Transition from fractal cracking to fragmentation due to projectile penetration

Abstract:

We present a theoretical study of the fracture of two-dimensional disc-shaped samples due to the penetration of a projectile focusing on the dynamics of fracturing and on the geometrical structure of the generated crack pattern. The penetration of a cone is simulated into a plate of circular shape using a discrete element model of heterogeneous brittle materials varying the speed of penetration in a broad range. As the cone penetrates a destroyed zone is created from which cracks run to the external boundary of the plate. Computer simulations revealed that in the low speed limit of loading two cracks are generated with nearly straight shape. Increasing the penetration speed the crack pattern remains regular, however, both the number of cracks and their fractal dimension increases. High speed penetration gives rise to a crack network such that the sample gets fragmented into a large number of pieces. We give a quantitative analysis of the evolution of the system from simple cracking through fractal cracks to fragmentation with a connected crack network. Simulations showed that in the low speed limit of loading the growing cracks proceed in discrete jumps separated by periods when the crack tips are pinned. The statistics of the size of jumps and of the waitng times shows scale free behaviour, i.e. power law distributions are obtained with universal exponents. Dependence on the loading speed was pointed out only for the cutoffs of the distributions. In the high speed limit of loading the sample falls apart forming a large number of fragments. The size of fragments proved to be power law distributed where dependence on the loading speed is observed only for the cutoffs. The value of the exponent has good agreement with experiments.