On the directional dependency of Mode I fracture toughness in anisotropic rocks

Abstract

This paper presents a theoretical and experimental analysis of the directional variations of different measures of Mode I fracture toughness in anisotropic rocks and possibly other types of solids. We report the theoretical basis for the directional dependence of three measures of fracture toughness: the critical stress intensity factor, the critical energy release rate and the critical strain energy density. The equivalency of these three measures in anisotropic materials is discussed. We then provide a full set of experimental results on the fracture toughness variation in an anisotropic rock that exhibits transverse isotropy. The results give supporting evidence that the critical Mode I stress intensity factor in fact varies with direction based on a sinusoidal function. This indicates that there exist two principal values of the fracture toughness along with the principal material directions within the plane. Once these two principal values are determined, all three measures of the fracture toughness can be predicted in any direction, provided that the elastic constants of the material are known, and that the symmetry condition employed in this analysis is fulfilled.