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

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, xi , which is inherent to cohesivezone models, is responsible for permitting fracture (and slip) at a corner. The work done against the tractions at a corner scales with xi(1-2n). and xi(1-2n), 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 xi = 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.

Automated summary

The stress singularities at corners of elastic bodies are not strong enough to cause fracture, unless there is a crack. This study re-examines these elastic stresses using cohesive-zone models and presents a framework to understand fracture at corners. It shows that the cohesive length, xi, plays a crucial role in allowing fracture (and slip) at a corner, and how stress-intensity factor and phase angle reduce to linear-elastic fracture mechanics in the case of a crack. The study also reveals that the normal and shear deformations across the interface at a corner are generally coupled, leading to complex behavior.