Cohesive-zone models and singularities at corners and cracks in homogeneous materials

Abstract

The stress singularities at corners in elastic bodies are not strong enough to provide a driving force for fracture, except in the limit of a crack. Here, we re-examine these elastic stresses from the perspective of cohesive-zone models. We present a general framework to understand fracture at corners, and define the magnitude of a stress-intensity factor and its phase angle, showing how these reduce to the familiar concepts of linear-elastic fracture mechanics (LEFM), in the special case of a crack. We discuss how the cohesive length, ξ, which is inherent to cohesive-zone models, is responsible for permitting fracture (and slip) at a corner. The work done against the tractions at a corner scales with ξ1−2n and ξ1−2m, where n and m are the strengths of the two elastic stress singularities. Therefore, except in the case of a crack, for which n=m=0.5 and the dependency on the cohesive length disappears, the work goes to zero in the classical elasticity limit of ξ=0, and neither fracture nor slip can occur.Using simple, uncoupled traction–separation laws, we show that the normal and shear deformations across the interface at a corner are generally coupled, despite the lack of explicit coupling in the laws. The crack-tip phase angle is shifted from the applied phase angle, and the properties of each traction–separation law affects the deformation in the other mode. These features lead to a very rich behavior that would be further complicated by consideration of more complex laws.