Rigid frictionless indentation on elastic half space with influence of surface stresses
Rigid frictionless indentation on elastic half space with influence of surface stresses
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DOI：
10.1016/j.ijengsci.2013.04.005
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发表时间：
2013-10
影响因子：
6.6
通讯作者：
Y. Pinyochotiwong;J. Rungamornrat;T. Senjuntichai
中科院分区：
文献类型：
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作者：
Y. Pinyochotiwong;J. Rungamornrat;T. Senjuntichai
本文将基于连续介质的概念应用于轴对称刚性无摩擦压头作用于考虑表面能效应的各向同性线弹性半空间的分析。通过采用完整的Gurtin-Murdoch连续介质模型来考虑表面应力的影响。利用标准的Love表示和Hankel积分变换，将该边值问题归结为一组对偶积分方程组，进而转化为等价的第二类Fredholm型积分方程组。然后，基于解的离散化和标准配置技术，采用选定的数值方法来构造其数值解。给出了块体内弹性场的数值结果，并对不同形状和不同深度接触半径的压头进行了比较。结果表明，表面自由能对体应力和位移的影响以及解的尺寸依赖性在离自由表面很近的区域变得更加明显。与已有的结果相比，残余表面张力对预测响应的贡献是明显的。该数学模型不仅为研究任意轴对称压头的力学性能和弹性场提供了一种新的途径，而且为纳米力学领域的进一步研究提供了重要的依据。
This paper proposes an application of continuum-based concepts in the analysis of an axisymmetric rigid frictionless indentor acting on an isotropic, linearly elastic half-space accounted for surface energy effects. The influence of surface stresses is considered by employing a complete Gurtin–Murdoch continuum model for surface elasticity. With use of standard Love’s representation and Hankel integral transform, such boundary value problem is reduced to a set of dual integral equations that can be further transformed into an equivalent Fredholm integral equation of the second kind. Selected numerical procedures based on the solution discretization and standard collocation technique are then implemented to construct its solution numerically. Obtained numerical results for elastic fields within the bulk are shown and compared for indentors of different profiles and contact radii at various depths. It is found that the influence of surface free energy on bulk stresses and displacements and the size-dependency of solutions become more apparent in a region very near the free surface. The significant contribution of the residual surface tension on predicted responses is obviously observed in comparison with existing results. The proposed mathematical model not only offers an alternative for specifically studying both mechanical properties and elastic fields for indentors of arbitrary axisymmetric profiles but also provides, in general, a crucial basis for further investigations in the area of nano-mechanics.