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The incorporation of the saturation of the tangential contact stress with the increase of the normal contact stress is required for the analysis of the friction phenomenon of solids and structures subjected to a high normal contact stress, which cannot be described by the Coulomb friction condition, in which the tangential contact stress increases linearly with the increase of the normal contact stress. In this article, the subloading-friction model, which is capable of describing the smooth elastic–plastic transition, the static–kinetic transition, and the recovery of the static friction during the cease of sliding, is extended to describe this property. Further, some numerical examples are shown, and the validity of the present model will be verified by the simulation of the test data on the linear sliding of metals.


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Subloading-friction model with saturation of tangential contact stress

Show Author's information Koichi HASHIGUCHI1,2( )Masami UENO3
Kyushu University, Fukuoka 819-0395, Japan
MSC Software Ltd., Tokyo 101-0054, Japan
University of the Ryukyus, Okinawa 903-0213, Japan

Abstract

The incorporation of the saturation of the tangential contact stress with the increase of the normal contact stress is required for the analysis of the friction phenomenon of solids and structures subjected to a high normal contact stress, which cannot be described by the Coulomb friction condition, in which the tangential contact stress increases linearly with the increase of the normal contact stress. In this article, the subloading-friction model, which is capable of describing the smooth elastic–plastic transition, the static–kinetic transition, and the recovery of the static friction during the cease of sliding, is extended to describe this property. Further, some numerical examples are shown, and the validity of the present model will be verified by the simulation of the test data on the linear sliding of metals.

Keywords: subloading-friction model, static/kinetic friction, high contact stress, monotonic/reciprocal sliding

References(40)

[1]
Seguchi Y, Shindo A, Tomita Y, Sunohara M. Sliding rule of friction in plastic forming of metal. Compt Meth Nonlinear Mech, University of Texas at Austin, 683–692 (1974)
[2]
Fredriksson B. Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems. Comput Struct 6(4–5): 281–290 (1976)
[3]
Michalowski R, Mróz Z. Associated and non-associated sliding rules in contact friction problems. Archiv Mech 30(3): 259–276 (1978)
[4]
Oden J T, Pires E B. Algorithms and numerical results for finite element approximations of contact problems with non-classical friction laws. Comput Struct 19(1–2): 137–147 (1984)
[5]
Oden J T, Pires E B. Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. J Appl Mech 50(1): 67–76 (1983)
[6]
Curnier A. A theory of friction. Int J Solids Struct 20(7): 637–647 (1984)
[7]
Cheng J H, Kikuchi N. An incremental constitutive relation of unilateral contact friction for large deformation analysis. J Appl Mech 52(3): 639–648 (1985)
[8]
Kikuchi N, Oden J T. Contact Problems in Elasticity: Society for Industrial and Applied Mathematics. Philadelphia (USA): Society for Industrial and Applied Mathematics, 1987.
[9]
Wriggers P, Vu Van T, Stein E. Finite element formulation of large deformation impact–contact problems with friction. Comput Struct 37(3): 319–331 (1990)
[10]
Perić D, Owen D R J. Computational model for 3-D contact problems with friction based on the penalty method. Int J Numer Methods Eng 35(6): 1289–1309 (1992)
[11]
Anand L. A constitutive model for interface friction. Comput Mech 12(4): 197–213 (1993)
[12]
Hashiguchi K. Foundations of Elastoplasticity: Subloading Surface Model, 3rd edn. Springer, 2017.
DOI
[13]
Hashiguchi, K. Nonlinear Continuum Mechanics for Finite Elasticity–plasticity: Multiplicative Decomposition with Subloading Surface Model. Elsevier, 2020.
[14]
Gearing B P, Moon H S, Anand L. A plasticity model for interface friction: Application to sheet metal forming. Int J Plast 17(2): 237–271 (2001)
[15]
Dieterich J H. Time-dependent friction and the mechanics of stick–slip. Pure Appl Geophys 116(4–5): 790–806 (1978)
[16]
Ruina A L. Friction laws and instabilities: A quasistatic analysis of some dry frictional behavior. Ph.D. Thesis. Providence (USA): Brown University, 1980.
[17]
Ruina A L. Slip instability and state variable friction laws. J Geophys Res Solid Earth 88(B12): 10359–10370 (1983)
[18]
Rice J R, Ruina A L. Stability of steady frictional slipping. J Appl Mech 50(2): 343–349 (1983)
[19]
Scholz C H. Rate-and state-variable friction law. Nature 391: 37–41 (1998)
[20]
Rice J R, Lapusta N, Ranjith K. Rate and state dependent friction and the stability of sliding between elastically deformable solids. J Mech Phys Solids 49(9): 1865–1898 (2001)
[21]
Kame N, Fujita S, Nakatani M, Kusakabe T. Effects of a revised rate- and state-dependent friction law on aftershock triggering model. Tectonophysics 600: 187–195 (2013)
[22]
Rabinowicz E. The nature of the static and kinetic coefficients of friction. J Appl Phys 22(11): 1373–1379 (1951)
[23]
Howe P G, Benton D P, Puddington I E. London–van der Waals attractive forces between glass surfaces. Can J Chem 33(9): 1375–1383 (1955)
[24]
Brockley C A, Davis H R. The time-dependence of static friction. J Lubr Technol 90(1): 35–41 (1968)
[25]
Kato S, Sato N, Matsubayashi T. Some considerations on characteristics of static friction of machine tool slideway. J Lubr Technol 94(3): 234–247 (1972)
[26]
Horowitz F G, Ruina A L. Slip patterns in a spatially homogeneous fault model. J Geophys Res 94(B8): 10279–10298 (1989)
[27]
Bureau L, Baumberger T, Caroli C, Ronsin O. Low-velocity friction between macroscopic solids. Comptes Rendus De l’académie Des Sci Ser IV Phys 2(5): 699–707 (2001)
[28]
Oldroyd J G. On the formulation of rheological equations of state. Proc Roy Soc A Mat Phys Eng Sci 200(1063): 523–541 (1950)
[29]
Hashiguchi K, Yamakawa Y. Introduction to Finite Strain Theory for Continuum Elasto-plasticity. Chichester (UK): John Wiley & Sons, 2012.
DOI
[30]
Wriggers P. Computational Contact Mechanics. Berlin (Germany): Springer Berlin Heidelberg, 2006.
DOI
[31]
Popov V L. Contact Mechanics and Friction: Physical Principles and Applications. Berlin (Germany): Springer Berlin Heidelberg, 2017.
DOI
[32]
Hashiguchi K, Ozaki S, Okayasu T. Unconventional friction theory based on the subloading surface concept. Int J Solids Struct 42(5–6): 1705–1727 (2005)
[33]
Hashiguchi K, Ozaki S. Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction. Int J Plast 24(11): 2102–2124 (2008)
[34]
Ozaki T, Yamakawa Y, Ueno M, Hashiguchi K. Description of sand–metal friction behavior based on subloading-friction model. Friction 10: 1660–1675 (2022)
[35]
Ozaki S, Hashiguchi K. Numerical analysis of stick–slip instability by a rate-dependent elastoplastic formulation for friction. Tribol Int 43(11): 2120–2133 (2010)
[36]
Hashiguchi K. Elastoplasticity Theory. Berlin (Germany): Springer Berlin Heidelberg, 2009.
DOI
[37]
Ozaki S, Hikida K, Hashiguchi K. Elastoplastic formulation for friction with orthotropic anisotropy and rotational hardening. Int J Solids Struct 49(3–4): 648–657 (2012)
[38]
Hashiguchi K, Ueno M, Kuwayama T, Suzuki N, Yonemura S, Yoshikawa N. Constitutive equation of friction based on the subloading-surface concept. Proc Roy Soc A Mat Phys Eng Sci 472(2191): 20160212 (2016)
[39]
Ozaki S, Matsuura T, Maegawa S. Rate-, state-, and pressure-dependent friction model based on the elastoplastic theory. Friction 8(4): 768–783 (2020)
[40]
Hashiguchi K. Multiplicative hyperelastic-based plasticity for finite elastoplastic deformation/sliding: A comprehensive review. Arch Comput Methods Eng 26(3): 597–637 (2019)
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Received: 28 January 2022
Revised: 04 March 2022
Accepted: 23 May 2022
Published: 26 August 2022
Issue date: June 2023

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