Non-Schmid Effects on the Behavior of Polycrystals with Applications to Ni3AI

The elastoviscoplastic single crystal constitutive model incorporating non-Schmid effects developed by Dao and Asaro (Mater. Sci. Eng. A, 1993, vol. 170, pp. 143-60) is introduced into Asaro and Needleman's (Acta Metall., 1985, vol. 33, pp. 923-53) Taylor-like polycrystal model as well as Harren and Asaro's (J. Mech. Phys. Solids, 1989, vol. 37, pp. 191-232) finite element polycrystal model. The single crystal non-Schmid effects, strain hardening, latent hardening, and rate sensitivity, are all described on the individual slip system level, while polycrystal mechanical properties on macroscale are predicted. In general, it is found that non-Schmid effects can have important influences on the "constant offset plastic strain yield surfaces," stress-strain behavior, texture development, and shear band formation. Finite element calculations show that with moderate non-Schmid effects, localized deformation within a polycrystal aggregate tends to initiate earlier and form sharper and more intense shear bands. Heavy shear banding is found to produce less pronounced textures, which is consistent with existing experimental evidence on Ni3A1. Examples with Ni3A1 demonstrate that the kind of non-Schmid effects existing in Ni3A1 can increase the generalized Taylor factor to values much higher than 3.06, raise the polycrystal strain hardening rate much higher than that which would be obtained using Schmid's rule, and influence the deformation texture.