Strain gradient plasticity modelling of cyclic loading in dispersion hardened materials

An analytical model, based on an isotropic strain gradient plasticity theory, describing work hardening during cyclic straining in a metal reinforced by a dispersion of non shearable particles is presented. The yield criterion is expressed in terms of isotropic and kinematic hardening contributions and the model is validated against full field finite element (FE) solutions on a 2D axi-symmetric unit cell model. Excellent agreement between analytical and FE results is obtained. The theory presented includes mixed energetic/dissipative contributions from higher order stresses in both bulk and at particle/matrix interfaces. In particular, the influence of a quadratic interface free energy that transitions into a linear form at some threshold value of plastic strain is investigated. It is shown that such an energy is capable of capturing the experimentally observed phenomenon of inflections in the reverse stress-strain curve. It is argued, based on the well known phenomenon where particles are shielded by Orowan dislocation loops during reverse strain, that an energetic interface contribution could be physically relevant for low plastic strains.