Macroscopic Yield Surface Research Articles

On the plastic yielding of porous metals

Accurate numerical results are presented for the stress-strain response of an elastic-plastic material containing a cubic array of spherical voids. Cases of both proportional macroscopic stressing and non-proportional macroscopic stressing are examined, and the numerical results are compared with the predictions of Gurson's (1977a, b) theory and Tvergaard's (1982) modification of it. It is determined that Gurson's original theory performs adequately in predicting the stress-strain response for the porous solid, at least for the axisymmetric stress histories investigated. In addition, the structure of the macroscopic yield surface is explored in detail, and it is demonstrated that a vertex exists at the loading point despite the fact that the plasticity formulation used to model the matrix material is characterized by a smooth yield function.

Theory of perfect plasticity of composite materials, taking account of volume compressibility

The practical importance and timeliness of the study of the mechanical macroscopic behavior of composite microinhomogeneous media are determined by its ability to give criteria for estimating the limiting load of various structural elements, the flow of multiphase dispersed systems, the deformation of materials made by powder metallurgy methods, etc. The theoretical prediction of the properties of composites is generally most effectively realized when their structural representations are based on the theory of random fields. Application of the “strong isotropy” hypothesis [1] for the statistical averaging of certain relations of a perfectly plastic body with microstructure permits the determination of its macroscopic yield surface.