Crack problem in piezoelectric materials: General anti-plane mechanical loading

Using linear piezoelectricity theory, the effect of a Griffith crack on stress and electric fields in an infinite piezoelectric material under electric and anti-plane mechanical loading has been studied by using appropriate boundary conditions. It is found that electric field is nonsingular in front of crack tip due to no free charge inside piezoelectric material and along crack faces. The singularity of electric displacement arises from the electromechanical interaction between electric and mechanical loading. Under far field loading condition, crack driving force is proportional to the square of the resultant remote stress generated by both mechanical loading and electric loading. At a given mechanical loading, electric loading can either increase or decrease the crack driving force, which depends on the relative direction of the electric field to that of mechanical loading.