Abstract
The Bauschinger effect refers to an observed asymmetry in the forward and reverse loading curves of a metal or an alloy. It is generally characterized by the reduction of the absolute value of the yield stress in reverse loading, as compared to the maximum stress imposed on the initial, or forward, loading. Thus, the Bauschinger effect contributes to the phenomena known as kinematic or anisotropic hardening. Symmetry in the loading curve is then referred to as isotropic hardening. Experimental investigations of anisotropic hardening in precipitation and dispersion hardened systems have shown differences in the Bauschinger effect between alloys having shearable and non-shearable precipitates: materials with strong, non-shearable obstacles to dislocation motion exhibit a larger degree of kinematic hardening, particularly at low strains. In the current work, these materials are modeled using a stochastic cellular automaton, with an array of coupled elements with stiffnesses and strengths corresponding to two phases in a dispersion hardened alloy. By imposing a local rule for the redistribution of stresses, various degrees of anisotropic hardening can be modeled. Model results are illustrated for both the cases of non-shearable and shearable particles.