An assessment of crack tip singularity models for use with isoparametric elements

Abstract

The use of finite element methods to analyse fracture problems is complicated by the stress field singularity which exists at the crack tip. The two most successful methods of approach would appear to be the so-called energy technique and the singularity function formulation. The necessity for extremely fine meshes in the crack tip region can be overcome by the use of special elements which incorporate the required stress singularity in their formulation. The aim of this paper is to develop various promising singularity function elements and assess their performance in the solution of standard test problems. These elements are based on the eight node parabolic isoparametric element; this being the most popular element in general use. Such crack tip elements may be readily incorporated into a mesh of standard isoparametric elements permitting numerical fracture studies to be undertaken without extensive mesh regeneration or refinement. In particular elements based on the use of distorted shape functions, standard shape functions, analytic solutions, a superposition process and a hybrid technique are considered. Test problems of both single and combined mode fracture are employed in the assessment of each model. It is also demonstrated that the hybrid element is a special case of the boundary integral method, and suggestions are made for possible future development.