Effects of material properties on the fragmentation of brittle materials

Abstract

We present a fundamental investigation of the influence of material and structural parameters on the mechanics of fragmentation of brittle materials. First, we conduct a theoretical analysis (similar to Drugan’s single wave problem, Drugan, W.J. (2001), Journal of Mechanical and Physics Solids 49, 1181–1208.) and obtain closed form solutions for a problem coupling stress wave propagation and single cohesive crack growth. Expressions for a characteristic fragment size s ₀ and a characteristic strain-rate ${\dot\varepsilon}_0$ are given. Next, we use a numerical approach to analyze a realistic fragmentation process that involves multiple crack interactions. The average fragment size s is calculated for a wide variety of strain-rates ${\dot \varepsilon}$ and a broad range of material parameters. Finally, we derive an empirical function that relates the normalized fragment size s/s ₀ to the normalized strain-rate ${\dot \varepsilon}/\dot{\varepsilon}_0$ and that fits all of the numerical results with a single master curve.