The Fracture Problem Of The Arc-cracks In An Electrostrictive Material

Electrostrictive materials, as a kind of smart materials, have very wide application in engineering since their coupling responses are proportional to the square of electric field. For example, these materials have been used to make transducers, sensors, converters and so on. On the other hand, their dielectric constants are in general connected with strains, so the constitutive equations of these materials are nonlinear. This implies that the studies on the electro-elastic fields in electrostrictive materials are more complex than those in piezoelectric materials. Thus, it is of theoretical and practical importance to study the electro-elastic fields in the electrostrictive materials.In fact, since the constitutive equations of electrostrictive materials are nonlinear, it is difficult to give the analytical solutions even for a crack within the framework of nonlinear theories. However, for the cases where the strain is so much small (under 10?6 or below) that the effect of the strains to the dielectric constants can be neglected, the non-linear mechanical-electric coupling problem can be simplified to a linear one. Based on this simplified method, the main works in the thesis are summarized as follows:In Chapter 1: a brief introduction is given to research background and development in this field.In Chapter2: using complex variable method, basic equations are outlined for the two-dimensional problems in a Cartesian coordinate system, and then they are extended to a polar coordinate system.In Chapter 3: for the case of one circular-arc crack, the solutions for complex potentials and intensity factors of total stresses are derived, and then numerical results are given to discuss the influence of the crack geometry and the dielectric constants inside the crack and the surrounding space on the intensity factors of total stresses. It is found that the total stresses always have a traditional singular type of r ?1/2 at the crack tip under pure electric loads. Especially, when the crack is filled with the same medium as that at infinity, no singularities exist. This implies that the applied electric field has no effects on crack growth.In Chapter 4: the works in Chapter is extended to the case of multiple circular-arc cracks, and the solutions for two symmetrical circular-arc cracks are presented in detail.In Chapter 5: the present work is summarized and some future works are remarked. This work is partially supported by the National Natural Science Foundation of China under Grant No. 10972103.