Generic Overlapping Cracks in Polymers: Modeling of Interaction

Abstract

This paper deals with modeling of the interaction in overlapping cracks that the authors have earlier identified to be generic to a wide range of polymeric systems (Ramasamy and Lesser, J Polym Sci B Phys, 2003). A complex stress function method is used for evaluating stress intensity factors for interacting cracks. The interaction between two parallel overlapping cracks is considered first. It is shown for this case that the stress intensity factor can fall below the threshold value when there is sufficient overlap, leading to arrest of crack growth at the overlapping tip. Then the interaction in a doubly periodic infinite array of cracks is considered. The interaction in the array is found to be non-linear. However, at a given stress level, the highest density of stable cracks is related to the threshold value for crack propagation K_th though a simple set of equations. It is also shown that in an infinite array of cracks, the energy release rate criterion for crack growth is different from the stress intensity factor criterion due to a reduced stiffness of the material.