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This paper details an experimental investigation of the clamping effect associated with thick-film piezoelectric elements printed on a substrate. The clamping effect reduces the measured piezoelectric coefficient, d33, of the film. This reduction is due to the influence of the d31 component in the film when a deformation of the structure occurs, by either the direct or indirect piezoelectric effect. Theoretical analysis shows a reduction in the measured d33 of 62%, i.e. a standard bulk lead zirconate titanate (PZT)-5H sample with a manufacturer specified d33 of 593pC/N would fall to 227.8pC/N. To confirm this effect, the d33 coefficients of five thin bulk PZT-5H samples of 220µm thickness were measured before and after their attachment to a metallized 96% alumina substrate. The experimental results show a reduction in d33 of 74% from 529pC/N to 139pC/N. The theoretical analysis was then applied to existing University of Southampton thick-film devices. It is estimated that the measured d33 value of 131pC/N of the thick-film devices is the equivalent of an unconstrained d33 of 345pC/N.
Torah et al. (Thu,) studied this question.