Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

Abstract

A model study on fractured systems was performed using a concept that treats isotropic cracked systems as ensembles of cracked grains by analogy to isotropic polycrystalline elastic media. The approach has two advantages: (a) Averaging performed is ensemble averaging, thus avoiding the criticism legitimately leveled at most effective medium theories of quasistatic elastic behavior for cracked media based on volume concentrations of inclusions. Since crack effects are largely independent of the volume they occupy in the composite, such a non-volume-based method offers an appealingly simple modeling alternative. (b) The second advantage is that both polycrystals and fractured media are stiffer than might otherwise be expected, due to natural bridging effects of the strong components. These same effects have also often been interpreted as crack-crack screening in high-crack-density fractured media, but there is no inherent conflict between these two interpretations of this phenomenon. Results of the study are somewhat mixed. The spread in elastic constants observed in a set of numerical experiments is found to be very comparable to the spread in values contained between the Reuss and Voigt bounds for the polycrystal model. Unfortunately, computed Hashin-Shtrikman bounds are much too tight to be in agreement with the numerical data, showing that polycrystals of cracked grains tend to violate some implicit assumptions of the Hashin-Shtrikman bounding approach. However, the self-consistent estimates obtained for the random polycrystal model are nevertheless very good estimators of the observed average behavior.