Effects of crack surface electrostatic tractions on the fracture behaviour of magnetoelectric composite materials

• Effects of crack surfaces electrostatic tractions on magnetoelectroelastic fracture behavior are investigated theoretically.
• Electrically and magnetically semi-permeable crack faces boundary condition is adopted.
• Influence of different electromagnetic property of crack interior is considered.
• All essential fracture mechanics parameters are derived in closed-form for easy use.

The fracture mechanics problem of a Griffith crack embedded in a two-dimensional magnetoelectric composite material subjected to coupling mechanical, electric and magnetic loads at infinity is investigated. The crack surfaces electrostatic tractions are taken into account and the crack is assumed to be electrically and magnetically semi-permeable. Explicit and closed form solutions of electric displacement and magnetic induction inside the crack, stress, electric displacement and magnetic induction intensity factors are derived based on the extended Stroh formalism and continuous distribution of generalized dislocation approach. Numerical computations are also carried out to illustrate the influence of electrostatic tractions on the crack tip field when the crack interior is filled with different dielectric medium. It is found that the electrostatic tractions on the crack surfaces have the tendency to close the crack thus retard the crack propagation, and the traditional traction-free crack model always overestimates the effect of applied magnetoelectric loads on the crack tip filed intensity factors. Crack surfaces electrostatic tractions cannot be neglected for large applied electric or magnetic load to mechanical load ratio, and small dielectric constant and magnetic permeability of the crack interior.