Improved Load-Deflection Method for the Extraction of Elastomechanical Properties of Circularly-Shaped Thin-Film Diaphragms

Abstract

The load-deflection (LD) method is a common and convenient procedure to extract the Young's modulus and the internal tensile stress of thin-film diaphragms from measurements of the maximum transverse deflection to a uniformly distributed load. This technique allows simultaneous determination of both parameters by fitting a theoretical to an experimental LD characteristic. Consequently, a proper knowledge of such a theoretical relationship is of utmost importance to obtain accurate values. We deduced a novel LD formula covering all relevant elastomechanical bending and stretching effects. It enables an easy but still accurate extraction of theYoung's modulus and the internal tensile stress from LD measurements on circularly-shaped diaphragms. This LD relationship was derived from an adaptation of Timoshenko's membrane bending theory, where the in-plane and the out-of-plane deflections were approximated by a series expansion and a polynomial, respectively. Utilizing the minimum total potential energy principle yielded an infinite-dimensional system of equations which was solved analytically resulting in a compact closed-form solution. The flexibility of our approach is demonstrated by extracting the Young's modulus and the internal tensile stress of three disparate diaphragm materials made of either sputtered AlN, PECVD SixNy, or microfiltered carbon nanotubes (bucky paper).