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J. Schalko, R. Beigelbeck, M. Stifter, M. Schneider, A. Bittner, U. Schmid:
"Improved Load-Deflection Method for the Extraction of Elastomechanical Properties of Circularly-Shaped Thin-Film Diaphragms";
Talk: Smart Sensors, Actuators, and MEMS V, Prag; 04-18-2011 - 04-20-2011.

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).

Circular thin-film diaphragms, load-deflection method, Young´s Modulus, inertial tensile stress

http://dx.doi.org/10.1117/12.886824