Variations of stress intensity factors of a semi-elliptical surface crack subjected to mode I, II, III loading

Abstract

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along the crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of a corner point singularity. It is known that the stress singularity at a corner point where the front of a three-dimensional (3D) crack intersects a free surface depends on Poisson's ratio and is different from the ordinary crack singularity. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along the crack front of a 3D semi-elliptical surface crack in a semi-infinite body under mode I, II, III loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r −3 using the stress field induced by a force doublet in a semi-infinite body as a fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mode I, II, III stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures as functions of the elliptical shape and Poisson's ratio.