A continuum theory of cohesive zone models: Deformation and constitutive equations

A general three-dimensional continuum constitutive theory of cohesive zone models is presented. This development is part of a larger theory in which fracture is studied using elements of continuum theories of interfacial evolution. The main thrust of this work is the establishment of a systematic procedure for deriving cohesive interphase constitutive equations, where crack deformation is accounted for not only via the opening displacement, but also via crack surface strain tensors. The material frame indifference axiom is used to show that in traditional cohesive zone models, where the opening displacement is the only crack deformation descriptor, cohesive forces must be pointwise parallel to the opening displacement itself. This result indicates that the use of additional crack surface strain measures is required for the description of realistic crack-tip microstructures with possible anisotropic behavior.