The stress intensity factors for a periodic array of interacting coplanar penny-shaped cracks

Abstract

The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar penny-shaped cracks. Kachanov’s approximate method for crack interactions [Kachanov, M., 1987. Elastic solids with many cracks: a simple method of analysis. International Journal of Solids and Structures 23 (1), 23–43] is employed to analyze both hexagonal and square crack configurations. In approximating crack interactions, the solution converges when the total truncation number of the cracks is 109. As expected, due to high density packing crack interaction in the hexagonal configuration is stronger than that in the square configuration. Based on the numerical results, convenient fitting equations for quick evaluation of the mode I stress intensity factors are obtained as a function of crack density and angle around the crack edge for both crack configurations. Numerical results for the mode II and III stress intensity factors are presented in the form of contour lines for the case of Poisson’s ratio ν=0.3. Possible errors for these problems due to Kachanov’s approximate method are estimated. Good agreement is observed with the limited number of results available in the literature and obtained by different methods.