Anisotropic elasto-plastic finite element analysis using a stress–strain interpolation method based on a polycrystalline model

Abstract

This paper describes a stress-strain interpolation method to model the macroscopic anisotropic elasto-plastic behavior of polycrystalline materials. Accurate analytical descriptions of yield loci derived from crystallographic texture [Int. J. Plasticity 19 (2003) This identification method depends on the crystallographic texture and should be applied each time that the plastic strain has induced a significant texture evolution. The stress-strain interpolation method accurately describes the anisotropic material behavior in a narrow stress direction defined by only five stress points. The cost of texture updating is then greatly reduced compared to a full analytical function of the yield locus. After the mathematical description of the stress-strain interpolation method, its validity is demonstrated on two non-radial strain paths. The simulations of a deep drawing experiment allow comparing model predictions and measurements. Accuracy and CPU time of the interpolation stress-strain method are judged against two other models, respectively based on a complete analytical yield locus and on the averaging of crystallite stresses.

Analysis of Texture Evolution and Hardening Behavior during Deep Drawing with an Improved Mixed Type FEM Element

“…Figure 2 presents the earing profile computed with the micro-macro Minty constitutive law [2]. The computation of texture evolution has been activated (curves called "Evol") or not, i.e.…”

“…These models are indeed very similar: they are both based on Taylor's model using initial texture, coupled with identical Swift (isotropic) and Teodosiu (mixed) hardening models. The main difference is the definition of the yield locus (see [2] and [1]). When texture evolution was computed throughout the simulation, a large effect of the hardening model was noticed.…”

“…"Minty" texture based yield locus [2] coupled with the microstructural Teodosiu and Hu hardening model [3, 4,5] were investigated. A particular attention was paid to their implementation in the self-made FE code LAGAMINE (developed at the M&S department since 1984; see [6,7] for some applications of this code).…”

Deep Drawing Simulations With Different Polycrystalline Models

“…It uses a linear stress-strain interpolation described by equation (1). τ =⋅• sCu (1) In this equation, σ is a 5-D vector containing the deviatoric part of the stress; the hydrostatic part being elastically computed according to Hooke's law. The 5-D vector u is the deviatoric plastic strain rate direction; it is a unit vector.…”

“…In order to take all these features into account during FEM simulations, the combination of a texture based yield locus (see [1]) and the Teodosiu's hardening model (see [2]) has been implemented in the FE code LAGAMINE (developed at the M&S department of the University of Liège).…”