Micromechanical Model and Associated Validation for Dynamic Failure of Brittle Materials Containing Pores and Slit-Like Flaws

Abstract

Characterizing dynamic failure is critically important to a number of applications, among others including armor, material fragmentation, and structural blast. In brittle materials, this failure is driven by crack growth from pre-existing flaws in the material microstructure. Structural scale models that explicitly address the cracks associated with each individual flaw are computationally infeasible; therefore, a model that accurately links flaw population to dynamic failure strength provides a much-needed connection between the microscale and macroscale. The current paper introduces a micromechanical model that addresses the effects of both air-entrained pores and slit-like flaws on the strain-rate dependent uniaxial compressive strength of the material. In particular, four variants of the model are addressed: a two-dimensional (2D) model with only pore flaws, a 2D model with both pores and slit-like flaws, a pseudo-three-dimensional (3D) model with only pore flaws, and a pseudo-3D model with both pores and slit-like flaws. To demonstrate the relative success of each of these approaches, the model is based on microstructural characterization and subsequent Kolsky bar tests on air-entrained mortar. Air-entrained mortar provides an excellent model material for this study, since the pore population introduced by air-entrainment is characterized relatively easily and the slit-like flaw population is deduced from the sand gradation. Furthermore, the sample sizes used in the Kolsky bar set-up are larger than the length scale of the microstructure of mortar, so that the samples are reasonably representative and provide a good basis of comparison with the micromechanics model. The micromechanics model is shown to provide reasonable agreement with experimentally obtained uniaxial compressive dynamic strength of air-entrained mortar.