Origin of the Bauschinger Effect in Amorphous Solids

Abstract

We study the structural origin of the Bauschinger effect by accessing numerically the local plastic thresholds in the steady state flow of a two-dimensional model glass under athermal quasistatic deformation. More specifically, we compute the local residual strength, $\Delta\tau^{c}$, for arbitrary loading orientations and find that plastic deformation generically induces material polarization, i.e., a forward-backward asymmetry in the $\Delta\tau^{c}$ distribution. In steady plastic flow, local packings are on average closer to forward (rather than backward) instabilities, due to the stress-induced bias of barriers. However, presumably due to mechanical noise, a significant fraction of zones lie close to reverse (backward) yielding, as the distribution of $\Delta\tau^{c}$ for reverse shearing extends quasilinearly down to zero local residual strength. By constructing an elementary model of the early plastic response, we then show that unloading causes reverse plasticity of a growing amplitude, i.e., reverse softening, while it shifts away forward-yielding barriers. This result in an inversion of polarization in the low-$\Delta\tau^{c}$ region and, consequently, in the Bauschinger effect. This scenario is quite generic, which explains the pervasiveness of the effect.