A two-step load-deflection procedure applicable to extract the Young's modulus and the residual tensile stress of circularly shaped thin-film diaphragms

Abstract

We report on a novel two-step load-deflection (LD) formula and technique that enables an accurate extraction of the Young's modulus and the residual tensile stress from LD measurements on circularly shaped thin-film diaphragms. This LD relationship is derived from an adaptation of Timoshenko's plate bending theory, where the in-plane and out-of-plane deflections are approximated by series expansions. Utilizing the minimum total potential energy principle yields an infinite-dimensional system of equations which is solved analytically resulting in a compact closed-form solution. In the appendant measurement procedure, the whole transverse bending characteristic of the diaphragm as a function of the radial coordinate is recorded for different pressure loads and introduced into the novel LD equation in order to determine the elastomechanical parameters of interest. The flexibility of this approach is demonstrated by ascertaining the Young's modulus and the residual tensile stress of two disparate diaphragm materials made of either micromachined silicon or microfiltered buckypapers composed of carbon nanotube compounds.