Extension of the visco-plastic self-consistent model to account for elasto-visco-plastic behavior using a perturbed visco-plastic approach

We propose a numerically stable and computationally efficient elasto-visco-plastic self-consistent (VPSC) crystal plasticity model, where the effect of elasticity on visco-plasticity is introduced as a perturbation to the visco-plastic regime. The perturbation enters as a fictitious visco-plastic eigen-strain rate and is derived from the elastic inclusion problem. As a consequence, the numerical efficiency of the VPSC model (Lebensohn and Tome 1993 Acta Metall. Mater. 41 2611-2624) is retained, with the added capability of predicting both, elastic and visco-plastic strain components in the grains. The proposed model (VPSC+) is validated by comparing with the self-consistent crystal plasticity model of Lebensohn and Tome (VPSC) (Lebensohn and Tome 1993 Acta Metall. Mater. 41 2611-2624), the elastic-rigid-plastic model (EPSC) of Turner and Tome (1994 Acta Metall. Mater. 42 4143-4153), and the elasto-visco-plastic model (EVPSC) developed by Wang et al (2010 J. Mech. Phys. Solids 58 594-612). The prediction of texture evolution, stress-strain response, strain rate sensitivity, and internal elastic strain evolution were consistent with those of the other models, in simulations of 316 L stainless steel and Mg AZ31 alloy. VPSC+ showed a superior numerical stability and computational speed when compared to EVPSC, and convergence was successfully achieved with relatively large increments. It is claimed that VPSC+ provides an elasto-VPSC constitutive law for polycrystalline metals applicable to simulation of large deformation, and which is numerically efficient for interfacing with finite element codes.