Measuring Material Coefficients of Higher Gradient Elasticity by Using AFM Techniques and Raman-Spectroscopy
Measuring Material Coefficients of Higher Gradient Elasticity by Using AFM Techniques and Raman-Spectroscopy
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DOI：
10.1007/978-3-642-36394-8_14
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Liebold;W. Müller
中科院分区：
文献类型：
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作者：
C. Liebold;W. Müller
微观试样的实验表明，材料的变形行为可以是尺寸依赖性的。例如，尺寸依赖性反映在亚微米尺度上的更硬的弹性响应中。对尺寸效应的定量理解对于微米和纳米尺寸系统的设计是重要的。本文采用高阶弹性理论描述微梁的弯曲行为。这些包括额外的材料参数，以描述的尺寸效应，他们超越了经典玻尔兹曼连续的限制。特别是偶应力和应变梯度理论的线弹性在这项工作中使用的高梯度理论的特殊例子。本文的另一个目的是通过测量极小的悬臂梁来确定长度尺度参数。特别是，偏转测量和力的数据被记录的硅和氮化硅制成的亚微米梁。测试是通过使用高灵敏度的原子力显微镜进行的。此外，拉曼光谱用于相同的目的。所得数据与细长梁弯曲的高弹性公式相吻合，并可用于计算高梯度系数。
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.