Surface Integral and Finite Element Hybrid Method for Three-Dimensional Analysis of Arbitrarily Shaped Surface Cracks

Abstract

A three-dimensional surface integral and finite element hybrid method has been developed for modeling arbitrarily shaped surface cracks in complex structural components. Accurate stress intensity factors were obtained by decomposing the problem into a surface integral model of the fracture in a domain of infinite extent and a finite element model of the uncracked domain. Boundary conditions were enforced by applying corrective traction to the surfaces of both constituent models. Coupling between the two formulations was minimized by implementing the fundamental solution for a force multipole near a planar free surface. Surface cracks intersecting nonplanar free surfaces were modeled in a piecewise linear fashion by deploying multiple sets of these functions. The effectiveness of this approach was demonstrated for well-documented cases, including a corner crack in a thick plate and a three-dimensional edge crack. The results of these benchmark studies will be used to develop a set of heuristics for assuring suitable finite element mesh densities in the vicinity of the fracture.