Interaction between the doubly periodic interfacial cracks in a layered periodic composite: Simulation by the method of singular integral equation

Abstract

In this paper, a doubly periodic interfacial cracking problem in a layered periodic composite is analyzed under antiplane shear loads. To further understand the interaction effect among the periodic interfacial cracks, four crack configurations are considered, namely a bilayered composite containing a single crack and a periodic array of collinear cracks, a layered periodic composite with a periodic array of parallel cracks and a doubly periodic rectangular array of cracks. In view of the periodic symmetry, the three periodic problems are transformed to a mixed boundary value problem for a single crack problem in an appropriate cell with the suitable periodic boundary conditions on its boundaries. The treatment skills for the periodic array of collinear cracks and the disposal techniques for the periodic array of parallel cracks are used together to solve the doubly periodic rectangular array of cracking problem. To demonstrate the computational accuracy of the present method, detailed comparative analyses are carried out. Numerical results are presented to show the interaction effect among the periodic interfacial cracks. For the doubly periodic rectangular array of cracking problem, parametric studies on the stress intensity factors leads out the following rule: the shielding effect of multiple parallel cracks and the amplifying effect of multiple collinear cracks exist simultaneously, and a coupled effect between geometrical and physical parameters on the interfacial fracture behavior exists clearly.