Linear elastic fracture mechanics in anisotropic solids : application to fluid-driven crack propagation

Abstract

Fracture mechanics is a field of continuum mechanics with the objective to predict how cracks initiate and propagate in solids. It has a wide domain of application. While aerospace engineers want to make sure a defect in a structure will not grow and possibly lead to failure, petroleum engineers try to increase the permeability of gas shale rocks by fracturing it. In this context, we introduce some elements of linear elastic fracture mechanics in anisotropic solids. Notably, a special attention is paid to transverse isotropy, often used to model rocks but also some piezoelectric materials or fiber-reinforced composites. We focus on brittle materials, that is, we consider only elastic deformations; we thus ignore dissipative phenomena other than the one associated with the creation of crack surface. This thesis aims at understanding and predicting how pressurized cracks propagate in anisotropic brittle solids, in the framework of linear elastic fracture mechanics. The elastic coefficients relevant to the study of a pressurized crack in such materials are identified. Interestingly, they are directly related to quantities easily measured in a lab at the macroscopic scale through indentation tests and acoustic measurements. As an application, the fluid-driven crack problem is addressed. It is shown that the classical tools of the isotropic fluid-driven crack model remain valid in anisotropy, provided the appropriate elastic constants are used. We introduce the concept of crack-shape adaptability: the ability of three-dimensional cracks to shape with the elastic content. This ability could be ruled by three criteria herein introduced. The first one is based on the maximum dissipation principle. The second one is based on Irwin's theory of fracture and the concept of stress intensity factors. As for the third one, it is based on Griffith's energetic theory. While the first criterion predicts that circular cracks are more favorable, the others predict that elliptical shapes are more likely to be seen. This thesis could be valuable in the context of the stimulation of unconventional oil and gas from organic-rich shale.