Fragmentation and granular transition of ceramics for high rate loading

Abstract

The paper presents a numerical model to study the transition of brittle materials from a cracked solid to a granular medium under impact loading. The model addresses competitive crack coalescence in the transition regime and provides insight into the onset of comminution and the initial conditions for subsequent granular flow. Crack statistics obtained from initial flaws using a wing crack growth-based damage model have been used to discretely model elliptical cracks in three dimensions. These discrete cracks are either generated randomly in space or with a constraint that minimizes the intersection between neighboring cracks. These cracks are then allowed to coalesce with nearby cracks along with favorable directions and the output fragment statistics are predicted. A simple statistical model is proposed that suggests a transition criterion resembling the one obtained from the numerical model. Initial fragments are power-law distributed similarly to experimental observations and particle-based models. A generalized form of a microstructure-dependent granular transition criterion based on a threshold measure of crack lengths has been proposed. This model can be implemented in numerical codes to activate granular physics and calibrate the initial conditions of granular flow, such as fragment size and morphology.

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

“…Under large forces, solids fracture and fragment. This process in which material breaks down into smaller components or comminution is relevant to many problems including the motion of tectonic plates [1,2], asteroid collisions [3], ice floes [4,5], ballistic armor [6][7][8][9], and high-pressure granular flow and compaction [10][11][12]. The extent of fragmentation is often measured through the distribution of the number of fragments N of mass M or N (M ) which is a common basis for continuum formulations of breakage mechanics [13][14][15][16].…”