Anisotropic post-yielding behaviour of directionally solidified, single-grained eutectics

Abstract

A previous analysis (Wakashima and Courtney 1980) of the initial yielding behaviour of aligned eutectics is extended to the post-yielding region. The analysis is based on the recognition that plastic deformation of aligned eutectics occurs by crystallographic slip in one of the phases prior to the yielding or fracture of the other phase. By incorporation of an energy minimum principle into the previous analysis, a method is derived for predicting the active slip systems and the amount of slip in each of them as a function of the (generally multiaxial) externally applied stress. This method is reduced to a non-linear optimization problem which can be solved numerically by an iterative technique of mathematical programming. Some numerical examples are given for fibrous and lamellar eutectics subjected to uniaxial tension along the growth direction. The general feature revealed by these examples is that deformation anisotropy results both from geometric and crystallographic anisotropy of the phases, the contribution of the latter diminishing in the later stages of deformation.