Analytical Studies on Mode III Fracture in Flexoelectric Solids

Abstract

Due to the stress concentration near crack tips, strong flexoelectric effect would be observed there, which might lead to new applications of flexoelectricity in material science and devices. However, different from the flexoelectric effect in cantilever beams or truncated pyramids, at the crack tip, multiple components of strain gradients with nonuniform distribution contribute to the flexoelectric effect, which makes the problem extremely complex. In this paper, with the consideration of both direct and converse flexoelectricity, the electromechanical coupling effect around the tip of a Mode III crack is studied analytically. Based on the Williams’ expansion method, the displacement field, polarization field, strain gradient field along with the actual physical stresses field are solved. A path-independent J-integral for Mode III cracks in flexoelectric solids is presented. Our results indicate that the existence of flexoelectricity leads to a decrease of both the J-integral and the out-of-plane displacement in Mode III cracks, which means that the flexoelectric effect around the tip of Mode III cracks enhances the local strength of materials.