A large deformation analysis of plates or membranes for the determination of Young's modulus and Poisson's ratio

Citation

Breton, Fabienne Anne (1995) A large deformation analysis of plates or membranes for the determination of Young's modulus and Poisson's ratio. Engineer's thesis, California Institute of Technology. doi:10.7907/0c9r-ve54. https://resolver.caltech.edu/CaltechETD:etd-03292007-093444

Abstract

An analytical method for determining Young's modulus and the Poisson's ratio of thin films is considered; the method is based on the load-deflection behavior of a rectangular membrane of finite aspect ratio n = b/a subjected to uniform pressure (c.f. figure 0.1). Following numerical analysis, previously published model results are shown to be inaccurate, especially for aspect ratios greater than 1.5. An improved model description decomposes the displacement field into two parts: following the Timoshenko formulation, the deflection is assumed to be sinusoidal near the edges, but for aspect ratios larger than unity the central portion parallel to the longer sides is assumed to bear two-dimensional character (the displacement field is independent of the coordinate parallel to the longer side). Using energy methods and including the effects of the residual stress, the load-deflection relationship for a rectangular membrane of arbitrary aspect ratio n = b/a, under uniform pressure, is obtained. Experiments are simulated by using numerical analysis. By comparing the numerical data of load-versus-deflection behavior to that for the energy based approximation, Young's modulus can be determined to within 2% of the value specified for the numerical analysis, provided that Poisson's ratio, v, is known. If the latter is not the case, the error increases to 14%, if the full range of Poisson's ratio (0 <= v <= 0.5) is admitted. Narrowing of the uncertainty through bounding Poisson's ratio is demonstrated. This result constitutes a significant improvement over the previous models which were shown to elicit errors on the order of 45%. A method to evaluate Poisson's ratio is also proposed. Making use of the load-deflection relationship for a rectangular plate of any aspect ratio, Poisson's ratio may be evaluated through the comparison of the load-deflection behavior of membranes of different aspect ratios. This method was found to be valid for materials with Poisson's ratio in the range {0.25, 0.5}. Since it is generally difficult to obtain homogeneous films, this study was extended to considerations for bimaterial plates in terms of an effective thickness that is well defined. A layer of the material under examination is deposited onto a well-characterized substrate so that a sandwich film results. Young's modulus of the material can then be deduced from the load-deflection data of the bimaterial film.

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