A strain-rate dependent tensile damage model for brittle materials under impact loading

Brittle materials are often subjected to high strain rate impact load, which could be imposed due to intentional demolition purposes or during ballistic impact on protective structures. Fragments of different sizes are generally observed by such impact, which are directly related to the strain rate experienced by the material at different locations. This thesis presents a rate-dependent constitutive model to predict such dynamic behaviour of brittle solid under tensile loading. A three-parameter rate dependent tensile damage model, under continuum mechanics framework, is developed for simulating the fragmentation of brittle materials subjected to high strain-rate loading. The damage model is formulated under the assumption that the isotropic and homogeneous material contains initial microcracks and the microcrack induced damage increases when a critical volumetric strain is exceeded. Considering the microcrack induced damage and energy into account, a quantitative and direct method is developed to determine the fragment size under a constant strain rate loading. In this model, instead of assuming spherical fragment, more realistic prolate spheroid fragment is assumed, which eventually determines the more accurate surface energy from a fragment. In addition, complete strain energy (until the fracture of the material) is considered which improves the global energy balance in predicting the size of a fragment. The parameters of this model can be conveniently calibrated by experimental data on fracture strength and strain rate. The proposed rate-dependent model is validated by a spall experiment of concrete and with a dynamic Brazilian disc experiment of sandstone. Both of these experiments are numerically simulated with the proposed model and the experimental observations are compared with the simulation. The predicted strain rate, fracture strength, fracture location and fragment size are in very good agreement with those obtained in the experiments