Effects of Preloading on Brittle Solids

Abstract

A general theory that addresses the preloading effects on the strength of brittle solids as a consequence of the progressive cracking is developed within the framework of continuum damage mechanics theories. To accommodate the effects of rotation of the loading paths in the stress-strain behavior of the material, an effective damage parameter is defined. The rate of the damage parameter is obtained from the consistency condition of the loading (damage) surface. Based on the directionality of the loading paths, damage is stored in appropriate directions through the components of material compliance. The compliance and inelastic strain tensors are separated into tensile and compressive components to address the material behavior in damage modes I and II, respectively. Due to the lack of experimental data that assess the effects of orthogonal preloading, the model is compared with failure simulations published by the University of Colorado. Stiffness recovery upon load reversal, an important feature of brittle solids, is modeled by introducing an effective compliance tensor in mode I. Finally, to demonstrate the model's ability to replicate both proportional and nonproportional stress paths, it is compared against the experimental data.