Interaction of a penny-shaped crack with an elliptic crack

Abstract

Three-dimensional problem of crack-microcrack interaction is solved. Both the crack and microcrack are embedded in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity. One of the cracks is circular while the other is elliptic and they are coplanar and are positioned in such a way that the axis of the elliptic crack passes through the centre of the circular crack. A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem. A series of transformations first reduce them to a quadruplet infinite system of equations. A series solution is finally obtained in terms of crack separation parameter β which depends on the separation of the crack microcrack centre. Analytical expression for the stress intensity factors have been obtained up to the order β6. Numerical values of the interaction effect have been computed for and results show that interaction effects fluctuate from shielding to amplification depending on the location of each crack with respect to the other and crack tip spacing as well as the aspect ratio of the elliptic crack. The short range interaction can play a dominant role in the prediction of crack microcrack propagation.