Abstract
Experiments on micro-specimens have shown that the deformation behavior of materials can be size dependent. The size dependence is, for example, reflected in a stiffer elastic response on the sub-microscale. A quantitative understanding of the size effect is important for the design of micro- and nanosize systems. In our paper higher-order theories of elasticity are used for the description of the bending behavior of micro-beams. These include additional material parameters in order to describe a size effect and they go beyond the limits of the classical Boltzmann continuum. In particular couple stress and strain gradient theory of linear elasticity are used in this work as special examples of higher gradient theories. Another objective of the paper is to determine the length scale parameters by measurements performed with extremely small cantilever beams. In particular, deflection measurements are performed and force data are recorded for submicron beams made of silicon and silicon nitride. The tests are performed by using a highly sensitive atomic force microscope. In addition Raman spectroscopy is used for the same purpose. The obtained data is fitted to the formulae of higher elasticity for the bending of slender beams and can be used for evaluation of higher gradient coefficients.
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The present work is supported by DFG MU 1752/33-1.
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Liebold, C., Müller, W.H. (2013). Measuring Material Coefficients of Higher Gradient Elasticity by Using AFM Techniques and Raman-Spectroscopy. In: Altenbach, H., Forest, S., Krivtsov, A. (eds) Generalized Continua as Models for Materials. Advanced Structured Materials, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36394-8_14
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DOI: https://doi.org/10.1007/978-3-642-36394-8_14
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