A new criterion based on the ratio of strain energy density for mixed-mode crack initiation prediction in ductile materials

In consideration of the different mechanisms of microscopic separation governed by dilation and microscopic shearing controlled by distortion on crack initiation, a new criterion based on the ratio of two strain energy densities (RSED) is proposed by differentiating the dilatational and distortional parts in strain energy density. The influence of the weights of two strain energy densities under different stress states on fracture resistance of crack initiation is also considered in the RSED criterion. The size and shape of the core region do not affect the direction and fracture resistance of crack initiation predicted by the RSED criterion. Moreover, the direction predicted by the RSED criterion is theoretically demonstrated to be identical to the orientations predicted by the maximum stress triaxiality (MST) criterion and the T criterion on crack initiation. The crack initiation directions which are obtained by the experiments for different materials and predicted by various criteria are found to be mostly coincident near the mode-I crack, and so are the fracture resistances. In the vicinity of the mode-II crack, the direction of crack initiation predicted by the RSED criterion shows a superior consistency for the experimental results of the ductile materials reported by Theocaris et al. (1982) and Kong et al. (1995) over the three classical criteria, such as the maximum tangential stress (MTS), the maximum energy release rate (MERR) and minimum strain energy density (MSED). The RSED criterion also has the potential to amend the issue of the underestimation for KIIC/KIC in some typical materials, e.g., the face-centered-cubic (f.c.c) metals. Therefore, the RSED criterion prefers to predict the direction and fracture resistance of crack initiation in ductile materials.

Automated summary

This study proposes a new criterion based on the ratio of two strain energy densities for predicting the direction and fracture resistance of crack initiation. Experimental and theoretical analysis show that this criterion has higher accuracy in predicting crack initiation in ductile materials.