An interphase approach of size effects in ductile porous materials

The aim of this paper is to develop a size-dependent Gurson type model. The approach is based on a micromechanical implementation of a local isotropic hardening able to account for different mechanisms responsible for size effects arising at the nanoscale (surface stress effects) and at the micronscale (strain gradient effects). The heterogeneity of hardening is accounted for by considering a finite number of spherical layers (Leblond et al. in Eur J Mech A 14:499–527, 1995; Morin et al. in Int J Solids Struct 118:167–178, 2017) in which hardening is described by a Taylor dislocation model. This introduces some strain gradient effect inducing a void size dependence. In the limit of a thin interphase, the model is shown to be very close to the imperfect coherent interface based model of Dormieux and Kondo (Int J Eng Sci 48:575–581, 2010) for nanoporous materials. In the case of micronscale voids, the model is assessed through comparison of its predictions with finite element cell calculations for different stress triaxiality. A good agreement is observed between the model predictions and numerical data from cell calculations performed by Niordson (Eur J Mech A 27:222–233, 2008).