Arc-shaped permeable interface crack in an electrostrictive fibrous composite under uniform remote electric loadings

• Arc-shaped interface crack embedded between a circular electrostrictive fiber and a foreign matrix.
• Crack faces are assumed to be permeable to an electric field.
• Mode-I and Mode-II stress intensity factors for the oscillatory singular stress field at the crack tips are obtained.
• Stress intensity factors typically increase as the fiber becomes harder.
• Remote electric loadings may actually prevent mode-I interfacial fracture.

We present a rigorous solution of the problem of an arc-shaped interface crack embedded between a circular electrostrictive fiber and a foreign matrix subjected to uniform remote electric loadings. The crack faces are assumed to be permeable to an electric field. Mode-I and Mode-II stress intensity factors for the oscillatory singular stress field at the crack tips are obtained using complex variable methods. We find that the stress intensity factors typically increase as the fiber becomes harder. For certain combinations of the arc length of the crack and material constants of the fiber-matrix system, we show that remote electric loadings may actually prevent mode-I interfacial fracture. In particular, we show that when the fiber-matrix system degenerates to a homogeneous electrostrictive material and the medium inside the crack is identical to that surrounding the material remotely, the application of remote electric loadings continue to have a significant influence on both mode-I and mode-II fracture.