Analysis of different damage configurations at a macro-crack tip

The solution of an infinite elastic plane containing a macro-crack and a cluster of micro-cracks is presented based on Muskhelishvili’s complex potential method. A step-by-step sub-problem procedure is used to satisfy the stress boundary conditions on each crack surface. A local damage parameter expressed by stress intensity factor is presented to evaluate the damage magnitude. Three damage configurations as parallel, radiating and arbitrarily oriented micro-cracks have been designed to simulate the damage around the macro-crack tip. The results show the micro-cracks located in front of the macro-crack tip have the amplifying effect on macro-crack growth, and the amplifying effect increases with the number of micro-cracks increase. Moreover, when the macro-crack length decreases or the distance between micro-cracks and macro-crack increases, the damage parameter of macro-crack and micro-cracks will decrease. It is found that the largest damage is the damage configuration of arbitrarily oriented micro-cracks among three damage configurations.