Solution of collinear cracks in an electrostrictive solid

Abstract

A general treatment is presented of the two-dimensional problem of N collinear cracks in an infinite electrostrictive material subjected to remote electric loads based on the complex variable method combined with analytical extension of the complex variable functions. First, for the case of permeable cracks, general solutions for the electric potentials, Maxwell stresses, electroelastic stresses and stress intensity factors are derived. As specific examples, explicit and concise results are obtained for the cases of one crack and two collinear cracks. Then, these results are extended to the cases of impermeable and conducting collinear cracks, respectively. It is found that, in general, the total stresses always have the classical singularity of the r ^{- 1/2} type at the crack tips, whereas the Maxwell stresses have an r ^{- 1} singularity for the above three crack models. Finally, it is concluded that the applied electric field may either enhance or retard crack growth depending on the electric boundary conditions adopted on the crack faces, and the Maxwell stresses on the crack faces and at infinity.

Keywords:

• electrostriction
• crack
• Maxwell stress
• functional materials

Acknowledgements

CFG thanks the financial support from the National Natural Science Foundation of China (#10672076) and the Australian Research Council (ARC) as Visiting Professor to the CAMT at Sydney University. YWM also thanks the ARC for supporting this research project (DP0665856). Finally, we thank Dr. Q. Jiang for helpful discussions which have clarified several important aspects of this paper.