Nanoindentation of a half-space due to a rigid cylindrical roller based on Steigmann-Ogden surface mechanical model

Li Xiaobao; Mi Changwen

摘要

In this article, a semianalytical method of solution is developed for the nanocontact problem of elastic half-space indented by a rigid cylindrical roller. The mechanical formulation is based on the complete version of Steigmann-Ogden surface elasticity theory. Surface tension, surface tensile stiffness and surface flexural rigidity of the half-space boundary are all taken into consideration. Fourier integral transform method converts the governing equations and displacement boundary conditions of the nanocontact problem into a singular integral equation. Gauss-Chebyshev quadrature and an iterative algorithm numerically solve this integral equation and the force equilibrium condition. The developed semianalytical solution is general in the sense that it can reduce to a few simplified theories. These include classical solution, considering only a single surface material parameter, and Gurtin-Murdoch surface elasticity theory, for which analytical kernel functions of the singular integral equation are presented. Dimension analysis demonstrates that the effects of Steigmann-Ogden surface elasticity on the two-dimensional Hertzian nanocontact properties are up to three dimensionless ratios among surface material parameters, shear modulus and the size of nanocontact. Moreover, least-squares regression analysis suggests that, in the presence of surface effects, an elliptic arc less than a half can represent the nanocontact pressure. When compared with their classical counterparts, lower maximum contact pressure and nonzero minimum pressure are found. Parametric experiments further show that surface tension and surface flexural rigidity significantly affect contact length, contact pressure, contact stiffness as well as displacements and stresses near the half-space boundary. In contrast, the effects of surface membrane stiffness are of secondary importance. In general, smaller indenters and larger surface constants lead to higher load-carrying capabilities of half-space and thus better mechanical responses.

机译：在本文中，为刚性圆柱辊凹入的弹性半空间的纳米接触问题而开发了一种半角质方法。机械配方基于Steigmann-ogden表面弹性理论的完整版本。表面张力，半空间边界的表面拉伸刚度和表面弯曲刚度都考虑。傅里叶积分变换方法将纳米接触问题的控制方程和位移边界条件转换为奇异积分方程。高斯-Chebyshev正交和迭代算法数值求解这种整体方程和力平衡条件。发达的半角质解决方案是一般的意义上，它可以减少少数简化的理论。这些包括经典解，考虑仅考虑单个表面材料参数和古霉菌 - 默多普表面弹性理论，呈现了奇异积分方程的分析核功能。尺寸分析表明，在表面材料参数，剪切模量和纳米型尺寸中，Steigmann-ogden-ogden表面弹性对二维Hertzian纳米接触性能的影响达到三维无量纲比率。此外，最小二乘回归分析表明，在表面效应存在下，小于半径的椭圆弧可以表示纳米接触压力。与其经典对应物相比，发现较低的最大接触压力和非零最小压力。参数实验进一步表明，表面张力和表面弯曲刚度显着影响了半空间边界附近的接触长度，接触压力，接触刚度以及位移和应力。相反，表面膜刚度的影响具有次要的重要性。通常，较小的压头和较大的表面常数导致半空间的载荷能力更高，从而更好的机械响应。

Nanoindentation of a half-space due to a rigid cylindrical roller based on Steigmann-Ogden surface mechanical model

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