Cracking in ferroelectric and antiferroelectric ceramic multilayer actuators

This paper models cracking in the poling process of a ferroelectric actuator and the operation of an antiferroelectric actuator. In each case, domain switching or phase transition produces large electric displacement and strain. Around an internal electrode edge, such strain causes cracking, which, in turn, is a precursor to electrical breakdown. We model domain switching or phase transition by large increases of both the electric displacement and field induced strain under a small change in the electric field near the coercive field. Ignoring the stress contribution to the electric field, we solve the electric field around the internal electrode edge for nonlinear electric field and electric displacement relations. We then solve a standard elastic residual strain problem to determine the stresses in the structure. Fracture mechanics is then used to determine the cracking conditions in actuators. We find that a critical thickness exists, below which cracking will not occur. This agrees with the prediction of Hao et al (1996), and Gong and Suo (1996).