A fundamental, two-dimensional finite-element analysis (FEA) of a coated flat surface in a fretting contact with a flat-rounded punch is presented with a detailed listing of all modelling steps. A large number of basic results from a parametric study has been derived, focusing on the stress analysis and the effect of coatings on the life expectancy of the coated solid, without actually getting into the ambiguities of life evaluation. The parameters included in the study are the metallic coating thickness (5, 20, and 50 μm) and elastic modulus, the endurance limit of the coated substrate, and the normal and tangential loads applied. A summary of the stress analysis results is presented in a figure with nine diagrams, which assists the quick selection of the optimum parameter values for maximizing the coating performance and minimizing the risk of fatigue within the design limits used in the study. The model is realistic in that it does not use idealized load distributions in the fretting contact but actual geometrical solids of finite dimensions in contact under the normal operating conditions, letting the FEA software resolve the loads and stresses, which are subsequently validated.
BhushanB.Principles and applications of tribology (USA: Wiley1999)
2.
HolmbergK.MatthewsA.BhushanB.‘Tribological properties of metallic and ceramic coatings’Modern tribology handbook (USA: CRC Press2001) ch. 23
3.
HogmarkS.JacobsonS.LarssonM.WiklundU.BhushanB.‘Mechanical and tribological requirements and evaluation of coating composites’Modern tribology handbook (USA: CRC Press2001) ch. 26
4.
JohnsonK. L.Contact mechanics (UK: Cambridge University Press1985)
5.
BurmisterD. M.‘The general theory of stresses and displacements in layered systems’J. Appl. Phys.162 (1945): 89–94
6.
BarovichD.KingsleyS. C.KuT. C.‘Stresses on a thin strip or slab with different elastic properties from that of the substrate due to elliptically distributed load’Int. J. Eng. Sci.23 (1964): 253–268
7.
ChenW. T.‘Computation of stresses and displacements in a layered elastic medium’Int. J. Eng. Sci.99 (1971): 775–800
8.
ChenW. T.EngelP. A.‘Impact and contact stress analysis in multilayered media’Int. J. Solids Struct.811 (1972): 1257–1281
9.
DhaliwalR. S.RauI. S.‘The axisymmetric Boussinesq problem for a thick elastic layer under a punch of arbitrary profile’Int. J. Eng. Sci.810 (1970): 843–856
10.
GuptaP. K.WalowitJ. A.‘Contact stresses between a cylinder and a layered elastic solid’Trans. ASME, J. Lubr. Technol.96 (1974): 250–257
11.
KennedyF. E.LingF. F.‘Elasto-plastic indentation of a layered medium’Trans. ASME, J. Eng. Mater. Technol.962 (1974): 97–103
12.
ChiuY. P.HartnettM. J.‘A numerical solution for layered solid contact problems with application to bearings’Trans. ASME, J. Lubr. Technol.1054 (1983): 585–590
13.
KingR. B.‘Elastic analysis of some punch problems for a layered medium’Int. J. Solids Struct.2312 (1987): 1657–1664
14.
KingR. B.O'SullivanT. C.‘Sliding contact stresses in a two-dimensional layered elastic half-space’Int. J. Solids Struct.235 (1987): 581–597
15.
O'SullivanT. C.KingR. B.‘Sliding contact stress field due to a spherical indenter on a layered elastic half-space’Trans. ASME, J. Tribol.1102 (1988): 235–240
16.
BhattacharyaA. K.NixW. D.‘Finite element simulation of indentation experiments’Int. J. Solids Struct.249 (1988): 881–891
17.
KomvopoulosK.‘Finite element analysis of a layered elastic solid in normal contact with a rigid surface’Trans. ASME, J. Tribol.1103 (1988): 477–485
18.
KomvopoulosK.‘Elastic-plastic finite element analysis of indented layered media’Trans. ASME, J. Tribol.1113 (1989): 430–439
19.
TianH.SakaN.‘Finite element analysis of an elastic-plastic two-layered half-space: Sliding contact’Wear1482 (1991): 261–285
20.
MontmitonnetP.EdlingerM. L.FelderE.‘Finite element analysis of elastoplastic indentation, part 2 - application to hard coatings’Trans. ASME, J. Tribol.1151 (1993): 15–19
21.
WangH. F.BangertH.‘Three-dimensional finite element simulation of Vickers indentation on coated systems’Mater. Sci. Eng. A1631 (1993): 43–50
22.
KralE. R.KomvopoulosK.BogyD. B.‘Finite element analysis of repeated indentation of an elastic-plastic layered medium by a rigid sphere, part 1: Surface results’Trans. ASME, J. Appl. Mech.621 (1995): 20–28
23.
KralE. R.KomvopoulosK.BogyD. B.‘Finite element analysis of repeated indentation of an elastic-plastic layered medium by a rigid sphere, part 2: Subsurface results’Trans. ASME, J. Appl. Mech.621 (1995): 29–42
24.
KralE. R.KomvopoulosK.‘Three-dimensional finite element analysis of subsurface stresses and shakedown due to repeated sliding on a layered elastic medium’Trans. ASME, J. Appl. Mech.634 (1996): 967–973
25.
KralE. R.KomvopoulosK.‘Three-dimensional finite element analysis of surface deformation and stresses in an elastic-plastic layered medium subjected to indentation and sliding contact loading’Trans. ASME, J. Appl. Mech.632 (1996): 365–375
26.
LovellM. R.KhonsariM.MarangoniR.‘Frictional analysis of MoS2 coated ball bearings: a three-dimensional finite element analysis’Trans. ASME, J. Tribol.1194 (1997): 754–763
27.
LovellM. R.KhonsariM.MarangoniR.‘Parameter identification of hysteresis friction for coated ball bearings based on three-dimensional FEM analysis’Trans. ASME, J. Tribol.1193 (1997): 462–470
28.
WongS. K.KapoorA.WilliamsJ. A.‘Shakedown limits on coated and engineered surfaces’Wear 203-204 (1997): 162–170
29.
SenS.AksakalB.OzelA.‘A finite-element analysis of the indentation of an elastic-work hardening layered half-space by an elastic-sphere’Int. J. Mech. Sci.4012 (1998): 1281–1293
30.
JiangY.XuB.SehitogluH.‘Three-dimensional elastic-plastic stress analysis of rolling contact’Trans. ASME, J. Tribol.1244 (2002): 699–708
31.
XuB.JiangY.‘Elastic-plastic finite element analysis of partial slip rolling contact’Trans. ASME, J. Tribol.1241 (2002): 20–26
32.
YeN.KomvopoulosK.‘Indentation analysis of elastic-plastic homogeneous and layered media: Criteria for determining the real material hardness’Trans. ASME, J. Tribol.1254 (2003): 685–691
33.
KuoC. H.KeerL. M.‘Contact stress analysis of a layered transversely isotropic half space’Trans. ASME, J. Tribol.1142 (1992): 253–262
34.
OvaertT. C.‘On the indentation of a transversely isotropic half-space with application to solid lubricant films’Trans. ASME, J. Tribol.1154 (1993): 650–657
35.
LovellM. R.‘Analysis of contact between transversely isotropic coated surfaces: Development of stress and displacement relationships using FEM’Wear2142 (1998): 165–174
36.
LovellM. R.‘Determination of compliance relationships for transversely isotropic hard surface coatings using the finite element method’Trans. ASME, J. Tribol.1213 (1999): 416–418
37.
MorrowC.LovellM.‘Numerical contact analysis of transversely isotropic coatings’Wear2361-2 (1999): 360–367
38.
MorrowC.LovellM.DengZ.‘Numerical contact analysis of transversely isotropic coatings: A cylinder within a circumferential groove’Trans. ASME, J. Tribol.1232 (2001): 436–440
39.
LovellM.MorrowC.‘Contact analysis of anisotropic coatings with application to ball bearings’STLE Tribol. Trans.491 (2006): 33–38
40.
KannelJ. W.DowT. A.DowsonD.‘Evaluation of contact stresses between rough-elastic and layered cylinders. In Proceedings of the 12th Leeds-Lyon Symposium on Tribology, Mechanisms and surface distress, Lyon, France, 1985 (Ed. DowsonD.), 1986, pp. 198–206 (Butterworth-Heinemann).
41.
SainsotP.LeroyJ. M.VillechaiseB.Effect of surface coatings in a rough normally loaded contact. In Proceedings of the 16th Leeds-Lyon Symposium on Tribology, Mechanics of coatings, Lyon, France, 1989, 1990, pp. 151–156 (Elsevier, Amsterdam).
42.
MerrimanT.KannelJ.‘Analyses of a role of surface roughness on contact stresses between elastic cylinders with and without soft surface coating’Trans. ASME, J. Tribol.1111 (1989): 87–94
43.
ColeS. J.SaylesR. S.‘A numerical model for the contact of layered elastic bodies with real rough surfaces’Trans. ASME, J. Tribol.1142 (1992): 334–340
44.
KadiricA.SaylesR. S.ZhouX. B.IoannidesE.‘A numerical study of the contact mechanics and sub-surface stress effects experienced over a range of machined surface coatings in rough surface contacts’Trans. ASME, J. Tribol.1254 (2003): 720–730
45.
CaiS.BhushanB.‘A numerical three-dimensional contact model for rough, multilayered elastic/plastic solid surfaces’Wear2597-12 (2005): 1408–1423
46.
CaiS.BhushanB.‘Three-dimensional dry/wet contact analysis of multilayered elastic/plastic solids with rough surfaces’Trans. ASME, J. Tribol.1281 (2006): 18–31
47.
KomvopoulosK.YeN.‘Three-dimensional contact analysis of elastic-plastic layered media with fractal surface topographies’Trans. ASME, J. Tribol.1233 (2001): 632–640
48.
LeroyJ. M.FloquetA.VillechaiseB.‘Thermomechanical behaviour of multilayered media: Theory’Trans. ASME, J. Tribol.1114 (1989): 538–544
49.
LeroyJ. M.FloquetA.VillechaiseB.‘Thermomechanical behaviour of multilayered media: Results’Trans. ASME, J. Tribol.1122 (1990): 317–323
50.
YeN.KomvopoulosK.‘Three-dimensional finite element analysis of elastic-plastic layered media under thermomechanical surface loading’Trans. ASME, J. Tribol.1251 (2003): 52–59
51.
GongZ.-Q.KomvopoulosK.‘Mechanical and thermomechanical elastic-plastic contact analysis of layered media with patterned surfaces’Trans. ASME, J. Tribol.1261 (2004): 9–17
52.
DjabellaH.ArnellR. D.‘Finite element comparative study of elastic stresses in single, double layer and multilayered coated systems’Thin Solid Films2351-2 (1993): 156–162
53.
StephensL. S.LiuY.MeletisE. I.‘Finite element analysis of the initial yielding behaviour of a hard coating/substrate system with functionally graded interface under indentation and friction’Trans. ASME, J. Tribol.1222 (2000): 381–387
54.
GongZ.-Q.KomvopoulosK.‘Effect of surface patterning on contact deformation of elastic-plastic layered media’Trans. ASME, J. Tribol.1251 (2003): 16–24
55.
NaghiehG. R.RahnejatH.JinZ. M.‘Characteristics of frictionless contact of bonded elastic and viscoelastic layered solids’Wear2322 (1999): 243–249
56.
YangJ.KomvopoulosK.‘Dynamic indentation of an elastic-plastic multi-layered medium by a rigid cylinder’Trans. ASME, J. Tribol.1261 (2004): 18–27
57.
YeN.KomvopoulosK.‘Effect of residual stress in surface layer on contact deformation of elastic-plastic layered media’Trans. ASME, J. Tribol.1254 (2003): 692–699
58.
OliveiraS. A. G.BowerA. F.‘An analysis of fracture and delamination in thin coatings subjected to contact loading’Wear198 (1996): 15–32
59.
SarmaB. Y.MayuramM. M.‘Some studies on life prediction of thermal sprayed coatings under rolling contact conditions’Trans. ASME, J. Tribol.1223 (2000): 503–510
60.
AslantasK.TasgetirenS.‘Debonding between coating and substrate due to rolling-sliding contact’Mater. Des.236 (2002): 571–576
61.
StewartS.AhmedR.‘Rolling contact fatigue of surface coatings - a review’Wear25311-12 (2002): 1132–1144
62.
BansalP.ShipwayP. H.LeenS. B.‘Finite element modelling of the fracture behaviour of brittle coatings’Surf. Coat. Technol.20018-19 (2006): 5318–5327
63.
ElsharkawyA. A.HolmesM. J. A.EvansH. P.SnidleR.‘Micro-elastohydrodynamic lubrication of coated cylinders using coupled differential deflection method’Proc. IMechE, Part J: J. Engineering Tribology 220 J1 (2006): 29–41
64.
FujinoT.IwamotoK.TanakaK.ShimaM.‘Stress distribution of coated film with a range of coated film thickness and elastic properties under a single EHL operating condition’Tribol. Int.4010-12 (2007): 1638–1648
65.
PolonskyI. A.ChangT. P.KeerL. M.SproulW. D.‘An analysis of the effect of hard coatings on near-surface rolling contact fatigue initiation induced by surface roughness’Wear2081-2 (1997): 204–219
66.
PolonskyI. A.KeerL. M.‘A fast and accurate method for numerical analysis of elastic layered contacts’Trans. ASME, J. Tribol.1211 (2000): 30–35
67.
Da SilvaBotelho T.ProgriR.InglebertG.Robbe-ValloireF.‘Elastoplastic indentation of a layered half-space with an infinite length cylinder’Mech. Mater.376 (2005): 629–639
68.
LiuS.PeyronnelA.WangQ. J.KeerL. M.‘An extension of the Hertz theory for 2D coated components’Tribol. Lett.184 (2005): 505–511
69.
HolmbergK.RonkainenH.LaukkanenA.WallinK.‘Friction and wear of coated surfaces - scales, modelling and simulation of tribomechanisms’Surf. Coat. Technol.2024-7 (2007): 1034–1049
DobromirskiJ. M.WaterhouseR. B.AttiaM. H.‘Variables in the fretting process: Are there 50 of them?’Standardisation of fretting fatigue test methods and equipment (Philadelphia, USA: ASTM STP1992): 60–66
72.
MadgeJ. J.LeenS. B.McCollI. R.ShipwayP. H.‘Contact-evolution based prediction of fretting fatigue life: Effect of slip amplitude’Wear2629-10 (2007): 1159–1170
73.
TsaiC. T.MallS.‘Elasto-plastic finite element ana-lysis of fretting stresses in pre-stressed strip in contact with cylindrical pad’Finite Elem. Anal. Des.362 (2000): 171–187
74.
WangR. H.JainV. K.MallS.‘A non-uniform distribution model for partial slip fretting contact’Wear2625-6 (2007): 607–616
75.
CiavarellaM.HillsD. A.MonnoG.‘The influence of rounded edges on indentation by a flat punch’Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science2124 (1998): 319–328
76.
DiniD.NowellD.‘Prediction of the slip zone friction coefficient in flat and rounded contact’Wear2543-4 (2003): 364–369
77.
NikasG. K. ‘Fullerene-based opportunities for robust engineering: making optimised surfaces for tribology’ (England: Mechanical Engineering Department, Tribology Group, Imperial College London2007) Technical report FOR-12/07,
78.
ÅsS. K.SkallerudB.TveitenB. W.HolmeB.‘Fatigue life prediction of machined components using finite element analysis of surface topography’Int. J. Fatigue2710-12 (2005): 1590–1596
79.
JaegerJ.New solutions in contact mechanics (UK: WIT Press2005)
80.
SchubertG.‘Zur frage der druckverteilung unter elastisch gelagerten tragwerken’Ing. Arch.133 (1942): 132–147
81.
SteuermanI. Ya.Contact problem of the theory of elasticity (1949): (Gostekhteoretizdat, Moscow and Leningrad) (Available from the British Library in an English translation by Foreign Technology Division, FTD-MT-24-61-70, 1970.)
82.
JaffarM. J.‘Computation of stresses and deformations for a two-dimensional sliding contact between an elastic layer and a rigid indenter with a rounded profile’J. Strain Anal. Eng. Des.382 (2003): 161–168
83.
ADINA theory and modelling guide volume I. Report ARD 06-7, November 2006. ADINA R&D Inc., 71 Elton Avenue, Watertown, MA 02472, USA, available from: http://www.adina.com
84.
IoannidesE.HarrisT. A.‘A new fatigue life model for rolling bearings’Trans. ASME, J. Tribol.1073 (1985): 367–377
