Brittle failure criteria for components containing U-notches under Mode I loading

In this study, a modified fracture criterion which satisfies the necessary stress and energy conditions is proposed for brittle materials. The criterion is based on the assumption that fracture is generated by the initiation of a crack with a finite length l_cm. In the proposed criterion, it is assumed that the crack length l_cm is an intrinsic material parameter, with a value between 0.8d_0m⩽l_cm⩽d_0m(=2(K_IC/σ_C)²/π). Here,d_0m is the characteristic length used in the mean stress criterion, and K_IC and σ_C are the fracture toughness and the tensile strength for the considered material, respectively. The stress and energy conditions for estimating the brittle fracture behaviour can be fulfilled progressively not simultaneously. However, both conditions must ultimately be fulfilled. Following tests on brittle materials, it has been shown that the predicted values of ultimate stress, based on the necessary stress and energy conditions, agree well with the experimental data.