Stress Concentration of an Ellipsoidal Inclusion of Revolution in a Semi-Infinite Body under Biaxial Tension

Abstract

This paper deals with a stress concentration problem of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r-and z-directions in semi-infinite bodies having the same elastic constants of the matrix and inclusion. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in the previous paper are used. Then the body force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield repidly converging numerical results for stress distribution along the boundaries of both the matrix and inclusion even when the inclusion is very close to the free boundary. Then, the effect of free surface on the stress concentration factor is discussed with varing the distance from the surface, shape ratio, and elastic ratio. Also the present results are compared with the ones of an ellipsoidal cavity in a semi-infinite body.