Fragmentation of brittle plates by localized impact

Abstract

We address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks randomly located over the surface and following distributions that come from an analysis of how the energy input propagates and dissipates over the material. The cumulative mass distributions F(m) we obtain are in excellent agreement with the data produced by Kadono [Phys. Rev. Lett. 78, 1444 (1997)]. In the small mass regime we get F(m)-∼ m-α, with 0.1 <-α < 0.3 for a broad range of dissipation strengths and total number of fragments. In addition we obtain the fractal dimension of the set of cracks and its correlation to the exponent α that account for the experimental results given by Kadono and Arakawa [Phys. Rev. E 65, 035107(R) (2002)].