Dynamic crack branching in anisotropic coal: a rate-dependent modeling approach and ABAQUS implementation

Why cracks in rocks bifurcate under dynamic impact and how to accurately model bifurcation behavior affected by existed natural fractures are urgent issues that need to be addressed in the study of rock dynamic fragmentation in-depth. In this study, it is theoretically analysed that the relationship between crack surface separation strain rate and crack propagation speed according to the geometric configuration of dynamic crack propagation. A constitutive model to describe the propagation and bifurcation of dynamic brittle cracks is proposed based on the empirical fracture energy rate-dependent model, and this model is written as an ABAQUS user subroutine to model the fragmentation process of coal samples with bedding under Hopkinson bar impact with cohesive element method. For dynamic fracture problems, an approach for determining the cohesive element size is proposed, which combines the cohesive zone length with the Grid Convergence Index (GCI) method. The location and timing of crack initiation are further clarified at the μs scale. Results show that for the dynamic impact test of Brazilian disc (BD) sample with beddings, crack initiation lags behind stress wave for 30 s before dynamic balance state, and the macro fracture is formed by the intersection of multiple cracks, which is significantly different from that of static BD test. The complex stress environment in the BD sample with beddings makes the initiation law of dynamic cracks uncertain. The number of main crack has a significant correlation with impact velocity, thus the meaning of the dynamic tensile strength calculated based on SHPB test cannot represent the real dynamic tensile strength, which is influenced by the beddings.