Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media

Widely used constitutive laws for engineering materials assume plastic incompressibility, and no effect on yield of the hydrostatic component of stress. However, void nucleation and growth (and thus bulk dilatancy) are commonly observed is some processes which are characterized by large local plastic flow, such as ductile fracture. The purpose of this work is to develop approximate yield criteria and flow rules for porous (dilatant) ductile materials, showing the role of hydrostatic stress in plastic yield and void growth. Other elements of a constitutive theory for porous ductile materials, such as void nucleation, plastic flow and hardening behavior, and a criterion for ductile fracture will be discussed in Part II of this series. The yield criteria are approximated through an upper bound approach. Simplified physical models for ductile porous materials (aggregates of voids and ductile matrix) are employed, with the matrix material idealized as rigid-perfectly plastic and obeying the von Mises yield criterion. Velocity fields are developed for the matrix which conform to the macroscopic flow behavior of the bulk material. Using a distribution of macroscopic flow fields and working through a dissipation integral, upper bounds to the macroscopic stress fields required for yield are calculated. Their locus in stress space forms the yield locus. It is shown that normality holds for this yield locus, so a flow rule results. Approximate functional forms for the yield loci are developed.