Application Of Hyper-singular Integral Equation Method To 3D Crack Embedded In Piezoelectric Materials

Because of coupled effects between the elastic and the electric fields, piezoelectric materials have been widely used as actuators and sensors. It is possible to make a system of intelligent composite materials by combing these piezoelectric materials with structural materials. While most piezoelectric materials are brittle, and both electrical and mechanical disturbances are present when servicing, the strength of them is weakened by the presence of defects such as voids and cracks. The reliability depends on the knowledge of applied mechanical and electric disturbances. When cracks are present, they may grow under service load and affect the performance of structures. In recent decades, fracture of piezoelectricity has been paid much more attention. So it is very important to make some research on it.Due to mathematical difficulties to treat the coupled electromechanical fields in piezoelectricity, the majority of the literatures concerning crack problems are based on two-dimensional assumptions. Comparatively, few numerical solutions are available in the literatures for three- dimensional crack problems in piezoelectric materials. Using hyper-singular integral equations combined with boundary element method, this paper makes some research on planar crack embedded in three-dimensional infinite transversely isotropic piezoelectric material, and numerical results of electric displacement and stress intensity factors are given. The main achievements are as following:1. Using given three-dimensional Green's functions of infinite transversely isotropic piezoelectric solid and Somigliana identity, hyper-singular integral equations for three-dimensional crack in transversely isotropic solid are derived, and the unknown functions are discontinuities of elastic displacements and electric potential;2. Based on the above theory, a numerical method is proposed to solve the hyper-singular integral equations by combining the boundary element method with the finite-part integral method;3. Using the above method, mode-I and mixed-mode crack problems of typical cracks are numerically calculated and the electroelastic intensity factors near the crack front are given, accuracy of results are found to be very high;4. To get a stable numerical results with a higher accuracy, square-root model, which is consistent with the singular index of discontinuities of electric potential and elastic displacements near the crack front, is used to modify the above method, then some numerical calculations of typical mode-I crack problems are made and numerical results of electric displacement and stress intensity factors near the crack front are given. The results are proved satisfactory.