Abstract
We present a theoretical study of the fracture of two-dimensional disc-shaped samples due to projectile penetration focusing on the geometrical structure of the 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.
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