A contour integral for three-dimensional crack elastostatic analysis

Abstract

A contour integral method for calculating stress intensity factors has been successfully applied to two-dimensional crack problems for both static and dynamic cases. In this paper the method is extended to three-dimensional static problems. By means of the displacement discontinuity method and the technique of variation of crack area, the required derivatives of traction and displacement for a reference problem are determined. The stress intensity factors are calculated by a contour integral with a non-singular integrand. The only absolute values of traction and displacement that are required for the real problem are on contours away from the crack-tip; they are determined by the dual boundary element method. For mixed-mode problems, the ratios of stress intensity factors are determined by the ratios of the mixed-mode discontinuity displacements near the crack front, all stress intensity factors can be calculated from only one reference solution.