The influences of Coulomb tractions on static and dynamic fracture parameters for semi-permeable piezoelectric cracks

In this paper, the influences of the induced Coulomb tractions on the static and dynamic crack-tip fracture parameters of semi-permeable piezoelectric cracks are studied and discussed. The static crack problems are solved by a static dual boundary element method (BEM), while the corresponding crack problems under dynamic impact loading are numerically analyzed by a time-domain BEM considering the inertial effects. In the numerical implementation, a collocation method is applied for the spatial discretization together with a quadrature formula for the temporal discretization. An iterative scheme based on the quasi-Newton method is adopted to solve the corresponding non-linear boundary-value problem resulted from the semi-permeable electric boundary conditions and the induced Coulomb tractions on the crack-faces. The crack-tip facture parameters involving the field intensity factors, the energy release rate and the mechanical strain energy release rate are evaluated by a displacement extrapolation method. Some examples are presented to compare the effects of the Coulomb tractions on the static and dynamic fracture parameters.