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Research Article | Open Access

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

Chenghui GAO1Henry PROUDHON2( )Ming LIU1( )
School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
Centre des Matériaux, MINES Paris Tech, Evry Cedex 91003, France
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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.

References

[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)
[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)
[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)
[4]
Ghosh A, Sadeghi F. A novel approach to model effects of surface roughness parameters on wear. Wear 338-339: 73-94 (2015)
[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)
[6]
Petean P G C, Aguiar M L. Determining the adhesion force between particles and rough surfaces. Powder Technol 274: 67-76 (2015)
[7]
Svetovoy V B, Palasantzas G. Influence of surface roughness on dispersion forces. Adv Colloid Interface Sci 216: 1-19 (2015)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[17]
Yan W, Komvopoulos K. Contact analysis of elastic-plastic fractal surfaces. J Appl Phys 84(7): 3617-3624 (1998)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[26]
Kogut L, Komvopoulos K. Analysis of the spherical indentation cycle for elastic-perfectly plastic solids. J Mater Res 19(12): 3641-3653 (2004)
[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)
[28]
Song Z, Komvopoulos K. Elastic-plastic spherical indentation: Deformation regimes, evolution of plasticity, and hardening effect. Mech Mater 61: 91-100 (2013)
[29]
Greenwood J A, Williamson J B P. Contact of nominally flat surfaces. Proc Roy Soc A 295(1442): 300-319 (1966)
[30]
Hertz H. Ueber die berührung fester elastischer körper. J Reine Angew Math 1882(92): 156-171 (1882)
[31]
Bush A W, Gibson R D, Thomas T R. The elastic contact of a rough surface. Wear 35(1): 87-111 (1975)
[32]
Persson B N J. Elastoplastic contact between randomly rough surfaces. Phys Rev Lett 87(11): 116101 (2001)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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.
[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)
[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)
[44]
Bouchaud E. Scaling properties of cracks. J Phys Condens Matter 9: 4319-4344 (1997)
[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)
[47]
Farhat C, Roux F X. Implicit parallel processing in structural mechanics. Comput Mech Adv 2: 1-124 (1994)
[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)
[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)
[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)
[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)
[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)
[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)
[55]
Etsion I, Kligerman Y, Kadin Y. Unloading of an elastic- plastic loaded spherical contact. Int J Solids Struct 42(13): 3716-3729 (2005)
[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)
[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)
[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)
[59]
Mata M, Alcalá J. The role of friction on sharp indentation. J Mech Phys Solids 52(1): 145-165 (2004)
[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)
[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)
[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)
[63]
Chatterjee B, Sahoo P. Finite-element-based multiple normal loading-unloading of an elastic-plastic spherical stick contact. ISRN Tribol 2013: 871634 (2013)
[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)
[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)
[66]
Peng W, Bhushan B. Three-dimensional contact analysis of layered elastic/plastic solids with rough surfaces. Wear 249(9): 741-760 (2001)
[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)
[70]
Kogut L, Etsion I. Elastic-plastic contact analysis of a sphere and a rigid flat. J Appl Mech 69(5): 657-662 (2002)
[71]
Gadelrab K R, Chiesa M. Numerically assisted nanoindentation analysis. Mater Sci Eng A 560: 267-272 (2013)
[72]
Kucharski S, Klimczak T, Polijaniuk A, Kaczmarek J. Finite-elements model for the contact of rough surfaces. Wear 177(1): 1-13 (1994)
[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)
[74]
Li L, Etsion I, Talke F E. Elastic-plastic spherical contact modeling including roughness effects. Tribol Lett 40(3): 357-363 (2010)
[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)
[77]
Berthoud P, Baumberger T. Shear stiffness of a solid-solid multicontact interface. Proc Royal Soc A 454(1974): 1615-1634 (1998)
[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)
[79]
Archard J F. Elastic deformation and the laws of friction. Proc Royal Soc A 243(1233) 190-205 (1957)
[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)
[82]
Bucher F, Knothe K, Theiler A. Normal and tangential contact problem of surfaces with measured roughness. Wear 253(1-2): 204-218 (2002)
[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)
[84]
Bhushan B. Principles and applications of tribology. Ind Lubr Tribol 51(6): 313 (1999)
[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)
[86]
Pohrt R, Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces. Phys Rev Lett 108(10): 104301 (2012)
[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)
[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)
[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)
[90]
Kadin Y, Kligerman Y, Etsion I. Unloading an elastic- plastic contact of rough surfaces. J Mech Phys Solids 54(12): 2652-2674 (2006)
[91]
King R B. Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23(12): 1657-1664 (1987)
[92]
Kagami J, Yamada K, Hatazawa T. Contact between a sphere and rough plates. Wear 87(1): 93-105 (1983)
Friction
Pages 587-602
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

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Received: 09 November 2017
Revised: 09 May 2018
Accepted: 05 September 2018
Published: 12 November 2018
© The author(s) 2018

This article is published with open access at Springerlink.com

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