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The friction of contaminated metal surfaces
264
THE
K.
T.
Fevodo
FRICTION
OF CONTAMINATED
METAL
SURFACES
SPUKR Limited,
(Received
Chapel-es-le-Faith
February
(Ct.
Britain)
21, 1965)
SUMMARY
The equation for junction growth is shown to apply to a range of metals on a crossed cylinder apparatus irrespective of whether they are clean or contaminated. INTRODUCTION
It has been shown1 previously that the ,u of soft metals at slip as measured on a crossed cylinder apparatus is given by an equation obtained by combining the equation for junction growth with a slip criterion. The p of such specimens were in good agreement2 with the measured ,B of nominally flat specimens. Provided an empirical correction was made to the junction growth equation it also applied3 to harder specimens. These specimens were normally refluxed in suitable solvents before friction measurements were made. The present paper shows how the theory can be applied to a wide range of metals both clean and contaminated. EXPERIMENTAL
DETAILS
The crossed cylinder apparatus and the technique used have been described previously”. The specimens were refluxed and then contaminated by dipping them into solutions of oil in a volatile solvent, or merely by wiping them with the fingers. The friction and area at slip were measured on a refluxed specimen, and again as the specimen was progressively contaminated. RESULTS
AND
DISCVSSIOKS
When two cylinders are loaded together, a static indentation area, /lo, is formed. If an increasing tangential force F is now applied, the area of contact A increases progressively according to the junction growth equation, but as A increases the shear stress over the junction growth falls until eventually the interface cannot transmit sufficient stress to keep the metal in the softer specimen plastic, when the surfaces slip over one another. This critical stress at which slip occurs depends upon the amount of contamination at the interface. The equation for junction growth? is taken to be p’ + iysz = k”d
FRICTION
OF CONTAMINATED
METAL
SURFACES
265
where p and s are the average normal and shear stresses over the circular contact area, o is the yield stress in shear, and LXand k are constants. Under normal load alone p2 = k’W = $02 the Meyer hardness of the specimen. Similarly there is some justification in putting $J = o to obtain LYS~= k2a2 or LX= kz. The junction growth equation can then be written in equivalent forms
p=;z J [($)’ - Ilk= &h-2
-
PO-94
Consequently as the surface of the specimen is progressively contaminated and p correspondingly reduced, the experimental points should fall on a smooth line when p is plotted against p,. Fairly smooth curves were obtained for some metals but in general there was considerable scatter. Much of this was due to inhomogeneity of the specimen; for example, on one typical antimony specimen the minimum value of $0 (5 kg load) was 25.6 and the maximum 44.0 kg/mm2. To allow for the variation in hardness a preliminary static indentation was made to determine $0 and then a friction measurement was made on the same indentation to obtain ,u and p,. The corrected value of 6, was then written as
P, = g.
po
where p. is the average value of PO. Some relaxation occurs with the softer metals, however, when the one contact is loaded the second time, and the indentation area A increases. Consequently A was measured in a separate series of measurements after one and two loadings to obtain average values of AO and AI from which the
PL2 ( mm’,/ kg) Fig.
I.
through
Plot of ~~2 us. Pa-2 for cadmium PO-” has slope 02.
(crosses)
and bismuth
(circles).
The straight
line drawn
Weav, 8 (1965) 264-269
266
R. T. SPURR
r:
PC2 hm*/kg)
Fig. 2. Plot of ,us2 us. P.-z through PO-z has slope cr.2.
for aluminium
(crosses)
and tin (circles).
ratio R = /lo/Al was determined. The relevant hardness PO = Rp so that the equation for ,U now becomes /_4= Q-2
-
The straight
line drawn
figure was taken to be
PO-94.
A further cause of scatter was work hardening and variation in work-hardening properties; this complication was reduced to some extent by using a relatively heavy normal load. The variation of $0 with load was obtained for all the metals and for the softer metals the @o/load curve was horizontal at 5 kg. Consequently the friction measurements were made with 5 kg. load; $0 was first determined and then ,u and $J, on the same scar. After all the friction measurements had been made the specimens were sheared in a simple grab to obtain G, the yield stress. There was again a surprising variation in u and $0 from specimen to specimen of the softer metals, probably due to slight variations in casting temperature, etc. WeUY, 8 (1965)
264-269
FRICTION OF CONTAMINATED
METAL SURFACES
Fig. 3. Plot of ~~2 OS. Pa-2 for antimony through PO-~ for zinc has slope ~2.
(circles) and zinc (crosses). The straight line drawn
Values of ,uz are plotted against Ps-2 in Figs. 1-3 and straight lines of slope & drawn through PO-~. It can be seen that the experimental values of pa fall near the ~2 lines for tin, bismuth, cadmium, aluminium, zinc and platinum. The experimental points for the other metals also fall about straight lines but the values of u calculated from the slopes were 10.1 and 15.3 for silver and copper compared with the experimental values of 13.9 and 19.3 kg/mmz. Antimony failed by brittle fracture at very low loads in the shear grab. The slope of the line drawn in Fig. 3 corresponds to ~7= 14 kg/mm2 which is about the value one would infer from its hardness, etc. As the squares of ,u and P, etc. are plotted in Figs. 1-3, any small errors in measuring the various properties are correspondingly magnified in the figures. Thus the equation $2 + 01~2= $02 = k%2 fits the experimental data quite well. The minimum values of p,, corresponding to the maximum values of p6, were substituted in the equation p, = Klo, and KI was determined. For bismuth, tin, zinc and cadmium, KI was approximately unity, for copper, platinum and silver, 1.2, 1.6 and 2.3, respectively, whereas for aluminium KI was only 0.6. It was shown previously3 that for refluxed specimens
Wear, 8 (1965) 264-269
268
R.
-r. SPURR
0.3-
0.2 -
O.l-
O.ooo5
Fig. 4. Plot of /.Q VS. Pg--z for platinum through PO--~ for platinum has slqx 02.
(circles)
P;’
(mm’,/ kg)
and silver
(crosses).
0.0010
The straight
line drawn
Fig. 5. Plot of pS2 us. P8c2 for copper
where VHN was the Vickers Hardness Number of the metal and ‘I a constant equal to about 31. This equation is consistent with eqn. (I) if VHN0.7 = 3&o, and this relationship held approximately for the experimental conditions obtaining. If PO was Weau, 8 (1965) 264-269
FRICTION OF CONTAMINATED used instead eqn.
of VHN0.7,
METAL SURFACES
ti was not constant,
269 but equal
to PO/a and the results
fitted
(I). Junction
scar on a very from
zero
growth
was also examined
clean specimen
up to the value
measurements,
particularly
tent
(I).
with
eqn.
by measuring
when the tangential
at which
force
slip occurred.
with the harder
There
metals,
the increase
in area of the
F was increased was much
progressively
scatter
in these
but again the results were consis-
ACKNOWLEDGEMENTS The author ments,
wishes to thank
and the Directors
Mr. N. MILLNER
of Messrs.
Ferodo
who made
Limited
most
of the measure-
for permission
to publish
this
paper.
REFERENCES I R. T. SPURR, Wear,5 (1962) 55. 2 R. T. SPVRR. A.S.M.E. Paper 64.WA/LUB-IO. 1964. 3 R. T. SPVRR, Wear, 7 (1964) 330. 4 J. S. MCFARLANE AND D. TABOR, Proc. Roy. Sot. (Londan),
Azoz
(1950)
244. Wear, 8 (1965) 264-269
THE
K.
T.
Fevodo
FRICTION
OF CONTAMINATED
METAL
SURFACES
SPUKR Limited,
(Received
Chapel-es-le-Faith
February
(Ct.
Britain)
21, 1965)
SUMMARY
The equation for junction growth is shown to apply to a range of metals on a crossed cylinder apparatus irrespective of whether they are clean or contaminated. INTRODUCTION
It has been shown1 previously that the ,u of soft metals at slip as measured on a crossed cylinder apparatus is given by an equation obtained by combining the equation for junction growth with a slip criterion. The p of such specimens were in good agreement2 with the measured ,B of nominally flat specimens. Provided an empirical correction was made to the junction growth equation it also applied3 to harder specimens. These specimens were normally refluxed in suitable solvents before friction measurements were made. The present paper shows how the theory can be applied to a wide range of metals both clean and contaminated. EXPERIMENTAL
DETAILS
The crossed cylinder apparatus and the technique used have been described previously”. The specimens were refluxed and then contaminated by dipping them into solutions of oil in a volatile solvent, or merely by wiping them with the fingers. The friction and area at slip were measured on a refluxed specimen, and again as the specimen was progressively contaminated. RESULTS
AND
DISCVSSIOKS
When two cylinders are loaded together, a static indentation area, /lo, is formed. If an increasing tangential force F is now applied, the area of contact A increases progressively according to the junction growth equation, but as A increases the shear stress over the junction growth falls until eventually the interface cannot transmit sufficient stress to keep the metal in the softer specimen plastic, when the surfaces slip over one another. This critical stress at which slip occurs depends upon the amount of contamination at the interface. The equation for junction growth? is taken to be p’ + iysz = k”d
FRICTION
OF CONTAMINATED
METAL
SURFACES
265
where p and s are the average normal and shear stresses over the circular contact area, o is the yield stress in shear, and LXand k are constants. Under normal load alone p2 = k’W = $02 the Meyer hardness of the specimen. Similarly there is some justification in putting $J = o to obtain LYS~= k2a2 or LX= kz. The junction growth equation can then be written in equivalent forms
p=;z J [($)’ - Ilk= &h-2
-
PO-94
Consequently as the surface of the specimen is progressively contaminated and p correspondingly reduced, the experimental points should fall on a smooth line when p is plotted against p,. Fairly smooth curves were obtained for some metals but in general there was considerable scatter. Much of this was due to inhomogeneity of the specimen; for example, on one typical antimony specimen the minimum value of $0 (5 kg load) was 25.6 and the maximum 44.0 kg/mm2. To allow for the variation in hardness a preliminary static indentation was made to determine $0 and then a friction measurement was made on the same indentation to obtain ,u and p,. The corrected value of 6, was then written as
P, = g.
po
where p. is the average value of PO. Some relaxation occurs with the softer metals, however, when the one contact is loaded the second time, and the indentation area A increases. Consequently A was measured in a separate series of measurements after one and two loadings to obtain average values of AO and AI from which the
PL2 ( mm’,/ kg) Fig.
I.
through
Plot of ~~2 us. Pa-2 for cadmium PO-” has slope 02.
(crosses)
and bismuth
(circles).
The straight
line drawn
Weav, 8 (1965) 264-269
266
R. T. SPURR
r:
PC2 hm*/kg)
Fig. 2. Plot of ,us2 us. P.-z through PO-z has slope cr.2.
for aluminium
(crosses)
and tin (circles).
ratio R = /lo/Al was determined. The relevant hardness PO = Rp so that the equation for ,U now becomes /_4= Q-2
-
The straight
line drawn
figure was taken to be
PO-94.
A further cause of scatter was work hardening and variation in work-hardening properties; this complication was reduced to some extent by using a relatively heavy normal load. The variation of $0 with load was obtained for all the metals and for the softer metals the @o/load curve was horizontal at 5 kg. Consequently the friction measurements were made with 5 kg. load; $0 was first determined and then ,u and $J, on the same scar. After all the friction measurements had been made the specimens were sheared in a simple grab to obtain G, the yield stress. There was again a surprising variation in u and $0 from specimen to specimen of the softer metals, probably due to slight variations in casting temperature, etc. WeUY, 8 (1965)
264-269
FRICTION OF CONTAMINATED
METAL SURFACES
Fig. 3. Plot of ~~2 OS. Pa-2 for antimony through PO-~ for zinc has slope ~2.
(circles) and zinc (crosses). The straight line drawn
Values of ,uz are plotted against Ps-2 in Figs. 1-3 and straight lines of slope & drawn through PO-~. It can be seen that the experimental values of pa fall near the ~2 lines for tin, bismuth, cadmium, aluminium, zinc and platinum. The experimental points for the other metals also fall about straight lines but the values of u calculated from the slopes were 10.1 and 15.3 for silver and copper compared with the experimental values of 13.9 and 19.3 kg/mmz. Antimony failed by brittle fracture at very low loads in the shear grab. The slope of the line drawn in Fig. 3 corresponds to ~7= 14 kg/mm2 which is about the value one would infer from its hardness, etc. As the squares of ,u and P, etc. are plotted in Figs. 1-3, any small errors in measuring the various properties are correspondingly magnified in the figures. Thus the equation $2 + 01~2= $02 = k%2 fits the experimental data quite well. The minimum values of p,, corresponding to the maximum values of p6, were substituted in the equation p, = Klo, and KI was determined. For bismuth, tin, zinc and cadmium, KI was approximately unity, for copper, platinum and silver, 1.2, 1.6 and 2.3, respectively, whereas for aluminium KI was only 0.6. It was shown previously3 that for refluxed specimens
Wear, 8 (1965) 264-269
268
R.
-r. SPURR
0.3-
0.2 -
O.l-
O.ooo5
Fig. 4. Plot of /.Q VS. Pg--z for platinum through PO--~ for platinum has slqx 02.
(circles)
P;’
(mm’,/ kg)
and silver
(crosses).
0.0010
The straight
line drawn
Fig. 5. Plot of pS2 us. P8c2 for copper
where VHN was the Vickers Hardness Number of the metal and ‘I a constant equal to about 31. This equation is consistent with eqn. (I) if VHN0.7 = 3&o, and this relationship held approximately for the experimental conditions obtaining. If PO was Weau, 8 (1965) 264-269
FRICTION OF CONTAMINATED used instead eqn.
of VHN0.7,
METAL SURFACES
ti was not constant,
269 but equal
to PO/a and the results
fitted
(I). Junction
scar on a very from
zero
growth
was also examined
clean specimen
up to the value
measurements,
particularly
tent
(I).
with
eqn.
by measuring
when the tangential
at which
force
slip occurred.
with the harder
There
metals,
the increase
in area of the
F was increased was much
progressively
scatter
in these
but again the results were consis-
ACKNOWLEDGEMENTS The author ments,
wishes to thank
and the Directors
Mr. N. MILLNER
of Messrs.
Ferodo
who made
Limited
most
of the measure-
for permission
to publish
this
paper.
REFERENCES I R. T. SPURR, Wear,5 (1962) 55. 2 R. T. SPVRR. A.S.M.E. Paper 64.WA/LUB-IO. 1964. 3 R. T. SPVRR, Wear, 7 (1964) 330. 4 J. S. MCFARLANE AND D. TABOR, Proc. Roy. Sot. (Londan),
Azoz
(1950)
244. Wear, 8 (1965) 264-269