To investigate the effects of intersection angle and depth of cross-fissures on the dynamic mechanical behavior of rock with internal cross-fissures, a damage constitutive model and a three-dimensional (3D) failure criterion for impact fracture were established within the bond-based peridynamics framework. By introducing bond force distance attenuation and progressive damage evolution mechanisms, a novel damage constitutive model was developed, and a dynamic 3D bond failure criterion was proposed to consistently couple the energy condition, strength constraint, and strain rate effect. Furthermore, the stretch corresponding to the peak bond force, traditionally solely determined by the macroscale strength, was extended to be jointly governed by the macroscale strength and bond microscale parameters. This modification characterizes the variability of the bond stretches corresponding to the peak bond forces in heterogeneous materials, thereby improving the model's capability to describe material heterogeneity and differences in local failure. 3D benchmark examples were conducted to compare various attenuation functions, quantitatively verifying that the exponential attenuation form yields the minimum overall error index. Based on three validation cases, the influences of internal cross-fissure angle and depth on impact stress response, 3D crack propagation path and energy distribution were systematically analyzed. Results indicate that under impact loading, increased cross-fissure depth decreases peak stress and energy utilization efficiency; at a constant depth, peak stress increases first and then decreases with the rising intersection angle. Crack propagation presents symmetry and eventually forms a funnel-shaped 3D crack, with the minimum damage degree inside the funnel.
Yu et al. (Mon,) studied this question.