A modified incubation time criterion for dynamic fracture of rock considering whole stress history

The objective of this paper is to deeply understand and analytically characterize the dynamic strength enhancement of rock. Inspired by the incubation time criterion, a modified dynamic fracture criterion consid-ering whole stress history, called the incubation characteristic time criterion, is proposed. The physical meaning of the modified criterion is interpreted by the hysteresis effect in dynamic fracture revealed by the experimental observation of microcrack kinematics. The dynamic tensile strength determined with the modified criterion is validated by comparing it with published experimental data and the determined result from the original incu-bation time criterion. Factors in the modified criterion that affect the ultimate dynamic fracture include the quasi-static tensile strength, incubation characteristic time and stress history. The sensitivity of dynamic tensile strength to fundamental material properties is analysed through the combination of the quasi-static tensile strength and the incubation characteristic time. In addition, three types of waveforms are used to investigate the effects of the stress history on the dynamic tensile fracture. Finally, the simple numerical implementation of the modified criterion combined with the classical linear elastic model visually reproduces the analytical calculation of dynamic fracture under different stress histories. In conclusion, the modified criterion provides a novel approach to determine the dynamic fracture of rock under arbitrary loading conditions by considering the whole stress history in comparison with the rate-dependent models.