On the global implicit criterion of a fracture propagation under mixed load

Validation is carried out of the previously proposed implicit criterion for choosing the direction of a fracture propagation under the complex loading characterized by the presence of all three modes of the stress intensity factors $K_{\mathrm{I}}$, $K_{\mathrm{II}}$, and $K_{\mathrm{III}}$. The criterion is based on the principle of local symmetry according to which the fracture propagates in the direction providing the zero values of the factors of both mixed modes $K_{\mathrm{II}}$ and $K_{\mathrm{III}}$. Since in the general case the two conditions cannot be satisfied simultaneously, the criterion is formulated as a minimization problem for a functional that contains the sum of the values of the mixed modes integrated along the entire front of the fracture. The formulation of the criterion includes some parameter that describes the effect of each of the mixed modes; the value of this parameter should be chosen by using the experimental data. Based on two fracture propagation experiments with complex mixed loading, validation of the criterion is carried out and some estimates are given for the interval of the best value of the weight parameter.