A Micromechanically Based Gurson-Type Model for Ductile Porous Metals Including Strain Gradient Effects

The aim of this paper is to propose some Gurson-like, second-gradient type model for porous ductile metals accounting for the fact that macroscopic mechanical fields can vary significantly over distances comparable to the void spacing. Although the idea is not new in principle, the present approach is original in that the model proposed is not based on purely heuristic grounds but on a rigorous micromechanical analysis. Its principle consists in extending Gurson’s study of some rigid-ideal plastic hollow sphere subjected to conditions of axisymmetric, homogeneous boundary strain rate, to conditions of inhomogeneous boundary strain rate. The resulting macroscopic yield criterion does not only involve ordinary macroscopic stresses but also “second-order” ones which can be interpreted as “moments” of the microscopic stresses. Its most surprising feature is the appearance of the “traces” of the “moment” in the square term instead of the “cosh”, as one would expect by analogy with the stresses.