Journal Home > Volume 7 , Issue 6
Friction 2019, 7(6): 587-602 https://doi.org/10.1007/s40544-018-0245-3
Research Article | Open Access | Issue | Published: 12 November 2018

Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface

Show Author's Information Chenghui GAO1,  Henry PROUDHON2( ),  Ming LIU1( )
School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Centre des Matériaux, MINES Paris Tech, Evry Cedex 91003, France
Keywords:
contact mechanics, indentation, surface analysis, finite element modeling, spherical indenter
Cite this article:
GAO C, PROUDHON H, LIU M. Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface. Friction, 2019, 7(6): 587-602. https://doi.org/10.1007/s40544-018-0245-3
Download citation
EndNote(RIS)
BibTeX

511

Views

17

Downloads

Citations

22

Crossref

N/A

WoS

24

Scopus

3

CSCD

Abstract Full text About this article

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.


menu
Abstract
Full text
Outline
About this article

Three-dimensional finite element analysis of shallow indentation of rough strain-hardening surface

Show Author's information Chenghui GAO1, Henry PROUDHON2( ), Ming LIU1( )
School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Centre des Matériaux, MINES Paris Tech, Evry Cedex 91003, France

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.

Keywords: contact mechanics, indentation, surface analysis, finite element modeling, spherical indenter

References(92)

[1]
Zhang S J, To S, Wang S J, Zhu Z W. A review of surface roughness generation in ultra-precision machining. Int J Mach Tools Manuf 91: 76-95 (2015)
DOI Google Scholar
[2]
Gupta M K, Sood P K. Surface roughness measurements in NFMQL assisted turning of titanium alloys: An optimization approach. Friction 5(2): 155-170 (2017)
DOI Google Scholar
[3]
Murashov M V, Panin S D. Numerical modelling of contact heat transfer problem with work hardened rough surfaces. Int J Heat Mass Transfer 90: 72-80 (2015)
DOI Google Scholar
[4]
Ghosh A, Sadeghi F. A novel approach to model effects of surface roughness parameters on wear. Wear 338-339: 73-94 (2015)
DOI Google Scholar
[5]
Wang Y C, Liu Y, Wang Z C, Wang Y M. Surface roughness characteristics effects on fluid load capability of tilt pad thrust bearings with water lubrication. Friction 5(4): 392-401 (2017)
DOI Google Scholar
[6]
Petean P G C, Aguiar M L. Determining the adhesion force between particles and rough surfaces. Powder Technol 274: 67-76 (2015)
DOI Google Scholar
[7]
Svetovoy V B, Palasantzas G. Influence of surface roughness on dispersion forces. Adv Colloid Interface Sci 216: 1-19 (2015)
DOI Google Scholar
[8]
Lyon K, Zhang Y Y, Mišković Z L, Song Y H, Wang Y N. Interaction of fast charges with a rough metal surface. Surf Sci 639: 32-38 (2015)
DOI Google Scholar
[9]
Liu Q F, Wang L, Shen S P. Effect of surface roughness on elastic limit of silicon nanowires. Comput Mater Sci 101: 267-274 (2015)
DOI Google Scholar
[10]
Nunez E E, Polycarpou A A. The effect of surface roughness on the transfer of polymer films under unlubricated testing conditions. Wear 326-327: 74-83 (2015)
DOI Google Scholar
[11]
Zhu Y, Chen X, Wang W, Yang H. A study on iron oxides and surface roughness in dry and wet wheel-rail contacts. Wear 328-329: 241-248 (2015)
DOI Google Scholar
[12]
Dawood H I, Mohammed K S, Rahmat A, Uday M B. The influence of the surface roughness on the microstructures and mechanical properties of 6061 aluminium alloy using friction stir welding. Surf Coat Technol 270: 272-283 (2015)
DOI Google Scholar
[13]
Curry N, Tang Z L, Markocsan N, Nylén P. Influence of bond coat surface roughness on the structure of axial suspension plasma spray thermal barrier coatings—Thermal and lifetime performance. Surf Coat Technol 268: 15-23 (2015)
DOI Google Scholar
[14]
Wang S. Real contact area of fractal-regular surfaces and its implications in the law of friction. J Tribol 126(1): 1-8 (2004)
DOI Google Scholar
[15]
Wang S, Shen J, Chan W K. Determination of the fractal scaling parameter from simulated fractal-regular surface profiles based on the weierstrass-mandelbrot function. J Tribol 129(4): 952-956 (2007)
DOI Google Scholar
[16]
Wang S, Komvopoulos K. A fractal theory of the interfacial temperature distribution in the slow sliding regime: Part II— Multiple domains, elastoplastic contacts and applications. J Tribol 116(4): 824-832 (1994)
DOI Google Scholar
[17]
Yan W, Komvopoulos K. Contact analysis of elastic-plastic fractal surfaces. J Appl Phys 84(7): 3617-3624 (1998)
DOI Google Scholar
[18]
Komvopoulos K, Gong Z Q. Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior. Int J Solids Struct 44(7-8): 2109-2129 (2007)
DOI Google Scholar
[19]
Gao Y F, Bower A F, Kim K S, Lev L, Cheng Y T. The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading. Wear 261(2): 145-154 (2006)
DOI Google Scholar
[20]
Bemporad A, Paggi M. Optimization algorithms for the solution of the frictionless normal contact between rough surfaces. Int J Solids Struct 69-70: 94-105 (2015)
DOI Google Scholar
[21]
Xu Y, Jackson R L, Marghitu D B. Statistical model of nearly complete elastic rough surface contact Int J Solids Struct 51(5): 1075-1088 (2014)
DOI Google Scholar
[22]
Yastrebov V A, Anciaux G, Molinari J F. From infinitesimal to full contact between rough surfaces: Evolution of the contact area. Int J Solids Struct 52: 83-102 (2015)
DOI Google Scholar
[23]
Greenwood J A. On the almost-complete contact of elastic rough surfaces: The removal of tensile patches. Int J Solids Struct 56-57: 258-264 (2015)
DOI Google Scholar
[24]
Berthe L, Sainsot P, Lubrecht A A, Baietto M C. Plastic deformation of rough rolling contact: An experimental and numerical investigation. Wear 312(1-2): 51-57 (2014)
DOI Google Scholar
[25]
Raffa M L, Lebon F, Vairo G. Normal and tangential stiffnesses of rough surfaces in contact via an imperfect interface model. Int J Solids Struct 87: 245-253 (2016)
DOI Google Scholar
[26]
Kogut L, Komvopoulos K. Analysis of the spherical indentation cycle for elastic-perfectly plastic solids. J Mater Res 19(12): 3641-3653 (2004)
DOI Google Scholar
[27]
Xu H, Komvopoulos K. Surface adhesion and hardening effects on elastic-plastic deformation, shakedown and ratcheting behavior of half-spaces subjected to repeated sliding contact. Int J Solids Struct 50(6): 876-886 (2013)
DOI Google Scholar
[28]
Song Z, Komvopoulos K. Elastic-plastic spherical indentation: Deformation regimes, evolution of plasticity, and hardening effect. Mech Mater 61: 91-100 (2013)
DOI Google Scholar
[29]
Greenwood J A, Williamson J B P. Contact of nominally flat surfaces. Proc Roy Soc A 295(1442): 300-319 (1966)
DOI Google Scholar
[30]
Hertz H. Ueber die berührung fester elastischer körper. J Reine Angew Math 1882(92): 156-171 (1882)
DOI Google Scholar
[31]
Bush A W, Gibson R D, Thomas T R. The elastic contact of a rough surface. Wear 35(1): 87-111 (1975)
DOI Google Scholar
[32]
Persson B N J. Elastoplastic contact between randomly rough surfaces. Phys Rev Lett 87(11): 116101 (2001)
DOI Google Scholar
[33]
Chang W R, Etsion I, Bogy D B. An elastic-plastic model for the contact of rough surfaces. J Tribol 109(2): 257-263 (1987)
DOI Google Scholar
[34]
Chang W R. An elastic-plastic contact model for a rough surface with an ion-plated soft metallic coating. Wear 212(2): 229-237 (1997)
DOI Google Scholar
[35]
Zhao Y W, Maietta D M, Chang L. An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow. J Tribol 122(1): 86-93 (1999)
DOI Google Scholar
[36]
Pei L, Hyun S, Molinari J F, Robbins M O. Finite element modeling of elasto-plastic contact between rough surfaces. J Mech Phys Solids 53(11): 2385-2409 (2005)
DOI Google Scholar
[37]
Hyun S, Pei L, Molinari J F, Robbins M O. Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E 70(2): 026117 (2004)
DOI Google Scholar
[38]
Poulios K, Klit P. Implementation and applications of a finite-element model for the contact between rough surfaces. Wear 303(1-2): 1-8 (2013)
DOI Google Scholar
[39]
Dong Q, Cao J G. Contact deformation analysis of elastic- plastic asperity on rough roll surface in a strip steel mill. J Fail Anal Prev 15(2): 320-326 (2015)
DOI Google Scholar
[40]
Liu Z Q, Shi J P, Wang F S, Yue Z F. Normal contact stiffness of the elliptic area between two asperities. Acta Mech Solida Sin 28(1): 33-39 (2015)
DOI Google Scholar
[41]
Liu H, Leray D, Colin S, Pons P, Broué A. Finite element based surface roughness study for ohmic contact of microswitches. In Proceedings of 2012 IEEE 58th Holm Conference on Electrical Contacts, Portland, OR, USA, 2012: 1-10.
DOI
[42]
Arrazat B, Mandrillon V, Inal K, Vincent M, Poulain C. Microstructure evolution of gold thin films under spherical indentation for micro switch contact applications. J Mater Sci 46(18): 6111 (2011)
DOI Google Scholar
[43]
Krim I, Palasantzas G. Experimental observations of self-affine scaling and kinetic roughening at sub-micron lengthscales. Int J Mod Phys B 9(6): 599-632 (1995)
DOI Google Scholar
[44]
Bouchaud E. Scaling properties of cracks. J Phys Condens Matter 9: 4319-4344 (1997)
DOI Google Scholar
[45]
Meakin P. Fractals, Scaling and Growth Far from Equilibrium. Cambridge (UK): Cambridge University Press, 1998.
[46]
Buczkowski R, Kleiber M, Starzyński G. Normal contact stiffness of fractal rough surfaces. Arch Mech 66(6): 411-428 (2014)
Google Scholar
[47]
Farhat C, Roux F X. Implicit parallel processing in structural mechanics. Comput Mech Adv 2: 1-124 (1994)
Google Scholar
[48]
Yastrebov V A, Durand J, Proudhon H, Cailletaud G. Rough surface contact analysis by means of the Finite Element Method and of a new reduced model. Compt Rend Mécan 339(7-8): 473-490 (2011)
DOI Google Scholar
[49]
Liu M, Proudhon H. Finite element analysis of contact deformation regimes of an elastic-power plastic hardening sinusoidal asperity. Mech Mater 103: 78-86 (2016)
DOI Google Scholar
[50]
Hughes T J R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Mineola, (NY): Prentice-Hall, 2000.
[51]
Mesarovic S D, Fleck N A. Frictionless indentation of dissimilar elastic-plastic spheres. Int J Solids Struct 37(46-47): 7071-7091 (2000)
DOI Google Scholar
[52]
Kral E R, Komvopoulos K, Bogy D B. Elastic-plastic finite element analysis of repeated indentation of a half-space by a rigid sphere. J Appl Mech 60(4): 829-841 (1993)
DOI Google Scholar
[53]
Yang F, Kao I. Interior stress for axisymmetric abrasive indentation in the free abrasive machining process: Slicing silicon wafers with modern wiresaw. J Electron Packag 121(3): 191-195 (1999)
DOI Google Scholar
[54]
Mata M, Anglada M, Alcalá J. Contact deformation regimes around sharp indentations and the concept of the characteristic strain. J Mater Res 17(5): 964-976 (2002)
DOI Google Scholar
[55]
Etsion I, Kligerman Y, Kadin Y. Unloading of an elastic- plastic loaded spherical contact. Int J Solids Struct 42(13): 3716-3729 (2005)
DOI Google Scholar
[56]
Sahoo P, Chatterjee B, Adhikary D. Finite element based elastic-plastic contact behaviour of a sphere against a rigid flat-Effect of strain hardening. Int J Eng Technol 2(1): 1-6 (2010)
Google Scholar
[57]
Chen W M, Li M, Cheng Y T. Analysis on elastic-plastic spherical contact and its deformation regimes, the one parameter regime and two parameter regime, by finite element simulation. Vacuum 85(9): 898-903 (2011)
DOI Google Scholar
[58]
Celentano D J, Guelorget B, François M, Cruchaga M A, Slimane A. Numerical simulation and experimental validation of the microindentation test applied to bulk elastoplastic materials. Model Simul Mat Sci Eng 20(4): 045007 (2012)
DOI Google Scholar
[59]
Mata M, Alcalá J. The role of friction on sharp indentation. J Mech Phys Solids 52(1): 145-165 (2004)
DOI Google Scholar
[60]
Brizmer V, Kligerman Y, Etsion I. The effect of contact conditions and material properties on the elasticity terminus of a spherical contact. Int J Solids Struct 43(18-19): 5736-5749 (2006)
DOI Google Scholar
[61]
Zait Y, Kligerman Y, Etsion I. Unloading of an elastic- plastic spherical contact under stick contact condition. Int J Solids Struct 47(7-8): 990-997 (2010)
DOI Google Scholar
[62]
Liu M, Proudhon H. Finite element analysis of frictionless contact between a sinusoidal asperity and a rigid plane: Elastic and initially plastic deformations. Mech Mater 77: 125-141 (2014)
DOI Google Scholar
[63]
Chatterjee B, Sahoo P. Finite-element-based multiple normal loading-unloading of an elastic-plastic spherical stick contact. ISRN Tribol 2013: 871634 (2013)
DOI Google Scholar
[64]
Chatterjee B, Sahoo P. Effect of strain hardening on unloading of a deformable sphere loaded against a rigid flat-A finite element study. Int J Eng Technol 2(4): 225-233 (2010)
Google Scholar
[65]
Du Y, Chen L, McGruer N E, Adams G G, Etsion I. A finite element model of loading and unloading of an asperity contact with adhesion and plasticity. J Colloid Interface Sci 312(2): 522-528 (2007)
DOI Google Scholar
[66]
Peng W, Bhushan B. Three-dimensional contact analysis of layered elastic/plastic solids with rough surfaces. Wear 249(9): 741-760 (2001)
DOI Google Scholar
[67]
Carmichael C. Kent's Mechanical Engineers' Handbook in Two Volumes. 12th ed. New York (USA): John Wiley & Sons, 1950.
[68]
Galambos T V. Guide to Stability Design Criteria for Metal Structures. 5th ed. New York (USA): Wiley, 1998.
[69]
Brizmer V, Zait Y, Kligerman Y, Etsion I. The effect of contact conditions and material properties on elastic-plastic spherical contact. J Mech Mater Struct 1(5): 865-879 (2006)
DOI Google Scholar
[70]
Kogut L, Etsion I. Elastic-plastic contact analysis of a sphere and a rigid flat. J Appl Mech 69(5): 657-662 (2002)
DOI Google Scholar
[71]
Gadelrab K R, Chiesa M. Numerically assisted nanoindentation analysis. Mater Sci Eng A 560: 267-272 (2013)
DOI Google Scholar
[72]
Kucharski S, Klimczak T, Polijaniuk A, Kaczmarek J. Finite-elements model for the contact of rough surfaces. Wear 177(1): 1-13 (1994)
DOI Google Scholar
[73]
Wang F S, Block J M, Chen W W, Martini A, Zhou K, Keer L M, Wang Q J. A multilevel model for elastic-plastic contact between a sphere and a flat rough surface. J Tribol 131(2): 021409 (2009)
DOI Google Scholar
[74]
Li L, Etsion I, Talke F E. Elastic-plastic spherical contact modeling including roughness effects. Tribol Lett 40(3): 357-363 (2010)
DOI Google Scholar
[75]
Bowden F P, Tabor D, Palmer F. The Friction and Lubrication of Solids. Oxford (UK): Clarendon Press 1954.
[76]
Johnson K L, Reviewer L M K. Contact mechanics. J Tribol 108(4): 659 (1986)
DOI Google Scholar
[77]
Berthoud P, Baumberger T. Shear stiffness of a solid-solid multicontact interface. Proc Royal Soc A 454(1974): 1615-1634 (1998)
DOI Google Scholar
[78]
Shankar S, Mayuram M M. Effect of strain hardening in elastic-plastic transition behavior in a hemisphere in contact with a rigid flat. Int J Solids Struct 45(10): 3009-3020 (2008)
DOI Google Scholar
[79]
Archard J F. Elastic deformation and the laws of friction. Proc Royal Soc A 243(1233) 190-205 (1957)
DOI Google Scholar
[80]
Levinson O, Etsion I, Halperin G. An experimental investigation of elastic plastic contact and friction of a sphere on flat. In STLE/ASME 2003 International Joint Tribology Conference, Ponte Vedra Beach, Florida, USA, 2003.
[81]
Buczkowski R, Kleiber M. Elasto-plastic statistical model of strongly anisotropic rough surfaces for finite element 3D-contact analysis. Comput Methods Appl Mech Eng 195(37-40): 5141-5161 (2006)
DOI Google Scholar
[82]
Bucher F, Knothe K, Theiler A. Normal and tangential contact problem of surfaces with measured roughness. Wear 253(1-2): 204-218 (2002)
DOI Google Scholar
[83]
Eid H, Adams G G, McGruer N E, Fortini A, Buldyrev S, Srolovitz D. A combined molecular dynamics and finite element analysis of contact and adhesion of a rough sphere and a flat surface. Tribol Transs 54(6): 920-928 (2011)
DOI Google Scholar
[84]
Bhushan B. Principles and applications of tribology. Ind Lubr Tribol 51(6): 313 (1999)
DOI Google Scholar
[85]
Liu M. Finite element analysis of large contact deformation of an elastic-plastic sinusoidal asperity and a rigid flat. Int J Solids Struct 51(21-22): 3642-3652 (2014)
DOI Google Scholar
[86]
Pohrt R, Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces. Phys Rev Lett 108(10): 104301 (2012)
DOI Google Scholar
[87]
Pastewka L, Prodanov N, Lorenz B, Müser M H, Robbins M O, Persson B N J. Finite-size scaling in the interfacial stiffness of rough elastic contacts. Phys Rev E 87(6): 062809 (2013)
DOI Google Scholar
[88]
Sneddon I N. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int J Eng Sci 3(1): 47-57 (1965)
DOI Google Scholar
[89]
Oliver W C, Pharr G M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7(6): 1564-1583 (1992)
DOI Google Scholar
[90]
Kadin Y, Kligerman Y, Etsion I. Unloading an elastic- plastic contact of rough surfaces. J Mech Phys Solids 54(12): 2652-2674 (2006)
DOI Google Scholar
[91]
King R B. Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23(12): 1657-1664 (1987)
DOI Google Scholar
[92]
Kagami J, Yamada K, Hatazawa T. Contact between a sphere and rough plates. Wear 87(1): 93-105 (1983)
DOI Google Scholar
Publication history
Copyright
Acknowledgements
Rights and permissions

Publication history

Received: 09 November 2017
Revised: 09 May 2018
Accepted: 05 September 2018
Published: 12 November 2018
Issue date: December 2019

Copyright

© The author(s) 2018

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).

Rights and permissions

This article is published with open access at Springerlink.com

The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Return