Interaction between a spherical inhomogeneity and two symmetrically placed penny-shaped cracks

Abstract

Stress analysis is carried out for a three-dimensional elastic solid containing an elastic spherical inhomogeneity and two coplanar penny-shaped cracks. Each of the two cracks is located on either side of the elastic spherical inhomogeneity and the geometry is subjected to uniform tensile stress at infinity. The interaction between the inhomogeneity and the cracks is tackled by the superposition principle of elasticity theory and Eshelby's equivalent inclusion method. Analytical solutions for the stress intensity factors on the boundaries of the cracks and the stress field inside the inhomogeneity are evaluated in series form. Numerical calculations are reported for several special cases, and show the variations of the stress intensity factors and stress field inside the inhomogeneity with the configuration and elastic properties of the solid and the inhomogeneity.