Frictional behaviour of metals on a crossed cylinder apparatus

Frictional behaviour of metals on a crossed cylinder apparatus


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R. T. SPURR Ferodo Ltd., Chapel-en-le-Frith, (Received





28, 1961)


It is shown that junction growth occurs until the normal stress over the junction falls to a fixed proportion of the yield shear stress of the specimen when slip occurs. An equation is given which permits an approximate calculation of cc.


Apparatus employing cross cylinders have been used in numerous investigations of friction. If the diameter of the cylinder is small, such devices have the experimental advantages that the specimens can readily be cleaned in a reflux condenser, a large number of measurements can be made on the one pair of specimens by rotating them slightly between measurements, with consequent reduction in scatter, and the damage due to sliding is localised and readily examined. A systematic examination of the friction of metals was made on such an apparatus and the results obtained are described below. EXPERIMENTAL


The apparatus used has been described previously 1. It consisted essentially of one cylinder, the “rod”, mounted on a trolley, and another shorter cylinder, the “specimen”, loaded against the rod and at right angles to it. Normal loads between 200 and 4,000 g could be used and the tangential force was applied to the trolley through a spring balance. Specimens were generally 3/16 in. in diameter; the lead, tin, bismuth, cadmium, zinc, silver, and antimony specimens were of Analar quality, the others, viz. aluminium, copper, molybdenum, silver, and platinum, were of unknown purity. The specimens were prepared by casting or turning, then polished with alumina and finally refluxed for at least an hour in carbon tetrachloride, except silver which reacted with the carbon tetrachloride, and lead which was scraped as it picked up alumina. RESULTS AND DISCUSSION

The p of the whole range of metal specimens was measured when slid against rods of molybdenum and glass (representative of high and low modulus materials), silver steel and silver (hard and soft metals), and against glass as an inert material. Despite the precautions taken there was considerable scatter. Different rods in general gave Wear,5 (1962)55-59

different values of ,u for the same specimens, but the log ,u KS. a specimen parameter curves were roughly parallel, suggesting that the rods were contaminated to differing degrees, e.g. the silver rod gave much lower frictions and had a slightl\- reddish colour. It was found that the ,LA of the metals correlated fairly well with the reciprocal of thcii hardness or of their elastic modulus, platinum and copper being outliers in the first cast, silver, antimonv and brass in the second. The elementary metals arc not the most convenient specimens to use as it is difficult to choose metals with a continuous variation in properties. Consequently, it was decided to use a range of 1% Sn solders; these solders give a continuous variation in hardness for example, and by judicious alloying, some properties could be altered more than others; thus the addition of 0.5 y/, arsenic doubled the hardness of pure leatl, with negligible effect on the elastic modulus or the surface energy. As it was suspected that the cleanliness of the rod rather than its composition influenced ,u, glass rods were used.








0 Atomic%



Fig. I.

Upper curve ,u, and lower curve reciprocal of the Vickers Hardness Number of the solders plotted against composition.

Measurements were first made on seven sets of specimens. Each set consisted of four solders (80, 60, 40 and 20 at.y$, lead) together with pure tin, and pure lead. Five friction measurements were made on each specimen using a normal load of 330 g and the Vickers Hardness (2.5 kg load) and shear strength CTof each specimen were also measured. The results were averaged and are given in Fig. I. It can be seen that there is a minimum in the ,u/composition curve at the eutectic composition and that a similar minimum occurs in the (V.H.N.)-r/composition curve. Examination showed that a wear scar was formed on the specimen considerably



larger than the area of indentation

A0 formed by the static load. The area of contact the tangential load F in increasing steps for a constant normal load L until slip occurred and it was found that A increased progressively with F. A was therefore


when applying

Such junction growth was observed by PARKER AND HA-KHZ, and by MCFARLANE AND TABOR~ who found that the increase in area was consistent with their modification of Von Mises equation, viz. pz + as2 = po2, where p = L/A, $0 = L/Ao, and s = F/A. For indium they found 01 = 3.3. BOWDEN AND ROWE determined LXfor Au, Ni, Pt and Ag and found it to be approximately 3. TABOR considers that LXshould be 25. Von Mises equation p2 + 3~2 = Y2, where Y is the yield stress in shear, has been found to apply when hollow cylinders are subjected to combined torsion and tension. The case of junction growth is not quite analogous, and there are the additional complications that only the average values of p and s can be measured ; contact occurs over a saddle-shaped

region when using crossed cylinders

and not over a circle ; and

the metals work harden. When a hard sphere indents a fully plastic material it has been suggested p,,, = 1.3 3, and that 3 is proportional to Y. Such proportionalities suggest we would not be greatly in error by following TABOR’S argument and replacing 3 by a constant OLbut considering 01to be independent of the metal, at least for materials of fairly similar properties like the solders. The variation of A with F was measured for the six Pb-Sn specimens using a normal load of 2,000 g. If p2 + o(s2 (AlAo) was plotted against (F/L)2; points fell about straight lines, and systematically between about 4 and 80




60 4.0

= po2 then e(F/L)2 = [(A/Ao)z - I.] Therefore there was much scatter but the experimental the corresponding values of 01 varied quite un9. 40 5.5

20 9.0



7.3 ave. 6.5

Much of the scatter was due to the inhomogeneity of the specimens; a 15% variation in the diameter of the static indentations could occur over the surface of the one specimen and as the expression for a involved the fourth power of the diameter, the resulting variations in 01 were large. Some of the variation was due to creep. Presumably the workhardening and creep properties also variedover the surface of a specimen. The area of contact therefore increases in a way consistent with the modified Von Mises equation, and the problem then becomes to determine when and why slip occurs. TABOR~ considers that the shear strength of the junction is limited by surface contamination to si and puts SI. = kla, where (T is the shear strength of the metal and kl is less than one. Combining this equation with that for junction growth he obtains p = Ix(kl-2 - I)-*. To check TABOR’S theory the area of the scar at slip AS, as well as F anda was measured on further sets of specimens. Some of the sets were purposely contaminated by dipping them into volatile solvents containing greases. Values of kl = F/A, were calculated and found to vary systematically with the composition of the solder, but if p at slip was put proportional toa, with p, = L/A, = ka, k was found to be reasonably constant and without systematic variation, for example, for five sets of refluxed specimens k varied between 0.67 and 0.91. The relationship p, = ko has some theoretical justification. As the tangential stress s is increased the normal stress p falls until at slip ss = ,up8, but p cannot decrease Wear, 5 (1962) 55-59

indefinitely if the junction is to remain plastic and it is reasonable to assume that the lower limit is $, and that fix ==f‘(o), i.e. ,U = s,if(a). Th e results suggest that f(0) -= fit7 and ,uS = s,/kcr, where /i is about 0.8. Thus once 9, = kcr no further increase take place and increasing 1: will cause the specimen to slip and accelerate.

in s can

When a contaminating film is present and is partially penetrated, the normal loacl is borne over the whole contact area A,, whereas only part A,’ of the contact area carries the tangential quently

load (it is assumed that the film has no shear strength).


1: S* :\ .,I,’ /A% S, ~~~ _ _ _ P -- ~ L K,’ l* ho‘& kn

where /? < I, and the criterion for slip becomes fi, = ho/B. In Fig. z the experimental values of ,U for refluxed and contaminated


are plotted against the composition of the solder for four typical sets of specimens, together with values obtained from the equation ,u = ss/Ka, and it can be seen that there is good agreement between the experimental suitable values of K are used.

I 100





and calculated

values of ,/A provided

0 Atomic % P b


Fig. L. Firm lines represent measured ,u of the solders, dashed lines corresponding of ,u.

calculated values

The equation for slip can be combined with the equation for junction growth to I ] * and for the solders it appears that 01is about 7 and K give p = [I/oL*] X [(p~/Ka)~about 0.8. In Fig. 3 values of ,u for LII= 7 and K = 0.8calculated from this equation are shown plotted against composition together with the experimental values for refluxed specimens. For comparison values of ,D are also given for K = 0.9. Measurements were also made over a range of loads; ,u tended to decrease with



increasing load and this decrease was due to a corresponding decrease in PO rather than to variations in 01or K. Measurements were made on other metals than the solders to determine whether the theories held for these as well, all the specimens being refluxed at the one time. Values of L/Ass for lead, tin, aluminium, zinc and brass lay between 1.0 and 1.2. The value for cadmium was rather higher, viz. 1.4, and for copper 2.2, which was much too high. Bismuth (1.6) and in particular antimony (12) were also too high but this was due to these metals failing by brittle fracture in the shear grab whereas they were ductile at the contact area during friction measurements.


0.6 -






0 Atwnic%



Fig. 3. Dashed lines, experimental ct = 7.0 and

values of p; upper and lower lines, calculated values of p for K = 0.8 and K = o.g respectively.

The ,u of the solders and of the elementary metals were also measured by loading disc. With the crossed cylinders plastic flow occurs over the whole contact area which co-operates as an entity, whereas with the large specimens contact occurs at dispersed areas where different circumstances apply. Opportunity for junction growth is much restricted, and for the solders, for example, there was only a small difference in p from specimen to specimen, and similarly the p of the elementary metals covered a smaller range than on the crossed cylinder apparatus. The theory should apply when hemispherical specimens are slid over flat surfaces. I/Z in. square, nominally flat, specimens against a rotating


The author wishes to thank Miss G. COTTRELL, who made most of the measurements, Mr. T. P. NEWCOMB for discussions, and the Directors of Ferodo Limited for permission to publish. REFERENCES

1 G. HUGHES AND R. T. SPURR, Proc. Phys. Sot. (London), 68B (1955) 106. 2 R. C. PARKER AND D. HATCH, Proc. Phys. Sot. (London). 6.?B (1950) 185. 3 J. S. MCFARLANE AND D. TABOR, Pr~c.~Roy. So;. (Londbn),-zozA(1950)-244. 4 F. B. BOWDEN AND G. W. ROWE, Proc. Roy. Sot. (London;), z33A (1956) 429. 5 D. TABOR, Proc. Roy. Sot. (London), 251A (1959) 378.

Wear, 5 (1962) 55-59