Analysis of two-dimensional contact problems considering surface effect
Analysis of two-dimensional contact problems considering surface effect
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考虑表面效应的二维接触问题分析
DOI：
10.1016/j.ijsolstr.2017.07.007
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发表时间：
2017-10-15
影响因子：
3.6
通讯作者：
Chen, Shaohua
中科院分区：
文献类型：
--
作者：
Jia, Ning;Yao, Yin;Chen, Shaohua
利用最近发展起来的连续介质理论，基于表面能密度的概念，考虑了表面效应对材料力学性能的影响，系统地研究了Boussinesq模型、刚性平头压头或圆柱压头冲压半无限大衬底的二维接触问题。对接触应力场和位移场进行了分析。与经典接触模型相比，压痕衬底的表面能密度只是一个附加参数，是影响接触性能的重要因素。结果表明，当考虑表面效应时，半无限大衬底发生硬化。标度分析进一步表明，只有当接触宽度与体表能密度与体剪切模的比值相当时，有表面效应的理论预测与无表面效应的经典接触解之间的差异才会变得显著。特别是在二维圆柱凸模问题中，凸模尺寸越小或外压载荷越小，表面效应理论模型预测的纳米压痕硬度与经典接触模型预测的纳米压痕硬度偏差越大。研究结果不仅有助于纳米压痕硬度的精确测量，而且有助于准确评价纳米材料和纳米器件的使用性能。(C)2017爱思唯尔有限公司。保留所有权利。
Two-dimensional contact problems including a Boussinesq model, a semi-infinite substrate punched by a rigid flat-ended indenter or a cylindrical one, are systematically investigated with a recently developed continuum theory, in which surface effect on mechanical properties of materials is considered based on the concept of surface energy density. The contact stress and displacement fields are analyzed. It is found that the surface energy density of the indented bulk substrate, as only one additional parameter, serves as an important factor to influence the contact properties in contrast to the classical contact models. All the results show that the semi-infinite substrate becomes hardened when the surface effect is considered. Scaling analysis further demonstrates that differences between the theoretical predictions with surface effect and the classical contact solutions without surface effect become significant only if the contact width is comparable with the ratio of the bulk surface energy density to the bulk shear modulus. Specially, in the two-dimensional cylindrical punch problem, the smaller the punch size or the external compressive load, the more serious the deviation of the nano-indentation hardness predicted by the theoretical model with surface effect and the classical contact one. The results should be helpful not only for precise measurement of nano-indentation hardness but also for accurate evaluation of service performance of nanomaterials and nano-devices. (C) 2017 Elsevier Ltd. All rights reserved.