An analytical model of constrained piezoelectric thin film sensors

Abstract

A new analytical model based on 2D electro-mechanical continuum model is developed to analyze the performance of constrained piezoelectric thin film sensors, surface-bonded or embedded in composite material system. Several non-classical effects, such as viscoelastic property of the bonding layer, AC dielectric loss, frequency-dependent effect of the resistivity of the film materials, and most importantly, the effect of constrained boundary on the capacitive performance are considered. The model is validated by comparing the results from electrostatics as well as a simplified model based on direct stress transfer and strain continuity at the film-substrate interface. Analytical solutions for specific cases of boundary constraints on the film, such as in-plane tensile stress, transverse normal stress and horizontal shear stress are reported. Numerical studies on the effect of these stresses on PVDF and PZT films with carbon-epoxy host structure are carried out. Effect of process-induced residual stress is also studied. The results show significant complexity, which is otherwise intractable using existing simplified approaches.