The effect of boundary conditions and sample aspect ratio on apparent d/sub 33/ 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 d/sub 33/ coefficient in piezoelectric ceramics is studied by direct quasistatic method. We show that at small aspect ratio (thickness/lateral dimension <0.1) the measured d/sub 33meas/ is as much as 30% lower than the true value, d/sub 33true/. Measured d/sub 33/ increases with increasing aspect ratio and reaches its true value at a threshold aspect ratio that is dependent on ceramic composition and is about /spl ap/0.5 in the case of soft and hard Pb(Zr,Ti)O/sub 3/. Experimental results show that, when the force is applied over the whole electroded surface of the sample, the d/sub 33/ 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 d/sub 33/ on transverse d/sub 31/ and shear d/sub 15/ coefficients. It is shown experimentally and by FEM that the value of d/sub 33/ 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 d/sub 31/ and d/sub 15/ coefficients on d/sub 33/ measurements also is considered.