The effect of hardness on the frictional behaviour of metals

The effect of hardness on the frictional behaviour of metals

Wear, 78 (1982) THE EFFECT OF METALS 297 297 - 304 OF HARDNESS ON THE FRICTIONAL BEHAVIOUR M. 0. A. MOKHTAR Mechanical (Received Design Depar...

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Wear, 78 (1982)




- 304




M. 0. A. MOKHTAR Mechanical (Received

Design Department, May 15, 1981;


of Engineering,

in revised form October

Cairo University,

Cairo (Egypt)

20, 1981)

Summary It is shown experimentally that hard metals have lower frictional resistance than softer metals owing to stronger interatomic linking bonds. In hard metals the atomic bonds are strong and hence the resistance to adhesion is increased, providing low frictional characteristics. Surfaces hardened by heat treatment are also characterized by low friction. This is explained by metallurgical changes leading to changes in the structure by phase transformation, increase in the surface energy and the induction of internal (residual) stresses.

1. Introduction Friction resistance has been accepted as a characteristic feature of rubbing surfaces which exhibits some correlation with the mechanical and physical properties of the mating metals. Bowden and Tabor [l] suggested a widely approved friction theory in which the coefficient p of friction is taken as a function of the shear stress r and the penetration hardnessp: JJ = T/P. Buckley [Z, 31 showed experimentally that there are some parameters, e.g. elastic (Young’s) modulus, hardness and surface energy, which govern the interaction of a surface with an opposing surface and should be considered in the evaluation of frictional behaviour. In another set of experimental investigations, Sikorski and coworkers [4, 51, Moore and Tegart [6] and Mokhtar et al. [7,8] showed that low coefficients of friction are obtained with metals of high elastic modulus, high hardness, high surface energy, high recrystallization temperature and high resistance to plastic flow. There are definite correlations between these properties and the frictional behaviour [ 7, 83. It has also been shown [ 7, 81 that metals with strong interatomic bonds are characterized by high strength properties, high hardness, relatively poor plasticity, lower adhesion and consequently reduced friction resistance and vice versa. Mokhtar [9] proposed that the coefficient of friction, being dependent on interatomic forces and metal structure and behaving in a periodic manner 0043-1648/82/0000-0000/$02.75

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with the atomic number, may be considered an intrinsic metal property with little dependence on environmental conditions. Rabinowicz [ 10, 111 concluded tnat as metals have high surface energies, ~ont~inants adsorb readily onto them. The existence of such a contaminating layer reduces the coefficient of friction. Also, by heat treatment, alloying or shot peening, increased hardness may result in lower frictional resistance. Mokhtar and Radwan [ 121 showed experimentally that the hardening of metals introduces residual stresses and allows phase tr~sformations which lower the strength of cofdwelded junctions with a subsequent reduction in adhesion and friction. The present work comprises an experimental investigation of the role of hardness in the frictional behaviour of metals.

2. Friction and hardness: ex~riment~


The results shown in Figs. 1 - 5 provide experimental evidence of the influence of hardness on the frictional behaviour of metals. The experimental correlation between the natural hardness and coefficient of friction for pure metals [ 7) is shown in Fig. 1. Metals with a high strength, a low tendency for plastic deformation and a high hardness, e.g. nickel and chromium, give relatively low coefficients of friction. Ductile soft metals such as lead and indium experience high frictional resistance. Although the values of the coefficient of friction given are those attained under atmospheric (air) conditions, the same trend in the behaviour is found at the relatively higher values measured in uucuo [ 1, 131. The variation in the coefficient of friction due to the effects of different heat treatment processes on ferrous and non-ferrous alloys is given in Figs. 2 - 5. Figure 2 shows the effect of heat treatment on friction for plain low carbon steel (0.12% C, 0.045% S). The specimens were treated to prevent phase transformation by heating to 500 “C and cooling in different quenching media [ 141, namely water, oil, air and furnace-hot air. Relevant






210 Hardness



3W Hardness



Fig. 1. Variation in coefficient themselves and against steel.

of friction

with hardness

for pure metals sliding against

Fig. 2. Variation steel (0.12% C).

of friction

with hardness

for heat-treated

in coefficient

plain low carbon

hardness values are given in Appendix A. By this technique, the rubbing surfaces contained residual stresses and were characterized by a hard outermost layer. Dry friction tests on a pin-and-disk machine [ 151 under a normal load of 10 N and a speed of 0.5 cm s-’ showed that the frictional resistance decreases with an increase in the surface hardness (Fig. 2). With plain medium carbon steel (0.54% C, 0.022% S), full heat treatment operations could be carried out on the metal structures to cause metallurgical changes by phase transformation [ 141. The specimens were heated to 900 “C and quenched in water, oil, air, sand and furnace-hot air. Relevant hardness values are given in Appendix A. Friction tests were conducted between two cylindrical specimens (40 mm diameter X 10 mm long) in line contact; details of the test can be found elsewhere [ 121. Results under dry and lubricated conditions were obtained with a load of 50 N and speeds of 0.4 and 0.8 m s I. Under lubricated conditions, the coefficient of friction maintains an almost constant low value irrespective of surface hardness. Under dry friction, the harder the specimen surface is, the lower the coefficient of friction (Fig. 3). Further friction tests were conducted on the following non-ferrous heat-treated metals: beryllium bronze (1.8% Be; 0.3% Cr; balance, Cu); brass (91.85% Cu; 0.91% Fe; 4.16% Sn;




I 200


I 300



Dry Frlctlo” 01, Lubricated





Fig. 3. Variation in coefficient carbon steel (0.54% C).




of friction

2Ql Hardness



700 EH

with hardness


for heat-treated




plain medium

320 Hardness

Fig. 4. Variation

in coefficient

of friction

with hardness

for heat-treated


Fig. 5. Variation

in coefficient

of friction

with hardness

for heat-treated


43l DPN



balance, Zn); 80-20 brass (20% Zn; 6.5% Ni; 1.75% Al; balance, a-brass); aluminium brass (22% Zn; 6.5% Ni; 2% Al; balance, a-brass). There was a decrease in frictional resistance with hardness in friction tests carried out with a pin-and-disk machine [15, 161 under a load of 15 N and a speed of 0.5 cm s-l, as shown in Figs. 4 and 5. Figures 1 - 5 confirm that there is generally a decrease in the coefficient of friction with hardness. The decrease is most marked with pure metals. A slight but recognizable decrease is also evident with heat-treated alloys.

3. Discussion Hardness is the resistance of a metal to indentation and is thus a measure of the resistance to plastic deformation of layers of metal at and near the surface. In hardness testing, the metal is indented by a special tip (ball, cone or pyramid): the indenter first overcomes the elastic deformation and then causes plastic deformation of the metal. For metals of low ductility, the metal structure is characterized by a high cohesive strength (strong interatomic bonds) with little plastic deformation; the hardness is thus high [14]. On pressing two surfaces together, intimate contact occurs at the mating peaks of surface asperities and the conditions become analogous to those of a hardness test. This basic plastic flow criterion represents the basis of adhesion theory [l] ; hard asperities indent into softer asperities, causing plastic deformation which is dependent on the applied load and the properties of the metal. The real area of contact is thus defined by the ratio A, = W/p of the applied normal load W to the hardness p. Under the action of the applied load, metal asperities form strong welded junctions; cold welding and junction growth in the area of contact have been experimentally confirmed [ 1, 1’7 - 221. The frictional resistance is, therefore, determined by the tangential force required to shear cold-welded junctions to allow motion. It is thus expected that the frictional behaviour of metals should correlate with their mechanical and physical properties [ 7, 81. The most important correlation is between friction and hardness, friction being inversely proportional to hardness [l - 161. Therefore, metal hardness or the hardness of hardened heat-treated surfaces, which controls plastic flow behaviour, is important in determining the final frictional resistance. In pure metals (Fig. l), the coefficient of friction tends to decrease with increase in hardness. Experimental evidence [l, 71 confirms the theoretical predictions [ 11 that when pure metals rub together the coefficient of friction obeys some linear function of the ratio of shear strength to hardness. Moreover, there are indications [5, lo] that the ratio of surface energy v to hardness p varies approximately inversely with hardness (v/p a p- 3’4). A large ratio of surface energy to hardness was found experimentally to


correspond to increased adhesion with a consequent increase in the coefficient of friction [5, 7, lo]. Hence, the influence of hardness on friction can be attributed first to the strong interatomic linking bonds, which minimize the plastic deformability of hard metals with a subsequent decrease in the ability of metals to adhere, and secondly to the fact that metals of higher hardness also have a higher surface energy; this results in the formation of weak asperity junctions which contribute to the resistance of surfaces to penetration and the requirement of higher work for adhesion. These situations eventually lead to a decrease in the coefficient of friction with hardness. When two dissimilar metals rub together, the frictional behaviour becomes analogous to that of a pair consisting of the softer metal: the value of the coefficient of friction is slightly decreased (Fig. 1). With metallic alloys, the surface hardness can be enhanced by proper heat treatment [ 141. There is also evidence that the surface energy is mainly influenced by heat treatment, alloying and shot peening [ 5, 111. With increasing hardness and surface energy, alloys are expected to have a lower coefficient of friction. Figures 2 - 5 confirm that heat-treated surfaces exhibit lower friction. Figure 2 shows that with low carbon steel the increase in surface hardness caused by quenching results in a decrease in the recorded values of the friction. This could be attributed to both the change in surface energy due to treatment and the induced residual stresses caused by the elastic distortion of the crystal lattice. At high surface energies, gases and contaminants tend to adsorb readily onto metal surfaces, causing reduced adhesion [ 10, 111. Even for clean metals, the effect of surface energy in resisting adhesion and surface penetration is known: thus lower friction is usually associated with metals of high surface energy. The induced residual (internal) surface stresses in the junction represent a weakness in the coldwelded junctions. Consequently, the fracture stress of the junctions is lower than that of stress-relieved surfaces. In further experimental investigations with plain medium carbon steel [ 121, the frictional resistance under dry sliding conditions decreased with hardness (Fig. 3). The effect of hardness on friction under boundarylubricated conditions was negligibly small. In these experiments, the effects of metallurgical changes and phase transformation on hardness and friction were readily identified. The effect of phase transformation during heat treatment is important in determining the crystalline structure of the metal (especially steels) and surface characteristics including hardness, surface energy and frictional resistance. With water-quenched specimens, where phase transformation had occurred [ 141, the hardness was raised to about thrice that of the annealed or furnace-cooled specimens and the coefficient of friction was reduced by about 20% - 25% (Fig. 3). From friction tests on some heat-treated non-ferrous alloys, namely brasses and beryllium bronze (Figs. 4 and 5), the results showed a similar mechanism of friction and correlation with factors inherent in the heat treatment process. The frictional resistance follows a similar trend of lower friction with harder surfaces.


4. Conclusions For pure metals rubbing against each other, a marked decrease in the coefficient of friction with hardness could be attributed to greater resistance of hard surfaces to adhesion which is due to the strength of the interatomic bonds and the high surface energy. The surfaces of heat-treated metals show increases in hardness and surface energy, contain residual stresses and exhibit possible phase transformation with a change in crystalline structure. Such surfaces are eventually less able to adhere; the contacting asperities form weak cold-welded junctions. As a result, lower friction is usually associated with harder surfaces.

Acknowledgment Grateful acknowledgment is due to Professor G. S. A. Shawki, Chairman, Mechanical Design and Production Department, Cairo University, for useful discussions.

References 1 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Parts I, II, Oxford University Press, Oxford, 1954,1964. 2 D. H. Buckley, The influence of various physical properties of metals on their friction and wear behaviour in vacuum, Met. Eng. Q., 7 (2) (1967) 44 - 53. 3 D. H. Buckley, Influence of atomic nature of crystalline materials on friction, ASLE Trans., 11 (2) (1968) 89 - 100. 4 M. E. Sikorski, J. R. Apen and N. A. Strakhov, Some experiments in friction and adhesion with the face-centered cubic metals, Bull. Am. Phys. Sot., 6 (1961) 75 - 82. 5 M. E. Sikorski, Correlation of the coefficient of adhesion with various physical and mechanical properties of metals, J. Basic Eng., 85 (2) (1963) 279 - 285. 6 A. J. W. Moore and W. J. McG. Tegart, Relation between friction and hardness, Proc. R. Sot. London, Ser. A, 212 (1952) 452 - 458. 7 M. 0. A. Mokhtar, M. Zaki and G. S. A. Shawki, Effect of mechanical properties on frictional behaviour of metals, Tribal. Int., 12 (6) (1979) 265 - 268. 8 M. 0. A. Mokhtar, M. Zaki and G. S. A. Shawki, Correlation between frictional behaviour and physical properties of metals, Wear, 65 (1) (1980) 29 - 34. 9 M. 0. A. Mokhtar, Friction: is it an intrinsic property of metals?, Wear, 72 (1981) 287 - 293. 10 E. Rabinowicz, Influence of surface energy on friction and wear phenomena, J. Appt. Phys., 32 (8) (1961) 1440 - 1444. 11 E. Rabinowicz, Friction and Wear of Materials, Wiley, New York, 1965. 12 M. 0. A. Mokhtar and M. A. E. Radwan, The influence of quenching techniques on frictional behaviour of carbon steels, Proc. Semin. on Heat and Mass Transfer, Dubrovnik, September 3 7, 1979, Hemisphere Publishing Corporation, Washington, DC, 1979. 13 D. Tabor, Friction properties of metals. In M. J. Neale (ed.), Tribology Handbook, Butterworths, London, 1975, Part CS. 14 Y. Lakhtin, Engineering Physical Metallurgy, Mir, Moscow, 1971 (Engl. transl.).

303 15 M. 0. A. Mokhtar, M. Zaki and G. S. A. Shawki, An experimental re-examination of kinetic friction, Tribal. Znt., 12 (6) (1979) 261 - 264. 16 M. Zaki, On the correlation between mechanical and physical properties of metals and their frictional characteristics, M.Sc. Thesis, Cairo University, 1978. 17 J. S, McFarlane and D. Tabor, Relation between friction and adhesion, Proc. R. Sot. London, Ser. A, 202 (1950) 244 - 253. 18 F. P. Bowden and G. W. Rowe, The adhesion of clean metals, Proc. R. Sot. London, Ser. A, 233 (1956) 429 - 442. 19 D. Mimer and G. W. Rowe, Fundamentals of solid phase welding, Metall. Rev., 7 (28) (1962) 433 - 480. 20 M. Cocks, Compressive and shearing forces in surface films in metallic contacts, Proc. R. Sot. London, Ser. B, 67 (1954) 238 - 248. 21 J. S. Courtney-Pratt and E. Eisner, Effect of tangential force on the contact of metallic bodies, Proc. R. Sot. London, Ser. A, 238 (1957) 529 - 550. 22 D. Tabor, Junction growth in metallic friction, Proc. R. SOC. London, Ser. A, 251 (1959) 378 - 393.



Heat treatments

and hardnesses

TABLE Al Heat treatment and hardness of steels Specimen symbol

Heat treatment -.-

Brine11 hardness (kgf mm-2)

Low carbon steels SL

Heated at 500 “C for 1 h and then furnace cooled and annealed


As SL but cooled for 15 min in furnace-hot air


As SL but cooled in air


As SL but quenched in oil


As SL but quenched in water


Medium SM

carbon steels

Heated at 900 “C for 1 h and then annealed


As SM but cooled in furnace-hot air


As SM but cooled in sand


As SM but cooled in atmospheric air


As SM but quenched in oil


As SM but quenched in water




Heat treatment Specimen symbol

and hardness Heat

of brasses treatment


Hardness (HDP 30)



Heated at 830 “C for 1 h and then furnace cooled




for 18 h at 600 “C






for 18 h at 500 “C!





for 2 h at 500 “C






for 1 h at 600 “C


Extruded condition

and cold

drawn to half-hard

62 110

Brass Non-treated




Heat treatment

and hardness

of beryllium


Specimen symbol



Hot rolled and solution treated (1 h at 790 “C, oil quenched)



As A0 but aged at 315 “C for 2 h



As Ao but overaged for 6 h

at 350 “C



As Ao but overaged for 24 h

at 350 “C



Cold rolled to half-hard condition (1 h at 790 “C, oil quenched)



As Bo but aged at 315 “C for 2 h



As Bo but aged at 375 “C for 6 h



As Bo but overaged for 24 h


co Cl


Condition nominally with coarser grains

Hardness (HDP 30)

at 375 “C as Bo but harder

As Co but aged at 350 “C for 6 h

230 362