Influence of a mobile incoherent interface on the strain-gradient plasticity of a thin slab

A thermodynamically consistent theory of strain-gradient plasticity in isotropic solids with mobile incoherent interfaces is developed. The gradients of plastic strain are introduced in the yield functions, both of the bulk and the interface, through suitable measures of material inhomogeneity; consequently, two internal length scales appear in the formalism. The rate-independent associative plastic flow rules, as proposed in the framework, are coupled with the kinetic law for interface motion. The theory is used to study plastic evolution in a three-dimensional, semi-infinite, thin slab of isotropic solid with a planar incoherent interface. The average stress-strain curves are plotted for varying length scales, mobilities, and average strain-rates. The effect of slab thickness and the two internal length scales on the hardening behavior of the slab is investigated. For all the considered cases, the stress-strain curves have two distinct kinks, indicating yielding of the bulk and at the interface. Moreover, once the interface yields, and is driven to move, the curves demonstrate both softening and rate-dependent response. The softening behavior is found to be sensitive to interface mobility and average strain-rates. These observations are consistent with several experimental results in the literature.