A Theory of Plasticity for Porous Materials and Particle-Reinforced Composites

Abstract

An energy criterion is introduced to define the effective stress of the ductile matrix, and with which Tandon and Weng’s (1988) theory of particle-reinforced plasticity is capable of predicting the desired plastic volume expansion under a pure hydrostatic tension. This modification also makes the theory suitable for application to porous materials at high triaxiality. Despite its simplicity, it offers a reasonable range of accuracy in the fully plastic state and is also versatile enough to account for the influence of pore shape. The theory is especially accurate when the work-hardening modulus of the ductile matrix is high, consistent with the concept of a linear comparison material adopted. If the matrix is also elastically incompressible, the theory with spherical voids is found to coincide with Ponte Castaneda’s (1991) lower bound for the strain potential (or upper bound in the sense of flow stress) of the Hashin-Shtrikman (1963) type, and with any other randomly oriented spheroidal voids, it provides an overall stress-strain relation which lies below this upper-bound curve. This energy approach is finally generalized to a particle-reinforced composite where the inclusions can be elastically stiffer or softer than the matrix, and it is also demonstrated that the prediction by the new theory is always softer than Tandon and Weng’s original one.