Abstract
Three-dimensional finite element modeling of the contact between a rigid spherical indenter and a rough surface is presented when considering both the loading and unloading phases. The relationships among the indentation load, displacement, contact area, and mean contact pressure for both loading and unloading are established through a curve fitting using sigmoid logistic and power law functions. The contact load is proportional to the contact area, and the mean contact pressure is related to the characteristic stress, which is dependent on the material properties. The residual displacement is proportional to the maximum indentation displacement. A proportional relationship also exists for plastically dissipated energy and work conducted during loading. The surface roughness results in an effective elastic modulus calculated from an initial unloading stiffness several times larger than the true value of elastic modulus. Nonetheless, the calculated modulus under a shallow spherical indentation can still be applied for a relative comparison.
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Acknowledgements
This project is supported by National Natural Science Foundation of China (Grant Nos. 51705082, 51875016), Fujian Provincial Minjiang Scholar (No. 0020-510486), and Fujian Provincial Collaborative Innovation Center for High-end Equipment Manufacturing (No. 0020-50006103).
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Chenghui GAO. He received his PhD in mechanical engineering from China Academy of Machinery Science & Technology in 1990, and is the founder and the leader of the Research Institute of Tribology in Fuzhou University. He was vicepresident of Fuzhou University, and has received many awards such as National Model Teacher, “Ten Thousand People Plan” Outstanding Teacher of the Ministry of Education, Fujian Provincial Outstanding Teacher, and Fujian Provincial Second Prize of Science and Technology Progress.
Henry PROUDHON. He received his PhD in engineering and science from Institut National des Sciences Appliquées de Lyonin 2005, and is now a CNRS research associate in Centre des Matériaux, MINES Paristech. Before joining the French National Centre for Scientific Research, Centre des Matériaux P.M. Fourt, in 2007, he served as a post-doctoral researcher at the University of British Columbia and at Institut National des Sciences Appliquées de Lyon. He won a RIST medal from the French Metallurgy and Material Society SF2M in 2013. His research topics include elasticity and plasticity of crystalline solids, fretting fatigue damage mechanisms, and multi-scale contact mechanics.
Ming LIU. He received his PhD in materials science and engineering from the University of Kentucky in 2012. He was a post-doctorate researcher at the Centre of Materials, Mines Paris Tech France in 2013, and at Washington State University in 2014. He joined the School of Mechanical Engineering and Automation, Fuzhou University in 2015, and became a professor and doctor supervisor thanks to Fujian Provincial Minjiang Scholar Program. His research focus is on micro/nano mechanical testing, characterization of advanced materials, and computational modeling of multiple physics problems.
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Gao, C., Proudhon, H. & Liu, M. Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface. Friction 7, 587–602 (2019). https://doi.org/10.1007/s40544-018-0245-3
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DOI: https://doi.org/10.1007/s40544-018-0245-3