Oscillatory Instability of Quasistatic Fluid-Driven Fracturing in Porous Materials

Oscillatory instabilities of dynamic fractures arise under mode-I loading as the crack velocity approaches or exceeds the Rayleigh wave speed, c_{R}. Anomalously, at velocities far below c_{R}, experiments reveal a distinct quasistatic oscillatory instability in fluid-driven fracturing of porous materials, formed by continuous bifurcations of "daughter cracks." This phenomenon falls outside the applicability of existing fracture theories. Our asymptotic stability analysis of wave-shaped cracks reveals that oscillations originate from the competition between the stabilizing effect of cohesive force in the process zone and the destabilizing effect of shear perturbations along the crack sides. We further derive the characteristic oscillation wavelength and demonstrate that it is jointly governed by the fracture process and fluid invasion. The findings broaden the physical basis of competing mechanisms governing oscillatory fracture instabilities.