Reliability of ceramic multilayer actuators: A nonlinear finite element simulation

In a ceramic multilayer actuator, the abrupt end of an internal electrode concentrates the electric field, inducing stresses in the ceramic. Crack nucleation and growth have been observed experimentally, but have not been well modeled due to the complex material behaviors. We write a finite element program to solve this coupled electromechanical problem. The material is taken to be nonlinearly dielectric with electrostrictive strain quadratic in electric displacement. The program solves field distributions in a multilayer actuator, which are combined with fracture mechanics to obtain cracking condition. The calculations are compared with the existing analytical solution under the small-scale saturation conditions, and then extended to the large-scale saturation conditions. We show that the cracking condition established under the small-scale saturation conditions gives useful estimate even when the saturation zone is comparable to the actuator layer thickness.