Anisotropic dilatation during phase transformation in steels can be caused by banded microstructure. As well as the directionality in mechanical properties, the anisotropic transformation strain can result in distortion and dimension change of the products. Hence, mechanical assessment of this phenomenon is of great importance. In this paper, a numerical approach using Crystal Plasticity Fast Fourier Transform (CPFFT) has been developed and used, reproducing the anisotropic transformation stain during heating (experimental results are reported in Part 1). It was confirmed by the numerical simulation that the banded microstructure in microstructure can be one of the most important reasons for the anisotropy of transformation strain.
InoueT, WangZG, MiyaoK.simulation of quenching process of carburized steel gear wheel under metallo-thermo-mechanical coupling Elsevier science publishers, Paris, B. V. North-Holland. Proc. IUTAM Thermomec. Coupling in Solids, 1987-5:257–262.
2.
JuD.Y, ZhangW.M, ZhangY.Modeling and experimental verification of martensitic transformation plastic behavior in carbon steel for quenching process. Mater Sci Eng A. 2006;438-440:246–250. Heat Treating 2000: Proc. of the 20th Conference (ASM International). 2000. doi: 10.1016/j.msea.2006.01.125
3.
Montalvo-UrquizoJ, LiuQ, SchmidtA.Simulation of quenching involved in induction hardening including mechanical effects. Comp Mater Sci. 2013;79:639–649. doi: 10.1016/j.commatsci.2013.06.058
4.
InoueT, OkamuraK.Material Database for Simulation of Metallo-Thermo-Mechanical Field.
5.
KopTA, SietsmaJ, van der ZwaagS.Anisotropic dilatation behaviour during transformation of hot rolled steels showing banded structure. Mater Sci Technol. 2001;17:1569–1574. doi: 10.1179/026708301101509629
6.
SiweckiT, KozielT, HutchinsonB, Effect of micro-segregation on phase transformation and residual stress. Mater Sci Forum. 2007;539-543:4596–4601. doi: 10.4028/www.scientific.net/MSF.539-543.4596
7.
JaramilloRA, LuskMT, MatayaMC.Dimensional anisotropy during phase transformations in a chemically banded 5140 steel. part I: experimental investigation. Acta Mater. 2004;52:851–858. doi: 10.1016/j.actamat.2003.11.017
8.
LeblondJB, MottetG, DevauxDC.A theoretical and numerical approach to the plastic behaviour of steels during phase transformations-I. derivation of general relations. J Mech Phys Solid. 1986;34(4):395–409. doi: 10.1016/0022-5096(86)90009-8
9.
BarbeF, QueyR, TalebL.Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei. Eur J Mech A Solid. 2007;26:611–625. doi: 10.1016/j.euromechsol.2006.09.005
10.
BarbeF, QueyR, TalebL, Numerical modelling of the plasticity induced during diffusive transformation. An ensemble averaging approach for the case of random arrays of nuclei. Eur J Mech A Solids. 2008;27:1121–1139. doi: 10.1016/j.euromechsol.2008.01.005
11.
BarbeF, QueyR.A numerical modelling of 3D polycrystal-to-polycarystal diffusive phase transformations involving crystal plasticity. Int J Plast. 2011;27:823–840. doi: 10.1016/j.ijplas.2010.09.008
12.
ConnollyDS, KoharCP, MishraRK, A new coupled thermomechanical framework for modeling formability in transformation induced plasticity steels. Int J Plast. 2018;103:39–66. doi: 10.1016/j.ijplas.2017.12.008
13.
MackerleJ.Finite element analysis and simulation of quenching and other heat treatment processes. Comput Mater Sci. 2003;27(3):313–332. doi: 10.1016/S0927-0256(03)00038-7
14.
MoulinecH, SuquetP.A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng. 1998;157:69–94. doi: 10.1016/S0045-7825(97)00218-1
EisenlohrP, DiehlM, LebensohnRA, A spectral method solution to crystal elasto-viscoplasticity at finite strains. Int J Plast. 2013;46:37–53. doi: 10.1016/j.ijplas.2012.09.012
17.
OtsukaT, BrennerR, BacroixB.FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation. Int J Eng Sci. 2018;127:92–113. doi: 10.1016/j.ijengsci.2018.02.008
18.
LeeS.-B, LebensohnRA, RollettAD.Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transfroms. Int J Plast. 2011;27:707–727. doi: 10.1016/j.ijplas.2010.09.002
19.
LebensohnRA, KanjarlaAK, EisenlohrP.An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int J Plast. 2012;32-33:59–69. doi: 10.1016/j.ijplas.2011.12.005
20.
AsaroRJ, RiceJR.Strain localization in ductile single crystals. J Mech Phys Solid. 1977;25:309–338. doi: 10.1016/0022-5096(77)90001-1
21.
AsaroRJ.Geometrical effects in the inhomogeneous deformation of ductile single crystals. Acta Metall. 1979;27:445–453. doi: 10.1016/0001-6160(79)90036-1
22.
PeirceD, AsaroRJ, NeedlemanA.An analysis of non-uniform and localized deformation in ductile single crystals. Acta Metall. 1982;30(6):1087–1119. doi: 10.1016/0001-6160(82)90005-0
23.
PeirceD, AsaroJ, NeedlemanA.Material rate dependence and localized deformation in crystalline solids. Acta Metall. 1983;31(12):1951–1976. doi: 10.1016/0001-6160(83)90014-7
24.
AsaroRJ, NeedlemanA.Texture development and strain hardening in rate dependent polycrystals. Acta Metall. 1985;33(6):923–953. doi: 10.1016/0001-6160(85)90188-9
25.
HutchinsonJW.Bounds and self-consistent estimates for creep of polycrystalline materials. Proc Roy Soc A. 1976;348:101–127. doi: 10.1098/rspa.1976.0027
26.
PanJ, RiceJR.Rate sensitivity of plastic flow and implications for yield-surface vertices. Int J Solids Struct. 1983;19(11):973–987. doi: 10.1016/0020-7683(83)90023-9
27.
ZhangD, LiS.A rate-dependent crystal plasticity analysis of orientation stability in biaxial tension of magnesium. J Mater Sci Technol. 2011;27:175–182. doi: 10.1016/S1005-0302(11)60045-5
28.
KurodaM, TvergaardV.Shear band development predicted by a non-normality theory of plasticity and comparison to crystal plasticity predictions. Int J Solids Struct. 2001;38:8945–8960. doi: 10.1016/S0020-7683(01)00166-4
29.
HamaT, KubokiA, TakudaH.Crystal-plasticity finite-element analysis of anisotropic deformation behavior in a commercially pure titanium grade 1 sheet. Int J Plast. 2017;91:77–108. doi: 10.1016/j.ijplas.2016.12.005
30.
HutchinsonJW.Elastic-plastic behaviour of polycrystalline metals and composites. Proc R Soc A: Math Phys Eng Sci. 1970;319:247–272. doi: 10.1098/rspa.1970.0177
31.
GreenwoodGW, JohnsonRH.The deformation of metals under small stresses during phase transformations. Proc R Soc A: Math Phys Eng Sci. 1965;283:403–422. doi: 10.1098/rspa.1965.0029
