Stress Concentration around a Spherical Cavity in a Semi-infinite Elastic Body under Uniaxial Tension

Abstract

This paper contains a three-dimensional solution for the stresses and deformations arising in a semi-infinite elastic body with a spherical cavity, when the body is subjected to uniaxial tension. The solution is presented in integral form and infinite series and is deduced with the aid of six stress functions combining the Boussinesq, Neuber and Dougall stress functions. Numerical results are given for the stresses on the surface of a spherical cavity and along the z-axis and at the plane boundary corresponding to several values of radius of the cavity. The results obtained thus are compared with the axi-symmetric solution in the previous paper.