A self-consistent approach describing the strain induced anisotropy: Case of yield surface evolution

The main goal of this work is to describe the evolution (expansion, translation, distortion and rotation) of the yield surface using a recent developed self-consistent model with small strains assumption. In fact, the ellipsoidal inclusion case in the simplified non-incremental interaction scheme has been developed by Abdul-Latif and Radi (2010) [4] showing the dependency of the elasto-inelastic behavior of polycrystals on the grain shape. The concept of yield surface is very important for evaluating the material work-hardening behavior beyond the yield point. Hence, a particular attention is made on the description of initial and subsequent yield surfaces. To show the predictive abilities of this model, these surfaces are simulated and then evaluated as a model response for different values of key model parameters (such as the grain aspect ratio α = a/b where a and b are the half-axes of the grain and the viscous parameter γ) subjected to radial proportional loading. Then, the effect of the two parameters on these surfaces will be discussed. Subsequent yield surfaces showed different proportions of translation, expansion, distortion and rotation. Moreover, the influence of the pre-loading nature on the subsequent yield surface evolution and its rotation will be then examined under three different loading conditions of tension, torsion, and combined tension–torsion proportional loading path. Some granular responses for pre-selected grains are also illustrated and discussed.