Localized deformation modes and non-Schmid effects in crystalline solids .1. Critical conditions of localization

A general strain rate independent crystallographic slip theory which incorporates non-Schmid effects, is presented. This constitutive law is a rate independent isothermal idealization of the theory developed by Dao and Asaro (1993). The non-Schmid factors are estimated for Ni3Al as well as for some simple metals. A general method to study the bifurcation modes for the general three-dimensional multiple slip geometry is described. Three-dimensional bifurcation analyses for single slip mode as well as multiple slip mode are presented. With moderate non-Schmid effects, coarse slip bands (CSB) are found possible in single slip modes as well as multiple slip modes, where critical localization criteria may be satisfied with significant strain hardening. Non-symmetric multiple slip geometries are examined and the bifurcation results show that shear bands close to the conjugate slip system are often more favored. Non-Schmid effects, elastic anisotropy and stress state may have important influences on the critical localization conditions. A mechanism for the transition from coarse slip bands to macroscopic shear bands (MSB) is suggested. The predictions of the theory are compared with existing experimental observations and good agreement is obtained for both the coarse slip bands and macroscopic shear bands.