A first step toward functionally graded plasticity in porous materials

Abstract

With an eye toward functionally graded plasticity in porous material, a homogenization scheme is developed to determine the overall elastoplastic behavior of a porous material with an interfacial ductile zone. The development involves four key steps: i) a linear comparison composite, ii) the secant moduli of the ductile phases, iii) an energy approach, and iv) a field-fluctuation method. With the aid of a 3-phase spherically concentric solid, the developed theory can be readily used to calculate the overall elastoplastic behavior of the porous material regardless whether the interfacial ductile layer is softer or stiffer than the matrix. To assess its accuracy, an exact local analysis is also carried out under pure dilatation, and comparison between the two indicates a close agreement. The theory is then applied to examine the influence of the ductile interfacial zone on the overall elastoplastic strength. The results show that its volume concentration and its relative stiffness to the ductile matrix can both have a very significant effect on the overall elastoplastic behavior of the porous material.