The effect of boundary conditions and sample aspect ratio on apparent d33 piezoelectric coefficient determined by direct quasistatic method.

The effect of boundary conditions (e.g., type of metal contacts) and sample geometry (e.g., sample aspect ratio) on measurements of direct longitudinal d33 coefficient in piezoelectric ceramics is studied by direct quasistatic method. We show that at small aspect ratio (thickness/lateral dimension <0.1) the measured d33meas is as much as 30% lower than the true value, d33true. Measured d33 increases with increasing aspect ratio and reaches its true value at a threshold aspect ratio that is dependent on ceramic composition and is about approximately 0.5 in the case of soft and hard Pb(Zr,Ti)O3. Experimental results show that, when the force is applied over the whole electroded surface of the sample, the d33 depends only on the aspect ratio and not size of samples. The experimental results are compared with simulations using finite element modeling (FEM) and are interpreted in terms of distribution of strain/stress within the sample, which leads to functional dependence of the measured d33 on transverse d31 and shear d15 coefficients. It is shown experimentally and by FEM that the value of d33 at low aspect ratios depends on the type of metallic contacts used to collect the charge and apply the pressure on the sample. Effect of nonlinearity of the d31 and d15 coefficients on d33 measurements also is considered.