Rough surface contact analysis by means of the Finite Element Method and of a new reduced model

Vladislav A. Yastrebov; Julian Durand; Henry Proudhon; Georges Cailletaud

doi:10.1016/j.crme.2011.05.006

Surface mechanics: facts and numerical models

Rough surface contact analysis by means of the Finite Element Method and of a new reduced model
[Analyse du contact entre surfaces rugueuses par la méthode des éléments finis et par une approche simplifiée]

Vladislav A. Yastrebov ¹ ; Julian Durand ¹ ; Henry Proudhon ¹ ; Georges Cailletaud ¹

¹ Centre des matériaux, Mines ParisTech, CNRS UMR 7633, BP 87, 91003 Evry cedex, France

Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 473-490.

Résumé
Abstract

Cet article présente deux approches dʼun contact normal sans frottement entre un matériau élastoplastique et un plan rigide : une simulation complète par élements finis et un modèle simplifié. Les deux approches utilisent un élement représentatif dʼune surface rugueuse mesurée expérimentalement. Le calcul complet a été réalisé avec le code éléments finis Zset en usant dʼune résolution parallèle du problème et celui-ci fournit la solution de référence pour le modèle simplifié. Celui-ci se nourrit dʼune série de courbes de réponse calibrées par des calcul éléments finis modélisant une seule aspérité ainsi que des règles pour tenir compte de lʼinteraction entre aspérités. Le modèle est alors capable de prédire la courbe charge–déplacement, lʼaire réelle de contact et le volume libre laissé entre les deux surfaces de contact au cours de la compression dʼune surface rugueuse par un plan rigide. Le temps CPU est de quelque secondes pour le modèle simplifié contre quelques jours pour le calcul complet par éléments finis.

This article presents two approaches of a normal frictionless mechanical contact between an elastoplastic material and a rigid plane: a full scale finite element analysis (FEA) and a reduced model. Both of them use a representative surface element (RSE) of an experimentally measured surface roughness. The full scale FEA is performed with the Finite Element code Zset using its parallel solver. It provides the reference for the reduced model. The ingredients of the reduced model are a series of responses that are calibrated by means of FEA on a single asperity and phenomenological rules to account for asperity–asperity interaction. The reduced model is able to predict the load–displacement curve, the real contact area and the free volume between the contacting pair during the compression of a rough surface against a rigid plane. The CPU time is a few seconds for the reduced model, instead of a few days for the full FEA.

Publié le : 2011-06-21

DOI : 10.1016/j.crme.2011.05.006

Keywords: Roughness, Normal mechanical contact, Real contact area, Free volume, Finite Element Method, Reduced contact algorithm
Mot clés : Rugosité, Contact mécanique normal, Aire de contact réelle, Volume libre, Méthode des éléments finis, Algorithme de contact simplifié

Affiliations des auteurs :

Vladislav A. Yastrebov ¹ ; Julian Durand ¹ ; Henry Proudhon ¹ ; Georges Cailletaud ¹

¹ Centre des matériaux, Mines ParisTech, CNRS UMR 7633, BP 87, 91003 Evry cedex, France

@article{CRMECA_2011__339_7-8_473_0,
     author = {Vladislav A. Yastrebov and Julian Durand and Henry Proudhon and Georges Cailletaud},
     title = {Rough surface contact analysis by means of the {Finite} {Element} {Method} and of a new reduced model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {473--490},
     publisher = {Elsevier},
     volume = {339},
     number = {7-8},
     year = {2011},
     doi = {10.1016/j.crme.2011.05.006},
     language = {en},
}

TY  - JOUR
AU  - Vladislav A. Yastrebov
AU  - Julian Durand
AU  - Henry Proudhon
AU  - Georges Cailletaud
TI  - Rough surface contact analysis by means of the Finite Element Method and of a new reduced model
JO  - Comptes Rendus. Mécanique
PY  - 2011
SP  - 473
EP  - 490
VL  - 339
IS  - 7-8
PB  - Elsevier
DO  - 10.1016/j.crme.2011.05.006
LA  - en
ID  - CRMECA_2011__339_7-8_473_0
ER  -

%0 Journal Article
%A Vladislav A. Yastrebov
%A Julian Durand
%A Henry Proudhon
%A Georges Cailletaud
%T Rough surface contact analysis by means of the Finite Element Method and of a new reduced model
%J Comptes Rendus. Mécanique
%D 2011
%P 473-490
%V 339
%N 7-8
%I Elsevier
%R 10.1016/j.crme.2011.05.006
%G en
%F CRMECA_2011__339_7-8_473_0

Vladislav A. Yastrebov; Julian Durand; Henry Proudhon; Georges Cailletaud. Rough surface contact analysis by means of the Finite Element Method and of a new reduced model. Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 473-490. doi : 10.1016/j.crme.2011.05.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.05.006/

Bibliographie
Cité par

[1] J.A. Greenwood; J.B.P. Williamson Contact of nominally flat surfaces, Proceedings of the Royal Society of London Series A, Volume 295 (1966), pp. 300-319

[2] A.W. Bush; R.D. Gibson; T.R. Thomas The elastic contact of a rough surface, Wear, Volume 153 (1992), pp. 53-64

[3] Y. Zhao; L. Chang A model of asperity interactions in elastic–plastic contact of rough surfaces, Journal of Tribology, Volume 123 (2001), pp. 857-864

[4] L. Pei; S. Hyun; J.F. Molinari; M.O. Robbins Finite element modeling of elasto–plastic contact between rough surfaces, Journal of the Mechanics and Physics of Solids, Volume 53 (2005), pp. 2385-2409

[5] E.J. Abbott; F.A. Firestone Specifying surface quality – a method based on accurate measurement and comparison, Mechanical Engineering, Volume 55 (1933), p. 569

[6] B. Bhushan Surface roughness analysis and measurement techniques, Modern Tribology Handbook, vol. 1, CRC Press, London, 2001, pp. 49-119

[7] D.J. Whitehouse; J.F. Archard The properties of random surface of significance in their contact, Proceedings of the Royal Society of London Series A, Volume 316 (1970), pp. 97-121

[8] A.W. Bush; R.D. Gibson; G.P. Keogh Strongly anisotropic rough surfaces, Journal of Lubrification Technology, Volume 101 (1979), pp. 15-20

[9] A.W. Bush; R.D. Gibson The elastic contact of a rough surface, Wear, Volume 35 (1987), pp. 87-111

[10] W.R. Chang; I. Etsion; D.B. Bogy An elastic–plastic model for the contact of rough surfaces, Journal of Tribology, Volume 109 (1987), pp. 257-263

[11] Y. Zhao; D.M. Maietta; L. Chang An asperity microcontact model incorporating the transition from elastic deformations to fully plastic flow, Journal of Tribology, Volume 122 (2000), pp. 86-93

[12] C. Vallet; D. Lasseux; P. Sainsot; H. Zahouani Real versus synthesized fractal surfaces: Contact mechanics and transport properties, Tribology International, Volume 42 (2009), pp. 250-259

[13] C. Vallet; D. Lasseux; H. Zahouani; P. Sainsot Sampling effect on contact and transport properties between fractal surfaces, Tribology International, Volume 42 (2009), pp. 1132-1145

[14] P. Sainsot; N. Jacq; D. Nélias A numerical model for elastoplastic rough contact, CMES, Volume 3 (2002) no. 4, pp. 497-506

[15] B.B. Mandelbrot The Fractal Geometry of Nature, Freeman, New York, 1982

[16] B. Bhushan Contact mechanics of rough surfaces in tribology: Multiple asperity contact, Tribology Letters, Volume 4 (1997), pp. 1-35

[17] B.N.J. Persson Theory of rubber friction and contact mechanics, Journal of Chemical Physics, Volume 115 (2001), pp. 3840-3861

[18] A. Majumdar; B. Bhushan Fractal model of elastic–plastic contact between rough surface, Journal of Tribology, Volume 113 (1991), pp. 1-11

[19] A. Majumdar; B. Bhushan Elastic–plastic contact model of bifractal surfaces, Wear, Volume 35 (1975), pp. 87-111

[20] C. Vallet, Fuite liquide au travers dʼun contact rugueux : application lʼétanchéité interne dʼappareils de robinetterie. PhD thesis, Ecole Nationale Supérieure dʼArts et Métiers, 2008.

[21] C. Farhat; F.-X. Roux Implicit parallel processing in structural mechanics, Computational Mechanics Advances, Volume 2 (1994), pp. 1-24

[22] B.N.J. Persson Contact mechanics for randomly rough surfaces, Surface Science Reports, Volume 61 (2006), pp. 201-227

[23] G.E. Farin Curves and Surfaces for CAGD: A Practical Guide, Morgan Kaufmann, 2002

[24] T. Dick; G. Cailletaud Fretting modelling with a crystal plasticity model of Ti6Al4V, Computational Materials Science, Volume 38 (2006), pp. 113-125

[25] B.N.J. Persson; O. Albohr; U. Tartaglino; A.I. Volokitin; E. Tosatti On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion, Journal of Physics: Condensed Matter, Volume 17 (2005), p. R1-R62

[26] P. Raghavan, DSCPACK: Domain-separator codes for the parallel solution of sparse linear systems, Tech. rep. CSE-02-004, Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802, 2002.

[27] K.L. Johnson Contact Mechanics, Cambridge University Press, 1987

[28] N. Kikuchi; J.T. Oden Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988

[29] P. Alart; A. Curnier A mixed formulation for frictional contact problems prone to newton like solution method, Computer Methods in Applied Mechanics and Engineering, Volume 92 (1991), pp. 353-375

[30] T.W. McDewitt; T.A. Laursen A mortar-finite element formulation for frictional contact problems, International Journal for Numerical Methods in Engineering, Volume 48 (2000), pp. 1525-1547

[31] J. Oliver; S. Hartmann; J.C. Cante; R. Weyler; J.A. Hernández A contact domain method for large deformation frictional contact problems. Part I: Theoretical basis, Computer Methods in Applied Mechanics and Engineering, Volume 198 (2009), pp. 2591-2606

[32] P. Wriggers Computational Contact Mechanics, Springer, 2006

Cité par Sources :

Commentaires - Politique