Variation of stress intensity factor along a small interface crack front in singular stress fields

Stress singularities usually occur at vertexes in three-dimensional joints. Cracks frequently initiate at the vertex, and the joint fails under an external force or a thermal load. In the present study, the stress distribution near a small crack occurring at a vertex in a three-dimensional joint under a tensile load is examined, and the stress intensity factors at the crack tip are investigated along the crack tip front. The joint is made of Si and resin. In the analysis, three kinds of crack shapes (triangular, quarter circular, and concave) are supposed as the initial crack shape. The stress distribution around the crack is normalized using the singular stress near the vertex since the crack exists in the singular stress field. The stress intensity factor varies along the crack tip from the inner point to the free surface. The value of the stress intensity factor varies following the order of the stress singularity at the point of the free surface. In this analysis, the stress intensity factor is expressed as a function of the distance from the cross point of the free surface and the crack tip. Specifically, the function is composed of an exponential function of the difference between the order of the stress singularity at the cross point and the crack tip.