Efficient fast Fourier transform-based numerical implementation to simulate large strain behavior of polycrystalline materials

Abstract

In this paper, a new full-field numerical framework is proposed to model large strain phenomena in polycrystals. The proposed framework is based on the elasto-viscoplastic (EVP) fast Fourier transform (FFT) formulation presented by Lebensohn et al. (2012) and the rate dependent crystal plasticity framework developed by Asaro and Needleman (1985). In this implementation, the full-field solutions of micromechanical fields are computed on a regular, voxelized representative volume element (RVE) in which either a single or multiple grid points represent a single grain. The Asaro and Needleman (1985) formulation coupled with a semi-explicit, forward gradient time-integration scheme (Peirce et al., 1983) is used to compute local stresses and the FFT-based method is used to find local strain fluctuations at each grid point. The proposed model is calibrated using experimental uniaxial tensile test results of aluminum alloy (AA) 5754 sheet and then used to predict texture evolution and stressstrain response for balanced biaxial tension and plane-strain tension along rolling (RD) and transverse (TD) directions. The predicted stress-strain and texture results show a good agreement with experimental measurements. The CPU time required by the proposed model is compared with the original EVP-FFT model for two separate cases and the proposed model showed significant improvement in computation time (approximately 100 times faster).

Data-driven texture design for nearly-isotropic elastic and plastic properties in titanium-based materials

“…This calculation is repeated for each discretized orientation and for loading along each of the orthogonal directions of x, y, and z. The EVP-FFT model was developed in 28 and has since been extensively used to predict micromechanical behaviors and properties in a vast range of polycrystalline materials [29][30][31][32] , especially in HCPs [33][34][35][36] . The advantage of employing the EVP-FFT technique in this work lies in that it accounts for the material's anisotropic response in the elastic regime through taking anisotropic elastic constants as an input.…”

“…Additionally, let us denote F ⊂ R d the polyhedron which comprises the feasible region of (31). For some vector π π π ∈ F, let J(π π π) = { j : e e e T j π π π = 0} = { j : π j = 0} be the set of the inequalities that are active on π π π.…”

“…Equivalently, for π π π ∈ F to be a vertex of F at least d − 3 inequalities of the form π j ≥ 0, j ∈ [d] must be satisfied with equality. In terms of (31), this implies that for an ODF to be a vertex of F, its sparsity must be k ≤ 3. Now, suppose that (31) has a unique solution.…”

Development of a new consistent discrete green operator for FFT-based methods to solve heterogeneous problems with eigenstrains

“…Heterogeneous materials with eigenstrains or thermal strains were treated with different FFT-based methods (Dreyer et al, 1999;Vinogradov and Milton, 2008;Liu et al, 2012;Anglin et al, 2014;Bertin et al, 2015;Donegan and Rollett, 2015;Graham et al, 2016;Jacques, 2016;Wang et al, 2016). The method was also applied to non-linear composite materials (Moulinec and Suquet, 1998;Michel et al, 2001), rigid-viscoplastic/ elasto-viscoplastic polycrystals (Lebensohn, 2001;Lee et al, 2011;Lebensohn et al, 2011Lebensohn et al, , 2012Suquet et al, 2012), continuum dislocation/ disclination mechanics Brenner et al, 2014;Berbenni et al, 2016;Djaka et al, 2017), deformation twinning (ArulKumar et al, 2015;Mareau and Daymond, 2016), fracture (Herrmann et al, 1999), damage (Spahn et al, 2014), nano-polycrystals (Upadhyay et al, 2016), non local polycrystal plasticity (Lebensohn and Needleman, 2016) and finite deformation (Lahellec et al, 2003;Eisenlohr et al, 2013;Shanthraj et al, 2015;DeGeus et al, 2017;Nagra et al, 2017;Vidyasagar et al, 2018).…”

Derivation of Higher-Order Terms in FFT-Based Numerical Homogenization

“…This idea has been introduced by Boutin [2], and we discuss here the algorithmic treatment in a unified framework. For the state-of-the-art in FFT-based numerical homogenization, we mention the work on augmented Lagrangians [13], the variational scheme based on the Hashin-Shtrikman energy principle [3,4,8], the polarization scheme [14,15], and the extension to nonlinear problems [5], elasto-plasticity [20], elasto-viscoplasticity [6], and large strains in polycrystals [18].…”