The Stress Field and Intensity Factor due to Crazes Formed at the Poles of a Spherical Inhomogeneity

The problem of two penny-shaped crazes formed at the top and the bottom poles of a spherical inhomogeneity has been investigated. The inhomogeneity is embedded in an infinitely extended elastic body which is under uniaxial tension. Both the inhomogeneity and the matrix are isotropic but have different elastic moduli. The analysis is based on the superposition principle of the elasticity theory and Eshelby's equivalent inclusion method. The stress field inside the inhomogeneity and the stress intensity factor on the boundary of the craze are evaluated in the form of a series which involves the ratio of the radius of the penny-shaped craze to the radius of the spherical inhomogeneity. Numerical examples show the interaction between the craze and the inhomogeneity is strongly affected by the elastic properties of the inhomogeneity and the matrix. The conclusion deduced from the numerical results is in good agreement with experimental results given in the literature.