Analytical and numerical investigations of dynamic crack propagation in brittle rocks under mixed mode loading

Abstract

Determination of dynamic fracture parameters of brittle rocks is of particular importance in assessing rock structure stability, rock strength and rock behavior under the effect of dynamic loading. Major dynamic fracture parameters including initial crack extension angle, stress intensity factors, fracture toughness and crack propagation path are directly affected by crack propagation speed (CPS). In this study, the dynamic form of the maximum tangential stress criterion (DMTS-Criterion) was used to determine the fracture parameters as a function of CPS under three loading conditions: 1) pure mode I, 2) pure mode II, and 3) mixed mode I-II. In addition, a dynamic two-dimensional crack propagation code (DTDCPC) was developed using the DDM to predict the crack trajectory in cracked semi-circular bend (SCB) specimens for different CPS values. CPS ranged from zero (the fully static case) to the Rayleigh wave speed (the fully dynamic case). The results showed that all fracture parameters increased by increasing CPS. In addition, under pure mode I, cracks only grew at acute angles (forward branching) and bifurcated when the CPS exceeded a critical value. Under mixed mode loading I-II and pure mode II, cracks grew at acute (forward branching) and obtuse (backward branching) angles. The backward branching of faults under pure mode II occurred in most rock types when crack propagation speed was greater than 0.81 of the Rayleigh wave speed. In addition, it was found that fracture toughness of pure mode II (KIIC), compared to that of pure mode I (KIC), decreased by increasing CPS to 0.76 of the Rayleigh wave speed, and cracks tended to grow under pure mode II. For high CPS, KIC was greater than KIIC, and cracks tended to grow under pure mode I. DTDCPC showed that the crack propagation path predicted in SCB-specimens deviated away from its original plane as CPS was increased, and the deviation of the crack propagation path decreased as the crack inclination angle increased.