The conventional contact mechanics does not account for surface tension; however, it is important for micro- or nanosized contacts. In the present paper, the influences of surface tension on the indentations of an elastic half-space by a rigid sphere, cone, and flat-ended cylinder are investigated, and the corresponding singular integral equations are formulated. Due to the complicated structure of the integral kernel, it is difficult to obtain their analytical solutions. By using the Gauss–Chebyshev quadrature formula, the integral equations are solved numerically first. Then, for each indenter, the analytical solutions of two limit cases considering only the bulk elasticity or surface tension are presented. It is interesting to find that, through a simple combination of the solutions of two limit cases and fitting the direct numerical results, the dependence of load on contact radius or indent depth for general case can be given explicitly. The results incorporate the contribution of surface tension in contact mechanics and are helpful to understand contact phenomena at micro- and nanoscale.
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Research-Article
General Relations of Indentations on Solids With Surface Tension
Jianmin Long,
Jianmin Long
Institute of Soft Matter Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China;
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China;
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Search for other works by this author on:
Yue Ding,
Yue Ding
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Search for other works by this author on:
Weike Yuan,
Weike Yuan
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Search for other works by this author on:
Wen Chen,
Wen Chen
Institute of Soft Matter Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
Search for other works by this author on:
Gangfeng Wang
Gangfeng Wang
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wanggf@mail.xjtu.edu.cn
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wanggf@mail.xjtu.edu.cn
Search for other works by this author on:
Jianmin Long
Institute of Soft Matter Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China;
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China;
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Yue Ding
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Weike Yuan
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
Wen Chen
Institute of Soft Matter Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, China
Gangfeng Wang
SVL,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wanggf@mail.xjtu.edu.cn
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wanggf@mail.xjtu.edu.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 2, 2017; final manuscript received March 4, 2017; published online April 5, 2017. Assoc. Editor: Harold S. Park.
J. Appl. Mech. May 2017, 84(5): 051007 (8 pages)
Published Online: April 5, 2017
Article history
Received:
January 2, 2017
Revised:
March 4, 2017
Citation
Long, J., Ding, Y., Yuan, W., Chen, W., and Wang, G. (April 5, 2017). "General Relations of Indentations on Solids With Surface Tension." ASME. J. Appl. Mech. May 2017; 84(5): 051007. https://doi.org/10.1115/1.4036214
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