Modeling of the Grain Shape Effect on the Elastic-Inelastic Behavior of Polycrystals With Self-Consistent Scheme

Based on a well established nonincremental interaction law for fully anisotropic elastic-inelastic behavior of polycrystals, tangent formulation-based and simplified interaction laws of softened nature are derived to describe the nonlinear elastic-inelastic behavior of fcc polycrystals. Using the Eshelby’s tensor, the developed approach considers that the inclusion (grain) form is ellipsoidal. It has been clearly demonstrated by Abdul-Latif et al. (2002, “Elastic-Inelastic Self-Consistent Model for Polycrystals,” ASME J. Appl. Mech., 69, pp. 309–316) for spherical inclusion that the tangent formulation-based model requires more calculation time, and is incapable to describe correctly the multiaxial elastic-inelastic behavior of polycrystals in comparison with the simplified model. Hence, the simplified nonincremental interaction is studied considering the grain shape effect. A parametric study is conducted showing principally the influence of the some important parameters (the grain shape $(α)$ and the new viscous parameter $γ$⁠) and the effect of their interaction on the hardening evolution of polycrystals. Quantitatively, it is recognized that the model describes suitably the grain shape effect together with the new viscous parameter $γ$ on the strain-stress behavior of aluminum and Waspaloy under tensile test.