Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material

• DOI: 10.1016/j.ijsolstr.2009.07.002
• Publication Date: 2009-07-09T09:06:24Z
• Authors: Jun-Hong Guo; Zi-Xing Lu; Hai-Tao Han; Zhenyu Yang
• Keywords: Exact solution; Piezoelectric materials; Mechanical Engineering; Applied Mathematics; Edge cracks; 02 engineering and technology; Condensed Matter Physics; Materials Science(all); 0203 mechanical engineering; Mechanics of Materials; Elliptical hole; Modelling and Simulation; Field intensity factors

AbstractBased on the complex variable method and the technique of conformal mapping, the anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material is studied. The exact solutions of field intensity factors and energy release rate are presented in closed-form with the assumption that the surfaces of the cracks and the elliptical hole are electrically impermeable. With the variation of the hole-size and the crack length, the present results can be reduced to the cases of two symmetrical edge cracks and a single edge crack emanating from a circular hole given by Wang and Gao [Wang, Y.J., Gao, C.F., 2008. The mode III cracks originating from the edge of a circular hole in a piezoelectric solid. International Journal of Solids and Structures 45, 4590–4599]. Moreover, new models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and a single edge crack emanating from an elliptical hole, two asymmetrical edge cracks emanating from a circular hole, T-shaped crack, cross-shaped crack and semi-infinite plane with an edge crack. Numerical examples are then conducted to reveal the effects of the hole-size and the crack length on the field intensity factors and the energy release rate.