Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms

In this work, we compare finite element and fast Fourier transform approaches for the prediction of the micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases—rolling of aluminum and wire drawing of tungsten—are used to evaluate the predictions of the two models. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison with the fast Fourier transform simulations. Figure 9 was corrected in this article on the 25 August 2009. The corrected electronic version is identical to the print version.

[1]  Dierk Raabe,et al.  Micromechanical and macromechanical effects in grain scale polycrystal plasticity experimentation and simulation , 2001 .

[2]  R. Lebensohn N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform , 2001 .

[3]  Carlos N. Tomé,et al.  Texture and strain localization prediction using a N-site polycrystal model , 2001 .

[4]  A. Rollett,et al.  Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper , 2008 .

[5]  R. A. Lebensohn,et al.  Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations , 2007 .

[6]  H. Wenk,et al.  Texture and Anisotropy , 2004 .

[7]  Hervé Moulinec,et al.  A numerical method for computing the overall response of nonlinear composites with complex microstructure , 1998, ArXiv.

[8]  Yonggang Huang,et al.  A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program , 1991 .

[9]  D. Sulsky Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[10]  Hermann Riedel,et al.  Modeling the evolution of texture and grain shape in Mg alloy AZ31 using the crystal plasticity finite element method , 2009 .

[11]  Yi Liu,et al.  Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals , 2004 .

[12]  J. Michel,et al.  Effective properties of composite materials with periodic microstructure : a computational approach , 1999 .

[13]  P. Dawson,et al.  Polycrystal plasticity modeling of intracrystalline boundary textures , 1999 .

[14]  Hermann Riedel,et al.  Multi-grain finite element model for studying the wire drawing process , 2007 .

[15]  Georges Cailletaud,et al.  Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries , 2005 .

[16]  Pedro Ponte Castañeda Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory , 2002 .

[17]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[18]  Abhishek Bhattacharyya,et al.  Evolution of grain-scale microstructure during large strain simple compression of polycrystalline aluminum with quasi-columnar grains: OIM measurements and numerical simulations , 2001 .

[19]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[20]  Ricardo A. Lebensohn,et al.  A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys , 1993 .

[21]  S. Ahzi,et al.  A new intermediate model for polycrystalline viscoplastic deformation and texture evolution , 2008 .

[22]  D. Jeulin,et al.  Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model , 2001 .

[23]  R. Lebensohn,et al.  Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals , 2009 .

[24]  R. Becker,et al.  Analysis of texture evolution in channel die compression. I, Effects of grain interaction , 1991 .

[25]  A. Molinari,et al.  Deformation modelling of multi-phase polycrystals: case of a quartz-mica aggregate , 1992 .