Study of size (aspect ratio) effect on longitudinal piezoelectric coefficient measured by quasistatic technique

Effect of sample size (aspect ratio or ratio of thickness to lateral dimension) on the value of the apparent direct longitudinal d₃₃ coefficient is investigated in hard and soft PZT using quasistatic Berlincourt-type technique. We show that at small aspect ratio (such as thickness/diameter=0.1) the measured d₃₃ is as much as 30% lower than the true value, d_33true. Measured d₃₃ increases with increasing aspect ratio and reaches its true value at a threshold aspect ratio that is equal to ≈0.5 for both soft and hard PZT. The experimental results are compared with simulations using Finite Element Modeling (FEM) and are interpreted in terms of inhomogeneous distribution of strain/stress within the sample, which leads to functional dependence of the measured d₃₃ on transverse d₃₁ and shear d₁₅ coefficients. Nonlinearity of the d₃₁ and d₁₅ coefficients also was taken into account in the finite element analysis. FEA and experimental results are in a good agreement.