An experimentally validated numerical model of indentation and abrasion by debris particles in machine-element contacts considering micro-hardness effects
Restricted accessResearch articleFirst published online May, 2012
An experimentally validated numerical model of indentation and abrasion by debris particles in machine-element contacts considering micro-hardness effects
Indentation and abrasion of machine-element contacts by solid contamination particles is a major problem in many industries and manufacturing processes involving the automotive, aerospace, medical and electronics industries among others. Published theoretical studies on indentation and soft abrasion of surfaces by ductile debris particles other than those of the author are based on several major simplifications concerning material properties, hardness, plasticity modelling, interfacial friction, kinematic conditions, etc. None of the studies published in the literature to date (2011) have those simplifications concurrently relaxed.
In view of the shortcomings of existing numerical models on debris particle indentation and abrasion, and given the importance of dent geometry and size on fatigue life of machine elements, a greatly improved numerical model has been developed based on the previous studies of the author. The new model deals with elastoplastic indentation and abrasion of rolling–sliding, dry and lubricated contacts by spherical particles of any hardness, from very soft (e.g. 40 HV) to very hard (e.g. over 1000 HV), including harder than the contact counterfaces. The model incorporates strain-hardening and strain-gradient or indentation-size micro-hardness effects with an expanding-cavity plasticity model, a localised treatment of friction, generalised boundary and kinematic conditions involving localised stick and slip of the particle, linear and nonlinear work-hardening models of the particle, a basic approach on pile-up/sink-in plasticity effects and several other improvements. The model has passed extensive validation tests and found to give realistic predictions that are quantitatively quite close to the experimental results published by independent researchers in the literature concerning dent dimensions and slope. Moreover, it has verified and explained theoretically for the first time the formation of dimples inside and outside dents experimentally observed in rolling and rolling–sliding contacts. This article presents the mathematics of the model, the validation procedure with several real cases from the experimental literature, and a parametric study to show the model’s predictions on precise dent geometry in several realistic cases.
NikasGK. A state-of-the-art review on the effects of particulate contamination and related topics in machine-element contacts. Proc IMechE Part J: J Engineering Tribology2010; 224(5): 453–479.
2.
NikasGK. Review of studies on the detrimental effects of solid contaminants in lubricated machine element contacts. In: HayworthGI (ed.) Reliability engineering advances. New York, USA: Nova Science Publishers, 2009, pp. 1–44.
3.
TrevorMH (ed.) Handbook of wear debris analysis and particle detection in liquids. English ed. London, UK: Kluwer Academic Publishers, 1993.
4.
KowandyCRichardCChenY-M. Correlation between the tribological behaviour and wear particle morphology – case of grey cast iron 250 versus graphite and PTFE. Wear2007; 262(7–8): 996–1006.
5.
KjerT. Particles in new motor oils. Wear1981; 69(3): 395–396.
LengJADaviesJE. Ferrographic examination of unused lubricants for diesel engines. Wear1988; 122(1): 115–119.
8.
StachowiakGWKirkTBStachowiakGB. Ferrography and fractal analysis of contamination particles in unused lubricating oils. Tribol Int1991; 24(6): 329–334.
9.
GlaeserWA. Wear debris classification. In: BhushanB (ed.) Modern tribology handbook, vol. 1, New York, USA: CRC Press, 2001, pp. 301–315.
10.
RoylanceBJWilliamsJADwyer-JoyceR. Wear debris and associated wear phenomena – fundamental research and practice. Proc IMechE Part J: J Engineering Tribology2000; 214(1): 79–105.
RonenAMalkinS. Wear mechanism of statically loaded hydrodynamic bearings by contaminant abrasive particles. Wear1981; 68(3): 371–389.
20.
RonenAMalkinS. Investigation of friction and wear of dynamically loaded hydrodynamic bearings with abrasive contaminants. J Lubr Technol1983; 105(4): 559–569.
21.
KhorshidEANawwarAM. A review of the effect of sand dust and filtration on automobile engine wear. Wear1991; 141(2): 349–371.
22.
FodorJ. Improving utilisation of potential i.c. engine life by filtration. Tribol Int1979; 12(3): 127–129.
23.
RonenAMalkinSLoewyK. Wear of dynamically loaded hydrodynamic bearings by contaminant particles. ASME J Lubr Technol1980; 102(4): 452–458.
24.
AkagakiTNakamuraMMonzenT. Analysis of the behaviour of rolling bearings in contaminated oil using some condition monitoring techniques. Proc IMechE Part J: J Engineering Tribology2006; 220(5): 447–453.
25.
MiettinenJAnderssonP. Acoustic emission of rolling bearings lubricated with contaminated grease. Tribol Int2000; 33(11): 777–787.
26.
PengZKessissoglouNJCoxM. A study of the effect of contaminant particles in lubricants using wear debris and vibration condition monitoring techniques. Wear2005; 258(11–12): 1651–1662.
27.
SariMRHaiahemAFlamandL. Effect of lubricant contamination on gear wear. Tribol Lett2007; 27(1): 119–126.
28.
MoonM. How clean are your lubricants?. Trends Food Sci Technol2007; 18(Suppl. 1): S74–S88.
29.
OkamotoJFujitaKToshiokaT. Effects of solid particles in oil on the life of ball bearings. J Mech Eng Lab (Tokyo)1972; 26(5): 228–238. (NASA Technical Translation; NASA TT F-15, 653; June 1974).
30.
DalalHCotellesseGMorrisonF. Progression of surface damage in rolling contact fatigue. Final Report, SKF Industries Inc., King of Prussia PA Research Lab, February 1974.
31.
BhachuRS. The influence of debris on rolling fatigue life. PhD Thesis, University of London, UK, 1980.
32.
SaylesRSMacphersonPB. The influence of wear debris on rolling contact fatigue. In: Rolling contact fatigue testing in bearing steels. ASTM STP 771. Philadelphia, PA, USA: ASTM, 1982, pp.255–275.
33.
WebsterMNIoannidesESaylesRS. The effect of topographical defects on the contact stress and fatigue life in rolling element bearings. In: Proceedings of the 12th Leeds–Lyon symposium on tribology, Lyon, France, 3–6 September 1985, paper no. VIII(iii), 1986, pp.207–221. London: Butterworth.
34.
BhachuRSaylesRSMacphersonPB. The influence of filtration on rolling element bearing life. In: (ShivesTRWillardWA (eds) Innovation for maintenance technology improvements. NBS-SP-640. NASA CR-172821. Washington, DC, USA: The National Aeronautics and Space Administration, 1981, pp. 326–347.
35.
NeedelmanWMZaretskyEV. Quantifying oil filtration effects on bearing life. NASA Technical Memorandum 104350, The National Aeronautics and Space Administration, Washington, DC, USA, June 1991.
36.
LoewenthalSHMoyerDW. Filtration effects on ball bearing life and condition in a contaminated lubricant. ASME J Lubr Technol1979; 101(2): 171–176.
37.
LoewenthalSHMoyerDWNeedelmanWM. Effects of ultra-clean and centrifugal filtration on rolling-element bearing life. ASME J Lubr Technol1982; 104(3): 283–291.
38.
NilssonROlofssonUSundvallK. Filtration and coating effects on self-generated particle wear in boundary lubricated roller bearings. Tribol Int2005; 38(2): 145–150.
39.
TallianTE. Prediction of rolling contact fatigue life in contaminated lubricant: Part II – Experimental. ASME J Lubr Technol1976; 98(3): 384–392.
40.
HamerJCLubrechtAAIoannidesE. Surface damage on rolling elements and its subsequent effects on performance and life. In: Proceedings of the 15th Leeds–Lyon symposium on tribology, Leeds, 6–9 September 1988, Elsevier Tribology and Interface Engineering Series, vol. 14, pp.189–197. Amsterdam, The Netherlands: Elsevier.
41.
Dwyer-JoyceRSHamerJCSaylesRS. Lubricant screening for debris effects to improve fatigue and wear life. In: Proceedings of the 18th Leeds–Lyon symposium on tribology, Lyon, France, 3–6 September 1991, Elsevier Tribology and Interface Engineering Series, vol. 21, pp.57–63. Amsterdam, The Netherlands: Elsevier.
42.
NixonHPZantopulosH. Fatigue life performance comparisons of tapered roller bearings with debris-damaged raceways. STLE Lubr Eng1995; 51(9): 732–736.
43.
ChaoKKSabaCSCentersPW. Effects of lubricant borne solid debris in rolling surface contacts. STLE Tribol Trans1996; 39(1): 13–22.
44.
VilleFNeliasD. Early fatigue failure due to dents in EHL contacts. STLE Tribol Trans1999; 42(4): 795–800.
45.
KahlmanLHutchingsIM. Effect of particulate contamination in grease-lubricated hybrid rolling bearings. STLE Tribol Trans1999; 42(4): 842–850.
46.
NéliasDVilleF. Detrimental effects of debris dents on rolling contact fatigue. ASME J. Tribol2000; 122(1): 55–64.
47.
General Motors Corporation. New departure handbook, 7th ed. Bristol, CT, USA: General Motors Corporation, 1971.
48.
SKF General Catalogue. Catalogue 5000 E, SKF, June 2003.
49.
CunninghamJSMorganMA. Review of aircraft bearing rejection criteria and causes. ASLE Lubr Eng1979; 35(8): 435–441.
50.
WedevenLD. Diagnostics of wear in aeronautical systems. Washington, DC: NASA TM-79185, The National Aeronautics and Space Administration, 1979.
51.
AiX. Effect of debris contamination on the fatigue life of roller bearings. Proc IMechE Part J: J Engineering Tribology2001; 215(6): 563–575.
52.
MizuharaKTomimotoMYamamotoT. Effect of particles on lubricated friction. STLE Tribol Trans2000; 43(1): 51–56.
53.
TomimotoMMizuharaKYamamotoT. Effect of particles on lubricated friction – theoretical analysis of friction caused by particles in journal bearing. STLE Tribol Trans2002; 45(1): 47–54.
54.
TomimotoMMizuharaKYamamotoT. Effect of particles on lubricated friction – verification of dead time phenomenon and friction theory. STLE Tribol Trans2002; 45(1): 94–102.
55.
GreenDALewisR. The effects of soot-contaminated engine oil on wear and friction: a review. Proc IMechE Part D: J Automobile Engineering2008; 222(9): 1669–1689.
56.
MasukoMSuzukiAUenoT. Influence of physical and chemical contaminants on the antiwear performance of model automotive engine oil. Proc IMechE Part J: J Engineering Tribology2006; 220(5): 455–462.
57.
YamaguchiESUntermannMRobySH. Soot wear in diesel engines. Proc IMechE Part J: J Engineering Tribology2006; 220(5): 463–469.
58.
BoothJENelsonKDHarveyTJ. The feasibility of using electrostatic monitoring to identify diesel lubricant additives and soot contamination interactions by factorial analysis. Tribol Int2006; 39(12): 1564–1575.
59.
NikasGK. Theoretical modelling of the entrainment and thermomechanical effects of contamination particles in elastohydrodynamic contacts. PhD Thesis, Department of Mechanical Engineering, Imperial College London, England, 1999.
60.
NikasGK. Particle entrainment in elastohydrodynamic point contacts and related risks of oil starvation and surface indentation. ASME J Tribol2002; 124(3): 461–467.
61.
EnthovenJCSpikesHA. Visual observation of the process of scuffing. In: Proceedings of the 21st Leeds–Lyon symposium on tribology. Leeds, 6–9 September 1994. Elsevier Tribology and Interface Engineering Series. vol. 30. Amsterdam, The Netherlands: Elsevier, 1995, pp. 487–494.
62.
NikasGKSaylesRSIoannidesE. Effects of debris particles in sliding/rolling elastohydrodynamic contacts. Proc IMechE Part J: J Engineering Tribology1998; 212(5): 333–343.
63.
WanGTYSpikesHA. The behaviour of suspended solid particles in rolling and sliding elastohydrodynamic contacts. STLE Tribol Trans1987; 31(1): 12–21.
64.
SatoHTokuokaNYamamotoH. Study of wear mechanism by soot contaminated in engine oil. SAE paper 1999-01-3573, 1999.
65.
GreenDALewisRDwyer-JoyceRS. The wear effects and mechanisms of soot contaminated automotive lubricants. Proc IMechE Part J: J Engineering Tribology2006; 220(3): 159–169.
66.
HamerJCSaylesRSIoannidesE. Deformation mechanisms and stresses created by 3rd body debris contacts and their effects on rolling bearing fatigue. In: Proceedings of the 14th Leeds–Lyon symposium on tribology, Lyon, 8–11 September 1987, Elsevier Tribology and Interface Engineering Series, vol. 12, pp. 201–208. Amsterdam, The Netherlands: Elsevier.
67.
HamerJCSaylesRSIoannidesE. Particle deformation and counterface damage when relatively soft particles are squashed between hard anvils. STLE Tribol Trans1989; 32(3): 281–288.
68.
VilleFNeliasD. Influence of the nature and size of solid particles on the indentation features in EHL contacts. In: Proceedings of the 24th Leeds–Lyon symposium on tribology, London, 4–6 September 1997. Elsevier Tribology and Interface Engineering Series, vol. 34, pp. 399–409. Amsterdam, The Netherlands: Elsevier.
69.
Dwyer-JoyceRSSaylesRSIoannidesE. An investigation into the mechanisms of closed three-body abrasive wear. Wear1994; 175(1–2): 133–142.
70.
Larsen-BadseJ. Influence of grit size on the groove formation during sliding abrasion. Wear1968; 11(3): 213–222.
71.
Larsen-BadseJ. Influence of grit diameter and specimen size on wear during sliding abrasion. Wear1968; 12(1): 35–53.
72.
RabinowiczEMutisA. Effect of abrasive particle size on wear. Wear1965; 8(5): 381–390.
73.
RichardsonRCD. The wear of metals by relatively soft abrasives. Wear1968; 11(4): 245–275.
74.
XuanJLHongITFitchEC. Hardness effect on three-body abrasive wear under fluid film lubrication. ASME J Tribol1989; 111(1): 35–40.
75.
WilliamsJAHyncicaAM. Abrasive wear in lubricated contacts. J Phys D Appl Phys1992; 25(1A): 81–90.
76.
HamiltonRWSaylesRSIoannidesE. Wear due to debris particles in rolling bearing contacts. In: Proceedings of the 24th Leeds–Lyon symposium on tribology, London, 4–6 September 1997, Elsevier Tribology and Interface Engineering Series, vol. 34, pp. 87–93. Amsterdam, The Netherlands: Elsevier.
77.
Dwyer-JoyceRS. Predicting the abrasive wear of ball bearings by lubricant debris. Wear1999; 233–235: 692–701.
78.
GrieveDGDwyer-JoyceRSBeynonJH. Abrasive wear of railway track by solid contaminants. Proc IMechE Part F: J Rail and Rapid Transit2001; 215(3): 193–205.
79.
NilssonRDwyer-JoyceRSOlofssonU. Abrasive wear of rolling bearings by lubricant borne particles. Proc IMechE Part J: J Engineering Tribology2006; 220(5): 429–439.
80.
Dwyer-JoyceRS. The effects of lubricant contamination on rolling bearing performance. PhD Thesis, Department of Mechanical Engineering, Imperial CollegeLondon, UK, 1993.
81.
VilleFNeliasD. An experimental study of the concentration and shape of dents caused by spherical metallic particles in EHL contacts. STLE Tribol Trans1999; 42(1): 231–240.
82.
UnderwoodRJ. The tribological effects of contamination in rolling element bearings. PhD Thesis, Department of Mechanical Engineering, Imperial CollegeLondon, UK, 2008.
83.
HamerJCHutchinsonJ. Denting of rolling element bearings by third body particles. PCS Report No. 33/92, Mechanical Engineering Department, Tribology Group, Imperial College London, UK, 1992.
84.
Dwyer-JoyceRSHamerJCSaylesRS. Surface damage effects caused by debris in rolling bearing lubricants, with an emphasis on friable materials. In: Proceedings of the IMechE, ‘Rolling element bearings – towards the 21st century’ symposium, London, UK, 16 November 1990, pp.1–8. London: Institution of Mechanical Engineers.
85.
SaylesRS. Debris and roughness in machine element contacts: some current and future engineering implications. Proc IMechE Part J: J Engineering Tribology1995; 209(3): 149–172.
86.
SaylesRSIoannidesE. Debris damage in rolling bearings and its effects on fatigue life. ASME J Tribol1988; 110(1): 26–31.
87.
SaylesRSHamerJCIoannidesE. The effects of particulate contamination in rolling bearings – a state of the art review. Proc IMechE Part G: J Aerospace Engineering1990; 204(G1): 29–36.
88.
Dwyer-JoyceRS. The life cycle of a debris particle. In: Proceedings of the 31st Leeds–Lyon symposium on tribology, Leeds, UK, 7–10 September 2004. Elsevier Tribology and Interface Engineering Series. vol. 48, pp. 681–690. Amsterdam, The Netherlands: Elsevier.
89.
KoCNIoannidesE. Debris denting – the associated residual stresses and their effect on the fatigue life of rolling bearings: an FEM analysis. In: DowsonDTaylorCMGodetMBertheD (eds) Tribological design of machine elements. Amsterdam, The Netherlands: Elsevier, 1989, pp. 199–207.
90.
KangYSSadeghiFHoeprichMR. A finite element model for spherical debris denting in heavily loaded contacts. ASME J Tribol2004; 126(1): 71–80.
91.
AntalucaENéliasD. Contact fatigue analysis of a dented surface in a dry elastic-plastic circular point contact. Tribol Lett2008; 29(2): 139–153.
92.
HutchingsIM. TRIBOLOGY – friction and wear of engineering materials. Oxford, UK: Butterworth-Heinemann, 1992.
93.
WilliamsJAHyncicaAM. Mechanisms of abrasive wear in lubricated contacts. Wear1992; 152(1): 57–74.
94.
FangLKongXZhouQ. A wear tester capable of monitoring and evaluating the movement pattern of abrasive particles in three-body abrasion. Wear1992; 159(1): 115–120.
95.
JohnsonKL. Contact mechanics. Cambridge, UK: Cambridge University Press, 1985.
96.
XuGSadeghiFCogdellJD. Debris denting effects on elastohydrodynamic lubricated contacts. ASME J. Tribol1997; 119(3): 579–587.
97.
NikasGKIoannidesESaylesRS. Thermal modelling and effects from debris particles in sliding/rolling EHD line contacts – a possible local scuffing mode. ASME J Tribol1999; 121(2): 272–281.
98.
NikasGKSaylesRSIoannidesE. Thermoelastic distortion of EHD line contacts during the passage of soft debris particles. ASME J Tribol1999; 121(2): 265–271.
99.
NikasGK. An advanced model to study the possible thermomechanical damage of lubricated sliding-rolling line contacts from soft particles. ASME J Tribol2001; 123(4): 828–841.
100.
TaborD. Indentation hardness and its measurement: some cautionary comments. In: BlauPJLawnBR (eds) Microindentation techniques in materials science and engineering. ASTM STP 889. Philadelphia, PA, USA: ASTM Press, 1986, pp. 129–159.
HutchinsonJW. Plasticity at the micron scale. Int J Solids Struct2000; 37(1–2): 225–238.
103.
SwadenerJGGeorgeEPPharrGM. The correlation of the indentation size effect measured with indenters of various shapes. J Mech Phys Solids2002; 50(4): 681–694.
104.
PharrGMHerbertEGGaoY. The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Mater Res2010; 40: 271–292.
105.
VilleFCoulonSLubrechtAA. Influence of solid contaminants on the fatigue life of lubricated machine elements. Proc IMechE Part J: J Engineering Tribology2006; 220(5): 441–445.
106.
XuGSadeghiFHoeprichM. Residual stresses due to debris effects in EHL contacts. STLE Tribol Trans1997; 40(4): 613–620.
107.
TallianTE. Prediction of rolling contact fatigue life in contaminated lubricant: part I – mathematical model. ASME J Lubr Technol1976; 98(2): 251–257.
108.
LubrechtAADwyer-JoyceRSIoannidesE. Analysis of the influence of indentations on contact life. In: Proceedings of the 18th Leeds–Lyon symposium on tribology, Lyon, France, 3–6 September 1991. Elsevier Tribology and Interface Engineering Series, vol. 21, pp.173–181. Amsterdam, The Netherlands: Elsevier.
109.
BeghiniEDwyer-JoyceRSIoannidesE. Elastic/plastic contact and endurance life prediction. J Phys D Appl Phys1992; 25(3): 379–383.
110.
AiXNixonHP. Fatigue life reduction of roller bearings due to debris denting. Part I: Theoretical modelling. Tribol Trans2000; 43(2): 197–204.
111.
LubrechtAAVennerCHLaneS. Surface damage – comparison of theoretical and experimental endurance lives of rolling bearings. In: Proceedings of the Japan international tribology conference, Nagoya, Japan, 29 October–1 November 1990, vol. 1, pp. 185–190. Japan: Japanese Society of Tribologists.
112.
GaoX-L. An expanding cavity model incorporating strain-hardening and indentation size effects. Int J Solids Struct2006; 43(21): 6615–6629.
113.
NikasGK. Mathematical analysis of the entrapment of solid spherical particles in non-conformal contacts. ASME J Tribol2001; 123(1): 83–93.
114.
NikasGK. A mechanistic model of spherical particle entrapment in elliptical contacts. Proc IMechE Part J: J Engineering Tribology2006; 220(J6): 507–522.
115.
NikasGK. Effects of operating conditions and friction on the entrapment of spherical debris particles in elliptical contacts. Proc IMechE Part J: J Engineering Tribology2007; 221(J6): 727–741.
116.
HamrockBJSchmidSRJacobsonBO. Fundamentals of fluid film lubrication, 2nd ed. New York, USA: Marcel Dekker, Inc, 2004.
117.
ChengY-TChengC-M. What is indentation hardness?. Surf Coat Technol2000; 133–134: 417–424.
118.
ChengY-TChengC-M. Scaling, dimensional analysis, and indentation measurements. Mater Sci Eng R2004; 44(4–5): 91–149.
119.
JohnsonKL. The correlation of indentation experiments. J Mech Phys Solids1970; 18(2): 115–126.
120.
MarchDM. Plastic flow in glass. Proc R Soc London Ser A1964; 279(1378): 420–435.
121.
HirstWHowseMGJW. The indentation of materials by wedges. Proc R Soc London Ser A1969; 311(1506): 429–444.
122.
BishopRFHillRMottsNF. The theory of indentation and hardness tests. Proc Phys Soc1945; 57(3): 147–159.
123.
HillR. The mathematical theory of plasticity. Oxford, UK: Oxford University Press, 1950(reprint).
124.
StudmanCJMooreMAJonesSE. On the correlation of indentation experiments. J Phys D Appl Phys1977; 10(6): 949–956.
125.
LawnBR. Indentation of ceramics with spheres: a century after Hertz. J. Am Ceram Soc1998; 81(8): 1977–1994.
126.
CahoonJBroughtonWKutzakA. The determination of yield strength from hardness measurements. Metall Mater Trans B1971; 2(7): 1979–1983.
127.
BhushanB. Principles and applications of tribology. Chichester, UK: Wiley, 1999.
128.
TaborD. A simple theory of static and dynamic hardness. Proc R Soc. London Ser A1948; 192(1029): 247–274.
129.
NikasGK. Boussinesq-Cerruti functions and a simple technique for substantial acceleration of subsurface stress computations in elastic half-spaces. Proc IMechE Part J: J Engineering Tribology2006; 220(1): 19–28.
130.
LoveAEH. A treatise on the mathematical theory of elasticity, 4th ed. New York, USA: Dover Publications, 1944(reprint).
131.
NikasGK. Fatigue life and traction modelling of continuously variable transmissions. ASME J Tribol2002; 124(4): 689–698.
132.
CoulonSVilleFLubrechtAA. Effect of a dent on the pressure distribution in dry point contacts. ASME J Tribol2002; 124(1): 220–223.
133.
CoulonSJubaultILubrechtAA. Pressure profiles measured within lubricated contacts in presence of dented surfaces. Comparison with numerical models. Tribol Int2004; 37(2): 111–117.
134.
TaljatBPharrGM. Development of pile-up during spherical indentation of elastic-plastic solids. Int J Solids Struct2004; 41(14): 3891–3904.
135.
BartierOHernotXMauvoisinG. Theoretical and experimental analysis of contact radius for spherical indentation. Mech Mater2010; 42(6): 640–656.
136.
HillRStorakersBZdunekAB. A theoretical study of the Brinell hardness test. Proc R Soc London Ser A1989; 423(1865): 301–330.
137.
HernotXBartierOBekoucheY. Influence of penetration depth and mechanical properties on contact radius determination for spherical indentation. Int J Solids Struct2006; 43(14–15): 4136–4153.
138.
KimSHLeeBWChoiY. Quantitative determination of contact depth during spherical indentation of metallic materials – a FEM study. Mater Sci Eng A2006; 415(1–2): 59–65.
139.
LeeHLeeJHPharrGM. A numerical approach to spherical indentation techniques for material property evaluation. J Mech Phys Solids2005; 53(9): 2037–2069.
140.
MatthewsJR. Indentation hardness and hot pressing. Acta Metall1980; 28(3): 311–318.
141.
NorburyALSamuelT. The recovery and sinking-in or piling-up of material in the Brinell test. J Iron Steel Inst1928; 117: 673–687.
TaborD. The hardness of metals. Oxford, UK: Clarendon Press, 1951.
144.
PooleWJAshbyMFFleckNA. Micro-hardness of annealed and work-hardened copper polycrystals. Scr Mater1996; 34(4): 559–564.
145.
SaraswatiEi Phyu PhyuTheintStephanD. High temperature storage (HTS) performance of copper ball bonding wires. In: Proceedings of the 7th electronic packaging technology conference, Singapore, 7–9 December2005, pp.1–6. Piscataway, NJ: IEEE.
146.
EksiAKuleckiMK. Hardness and densification behaviour of copper and bronze powders compacted with uniaxial die and cold isostatic pressing processes. Metallurgija2004; 43(2): 129–134.
147.
ChowdhuryMANuruzzamanDMRahamanML. Variation of friction coefficient of copper with sliding velocity and relative humidity. J Adv Res Mech Eng2010; 1(3): 142–146.
GuoYBLiuCR. Mechanical properties of hardened AISI 52100 steel in hard machining processes. ASME J Manuf Sci Eng2002; 124(1): 1–9.
150.
ASM International. ASM handbook: mechanical testing and evaluation, Vol. 8, Materials Park, OH: ASM International, 2000.
151.
MitchellDJMecholskyJJAdairHH. Effects of particulate debris morphology on the rolling wear behaviour of all-steel and Si3N4–steel bearing element couples. Oak Ridge National Laboratory, Oak Ridge, TN, USA, http://www.osti.gov/bridge/servlets/purl/3465-J5EaXl/webviewable/3465.pdf (1999, accessed 13 December 2011).
