An elastic-constant stress cohesive zone model for an orthotropic piezoelectric actuator adhesively bonded to a substrate

Abstract

One of the common failure mechanisms observed in electromechanical systems utilizing actuators, sensors, or flexible electronics is the occurrence of interfacial debonding. In this paper, an elastic-constant stress cohesive zone model is constructed to analyze the interface behavior of piezoelectric actuators used in electromechanical systems when imperfectly bonded to a host medium. The analytical formulation treats the piezoelectric actuator as an orthotropic thin film, employing the membrane assumption. It is assumed that the cohesive zone extends from a point, initially unknown, to the edge of the film. The governing integro-differential equation is solved for various bonding scenarios, including perfect bonding with cohesive zones at the edges, an elastic case with a delaminated zone at the center, and an elastic case with both a delaminated zone at the center and cohesive zones at the edges of the film. Detailed examinations are conducted to explore the effects of stiffness ratio parameters and critical actuating voltage on the stresses within the film and substrate as well as the cohesive zone length. The results indicate that the cohesive zone length covers 45% of the film length when the actuating voltage has a fivefold increase over the critical threshold. For the imperfect bonding, the surface in-plane stress of the substrate exhibits a tensile peak near the boundary of the cohesive zone in addition to compressive singularities at the edges of the film. The shear stress singularity factor has an asymptotic behavior as the actuating voltage goes beyond the critical threshold. The critical actuating voltage reduces by a factor of 5% only if the delamination length does not exceed 70% of the film length.