A modified phase-field model for predicting mixed-mode fracture in rock-like materials

Abstract

A phase-field model can continuously smear sharp cracks into diffusive zones with finite width in which the critical energy release rate is commonly determined as constant. However, such an assumption may be insufficient in the case of rock-like materials since the energy release rate can be different for modes I and II cracks. If not accounted for, this could compromise the accuracy of the correct propagation of both wing and secondary cracks. This study proposes an extended, modified phase-field model for simulating a series of Brazilian discs made of a three-dimensional (3D)-printed rock-like material through a time-independent plane strain model. The phase-field model accounts for the splitting of different energy release rates for modes I and II to capture the complex fracture behavior. The novelty of this study lies in not only the theoretical development of the distinction of surface energy release rates but also the qualitative and quantitative assessment of mixed-mode fracture behaviors, which guarantees good predictive capabilities for the location of crack initiation and the direction of crack propagation in various practical applications. Moreover, the modified phase-field model can be implemented easily and fast without introducing new parameters. The numerical results are first validated against experimental data. The impact of the modified energy release rate on crack propagation, particularly on wing cracks, is then numerically investigated. The results show that wing cracks become more dominated by tensile stresses with a decrease in the ratio of modes I and II energy release rates. The phase-field simulations with the modified energy release rate proposed here can reproduce the experimental results both qualitatively and quantitatively with respect to crack propagation patterns, peak loads, crack coalescence loads and coalescence type.