Jun Lei

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.

Time-domain BEM for transient interfacial crack problems in anisotropic piezoelectric bi-materials

A time-domain boundary element method (BEM) together with the sub-domain technique is applied to study transient response of interfacial cracks in piecewise homogeneous, anisotropic and linear piezoelectric bi-materials under electrical and mechanical impacts. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are implemented at the tips of the interface cracks. To determine the real or complex dynamic stress intensity factors and the dynamic electrical displacement intensity factor of the interfacial cracks, an explicit extrapolating formula in a typical state of the crack plane perpendicular to the poling direction is presented in this paper. Numerical examples are presented; and the effects of the load combination and material combination on dynamic intensity factors and dynamic energy release rate are discussed.

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.

Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites

Abstract To determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.