Cohesive-zone models and singularities at corners and cracks in homogeneous materials
Journal of the Mechanics and Physics of Solids(2023)
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.
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Key words
Corners,Mixed-mode fracture,Cohesive-zones,Singularities
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