A micromechanical model for the fracture process zone in ferroelectrics

Abstract

Piezoelectric and ferroelectric ceramics find an application as actuators, sensors or ultrasonic transducers in many fields of technology. Because of their brittleness, problems of strength and reliability have to be major subjects of investigation. In general, the ceramic material is exposed to combined electromechanical loading conditions. An influence of the electric field upon the fracture toughness has been observed by many researchers. An established fracture criterion for ferroelectrics is not known, though. Our investigations deal with the calculation of ferroelectric/ferroelastic domain switching events near the tip of an electromechanically loaded crack. The calculations are based on a semi-analytical solution of the piezoelectric field problem yielding electric and mechanical fields around a crack tip. By means of a switching criterion, the specific work is related to a threshold value, deciding upon location and species of switching events. The thus determined extension of the fracture process zone is the basis for calculating changes in the fracture toughness due to domain processes. Thereby a fracture criterion is suggested, which requires a pure mechanical stress analysis. The influence of electric fields is taken into account permitting the critical value to be a function of the electric field. Results for one special configuration of poling and electric field directions are compared to experimental findings.