The Coulombic traction on the surfaces of an interface crack in dielectric/piezoelectric or metal/piezoelectric bimaterials

This paper deals with the Coulombic traction usually neglected, but inherently acting, on the surfaces of an interface crack in dielectric/piezoelectric or metal/piezoelectric bimaterials. The dielectric material phase is treated as a special kind of piezoelectric material with a little piezoelectricity, whereas the metal phase is treated as another special kind of piezoelectric material with an extremely large permittivity and an extremely small piezoelectricity. The permittivity of the medium inside the crack gap is accounted for either. The normal electric displacement component and the Coulombic traction on the crack surfaces are unknown, and are determined from a cubic equation deduced from the extended Stroh formula. Numerical results for the Coulombic traction in both kinds of bimaterials reveal that in most cases its magnitude is remarkable and cannot be entirely neglected when the applied electric field is higher. It is concluded that in most cases the Coulombic traction yields significant influence on the effective stress intensity factor at the crack tip and may influence the fracture behavior in such kinds of bimaterials. As compared to homogenous piezoelectric materials, the metal phase always decreases the Coulombic traction, whereas the dielectric phase decreases it under the negative electric field and increases it under the positive electric field. In all cases, BaTiO3 always yields a much larger Coulombic traction than PZT-4.