Theoretical and experimental investigation of mixed-mode dynamic fracture in high-temperature-treated sharp V-notched granite

Crack initiation in heat-treated rock under impact loading remains a critical issue in deep underground engineering, particularly in environments prone to blasting and rockbursts. However, the mixed-mode initiation and early propagation of cracks emanating from sharp V-notches in thermally damaged granite under dynamic loading have not yet been well quantified. In this study, a Split Hopkinson Pressure Bar (SHPB) system combined with high-speed photography was used to investigate the mixed-mode (I + II) dynamic fracture behavior and loading-rate dependence of sharp V-notched Brazilian disc (SV-BD) granite specimens subjected to high-temperature treatment. First, static tests were conducted to determine the temperature dependence of the relevant physical and mechanical properties, and the resulting data were used to calibrate a temperature-dependent damage model. High-speed imaging was then employed to capture the crack initiation and propagation processes in real time, enabling accurate identification of the instant of crack initiation. Finally, a modified finite fracture mechanics (MFFM) model was developed by incorporating the singular V-notch stress field, T-stress, and incubation-time effects. Matched asymptotic and finite-element analyses were performed to obtain the stress and energy coefficients required by the model. The proposed model was then used to examine the effects of temperature, loading rate, and mode mixity on the critical extension length, initiation angle, and mixed-mode fracture toughness, and it reproduced the experimentally measured crack-initiation envelope more accurately than conventional finite fracture mechanics.