A multiscale perspective on the kinetics of solid state transformations with application to bainite formation

Claas Hüter; Mingxuan Lin; Diego Schicchi; Martin Hunkel; Ulrich Prahl; Robert Spatschek; Claas Hüter; Mingxuan Lin; Diego Schicchi; Martin Hunkel; Ulrich Prahl; Robert Spatschek

doi:10.3934/matersci.2015.4.319

AIMS Materials Science

2015, Volume 2, Issue 4: 319-345. doi: 10.3934/matersci.2015.4.319

Previous Article Next Article

Research article Special Issues

A multiscale perspective on the kinetics of solid state transformations with application to bainite formation

1.
Max-Planck Institut für Eisenforschung GmbH, 40237 Düsseldorf, Germany;
2.
RWTH Aachen University, Department of Ferrous Metallurgy, 52056 Aachen, Germany;
3.
IWT Stiftung Institut für Werksto technik, 28359 Bremen, Germany;
4.
Forschungszentrum Jülich, Institute of Energy and Climate Research, 52425 Jülich, Germany

Received: 29 May 2015 Accepted: 27 August 2015 Published: 17 September 2015

We give an excerpt of recent developments in the experimentally benchmarked modeling of bainite formation in the press hardening process. As the press hardening process poses a heavily multi-parameter dependent modeling challenge, we focus on three main branches which complement each other. We emphasise the combination of basic sharp interface and phase field models with pragmatically adapted multi phase field models and experimentally parametrized implementations of the Johnson-Mehl-Avrami model. In the basic thermodynamic modeling part, we review fundamental aspects of displacive and diffusional-displacive transformations to predict dominant transformation morphologies. These results provide a link to multi-phase-field implementations which allow to simulate isothermal bainitic transformations, supported by available material data from thermodynamic databases. Excellent agreement with experiments, e.g. scanning electron microscopy for the transformed bainite in the high-carbon steel 100Cr6 shows the value of these model implementations. The further connection to Johnson-Mehl-Avrami models offers to extend the understanding to transformation plasticity for the press hardening steel 22MnB5.
- bainite formation,
- press hardening,
- phase field modeling,
- elasticity,
- transformation plasticity
Citation: Claas Hüter, Mingxuan Lin, Diego Schicchi, Martin Hunkel, Ulrich Prahl, Robert Spatschek. A multiscale perspective on the kinetics of solid state transformations with application to bainite formation[J]. AIMS Materials Science, 2015, 2(4): 319-345. doi: 10.3934/matersci.2015.4.319

Related Papers:

Abstract

We give an excerpt of recent developments in the experimentally benchmarked modeling of bainite formation in the press hardening process. As the press hardening process poses a heavily multi-parameter dependent modeling challenge, we focus on three main branches which complement each other. We emphasise the combination of basic sharp interface and phase field models with pragmatically adapted multi phase field models and experimentally parametrized implementations of the Johnson-Mehl-Avrami model. In the basic thermodynamic modeling part, we review fundamental aspects of displacive and diffusional-displacive transformations to predict dominant transformation morphologies. These results provide a link to multi-phase-field implementations which allow to simulate isothermal bainitic transformations, supported by available material data from thermodynamic databases. Excellent agreement with experiments, e.g. scanning electron microscopy for the transformed bainite in the high-carbon steel 100Cr6 shows the value of these model implementations. The further connection to Johnson-Mehl-Avrami models offers to extend the understanding to transformation plasticity for the press hardening steel 22MnB5.

References

[1]	Smith CS (1960) A History of Metallography, University of Chicago Press.
[2]	Fielding L (2013) The bainite controversy. Mater Sci Techn 29:383–399. doi: 10.1179/1743284712Y.0000000157
[3]	van Bohemen S, Siemtsma J (2008) Modeling of isothermal bainite formation based on nucleation kinetics. Int J Mat Res 99:739–747. doi: 10.3139/146.101695
[4]	Gaude-Fugarolas D, Jacques PJ (2006) A new physical model for the kinetics of the bainite transformation. ISIJ Inter 46:712–717. doi: 10.2355/isijinternational.46.712
[5]	Rees GI, Bhadeshia H (1992) Bainite transformation kinetics Part 1: Modified model. Mater Sci Techn 8:985–993. doi: 10.1179/mst.1992.8.11.985
[6]	Tzeng TC (2000) Autocatalysis in bainite transformations. Mater Sci Eng A 293:185–190. doi: 10.1016/S0921-5093(00)01221-1
[7]	Zolotoresvky N, Nesterova E, Titovets Y, et al. (2013) Modeling the effect of austenite deformation on the bainite structure parameters in low carbon microalloyed steels. Int J Mat Res 104:337–343. doi: 10.3139/146.110872
[8]	Hunkel M, Lübben T, Hoffmann F, et al. (1999) Modellierung der bainitischen und perlitischen Umwandlung bei Stählen. HTM Härterei-Techn Mitt 54:365–373.
[9]	Quidort D, Brechet YJM (2002) A model of isothermal and non isothermal transformation kinetics of bainite in 0.5% C steels. ISIJ Inter 42:1010–1017.
[10]	Maier H-J, Ahrens U (2002) Isothermal bainitic transformation on low alloy steels: factors limiting prediction of the resulting material’s properties. Z Metallk 93:712–718. doi: 10.3139/146.020712
[11]	Freiwillig R, Kudrman J, Chraska P (1976) Bainite transformation in deformed austenite. Metall Trans A 7:1091–1097. doi: 10.1007/BF02656591
[12]	Holzweissig M, Canadinc D, Maier H-J (2012) In-situ characterization of transformation plasticity during an isothermal austenite-to-bainite phase transformation. Mater Char 65:100–108. doi: 10.1016/j.matchar.2012.01.007
[13]	Su T, Veaus M, Aeby-Gautier E, et al. (2003) Effect of tensile stresses on bainitic isothermal transformation. J Phys IV France 112:293–296. doi: 10.1051/jp4:2003886
[14]	Su T, Aeby-Gautier E, Denis S (2006) Morphology changes in bainite formed under stress. Scripta Mater 54:2185–2189. doi: 10.1016/j.scriptamat.2006.02.031
[15]	Hase K, Garcia-Mateo C, Bhadeshia H (2004) Bainite Formation influenced by large stress. Mater Sci Techn 20:1499–1505. doi: 10.1179/026708304X6130
[16]	Kundu S, Hase K, Bhadeshia S (2007) Crystallographic texture of stress affected bainite. Proc Royal Soc A 463:2309–2328. doi: 10.1098/rspa.2007.1881
[17]	Fuijiwara K, Okaguchi S, Ohtani H (1995) Effect of hot deformation on bainite structure in low carbon steels. ISIJ Inter 15:1006–1012.
[18]	Min J, Lin J, Min Y, et al. (2012) On the ferrite and bainite transformation in isothermally deformed 22MnB5 steels. Mater Sci Eng A 550:375–387. doi: 10.1016/j.msea.2012.04.091
[19]	Nikravesh M, Naderi M, Akbari GH (2012) Influence of hot plastic deformation and cooling rate on martensite and bainite start temperatures in 22MnB5 steel. Mater Sci Eng A A 540:24–29. doi: 10.1016/j.msea.2012.01.018
[20]	Karbasian H, Tekkaya AE (2010) A review on hot stamping. J Mat Proc Tech 210:2103. doi: 10.1016/j.jmatprotec.2010.07.019
[21]	Feuser P, Schweiker T, Merklein M (2011) Partially hot-formed parts from 22MnB5 - process window. ICTP Aachen 10:408.
[22]	Chen L (2002) Phase fields models for microstructure evolution. Annu Rev Mater Res 32:113. doi: 10.1146/annurev.matsci.32.112001.132041
[23]	Wang Y, Jin YM, Khachaturyan AG (2004) The effects of free surfaces on martensite microstructures: 3D phase field microelasticity simulation study. Acta Mat 52:1039. doi: 10.1016/j.actamat.2003.10.037
[24]	Micress microstructure evolution simulation software, www.micress.de.
[25]	Loginova I, Agren J, Amberg G (2004) On the formation ofWidmanstätten ferrite in a binary Fe-C phase-field approach. Acta Materialia 52:4055–4063. doi: 10.1016/j.actamat.2004.05.033
[26]	Song W, Prahl U, Bleck W, et al. (2011) Phase field simulations of bainitic phase transformation in 100Cr6. Supplemental proceedings: Materials Fabrication, Properties, Characterization, and Modeling 2:417–425.
[27]	Song W (2014) Characterization and simulation of bainite transformation in high carbon bearing steel 100Cr6, PhD thesis RWTH Aachen University.
[28]	Arif T, Qin R (2013) A phase field model for bainitic transformation. Computational Materials Science 77:230–235. doi: 10.1016/j.commatsci.2013.04.044
[29]	Arif T, Qin R (2014) A phase field model for the formation of martensite and bainite. Advanced materials research 922:31–36. doi: 10.4028/www.scientific.net/AMR.922.31
[30]	Qin R, Bhadeshia H (2009) Phase field model to study the effect of interface anisotropy on the crystal morphological evolution of cubic metals. Acta Materialia 57:2210–2216. doi: 10.1016/j.actamat.2009.01.024
[31]	Bhadeshia H (1987)Worked examples in the geometry of crystals, Institute of metals, London and Brookfield.
[32]	Bouville M, Ahluwalia R (2006) Interplay between diffusive and displacive phase transformations: Time-Temperature-Transformation diagrams and microstructures. Phys Rev Lett 97:055701. doi: 10.1103/PhysRevLett.97.055701
[33]	Kundin J, Raabe D, Emmerich H (2011) A phase field model for incoherent martensitic transformations including plastic accommodation processes in the austenite. Journal of the mechanics and physics of solids 59:2082–2102. doi: 10.1016/j.jmps.2011.07.001
[34]	Kundin J, Pogorelov E, Emmerich H (2015) Numerical investigation of the interaction between the martensitic transformation front and the plastic strain in austenite. Journal of the mechanics and physics of solids 76:65–83. doi: 10.1016/j.jmps.2014.12.007
[35]	Levitas V, Javanbakht M (2013) Phase field approach to interaction of phase transformation and dislocation evolution. Applied Physics Letters 102:251904. doi: 10.1063/1.4812488
[36]	Roters F, Eisenlohr P, Hantcherli L, et al. (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite element modeling: Theory, experiments, applications. Acta Materialia 58:2210–2216.
[37]	Johnson W, Mehl R (1939) Reaction kinetics in process of nucleation and growth. Trans AIME 135:416–458.
[38]	Avrami M (1941) Kinetics of phase change III: granulation, phase change and microstructure. J Chem Phys 9:177–184. doi: 10.1063/1.1750872
[39]	Lee G, Kim S, Han H (2009) Finite element investigations for the role of transformation plasticity on springback in hot press forming process. Comp Mater Sci 47:556567.
[40]	HunkelM(2012) Anisotropic transformation strain and transformation plasticity: two corresponding effects. Mat -wiss u Werkstofftech. 43:150–157.
[41]	Lütjens J, Hunkel M (2013) The influence of the transformation plasticity effect on the simulation of partial press-hardening. Proc 4th Int Conf CHS2 319–327.
[42]	Brener EA, Marchenko VI, Spatschek R (2007) Influence of strain on the kinetics of phase transitions in solids. Phys Rev E 75:041604. doi: 10.1103/PhysRevE.75.041604
[43]	Fratzl P, Penrose O, Lebowitz JL (1999) Modelling of Phase Separation in Alloys with Coherent Elastic Misfit. J Stat Phys 95:1429. doi: 10.1023/A:1004587425006
[44]	Freund L (1998) Dynamic fracture mechanics, Cambridge University Press.
[45]	Spatschek R, Brener E, Karma A (2011) Phase field modeling of crack propagation. Phil Mag 91:75. doi: 10.1080/14786431003773015
[46]	Chien FR, Clifton RJ, Nutt SR (1995) Stress-induced phase transformation in single crystal titanium carbide. J Am Ceram Soc 78:1537. doi: 10.1111/j.1151-2916.1995.tb08849.x
[47]	Spatschek R, Müller-Gugenberger C, Brener E A, et al. (2007) Phase field modelling of fracture and stress-induced phase transitions. Phys Rev E 75:066111. doi: 10.1103/PhysRevE.75.066111
[48]	Spatschek R, Eidel B (2013) Driving forces for interface kinetics and phase field models. Int J Solid and Structures 50:2424. doi: 10.1016/j.ijsolstr.2013.03.016
[49]	Steinbach I (2011) Phase field models in materials science. Modelling and Simulation in Materials Science and Engineering 17:073001.
[50]	Steinbach I, Shchyglo O (2011) Phase field modelling of microstructure evolution in solids: Perspectives and challenges. Current opinion in solid state and materials science 15:87. doi: 10.1016/j.cossms.2011.01.001
[51]	Rao M, Sengupta S (2003) Nucleation of solids in solids: ferrite and martensite. Phys Rev Lett 91:045502. doi: 10.1103/PhysRevLett.91.045502
[52]	Brener EA, Iiordanskii SV, Marchenko VI (1999) Elastic effects on the kinetics of a phase transition. Phys Rev Lett 82:1506. doi: 10.1103/PhysRevLett.82.1506
[53]	Brener EA, Boussinot G, Hüter C, et al. (2009) Pattern formation during diffusional transformations in the presence of triple junctions and elastic effects. J Phys Cond Mat 21:464106. doi: 10.1088/0953-8984/21/46/464106
[54]	Pilipenko D, Brener EA, Hüter C (2008) Theory of dendritic growth in the presence of lattice strain. Phys Rev E 78:060603. doi: 10.1103/PhysRevE.78.060603
[55]	Ivantsov GP (1947) PhD thesis Akad. Nauk. SSSR.
[56]	Steinbach I, Pezzolla F (1999) A generalized field method for multiphase transformations using interface fields. Physica D: Nonlinear Phenomena 134:385–393. doi: 10.1016/S0167-2789(99)00129-3
[57]	Song W, von Appen J, Choi P, et al. (2013) Atomic-scale investigation of epsilon and theta precipitates in bainite in 100Cr6 bearing steel by atom probe tomography and ab initio calculations. Acta Materialia 61(20):7582–7590.
[58]	Eiken J, Boettger B, Steinbach I (2006) Multi-phase-field approach for multi-component alloys with extrapolation scheme for numerical application. Phys Rev E 73:066122. doi: 10.1103/PhysRevE.73.066122
[59]	Steinbach I, Pezzolla F, Prieler R (1995) Grain selection in faceted crystal growth using the phase field theory. In: The 7th conference on on modeling of casting, welding and advanced solidification processes.
[60]	Lukas H, Fries S, Sundman B (2007) Computational thermodynamics: The CALPHAD method, Cambridge University Press.
[61]	Rees GI, Shipway PH (1997) Modelling transformation plasticity during the growth of bainite under stress. Materials Science and Engineering A 223:168–178. doi: 10.1016/S0921-5093(96)10478-0
[62]	Wolff M, Böhm M, Dalgic M, et al. (2008) Evaluation of models for TRIP and stress-dependent transformation behavior for the martensitic transformation of the steel 100Cr6. Comput Mater Sci 43:108114.
[63]	Denis S (1997) Considering stress-phase transformation interaction in the calculation of heat treatment residual stresses. Series: International Centre for Mechanical Sciences 368:293–317.
[64]	Leblond J, Deveaux JC (1989) Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases. Int J Plasticity 5:551–572. doi: 10.1016/0749-6419(89)90001-6
[65]	Fisher FD, Sun QP, Tanaka K (1996) Transformation-induced plasticity. Appl Mech Rev 49:317364.
[66]	Leblond JB, Deveaux J (1984) A new kinetic model for anisothermal metallurgical transformation in steels including effect of austenite grain size. Acta Metallurgica 32:137146.
[67]	ASTM International standard test methods for tension testing of metallic materials (2011). Available from: www.astm.org.
[68]	HunkelM(2009) Anisotropic transformation strain and transformation plasticity: two corresponding effects. Mat -wiss u Werkstofftech. 40(5-6):466–472.
[69]	Devaux J, Leblond JB, Bergheau JM (2000) Numerical study of the plastic behaviour of a low alloy steel during phase transformation. Journal of Shanghai Jiaotong University 3:206–212.
[70]	Zwigl P, Dunand DC (1997) A non-linear model for internal stress superplasticity. Acta Materialia 45(12):5285–5294.
[71]	Schicchi DS, Hunkel M (2015) Transformation plasticity effect during bainite transformation on a 22MnB5 Steel Grade. IDE 2015, Bremen, Germany.

Reader Comments

Your name:*

Email:*
© 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)