A Micromechanical Model for High-Strain-Rate Behavior of Ceramics

A constitutive model applicable to brittle materials such as ceramics subjected to biaxial compressive loading is developed. The model is based on non-interacting sliding microcracks that are uniformly distributed in the material. Tension cracks nucleate and propagate from the tip of the sliding cracks in the direction of maximum applied compression when the stress-intensity factor reaches its critical value. For high strain rate deformation, the rate of crack growth is governed by a universal relation in dynamic fracture. The constitutive model provides strain components for plane deformation which consists of an elastic part and a part due to sliding and growth of the tension cracks. The failure of the material is linked to a critical density of damage and hence a critical length for the tension cracks. The constitutive model is used to study material behavior under uniaxial compressive constant strain rate loading. A critical strain rate beyond which the material would exhibit rate sensitivity is proposed. The model predicts the failure or peak strength to increase with increasing strain rate. For engineering ceramics, the rate sensitivity exponent is found to be a function of the relation between the rate of crack growth and the toughness of the material. The model predictions are compared with the rate-dependent behavior of a hot pressed aluminum nitride tested in uniaxial compression in the strain rate range of 5 × 10^(−6)−2 × 10^3 s^(−1)