Uncoupled, asymptotic mode III and mode E crack tip solutions in non-linear ferroelectric materials

Complete asymptotic solutions for the mode III, longitudinal or anti-plane shear, and mode E applied electric field with conducting or insulating crack cases are presented for idealized ferroelectric switching materials. The mathematical procedure required to solve these problems has been presented by Rice (J. Appl. Mech. 34 (1967) 287). The constitutive behavior of the material is specified by an initial linear response, a segment of non-hardening switching behavior, i.e. perfect plasticity in the mechanical case, and finally a region where lock-up occurs. The crack tip solution is characterized by an outer solution with a standard r−1/2 singularity that is not centered on the crack tip, a switching zone with the solution given by a simple radial slip line field, and an inner lock-up region which surrounds the crack tip.