How to obtain a more accurate maximum energy release rate for mixed mode fracture

Abstract

Energy release rate (ERR) is considered one of the most widely employed fracture criteria. However, for mixed mode fracture situations, the exact computation of ERR for an infinitesimal branch crack is challenging. With some assumptions, Nuismer's theoretical expression (Int. J. Fracture. 11 (1975)) has been used to determine the ERR. In this work, we investigate its deviation. Based on St. Venant's theorem, it is first proved that the stress intensity factor (SIF) of a branch crack is almost independent of its length when the branch crack is small enough as compared to the main crack, which enables us to more accurately obtain the ERR and SIF of an infinitesimal branch crack by simulating a finitely short branch crack in finite element simulations. More accurate curves for the maximum ERR and the corresponding branch angle under any mixed mode are provided. From results of more accurate simulation, we find that Nuismer's model has the maximum difference of 11.2% in the maximum ERR and the 7.1% difference in the branch angle prediction. These are also the differences of predictions between the maximum circumferential stress criterion and the maximum energy release rate criterion.

Keywords

• Energy release rate
• Mixed mode fracture
• Kinking