A phase field model with the mixed-mode driving force of power-law relation

Abstract

A new phase field model is proposed through introducing the mixed-mode critical energy release rate (ERR) following the power-law relation as the crack driving force. Compared with the classical phase field models involving only mode-I critical ERR GIC, the present phase field model takes mode-II critical ERR GIIC into account and introduces two power-law factors. As a result, a pure mode-II crack propagation can be observed in the present simulation of a single material under shear loading when the mode-I critical ERR is significantly larger than the mode-II one. A phase field simulation on a symmetric three-point bending semi-circular Brazilian disc specimen of polymethylmethacrylate shows that a better agreement with experimental results can be achieved through adjusting the power-law factors. Then, a shear test of a single edge notched plate is simulated and the results show that: (i) The peak load decreases gradually as either power-law factor increases. (ii) The mixity factor (GIIC/GIC) affects not only the cracking mode but also the brittle or tough extent. With the increase of the mixity factor, the initial crack deflection angle converges to a constant value of 70.8±0.5°, which is close to 70.5° predicted by the classical maximum tangential stress criterion. (iii) The energy split methods have an obvious effect on the crack propagation behaviors. For the volumetric-deviatoric split method, a pure mode-II crack propagation is observed when the mixity factor approaches zero and a pure mode-I crack propagation occurs when the mixity factor is no less than 4.0. For the spectral decomposition split method, a mode-I crack propagation always occurs regardless of the mixity factor. To summarize, with the change of the power-law factors and critical ERRs, diverse cracking modes can be predicted by the present phase field model.