A micromechanics based model to predict micro-crack coalescence in brittle materials under dynamic compression

Abstract

Dynamic compressive failure of brittle materials follows a progression from micro-cracks initiating and growing at pre-existing material defects or flaws, to micro-crack coalescence, to comminution and full fragmentation. Current damage-based models are able to represent the dynamic growth of cracks, but they do not capture the effects of crack coalescence among the large populations of cracks that grow under high strain rate conditions. This paper proposes a probabilistically-based approach to incorporate micro-crack coalescence into constitutive models of dynamic brittle failure. The basic idea is to represent the full population of cracks by a set of representative cracks that evolve in both number and size, consistent with the underlying growth and coalescence of the crack population. Numerical examples show that considering coalescence has a significant effect on the predicted compressive peak stress in the material under uniaxial compression, in particular for lower strain rates and higher flaw density. The resulting constitutive model is also incorporated into a finite element model of a spherical impact test, which shows that adding coalescence to the constitutive model leads to an increased prediction of damage localization.