×

FFT-based micromechanical simulations of transformation plasticity. Comparison with a limit-analysis-based theory. (English) Zbl 1478.74012

Summary: This work addresses the numerical simulation of transformation plasticity by using a numerical scheme based on the fast Fourier transform (FFT). A two-phase material with isotropic thermo-elastoplastic phases is considered. Together with prescribed transformation kinetics, this permits to describe the plasticity induced by the accommodation of the volume change accompanying the phase transformation (Greenwood-Johnson mechanism). We consider random distributions of \(\alpha\)-phase nuclei within a homogeneous \(\gamma\)-phase matrix, with an isotropic growth law of the nuclei. The numerical results are compared to a recently proposed limit-analysis-based theory [Y. El Majaty et al., “A novel treatment of Greenwood-Johnson’s mechanism of transformation plasticity – case of spherical growth of nuclei of daughter-phase”, J. Mech. Phys. Solids 121, 175–197 (2018; doi:10.1016/j.jmps.2018.07.014)], which permits in particular to account for a nonlinear dependence of the “transformation plastic strain” with the stress applied. A very good agreement between the FFT simulations and the theory is obtained, for uniaxial and multiaxial loadings, over a wide range of stresses applied.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74N99 Phase transformations in solids
74S25 Spectral and related methods applied to problems in solid mechanics
74F05 Thermal effects in solid mechanics

Software:

Neper
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Barbe, F.; Quey, R., A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity, Int. J. Plast., 27, 6, 823-840 (2011) · Zbl 1453.74069
[2] Barbe, F.; Quey, R.; Taleb, L., Numerical modelling of the plasticity induced during diffusive transformation. Case of a cubic array of nuclei, Eur. J. Mech. A, 26, 4, 611-625 (2007) · Zbl 1261.74007
[3] Barbe, F.; Quey, R.; Taleb, L.; de Cursi, E. S., 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, 27, 6, 1121-1139 (2008) · Zbl 1151.74399
[4] Brenner, R.; Lebensohn, R.; Castelnau, O., Elastic anisotropy and yield surface estimates of polycrystals, Int. J. Solids Struct., 46, 16, 3018-3026 (2009) · Zbl 1167.74367
[5] Cherkaoui, M.; Berveiller, M.; Lemoine, X., Couplings between plasticity and martensitic phase transformation: overall behavior of polycrystalline TRIP steels, Int. J. Plast., 16, 10-11, 1215-1241 (2000) · Zbl 1064.74637
[6] Coret, M.; Calloch, S.; Combescure, A., Experimental study of the phase transformation plasticity of 16MND5 low carbon steel under multiaxial loading, Int. J. Plast., 18, 12, 1707-1727 (2002)
[7] Coret, M.; Calloch, S.; Combescure, A., Experimental study of the phase transformation plasticity of 16MND5 low carbon steel induced by proportional and nonproportional biaxial loading paths, Eur. J. Mech. A, 23, 5, 823-842 (2004) · Zbl 1058.74502
[8] Desalos, Y., Comportement Mécanique et Dilatométrique de l’Austénite Métastable de l’Acier A533IRSID Report 95349401 (1981), Rapport
[9] Diani, J.; Sabar, H.; Berveiller, M., Micromechanical modelling of the transformation induced plasticity (TRIP) phenomenon in steels, Internat. J. Engrg. Sci., 33, 13, 1921-1934 (1995) · Zbl 0899.73462
[10] El Majaty, Y.; Leblond, J.-B.; Kondo, D., A novel treatment of Greenwood-Johnson’s mechanism of transformation plasticity - Case of spherical growth of nuclei of daughter-phase, J. Mech. Phys. Solids, 121, 175-197 (2018)
[11] Fischlschweiger, M.; Cailletaud, G.; Antretter, T., A mean-field model for transformation induced plasticity including backstress effects for non-proportional loadings, Int. J. Plast., 37, 53-71 (2012)
[12] Fukumuto, M.; Yoshizaki, M.; Imataka, H.; Okamua, K.; Yamamoto, K., Three-dimensional FEM analysis of helical gear subjected to the carburized quenching process, J. Soc. Mater. Sci. Japan, 50, 6, 598-605 (2001)
[13] Gallican, V.; Brenner, R., Homogenization estimates for the effective response of fractional viscoelastic particulate composites, Contin. Mech. Thermodyn., 31, 3, 823-840 (2019) · Zbl 1442.74014
[14] Ganghoffer, J.; Denis, S.; Gautier, E.; Simon, A.; Sjostrom, S., Finite element calculation of the micromechanics of a diffusional transformation, (Mechanical Behaviour of Materials VI (1992), Elsevier), 165-170
[15] Greenwood, G. W.; Johnson, R., The deformation of metals under small stresses during phase transformations, Proc. R. Soc. Lond. A, 283, 1394, 403-422 (1965)
[16] Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth: Part I — Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99, 1, 2-15 (1977)
[17] Hill, R., The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, 15, 2, 79-95 (1967)
[18] Kempen, A.; Sommer, F.; Mittemeijer, E., Determination and interpretation of isothermal and non-isothermal transformation kinetics; the effective activation energies in terms of nucleation and growth, J. Mater. Sci., 37, 7, 1321-1332 (2002)
[19] Lebensohn, R. A.; Brenner, R.; Castelnau, O.; Rollett, A. D., Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper, Acta Mater., 56, 15, 3914-3926 (2008)
[20] Lebensohn, R. A.; Kanjarla, A. K.; Eisenlohr, P., An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials, Int. J. Plast., 32, 59-69 (2012)
[21] Leblond, J.-B.; Devaux, J.; Devaux, J., Mathematical modelling of transformation plasticity in steels I: case of ideal-plastic phases, Int. J. Plast., 5, 6, 551-572 (1989)
[22] Lee, S.-B.; Lebensohn, R.; Rollett, A. D., Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier transforms, Int. J. Plast., 27, 5, 707-727 (2011) · Zbl 1405.74012
[23] Magee, C. L.; Paxton, H. W., Transformation Kinetics, Microplasticity and Aging of Martensite in Fe-31 NiTechnical Report (1966), Carnegie Inst. of Tech.: Carnegie Inst. of Tech. Pittsburgh, PA
[24] Mandel, J., Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique, (Applied Mechanics (1966), Springer), 502-509
[25] Miyao, K.; Wang, Z.; Inoue, T., Analysis of temperature, stress and metallic structure in carburized-quenched gear considering transformation plasticity, J. Soc. Mater. Sci. Japan, 35, 399, 1352-1357 (1986)
[26] Monchiet, V.; Charkaluk, E.; Kondo, D., A micromechanics-based modification of the gurson criterion by using eshelby-like velocity fields, Eur. J. Mech. A, 30, 6, 940-949 (2011) · Zbl 1278.74024
[27] Moulinec, H.; Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Engrg., 157, 1-2, 69-94 (1998) · Zbl 0954.74079
[28] Offerman, S.; Van Dijk, N.; Sietsma, J.; Lauridsen, E.; Margulies, L.; Grigull, S.; Poulsen, H.; van der Zwaag, S., Phase transformations in steel studied by 3DXRD microscopy, Nucl. Instrum. Methods Phys. Res. B, 246, 1, 194-200 (2006)
[29] Offerman, S.; Van Wilderen, L.; Van Dijk, N.; Sietsma, J.; Rekveldt, M. T.; Van der Zwaag, S., In-situ study of pearlite nucleation and growth during isothermal austenite decomposition in nearly eutectoid steel, Acta Mater., 51, 13, 3927-3938 (2003)
[30] Otsuka, T., Modélisation Micromécanique de la Plasticité de Transformation dans les Aciers par Homogénéisation Numérique Fondée sur la TFR (2014), Université Paris 13, (Ph.D. thesis)
[31] Otsuka, T.; Brenner, R.; Bacroix, B., FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation, Internat. J. Engrg. Sci., 127, 92-113 (2018) · Zbl 1423.74717
[32] Quey, R.; Dawson, P.; Barbe, F., Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing, Comput. Methods Appl. Mech. Engrg., 200, 17-20, 1729-1745 (2011) · Zbl 1228.74093
[33] Suquet, P.; Moulinec, H.; Castelnau, O.; Montagnat, M.; Lahellec, N.; Grennerat, F.; Duval, P.; Brenner, R., Multi-scale modeling of the mechanical behavior of polycrystalline ice under transient creep, Procedia IUTAM, 3, 76-90 (2012)
[34] Taleb, L.; Cavallo, N.; Waeckel, F., Experimental analysis of transformation plasticity, Int. J. Plast., 17, 1, 1-20 (2001)
[35] Taleb, L.; Petit, S.; Jullien, J.-F., Prediction of residual stresses in the heat affected zone, (J. Phys. IV (Proceedings), Vol. 120 (2004), EDP sciences), 705-712
[36] Taleb, L.; Sidoroff, F., A micromechanical modeling of the Greenwood-Johnson mechanism in transformation induced plasticity, Int. J. Plast., 19, 1821-1842 (2003) · Zbl 1098.74550
[37] Vincent, Y.; Bergheau, J.-M.; Leblond, J.-B., Viscoplastic behaviour of steels during phase transformations, C.-R. Méc., 331, 9, 587-594 (2003)
[38] Weisz-Patrault, D., Multiphase model for transformation induced plasticity. Extended Leblond’s model, J. Mech. Phys. Solids, 106, 152-175 (2017)
[39] Wong, S. L.; Madivala, M.; Prahl, U.; Roters, F.; Raabe, D., A crystal plasticity model for twinning- and transformation-induced plasticity, Acta Mater., 118, 140-151 (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.