Bifurcation criterion and the origin of limit crack velocity in dynamic brittle fracture

By employing a variational phase field model, we investigated the dynamic brittle fracture of poly (methyl methacrylate) (PMMA) through computer simulation. Without the explicit fracture criterion, current simulations not only successfully reproduced the crucial experimental observations on crack propagation, such as crack patterns, velocity evolutions and limit crack velocity but also discovered some new features not reported in the experimental study yet. Through quantifying the energy flux into the crack tip and fracture energy, we observed that the crack bifurcation of PMMA always occurs with the energy flux into the crack tip exceeding a critical value and proposed that crack bifurcation obeys an energy criterion. Based on this criterion, the long-standing challenge of limit crack velocity in experiments is successfully predicted by continuum theory, which unveils that crack bifurcation sets the upper limit for crack velocity. Combining the crack bifurcation criterion and continuum theory provides a rational explanation for complex path selection of cracks.