On yielding and deformation of porous plastic materials

Abstract

A non-associated flow rule is introduced in this paper to characterize the yield and subsequent plastic deformation of porous solids. The pressure sensitive yield function has the form of that suggested by Gurson and Tvergaard. A macroscopic plastic potential is assumed to exist for porous plastic materials, and plastic strain increment is along the normal to the macroscopic plastic potential. The yielding function, the flow rule and the evaluation of the void volume fraction compose the non-associated constitutive model for porous plastic materials. Detailed finite element analysis on an axisymmetric unit cell is performed; the unit cell is a representative volume element of porous materials. The results show that the yield and deformation of the cell with the aspect ratio of π/4 is isotropic, and the yield can be described well by the Gurson–Tvergaard yield function with the parameters q 1=1.35, and q 2=0.95. The post-yield response of the unit cell is in good agreement with the prediction of the non-associated constitutive model.