| Similar to the case in traditional solid materials, defects such as crack and hole existing inelectrostrictive materials (EMs) will lead to high local field, resulting from cracking and crack growthin EMs under electric loading, and finally results in the failure of the materials. Hence, it is important toanalyze the fracture problems of EMs with defects. Based on the complex variable theory and basicequations of EMs, in the present work the2D problems in EMs containing an elliptical hole, cracks andelectrodes are studied, respectively. The result is extended to the case of the3D problems in EMscontaining a flat elliptical crack. The main contents are as follows:1. We analyzed the2D problem of EMs containing a single crack. Firstly, for an infiniteelectrostrictive plate which contains a single crack, starting from elliptic hole we discussed the effect ofMaxwell’s stresses inside the elliptical hole on the stress field around the elliptical hole. Then, when theelliptic hole degenerates into a crack, the intensity factors of total stresses are presented in close form.Numerical results of stresses around the hole and crack are given in order to discuss the effect ofmaterial constants and elliptic-hole size on the fracture behaviors of the material. Secondly, for a finiteplate containing an elliptic hole or crack, we obtained the solutions for electric fields and stress fieldsby using Faber series expansion together with the least square boundary collocation technique.Numerical results are presented to analyze the effect of the plate geometry on the fracture.2. We derived the general solutions for the2D problem of an infinite electrostrictive solid with Ncollinear cracks. Firstly, the electric potentials are obtained, and then the general solutions of stressintensity factors are presented for the cases of permeable, impermeable and conducting cracks,respectively. Then, as a special case, explicit and closed-form solutions are given for two collinearcracks. Finally, some numerical examples are given to discuss the effect of electric boundary conditions,material constant and crack size on stress intensity factors.3. We studied the effects of dielectric breakdown on a conductive crack or an electrode in anelectrostrictive material. By using the strip dielectric breakdown (DB) model, we studied dielectricbreakdown problem of a conducting crack and obtained the stress intensity factors in close-form. Then,complex functions and stress intensity factors are derived for a soft and a rigid electrode, respectively.Finally, we analyzed the effect of DB on the intensity factors of total stresses around the tip of anelectrode.4. We dealt with the3D problem of an infinite electrostrictive solid with a flat elliptical crack.According to existing solutions of the similar problems in pure elastic materials, we derived the explicit solution of displacement function and obtained stress field near the crack and displacement of cracksurface by displacement function method. As a result, the general solution of the stress intensity factoris derived, and then the corresponding solutions for a penny-shaped crack and impermeable line-crackare presented as special cases of the present work. Finally, numerical results are given to discuss theeffect of environment at infinity and electric fields inside the crack on the stress-intensity factors. |
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