An Equivalent Indentation Method for the External Crack with a Dugdale Cohesive Zone

Abstract

An equivalent indentation method is developed for the external crack problem with a Dugdale cohesive zone in the both axisymmetric and two-dimensional (2D) cases. This is achieved based on the principle of superposition by decomposing the original problem into two simple boundary value problems, with one considering action of a constant traction within the cohesive zone, and the other corresponding to indentation by a rigid concave punch. Closed-form expressions are derived for the distributions of displacement and traction on the crack interface, which are consistent with the classical results in fracture mechanics. Results show that the interfacial traction distributions in the axisymmetric and 2D cases share the similar mathematical forms except for different coordinate parameters. Finite element analysis is performed to validate the obtained analytical solutions. The proposed method relies solely on a few contact solutions on the surface irrespective of a general elasticity solution in the whole body, and it may find applications in the external crack analysis and adhesive contact model involving functionally graded elastic solids or piezoelectric materials.