A penny-shaped crack above the pole of a spherical inhomogeneity

摘要

Stress investigation for the problem of a penny-shaped crack located above the pole of a spherical particle (inhomogeneity) in 3D elastic solid under tension has been carried out. Both the inhomogeneity and the solid are isotropic but have different elastic moduli. The analysis is based on Eshelby's equivalent inclusion method and superposition theory of elasticity. An approximation according to the Saint-Venant principle is made in order to decouple the interaction between the crack and the inhomogeneity. An analytical solution for the stress intensity factors on the boundary of the crack is thus evaluated. It is found that both Mode Ⅰ and Mode Ⅱ intensity factors exist, even the loading applied at infinity is uniform tension. Results obtained show that shielding and anti-shielding (amplifying) effects of the inhomogeneity to the crack are solely determined by the modulus ratios of the inhomogeneity to the matrix. Numerical examples also indicate the interaction between the crack and the inhomogeneity is strongly influenced by the distance between the centers.