Modeling crack propagation in heterogeneous granite using grain-based phase field method

Abstract

The cracking behavior and mechanical properties of brittle rocks is controlled by its microstructure. In this work, an extended grain-based phase field method (GB-PFM) based on Voronoi tessellation technology is proposed to investigate the mechanical properties and crack propagation in heterogeneous brittle rocks by considering material heterogeneities and microstructure heterogeneities at the grain scale. Then, a trial and error calibration procedure is developed after comprehensive study of uncertain parameters such as grain boundaries thickness and critical energy release rate. It is shown that greater grain boundaries thickness results in a lower tensile strength and lower Young’s modulus, and greater number of intergrain cracks. Then, a group of models with single pre-existing flaw (flaw inclination angles: 0°, 30°, 45°, 60°, 90°) are built according to calibration parameters to study the mechanical properties and cracking behavior of heterogeneous granite under direct tension. The path of the macrocracks obtained from GB-PFM shows a more noticeable tortuous nature as compared with that results by others phase field methods. The variation of flaw inclination has an obviously influence on crack propagation. Failure patterns obtained by GB-PFM revealing the macrocracks are composed of intragrain and intergrain cracks at the microscopic view. Moreover, the stress field distribution obtained by GB-PFM is agree well with the theoretical analyses and other numerical simulations. The above simulated results prove that the GB-PFM provides an applicable numerical method for efficiently reproducing the microstructure and the related crack propagation of brittle crystalline rocks, which greatly expand the application of the phase field methods.