Abstract:

In this paper, a general solution technique is outlined for the case of surface craoks in a three dimensional body. Around the crack front, a singular stress element is constructed on the basis of a known asymptotic solution of the problem under consideration. Numerical results are reported that are obtained with the proposed sub-region mixed finite element approach. The results are compared with those given in the literature for different situations showing that they are accurate with a much lower computational effort. The proposed method offers the following advantages: 1. the singular stress element possesses the square root singular stress behavior, so an expensive mesh refinement in the stress concentration region is avoided. 2. Since the stress intensity factors are obtained directlly, the accuracy loss in the computational process is decreased. 3. The conjunction conditions of displacements and stresses on the interface between both region. Ⅰ and Ⅱ, are satisfied in an integral sense and the convergence of the solution is thus guaranteed.

Key words: FEM, sub-region mixed FEM, surface crack