Effective permittivity of air-filled cracks in piezoelectric ceramics due to crack bridging

Fracture mechanical investigations of non-conducting, air-filled cracks in piezoelectric ceramics require knowledge of the electrical permeability of the crack gap. It is well known from experiments that this electrical permeability is significantly greater than the electrical permeability of an air-filled gap with smooth faces as considered in common crack models. The present paper assesses the origin of this phenomenon by investigating the effect of crack bridging on the electrical permeability of non-conducting air-filled cracks in piezoelectric ceramics. Regions of crack bridging are identified and quantified from the crack face topography of a crack in the soft PZT ceramic PIC151, which was measured by optical 3-D microscopy after total failure of the specimen. Based on a simple homogenization approach, the dielectric properties of the realistic ceramic face gap system are quantified by means of the effective permittivity of a hypothetical medium in an idealized crack with the same crack opening and smooth faces. The effective permittivity derives to a function of the crack opening, which increases with increasing crack opening at small crack openings. For PIC151, the computed maximum effective permittivity is 46 times the permittivity of air. Despite the simplifications and assumptions adopted within the proposed model, the comparison between the predicted and measured electric potential drop across an indentation crack in the PZT ceramic Vibrit1100 reveals an overall good agreement. In conclusion, the paper provides evidence that crack bridging is indeed the reason for the increased electrical permeability of such cracks.