Analytical solution of the stress field and plastic zone at the tip of a closed crack - Wu, Guanzhong; Wang, Wensong; Peng, Shaochi (Frontiers in Earth Science, 2024)
The investigation of stress field and plastic zone distribution at the closed crack tip provides a fundamental basis for failure analysis and life prediction of geotechnical materials. In this study, we employ the superposition principle to obtain complex function solutions for the stress field and displacement field at the crack tip. Furthermore, we analyze the plastic zone distribution at the crack tip based on the Mohr Coulombs criterion. We investigate how factors such as crack angle, confining pressure, and material properties influence the stress field, displacement field, plastic zone size, and crack propagation direction. Our results demonstrate that this method effectively characterizes the distribution of stress field and displacement field at closed crack tips. Moreover, we elucidate that wing cracks are primarily formed due to tension-shear coupling effects. Lower crack angles and higher confining pressures effectively suppress slip between crack surfaces by reducing tension-shear coupling effects and inhibiting wing foil crack development. The results further indicate that the rock cohesion and internal friction angle exert negligible influence on the stress field, displacement field, plastic zone shape at the crack tip, as well as the growth direction of new cracks.