An anisotropic damage model with defect-crack interactions for heterogeneous brittle media under high-rate loading

A defect-crack interaction informed anisotropic damage modeling framework is proposed to predict the uniaxial compressive strength of heterogeneous brittle materials under high-strain-rate loading (strain rates of 102s−1 – 103s−1). The model is capable of accounting for the effect of interaction stress fields, produced by pre-existing defects, on cracks in a brittle material, allowing for the incorporation of material microstructure. The interaction-modified stresses are computed using the superposition technique where mean stress fields from a homogenization-based approach and perturbation stress fields from spherical-harmonics-expansion-based approach are superimposed. Sliding-crack model is employed to represent crack extension under compression, and dynamic wing-crack growth is computed under the influence of the interaction stresses. The directional influence of wing-crack growth is incorporated through an anisotropic damage model where a tensorial damage metric is employed. A linear, anisotropic increment in material compliance is derived accounting for the effect of interactions on micro-cracking based damage. Model parameters can be estimated from microstructural information and/or strength, damage and volumetric strain observed in experiments. The calibrated model is used to predict uniaxial compressive strength at varying strain rates of an engineering ceramic with good experimental match. We compare this model’s effectiveness with that of some existing micromechanics models for dynamic failure of brittle materials.