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Elastoplastic contact mechanics model of rough surface based on fractal theory

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Abstract

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

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Authors and Affiliations

  1. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yuan Yuan, Li Gan & Kai Liu

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Xiaohui Yang

Authors
  1. Yuan Yuan
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  2. Li Gan
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  3. Kai Liu
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  4. Xiaohui Yang
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Corresponding author

Correspondence to Yuan Yuan.

Additional information

Supported by National Natural Science Foundation of China(Grant Nos. 51105304, 51475364), and Shaanxi Provincial Natural Science Basic Research Plan of China(Grant No. 2015JM5212)

GAN Li, born in 1990, is currently a master candidate at Xi’an University of Technology, China. His research interests include rough surface mechanical properties.

LIU Kai, born in 1957, is currently a professor and a PhD candidate supervisor at Xi’an University of Technology, China. His research interests include mechanical transmission theory and application.

YANG Xiaohui, born in 1979, is currently a PhD candidate and a senior engineer at Xi’an Jiaotong University, China. His main research interests include the structure stability analysis and the fatigue life prediction.

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Yuan, Y., Gan, L., Liu, K. et al. Elastoplastic contact mechanics model of rough surface based on fractal theory. Chin. J. Mech. Eng. 30, 207–215 (2017). https://doi.org/10.3901/CJME.2016.0624.079

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  • DOI: https://doi.org/10.3901/CJME.2016.0624.079

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