Stress intensity factors for two coplanar penny-shaped cracks under uniaxial tension

Abstract

This paper presents an approximate analytical solution for the three-dimensional problem of two coplanar penny-shaped cracks contained in an infinite isotropic matrix. The two cracks have different sizes but are located in the same plane. The stress applied on the matrix is at infinity which is uniform and perpendicular to the plane of the cracks. The superposition principle of elasticity theory and Eshelby's equivalent inclusion method are employed for the analysis. In the solution process, a variable δ is introduced to represent the ratio of the radius of the larger crack to the center distance between the cracks. The stress intensity factors on the boundaries of the cracks is evaluated in a simple series form of δ. Numerical examples have shown that the interaction between the cracks are strongly affected by the center distance of the two cracks. The stress intensity factors (SIFs) reach the biggest values when the cracks nearly touch with each other, while the variation of SIFs due to the interaction of the cracks becomes negligible when the center distance between them is larger than two times the sum of the radii of the two cracks. This result is found to be in good agreement with the data available in open literature.