and different cooling conditions Steel 12 (T an = 850 C; CR= 1.2K/s): Mathematical description of the deviated dilatometer curve (according to the temperature) with Gauss Error Distribution Curve inclusive the transformed phase amounts Original measured and deviated dilatometric curves at continuous cooling conditions with cooling rates of 10 K/s and 20 K/s after annealing at 850 C Calculated phase amounts of Steel 12 which occur at continuous cooling conditions after annealing at 850 C Figure 95: Carbides found on grain boundaries (upper right) and within grains (lower images) in DP-Al steel 1 quenched from 400 C after intercritical annealing Figure 96: Figure 97: Figure 98: Figure 99: EDX-mappings of carbide particles found in DP-Al samples quenched from 400 C Dilatation signal for samples from steel 6, DP-Al high C, quenched from 1250 C and annealed at 400 C for different times EBSD pattern from a steel 6, DP-Al high C sample annealed 40 s at 400 C Martensite grains without and bainite grains with cementite in steel 6, DP-Al high C annealed 40s at 400 C Figure 100: Cycle and dilatometer signal for a treatment with steel Figure 101: Figure 102: Figure 103: Figure 104: Figure 105: Figure 106: Sample from 300 C containing grains with and without cementite (left) and sample from 350 C with nearly only grain structures with cementite (right) Comparison between a micrograph etched with Nital at 2% and LePera s Schematic of the 1-D diffusion model for the simulation of austenitization during intercritical annealing Calculated C-concentration profiles and position of the fcc/bcc moving boundary at various moments, during intercritical annealing Calculated driving-force for the nucleation of bainitic ferrite in paraequilibrium with austenite, for steel TRIP-Si, previously intercritically annealed at (a) 780 C, (b) 800 C and (c) 820 C Normalised dilatation signals and bainite fractions determined by metallographic means for the isothermal transformation of a DP-K 34/60 after intercritical annealing (left), simulation parameters and computed bainite fractions using the modified Azuma model and computed interfacial energies (right). The isothermal transformation temperatures are given in C Figure 107: Isothermal transformation behaviour of DP-K34/60 as TTT-plot. The measured dilatation in Figure 106 is given as a false colour plot, the simulation results (N 0 =2e 17 m -1 ) as lines of isofractions. The solid 8

11 Figure 108: Figure 109: Figure 110: Figure 111: Figure 112: blue lines denote the bainitic ferrite fractions, the dashed green lines the cementite precipitation out of austenite Continuous Cooling Transformation chart for steel 2 (DP, Si). Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The red figures indicate the computed bainite fractions. The green line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model Measured continuous cooling transformation chart of Steel 3 (TRIP, Al), overlaid with simulation results.. Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The bracketed red figures indicate the computed bainite fractions. The blue line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model a. Microstructure obtained by LOM. b. Pictorial view of the segmentation matrix. c. Carbon distribution profile after annealing. d. Recrystallized ferrite grains Intercritical annealing simulations at 750ºC for steel 12. a. Isothermal transformation kinetics at 400ºC. b. Isothermal transformation kinetics at 450ºC. c. Isothermal transformation kinetics at 500ºC Comparison between real and simulated microstructures for steel 12 annealed at 750ºC a-b. 450ºC. c-d. 500ºC Figure 113: Transformation kinetics for continuous cooling transformations for steel 12 annealed at 800ºC. a. 60 K/s. b. 40 K/s. c. 10 K/s. d. 5 K/s Figure 114: Comparison between real and simulated microstructures for continuous cooling simulations for steel 12 annealed at 800ºC. a-b. 60 K/s. c-d 5 K/s Figure 115: Transformation kinetics for continuous cooling transformations for steel 13 annealed at 800ºC. a. 60K/s. b. 40K/s. c. 20K/s. d. 10K/s. e. 5K/s. f. 2.5K/s Figure 116: Comparison between real and simulated microstructures for continuous cooling conditions for steel 13 annealed at 800ºC. a-b. 60K/s. c-d. 5K/s Figure 117: Figure 118: Figure 119: Calculated vol. fraction of bainitic ferrite as a function of holding time at 400 C, for various nucleation-site densities of bainitic ferrite, in steel TRIP-Si previously intercritically annealed at 820 C Calculated vol. fraction of bainitic ferrite as a function of holding time at 400 C, for various ferrite/austenite interfacial energies, in steel TRIP-Si previously intercritically annealed at 820 C Calculated vol. fractions of bainitic ferrite, in TRIP-Si steel intercritically annealed at 800 C, for different isothermal transformation temperatures Figure 120: Calculated TTT diagram for bainitic ferrite in steel TRIP-Si, as derived from the results of Figure Figure 121: Figure 122: Figure 123: Calculated TTT diagram for bainitic ferrite in steel TRIP-Si, showing the effect of intercritical annealing temperature on the overall kinetics of the bainitic transformation Example calculation showing the effect of austenite grain size on the kinetics of the bainitic transformation Comparison between dilatometric results and model calculations for steel TRIP-Si, fully austenitized at 1250 C/30mins and subsequently isothermally treated at (a) 350 C, (b) 400 C and (c) 450 C Figure 124: Comparison between dilatometric results and model calculations for steel CP, fully austenitized at 1250 C/5mins and subsequently isothermally treated at (a) 350 C, (b) 400 C and (c) 450 C Figure 125: Austenite grain size influence on the transformation. Isothermal holding at 400ºC. Steel Figure 126: Figure 127: Figure 128: Figure 129: Figure 130: Figure 131: Figure 132: Figure 133: Martensite start temperature as a function of carbon concentration Comparison between normalized nucleation probabilities as a function of temperature Material for the analysis of the influence of manganese and chromium Phase transformation behaviour of steel 10, steel 12 and steel 13 during continuous cooling after annealing at 850 C, 825 C and 800 C Effect of manganese and chromium on the phase transformations with an continuous cooling rate of 20K/s after annealing at 825 C for 60sec Effect of manganese and chromium on the phase transformations with an continuous cooling rate of 20K/s after cooling from 825 C Continuous Cooling Transformation chart of a DP-W 700 after quenching from 10s at 1300 C. Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The red figures indicate the computed bainite fractions. The green line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model Continuous Cooling Transformation chart for steel 2 (DP, Si). Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The red figures indicate the computed bainite fractions. The green line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model

12 Figure 134: Figure 135: Figure 136: Transformation chart of Steel 2 computed using the TK-StripCam Transformation model Measured continuous cooling transformation chart of Steel 3 (TRIP, Al), overlaid with simulation results.. Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The bracketed red figures indicate the computed bainite fractions. The blue line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model Computed transformation chart of Steel 3 (TRIP, Al) using the TK-StripCam transformation model Figure 137: Calculated vol. fraction of bainitic ferrite as a function of holding time at 350 C, for three different C- contents of the steel CP Figure 138: Calculated vol. fraction of bainitic ferrite as a function of holding time at 400 C, for three different C- contents of the steel CP Figure 139: Calculated vol. fraction of bainitic ferrite as a function of holding time at 450 C, for three different C- contents of the steel CP Figure 140: Calculated C-content of austenite as a function of holding time at 450 C, for three different nominal C- contents of the steel CP Figure 141: Figure 142: Figure 143: Figure 144: Figure 145: Figure 146: Figure 147: Calculated paraequilibrium driving-force for the nucleation of bainitic ferrite as a function of holding time at 450 C, for three different nominal C-contents of the steel CP Calculated vol. fraction of bainitic ferrite as a function of holding time at 350 C, for three different Mn-contents of the steel CP Calculated vol. fraction of bainitic ferrite as a function of holding time at 400 C, for three different Mn-contents of the steel CP Calculated vol. fraction of bainitic ferrite as a function of holding time at 450 C, for three different Mn-contents of the steel CP Calculated paraequilibrium driving-force for the nucleation of bainitic ferrite as a function of holding time at 400 C, for three different nominal Mn-contents of the steel CP Calculated vol. fraction of cementite precipitated in austenite as a function of holding time at 350 C, for three different Mn-contents of the steel CP Calculated vol. fraction of bainitic ferrite as a function of holding time at different transformation temperatures, for two different Cr-contents of the steel CP

13 FINAL SUMMARY 1 Objectives of the Project Bainite is nowadays playing a major role in the microstructure and mechanical properties in a variety of industrially-produced steel grades. Multiphase transformation-induced plasticity (TRIP) steels for automotive applications, ultra-low carbon bainitic (ULCB) steels for pipeline applications are some examples of the increasing involvement of bainite as a microstructural constituent in steels. Nevertheless, optimization of the production and exploitation of bainite-involving steel grades and, more importantly, optimization of the design of new alloy compositions and/or processing routes, necessitate the clarification of the effect of chemical composition and heat-treatment conditions on the evolution of the bainitic transformation. This in turn creates a necessity for the development of appropriate models, with the highest possible degree of accuracy and applicability. However, because of the great morphological variety under which bainite can exist, and because of the complex situation of transforming into bainite not all controlling processes of the bainitic transformation are understood and until today are discussed with controversy and disagreement. As a consequence of these difficulties associated with the bainitic transformation, such modelling tools of practical generality and applicability have not been developed. The projects major objective was to achieve the development of a physically-based approach, or of a combination of appropriate physical approaches to describe the overall, macroscopic kinetics of the bainitic transformation in dual-phase, TRIP and complex-phase steels, with the highest possible degree of qualitative and quantitative accuracy, and with the widest possible field of applicability with respect to alloy compositions and cooling conditions. 2 Comparison of initially planned activities and work accomplished The project has been divided into five work packages based on each other, namely - WP1: Literature Study - WP 2: Material Supply - WP 3: Bainite Design for Homogeneous Austenite - WP 4: Bainite Design for Heterogeneous Structures with Inhomogeneous C Distribution in Austenite - WP 5: Validation and Conclusions The particular objectives that were originally planned and the progress made within each one of these WP is summarised task by task in the following. 2.1 WP1: Literature Study The objective of this work package was the analysis and evaluation of existing models in literature in combination with published experimental data. The results of this work package formed the base for the model development in the further course of the project. Task 1.1: Task 1.2: Task 1.3: Retrieval of existing Model Approaches and Experimental data Application of Existing Approaches to Existing Experimental Data Evaluation of Existing Approaches Assessment of Controlling Mechanisms. 11

14 Within WP1 a theoretical basis and the theoretical guide lines for further execution of the project were worked out. It was the task of the involved partners RWTH and UTK during the first half year of the project to carry out an extensive and comprehensive study of literature for the latest knowledge in the field of transformation to bainite. The aim of Task 1.1 was a retrieval of existing model approaches and experimental data from literature. Also existing data at the industrial partners were provided. Task 1.2 was focused on the application of existing models and testing them by existing data. The aim of Task 1.3 was an evaluation of existing approaches and an assessment of controlling mechanisms. From this work a particular bainite transformation model has been chosen and implemented by different partners. This model is based on the work of Azuma et al. [1] and has accordingly been named Azuma model within the consortium. 2.2 WP 2: Material Supply The objective of WP2 has been to select suitable material for the experimental work based on the needs for model development as defined in WP1. Task 2.1 Task 2.2 Definition of Materials Laboratory and industrial Production and Distribution Different steel grades have been selected with compositions in the range of current industrial interest for DP-, TRIP- and CP-steels and with variations of the most important alloying elements that influence bainite transformation. Industrial material has been sampled from production by the industrial partners ThyssenKrupp Steel Europe AG (SE-AG) and Voestalpine. Further laboratory produced heats have been provided by SE-AG. Sheets of these materials have been distributed amongst the consortium for experimental investigations. 2.3 WP 3: Bainite Design for Homogeneous Austenite In WP3 it was planned to extend one or several of the models chosen in WP1 and fit it against experimental data for the use for bainitic transformation in hot rolling. Both isothermal as well as continuous cooling transformation kinetics for homogeneous austenite into bainite have been determined by dilatometer measurements. In the following the microstructure has been analysed by methods of optical microscopy and additional investigation methods like TEM, EBSD and others where necessary. On the numerical side thermodynamic and kinetic simulations have been carried out, using tools like ThermoCalc and DICTRA. A final objective of this work package has been to fit free parameters of the developed model or models with the experimental data obtained from the other tasks in this work package. Task 3.1 Task 3.2 Task 3.3 Task 3.4 Experimental Micro Structural Characterization Thermodynamic + DICTRA Calculations Model Development On the experimental side those steels provided from WP2 have been thoroughly characterised concerning their transformation behaviour by conducting dilatometer experiments. Further it could be shown that both the austenite grain size and a deformation prior to the bainite formation both strongly 12

15 influence the bainite transformation kinetics. A smaller grain leads to a faster kinetics as well as a prior deformation, especially for the formation of upper bainite. Suggestions have been made as how these effects could be incorporated into the implementation of the bainite transformation model. The microstructure of these specimens has been characterised, especially the continuous cooling and isothermal transformations have been studied. An attempt to distinguish between martensite and bainite by applying EBSD measurements has not been successful. But within WP4 a method combining EBSD and TEM investigations has been successfully applied. On the theoretical side calculations have been made concerning the influence of temperature and of alloying elements on interfacial energies. It was found that both the chemical composition and the temperature have a tremendous influence on the interfacial energies. Accordingly temperature dependent interfacial energies have been computed with MatCalc. A corresponding model was incorporated into the bainite transformation model code. This has been regarded as necessity as the interfacial energies have a tremendous effect on the transformation kinetics. While the driving forces have a square influence on the nucleation, interfacial energies have a cubic one. The interfacial energy model chosen for implementation is the same that is used in MatCalc. It is a nearest neighbour broken bond (NNBB) model. For the computational approach the suggestions of Sonderegger [2,3] and Kozeschnik [4,5] et al. are applied. The driving forces on the other hand have been retrieved from thermodynamic databases, as well as the paraequilibrium concentrations. As thermodynamic software mainly different versions of ThermoCalc have been used together with distinct versions of the thermodynamic databases TCFE. As this TCFEdatabase did not consider the influence of silicon and aluminium in the computation of paraequilibrium cementite this effect has been considered accordingly. The reason for this step has been, that Silicon and Aluminium are found to be present in paraequilibrium cementite, they have a strong influence on the cementite precipitation and they are usually applied in commercial steels in order to control cementite precipitation. Next to the bainite transformation model, implemented by the use of the finite differences method, a Cellular Automaton model has been developed. It uses probability distribution functions to describe the probability of a transformation for a given temperature and chemical composition. These probability distribution functions are computed by applying the so called Azuma model. One main advantage of this approach is that it allows the computation of 2D and 3D microstructures with the consideration of the carbon redistribution. It is further possible to set an arbitrary initial microstructural state, e.g. with a given inhomogeneous distribution of carbon or a certain grain size distribution. Finally the different implementations of the bainite transformation model have successfully been validated against experimental data. 2.4 WP 4: Bainite Design for Heterogeneous Structures with Inhomogeneous C Distribution in Austenite On the basis of the physically based approaches for bainitic transformation reviewed in WP1 and on the models developed in WP3 for the transformation from homogenous austenite, models of bainitic transformation for the more general situation of heterogeneous starting structures have been developed in WP4. Here the situation has been more complicated than in WP3, because both structural and compositional heterogeneity had to be accounted for. These steels usually show pronounced segregations and the transformation starts during cooling from an intercritical austenite ferrite state. Not only carbon is distributed inhomogeneously, other important alloying elements are segregated, too. Therefore models that work for transformation from homogeneous austenite need to be expanded. Further it was envisaged to develop a 3-D numerical discrete model of the kinetics of bainitic transformation, accounting for differences in local composition and for realistic microstructural morphologies and sizes. The work package has been structured into five separate tasks: 13

16 Task 4.1 Task 4.2 Task 4.3 Task 4.4 Task 4.5 Cold Strip Characterization Experimental Micro Structural Characterization Thermodynamic + DICTRA Calculations Model Development In WP 4 once more the model approaches from WP 3 has been used on a broader basis in order to simulate the more complex situation of starting the transformation out of an inhomogeneous situation. Such situations are given when DP-, TRIP- or CP-steels are produced in thermal cycles starting in the intercritical austenite /ferrite regions. A similar case arises, if transformations prior to the bainite formation occur. Not only carbon is distributed inhomogeneous, other important alloying elements might be segregated too. It has been envisaged to develop a 3-D numerical discrete model of the kinetics of bainitic transformation, accounting for differences in local composition and for realistic microstructural morphologies and sizes. On the experimental side of this workpackage according transformation kinetics have been measured. In order to characterize the transformations both the dilation curves and the resulting microstructures have been characterized in great detail. Experimental tests have been conducted starting from different soaking temperatures, resulting in different austenite fractions in the intercritical region. Experimentally the influence of the starting intercritical temperature, and of the according austenite fraction in the intercritical region, on the transformation kinetics during cooling could be shown. It further has been shown, that the starting austenite grain size is an important parameter that influences the transformation kinetics in a way that for austenite grain sizes above 10µm smaller grains result in faster kinetics and a smaller total amount of bainite. For the evaluation of the dilatometric results a procedure to separate the dilation signal into different contributions has successfully been developed and implemented. The aim of this process is separate the dilatation signal into the contributions coming from ferrite-, bainite- or martensite transformation Further additional steels with a chemical composition similar to other steels in the project, but a higher carbon content, have been defined for production in WP2. The aim of this step has been to mimic an austenite composition as it occurs during intercritical annealing of the former steels, but with a fully austenitic state which eases dilatometric investigations by a higher gain of the measured signal. DICTRA computations have been performed in order to study the transformation and carbon distribution during intercritical annealing. This has been an important step in order to define the initial state of the austenite at the end of the intercritical annealing and prior to the cooling down to the bainite transformation temperature. From these simulations especially the initial carbon profile could be determined. For inhomogeneous situations the combination of DICTRA model and bainite model are working well. By DICTRA the separation between ferrite and austenite as well as the carbon distribution can be computed. The result gives the starting condition for the transformation into bainite. Concerning the bainite transformation model development basically the same model has been applied as within WP3, but it has been enhanced to consider a partial austenitic microstructure with increased carbon content. Both isothermal and continuous cooling simulations have been conducted to validate the model in the case of heterogeneous conditions. For the Cellular Automaton model additional probability functions have been introduced to add the transformation into e.g. ferrite and martensite into the model. Further a procedure has been developed and implemented in order to introduce realistic grain structures into the model. Several simulations have been conducted considering different inhomogeneous microstructures and segregation states as 14

17 determined by according investigations. These validating computations resulted in a good agreement with measured transformation data and phase fractions. It has been shown that the bainite models are able to describe the bainitic part of the transformation correctly, when material is cooled from the intercritical region. When cooling from the intercritical region the 3D model combined with the according ferrite and bainite models describe the formation of ferrite and bainite in good agreements with the experimental results. However it could also be shown that a realistic starting grain structure has to be incorporated into the model. Accordingly a procedure was developed to transfer realistic grain structures from metallography into the model. 2.5 WP 5: Validation and Conclusions Within WP 5 the approaches developed in WP 3 and 4 and the appropriate parameters have been validated and based on these results it was planned to obtain a final evaluation of the models and conclusions. Task 5.1 Task 5.2 Task 5.3 Task 5.4 Task 5.5 Parametric Analysis / Field of Application Validation Against Untrained Data Calculation of Examples for which Older Models from Literature Failed Application Cases Guide Lines Particularly parameter studies have been performed not only about the temperature and the composition depending influences, but also concerning the other adjustable parameters. Therefore especially the influence of the initial nucleation density and the interfacial energies on the bainite transformation behaviour has been studied. Thereby it could be shown that smaller interfacial energies accelerate the bainite formation kinetics. Further several simulations have been carried out for different cooling conditions and to adjust the models to the transformation kinetics which have been measured experimentally for different initial microstructures. Namely a series of typical TTT-diagrams and CCT-diagrams could be derived and the influence of the intercritical annealing temperature on TTT-diagrams has been discussed. 3 Description of Activities and Discussion As a result of an extensive literature review of bainitic models an overview of such models has been compiled. In this overview the most noteworthy models and their significant features have been compiled. From these, one model has been chosen as the most promising one for further exploration and expansion. This model, based on the work of Azuma et al. [1] has several benefits over other models cited in literature. Namely the nucleation based model uses thermodynamic descriptions of the driving forces and to assess the chemical composition of different phases. This reduces the number of necessary fitting factors tremendously. At the same time these values can be determined for a wide range of steels, which is only limited by the applicability of the applied thermodynamic databases. Finally the controlling mechanisms of the bainite transformation have been identified from this review of different modelling approaches in literature. For the development and validation of the implemented models a set of steel compositions has been determined, of which most have been sampled from commercial production, while a smaller complementary set has been produced by laboratory means. This material has been distributed amongst the partners for further investigation and characterisation. 15

18 Both in WP3 and WP4 series of laboratory cycles have been performed in order to study the bainite formation for different cooling rates respective distinct isothermal holding temperatures. This covered fully bainitic microstructures, heterogeneous transformations, as well as transformation from only partial austenized microstructures. Further the influence of different austenitic grain sizes, chemical compositions and a prior austenite deformation on the bainitic transformation has been determined. The obtained microstructures have been characterised by optical light microscopy (OLM) and if necessary by more sophisticated methods like TEM and EBSD. These results completed the dilatation measurements which have also been evaluated in order to determine which phase formed to what quantity and at which temperature. Both the location and composition of cementite has been characterized. Though it is repeatedly noted in literature that the cementite precipitated during the bainite formation can be described by paraequilibrium, this could not clearly be confirmed by own investigations. However it could be confirmed by own measurements, that the cementite contains some aluminium, which would not be the case for orthoequilibrium. These investigations showed that often AlN is conjunct with cementite, which might be attributed to the precipitation of aluminium out of the paraequilibrium cementite. To simulate the state of the microstructure, especially the austenite formation and the carbon distribution, DICTRA computations have been performed. The results of these simulations gave important hints on the initial state of the intercritical annealed microstructure prior to cooling. Such simulations are able to predict both phase fractions and the carbon distribution which are necessary starting conditions for simulations of the bainite transformation during the subsequent cooling. The bainite transformation model has been implemented in two ways. UTH and SE-AG both implemented finite differences approaches, CEIT has used the model to describe probability distribution curves which have been introduced to a Cellular Automaton model. The benefit of the latter approach is that it incorporates the carbon diffusion from one cell to another. Further different initial starting conditions can be considered, such as grain size effects, heterogeneous microstructures or inhomogeneously distributed carbon content. Both UTH and SE-AG introduced a series of improvements to the model as it is described in the original paper. Some parts of the mathematical formulation of the model have been corrected. Other details have been added from further sources. Both UTH and SE-AG use ThermoCalc to obtain the necessary driving forces and chemical compositions taking into account paraequilibrium boundary conditions. Two different approaches are applied for this task. UTH uses ThermoCalc as standalone application and derives carbon content and temperature dependent equations. SE-AG has implemented the whole bainite transformation model in Matlab and uses a software interface to ThermoCalc to directly compute the necessary data from within the model. Lookup tables are used to reduce the computational effort. A significant improvement has been achieved by computing the interfacial energies, which have a tremendous effect on the nucleation processes as they are modelled within the chosen approach. Therefore the NNBB model suggested by Sonderegger et al. [3] has been implemented. The same model is implemented in the commercial software MatCalc. Comparisons between MatCalc and the own implementation showed good agreement in some cases, in other cases significant divergences were observed. Further investigations let assume, that the underlying thermodynamic databases are probably the origin of these differences. CEIT uses the bainite transformation model to compute probability distributions of the transformation kinetics in dependence of the local temperature and austenite carbon content. In a similar way the ferrite and martensite transformations have been modelled and introduced to the Cellular Automaton model. Further the temperature dependent carbon diffusion between the cells of the Cellular Automaton model is considered. This approach allows not only the simulation of heterogeneous transformations, but is also interesting as it allows considering distinct initial starting conditions. Further this approach has the advantage of describing 2D and even 3D microstructural evolutions. 16

19 Systematic parameter variations have been used to study the reaction of the model to the according changes of the parameters and to understand the interaction of the underlying coupled processes. Further the models have been validated against experimental data of the sampled steels. Herby CEIT also studied the influence of different respective heterogeneous initial microstructures as well as inhomogeneously distribution of the initial carbon content. Finally the transformations of some commercial steels have been simulated and those results have been compared with according experimental results. The results of these computations showed, that the implemented models are capable to describe the bainite transformation in modern multiphase steels. Obviously the chosen modelling approach incorporates also limits for its applicability. For the finite difference model these are namely: Based on the assumption of a nucleation driven approach no growth of bainitic ferrite or cementite precipitates is considered within the model. If growth phenomena become important in a bainite transformation one may suppose that the model tends to underestimate the kinetics and formed amounts of the bainite transformation. The implemented model assumes paraequilibrium, a thermodynamic boundary condition that neglects the diffusion of matrix atoms. While this is plausible for short annealing times it may be not for prolonged annealing treatments. The assumed instantaneous redistribution of carbon in paraequilibrium becomes unrealistic for very low temperatures. Experimental details of Caballero et al. [6] show that at 200 C the redistribution of carbon in order to reach paraequilibrium may take more than 100 hours. At such low temperatures the model overestimates the bainite transformation kinetics. Finally some aspects, like grain size, residual stress respective recrystallization state are not considered in the finite difference model. For example it has been shown that both the austenite grain size and a deformation prior to the transformation both influence the bainite formation kinetics. So far especially the initial nucleation density value N 0 has been used as an adjustable parameter to account for these effects. A reasonable method to predict this value has not been developed within this project. Some of these points are overcome by the implementation of the Cellular Automaton model. It is able to consider the temperature dependent carbon diffusion from one cell to another. Though not implemented it would theoretically be possible to incorporate the diffusion of matrix atoms in a similar way. Further it takes into account microstructural effects and even different morphologies or inhomogeneous chemical starting conditions. Within the project several examples for isothermal and continuous cooling transformations of commercial steels have been simulated, as well as numerous parameter studies. As supposed the wide validity range of the implemented models could be confirmed. Further the predicted microstructural features are in alignment with the experimental data. 4 Conclusions Within the project the consortium has developed and implemented two bainite transformation models that have wide applicability and the ability to predict different aspects of the bainite transformation. One model, the so called Azuma model, is limited to the bainite transformation. This model in its core is based on the work of Azuma et al. [1], though several enhancements were introduced within the project. A significant improvement was achieved by the computation of the interfacial energies, which have been used as fitting factors in the original work. This sub model uses a nearest neighbour broken bound model and is based on the approach suggested Sonderegger et al. [3]. 17

20 Several other improvements to the model have been introduced and described in greater detail within this report. The other model is a Cellular Automaton model which uses statistical descriptions of the occurring transformation processes. The large benefit of this model is the ability to simulate 2D and 3D transformation processes and how they are influenced by chemistry, process conditions, grain size and the initial distribution of chemical elements. Unlike the so called Azuma model the Cellular Automaton model is not limited to the bainite transformation but is able to predict the whole microstructural evolution. To assess the necessary transformation probabilities it relies on other transformation models, like the so called Azuma model for the bainite transformation. For both models extensive parameter studies have been performed and both have been validated using a large database of experimental data produced within this project. Due to the nature of this project these experimental data mainly focus on the bainite transformation, but also data of heterogeneous transformation have been compiled by the consortium. These data combine a detailed analysis of the transformation behaviour with exhaustive microstructural investigations. As the Cellular Automaton model is also based on the same metallurgical model, both developed approaches are able to describe the same fundamental processes connected to the bainite formation. Not only from a theoretical point of view the described connection of bainite formation and cementite precipitation is essential. For the scientific side it helps to understand the distribution of carbon amongst the different phases and how the enrichment of carbon in austenite may lead to a transformation stasis. This stasis may be overcome by cementite precipitation, which draws substantial amounts of carbon out of the austenite. From the technological and steel design viewpoint the carbon distribution amongst the phases and the described cementite precipitation are crucial as they determine the steel characteristics in terms of strength, toughness, retained austenite stability and so on. The broad applicability of the model and the reduced number of fitting parameters make the models even more interesting for steel design. For this application often early predictions are required when no respective only few experimental data are available, yet. The same is true concerning the influence of variation of the chemical composition. In steel design stability analysis for given chemical compositions and processing parameters are an important tool, which require robust models with a wide range of applicability and reliability. These requirements are met by the models developed in the course of this project. 5 Exploitation and impact of the research results Within the project the consortium has developed and implemented two bainite transformation models that have wide applicability and the ability to predict different aspects of the bainite transformation. The models enable the user of simulating especially the bainite transformation in detail, considering various aspects which influence the bainite transformation. For example the models can be used to assess the influence of changes to the chemical steel composition or an altered cooling curve on the bainite transformation. The Cellular Automaton model is even capable of predicting the evolution of a whole microstructure. The bainite transformation model on the other side gives a great insight into the bainite formation, including the cementite precipitation out of austenite respective ferrite, considering various aspects which influence the bainite transformation. The models give an insight in the interaction of bainite formation and cementite precipitation, namely that the enrichment of carbon in austenite may lead to a transformation stasis that is overcome by cementite precipitation. By this cementite precipitation substantial amounts of carbon are drawn out of the austenite. In the following the bainite transformation is enabled to proceed. Both the precipitation of cementite and the final carbon content in the austenite are important details in steel design, as they substantially determine important factors like toughness, strength and retained austenite stability. 18

21 At SE-AG the bainite transformation model developed and validated within this project has already been applied in the development of new bainite containing steel grades like X70, a line pipe steelgrade which is typically produced with hot strip thicknesses of 18 mm and more. The newly developed bainite transformation model been used to analyse the bainite transformation and how it is influenced by both the steels chemical composition and different cooling rates. On basis of these simulations an improved cooling strategy for this line pipe steel has been proposed, which ensures the aspired homogeneous bainitic microstructure despite the strip thickness of one inch. Further the possibility to implement this model into the hot strip simulation tool TK-StripCam is currently analysed. This latter aspect is also mentioned in a contribution of Paul et al. for the SteelSim conference 2011 [7]. 19

22

23 APPENDIX I: WP APPENDICES 1 WP1: Literature Study Within WP1 a theoretical basis and the theoretical guide lines for further execution of the project were worked out. It was the task of the involved partners RWTH and UTH during the first half year of the project to carry out an extensive and comprehensive study of literature for the latest knowledge in the field of transformation to bainite. The aim of Task 1.1 was a retrieval of existing model approaches and experimental data from literature. Task 1.2 was focused on the application of existing models and testing them by existing data. The aim of Task 1.3 was an evaluation of existing approaches and an assessment of controlling mechanisms. 1.1 Retrieval of Existing Model Approaches and Experimental Data Existing models The bainitic transformation proceeds by the nucleation and growth mechanisms. Two opposing doctrines have been proposed, regarding the controlling process of the bainitic transformation: diffusion-controlled growth and nucleation-control. According to the first approach, the rate of the transformation is determined by the growth-rate of bainitic ferrite laths in austenite, which is considered to take place under diffusion-control. The opposing approach supports the idea that the overall transformation rate is determined by the rate at which bainitic ferrite nucleates in austenite. Up to now the controversy among the metallurgical community about these two opposing views remains unsolved. Published modelling approaches are based either on the diffusion-control or on the nucleation-control mechanism. Most of the models summarized in Table 1 however are based on the nucleation-control mechanism, which presents certain advantages over diffusion-control. The most complete existing model is definitely the one presented by Azuma et al. [1]. Its major advantage over other existing models is that it takes into account and quantifies the precipitation of cementite during the bainitic transformation. This allows for a more realistic modelling of the bainitic transformation overall and, furthermore, it widens the range of applicability of the model to practically any steel composition and heat-treatment route (e.g. holding time at transformation temperature range). Other proposed models which neglect carbide precipitation and focus solely on the kinetics of bainitic ferrite, are inevitably limited to be best applicable only to steel compositions for which carbide precipitation is severely suppressed, e.g. in steels containing Si and/or Al in excess of 1 mass %. But even in these cases, cementite will eventually precipitate at prolonged transformation times, which means that neglecting carbide precipitation poses limitations not only with respect to steel composition, but also with respect to heat-treatment conditions. The model of Azuma et al. [1] also manages to account for a number of significant aspects of the bainitic transformation. Due to its structure it can discriminate and identify the evolution of upper and lower bainite, depending on the chemistry of the steel and transformation temperature. Furthermore, it takes into account and calculates important microstructural features of bainite, such as the size of bainitic ferrite platelets and the size of cementite particles, as well as the variation of these microstructural features during the transformation (e.g. gradual refinement of bainitic ferrite platelets due to the gradual enrichment of untransformed austenite in carbon). Finally, although lacking in the form presented in reference [1], the model can be easily modified, in order to be applied for continuous-cooling transformation and to take into account the grain-size of parent austenite, the later feature being of great interest for application in multi-phase TRIP steels. 21

24 Model and related references Year Controlling process Type of heattreatment Rees Nucleation Bhadeshia [8] control Quidort Diffusion Brechet [9 11] control Matsuda Nucleation Bhadeshia [12] control Azuma et al. [1] Gaude- Fugarolas- Jacques [13] 2005 Nucleation control 2006 Nucleation control Katsamas [14] 2006 Nucleation control Carbide precipit. Chemical composition limitations Comments Isothermal No Si + Al > 1% * Accounts for autocatalytic nucleation, austenite grain size, incomplete reaction phenomenon, does not provide quantitative information for M 3C Isothermal & continuous cooling Isothermal & continuous cooling No Si + Al > 1% * Calculated α B sub-unit growth-rates significantly higher than experimental, does not account for incomplete reaction phenomenon, does not provide quantitative information for M 3C No Si + Al > 1% * Accounts for autocatalytic nucleation, austenite grain size, incomplete reaction phenomenon, does not provide quantitative Isothermal Yes Fundamentally none information for M 3C Accounts for autocatalytic nucleation, incomplete reaction phenomenon, subunit refinement, calculates vol. fraction, size & distribution of carbides, identifies upper & lower bainite Isothermal No Si + Al > 1% * Accounts for autocatalytic nucleation, austenite grain size, incomplete reaction phenomenon, does not provide quantitative information for M 3C Isothermal No Si + Al > 1% * Semi-empirical model for calculation of retained austenite in multiphase TRIP steels, can calculate vol. fraction of α B indirectly * Since these models neglect carbide precipitation, they would be more realistically applicable in steels containing Si and/or Al in excess of 1% mass, in order for cementite precipitation to be drastically suppressed. Table 1: Summary of most worth-noting, published models for bainite kinetics. Besides calculating vol. fractions, the model of reference [1] manages to provide quantitative information about a series of very interesting features, such as the average carbon content and yieldstrength of untransformed austenite, the average size of cementite precipitates, the average size of ferrite platelets, etc, all as functions of temperature and time. In conclusion, concerning the evaluation of existing models retrieved from literature, the model by Azuma et al. seems to be the most complete, and presents the greatest potential for wide applicability in comparison to the other reported models. TK-StripCam The TK-StripCam model available at SE-AG has been developed in a series of ECSC projects [15 17]. It couples different process and material models in order to follow the evolution of the microstructure during hot rolling in order to predict the final microstructure of the hot strip and its mechanical properties. Originally developed for microalloyed and CMn steels the transformation into the different phases is described by Avrami-Type equations. Though the model, namely its bainite model, has been further developed [17], its usage for multiphase steels is limited to hot rolling and tight boundary conditions. Further no details on the structure of the formed bainite are possible and it cannot be applied to the transformations during annealing Available data for the bainite start temperature For transformation during continuous cooling it is very important to know the bainite start temperature. In many cases this temperature is just described by empirical equations. A literature review has been done to show the advantage of the physically based equations used within the Azuma model. The effect of alloying elements on the bainite start temperature (B S ) was described by regression analysis for several experimental data. In the following all concentrations are in wt.-%. The first equation was proposed by Steven and Haynes [18] : 22

25 B S ( C) = [ C] 90 [ Mn] 37 [ Ni] 70 [ Cr] 83 [ Mo] Kirkaldy and Venugopalan [19] modified this formula by using US Steels isothermal transformation diagrams of low and high alloy steels. Their result is represented by equation (2): (1) B S ( C) = ,7 [ C] 75 [ Si] 35 [ Mn] 15,3 [ Ni] 34 [ Cr] 41,2 [ Mo] (2) Zhao [20] made a systematic evaluation of Fe-C, Fe-N, Fe-Ni, Fe-Cr, Fe-Mn, Fe-Mo, Fe-Co, Fe-Cu and Fe-Ru alloys which lead to the following term for B S : B S ( C) = ,63 [ C] + 126,6 [ C] 66,34 [ Ni] + 6,06 [ Ni] Ni ,66 [ Cr] + 2,17 [ Cr] 91,68 [ Mn] + 7,82 [ Mn] 0,3378 [ Mn] 42,37 [ Mo] + 9,16 [ Co] 0,1255 [ Co] 46,15 [ Ru] 2 + 0, [ Co] 3 0,232 36,02 [ Cu] [ ] (3) Wang and Kao [21] introduced a parameter Mn eq that describes the influence of Mn, Mo and Ni on B s : Mn eq = [ Mn] + 3,43 [ Mo] + 0,56 [ Ni] (4) The decrement of the B s is then given by: B ( C) = 36, 6 (5) S Mn eq Kunitake and Okada [22] came to the conclusion, that the measured B s temperature for steels with a greater Ni or Cr content is much higher than that predicted by Steven and Haynes. The formula according to Kunitake and Okada, which also includes a coefficient for Si, is as follows: B S ( C) = [ C] 216 [ Si] 85 [ Mn] 37 [ Ni] 47 [ Cr] 39 [ Mo] (6) Li et al. [23] used the equation by Kirkaldy [19] but set the Si content constant at 0.25 wt.%, as most low alloy steels exhibit a silicon content in this order of magnitude. The equation for B s is then expressed by: B S ( C) = [ C] 35 [ Mn] 15 [ Ni] 34 [ Cr] 41 [ Mo] (7) Taking equation (1), (2) and (6) into consideration and using data published in the Atlas of timetemperature diagrams for irons and steels, which include low alloy steels and steels with Ni and Cr contents up to 4.5 wt.%, Lee [24] made the following regression equation: ( C) = [ C] 59 [ Mn] 39 [ Ni] 68 [ Cr] 106 [ Mo] B S [ Mn] [ Ni] + 6 [ Cr] + 29 [ Mo ] 2 (8) 23

26 Another equation especially for forging steels can be found in [25] where the Bainite start temperature is given in Kelvin: B S ( K) = [ C] 36,5 [ Si] 62,3 [ Mn] 47,8 [ Cr] 160 [ V ] 77,5 [ Mo] (9) As all these equations come from regression analysis, it is important to consider which steels were used for the regression analysis. Table 2 shows the range of chemical compositions (in wt-%) of the steels used to create the different equations. Only in these ranges, the equations give reliable results. C [wt-%] Mn [wt-%] Si [wt-%] Mo [wt-%] Cr [wt-%] Ni [wt-%] Cu [wt-%] Steven et al. [18] 0,1-0,55 0,2-1,7-0,0-1,0 0,0-3,5 0,0-5 - Kirkaldy et al. [19] Only examples given Zhao [20] [21] Wang 0,021-0,056 1,41-1, ,17 0,0-0,35-0,0-0,3 - Kunitake et al. [22] 0,11-0,56 0,34-1, ,40 0,07-1,99 0,14-4,80 0,23-4,33 - Li et al. [23] 0,2-0,41 0,31-1,01 0,1-0,28 0,00-0,44 0,02-0,98 0,02-3,04 0,05-0,11 Lee [24] 0,10-0,80 0,26-1,63 0,13-0,67 0,00-1,96 0,00-4,48 0,00-4,34 - Takada [25] 0,11-0,40 0,50-2,52 0,31-1,26-0,20-1,96 0,012 - Table 2: Validation ranges for the B s -Temperature models of different authors. An application of these equations for one of the steels used within this project shows their weakness. As an example for the TRIP-Al, the computed bainite start temperature vary between 463 C and 635 C, whereas the experimentally determined B s -Temperature of this steel is at around 550 C for slower cooling rates and drops down to the M S -Temperature around 430 C at higher cooling rates (Figure 69). The cooling rate is not considered by none of these equations as they are designed to compute the bainite start temperature B S, which is defined as the maximum temperature at which bainite can form. However to define an industrial production cycle the interaction of specific cooling rates and transformation progress is a key feature. For instance the production of dual phase steels in a continuous annealing line is linked to specific cooling patterns, which are defined by the layout of the production line. During the design of such a DP-steel grade the desired ferrite-martensite microstructure has do be ensured, while respecting the operational limits of the given production line. In other words, the chemical design of the steel has to aim for a low bainite kinetics within these given production parameters. This dynamic interaction could not be expressed by any of the above equations Experimental data of bainite transformation kinetics A wide variety of experimental measurements of the overall bainitic transformation kinetics are available in literature, regarding a variety of steel compositions. Table 3 summarizes the references and the corresponding steel compositions, temperature ranges, and other experimental conditions, for which experimental data regarding the vol. fraction of bainite as a function of transformation time were found in literature. More details about the experimental procedures are given in the corresponding references. 24

27 Jacques 26 Reference Steel composition (in % mass) Temperature C Mn Si Ni Al Mo/Cr range (in C) Comments Azuma isothermal holding isothermal holding Quidort isothermal hold. & continuous cooling Rees et al. 8,12] Gaude- Fuganrolas / isothermal hold. & continuous cooling isothermal holding Table 3: Summary of literature sources reporting experimental data of bainitic transformation kinetics. As shown in Table 3, experimental data are available for steels with C-contents ranging from mass %, i.e. from low to medium carbon steels. Furthermore, steels containing varying amounts of Si and/or Al have been examined which gives an opportunity to study the bainitic transformation with and without the presence of carbides. All the experimental investigations have included isothermal bainitic transformations. The usual temperature range of these experiments is 300 C 450 C, which is the temperature range of practical interest for the bainitic transformation. Nevertheless, a few investigations dealt with the bainitic transformation under continuous cooling, with the corresponding experimental cooling rates varying between C/sec and 8 C/sec Existing data For further evaluation of the Azuma model and for doing an assessment of the controlling mechanisms in bainitic transformations more experimental data was needed. Therefore SE-AG provided such data from previous investigations at SE-AG. These data include continuous cooling transformation data from the austenite region for 14 different carbon steels as well as for a DP steel and for a TRIP steel. For all steels the thermal cycles and the austenite grain structure before the start of the transformation are known. For the TRIP steel additional the different dilatation signals are given. The upper image in Figure 1 shows as an example the transformation diagram for one of the carbon steels. The lower figure gives an example for the dilatation signal during transformation while cooling. Further the isothermal transformation kinetics measurement of a DP steel after intercritical annealing has been provided. The industrially sampled DP steel has a similar chemical composition as steel 2 investigated within this project. The details of these data are given in

28 Dilatation Temperaturein C Figure 1: Continuous cooling transformation for a carbon steel (top), dilatation signal for one of the cooling cycles of a TRIP steel (bottom). For the evaluation of the Azuma model voestalpine provided already existing results from former investigations. The results refer to the materials No. 13 and 14 in Table 4, i.e. the description of WP2. Using a Bähr dilatometer DIL805 A/D samples from these materials were given thermal treatments as shown in Figure 2. The phase amounts transformed during cooling down from the annealing to the soaking temperatures were calculated concerning the procedure as described in Figure 3. As indicated the green and the pink curves have been computed from fits to the ferrite respective austenite dilatation lines. Based on these two curves the transformed fractions during cooling can be determined as indicated by the red brackets. 26

29 Figure 2: Heating cycles for investigation with complete austenitization incl. simulation limits. Figure 3: Schematic procedure of calculating the transformed phase amounts. Figure 4 shows the whole transformations which took place subsequent to the annealing treatment. In these diagrams the x-axis are labelled concerning the soaking temperatures. Figure 5 illustrates some examples of measured transformation which took place during the isothermal annealing treatment. 27

30 Figure 4: Overview of the transformed phase amounts of steel 13 (left) and steel 14 (right). Figure 5: Calculated transformation curves during isothermal soaking of steel 13 (upper line of figures) and steel 14 (lower line of figures) at different soaking temperatures (300 C, 450 C, 550 C). 1.2 Application of existing modelling approaches to experimental data The extensive literature review of task 1.1 has pointed out that the modeling approach proposed by Azuma et al. [1] presents certain significant advantages over those modeling approaches proposed by other researchers [9 14]. For these reasons the approach of Azuma et al. was chosen to be transferred into a computable form and later into a program code. An additional reason for this choice was that, once this complex modeling approach was studied, analyzed, implemented and applied by own means, then it would be easier, through the experience obtained, to do the same, if necessary, to the other existing models which are of a substantially simpler structure. 28

31 During implementing the approach into a program code, following significant problems were encountered and had to be solved: The structure of the model was very complicated, since it involves the simultaneous treatment of three discrete transformations. In addition, as the calculation proceeds in time, the values of several involved quantities and parameters have to be continuously updated. The description of the mathematical formulation of the model in the original paper contained many errors which had to be identified and properly corrected. The description of the model in the original paper was very brief, and almost no critical, practical details for the application of the model were reported there. Assessment of additional literature sources was needed, in order to obtain critical details that were absolutely necessary for the establishment of an application procedure. Later especially the interfacial energy has been identified as being crucial for obtaining proper results. In the original paper constant values have been applied. However the model results could significantly be improved by using properly computed interfacial energies Structure of the model code All the aforementioned problems were properly addressed and an algorithm for transferring the model into a computable form was established by UTH. The major steps of the algorithm are listed below: 1. Transformation temperature (T) and time-step (Δt) for the calculations are set. / 2. The C-contents of ferrite ( x α γ / ) and austenite ( x γ α ) in paraequilibrium are calculated. Co, Co, 3. The thermodynamic driving-force for nucleation of ferrite ( G γ α no, ) in paraequilibrium with austenite is calculated. 4. Values are set for the ferrite/austenite (σ α/γ ), cementite/austenite (σ θ/γ ) and cementite/ferrite (σ θ/α ) / interfacial energies and the corresponding nucleation-site densities (N o, N θ γ, o / N θ α ). o 5. The activation energy for paraequilibrium nucleation of ferrite in austenite is calculated: α / γ 3 * 16 π ( σ ) G = N T γ α, o B 2 3 A γ α ( Gvo, ) [ ( ) 2540] 6. The initial primary nucleation-rate density of ferrite is calculated: γ * G α kt Q, o B C γ αb I = N exp exp o, pr o h RT RT 7. The initial overall nucleation-rate density of ferrite is calculated: I = (1 + β f ) I α B α B α B o o opr, 8. The initial yield-stress of austenite is calculated: S T T = [ ( 298) ( 298) γ, o T + w + w + w 8 3 γ ( 298) ]15.4 ( ) Co, Si Mn 9. The size of the bainitic ferrite platelet is calculated: 29

32 γ a ( ) W = T T G S α, o B no, γ, o / 10. The C-contents of cementite ( x θ γ / ) and austenite ( x γ θ ) in paraequilibrium are calculated. Co, 11. The thermodynamic driving-force for nucleation of cementite ( G γ θ no, ) in paraequilibrium with austenite is calculated. 12. The activation energy for paraequilibrium nucleation of cementite in austenite is calculated: 16 π ( σ ) θ / γ 3 * G = γ θ, o 2 3 γ θ ( Gvo, ) N A 13. The initial nucleation-rate density of cementite in austenite is calculated: I γ * kt Q G C γ θ, o = N exp exp ο h RT RT θ / γ θ / γ o / 14. The C-contents of cementite ( x θ α / ) and ferrite ( x α θ ) in paraequilibrium are calculated. Co, 15. The thermodynamic driving-force for nucleation of cementite ( G α θ no, ) in paraequilibrium with ferrite is calculated. 16. The activation energy for paraequilibrium nucleation of cementite in ferrite is calculated: 16 π ( σ ) θ / α 3 * G = α θ, o 2 3 α θ ( Gvo, ) N A 17. The initial nucleation-rate density of cementite in ferrite is calculated: I α * kt Q G = N exp exp ο h RT RT θ / α θ / α C α θ, o o 18.Time is increased by Δt. 19. The extended vol. fraction increment of bainitic ferrite is calculated: f = I v t αb, ext αb 0 1 o αb, o Co, Co, 20. The real vol. fraction increment of bainitic ferrite is calculated: ( o o o ) f = f f f f αb αb, ext αb θ / γ θ / α The vol. fraction of bainitic ferrite at time t 1 is calculated: f = f + f α B α B α B 1 o The extended vol. fraction increment of cementite in austenite is calculated: 25π = 4 γ γ / θ γ ( x x Co, Co, ) D t C θ γ γ θ γ γ θ ( x x Co, Co, )( x x Co, Co, ) θ / γ, ext θ / γ f I t 0 1 o / / / 23. The real vol. fraction increment of cementite in austenite is calculated: α ( o o o ) f = f f f f θ / γ θ / γ, ext B θ / γ θ / α The vol. fraction of cementite in austenite at time t 1 is calculated: 30

33 f = f + f θ / θ / θ / 1 o The extended vol. fraction increment of cementite in ferrite is calculated: 25π = 4 α α / θ α ( x x Co, Co, ) D t C θ α α θ α α θ ( x x Co, Co, )( x x Co, Co, ) θ / α, ext θ / α f I t 0 1 o / / / 26. The real vol. fraction increment of cementite in ferrite is calculated: α ( o o o ) f = f f f f θ / α θ / α, ext B θ / γ θ / α The vol. fraction of cementite in ferrite at time t 1 is calculated: f = f + f θ / α θ / α θ / α 1 o 0 1 Important notice: As the transformation proceeds in time, new cementite particles will nucleate and grow during every time-step, but also already existing (i.e. formed in previous timesteps) cementite particles will continue to grow. In order to take these processes simultaneously into account, it can be shown that the vol. fraction of cementite at time t n is given by: n ( ) γ γ / θ γ ( x x Cn, 1 Cn, 1) D t C n 1 θ / γ γ θ / γ γ / θ ( x x )( x x ) θ / γ θ / γ 25π θ / γ θ / γ θ / α ( 1 αb ) f = f + I t f f f n n 1 i i n 1 n 1 n 1 4 i= 0 Cn, 1 Cn, 1 Cn, 1 C, n 1 for cementite in austenite, and by: n ( ) α α / θ α ( x x C, n 1 C, n 1) D t C n 1 θ / α α θ / α α / θ ( x x )( x x ) θ / α θ / α 25π θ / α θ / γ θ / α ( 1 αb ) f = f + I t f f f n n 1 i i n 1 n 1 n 1 4 i= 0 C, n 1 Cn, 1 Cn, 1 Cn, 1 for cementite in ferrite. 28. The average mole-fraction of C in austenite is updated: x γ ( αb / / / ) x f x + f x = B 1 f f γ α γ θ γ θ γ Co, 1 Co, 1 Co, C,1 α θ / γ The average mole-fraction of C in ferrite is updated: x α x f x = 1 f α α / γ θ / α Co, 1 Co, C,1 θ / α The new values of activation energies for paraequilibrium nucleation are calculated. 31. The procedure is repeated for the next timestep Application of the model After establishing the algorithm described above, the kinetic model was implemented in a computable form by UTH. The model was then first applied, in order to compare the results with the corresponding, existing calculations, reported in reference [1]. This way the correct transfer of the model from paper to computable form could be evaluated. Calculations were performed for a 0.60C 1.50Mn 1.50Si (in % mass) steel composition, i.e. identical to the composition used in [1]. During these calculations different aspects of the bainitic transformation were examined, for cycles in which austenite transforms isothermally to bainite. Some of these aspects were: 31

34 Interrelation between the kinetics of cementite precipitation in austenite and the amount of bainitic ferrite formed, Evolution of the austenite C-content during the transformation in terms of enrichment by ferrite formation and depletion by cementite precipitation, Effect of the austenite C-content on the size of bainitic ferrite platelets, Influence of the interfacial energy between cementite and austenite on transformation kinetics Influence of the interfacial energy between ferrite and austenite on transformation kinetics Influence of nucleation-site density of ferrite in austenite on transformation kinetics As mentioned previously, the purpose of these calculations was to compare the results of this research against the results of the original paper [1], so that it could be verified that the model and the application procedure have been correctly interpreted and implemented. The values of all adjustable parameters have been set to the ones proposed in the original paper, so that a direct comparison between calculations of the present research and of the original paper can be made. As shown in the example of Figure 6, the corresponding diagrams of the original paper and of this research are directly compared and there is good coincidence between the calculations. Figure 7 depicts an example of the effect of nucleation-site density of bainitic ferrite (N o ) on the kinetics of the transformation at 400 C. As shown, higher values of N o accelerate the kinetics of both bainitic ferrite and of cementite precipitation in austenite. However, the maximum values of the vol. fractions of the phases do not seem to be affected. Figure 8 shows an example of the effect of the ferrite/austenite interfacial energy on transformation kinetics. As expected, the lower the interfacial energy, the faster the kinetics of bainitic ferrite become. This also leads to a slight acceleration of cementite precipitation in austenite. In Figure 9 the average C-content of austenite is depicted as a function of time, together with the vol. fractions of bainitic ferrite, austenite and cementite in austenite. As shown, the rapid enrichment austenite in carbon causes the first plateau of the vol. fraction of bainitic ferrite, before cementite starts to precipitate ( transformation stasis ). However, as soon as cementite begins to precipitate in austenite, it draws substantial quantities of carbon out of the matrix, as shown by the rapid decrease of the average C-content of austenite. Thus, more bainitic ferrite is allowed to form. Figure 6: Comparison between results of Azuma et al. [1] and of this project. 32

35 Figure 7: An example of the effect of nucleation-site density of bainitic ferrite on transformation kinetics. Figure 8: An example of the effect of ferrite/austenite interfacial energy on transformation kinetics. 33

36 Figure 9: Interdependence between C-content of austenite and vol. fractions of the phases during the bainitic transformation. 1.3 Evaluating of existing Approaches Assessment of controlling mechanisms A critical assessment of the different modelling approaches reported in literature was attempted. As mentioned earlier, a few approaches adopt the diffusion-controlled growth theory, whereas the majority follows the nucleation-control theory. Both theories present certain controlling mechanisms, which are outlined below. Starting with the diffusion-controlled growth theory, and more specifically with the thermodynamic aspects of it, in cases where the bainitic transformation proceeds to completion, i.e. when the growth of bainitic ferrite is accompanied by the precipitation of carbides, the final volume fraction of bainitic ferrite can be deduced by the nominal C-content of the steel. However, in cases where carbide precipitation is suppressed, e.g. in steels containing Si or Al in excess of 1% mass, this is not a straightforward task, as the transformation evolves in two-steps. In the first step the growth of bainitic ferrite takes place, whereas the second step involves the precipitation of cementite particles from the carbon supersaturated, untransformed austenite. In the diffusion-controlled growth theory, it is assumed that the reconstructive formation of bainitic ferrite continues, as long as equilibrium or paraequilibrium conditions are maintained, in the absence of cementite precipitation. In order to explain the experimentally observed transformation arrest, this theory needs to introduce an additional mechanism, such as the solute-drag effect. Efforts have been made to explain this arrest, by employing the drageffect of elements like Mo on the movement of the transformation front. However, quantitative results were not satisfactory. Furthermore, there is a difference between measurements of substitutional alloying element concentrations on transformation interfaces. A significant number of investigations, which conducted very fine-scale analyses using AP-FIM, did not report any substantial segregation of substitutional alloying elements. Therefore, the diffusion-controlled growth theory faces an important problem, already from the thermodynamic part of the transformation. As regards the kinetic aspects of the diffusion-controlled growth theory, a significant number of literature sources report experimentally determined growth-rate measurements of bainitic ferrite, for a variety of steel compositions. There appear to be large differences among the measured transformation rates. The well-known model proposed by Trivedi [27] has been reported to be applicable for the prediction of bainitic ferrite laths growth-rate, although the measured growth-rates are somewhat smaller than the corresponding calculated ones. It is, however, worth-noting that bainite consists of very fine platelets (sub-units) of ferrite, with a thickness of μm at 400 C. This thickness decreases with decreasing transformation temperature and/or increasing C-content of the steel, since both these 34

37 factors cause an increase in the yield-strength of the surrounding austenitic matrix, and thus its ability to accommodate the plastic deformation caused by the growing sub-unit is reduced. The fine substructure of bainite has been also reproduced in three-dimensional manner, supporting the idea of autocatalytic nucleation of ferrite. These investigations indicate that the growth-rates discussed in [9] could have been referring to sheaves of bainite, i.e. to accumulation of sub-units, rather than to individual bainitic ferrite sub-units. The larger growth-rates observed in the low-si steel examined in [9] can be attributed to the precipitation of cementite particles. Cementite precipitation causes a reduction of carbon supersaturation in the untransformed austenite, which in turn leads to an increase of the total amount of bainite. This results in larger sheaves of bainite, which can easily be misinterpreted as an increase of the growth rate. As mentioned previously, with the diffusion-controlled growth theory it is always necessary to adopt the solute-drag effect. Although in calculated results using this approach a segregation of Mo is reported, a significant number of fine-scale analytic measurements report no segregation of substitutional alloying elements at the transformation interfaces [28 31]. This constitutes another serious drawback of this theory. In steels containing strong carbide-forming elements, such as W and Mo, alloyed carbides formation has been reported to take place at the transformation interfaces, a fact suggesting long-range diffusion of substitutional alloying elements during or after the formation of bainite [32,33]. However, the necessary investigations on the sequence of the reactions are still lacking. Finally, the inadequate adaptation of the Johnson-Mehl-Avrami-Kolmogrov (JMAK) equation on numerous experimental data, as well as the coincidence of the bainite and martensite surface-relief effect, confirmed by the investigations reported in references [34,35], constitute additional weak-points of the ability of the diffusion-controlled growth theory to accurately describe bainite kinetics. On the other hand, as regards the thermodynamic aspects of the nucleation-control theory, calculation of the maximum possible amount of bainitic ferrite is easy, due to the assumption of diffusionless ferrite growth. Experimentally determined C-concentrations in retained austenite fall closely to the calculated T o lines of the corresponding investigated steel compositions. The negative slope of the T o line implies that the C-concentration in retained austenite has to be greater at lower bainitic transformation temperatures, which also comes in agreement with experimental measurements. The effect of substitutional alloying elements on the C-content of retained austenite can also be attributed to the effect of these elements on the T o line of the steel [36]. Most of the substitutional alloying elements decrease the C-content at the T o line, except of Si, Al and Co. Aluminium and cobalt increase the C- content at the T o line, whereas silicon does not have much of an effect. This tendency corresponds, from a quantitative point of view, to the effect of those elements on the maximum thermodynamically allowed C-concentration in retained austenite, which in turn corresponds to the maximum thermodynamically possible degree of transformation. As regards the kinetic aspects of this theory, the nucleation-control approach is based on the displacive and diffusionless characteristics of the formation of bainitic ferrite sub-units. The basic idea is that the growth of each individual sub-unit is adequately fast, so that the transformation rate is determined by the successive nucleation events of bainitic ferrite. A first mathematical formulation of this approach was attempted by Bhadeshia [37], and later modified by Rees et al. [38]. The nucleation-control approach is best applicable to steels where no carbide precipitation is expected to occur, in which case the transformation is assumed to continue until the C-content of untransformed austenite reaches the T o line. In this approach the spatial dimensions of the bainitic ferrite sub-unit have to be known a priori. According to an investigation by Van Dooren et al. [39], the thickness of the sub-units is determined by a balance between the chemical free energy released by the formation of a sub-unit and the deformation energy stored in the surrounding austenite due to the growth of the sub-unit. In cases where carbide precipitation is suppressed, this approach can be applied to predict the degree of transformation and the C-content of untransformed austenite. However, some carbide formation is always present in real heattreatments, in which case the nucleation-control approach has to take into account carbide precipitation, both in austenite and bainitic ferrite. 35

38 Within the context of the nucleation-control approach, bainitic ferrite nucleates with carbon partitioning, but grows without any partitioning. Nucleation theory of bainite has been found to be realistic for high carbon steels, in which austenite retention at ambient temperature is important and can be achieved by adequate carbon enrichment of the austenite. The bainitic ferrite sub-units are supersaturated with C during their growth. However, the excess C is soon rejected out of the sub-unit into the surrounding austenite, due to the relatively high temperatures associated with the bainitic transformation. This redistribution of C tends to stabilize austenite. At the lower temperature range of the bainitic transformation, the mobility of C atoms is relatively small. Thus, carbides usually manage to precipitate inside the sub-units, before C is evacuated to the surrounding austenite, and the morphology known as lower bainite is obtained. In contrast, at the higher temperature range of the bainitic transformation, C is more mobile and manages to escape to the surrounding austenite, which is gradually enriched in C. Carbide precipitation is then taking place inside the untransformed austenite, leading to the morphology known as upper bainite. As already mentioned earlier, a very integrated modelling effort has recently presented by Azuma et al. [1], based on the principles of nucleation-control theory. The model takes simultaneously into account all the aforementioned metallurgical processes that may occur during the bainitic transformation. The model can predict the overall transformation kinetics, with and without the precipitation of cementite. As a result, the two-step transformation at relatively high temperatures can be reproduced and the appearance of lower bainite at lower transformation temperatures can be captured. In the case of the bainitic transformation in multiphase TRIP steels, the bainitic ferrite sub-units nucleate close to each other, due to the spatial restrictions imposed by the small size of parent austenite grains. In such cases, it is important to account for the nucleation of sub-units at austenite grain surfaces, as well as on other sub-units. A recent model by Matsuda et al. [12] deals with this concept. Another very recent model by Gaude-Fugarolas et al. [13] has been specially designed, in order to account for the small austenitic grain sizes encountered in multiphase TRIP steels. However, both these models assume full carbon redistribution in the austenite and do not take into account the possibility for cementite precipitation in neither bainitic ferrite nor austenite. After implementing the above described critical assessment of published models dealing with the kinetics of the bainitic transformation, it was concluded that the approach proposed in reference [1] was the most integrated in terms of the metallurgical processes that it takes into account. The major advantages of this particular model over other existing modelling approaches have been described in detail previously (task 1.1) and are not repeated here. Subsequently, the model of [1] was considered to provide the best possible modelling background, upon which the extended models of work-packages 3 and 4 could be based and developed. 36

39 2 WP 2: Material Supply The purpose of this work package has been to provide material for the subsequent investigations. The industrial partners SE-AG and Voestalpine provided industrial sampled material. SE-AG completed these by laboratory heats. 2.1 Definition of materials Table 4 gives an overall view about the materials that have been investigated within this project. Steels A, and 1 to 5 were chosen because they are in their composition within the range given in the proposal of the project. Beside steel 4 these 6 steels have been industrially produced. Existing results from steels 13 and 14 are chosen by Voestalpine for testing the implemented model. Steels 10, 11, 13 were investigated to see the influence of Chromium and Manganese. All the steels observed in this project transform very fast from homogenous austenite because of their low carbon contents ( wt.-%). Even at high cooling rates transformation from homogeneous austenite occurs already during cooling. Therefore in most cases it is not possible to get a pure isothermal transformation which is necessary to verify the Azuma model in the first stage of this project. To get rid of this problem SE-AG and RWTH defined four new experimental materials where the transformation during cooling is retarded by higher carbon contents. This was done for the two dual phase steel alloying concepts (aluminium and silicon alloyed). Additionally these melts have been used to investigate the influence of molybdenum and chromium. Therefore for the aluminium alloyed dual phase steel also different amounts of chromium and molybdenum were added. Although there have been concerns as potentially some mutual effects might occur in alloys with high chromium and high molybdenum content it was decided to use these elements in order to investigate their effect and to ensure a complete isothermal transformation. The chemical compositions of these 4 additional steels are given in Table 4 under the steels designated 6,7,8,9. The alloys with higher carbon contents are not only helpful to investigate the transformation from homogenous austenite but also to simulate the bainitic transformation from material with heterogeneous carbon distribution. Especially in the production of multiphase steels the bainitic transformation often takes place from regions enriched with carbon after intercritical annealing. As the dilatometers at Voestalpine and at RWTH are equipped to use flat samples, Voestalpine could use cold strip material also for investigations from the full austenite. 37

40 Table 4: Materials selected for laboratory investigations 2.2 Laboratory and industrial production and distribution If available, transfer bar material of these 14 steels was used to prepare the specimen in order to investigate the transformation from austenite into bainite. The produced specimen were taken outside the centre plane of the transfer to avoid segregation. The cold rolled material used by Voestalpine was sampled from industrial production, while for the steels with increased carbon content pilot plant castings were carried out at SE-AG. After cutting and reheating these pilot plant slabs were hot rolled in order to get a homogenised microstructure with reduced segregation. Table 4 also indicates which partner produced which material and to whom of the partners SE-AG, RWTH and Voestalpine the material was sent to for conducting the dilatometer tests. 38

41 3 WP 3: Bainite Design for Homogeneous Austenite 3.1 Experimental For further evaluation of the Azuma model and for doing an assessment of the controlling mechanisms in bainitic transformations more experimental data were needed. Therefore SE-AG and Voestalpine provided such data from previous investigations. Additionally the partners RWTH-Aachen, Voestalpine and SE-AG conducted laboratory investigations. These data include continuous cooling transformation data from the austenite region for 14 different carbon steels as well as for a DP steel and for a TRIP steel. RWTH-Aachen In first experiments with industrial produced DP-steel it was seen that these low carbon steels transform so fast, that transformation during cooling cannot be avoided even at high cooling rates (100 K/s). Only at extreme high cooling rates (300 K/s) it is possible to avoid this transformation but then the dilatation signal is very bad due to overshooting and oscillating. Therefore it was decided to do experiments with the four experimental high carbon melts. These have been denoted as steels 6, 7, 8 and 9 in Table 4. With these steels it was possible to get a pure isothermal transformation and dilatation signals of high quality. The samples were cut from the transfer bars of these steels. To get comparable results, all four steels were annealed with the same cycles which are shown in Table 5. heating rate [K/s] Austenitisation temperature [ C] annealing time [s] cooling rate to soaking temperature [K/s] Soaking temperature [ C] Soaking time [s] cooling rate to room temperature [K/s] approx approx approx approx approx approx approx approx approx approx approx approx approx approx approx approx / / / / Table 5: Annealing cycles for the four alloys with higher carbon content. After annealing the amounts of the different phases were determined by metallography. In the following section the dilatation curves and the results from metallography are shown for all four alloys. In some cases the dilatation signal shows some oscillation because of the high cooling rate. In many cases it was not easy to distinguish between martensite and bainite. The amounts of the different phases were determined by well-experienced technicians unknowingly the heat treatment of the samples. This was done to reduce bias. To compare the kinetics at the different soaking temperatures only those cycles were selected which lead to a 100% bainitic microstructure. From Table 6 to Table 9 it is shown that 100 % bainitic microstructures occur for all four steels at soaking temperatures between 350 C and 450 C. The results of metallography reported that bainite also forms in DP-Si_high C, Mo, Cr and DP-Si_high C at a soaking temperature of 300 C. But the comparison of the dilatation curves with those of the quenched samples shows that this must be tempered martensite. In all four steels the bainitic transformation is accelerated with increasing temperature between 350 C and 450 C. As an example for all four steels the results of DP-Al_high C are shown in Figure 10. Those for the other three steels are given in Figure 11 to Figure

42 To see the influence of chromium and molybdenum on the transformation kinetics the dilatation curves of steel 8 were compared with steel 7 and steel 9 respectively. In Figure 15 it is shown that chromium accelerates the transformation in the beginning of the transformation but retards the total reaction rate at 400 C as well as 450 C. Figure 16 shows the influence of molybdenum, which reduces the incubation time and retards the reaction rate in the same way as chromium. The earlier start of transformation can be explained by the increase of driving force for nucleation due to the ferrite forming elements Chromium and Molybdenum. The retardation of reaction rate is not clear yet, but could be explained by a solute drag like effect due to the large Molybdenum and Chromium atoms. Figure 10: Dilatation curves for transformation from homogenous austenite for DP-Al_high C at different holding temperatures. Holding temperature Microstructure 650 C Ferrite 12%, Martensite 88% 600 C Ferrite 4%, Pearlite 29%, Martensite 67% 550 C Ferrite 28%, Martensite 72% 500 C Pearlite 2%, Bainite 98% 450 C Bainite 100% 400 C Bainite 100% 350 C Bainite 100% 300 C Bainite 60%, Martensite 40% quench Martensite 100% Table 6: The phase fractions after the different annealing cycles of DP-Al_high C. 40

43 Figure 11: Dilatation curves for transformation from homogenous austenite for DP-Si_high C at different holding temperatures. Holding temperature Microstructure 650 C Martensite 100% 600 C Ferrite 1%, Martensite 99% 550 C Ferrite 4%, Martensite 96% 500 C Bainite 99%, Martensite 1% 450 C Bainite 100% 400 C Bainite 100% 350 C Bainite 100% 300 C Bainite 100% quench Martensite 100% Table 7: The phase fractions after the different annealing cycles of DP-Si_high C. 41

44 Figure 12: Dilatation curves for transformation from homogenous austenite for DP-Si_high C, Mo, Cr at different holding temperatures. Holding temperature Microstructure 650 C Ferrite 4%, Pearlite 2%, Martensite 94% 600 C Ferrite 9%, Bainite 1%, Martensite 90% 550 C Ferrite 10%, Pearlite 1%, Bainite 4%, Martensite 85% 500 C Bainite 80%, Martensite 20% 450 C Bainite 100% 400 C Bainite 100% 350 C Bainite 100% 300 C Bainite 100% quench Martensite 100% Table 8: The phase fractions after the different annealing cycles of DP-Si_high C, Mo, Cr. 42

45 Figure 13: Dilatation curves for transformation from homogenous austenite for DP-Si_high C, Cr at different holding temperatures. Holding temperature microstructure 650 C Ferrite 4%, Pearlite 96% 600 C Ferrite 1%, Pearlite 99% 550 C Ferrite 8%, Martensite 92% 500 C Bainite 98%, Martensite 2% 450 C Bainite 100% 400 C Bainite 100% 350 C Bainite 100% 300 C Bainite 70%, Martensite 30% Quench Ferrite 1%, Martensite 99% Table 9: The phase fractions after the different annealing cycles of of DP-Si_high C, Cr. 43

46 Figure 14: Isothermal bainitic transformation from homogenous austenite for DP-Al_high C at different soaking temperatures. Figure 15: Influence of chromium on the isothermal bainitic transformation from homogenous austenite at two different soaking temperatures. 44

47 Figure 16: Influence of molybdenum on the isothermal bainitic transformation from homogenous austenite at three different soaking temperatures. SE-AG SE-AG executed experimental work with transfer bar material from steel no 2, 3, 4 and 5 using dilatometer tests with a BÄHR dilatometer. The cylindrical samples (4 mm Ǿ x 9 mm) were prepared from the homogeneous region of the bar away from the centre plane. The thermal cycles that were used are similar to those of Figure 2. The only different was that the annealing treatments in the austenite range was not only 60s at 850 C as shown in that figure but also 5 min at 1150 C as well as 5 respective 30 min at 1250 C. The annealing temperatures 1150 C or 1250 C were chosen because otherwise the austenite grain structure was so fine that most transformation occurred already during cooling to soaking temperature. So in many cases quenching from annealing temperature to soaking temperature was possible without transformation during quenching, so that the bainite transformation at soaking temperature started from the complete austenite. The annealing temperature of 850 C was only used for steel 5. Figure 17: Dilatation signal for steel 5 during cooling with an intermediate isothermal holding ( C) from 5 min. austenitisation at 850 C (left) respective 1250 C (right). Figure 17 to Figure 21 show examples for the dilatation during cooling from austenitisation temperatures. The vertical parts of the dilatation signals indicate the transformation at the constant soaking temperatures. It can be seen for example, that in the right side of Figure 17 the isothermal transformation starts from the complete austenite for the cycles with 400 C, 450 C and 500 C soaking temperature, while for the other cycles transformation starts already before reaching the soaking temperature. 45

48 Figure 18: Kinetics of isothermal (300 to 500 C) transformation of steel 5 during 1800s after quenching from 850 C (left) respective 1250 C (right). Figure 18 to Figure 21 also give the kinetics of the transformation during the isothermal soaking. The registration of the curves started some K before reaching the exact soaking temperature. Therefore some of the curves show a decline at the beginning. Special test were made to see the starting austenite grain size at the end of the annealing period: Samples were quenched at the end of annealing time to temperatures where just transformation to ferrite started and kept some time at that temperature. During this time at that ferrite starting temperature some ferrite was formed along the austenite grain boundaries and so marking the shape of the austenite grains. After quenching the samples to room temperature by optical metallography easily the size of the former austenite grains could be detected. Examples can be seen within the diagrams. Clearly the influence of the starting austenite grain size could be seen. The smaller the grain size the faster the bainite transformation kinetics. Figure 22 gives an example of studies on steel 2 where the austenitisation conditions was changed systematically in order to achieve distinct initial austenite grain sizes. The microstructures of all samples after quenching from soaking temperature were analysed by optical microscopy at RWTH. The analysed results concerning martensite, bainite and retained austenite agreed quite well with the information from the dilatation signal. Differences concerning the amount of bainite content were in the range of few %. So the dilatation signal can be regarded to give reliable information about transformed fractions see also WP 3.2. Figure 19: Dilatation signal for steel 2 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right). 46

49 . Figure 20: Dilatation signal for steel 3 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right). Figure 21: Dilatation signal for steel 4 during cooling from 5 min austenitisation at 1250 C (left) and isothermal ( C) transformation during 1800 s after quenching from 5 min at 1250 C (right). 47

50 100, Steel 2, DP-Si Comparison: AT=1250 C, 5 min or 1150 C, 5min Fraction of transformation in % 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, _1250 C_500 C _1250 C_450 C_b _1250 C_400 C _1150 C_5min_500 C _1150 C_5min_450 C _1150 C_5min_400 C 0,1 1, 10, 100, 1000, 10000, Time in s 100, Steel 2 DP-Si: Comparison: AT=1250 C, 5min or 30min, F ra ctio n o f tra n s form a tio n in % 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, _1250 C_500 C _1250 C_450 C_b _1250 C_400 C _1250 C_350 C _1250 C_30min_500 C _1250 C_30min_450 C _1250 C_30min_400 C _1250 C_30min_350 C 0,1 1, 10, 100, 1000, 10000, Time in s Figure 22: Influence of the austenitisation conditions during the isothermal transformation ( C) of steel 2. Above: 5min at 1250 C (solid) respective 5min at 1150 C (dashed) austenitisation, Below: 1250 C austenitisation for 5 min (solid) and 30 min (dashed). 48

51 Voestalpine voestalpine carried out laboratory experiments on steels 10, 11, 12 and 2 to arrange similar investigations as done with steel 13 and 14 see WP The same thermal cycles were used for steel 10, 11 and 12 as shown in Figure 2. The chemical composition of steel 2 makes it necessary to elevate the annealing temperature up to 900 C to reach full austenitization. The calculation of the transformed phase amounts was realized as described in Figure 3. Figure 23 and Figure 24 demonstrate the occurring phase transformations subsequent to the annealing treatment. Figure 23: Overview of the transformed phase amounts of steel 10 (left) and steel 11 (right) Figure 24: Overview of the transformed phase amounts of steel 12 (left) and steel 2 (right) Figure 25 to Figure 28 represent some measured kinetic curves of occurring transformations while soaking at different isothermal soaking temperatures (300 C, 450 C, 550 C). 49

52 Figure 25: Transformation curves calculated from measured data during isothermal soaking of steel 10 at different soaking temperatures (300 C, 450 C, 550 C) Figure 26: Transformation curves calculated from measured data during isothermal soaking of steel 11 at different soaking temperatures (300 C, 450 C, 550 C) Figure 27: Transformation curves calculated from measured data during isothermal soaking of steel 12 at different soaking temperatures (300 C, 450 C, 550 C) 50

53 Figure 28: Transformation curves calculated from measured data during isothermal soaking of steel 2 at different soaking temperatures (300 C, 450 C, 550 C) Bainitic Transformation Kinetics from Deformed Austenite The bainitic transformation is not only important for cold rolled products, which are in the focus of this project, but also for hot rolled products like hot rolled DP and TRIP steels. To see if the Azuma model could be extended to these processing routes, deformation experiments were done in dilatometer with the DP, Al high C as well as a DPW600 (an industrial hot rolled DP-steel). The thermo-mechanical cycles used for both steels are shown in Figure 29a. Round specimens were heated to 1250 C for 5 min. to get a homogenous austenite structure. Afterwards the sample was cooled to a temperature were no fast recrystallization occurs during deformation (830 C). At this temperature the samples were deformed with a strain rate of 1/s and deformation degrees of 0, 0.3, and 0.6. At the end the samples were cooled to isothermal holding temperature for transformation. First experiments were done with the steel DP, Al high C to see the influence of different degrees of deformation in austenite on the pure isothermal bainitc transformation. As can be seen in Figure 29 b-d the influence of deformation becomes more important at higher isothermal transformation temperatures. While at 400 C there is no effect and at 450 C there is only little effect on the transformation, at 500 C the transformation is heavily accelerated by prior deformation. An explanation could be that at higher temperatures the diffusion plays a larger role for the transformation. Due to the increasing dislocation density with higher deformation, the transformation is then accelerated. 51

54 a.) b.) c.) Figure 29: d.) Experimental time-temperature cycle (a) and the corresponding isothermal dilatation curves at 400 C (b), 450 C (c) and 500 C (d). For the industrial DPW 600 with a carbon content of wt.-% the results become much more complicated, Figure 30. Here the deformation of austenite does not only influence the isothermal bainitic transformation. It can be seen that both the transformation before reaching the isothermal transformation at 400 C and the fraction of the isothermal transformation are also increased with increasing deformation. The results from LOM (Figure 31) reported that the microstructure composed of the mixture of bainite and martensite, with little ferrite at φ of 0,6. The morphology of the bainite was shifted to be globular bainite by deformation. 52

55 Figure 30: Transformation kinetics at 400 C of DPW 600 after different degrees of deformation. Figure 31: The microstructure in the samples of DPW600 after annealing with the cycle in Figure 2 with applying an isothermal holding temperature of 400 C. These few experiments show already, that the deformation can t be introduced to the Azuma model that easily. The description of the initial condition of austenite before bainite transformation becomes very difficult. The effect of deformation on effective grain size and therefore on the nucleation density could maybe be described by an S V function, were also deformation bands should be taken into account. Additionally the state of recrystallization must be described, as this influences the strength of the austenite and therefore should also have an impact on the size of bainite sub units. Beside that the description of transformations prior to the bainite transformation becomes also more complicated and can t be treated with relatively simple DICTRA calculations anymore. This is again important to know, as the ferrite formation leads to a carbon enrichment in austenite. Further research is needed to understand the effect of deformation on the bainite kinetics and altogether the development of these models would be enough work for another RFCS project. 3.2 Microstructural Characterization The total transformation kinetics calculated by using the Azuma-model can be fitted by dilatation data. But additionally the model delivers several microstructural features like phase fractions, carbide size in austenite, carbide size in ferrite and so on. To prove if the model predicts these features correctly SE- AG and RWTH performed additional experiments for microstructural characterization. The annealing cycles, discussed below, were done at RWTH and the analysis was done at SE-AG. 53

56 Microstructure development during isothermal transformation: To see how the microstructure develops with time during the isothermal holding RWTH made stepwise quenching experiments. This means that the samples were hold at 400 C for different intervals and quenched after it. The annealing cycle is shown in Figure 32. For these experiments the steel DP-Al high C was used to assure 100% isothermal transformation C; 300s 200 K/s Temperature 400 C; t = 10s, 20s, 30s, 40s, 100s 200 K/s Figure 32: Time Annealing cycle for DP-Al high C for stepwise quenching. After these cycles the samples have a mixed microstrucure of bainite, martensite und possibly retained austenite. The first task is to determine the phase fractions. This has been carried out by EBSD at SE- AG because it is not possible by light optical microscopy. To see if the Azuma-Modell predicts the carbon redistribution during the bainitic transformation properly the carbon content in the retained austenite rather in the martensite (prior austenite) has been measured. This can be done by EBSD from the difference in the lattice parameters of austenite and martensite. The third task here is to observe the evolution of carbide distribution during isothermal holding. Therefore different investigation techniques were conducted at SE-AG. Beside the dilatometric experiments and the calculation of interfacial energies RWTH carried out several metallographic analyses for several experiments performed by SE-AG. This includes: Determination of grain size and phase fractions for TRIP-Al Determination of grain size and phase fractions for TRIP-Si Determination of grain size and phase fractions for DP-Al Determination of grain size and phase fractions for Voest_CP The metallographic characterization for steels 10, 12 and 13 resulting from isothermal holding cycles done at Voestalpine was carried by optical microscopy at CEIT. For steel 10, the phase fractions obtained from the metallographic analysis are presented in Table 10. For 300ºC and 350ºC holding temperatures, the samples were predominantly martensitic. Since the samples were fully austenized, these transformations occurred during cooling from the annealing to the holding temperature. The average austenite grain size for these samples was 9µm. This explains the fast transformation from austenite to ferrite and bainite during the cooling period, done at 50K/s. 54

57 For holding temperatures above 400ºC the microstructure consisted predominantly in a mixture of ferrite and bainite. Several localized islands of martensite were observed. This places the M S temperature somewhere between 350ºC and 400ºC. The maximum volume fraction of bainite was observed at 400ºC. From the increase in the amount of ferrite from the sample kept at 500ºC with respect to the other samples it was concluded that at this temperature the bainitic transformation and the ferritic transformation coexist. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 10: Trace Trace Phase fractions for steel 10 annealed at 850ºC for different holding temperatures Table 11 shows the obtained phase fractions for steel 12. The average austenite grain size observed was 9µm. As in steel 10, this fine grain size drives the formation of pro-eutectoid ferrite during the cooling period. For this steel, the amount of ferrite formed during cooling was less with respect to steel 10. For holding temperatures below 400ºC the samples analyzed were mostly martensitic. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 11: Phase fractions for steel 12 annealed at 850ºC for different holding temperatures. For steel 13, the transformation of austenite to pro-eutectoid ferrite occurred much faster than for steel 10 and 12. The obtained phase distributions for each holding temperature analyzed are presented in Table 12. As for the previous steels, the samples that were held at temperatures lower than 400ºC were mostly martensitic with ferrite grains forming at the austenite grain boundaries. These results set the MS temperature for these three steels between 350ºC and 400ºC. The austenite grain size for this steel was slightly finer with respect to steel 10 and 12, with an average grain size distribution of 8µm. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 12: Trace Phase fractions for steel 13 annealed at 850ºC for different holding temperatures. To determine the influence of the cooling rate in the transformation, characterization for steels 10, 12 and 13 resulting from continuous cooling conditions was carried out. Results for steel 10 are shown in Table 13. As it was also observed for the isothermal case, transformations occur during cooling, even at fast cooling rates. 55

58 Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 13: Phase fractions for steel 10 annealed at 850ºC for different holding temperatures. Table 14 presents the phase fraction obtained for steel 12 at different cooling rates. At a cooling rate of 80K/s, only a small fraction of ferrite was observed. The samples from this steel composition showed the least amount of ferrite with respect to the other two steels. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 14: Phase fractions for steel 12 annealed at 850ºC for different cooling rates. As seen in Table 15, samples from steel 13 transformed mostly to ferrite. This is due to the fine grain size and reduced carbon content. Even at 60K/s, a third of the sample transformed to ferrite. For cooling rates below 20K/s, the fraction for each component phase showed little variation with respect to other cooling rates. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 15: Phase fractions for steel 13 annealed at 850ºC for different cooling rates. These metallographic results show that transformation data obtained from dilatometry alone are often insufficient. More often than not differences will be observed between the metallographic and the dilatometric results. For instance for steel 12 the evaluation of the transformation determined by dilatometric means in Figure 24 show in some parts significant differences to the metallographic results 56

59 in Table 11. There are several explanations to these different results obtained by the two independent methods. First of all we have to consider that the dilatation signal is measured in respect over the whole specimen length including all different sorts of gradients that might occur, whereas a metallographic investigation focuses on one or several very small and hopefully representative areas. Then one has to keep in mind that the residual austenite in these graphs results from the gap between the cooling curve and the polynomial fit to the ferrite dilatation. As the example in Figure 3 shows, this fit is not always perfect. This has to be expected, as the final dilatation signal is connected to a mixed microstructure which has a different thermal expansion coefficient than ferrite. Additionally existing residual austenite might transform after the end of the experiment at some ambient temperature during cooling to room temperature or during preparation of the metallographic specimen. Finally it has to be considered, that the metallographic characterisation quantifies the phases which are present in the final microstructure whereas the different coloured areas in the graphs do not denote specific phases, but different areas of transformation in respect to the soaking treatment. For instance, for low soaking temperatures the blue coloured area in Figure 24 includes ferrite, bainite and to a large content martensite. Differentiation between bainite and martensite: The question in these experiments was to see whether it is possible to distinguish between martensite and bainite clearly in samples where both microstructures occur. The DP-Al high C steel was used for this experiment. The thermal cycles are shown in Figure 33. Due to dilatation data the sample held at 350 C should have a fully bainitic microstructure while the sample held at 300 C should have a mixed microstructure containing bainite and martensite. To distinguish between the two phases EBSD measurements were performed at SE-AG. The idea is to separate martensite from bainite by the image quality of the EBSD pattern and by misorientations that can be measured within the grains. Figure 34 shows EBSD results for a sample quenched from 350 C. However it has to be stated that for the investigated specimen it is difficult if not to say impossible to separate bainite from martensite solely on the base of EBSD measurements. Thus another approach has been developed within the project, which is described in WP4. Figure 33: Annealing cycle for DP-Al high C. 57

60 orientation difference between nighbouring points Figure 34: EBSD maps for a DP-Al high C sample quenched from 350 C. 3.3 Thermodynamic + DICTRA Calculations In order to apply and exploit the selected kinetic model for the bainitic transformation in the steels of interest, a series of cumbersome thermodynamic calculations have to be performed. For example, calculation of the thermodynamic driving-forces for the nucleation of the product phases (i.e. bainitic ferrite and cementite) in paraequilibrium with the respective parent phases, as functions of transformation temperature and C-content of parent austenite, is necessary, since these functions are required input to the kinetic model. Driving-forces under paraequilibrium are of special importance in the kinetic model and the method to calculate them has to be extended to all the major alloying elements in the steels under consideration. It is also necessary to calculate paraequilibrium concentrations between the involved phases, as well as the molar volumes of the product phases. Since there is no readily available computational thermodynamics software to implement the aforementioned calculations automatically, a methodology had to be developed towards this direction. This work was performed by UTH in the framework of the present task, as well as within task 5.4. As the bainitic transformation in steels evolves, three simultaneous phase-transformations take place in the system: γ γ + α Β (10) γ γ + θ γ (11) α Β α Β + θ α (12) In transformation (10), parent austenite (γ) of nominal C-content transforms to bainitic ferrite (α Β ). The untransformed fraction of austenite (γ ) is substantially enriched in C compared to parent austenite, due to the carbon rejected by bainitic ferrite. In transformation (11), cementite (θ γ ) precipitates from C-rich austenite (γ ). Precipitation takes place within the austenitic grains, leading to the morphology known as upper bainite. The precipitation of cementite reduces drastically the C-content of austenite, so that the remaining austenite (γ ) contains substantially lower amounts of carbon. In transformation (12), cementite (θ α ) precipitates in bainitic ferrite, leading to the morphology known as lower bainite. As in the case of austenite, cementite draws carbon from bainitic ferrite, leaving the later with even lower C-content (α Β). During the bainitic transformation, the aforementioned phase-transformations take place under paraequilibrium conditions. Calculation of paraequilibrium driving-forces for the nucleation of the product phases is not a straightforward task and cannot be performed directly in Thermo-Calc software. In order to perform these calculations a modification was necessary, by intervening in the Gibbs Energy System (GES) module of Thermo-Calc software. 58

61 Haidemenopoulos et al. [40] and Olson et al. [41,42] established a technique, by which paraequilibrium thermodynamic calculations can be performed in multicomponent steels, containing various substitutional alloying elements. The fundamental idea behind this technique is that in a multicomponent steel Fe-C-M 1 -M 2 - -M n, where M i represent the substitutional alloying elements of the steel, all substitutional elements (including Fe) can be replaced by a fictitious element, Z, so that the alloy reduces to a pseudo-binary Z-C system. The thermodynamic conditions for two multi-component solid phases, α 1 and α 2, to exist in paraequilibrium are the following: µ = µ a1 a2 C C (13) y = y a1 a2 j j (14) In order for these two phases to exist in paraequilibrium, the chemical potential of C (μ C ) has to be the same in the two phases, and the site-fractions of each substitutional element (y j ) have to be the same in the two phases. The site-fraction of a substitutional element j, y j, is defined by: y j x j = 1 x C In Eq. (15) x j and x C are the usual mole-fractions of substitutional element j and of carbon, respectively. The chemical potential of the fictitious element Z, which replaces all substitutional elements of the steel, is defined by: a1 a1 µ Z = y jµ j (16) a2 a2 µ Z = y jµ j (17) (15) Now, paraequilibrium conditions for the actual steel reduce to the corresponding orthoequilibrium condition for the pseudo-binary Z-C system: µ = µ a1 a2 C C µ = µ a1 a2 Z Z The molar Gibbs free energy of a phase (α) in the pseudo-binary Z-C system is given by the following expression: (18) (19) (20) In Eq. (20), y j, y C and y Va represent the site-fractions of substitutional elements, carbon and vacancies, respectively, o, G α jc : and o, G α jva : atoms and vacancies, respectively, and are the lattice-stability parameters of substitutional element j with carbon xs, G α m is the term representing the excess Gibbs energy of mixing mag, G α m is the magnetic ordering energy contribution term. In the CALPHAD method, the excess 59

62 Gibbs energy of mixing term ( G α ) is approximated by a Redlich-Kister-Muggianu polynomial expansion [43]. xs, m The expanded form of the molar Gibbs free energy of phase (α), after introducing the Redlich-Kisterxs, Muggianu polynomial approximation for G α m, has the following form: (21) In Eq. (21) L s represent the interaction parameters of the corresponding substitutional elements with carbon atoms and vacancies. The various lattice stabilities and interaction parameters are functions of temperature and pressure, which are contained in special thermodynamic databases included in Thermo- Calc software. The energy contributed to the system by magnetic ordering effects ( G following expression: mag, α α T Gm = RTln( β + 1) f α TC mag, m α ) is determined by the In Eq. (22), T α C is the critical Curie temperature and β α the average Bohr magneton of the phase. Both these quantities are also approximated by a Redlich-Kister-Muggianu polynomial expansion. In a similar manner, the molar Gibbs free energy of a phase (α) in the fictitious binary Z-C system is given by: (22) (23) Cross-examining equations (20) and (23), it is evident that there is a one-to-one correspondence between parameters in the molar Gibbs free energy descriptions of the phases of the actual steel and of the binary Z-C system. Thus, all parameters of the Z-C system (i.e. lattice stabilities, interaction parameters, Bohr magnetons and critical Curie temperatures) can be determined by the corresponding parameters of the actual steel. In order to determine the thermodynamic description of every phase in 60

63 the Z-C system, the lattice stabilities, interaction parameters, critical Curie temperatures and average Bohr magnetons of each phase have to be determined, as functions of the corresponding parameters of the phases of the actual multicomponent system. All the conversion equations are introduced into Thermo-Calc, in order to thermodynamically describe the Z-C system in the software. This is performed through intervention to the Gibbs Energy System (GES) module of Thermo-Calc. After the description has been appropriately introduced there, then the driving-force for the nucleation of a phase in the Z-C system can be calculated under orthoequilibrium conditions. These calculated driving-forces for nucleation represent the corresponding driving-forces for the nucleation of the same phase in the actual multicomponent steel, but for paraequilibrium conditions. By employing the methodology described above, the driving-forces for nucleation of the involved product phases under paraequilibrium conditions have been calculated, as functions of temperature and C-content of the parent phases, for many of the steel grades examined in the project. These results are of great value, since such research work is very scarce in literature. Table 16 summarizes the aforementioned calculated functions for each steel grade. 61

64 Steel TRIP- Si CP VA DP 1.8Mn -0.8Cr VA DP 2.2Mn -0.8Cr Function of driving-force for nucleation under paraequilibrium γ α γ 2 γ γ 2 γ B G ( XC) X C ( XC) = X T + n C ( C) X X T C γ 2 3 γ 2 2 ( ) ( ) γ γ γ C C C α α C ( C) T 2 2 ( ) ( ) γ θ G = X X ln X T n α θ B G = X ln X n γ αb G = T + n γ γ γ γ X X X 5.94 X 11.9 C C C C ( ) ( ) X X X T C C C γ θ γ γ G = X ln C ( XC) T n α θ α α B G = X ln C ( XC) T n 3 2 γ γ 3 γ 3 2 ( C) ( ) ( ) γ α γ 2 γ γ 2 γ B G = X X X X T + n C C C C 2 γ γ X X T C γ θ γ γ G = X ln(x ) T n C C α θ α α G = X ln(x ) T n C C ( ) ( ) γ α γ 2 γ γ 2 γ B G = X X X X T + n C C C C ( ) T ( ) γ γ 2 5 γ 6 γ X X X 3 10 X 5 10 T C C C C γ θ G = + n n α ln C γ γ X ln(x ) T C C α θ G = + α X (X ) T C TRIP- Al DP-Si Table 16: Calculated thermodynamic driving-forces for the nucleation of product phases in paraequilibrium with the corresponding parent phase for selected steel grades. 62

65 In Table 16, G γ θ n B G γ α n stands for the nucleation of bainitic ferrite in paraequilibrium with austenite, for the nucleation of cementite in paraequilibrium with austenite and of cementite in paraequilibrium with bainitic ferrite (all in J/mol). X γ C G α θ B n for the nucleation is the average C-content in α X C austenite, the average C-content in bainitic ferrite (both expressed as mole-fractions) and T the absolute transformation temperature (in degrees K). Examples of the results of the aforementioned thermodynamic calculations are shown in Figure 35, which depicts calculated driving-forces for nucleation of bainitic ferrite in paraequilibrium with austenite for steel CP, as a function of transformation temperature and average C-content in austenite, and in Figure 36, which depicts the corresponding curves for the nucleation of cementite in paraequilibrium with austenite. Figure 35: Calculated driving-forces for the nucleation of bainitic ferrite in paraequilibrium with austenite for steel CP. Figure 36: Calculated driving-forces for the nucleation of cementite in paraequilibrium with austenite for steel CP. The aforementioned methodology was also applied in order to calculate the C-content of phases in paraequilibrium between them, which is also necessary input to the kinetic model. A typical result of 63

66 such calculations is depicted in Figure 37, which shows a part of the calculated paraequilibrium phasediagram for ferrite and austenite for steels CP and TRIP-Si. Results of this kind are also of great value, since they are very scarce in literature. Figure 37: Calculated ferrite/austenite paraequilibrium phase-boundaries for steels CP and TRIP-Si. At SE-AG a somewhat different approach has been chosen. For model development the Matlab, a highlevel technical computing language, has been choosen. ThermoCalc provides an according low-level interface API to Matlab. This interface allows setting up thermodynamic systems and to perform basic computations which are usually limited to orthoequilibrium. At SE-AG an according high-level interface has been written on top of this low-level API which simplifies standard tasks and eases more demanding thermodynamic computations such as under paraequilibrium conditions. The benefit of this approach becomes very obvious in a model development as in the current project. Instead of computing the different driving forces and concentrations in ThermoCalc which then have to be introduced into the model, it is possible to directly access these data from within the model. This is possible in dependency of any given temperature and/or chemical composition, as long as the limitations of the according underlying thermodynamic database are obeyed. Despite the distinct approaches comparisons between the resulting driving forces have shown that the outcome of both methods differs only marginally. These differences might well be attributed to different TCFE-database versions applied by UTH and SE-AG. 3.4 Model Development Finite Differences Model The kinetic model described in detail within has been implemented by UTH in a computable form and validated against the data given in the original paper [1]. A similar implementation [44] at SE-AG of this model has been reworked and adopted based on the improvements suggested by UTH within this project. The most important differences of this MATLABimplementation can be summarized in four points: a finite differences (FD) solver is used which applies an adaptive selection of time step width in dependence of the current overall transformation kinetics, the paraequilibrium (PE) driving forces and PE carbon contents are retrieved from ThermoCalc (TC) via the Matlab-TC interface in dependence of temperature and current chemistry composition, which changes due to the carbon redistribution. 64

67 instead of using constant values or predefined equations the interfacial energies are computed by the generalized Nearest-Neighbor Broken-Bond (NNBB) model proposed by Sonderegger et al. [3,45] using ThermoCalc to derive the necessary thermodynamic data. the influence of Silicon and Aluminium to PE cementite precipitation, which was not considered in former TC databases was implemented. However by the recent change to the latest version TCFE6 the necessity of these own implementations has been overcome as the Si and Al interaction on cementite has been included in the thermodynamic database [46]. The implementation of the last three points has been kept flexible in such way that those driving forces, carbon contents and interfacial energies can be used, which have been proposed by either the original paper [1] or UTH by passing according parameters to the model. The reason for this has been the ability to obtain comparable results with either the work of Azuma et al. or the UTH model for further validation and comparison. As can be taken from the flow chart of the SE-AG programme code in Figure 38 the thermodynamic part of the code is calculated in a side branch of the code. Especially for the relevant steel composition the driving forces for the nucleation of cementite or ferrite under paraequilibrium are precomputed as a function of the carbon content and temperature. These computed lookup tables are stored as a close meshed net of separate values. Figure 39 shows such an exemplaric net for a steel with 0.15% C, 2.2% Mn, 0.8 % Cr and 0.1% Si. The finite differences solver with the modified Azuma model retrieves the thermodynamic data whenever needed from these tables by interpolating between neighbouring stored values. Readand processparameters ExistingTC-data filefor steel? Yes ReadTC-datafile No ComputenewTC-lookuptables WriteTC-datafile Run FD-solveron Azumamodel PrecomputedtablesforTC-data Plot transformationcurves Figure 38: Flow chart of the SE-AG implementation of the bainite model. 65

68 TC Thessaly F n fcc-bcc [J/mol] Temp [K] Thessaly: from function given by UTH TC: computed with TKSE Matlab implementation using TCFE C [wt-%] Figure 39: Calculated driving forces for ferrite nucleation from austenite for Steel 12 (VA-DP 2.2Mn 0.8Cr) Interfacial energies The Azuma model needs several parameters as input to compute the kinetics of the bainitic transformation. Some of them are already available through thermodynamic calculations such as the driving forces (ΔG) for the formation of ferrite, cementite in austenite and cementite in ferrite. The others like the autocatalytic nucleation factor β are generally treated as fix parameters. The remaining parameters, namely the interfacial energies (σ α/γ, σ α/cem, σ γ/cem ) and the nucleation densities (N α/γ, N α/cem, N γ/cem ), are treated in the original paper as fitting parameters to adjust the model on the experimental dilation curves. In other words, these parameters do not follow any physical rules. But a physical based model should have as few fitting parameters as possible. Although there are some theoretical nucleation models, the nucleation density is not easy to predict properly at the moment. After first trials in the within the first half of 2009, RWTH went further on to calculate interfacial energies by using the commercial software MatCalc. This software is able to describe the formation and growth of precipitates within a given matrix as a function of time and temperature. In this software is integrated also a model for calculating interfacial energies. The generalized nearest-neighbor brokenbond model by B. Sonderegger and E. Kozeschnik employed in the program is an extension of the classical nearest neighbor broken-bond model [3] and gives good estimation for the interfacial energies. As first trials, the interfacial energies for the TRIP-Al and TRIP-Si steels were calculated as a function of carbon content and temperature over a wide range. Compared with the values for interfacial energies of the DP-steel (determined by UTH within the second half of 2008) the results are in a realistic range. While in the first half of 2009 reliable values were only available for the interfacial energy between ferrite and austenite (σ α/γ ) now also values for the interfacial energy of cementite in ferrite (σ α/cem ) and cementite in austenite (σ γ/cem ) could be calculated. The interfacial energies were calculated in the temperature range between 350 C and 600 C as this is the region of major interest concerning the bainitic transformation. The carbon enrichment of the retained austenite during the transformation was taken into account by calculating the interfacial energy as a function of carbon content ranging from the initial carbon content of the respective steel until 1.5 wt.-% carbon. The interfacial energies were calculated for all steels used within this project. The values were provided to the project partners. In Figure 40, Figure 41 and Figure 42 the interfacial energies are shown exemplary for the steel DP-Si. The trend for the three different interfacial energies can be observed in all steels. The interfacial energy between ferrite and austenite (σ α/γ ) is strongly dependent on the temperature. As can be seen from 66

69 Figure 40, the values decrease from more than J/m² down to J/m² with increasing temperature. Although the absolute values are relative small this means a change of more than 25 %. It is obvious, that this effect strongly influences the bainite kinetics. In contrast the carbon content seems to play a minor role for the interfacial energy between ferrite and austenite. Here an increase of carbon content from 0.1 wt.-% to 1.5 wt.-% results in decrease of the interfacial energy of maximal 2.9 %. Figure 40: Calculated interfacial energy σ α/γ as a function of carbon content and temperature for DP-Si. Figure 41: Calculated interfacial energy σ γ/cem as a function of carbon content and temperature for DP-Si. Looking at the interfacial energy between austenite and cementite, the situation is different, Figure 41. The interfacial energy again decreases with increasing temperature, but the effect is not as strong as for 67

70 the interfacial energy σ α/γ. Within the temperature range from 350 C to 600 C the observed decrease of interfacial energy is approx. 7.5 %. While for σ α/γ an increase of carbon results in a very small decrease of interfacial energy, for σ γ/cem it is the opposite. With the same increase of carbon content here we have an increase of approx. 9% in the interfacial energy. The effect varies a little bit at the different temperatures. At 350 C it is only an increase of 8.7 % while at 600 C it is an increase of 9.3%. Between ferrite and cementite the interfacial energy σ α/cem is three times larger than for σ α/γ and σ γ/cem, Figure 42. Here the energy increases with approx. 4% with increasing temperature. The effect of carbon content lies within the same range. An increase of carbon content from 0.1 wt.-% to 1.5 wt.-% results in an increase of interfacial energy of approx. 4.9 %. Figure 42: Calculated interfacial energy σ α/cem as a function of carbon content and temperature for DP-Si. As can be seen from this example, the interfacial energies are really sensitive with respect to the temperature and the carbon content. In the following the effect of other alloying elements like, Chromium, Manganese, Molybdenum, Aluminium and Silicon was studied. The effect of Chromium was studied with the chemical composition of the melts provided by Voestalpine. As can be seen from the alloy name already, the Chromium content is varied from 0.3 wt.- % (VA-DP+2.2Mn+0.3Cr) over 0.5 wt.-% (VA-DP+2.2Mn+0.5Cr) to 0.8 wt.-% (VA- DP+2.2Mn+0.8Cr). For VA-DP+2.2Mn+0.3Cr and VA-DP+2.2Mn+0.5Cr the basic composition stayed the same, for VA-DP+2.2Mn+0.8Cr the manganese and molybdenum contents are a little bit higher and the silicon content is a little bit lower. 68

71 a.) b.) c.) d.) e.) f.) g.) h.) i.) Figure 43: Influence of Chromium on the calculated interfacial energies σ α/γ (a-c), σ γ/cem (d-f) and σ α/cem (g-i) as a function of carbon content and temperature for VA-DP+2.2Mn+0.3Cr, VA-DP+2.2Mn+0.5Cr and VA- DP+2.2Mn+0.8Cr. As can be seen in Figure 43 the influence of chromium is different for the three interfacial energies. With increasing chromium content σ α/γ first decreases 4-10 %. But when the chromium content increases further to 0.8 wt.-% the same values are reached as for 0.3 wt.-% chromium. This effect could come from the slightly different chemical composition of VA-DP+2.2Mn+0.8Cr. But as can be seen from the following diagrams, the effect shouldn t be so large. The effect of the interfacial energy 69

72 between cementite and austenite is much smaller. For σ γ/cem a continuous decrease can be observed with increasing chromium content. With a maximal increase of 2% between 0.3 and 0.8 wt.-% chromium this effect is not relevant. Also the last of the three values σ α/cem decreases continuous with increasing chromium content. The change of interfacial energy from 0.3 wt.-% to 0.8 wt.-% chromium is with maximal 3 % also little. The effect of manganese was studied also with the steels from Voestalpine. In the steels VA- DP+1,8Mn+0,8Cr, VA-DP+2,0Mn+0,8Cr and VA-DP+2,2Mn+0,8Cr the manganese content varied between 1.8 wt.-%, 2.0 wt.-% and 2.2 wt,-% respectively. The effect of manganese is much smaller than that of chromium. The results are shown in figure 5. The change for σ α/γ reaches barely plus 0.4 %. For the other two interfacial energies the effect looks similar. For σ γ/cem with increasing manganese content a maximal decrease of 1.1 % and for σ α/cem of 0.9 %is observed. The effect of molybdenum can be seen in Figure 45 exemplary. From DP-Si-Cr+highC-noMo to DP- Si-Cr+highC the molybdenum content increases from 0 wt.-%. to 0.22 wt.-%. The effect of molybdenum is also relative small. With an increase of maximal 0.2 % σ α/γ it is nearly constant. Similar results can be seen for σ γ/cem and σ α/cem. These values both decrease by 0.8 %. Although the in TRIP-Si and TRIP-Al not only the silicon and aluminum contents change, the calculated results are shown here to get a feeling for the difference in the interfacial energies of silicon and aluminum alloyed TRIP-steels. The interfacial energies are shown in Figure 46. The interfacial energies between ferrite and austenite differ in the range of - 3 % to + 8% for the two TRIP-steels. The largest difference is observed for σ γ/cem with 30 %. For σ α/cem the alloying effect is smaller again and a difference of only 2 3 % occurs. 70

73 a.) b.) c.) d.) e.) f.) g.) h.) i.) Figure 44: Influence of Manganese on the calculated interfacial energies σ α/γ (a-c), σ γ/cem (d-f) and σ α/cem (g-i) as a function of carbon content and temperature for VA-DP+1,8Mn+0,8Cr, VA-DP+2,0Mn+0,8Cr and VA- DP+2,2Mn+0,8Cr. 71

74 a.) b.) c.) d.) e.) f.) Figure 45: Influence of Molybdenum on the calculated interfacial energies σ α/γ (a-b), σ γ/cem (c-d) and σ α/cem (e-f) as a function of carbon content and temperature for DP-Si-Cr+highC-noMo and DP-Si-Cr+highC. 72

75 a.) b.) c.) d.) e.) f.) Figure 46: Calculated interfacial energies σ α/γ (a-b), σ γ/cem (c-d) and σ α/cem (e-f) as a function of carbon content and temperature for TRIP-Si and TRIP-Al. 73

76 3.4.3 Interfacial Energies Model Implementation As described above the interfacial energy has a tremendous influence on nucleation processes. In the first implementations of the bainite transformation model a constant interfacial energy with a value of 0.06 J/m² has been used as indicated in the paper of [1]. Subsequent analysis showed that the interfacial energy should be temperature and possibly carbon content dependent. The RWTH presented computations performed with MatCalc, developed by Kozeschnik et al. The application of the software [5,47 50] and the underlying model [3,4] are described in a number of papers mostly dealing with nucleation processes of carbo-nitrides respective aluminium nitrides. Jung et al. [51] have compared the underlying nearest neighbour broken bonds model (NNBB) with ab inito computations. Though in direct comparison they observed some small differences between the γ NNBB and γ ab initio values, they consider the NNBB model as a reasonable approach to estimate the interfacial energies. The RWTH Aachen has computed interfacial energy values γ for the fcc-bcc, cem-fcc and cem-bcc interfaces. The results for the fcc-bcc interface are similar to those values reported in [1]. This is also true for an implementation programmed by SE-AG using Matlab with the according ThermoCalc interface. Like the MatCalc solution the implemented approach is based on the model described by Kozeschnik and Sonderegger [2 4,45] : where n s is the number of atoms per unit interface area, z s the number of bonds per interface atom across the interface area and z L is the coordination number of one atom. In [3] the structural factor z - S,eff/z L,eff has been derived for up to 100 nearest neighbour shells in fcc and bcc systems. In this study the structural factor of for bcc and for fcc systems has been determined with an anisotropy of 18% depending on the interface orientation. The enthalpy of solution is computed from thermodynamic databases, in the case of the SE-AG implementation ThermoCalc via the MatLab-TC interface API: While this approach worked very well for the austenite-ferrite interface, the interfacial energies computed with MatCalc for the cem-fcc interface which are in the range of 0.05 to 0.1 J/m² are somewhat low in respect to other literature sources which are in the range of J/m² [50], 0.15 J/m² [4] to 0.3 J/m² [1]. Further such low interfacial energies result in an excessive carbide formation out of the austenite phase during the bainite transformation. On the other hand the results prescribe the expected dependency in respect to temperature and austenite carbon content. With the Matlab implementation of the model using the TCFE database the computed cem-fcc interfacial energies are in the lower range of the data cited in literature. If these values are applied, an excessive cementite precipitation does not occur. The interfacial energies of about 0.21 J/m² for the cem-bcc interface are also somewhat lower than those reported by Chiou et al. [52] who reported a value of about 0.24 J/m² computed by ab initio using VASP (Vienna ab initio Simulation Package). However these lower values did not lead to numeric stability problems with the FD solver or excessive cementite precipitation like in the case of the cementite-austenite interface. Thus the values computed by RWTH-Aachen have successfully been applied for the computations, which results in noticeable but still small cementite precipitation from the bainitic ferrite. The Matlab implementation which uses the TCFE database results in interfacial energies which are very close to those computed by MatCalc. In summary the NNBB model implemented by SE-AG in Matlab to compute the interfacial energies results in the computation of values in a very reasonable range. The application of these data did not lead to numerical problems or excessive carbide formation. Therefore their data are routinely applied in further computations. 74

77 Surface effects Concerning the interfacial energies computed by the model suggested by Kozeschnik and Sonderegger a scaling factor has been introduced by SE-AG. Sonderegger [53] emphasises that a value of 70-80% of the computed interfacial energy should be used to attribute for surface effects which origin from the precipitates curvature. However this is stated in context with Nb(C,N) precipitation where the precipitate radius is considerably smaller than in the case of bainite formation. Following the arguments of Sonderegger, if a surface effect has to be considered for bainite transformation it should be less pronounced than for Nb(C,N) precipitates. Thus larger scaling factors in the range between 0.8 and 1 have been used within the bainite transformation model. Comparison In the following the interfacial energies between ferrite (bcc) and austenite (fcc) are compared. The RWTH-Aachen used MatCalc for the computations, whereas SE-AG implemented the model presented by Kozeschnik and Sonderegger using thermodynamic data obtained from ThermoCalc. In the according figure the SE-AG results have been marked by circles. Both results computed by RWTH-Aachen and SE-AG are in the same order of magnitude. In the case of Steel 2 presented in Figure 47 the situation for low carbon contents are very similar, however the RWTH results show nearly no dependency from the carbon content. The same is observed for the other steels (3-6) which have been compared exemplarily. RWTH TKSE σ α B [J/m²] T [ C] C [wt-%] Figure 47: Comparison of the bcc-fcc interfacial energies for Steel2, DP-Si obtained by RWTH and SE-AG To understand these differences both partners compared their models and databases they use. It became clear, that both partners used the same model, so that the differences must result from the databases. While SE-AG used the TCFE6 database from ThermoCalc, RWTH uses the database implemented in MatCalc. 75

78 As can be seen in Figure 48 these databases show differences in phase fractions and therefore also in the mixing enthalpy, which is an important input parameter for calculating the interfacial energy. Figure 48: Comparison of the ferrite phase fraction in DP-Al at 550 C and the corresponding mixing enthalpy for calculations with MatCalc (RWTH) and ThermoCalc (SE-AG). Discussion As show above, both MatCalc and the implementation of SE-AG result in very similar interfacial energies for low carbon contents. However the higher the carbon content within the austenite the larger the difference in the interfacial energy becomes. This is important for the discussed bainite model, as the interfacial energy has such a tremendous influence on nucleation processes. Unfortunately the computed results, especially the dependency of the carbon content, cannot be compared with measurement data. Thus it is difficult to judge which of the computed interfacial energies should be used within the Azuma model. On one hand we are comparing the results of MatCalc, a software that has been successfully applied in several papers, on the other side the SE-AG implementation in Matlab. Given the models simplicity an erroneous implementation seems to be unlikely. As discussed above the differences seem to origin from the different thermodynamic databases used in both cases. In earlier versions MatCalc was repeatedly cited [4,5,50,54] using the thermodynamic database TCFE3 provided by ThermoCalc SA respectively a modified version of it. Unfortunately no literature seems to be available as to which data have been complied in the modified version of this database. In contrast for the computations at SE-AG the ThermoCalc databases TCFE4 has been used with the corrections described in Later on this solution has been replaced by the more recent versions TCFE6.1 respective TCFE6.2. In the context of this project the most important change resulting from the change of the thermodynamic database has been the incorporation of Si and Al in the cementite lattice. Especially in the PE nucleation of bainitic cementite the lattice atoms remain at their original location, as the low bainite transformation temperatures do not allow diffusion within a reasonable amount of time, while for the smaller interstitial carbon slow diffusion is observed. The thus resulting trapping of silicon and aluminium in the cementite has a tremendous effect on the thermodynamic properties of cementite Influence of Si and Al on PE cementite In former ThermoCalc databases the influence of Silicon and Aluminium to PE cementite precipitation was not considered. The addition of these elements has a pronounced effect on the cementite precipitation. For example TRIP and bainitic steels are usually either Si or Al alloyed in order to reduce the cementite precipitation [55,56], higher levels of these alloying elements can even impede cementite precipitation [6,57,58]. 76

79 In order to account for these effects SE-AG adjusted the driving forces obtained from ThermoCalc [43]. In the past SE-AG has programmed a software layer in Matlab between the low level interface routines provided by ThermoCalc and the models developed by SE-AG in the Matlab environment such as the bainite model. This intermediate software layer acts as high level interface to the ThermoCalc-API. It eases the access to the ThermoCalc interface and it provides advanced thermodynamic models which are not provided by the ThermoCalc interface. This software layer is also suitable to implement according corrections as deemed necessary in the case of the Silicon and Aluminium influence on cementite precipitation. For cementite precipitation out of ferrite this was done initially on basis of the estimate of Ghosh and Olson [42]. Miyamoto and Oh [59] confirmed their experimentally obtained value by applying ab-inito computations based on the VASP code. For Si 3 C Jang et al. have proposed similar values [60,61] also obtained from ab-intio computations using the WIEN2K code. The overview of the proposed enthalpy values in Table 17 shows that especially for Al 3 C some discrepancies between the proposed values exist. For the precipitation of cementite out of austenite Kozeschnik et al. [62] made similar considerations which have been applied accordingly. The adjustments have been validated against the data given in Ghosh et al. [42] and Kozeschnik et al. [62]. However by the recent introduction of the thermodynamic database version TCFE6 the necessity of these implementations has been overcome. From TCFE6 on the Si and Al interaction on cementite has been included in the thermodynamic database on basis of some of the citations mentioned above [46]. kj/mol Ghosh and Olson [42] G. Miyamoto [59] J.H. Jang [60,61] Method Experimental ab-initio (VASP) ab-initio (WIEN2K) Cr 3 C - -33,0 - Mn 3 C - -26,7-52,7 Fe 3 C - 18, Si 3 C ,4 Al 3 C ,8 Table 17: Enthalpy values H [kj/mol] for different Carbides from Literature Cellular Automaton Model The principle behind the modelling approach used by CEIT consists in mapping the simulated volume into discrete small cubic elements (voxels), and solving Azuma's model equations for homogeneous continuum conditions at each point. The main assumption is that the properties of these small volume elements are homogeneous, so an appropriate scale for volume discretization must be performed. Recently, with the increase in computer power and better numerical algorithms, computer simulations have been used widely to describe and study the microstructural evolution and kinetics of phase transformations [63 66]. Monte Carlo (MC) methods are of practical importance because phenomena that are difficult to quantify can be treated as distributions of random numbers. MC sampling methods are frequently used in the framework of Cellular Automata (CA) [67 69]. The system is represented as a grid with specific local relationships. In the framework of CA, one or several dynamic particularities can be treated as either deterministic or stochastic, with sampling based on MC techniques [63]. The basic idea of using a CA is to describe the evolution of a complex system by means of the interactions between constituents following simple generic rules. The computational model developed takes as input parameters the chemical composition and thermodynamic description of the steel to be modelled, an initial grain size distribution, and the thermal cycle used. With these initial parameters, the volume is discretized and Azuma's Model equations are transformed into probability distribution functions, solved at each voxel with the help of MC sampling and CA algorithms. Carbon is redistributed in the matrix using a finite-differences diffusion algorithm. The resulting microstructure is used as input and it is again solved point wise with Azuma's Model 77

80 equations. The flowchart outlining the model steps is shown in Figure 49. The simulation stops when the thermal cycle finishes, just before quenching. Figure 49: Modelling approach flowchart. CA model description The Cellular Automaton model developed was defined in a 3-D cubic lattice. The neighbours of each cell are described in a Moore-type neighbourhood where only nearest and next-nearest neighbours are considered, as seen in Figure 50. The 2-D case is a special 3D case in which one edge of the simulated volume is equal to 1. For this case, each cell has 4 face and 4 vertex neighbours. Different weights are given to each neighbour to bias the influence exerted on the centre voxel. The weights depend on the inverse of the distance between the two voxels, as shown in Table 18. The advantage of this discrimination method is that all elements have the same shape, size, number of neighbours, and share the same interface between them. The position of a voxel is defined by its centre. Figure 50: The Moore neighbourhood definition domain. Neighbour Type Number Weight Normalized weight Table 18: Face 4 1 ( 2 2) 4 Vertex ( 2 1) 4 Weights assigned to different types of neighbours. To simulate transformation, each cell has three state variables: one phase state variable representing if the cell is austenite, ferrite, martensite, cementite, or it is an interface cell. A variable representing the carbon concentration, and one representing the austenite or ferrite grain number, used to define the grain boundary voxels. Experimental evidence shows that nucleation is favoured at grain boundaries [66]. To determine the influence of austenite grain size in the transformation different grain size structures were generated using a Monte Carlo Q-state Potts model. The detailed mathematical description is described in the literature [65]. 78

81 At the beginning of the simulation, the system is initialized with a unique austenite phase with an average carbon concentration c 0, a start system temperature T, and an austenite grain size distribution. As each cell transforms, it will eject a fraction of its carbon content (c γ - c α,paraeq ) to its neighbouring cells. The neighbouring cells change their phase variable from austenite to interface. As the simulation proceeds, ferrite grains will start to nucleate and grow, enriching the remaining austenite with carbon. Carbon diffuses into the matrix as a function of temperature and concentration. Austenite voxels surrounding the newly transformed ferrite voxels show a much higher carbon concentration as shown in Figure 51. When the temperature range is within the scope of Azuma s model, bainitic ferrite and carbides will begin to appear. If the transformation temperature is below M S, ferrite and bainite transformations will stop immediately. By the time the simulation is complete, if there are remaining voxels untransformed, the model will classify them as retained austenite. Figure 51: Modelled microstructural carbon concentration map and distribution. Using Azuma's Model equations as a basis for the Automaton model Azuma's model handles the bainitic transformation as a series of coupled rate equations describing the kinetics of each component phase [1]. Nucleation rate equations are given by Azuma's model as continuum equations for the case of a homogeneous matrix. The initial nucleation rate for bainitic ferrite is given by, RT I 0 =N 0 h exp Q γ C exp Gγ αb RT RT Where N 0 is the initial site density, R and h are the gas and Planck constants and T is the temperature in K. Q γ C is the activation energy for carbon diffusion in austenite, ΔG γ αb is the driving force for bainitic ferrite formation. To use the Azuma's model statistical rate equations as the basis for the transformation using a CA algorithm, these equations must be rendered into a probabilistic analogue that allows calculating the rate of the transformation in terms of cell switching probabilities. To obtain normalized and scaleindependent switching probabilities from Azuma's model, the rate equations were separated into a non- Boltzmann part x 0 that depends weakly on temperature, and a Boltzmann part w with an exponential dependence on temperature [70,71] I α B 0 = x& 0 w Where the non-boltzmann term, x 0, is given by, x & = 0 N 0 kt h And the Boltzmann component w, 79

82 = RT G RT Q w B c * exp exp α γ γ The Boltzmann factor w, represents the probability for cell switches. To obtain a scalable nucleation rate, it is necessary to map the rate equation with the lattice parameter λ m, determined in the volume discretization leading to the equation, ( )w v w x I m B λ α = = 0 0 & Where v is given by, h T k N B λ m ν 0 = To transform this equation into a probability distribution function that will determine the cell switches as a function of the local temperature, it must be rewritten as, w x w w x I m B ˆ ˆ = = = ν ν ν ν ν λ α & & where the normalized switching probability becomes = RT G RT Q w B c * exp exp ˆ 0 α γ γ ν ν = RT G RT Q h T k N B B c B m * 0 exp exp 0 α γ γ α λ ν The value for the normalization, v 0 can be determined by assuming that the maximum occurring switching probability should assume a value less or equal to one, 1 exp exp ˆ! 0 max * 0 = RT G RT Q h T k N w B B c B m α γ γ α λ ν with = RT G RT Q h T k N B B c B m * 0 exp exp 0 0 α γ γ α λ ν ν When ˆ w max =1, the normalization factor ν 0 equals the maximum value obtained in the system over the complete temperature range of the thermal treatment used. This normalization must be calculated just once per simulation. Inserting the obtainedν 0 into ˆ w max gives, = RT G RT Q w B B local c * exp exp ˆ 0 α γ γ α ν ν This equation is the probabilistic analogue to Azuma s model rate, governing the transformation of each volume element from austenite to bainite. During normalization the initial nucleation site density term N 0 vanishes. This yields an expression for calculating the bainitic transformation as a function of temperature and energy only. Probability distribution functions for carbide precipitation were obtained following the same procedure. Azuma's Model equations predict nucleation of ferrite only in the bainitic region. During the cooling period, before reaching holding temperatures and when using continuous cooling cycles, the 80

83 temperature range is outside the scope of the model kinetics. It was concluded form that additional transformations should be incorporated into the model so that the appropriate initial conditions for the bainitic transformation were taken into account. To achieve this, a ferrite nucleation and growth model, and a martensite transformation model were coupled into the CA modelling framework. Based on classical nucleation theory, the ferrite nucleation rate is described by [72], I F = K 1 D γ ( kt) 1 2 K exp 2 kt G v ( ) 2 Where I F is the ferrite nucleation rate, K 1 is a constant related to the nucleation site density J 3 mol -2, K 2 is a constant related to austenite ferrite interface energy Jm 3, D γ is the carbon diffusion coefficient in austenite, k is the Boltzmann constant, T is the temperature in Kelvin, and G v is the driving force for ferrite nucleation per unit volume. Nucleation of ferrite is assumed to occur at the grain boundary interface. The growth of pro-eutectoid ferrite is assumed to be a diffusion-controlled transformation. The growth velocity v of a ferrite grain is expressed by [72], 1 v = ( c γ α /γ cα α /γ) D c γ c α γ D α n α /γ In general, the interface velocity v can be written as n α /γ v = M G Where M is the effective interface mobility and G is the driving force. The effective interface mobility is given by, M = M 0 exp Q RT Where M 0 is a pre-exponential factor, Q is the activation energy for boundary diffusion, R is the gas constant and T is temperature in K. As soon as a ferrite cell gets nucleated it will begin to grow towards its neighbouring cells with an interface velocity v. At time t, the growth length of a ferrite cell can be described by l = t t 0 vdt Where t 0 is the time when the cell nucleates and v is the growth velocity. A growing cell will transform into a ferrite cell when its fraction transformed f f equals 1. f f = l λ m It was observed that at some transformation temperatures, Azuma s model predicted a bainitic transformation while the metallographic investigations showed it consisted in a martensitic specimen. To introduce a lower limit for the bainitic transformation the martensite transformation model proposed by Koistinen & Marburger was coupled into the CA. The model describes the fraction of martensite transformed as a function of the difference between the martensite start temperature M S and the system temperature 81

84 { ( )} 1 f m =exp C 6 M S T Where C 6 is an empirical constant 0.011K -1 [64]. To determine M S, an empirical equation proposed by P.Payson [73] was used since it predicted a MS consistent with observations in the steels studied. M S = C 33.3Mn 11.1Si 27.8Cr 16.7Ni 11.1Mo in K The dynamical evolution of the automaton takes place through the application of these switching rules on each lattice cell, determining the state of each lattice point as a function of its previous state and the state of the neighbouring sites. The resulting probability distribution functions were coupled with a Monte Carlo volume sampling method to avoid local transformation bias. For each MCS, the probability for a voxel to transform into ferrite, cementite, martensite, or remain as enriched austenite is calculated only once. With this numerical scheme, simulations will be able to provide quantitative data about the kinetics of the reaction and also the final morphology. To validate the numerical model developed at CEIT for isothermal holding conditions, steels 12 and 13 were selected. The chemical composition is presented in Table 19. The simulation domain was mapped into a 3-D 200x200x1 cubic lattice with a lattice spacing λ m of 0.5μm. An initial austenite grain distribution of 8µm was used, consistent with the results from the microstructural characterization. The steel was annealed at 850ºC for 60s and cooled down at 50ºC/s with helium gas to reach the holding temperature for isothermal transformation to bainite. The samples were held for 1800s at the transformation temperature and quenched to room temperature at 80ºC/s. The same sequence was followed in the simulations. Four holding temperatures were simulated: 350ºC, 400ºC, 450ºC and 500ºC Steel Nr. Material C Si Mn Al Cr Mo 12 DP 2.2Mn 0.8Cr DP 1.8Mn 0.8Cr Table 19: Chemical composition of steels 12 and 13 in weight percent. Figure 52 presents a comparison between the different transformation products evolution in time obtained by the model and the dilatometer curve obtained experimentally at a holding temperature of 350ºC. The curve labelled Phase Sum is given by the model and is composed by the sum of each of the different transformation products. For comparison purposes, this curve will be the one evaluated against the curve obtained experimentally. For this holding temperature the dilatometer curve and the curve obtained by the model differ in the amounts predicted for each transformation product. At the beginning of the transformation, the dilatometer signal gives an approximate 30% of transformation, while the model predicts around 10% combining pro-eutectoid ferrite and bainite. However, after the microstructural characterization of the sample it was found that the amount of transformation products before reaching the M S temperature is in close relationship with that predicted by the model. Reasons for the discrepancy with the dilatometer signal may be due to experimental errors. At the 10s mark in the x-axis, the martensite transformation dominates and the model predicts that change in the behaviour of the transformation as well. 82

85 Figure 52: Isothermal transformation kinetics for each transformation product at 350ºC holding temperature. Steel 12. Besides describing the evolution of the transformation in time, the CA implementation of the model also renders microstructural information. Figure 53 shows the comparison between the microstructure obtained experimentally and that given by the model. In the real microstructure, brown-white areas correspond to martensite, blue to ferrite, and violet-grey to bainite. In the microstructure obtained by simulation, purple voxels represent ferrite, grey voxels correspond to bainitic ferrite, light green voxels represent martensite, and white voxels are voxels left with untransformed austenite. Black pixels correspond to the initial austenite grain boundaries and are left for comparison purposes. Figure 53: Comparison between LOM and microstructure obtained by the model at 350ºC. Steel 12 Comparing the obtained microstructure and the experimentally obtained one, it is observed that the distribution and apparent volume fraction of the transformation products show a good agreement. Ferrite grains are evenly distributed in the grain boundaries of the parent austenite phase, and a small volume fraction of bainitic ferrite was observed and predicted by the model. For the remaining holding temperatures studied the transformation occurred in the temperature range above the M S temperature where the transformation is dominated by the bainitic mechanism. Figure 54 shows good agreement between the dilatometer curves and the transformation curves obtained by the model for 400ºC and 450ºC holding temperatures. The ferrite nucleation and growth model used reproduces the first part of the transformation, setting the appropriate initial conditions for the bainitic transformation, described by Azuma s model. For the bainitic part of the transformation, the agreement between the experimental and the model results is remarkable, considering the CA implementation of the model takes only the thermodynamic description of the system and the parent austenite grain size distribution, removing the fitting parameters from the original model. 83

86 Figure 54: Isothermal transformation kinetics for 400ºC and 450ºC. Steel 12. Figure 55: a. 400ºC holding temperature transformation microstructure obtained by LOM. b. Modelled microstructure 400ºC. c. 450ºC microstructure obtained by LOM. d. Modelled microstructure 450ºC. Steel 12. With respect to the microstructures obtained by the model for these transformations, Figure 55 shows that there is also a good agreement between the distribution and volume fraction of the transformation products. The volume fraction of ferrite represents approximately 15% of the transformation that agrees with the model results. The modelled microstructures share similar features since they are initialized using the same template. However it can be observed that there is a larger percentage of untransformed austenite voxels, represented in white, with respect to the one obtained for a holding temperature of 400ºC. Similar results were observed in the real microstructures. The transformation curves for the transformation holding temperature of 500ºC are presented in Figure 56. At this holding temperature, the model predicts a simultaneous transformation from austenite into ferrite and bainite. Comparing the dilatometer curve with the Phase sum curve, it can be observed that 84

87 there is good agreement between them. This again confirms the need to couple several models in order to accurately describe the austenite decomposition into different transformation products. Figure 56: Isothermal transformation kinetics for 500ºC. Steel 12. Figure 57: Isothermal transformation kinetics. a. 350ºC holding temperature. b. 400ºC. c. 450ºC. d. 500ºC. Steel

88 Figure 58: a. Microstructure obtained by LOM 350ºC. b. Microstructure obtained by simulation 350ºC. c. Microstructure obtained by LOM 450ºC. Microstructure obtained by the model 450ºC. Steel 13 For steel 13, the same holding temperatures were considered to test the model. The transformation curves obtained by the model and their experimental counterparts are shown in Figure 57. The comparison between the real microstructures and those calculated by the model for 350ºC and 450ºC holding temperatures are shown in Figure 58. The model was also tested for continuous cooling conditions using steel 12 and 13. For both steels, simulations were carried out for five different cooling rates: 60K/s, 40K/s, 20K/s, 10K/s and 5K/s. For steel 12 the transformation kinetics curves for all the cooling rates and the microstructural results obtained for 60K/s and 5K/s starting from 850ºC are presented in Figure 59 and Figure 60 respectively. It can be seen from the results that the model developed correctly describes the transformations taking place during cooling from annealing to room temperature. The Phase Sum curve shows a good approximation to the dilatometer curve for the different cooling rates studied. The microstructural features obtained with the model also show good agreement in both distribution of transformation products and volume fraction. Due to differences in the lighting conditions, the colours of each transformation product in Figure 60c are slightly different to those in other samples shown. White areas represent martensite, ferrite is etched as the pale yellow background and bainite is observed as the darker yellow zones. For steel 13, simulations were conducted using the same cooling rates as for steel 12. Results are shown similarly in Figure 61 and Figure 62. As in the isothermal holding case, steel 13 transforms mostly to ferrite even at fast cooling rates. This is due to the small grain size of the steel and also the reduction in manganese compared with steel 12. This is observed in the dilatometer curves and in the samples characterized. The model accurately replicates this effect both in the kinetics and in the simulated microstructure. As in the previous examples, the fraction and distribution of each different transformation product are in good agreement with the experimental results. 86

89 Differences in the morphology of the microstructures are due to rolling effects that cause a band-like structure. The grain distribution used in these simulations consists of equiaxed initial austenite grains. If elongated grains were used, the simulated microstructure morphology will also be changed. This will be explained and shown in more detail in following sections. The complete set of results for the transformation products obtained from the isothermal holding simulations are presented in Table 20 for steel 12 and in Table 21 for steel 13. For continuous cooling simulation, the results are in Table 22 and Table 23. A comparison of these simulated results with the experimentally determined microstructures in Table 11 to Table 15 shows a reasonable agreement in most cases. However in some instances, e.g. the isothermal holding of steel 12 at 500 C and that of steel 13 at 350 C result in a strong overestimation of the formed ferrite fraction. Subsequently the predictions of the remaining phases show also major discrepancies. These examples show the importance of the single transformation models for the correct prediction of the following transformation. Figure 59: a. Transformation kinetics at 60K/s. b. Transformation kinetics at 40K/s. c. Transformation kinetics at 20K/s. d. Transformation kinetics at 10K/s. Steel

90 Figure 60: a. Microstructure obtained by LOM 60K/s. b. Modelled microstructure 60K/s. c. Microstructure obtained by LOM 5K/s. d. Modelled microstructure 5K/s. Steel 12. Figure 61: a. Transformation kinetics at 60Ks. b. Transformation kinetics at 40Ks. c. Transformation kinetics at 20Ks. d. Transformation kinetics at 10Ks. Steel

91 Figure 62: a. Microstructure obtained by LOM 60 K/s. b. Modelled microstructure 60 K/s. c. Microstructure obtained by LOM 5 K/s. d. Modelled microstructure 5 K/s. Steel 13. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 20: Steel 12 annealed at 850ºC. Simulation results for isothermal holding transformations. Holding temperature [ºC] Ferrite [%] Table 21: Bainite [%] Martensite [%] Ret. Austenite [%] Steel 13 annealed at 850ºC. Simulation results for isothermal holding transformations. 89

92 Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 22: Steel 12 annealed at 850ºC. Simulation results for continuous cooling transformation. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 23: Steel 13 annealed at 850ºC. Simulation results for continuous cooling transformations. 90

93 4 WP4: Bainite Design for Heterogeneous Structures with Inhomogeneous Carbon Distribution in Austenite 4.1 Cold Strip Characterization Quenched samples that were annealed in the intercritical range were analysed at SE-AG concerning their amount of ferrite, martensite (i.e. former austenite) the grain structures and homogeneousness of alloying components. Figure 63 shows examples of such investigations. The material steel 4 is from a laboratory heat and appears quite homogeneous. a) b) Figure 63: a: Grain structure in steel 4 (cold rolled state), b: homogeneous distribution of main elements in the cold rolled state of steel 4. Materials that originated from industrial production show a slightly banded structure in rolling direction. Examples can be seen in Figure 64 for the microstructure, respective Figure 65 and Figure 66 for microprobe investigations. The results of the investigations in WP 4.1 characterize the starting structures including the fractions of ferrite and austenite at the end of the intercritical annealing. Figure 64: Microstructures in materials TRIP-Al (steel 3) and DP-Al (steel 1) quenched out of the intercritical region. 91

94 Figure 65: Microprobe analysis of the Trip-Al steel, sampled from industrial production. Figure 66: Microprobe analysis of the DP-Al steel, sampled from industrial production. 92

95 4.2 Experimental RWTH-Aachen In this workpackage RWTH-Aachen performed dilatation experiments for intercritical annealing for three steels: aluminum alloyed TRIP steel, silicon alloyed TRIP steel and aluminum alloyed dual phase steel. The samples were made from a cold rolled sheet with a reduction of 60% during cold rolling. For the first experiments all three steels were annealed with the same parameters although these parameters are not adequate to adjust a microstructure as in industrial produced steels. The cycles used for the steels are shown in Table 24. heating rate [K/s] Austenitisation temperature [ C] annealing time [s] cooling rate to soaking temperature [K/s] Soaking tempearture [ C] Soaking time [s] cooling rate to room temperature [K/s] approx approx approx approx approx approx approx approx approx approx approx approx approx approx approx approx / / / approx. 300 Table 24: Annealing cycles for the three alloys having a higher carbon content. Due to the fast transformation which already occurred during cooling it was tried to quench to soaking temperature with the highest possible cooling rate. Because of the small fraction of austenite during intercritical annealing the dilation signals in these experiments were much smaller. The results were similar to those in WP 3. In Figure 67 an example is shown for the influence of the soaking temperature on the reaction kinetics. With increasing soaking temperature not only the velocity of transformation but also the amount of transformation increases. For metallography the samples of the three steels were sent to CEIT. Figure 67: Isothermal bainitic transformation after intercritical annealing for 60 s at 850 C of aluminium alloyed TRIP steel at different soaking temperatures. 93

96 4.2.2 SE-AG SE-AG made continuous cooling tests with steel 3, TRIP Al. In these tests by use of dilatometer samples were heated up to 1300 C, annealed at that austenite temperature for 10 s and were afterwards cooled down to RT continuously with different constant cooling rates in each case. The t 8/5 times for that cooling rates were in the range between 1s and 100s. Similar to former tests the austenite grain sizes before transformation was determined by keeping a sample for short time in the ferrite region and quenching them down afterwards to room temperature. In these samples martensite was decorated by small borders of ferrite along the former austenite grains. Retained austenite was measured by X-ray diffraction. Figure 68 shows the transformation kinetics for different cooling rates. Figure 68: Transformation during continuous cooling of steel 3, TRIP Al, from 1300 C. Figure 69: Continuous cooling transformation-diagram for steel 3 (TRIP, Al) after 10 s at 1300 C. From the results of the measured dilatometer signals in combination with optical metallography and X- Ray diffraction a CCT diagram was constructed as shown in Figure 69: Fast cooled samples transform to martensite or a mixture of bainite and martensite. Samples with slower cooling rates transform first to some content of ferrite/pearlite before bainite is formed. Figure 70 shows the transformation behaviour as a function of time. The results of these experiments have been used for modelling the influence of Al on the transformation kinetics. 94

97 Figure 70: Influence of time on the transformation during continuous cooling steel 3, TRIP Al, from 1300 C. Further SE-AG provided data for samples on the transformation kinetics of an intercritically annealed DPsteel from former investigations. As can be taken from Table 25 the chemical composition of this steel is similar to DP Si out of this project. The plates have been sampled in the cold rolled, work hardened state. The laboratory annealing on a Gleeble 3500 thermo-mechanical simulation system was carried out in a cycle reassembling the simplified annealing cycle of a hot dip galvanizing line except for the last part where the isothermal transformation has been studied. The lower part of Table 25 gives the thermal cycle, which has been applied. The specimen have been annealed for 84 s in the austenite/ferrite range at 780 C, cooled down to 680 C within 50 s and afterwards within 8 s to temperatures between 550 C and 350 C for an isothermal treatment over 200s. At the end the samples were quenched for analysis. During the cycle the dilatation signal of the samples was measured by a laser system. The resulting dilation data of the isothermal part are given in Figure 71, while Table 26 shows the result of the analysis of the microstructure by OM and X-ray diffraction. C Mn Si S N Al P Cr Cu Mo 0.098% 1.34% 0.17% 0.001% 0.004% 0.036% 0.013% 0.016% 0.12% 0.24% Table 25: Chemical composition of the DP-steel and annealing cycles 95

98 Figure 71: Dilatation signal during the isothermal part of the cycle. Table 26: Microstructural characterisation of the samples after quenching VOESTALPINE Voestalpine focussed investigations according to WP4 on steel 12 because the first results of this steel gave a good completion to the already available results of steel 13 and 14. Steel 12 was used to deliver experimental data of bainitic transformation after intercritical annealing. To obtain a wide range of different grades of austenitization, several preliminary tests took place. The best results could be achieved with the same heating cycles as shown in Figure 2 but with lower annealing temperatures (800, 775 and 750 C). Grades of Austenitization For further analysis it became important to find a method, which permits a clear analysis to calculate the grade of austenitization. The knowledge of that amount of ferrite, which is existing already before cooling is necessary, to allow a substantiate calculation of the occurring transformations. Voestalpine investigated four different methods to measure the amount of ferrite, which is still existing at cooling start. These four methods are described as follows: Calculations from Isothermal Measurements A direct calculation of the grade of austenitization can be achieved with the method of the Law of Lever from isothermal measured dilatometric curves as shown in Figure 72. For this purpose the dilatometric curves of the samples which were annealed in the full austenitic range and the intercritical annealed samples were put on the top of each other. In a first step the heating parts and the cooling parts of the curves were fitted with adequate polynomials. The distance between α-fit and γ-fit at the end of heating equates to full austenitization. The smaller length between α-fit and α (χ) + γ (c) - fit corresponds to the grade of austenitization. 96

99 Figure 72: Description of using the "Law of Lever". Figure 73 shows the application of this method to the measured data. Instead of using only one dilatometric curve which was annealed in the full austenitic range, it was decided, that the curves from the material which is annealed in the full austenitic range and the intercritical annealed sample with the same soaking temperature are compared. Figure 73: Procedure of calculating the grades of austenitization (T AN = 750 C). Table 27 summarizes the calculated grades of austenitization from the dilatometric curves of the isothermal measurements. The wide scattering of the results are hardly explainable, so it is a common way to use the average grade of austenitization of all calculated results. In some cases these calculations are not possible, because the broadening of the α- to γ- transformation from the intercritical annealed sample is higher than those of the reference. 97

100 T soaking Grades of Austenitization [%] [ C] T an = 750 C T an = 775 C T an = 800 C not possible not possible not possible not possible Average Table 27: Grades of austenitization calculated out of isothermal data. Calculations from Heating Cycles with Continuous Cooling In a further step calculations with the method of the Law of Lever were realized at the results of continuous cooled samples. These samples were cooled with helium (cooling rates about 300K/s), that s the reason why no phase transformations in the bainitic range can be observed in Figure 74. Of course, the cooling cycles don t affect the grades of austenitization, but these samples were necessary for the further methods. It was suggested to use these samples to get more comparable results for discussing. Table 28 summarizes the calculated grades of austenitization. Figure 74: Procedure for calculating the grades of austenitization for helium-cooled samples. 98

101 Grades of Austenitization [%] T an = 750 C T an = 775 C T an = 800 C T an = 825 C He-quench Table 28: Grades of austenitization calculated out of helium-cooled measurements. For confirming the dilatometric measurements, voestalpine prepared micrographs of the continuous cooled samples. As expected, no transformation at cooling took place and so the microstructure only consist of ferrite which still consist at the end of the annealing treatment and martensite, which was transformed from austenite. The amount of ferrite decreases with rising annealing temperature, what leads to higher grades of austenitization. Figure 75 summarizes the developing microstructure. Figure 75: Micrographs of helium - cooled samples etched with Le Pera. X-ray Diffraction Measurements of the Helium-Cooled Samples As already discussed, no phase transformation could be observed after continuous cooling with helium, down from the annealing temperatures to room temperature. So the microstructures of these samples only consist of ferrite which wasn t transformed into austenite at the annealing treatment and martensite. So the amount of ferrite at the final microstructures is equal to the amount of ferrite at the end of annealing. X-ray diffraction measurements permit a separation between ferrite and martensite because of their different lattice constants which occur from the carbon content in the martensite lattice. By comparing the ratios between the measured intensity spectra peaks given in Figure 76, it is possible to calculate the pre-existing amount of ferrite. The small carbon contents in the occurring martensite leads to a small shift of the ferrite and martensite peaks. The occurring overlapping of them makes a separation of ferrite and martensite quite difficult and allows space for speculations. So that method is unfitting for the occurring carbon contents in the transformed martensite, even though the results in Table 29 show the expected trend. Also in comparison with the dilatometric measurements, the results fit acceptable. 99

102 Grades of Austenitization [%] T an = 750 C T an = 775 C T an = 800 C T an = 825 C X-ray Table 29: Calculated grades of austenitization out of x-ray diffraction measurements. Figure 76: Intensity spectra resulting of different annealing temperatures. Image Analysis of Continuous Cooled Samples with Helium A segmentation of occurring phases (ferrite and martensite) in the micrographs allows the evaluation of the amount of ferrite. The major disadvantage of this method is that there is a lower limit for the detection of ferrite in the microstructure. Table 30 demonstrates that only the samples with the low annealing temperatures provide results. The segmentations of the microstructures of T an = 750 C and T an = 775 C are shown in Figure 77. Voestalpine compared in a final step the results of the different methods. The summary is given in Figure 78. It can be figured out, that all methods show the same trend and also the numerical values fit adequate. Only the image analysis underestimates the ferrite contents. In consequence of these investigations, it is substantiate to calculate the grade of austenitization in future directly out of the measured dilatometric curves. Table 30: Grades of Austenitization [%] T an = 750 C T an = 775 C T an = 800 C T an = 825 C I.A not possible not possible Calculated grades of austenitization from image analysis. 100

103 Figure 77: Segmentations of the microstructures for calculating the grades of austenitization. Figure 78: Compared grades of austenitization calculated with different methods. 101

104 Results of bainitic transformation after incomplete austenitization for steel 12 T an = 750 C_t an = 60s_T soak = C Voestalpine started calculating the transformation amounts after the necessary time-consuming investigations concerning the grade of austenitization. The results of the calculations from the intercritical annealed samples at 750 C are summarized in Table 31 and Figure 79. The analyses are similar to former investigations what allows a simple comparison of the results. soaking temperature already transformed before reaching the soaking temperature transformation during soaking transformation after soaking residual austenite residual ferrite (100% - austenitization) [ C] [%] [%] [%] [%] [%] Table 31: Transformed phase amounts of steel 12 after annealing at 750 C for 60s. Figure 79: Overview of transformed phase amounts of steel 12 after annealing at 750 C for 60s. Voestalpine calculated in a further step the kinetics of the phase transformations after intercritical annealing at 750 C in the bainitic range. The results are given in Figure

105 Figure 80: Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 750 C for 60s. T an = 775 C_t an = 60s_T soak = C The results of the proceeding phase transformations after annealing at 775 C for 60s of steel 12 is given in Table 32, Figure 81 and Figure 82. soaking temperature already transformed before reaching the soaking temperature transformation during soaking transformation after soaking residual austenite residual ferrite (100% - austenitization) [ C] [%] [%] [%] [%] [%] Table 32: Transformed phase amounts of steel 12 after annealing at 775 C and 60s. 103

106 Figure 81: Overview of transformed phase amounts of steel 12 after annealing at 775 C for 60s. Figure 82: Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 775 C for 60s. 104

107 T an = 800 C_t an = 60s_T soak = C The results of the proceeding phase transformations after annealing at 800 C for 60s of steel 12 is given in Table 33, Figure 83 and Figure 84. The first results of Azuma - model showed that a time-dependent description of the occurring phase transformation will have some advantages. So voestalpine modified their results to provide an easy comparable plot to the model. The main point of these plots is a time-offset at cooling start, so the phase transformation at cooling until reaching soaking temperature and the phase transformation during soaking can be detected. Some of these results are given in Figure 85 to Figure 87. soaking temperature already transformed before reaching the soaking temperature transformation during soaking transformation after soaking residual austenite residual ferrite (100% - austenitisation) [ C] [%] [%] [%] [%] [%] Table 33: Transformed phase amount of steel 12 after annealing at 800 C for 60s. Figure 83: Overview of transformed phase amounts of steel 12 after annealing at 800 C for 60s. 105

108 Figure 84: Calculated transformation curves during isothermal soaking of steel 12 at different soaking temperatures (450 C, 500 C, 550 C) after annealing at 800 C for 60s. Figure 85: Time dependent phase transformation curves of steel 12 after annealing at 750 C for 60s and different soaking temperatures. 106

109 Figure 86: Time dependent phase transformation curves of steel 12 after annealing at 775 C for 60s and different soaking temperatures. Figure 87: Time dependent phase transformation curves of steel 12 after annealing at 800 C for 60s and different soaking temperatures. 107

110 Figure 88: Heating cycles for dilatometric investigations with complete and incomplete austenitization. According to the work package description of WP 4, a series of heating cycles with continuous cooling conditions were developed to produce data from homogenous austenite as well as from intercritical annealed conditions. A schematic plot of these heating treatments is given in Figure 88. Former investigations have shown, that annealing at 850 C and 60s would be sufficient to produce homogenous austenite, while lower annealing temperatures would lead to an intercritical initial state. Small temperature steps of 25 C starting from an annealing temperature from 850 C down to 825 C and 800 C would help to learn about the sensitivity of the Azuma - model. Producing date with different cooling rates in a wide range would allow a testing of the limitation of the model. The large variations of the influencing factors lead to a high number of heating cycles by what the investigations started first only for steel 12 and 13. An essential part for further simulations is the knowledge of the amount of ferrite at cooling start. A summary of these amounts is given in Table 34. Sample Grades of Austenitization [%] T AN = 800 C T AN = 825 C T AN = 850 C VA_DP_2.2Mn_0.8Cr VA_DP_1.8Mn_0.8Cr Table 34: Grades of austenitization of investigated materials. The measured temperature depending dilatation allows an analysis of the occurring phase transformations which took place under continuous cooling conditions. The main calculation steps are similar to the analysis of the measurements with isothermal soaking temperatures. The subsequent phase transformations depend on the cooling rates down to room temperature. According to the dilatometric investigations with heating cycles including isothermal soaking temperatures, the calculations show the amount of transformation (in % ) vs. the logarithmic cooling time (in s ) in an identical way. In collaboration with retained austenite measurements and the calculated grades of austenitization, it is possible to describe the amounts and the kinetics of the whole phase transformation behaviour. Some results of the transformation behaviours of steel 12 after 60s annealing at 800 C, 825 C and 850 C are summarized in Figure 89, Figure 90 and Figure 91. As expected, higher cooling rates shift the transformation curves to shorter times because the transformation temperatures are reached faster. It 108

111 is also plausible that the amount of retained austenite is higher at low cooling rates because of preferred carbon redistribution and that incomplete austenitization leads to faster transformation behaviour of the first detectable transformation. The discontinuities of the phase transformation curves suggest different transformation stages which are a result of the carbon redistribution from austenite to ferrite as well as saturation and precipitation of carbon. This assumption is supported by the fact, that in the case of incomplete austenitization, the described discontinuities show a stronger forming. Figure 89: Time dependent phase transformation curves of steel 12 after annealing at 800 C for 60s and different cooling conditions. Figure 90: Time dependent phase transformation curves of steel 12 after annealing at 825 C for 60s and different cooling conditions. 109

112 Figure 91: Time dependent phase transformation curves of steel 13 after annealing at 800 C for 60s and different cooling conditions. Additional calculations were done to allow a detection of the individual amounts of generated phases in a temperature-dependent way. The main steps of the calculations are summarized below: 1. Mathematical fit of the heating part (α-fit) and the cooling part (γ-fit) of the dilatometer curve with adequate polynomials (compare with heating cycles including isothermal soaking treatment ) 2. Calculation of the grade of austenitization 3. Measurement of retained austenite 4. Deviation of the dilatometer curve according to the temperature (Figure 92). This is done by computing the dilatation in relation to the polynomials determined in step 1. by applying the lever rule. The resulting transformation curve is then differentiated in respect to the temperature. 5. Mathematical description of the deviated dilatometer curve with a Gauss Error Distribution Curve 6. Peaks of the deviation provide proportions of transformed amounts (Integration of phase 1, phase 2, phase 3, phase 4, Phase 5, retained austenite and grade of austenitization = 100% transformation) A schematic plot of the analysis method is given in Figure 92. It allows a clear statement what annealing and cooling conditions lead to the formation of several phases and further in which ratio they occur. This will support the assessment of light optical investigations and gives important information about the amount of ferrite at the beginning of the bainitic transformation. The occurring phase transformations of steel 12 after an annealing treatment in the full austenitic range at 850 C and the deviated dilatometric curves (according to the temperature) and the original measured curves, fitted with adequate polynomials are summarized in Figure 93. These analyses allow a first overview of the phase transformation trends because the area of the occurring peaks in a several temperature range equates to special types of phases. That means that the area at high temperatures is equivalent to ferrite, while the amounts of upper and lower bainite occur at intermediate temperatures. At temperatures below the martensite start temperature occurring phase transformations lead to martensite. 110

113 Figure 92: Steel 12 (T an = 850 C; CR= 1.2K/s): Mathematical description of the deviated dilatometer curve (according to the temperature) with Gauss Error Distribution Curve inclusive the transformed phase amounts. Figure 93: Original measured and deviated dilatometric curves at continuous cooling conditions with cooling rates of 10 K/s and 20 K/s after annealing at 850 C. Careful analysis of the deviated dilatometric curves illustrate, that the fittings of the Gauss error distribution curves is ambiguous, if an overlapping of the curves occur. 111

114 A way to get useful results is, to work with an additional plot, which summarizes the calculated phase amounts against the continuous cooling rates. If the development of the courses is plausible, the Gauss error distribution curves should give a correct fit of the deviated curve. Figure 94 shows the development of the transformation products for steel 12 after annealing at 850 C and continuous cooling conditions in the range of 0.6K/s up to the maximum cooling rate. These calculations show, that small amounts of ferrite at the beginning of the cooling treatment, lead to higher amounts of ferrite. The reason for these differences could be found in the still existing nucleation sites for ferrite in intercritical annealed material before the cooling treatment starts, while such sites must be first generated in the case of a material, which is annealed in the full austenitic range. The calculations evidence, that already small amounts of ferrite lead to different transformation amounts. The change of the starting conditions may help to get an idea about the sensitivity of the Azuma - Model. Figure 94: Calculated phase amounts of Steel 12 which occur at continuous cooling conditions after annealing at 850 C. 4.3 Microstructural Characterization The total transformation kinetics calculated by using the Azuma-model can be fitted by dilatation data. But additionally the model delivers several microstructural features like phase fractions, carbide size in austenite, carbide size in ferrite and so on. To prove if the model predicts these feature correctly SE-AG and RWTH performed additional experiments for microstructural characterization. The annealing cycles, discussed below, were done at RWTH and the analysis was done at SE-AG Characterization of the chemical composition of austenite after intercritical annealing In these experiments, three steels (TRIP-Al, TRIP-Si and DP-Al low C) were intercritically annealed and quenched after it. The light optical analyses gave the amounts of ferrite and martensite, which is the amount of austenite during intercritical annealing. The samples were than scanned using EPMA 112

115 (Electron Probe MicroAnalysis) to observe the element distribution. This was done to see if the substitutional elements are distributed homogenously through ferrite and austenite or if there is an enrichment or depletion of some alloying elements in ferrite or austenite. If there is enrichment it should be considered in the Azuma-Modell. Also in this work package RWTH performed metallographic analysis via LOM for several samples. For the steel Voest_CP, which was annealed by SE-AG, phase fractions and grain sizes were determined. Further specimen of DP-Al, TRIP-Si, TRIP-Al, which were intercritically annealed with subsequent isothermal transformation were additionally prepared for further analysis at CEIT Chemical composition of carbides In theory aluminium should occur in carbides building under paraequilibrium [74]. Therefore a sample of the industrially produced steel DP-Al (low C) was annealed intercritical, at 850 C for 60s and cooled down to 400 C. At this temperature the sample was held for 650s. TEM analyses and EDX mappings were performed at SE-AG to see the chemical composition of the precipitated carbides. EBSD measurements were conducted to separate bainitic structures from martensite. SE-AG in combination with RWTH made investigations to characterize microstructures by the use of electron microscopy. For the tests described below all the heat treatments were made using a dilatometer at RWTH, while analysis by electron microscopy was done at SE-AG. During a first series of tests samples from DP Al steel 1 using a dilatometer were annealed in the intercritical range at 850 C and quenched down to RT. Other samples were rapidly cooled from 850 C to 400 C, annealed at that temperature until end of bainite transformation and then quenched to RT. The question on one hand was whether is would be possible to distinguish by EBSD technique between matensite and Bainite. On the other hand information was expected concerning cabides in the sample coming from 400 C. An example of the obtained EBSD images has been given in section 3.2, especially Figure 34. Figure 95 gives an overview of the precipitated carbides within the DP-Al steel 1 which has been quenched from 400 C after intercritical annealing. The EDX-mapping in Figure 96 indicates that the cementite contains some aluminium, though the presence of the attached aluminium-nitrides visually reduces this level by their own strong signal resulting from even higher aluminium contents. Figure 95: Carbides found on grain boundaries (upper right) and within grains (lower images) in DP-Al steel 1 quenched from 400 C after intercritical annealing. 113

116 Figure 96: EDX-mappings of carbide particles found in DP-Al samples quenched from 400 C. The result of these investigations was, that it was not clear to decide by EBSD what is bainite and what is martensite. Neither contrast, the misorientations within the grains nor the orientation relationships of grains gave any clear information. Carbides from the 400 C sample could be more clearly identified as is shown by the examples in Figure 96. In a second series of tests samples of steel 6, DP Al- high C, were austenitized at 1250 C, quenched to 400 C and annealed there for different times between 10 and 100s followed by quenching. Other samples were directly quenched from 1250 C to RT. Figure 97 shows the dilatation signal for some of these tests. Figure 97a shows that samples quenched directly from 1250 C transform to martensite at about 350 C. Samples that are annealed 100s at 400 C transform nearly completely into bainite see Figure 97c. Specimen like the example shown in Figure 97b, with a shorter annealing time at 400 C, show beside the transformation to bainite at 400 C an additional transformation to martensite during quenching from 400 C to RT. So in the specimen of the complete series, with holding times from 0 s to 100 s at 400 C, a rising amount of bainite should be found. The aim was to detect this tendency by electron microscopy. a) 0s 400 C b) 30s 400 C c) 100s 400 C Figure 97: Dilatation signal for samples from steel 6, DP-Al high C, quenched from 1250 C and annealed at 400 C for different times. 114

117 Figure 98: EBSD pattern from a steel 6, DP-Al high C sample annealed 40 s at 400 C. Figure 99: Martensite grains without and bainite grains with cementite in steel 6, DP-Al high C annealed 40s at 400 C. Again and similar to the results from the tests discussed above the investigation with EBSD gave no clear results. But what could be seen was a tendency that from pure martensite to pure bainite the fraction of well visible straight former austenite grain boundaries (see red arrow in Figure 98) that should be characteristic for martensite was reduced in favour of more diffuse boundaries as shown with the blue arrow and more characteristic for bainite. A clearer distinction between martensite and bainite could be obtained by looking on cementite. Martensite that is formed during quenching should contain no cementite while bainite formed at 400 C should. Indeed this could be confirmed by the results from TEM as shown in Figure

118 In a third series of tests samples from the same steel 6 DP-Al high C were austenized at 1250 C, quenched to 350 C or 300 C and annealed at those temperatures until to the end of transformation. The thermal cycles as well as the dilatometer signal from this cycle can be taken from Figure 100. As can be seen in the dilatation signal the sample that is quenched to 300 C shows some transformation to martensite before the isothermal temperature is reached. During isothermal annealing about 50% bainite is formed. In opposition to that the 350 C sample only should contain traces of martensite that might be formed during the quench from 350 C to RT. The aim of TEM investigation was to confirm this interpretation. Figure 100: Cycle and dilatometer signal for a treatment with steel 6. As above the results from EBSD investigation were not clear in this case, either. But clear results came from carbon replica samples under TEM: As can be seen in Figure 101 samples quenched from 300 C contained grain structures with and without cementite. In contrast those specimens quenched from 350 C mainly cementite containing structures were visible. Figure 101: Sample from 300 C containing grains with and without cementite (left) and sample from 350 C with nearly only grain structures with cementite (right). From all the investigations by electron microscopy it can be concluded, that EBSD investigation alone gave no clear results, but a combination of EBSD with cementite investigations by TEM gave hints about the type of microstructure. But because of the limited local range of visibility these results give no quantitative answers but only qualitative ones and thus can substantiate results from dilatation. 116

119 In summary it can be concluded: - Distinction between martensite and bainite only by EBSD is difficult. - Fine (Ti,Mo)(C,N) particles are precipitated inside the grains. - (Fe, Mn) 3 C particles were found on grain boundaries, often nucleated on AlN. - The Mn-content within the (Fe, Mn) 3 C particles is close to the matrix concentration. - The Al or Ti levels are slightly raised in (Fe, Mn) 3 C Microstructural characterisation The metallographic characterization from samples resulting from intercritical annealing conditions was done by optical microscopy. Due to the fine microstructure and the multiphase components appearing it was necessary to try different etching techniques. As shown in Figure 102, using Nital as etchant does not resolve the different phases appearing. Instead, for the characterization LePera's etchant was used. This gave a color etching of the sample in which the different transformation products were distinguishable and their volume fraction could be determined. Due to the fine structures appearing in samples from steels 12 and 13 sometimes it was difficult to differentiate between the component phases. For these cases, FEG-SEM microscopy was used in order to confirm the observations. Figure 102: Comparison between a micrograph etched with Nital at 2% and LePera s. For steel 12, the results for isothermal holding cycles starting from two different annealing temperatures were analyzed. Table 35 and Table 36 show the phase fractions for this steel annealed at 775ºC and 750ºC. With respect to the fully austenized samples from the same steel, a larger fraction of ferrite was observed, as it was expected. It was also noted that the martensite fraction for both annealing temperatures was greater for holding temperatures above 400ºC than for the fully austenized sample, where only small islands of martensite were observed. This is due to the carbon enrichment of the austenite matrix from ferrite growth, leaving zones with a carbon concentration high enough to stabilize the austenite during the bainitic transformation. It was also observed for these steels that whenever the ferrite transformation has enough time, the resulting microstructure shows a band-like morphology. After annealing at 775ºC, steel 12 shows qualitatively the same results as for the fully austenized samples. The maximum bainite fraction observed occurs at 400ºC and ferrite can transform at 500ºC, making samples at this holding temperature to have the largest fraction. Samples isothermally held at 117

120 300ºC and 350ºC show a large fraction of martensite, meaning that these transformation temperatures occur below M S. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 35: Phase fractions for steel 12 annealed at 775ºC for different holding temperatures. Samples from steel 12 annealed at 750ºC showed a greater ferrite fraction. For samples isothermally held above 400ºC, the amount of bainite decreased with respect to other annealing temperatures and the fraction of martensite increased. These results show that carbon enrichment of the matrix slows down the bainitic transformation, stabilizing the austenite matrix. After quenching, this enriched austenite transforms into martensite or remains as retained austenite, depending on the carbon concentration. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 36: Phase fractions for steel 12 annealed at 750ºC for different holding temperatures. To compare the difference in the kinetics of the transformation during continuous cooling between fully austenitic samples and intercritically annealed, metallographic characterization was carried out for steels 12 and 13. The analyzed samples were annealed at 800ºC and cooled down to room temperature. The amount of retained ferrite during annealing was determined by optical microscopy to be 5% for steel 12 and 14% for steel 13. Table 37 shows the phase fractions obtained for steel 12 for continuous cooling conditions after annealing the samples at 800ºC. It was observed that for fast cooling rates the bainitic transformation does not have enough time to evolve. For slower cooling rates, ferrite growth and the subsequent reduction in available nucleation sites as well as carbon enrichment of the austenitic matrix slowed down the transformation. For steel 13 annealed at 800ºC, the phase fractions for different cooling rates are presented in Table 38. For slow cooling rates, the final ferrite fraction for the samples with respect to steel 12 annealed at the same temperature is not as pronounced as in the case where the transformation starts from a fully austenitic sample. However, for fast cooling rate the difference in ferrite fraction for both steels is around 20%. As in steel 12, there is only a small fraction of bainite formed during the transformation for all the cooling rates. It was concluded that the same reasons that hold back the bainitic transformation for steel 12 apply to steel

121 Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 37: Phase fractions for steel 12 annealed at 800ºC for different cooling rates. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 38: Phase fractions for steel 13 annealed at 800ºC for different cooling rates. 4.4 Thermodynamic and DICTRA Calculations In this task, UTH focused on thermodynamic and DICTRA calculations for the two TRIP-steel grades of the project (TRIP-Si and TRIP-Al), so as to obtain the necessary input data for the application of the bainitic transformation kinetic model on these steels, which was subsequently performed in the framework of task 5.1. The standard heat-treatment route applied to cold-rolled TRIP-steel grades comprises of an initial stage of intercritical annealing, immediately followed by isothermal holding in the bainitic temperature range. During the intercritical annealing stage, the initial ferrite-pearlite microstructure of the steel converts to a mixture of austenite and ferrite. It is a large fraction of this austenite, which subsequently transforms to bainite, during the second stage of the heat-treatment, while the rest of the austenite gradually stabilizes, in order to be retained in the final microstructure. The amount of austenite that forms during the intercritical annealing stage depends on the temperature level and the temporal duration of the annealing. The temporal duration of the annealing is usually short, in the order of sec, whereas the temperature is kept within the (α+γ) phase field. Transformation of the initial microstructure of the steel, which consists of pearlite and proeutectoid ferrite, is purely diffusional and takes place by the nucleation and growth of austenite, preferably on and/or inside pearlitic colonies. Pearlite dissolves very rapidly, as it transforms to austenite of eutectoid composition with respect to carbon, i.e. austenite with high carbon-content. Due to the very short diffusion distances involved, the conversion of pearlite to high-carbon austenite is considered to be very fast. However, the second stage of austenitization, which involves the further growth of austenite in expense of proeutectoid ferrite grains, is substantially slower and determines the overall rate of austenitization during intercritical annealing. In order to model the kinetics of the bainitic transformation in TRIP-steels, it is necessary to have information regarding the amount and chemical composition of austenite at the end of the intercritical annealing stage and, thus, at the beginning of the bainitic treatment stage. To do so, it is necessary to go one step before, i.e. to model the austenitization process during intercritical annealing. 119

122 Simulation of the austenitization process during intercritical annealing was performed, by setting-up a one-dimensional (1-D) moving-boundary model, of the geometry shown in Figure 103. In this model, pearlite is assumed to transform very fast, producing austenite (fcc) of eutectoid composition. This austenite area is depicted on the left side of Figure 103. Subsequent growth of this initial austenite in expense of proeutectoid ferrite is then simulated, by solving the corresponding diffusion and massbalance equations. As a result, the amount of austenite formed, as well as its chemical composition, can be determined as functions of intercritical annealing temperature and temporal duration. The model was solved by employing DICTRA software and the corresponding thermodynamic/kinetic databases. x fcc proeutectoid bcc direction of fcc/bcc advancing interface 0.86 μm 2 μm Figure 103: Schematic of the 1-D diffusion model for the simulation of austenitization during intercritical annealing. In the simulations, the temporal duration of intercritical annealing was assumed to be 90 sec. In the case of TRIP-Si steel, three different levels of intercritical annealing temperature were selected, i.e. 780 C, 800 C and 820 C. The initial mole fraction of austenite and the initial compositions of austenite (fcc) and proeutectoid ferrite (bcc) were calculated by Thermo-Calc at a temperature T s = 714 C, at which all pearlite has converted to austenite. In the case of TRIP-Al steel, four different levels of intercritical annealing temperature were selected, i.e. 780 C, 800 C, 820 C and 850 C. Once again, the initial mole fraction of austenite and the initial compositions of austenite (fcc) and proeutectoid ferrite (bcc) were calculated by Thermo-Calc at a temperature T s = 731 C, at which all pearlite has converted to austenite in this particular steel. A typical result of such simulation with DICTRA software is depicted in Figure 104, which shows carbon composition profiles in the two phases, as well as the movement of the interface, at different moments during the annealing. As shown, the initial high-carbon austenite region (left-hand side) advances in expense of proeutectoid ferrite (right-hand side), as time elapses. As the volume fraction of austenite increases, its carbon content gradually reduces. 120

123 DICTRA ( : ) : TIME = 10,50, CELL #1 WEIGHT-PERCENT C Figure 104: DISTANCE Calculated C-concentration profiles and position of the fcc/bcc moving boundary at various moments, during intercritical annealing. The results of these simulations are summarized in Table 39 and Table 40, for steels TRIP-Si and TRIP-Al, respectively. The calculated quantities of interest are the vol. fraction and the chemical composition of austenite at the end of the intercritical annealing stage, since they constitute the starting conditions of austenite at the subsequent bainitic treatment stage. As shown in Table 39 for steel TRIP- Si, the amount of austenite formed during intercritical annealing varies from 45 vol.% (780 C) to 65 vol. % (820 C). As expected, the carbon content in austenite also varies significantly with annealing temperature, in contrast to the substitutional elements (Mn, Si). In the case of steel TRIP-Al (Table 40), the amount of austenite formed during intercritical annealing varies from 32 vol.% (780 C) to 46 vol. % (850 C), which is considerably lower than in TRIP-Si steel. 780 o C 800 o C 820 o C Vol. fraction of austenite Mole-fraction C in austenite 2.27E E E-2 Mole-fraction Mn in austenite 2.87E E E-2 Mole-fraction Si in austenite 2.41E E E-2 Table 39: Calculated vol. fraction and chemical composition of austenite in TRIP-Si steel, after intercritical annealing at various temperatures. 121

124 780 o C 800 o C 820 o C 850 o C Vol. fraction of austenite Mole-fraction C in austenite 2.80E E E E-2 Mole-fraction Mn in austenite 2.93E E E E-2 Mole-fraction Al in austenite 1.34E E E E-2 Table 40: Calculated vol. fraction and chemical composition of austenite in TRIP-Al steel, after intercritical annealing at various temperatures. As already reported in task 3.3, also within the framework of this task the appropriate thermodynamic calculations were performed, in order to determine paraequilibrium nucleation driving forces, paraequilibrium compositions of phases, etc, during the bainitic transformation for steels TRIP-Si and TRIP-Al. For these calculations the methodology developed and already reported in detail in task 3.3 was applied, and all the necessary thermodynamic functions were determined for steels TRIP-Si and TRIP-Al. Separate calculations had to be performed for every different intercritical annealing temperature for each steel, due to the different status of the resulting austenite. For example, Figure 105(a)-(c) depicts calculated paraequilibrium driving-force for the nucleation of ferrite in austenite, for the case of steel TRIP-Si intercritically annealed at 780 C, 800 C and 820 C, as a function of bainitic treatment temperature and C-content of austenite. These DICTRA simulations confirm that the influence on the alloying elements with the exception of carbon is low and the assumption of paraequilibrium conditions is therefore justified. In the present case the phase fractions and distribution of the alloying elements is required as starting point for transformation simulations during cooling following the intercritical annealing. Here thermodynamic computations obeying paraequilibrium conditions are usually sufficient and have been applied if not stated otherwise. 122

125 TRIP-Si steel 1000 Intercr. anneal. 780 o C f o γ = ΔG γ->α n, (J/mol) mole fraction C in austenite TRIP-Si steel Temperature, (K) (a) Intercr. anneal. 800 o C f o γ = ΔG γ->αb, (J/mol) n mole fraction C in austenite 1.87e2 3.5e2 5e2 7.5e TRIP-Si steel temperarure (K) (b) 1000 Intercr. anneal. 820 o C f o γ = ΔG γ->αb, (J/mol) n mole fraction C in austenite 1.5e2 3.5e2 5e2 7.5e2 1.0e temperarure (K) Figure 105: (c) Calculated driving-force for the nucleation of bainitic ferrite in paraequilibrium with austenite, for steel TRIP- Si, previously intercritically annealed at (a) 780 C, (b) 800 C and (c) 820 C. 123

126 4.5 Model Development Finite Differences Model For the application on partly transformed microstructures SE-AG modified its implementation of the bainite model in such a way that it would account for a given austenite fraction and adjust the initial austenite carbon content according to equilibrium considerations. SE-AG tested this programme code by simulating the isothermal transformation behaviour for a steel DP-K 34/60. This steel has a composition similar to steel 2. As described in (Table 25), the steel was experimentally investigated with temperature cycles coming starting in the intercritical austenite/ferrite region, cooling down to different testing temperatures, where the isothermal transformation was studied, and quenched at the end. This steel was chosen because the microstructures at the end of intercritical annealing, at the beginning of the isothermal part and at the end of the cycle was known from former metallographic investigations. In the left side of Figure 106 the measured dilations signals presented in Figure 71 have been enriched with the bainite fractions determined by metallographic means (Table 26). If the steel was quenched before the isothermal holding stage, 25-30% of martensite has been determined. The bainite transformation was calculated in the simulation by assuming a carbon distribution between austenite and ferrite corresponding to paraequilibrium at the beginning of the isothermal part considering an initial austenite fraction of 30%. With temperature depending interfacial energy computed as described above and with the parameters given in the right side Figure 106 the model could be fitted by adjusting the initial site density N 0 resulting in the calculated transformation behaviour as given in the right side of Figure 106. The predicted final fractions of bainite correspond well with the results from metallography as given in the left diagram, except for the isothermal holding temperature of 500 C where also the transformation kinetics is somewhat different from the experimental data.. Figure 106: Normalised dilatation signals and bainite fractions determined by metallographic means for the isothermal transformation of a DP-K 34/60 after intercritical annealing (left), simulation parameters and computed bainite fractions using the modified Azuma model and computed interfacial energies (right). The isothermal transformation temperatures are given in C. 124

127 In Figure 107 the experimental data are given as false colour plot and are overlaid with a plot of isofractions for bainitic ferrite (solid blue) and the cementite fraction precipitated out of austenite (dashed green). In this case the effect of a higher initial nucleation density of N 0 =2e 17 m -1 has been investigated. This plot shows that the model predicts a carbide precipitation between 350 and 450 C that starts after about 100s isothermal holding. Figure 107: Isothermal transformation behaviour of DP-K34/60 as TTT-plot. The measured dilatation in Figure 106 is given as a false colour plot, the simulation results (N 0 =2e 17 m -1 ) as lines of isofractions. The solid blue lines denote the bainitic ferrite fractions, the dashed green lines the cementite precipitation out of austenite. Figure 108 gives an example of continuous cooling simulations. The bainite transformation for steel 2 (DP, Si) has been computed for the measured cooling curves. The only changing parameters passed to the model have been the cooling curve and the according austenite fraction in order to consider the prior transformations. Further, on basis of the austenite composition predicted by the bainite model the martensite start temperature has been estimated and plotted as well. Overall the computed transformation agrees very well with the measurement data. The bainite start temperature, indicated by the red line, respective the bainite fraction denoted by the red numbers, are in a fairly good agreement with the according measured data drawn in black. The same procedure as for steel 2 has been repeated for steel 3 (TRIP, Al) in Figure 109. As for the steel 2 a good agreement of the computational results with the measured data can be observed. These tests show again that the extended Azuma model in principle works with inhomogeneous starting conditions when the situation at the beginning of the bainite transformation is known. 125

128 Figure 108: 1000 Continuous Cooling Transformation chart for steel 2 (DP, Si). Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The red figures indicate the computed bainite fractions. The green line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model. ATU - Steel 3 TRIP, Al: N0 2.00e Temperature [ C] t8/5-time [s] Figure 109: Measured continuous cooling transformation chart of Steel 3 (TRIP, Al), overlaid with simulation results.. Black lines and figures refer to the measured data. The red line denotes the bainite start temperature and was computed by passing the measured ferrite fractions to the bainite model. The bracketed red figures indicate the computed bainite fractions. The blue line indicates the computed martensite start temperature, based on the chemical composition of austenite as predicted by the bainite model. 126

129 4.5.2 Cellular Automaton Model With the purpose of obtaining a better approximation of the kinetics of the transformation and the final microstructure, a model was developed at CEIT in order to introduce microstructural features obtained directly from metallographic characterization into the CA model. The motivation to develop this approach came from the realization that to accurately model the transformation from austenite into ferrite, bainite, martensite, or cementite special attention must be taken regarding initial conditions. For transformations where the initial system is not homogeneous, i.e. intercritical annealing conditions, additional information must be introduced into the model. The framework developed in WP3 requires an initial austenite grain size distribution. Carbon is homogeneously distributed in the matrix before the ferrite transformation begins. During intercritical annealing conditions, carbon is heterogeneously distributed in the matrix and the presence of ferrite grains alters the possible nucleation sites, so the initial carbon distribution, the ferrite grain distribution and the austenite grain size distribution must be known beforehand. The essence of the model developed is shown in Figure 110. The first step is to obtain a metallographic sample with the initial conditions required. Figure 110a shows a sample from steel 12 annealed at 750ºC for 60s and then quenched with helium at 170K/s. The specimen consists of ferrite and martensite. Figure 110: a. Microstructure obtained by LOM. b. Pictorial view of the segmentation matrix. c. Carbon distribution profile after annealing. d. Recrystallized ferrite grains. Using image analysis software, a section of the sample consistent with the scale used in the discretization is selected and segmented into its product phases. The resulting image is transformed into 127

130 a matrix containing grayscale values. By applying an intensity threshold, the grayscale matrix is transformed into a matrix consisting only in ones and zeros. The pictorial view of this distribution matrix can be seen in Figure 110b, where the red areas represent ferrite and blue areas the martensite segment. The model takes the distribution matrix and simulates annealing conditions. At the beginning of the simulation carbon is distributed homogeneously throughout the system. During the annealing time, carbon is ejected from the ferrite phase into the austenite phase, increasing gradually its carbon content. During this stage ferrite nucleation or growth is not allowed. The carbon profile obtained is shown in Figure 110c. The ferrite from the distribution matrix is recrystallized into smaller grains consistent with the austenite grain size of the steel selected and the annealing conditions, resulting in the initial ferrite grain distribution. To validate the modeling approach, several simulations were carried out for steels 12 and 13. Emphasis was put less on the correct description of the bainite transformation but the prediction of the overall multiphase microstructure by the CA model, coupling several successive transformations. Distinct microstructures as they have been obtained for steels 12 and 13 are required in order to study the effect of the different compositions and process parameters on the model predictions. The carbon distribution and ferrite grain distributions were obtained once for each annealing temperature. The same initial conditions were used for both isothermal holding and continuous cooling transformations. Figure 111 presents the comparison between the dilatometer curve and the results obtained from the simulation for steel 12 annealed at 750ºC. The initial ferrite volume fraction was selected to match the dilatometer data. For the transformations at 400ºC and 450ºC, the Phase Sum curve shows a good agreement with the dilatometer curve. At 500ºC holding temperature, the model predicts a greater ferrite fraction and the Phase Sum curve has a difference of about 10% with respect to the experimental curve. On the other side this figure also shows a systematic drawback of the modelling approach. Due to the description of the different transformations by overlapping probability functions it is possible that the CA model predicts concurrent ferrite and bainite transformations. The microstructures generated by the model for 450ºC and 500ºC holding temperatures are shown in Figure 112. The morphology of the simulated microstructures reproduces features observed in the real microstructures. For both holding temperatures, the distribution and the fraction of transformation products show good agreement with the experimental results. To test the behaviour of the model for the case of continuous cooling transformations, two more sets of simulations were carried out. The initial conditions for the simulations were obtained from microstructural data from He-quenched samples annealed at 800ºC for steels 12 and 13 using the same framework explained. The initial volume fractions of ferrite were determined to be 4.8% for steel 12 and 15% for steel 13. For steel 12, simulations to study the transformation behaviour of the steel and the one predicted by the model were carried out at 60 K/s, 40 K/s, 10 K/s, and 5 K/s. Figure 113 shows a comparison between the transformation kinetics obtained by dilatometry and those obtained by the model. For 60 K/s and 40 K/s, the ferrite transformation kinetics show different transformation kinetics from those obtained with the dilatometer. However, the phase fraction obtained matches that of the dilatometer signal and the one obtained from microstructural characterization. 128

131 Figure 111: Intercritical annealing simulations at 750ºC for steel 12. a. Isothermal transformation kinetics at 400ºC. b. Isothermal transformation kinetics at 450ºC. c. Isothermal transformation kinetics at 500ºC. Figure 112: Comparison between real and simulated microstructures for steel 12 annealed at 750ºC a-b. 450ºC. c-d. 500ºC. The microstructures generated by the model are shown in Figure 114. A good agreement between the real and simulated microstructures was observed. For the microstructure generated after simulating the 129

132 transformation at a cooling rate of 60 K/s, the ferrite distribution shows a similar pattern to that obtained experimentally. Also, the shape and size of the transformation products show a good approximation. This confirms the hypothesis that the initial conditions are determinant in the evolution of the microstructure. It also proves that the model developed is able to reproduce the final microstructure obtained experimentally when the initial conditions for the simulation are chosen carefully, or as in this modelling approach, directly from real microstructural data. For steel 13 the obtained transformation curves are shown in Figure 115. For this steel, simulations were carried out for six different cooling rates. For 60 K/s and 40 K/s, the Phase Sum curve shows an overall good approximation with the dilatometer curve. The start temperature for each of the different transformation product accurately matches those observed experimentally. The obtained volume fraction for each component phase also agrees with the experimental values. For 20 K/s the dilatometer and the Phase sum curve show a good agreement but the curves appear shifted in time. At the beginning of the transformation the difference is approximately 3s. As the transformation proceeds, the model curve lags behind the dilatometer curve. This can be clearly observed from the time where the martensite transformation begins. A similar behaviour was observed for 10 K/s and 5 K/s curves. This can be due to propagation of numerical errors throughout the simulation in how the model relates each MCS with time. However, this time difference is not as acute in other simulations. Since the model curve is compared to an experimentally obtained curve, the time difference may also be attributed to a combination of error propagation of the measuring equipment and the numerical implementation of the model. The reason for this assumption is that for the 2.5 K/s curve this time difference is not as pronounced. Theoretically, this would be the case where error propagation for the model would be the greatest with respect to the time scaling. Figure 113: Transformation kinetics for continuous cooling transformations for steel 12 annealed at 800ºC. a. 60 K/s. b. 40 K/s. c. 10 K/s. d. 5 K/s. 130

133 Figure 114: Comparison between real and simulated microstructures for continuous cooling simulations for steel 12 annealed at 800ºC. a-b. 60 K/s. c-d 5 K/s. The real and simulated microstructures for 60 K/s and 5 K/s are shown in Figure 116. The model microstructure predicts large ferrite grain sizes with martensite forming where neighbouring ferrite grains meet. This is due to the local increase in carbon content as ferrite grains grow. A similar behaviour was observed in the real microstructures. Due to the band-like structure, martensite was observed between the ferrite bands. At 5 K/s carbon has time to diffuse along the matrix, so the band-like structure is less pronounced. The complete set of results for the transformation products obtained from the isothermal holding simulations for annealing 750ºC is presented in Table 41 for steel 12. For continuous cooling simulations for an annealing temperature of 800ºC, the results are in Table 42 and Table 43 respectively. The comparison of these computed results with the according phase fractions presented in Table 36 for the isothermal holding experiments on steel 12 shows that the ferrite fraction is predicted fairly in all cases, while martensite fraction is underestimated somewhat, for the holding temperature of 400 C this underestimation becomes significant. The predicted bainite fraction is quite reasonable, except for the holding temperature of 500 C where only half of the observed bainite fraction is predicted. In the cases of the continuous cooling experiments, Table 37 and Table 38, the prediction for the higher cooling rates is reasonable, while for the slower cooling rates the bainite fraction is overestimated in case of steel 12. For steel 13 it is the martensite fraction, which becomes more and more overestimated by the model the slower the cooling rate mecomes. 131

134 Figure 115: Transformation kinetics for continuous cooling transformations for steel 13 annealed at 800ºC. a. 60K/s. b. 40K/s. c. 20K/s. d. 10K/s. e. 5K/s. f. 2.5K/s. Holding temperature [ºC] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 41: Steel 12 annealed at 750ºC. Simulation results for isothermal holding transformations. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 42: Steel 12 annealed at 800ºC. Simulation results for continuous cooling transformations. 132

135 Figure 116: Comparison between real and simulated microstructures for continuous cooling conditions for steel 13 annealed at 800ºC. a-b. 60K/s. c-d. 5K/s. Cooling Rate [K/s] Ferrite [%] Bainite [%] Martensite [%] Ret. Austenite [%] Table 43: Steel 13 annealed at 800ºC. Simulation results for continuous cooling transformations. 133