Effects of nonuniform initial stress state on apparent fracture toughness

Abstract

We analyze the nonuniform stress state in the vicinity of the fracture tip and its impact on apparent fracture toughness. It is shown that prescribing the boundary conditions at the deformed fracture faces allows one to take into account the effect of nonuniform tectonic stresses acting in the plane of the fracture. We conclude that the fracture may take an ellipsoidal form (aspect ratio departs from unity) as a result of interactions with anisotropic distribution of initial stresses, which leads to nonuniform growth in longitudinal and vertical directions. An expression for the effective stress intensity coefficient (fracture toughness) is obtained as a function of the nonuniform initial stress state. A simplified asymptotic approximation to the solution for the effective apparent fracture toughness is given, which may be further implemented into the near-tip asymptotics used in the form of a tip element in the numerical implementation of a Planar3D approach to hydraulic fracture simulation.