Rate sensitivity of fracture trajectory

Abstract

Abstract The coupling of crack growth rate with the crack trajectory is critical for adequate modeling and control of hydraulic fracture initiation and growth and has many important field applications. The identification of optimal breakdown rate for minimizing the near-wellbore fracture tortuosity and the evaluation of fracture penetration depth in previously undrained low-permeability formations during refracturing operations are two applications with significant economic impact. Both of these problems require an adequate account of the rate effect on fracture curvature during its quasi-static growth. A variety of criteria for the direction of crack growth have been proposed since the early sixties. Some of them are expressed as the maximum of certain stress components or as strain energy density in the vicinity of the crack tip. Others use fracture mechanics parameters, such as the maximum stress intensity factor K I , vanishing stress intensity factor, K II , or the maximum of the energy release rate, G I . Recent experimental examination of the above criteria revealed their inadequacy in cases when a process zone (PZ) is formed in front of the crack tip. The PZ in the form of strain localizations is usually created in the vicinity of the crack tip as a material response to stress concentration. It is commonly observed at various loading conditions in metals, polymers, overconsolidated clays, and rocks. Thus, the equations for crack trajectory and for growth rates along the trajectory are still open to debate. A new application of the least-action principle of classical mechanics to the crack growth problem is presented. It leads to the identification of the crack driving forces, including the conjugate to the curvature of the crack trajectory. Such consideration suggests that the crack trajectory depends on the crack growth rate during quasi-static fracture propagation. The experimental setup of laboratory tests designed and performed to examine the rate dependency of fracture curvature are presented, and the test results support this proposition.