Armor ceramics are commonly used in body and vehicle protection systems. Brittle ceramics subjected to high strain-rate loading exhibit a distributed fracture pattern, which eventually produces a dense assembly of granular ceramic solids. This study proposes an analytical model to predict such granular phase transition and a constitutive model for the produced granular fragments.
Granular phase transition under impact loading is investigated by examining buckling of micro-columns between crack planes to formulate the expected value of ‘failed area fraction’ for materials with random crack spacing. When the failed area fraction reaches a critical threshold level, the fractured material transitions into a granular medium. This critical threshold is determined by implementing the analytical model into the Paliwal-Ramesh damage model and determining the transition values corresponding to which we have a sudden increase in the failed area fraction. Additionally, the fragment size distribution at granular phase transition is predicted. Preliminary investigation suggests an exponential fragment size distribution at granular phase transition.
A micromechanics-inspired constitutive model is developed for granular fragments based on a recently introduced breakage mechanics theory for crushable and dilative sands. The model takes into account the influence of the initial grain size distribution (GSD) and tracks its evolution. The GSD predicted by the granular phase transition model used as an input for the constitutive model. Three primary dissipation mechanisms, breakage of particles, reorganization of fragments and frictional interactions, which dictate the overall material response are considered in the formulation. The rate-dependency is modeled by employing the overstress theory of viscoplasticity. Particle crushing and dilation are identified as two computing processes, which lead to an ultimate critical state expressed in terms of stress, void ratio and breakage.