This paper presents an analysis of the elastic wave propagation in brittle materials containing a distribution of microcracks. The crack-size distribution is assumed to be isotropic and exponential. The evolution of the mean crack size is described by a rate-dependent damage model based on the mechanics of microcracks. The analysis shows that the elastic wave speeds of a brittle material are sensitive to the change in the mean size of the distributed cracks in the material. The dependence of the wave speeds on the applied strain can also be used to validate the damage model. An example of a brittle ceramic under uniaxial-strain tension is presented to show quantitatively the changes in the longitudinal and shear wave speeds as functions of the applied strain. Explicit relations between the wave speeds and the mean crack size in the material are given.

A three-dimensional rate-dependent model has been developed for damage and failure of brittle materials under impact. The model extends a recently developed, crack-mechanics based damage model [Zuo et al., Int. J. Solids Struct. 43, 3350 (2006)] to high rate problems by incorporating a nonlinear equation of state (EOS) and porosity growth. The pressure-volume response developed by Addessio and Johnson for ceramics under impact [J. Appl. Phys. 67, 3275 (1990)] was adapted to the current model. The model has been numerically implemented and the responses of a ceramic (silicon carbide) under various loading paths are shown. These responses are compared with those predicted by the existing model (having a linear equation of state) to illustrate the effects of nonlinear EOS and porosity.