Combined voids size and shape effects on the macroscopic criterion of ductile nanoporous materials

In this paper, we investigate the interfacial stress effects on the macroscopic yield function of ductile porous media containing nanosized spheroidal cavities. The solid matrix is assumed rigid-ideal plastic and of von Mises type with associated flow rule. We then perform limit analysis of a spheroidal unit cell containing a confocal spheroidal (prolate or oblate) cavity and subjected to arbitrary mechanical loadings. Voids size effects are captured by considering at the interface between the matrix and the cavity a surface stress model which relates the jump of the traction vector to the interfacial residual stress and interfacial plastic strain. This accounts for a thin shell of material in which occurs a strong plastic strain accumulation. We then provide a closed-form two-field based estimate of the overall dissipation which contains additional terms related to the interfacial plasticity. By taking advantage of this result, we derive parametric equations of the macroscopic yield surface of the nanoporous plastic material. The obtained estimates are assessed through comparisons with numerical data. Finally, it is shown that the resulting macroscopic criterion of the nanoporous material exhibits specific features such as (i) a dependence of the yield stress on the size of the spheroidal nanovoids, (ii) asymmetry between the yield stress in uniaxial tension and compression, (iii) more pronounced size effects for oblate voids than for prolate ones.