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The effect of pressure on the frictional properties of polymers
Wear, 34 (1975) 29 - 38 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
THE EFFECT OF PRESSURE ON THE FRICTIONAL POLYMERS*
29
PROPERTIES OF
B. J. BRISCOE and D. TABOR Physics and ~hern~t~ (Ct. Britain)
of Solids, Caue~dish LQ&orato~, ~n~ue~ity of Cambridge
(Received February 20,1975)
Summary
This paper describes a study of the effect of pressure on the shear properties of very thin polymeric films. It is found that pressure increases the shear yield stress, the increase being approximately proportional to the applied pressure. These results are compared with those obtained (by other workers) on bulk polymer specimens. They aiso find a marked increase in shear strength with pressure. The results qu~i~~vely resemble those obtained with thin polymeric films but there is a rather large quantitative discrepancy. It is suggested that this is due, at least in part, to the fact that the thin film is constrained to shear in a very narrow well defined plane. The effect of temperature on the shear strength of thin polymethyimethacrylate (PITA) films is also described. The shear strength falls markedly at a critical temperature which corresponds to the glass transition temperature of the polymer. This critical temperature is affected by the sliding speed and is increased if the contact pressure is increased.
Many areas of tribology may be considered as the shearing of polymeric films or the sliding of such films over each other. For example, when sliding metallic surfaces are separated by a layer of lubricating oil, organic material may be either absorbed or chemically formed at the metal surfaces. In many cases these layers may be regarded as thin ,films of organic polymers. If the oil contains polymeric viscosity-improvers these additives may well adsorb at the interface. Alternatively the polymer may form from degradation products. Here we may include the classical “friction polymer” or “friction resin”. Recent work by Furey [l] has also described the lubricating action of in situ formed polymers where monomer polymerises on the hot surfaces of the contacting metals. It may also be useful to regard the *Paper presented at the Tribology Session of the Eighth Israel Conference on Mechanical Engineering, Technion, Haifa, 23 - 24 September, 1974.
30
liquid oil as a polymer when it is subjected to high hydrostatic stresses in the sliding contact. Johnson and Roberts [ 21 speculate that under sliding contact hydrocarbon oils behave as viscoelastic solids rather than viscous fluids. Under fully fluid lubricating conditions the polymer films play no part in the sliding process. However when the fluid film thickness decreases asperity contact takes place and the surfaces are then protected by the polymeric layers. Further a high proportion of the sliding friction is dissipated within these thin surface layers. The present paper presents data which may be used in the calculation of this frictional energy. A range of polymers is considered and as a first step these materials may be regarded as model surface films. Their mechanical properties are studied under those conditions which might exist at contacting asperities: that is at high pressure (up to 5 X 10’ Pa, 50 k Bar, 8 X lo5 p.s.i., 5 X lo4 atm), high temperatures (reaching 200 “C) and at high strain rates and large strains. Finally we may note here that polymers are used either as bulk materials or as thin films in dry bearings. The data described may also be useful in these applications. The present paper deals mainly with the effects of pressure although reference is made to certain aspects of the temperature and velocity dependences. Most of the data were obtained by depositing the polymers as thin films on hard smooth substrates and then sliding the films over each other under a range of contact pressures, temperatures and sliding velocities. These data are compared with the observed properties of bulk specimens under comparable pressures and tested at similar strain rates but at much lower strains. The materials
and sample preparations
The polymers fall into three groups: (a) typical semicrystalline polymers; the polymer studied was low density polythene (LDPE) supplied by ICI, grade WNC71 density 0.92 g cm-‘; (b) two “low friction” polymers; high density polythene (HDPE) B.P. grade Marlex 6001, density 0.96 g cm-‘, average molecular weight cu. 30,000; polytetrafluorethylene (PTFE) 60% crystallinity; (c) an amorphous polymer, polymethylmethacrylate (PMMA) ICI commercial grade, additive free. Low density polythene and polymethylmethacrylate were deposited as thin films from dilute solutions of p-xylene and chloroform respectively. The films were then annealed at 80 “C!for 6 h in vacuum before use. The films were typically between 150 nm and 200 nm in thickness. The low friction polymers were repeatedly rubbed over the surfaces of the supports at 20 “C for PTFE and 50 “C for HDPE. It was shown many years ago by Bowers, Clinton and Zisman [3] that this procedure deposits thin layers of highly drawn polymer on the substrate. This has been confirmed in a later, more detailed study by Pooley and Tabor [4] who also showed that the film
31
is only about 10 nm thick. The molecular chains appear to be orientated in the direction of rubbing and the layer comprises at most twenty, or perhaps fewer, orientated chains. Experimental technique The apparatus and experimental procedure has been described elsewhere in detail [ 5,6] . The substrates were a flamed glass flat and flamed glass spherical indenters. Glass has the advantage that it can be prepared with a good surface finish and it deforms almost wholly in an elastic manner. The films-were deposited on the glass flat. The indenter was loaded against the film and repeated traversals of the indenter were made over the “lubricated” flat. The area of contact was estimated from the Hertz elastic deformation analysis of the substrate material and it was assumed that this calculated area was the area of the film undergoing deformation in shear. Further it was assumed that no glass-glass contact occurred and all the energy was dissipated within the polymer. Careful optical and electron microscopic examination of the glass surfaces both before and after sliding indicated this was generally the case. By varying the contact load (IV) from 10 mg to 20 g and by the use of a range of indenters the radii of which varied from 4 pm to 2.5 mm the calculated contact pressure (P) could be varied from about 10’ Pa to over 10’ Pa. This pressure range covers the flow stresses of most engineering materials. During the sliding experiments the frictional force was monitored. Simply dividing this force by the calculated area of contact gives the critical shear stress or a flow stress (7) for the polymer film. The temperature of the film as well as the sliding velocity were also varied. Results Figure 1 shows the calculated shear flow stress (subsequently denoted as shear strength) against the mean calculated pressure at 20 “C for the four polymers described earlier. The sliding speed was approximately 0.03 mm s-’ which, assuming that the thickness of polymer undergoing shear was the same as the initial film thickness, corresponded to a strain rate of approximately lo3 s-l (for HDPE and PTFE) and lo2 s-l for LDPE and PMMA. (Experiments were not carried out at significantly higher sliding velocities (or strain rates) since this introduces the complication of frictional heating.) We note that without exception increasing the contact pressure causes an increase in the shear strength although the absolute magnitude of the shear strength varies from one polymer to another. This data is similar to that reported many years ago by Bridgman [ 71 and his collaborators using opposed anvils. More recently Bowers [8] and Towle [9] have published similar data on polymers over limited ranges of pressure. Bowers used essentially the same technique as that described here. Figure 2 shows the same data as those in Fig. 1 but plotted on linear coordinates over a limited range of pressure. It is apparent that in most cases the shear strength is linearly dependent on the pressure, P:
32
I PMMA
Pp
lo6
1 IO7 Moan
I
I
lo8
IO3
calculated
pressure
/ Pa
Fig. I. The effect of pressure on the shear strength of polymeric films. Although the absolute values of the calculated shear strength differ, all the polymers show similar increases in strength with increasing pressure.
r=ro
-tap
(1)
where r. and (Yare constants*. The two constants are functions of temperature and strain rate and the polymer. 7. appears to be critically dependent upon temperature and strain rate whilst LYis less so. From a knowledge of (Y and r. and the mechanical properties of the substrates as well as the contact conditions, it is therefore possible in principle to estimate the sliding friction of ductile solids lubricated with thin polymeric or similar organic films. Assume that the true area A supporting the normal load W is determined solely by the plastic yield pressure 23 of the solid. (This quantity is essentially the same as the indentation hardness of the solid.) Then A = W/H. If no penetration of the polymeric film occurs during sliding the frictional force F is simply the force to shear the film trapped between the surfaces over the area A. Thus F = AT. But this film is subjected to a pressure H so that T = r. + 0rH. Consequently the coefficient of friction p may be written ,+LL2+,
w
(21
HH
For most metals H % r. so that the first term is small compared with (Y. Consequently w is very nearly equal to the pressure coefficient 01of the lubricant film under the contact conditions. Within certain ranges of temperature and strain rate orappears not to be critically dependent on these *In the case of PTFE we observe a phase change at about 5 tion has been noted previously by Bowers [ 81.
X
lo8 Pa. This transi-
33
-
Moan
calculated
prossuro
--,PTFE
/Pa
Fig. 2. Plot showing the linear dependence of the shear strength with contact pressure.
variables. A complete analysis of a real lubricated system would require an estimate of the amount of asperity (solid-solid) contact through the lubricant film as well as any resistance arising from the fluid or hydrodynamic friction. The present shear results on thin films may be compared with those obtained by Ward et al. [lo - 121 on bulk specimens. Their experiments were carried out in torsional shear under various hydrostatic pressures and their data has to be extrapolated to a similar strain-rate to that estimated to apply in the thin-film work described above. The comparison for PMMA is shown in Fig. 3. The shear strength for the bulk specimen is five to ten times larger than for the thin film over the pressure range considered. On the other hand the variation of shear strength with pressure is similar in both types of experiment. This is shown in Table 1 which summarises these data as well as other results on PMMA and HDPE. It may be concluded that whilst r. differs by a large factor in the two types of experiments the value of OLis almost the same. There are at least two possible explanations for this discrepancy. First the strain in the bulk experiments did not exceed about 30% at failure whereas in the thin film experiments the strains are presumably very much larger. Secondly in the thin film experiments the shear process is constrained to a very narrow zone. This not only changes the conditions of shear: it also
lo8
lo9
Prossure/Pa Fig. 3. Comparison of current data (A) for PMMA with that obtained by Ward et al. [ 111 on bulk specimens (B). The present high strain data are a factor of ten or less, in some cases. than the low strain data observed for the bulk materials.
TABLE 1 Comparison of present data with data obtained from measurements on bulk specimens at 20 “C
Bulk
Polymer
ToPa)
HDPE HDPE HDPE
1.4 1.7 2.8
a
P-(Pa)
x 10’ x 10’ x 10’
0.034 0.05 0.09
5x
lo8
(a)
r(s-l)
Ref. No.
5 x lo-* 2 x 1O-3
10, 11,12 13 (b) 14 (c)
Film
HDPE
0.3
x 10’
0.09
2 x log
lo3
Present paper
Buhk
PMMA PMMA
5.03 x 10’ 1.4 x 1oa
0.20 0.16
5 x lo8
5 x lo-*
lO,ll, 11 (d)
Film
PMMA
1.2
0.24
5x
102
Present paper
(a) (b) (c) (d)
x 10’
log
12
maximum pressure obtained in plain strain compression obtained in tensile tests data of Ward extrapolated to lo2 s-l strain rate.
tends to produce a high degree of molecular orientation in the polymer. In some cases this may be the major factor. For example, if a hemisphere of HDPE is slid over a clean smooth glass plate a very thin film of highly oriented polymer is laid down on the glaS8surface. From the width (d) of the film the area of contact being sheared (nd2/4) may be estimated. From the frictional force the shear strength at the interface may be calculated [4]. The value obtained at room temperature is about 4 X lo6 Pa. The contact pressure is determined by the yield pressure of the polymer, about 3 X 10’ Pa.
35
Tg 26-
16
I
I
I
I
I
I
I
I
20
40
60
00
100
120
140
160
Temperature
I
/“C
Fig, 4. Shear strength as a function of temperature for PMMA films at a contact pressure of 2 X 10’ Pa and a sliding velocity of 0.03 mm s-l. The glass transition temperature, Tg,is marked at 125 “C.
TABLE 2 Shear strength comparisons: Polymer
HDPE PMMA
thin film, friction and bulk at 20 “C
Contact pressure (Pa)
Shear strength (Pa)
(Amox. 1
Thin film
Friction
Bulk
3 x 10’ 3 x 10’
4 x106 1.1 x 10’
4 x106 0.8 x 10’
14 - 28 X lo6 15 x 10’
Figure 2 shows that at this contact pressure the shear strength of a thin film of HDPE is also about 4 X lo6 Pa: whereas the bulk shear strength lies between 14 and 28 X lo6 Pa (see Table 1). Evidently the shearing of the interface in the polymer-glass friction experiments reproduces interfacial material with the same shear properties as in the thin-film experiments. With PMMA a similar comparison cannot be made with the same confidence since in the sliding of a PMMA hemisphere over clean glass at room temperature there is often no detectable transfer: sliding appears to occur truly at the polymer glass interface [ 41. However an estimate of the inter-facial shear strength can be made and a value of about 0.8 X 10’ Pa is deduced. This occurs at a contact pressure of 3 X 10’ Pa. From Fig. 3 this may be compared with the shear strength, at the same pressure, of a thin film of PMMA -1.1 X 10’ Pa and with the bulk polymer -15 X 10’ Pa. Here again (although in this case orientation of the polymer at the interface is not established) when shearing is confined to a narrow plane the shear properties of the polymer resemble those in the thin-film experiments rather than those of the bulk material (see Table 2).
36
There is another type of experiment with PMMA which again provides a comparison of the shear properties of a thin film deposited on a hard substrate and those of the bulk polymer; the effect of temperature on the shear strength. This is shown in Fig. 4 for a PMMA film at a constant contact pressure of 2 X lo8 Pa and a sliding velocity of 0.03 mm s-l (a nominal strain rate of about 1 s-l). The shear strength remains effectively constant up to 125 “C but above this temperature there is a marked fall in the shear strength. The phenomenon is reversible and is ascribed to the transition from a “glassy” to a “rubbery” material. Further, as the contact pressure is increased the transition temperature increases by about 3 “C per 1000 atm [15]. These results may be compared with the bulk properties of PMMA. Experiments carried out in a torsion-pendulum apparatus where the strain rate and the total strains are very small and where the pressure can be applied hydrostatically show that a true glass-transition occurs at 115 “C [16] thus resembling the transition observed in the friction experiments. On the other hand in the torsion-pendulum experiments pressure increases the glass transition temperature by about 30 “C!per 1000 atm [16] compared with 3 “C per 1000 atm in the friction experiments. The difference in the pressure coefficients may be due to a real difference in the action of the compressive stresses or to the large difference in the strain-rates and total strains in the two types of experiment compared. It does not appear to be due to viscoelastic retardation effects [17, 181 which could conceivably operate in the thin film experiment [ 21. On the other hand, as pointed out above, the thin film is constrained to shear in a very restricted direction: if this produces well oriented polymer chains the free volume will be less than in the bulk experiments: consequently the effect of pressure on the glass transition temperature will be less. Although none of these explanations is proven the main conclusion is that the shear behaviour of thin films qualitatively resembles that of bulk polymer: quantitatively the differences are appreciable. Conclusions This paper has described some of the effects of contact pressure on the shear strength of polymeric films. As contact pressure is increased the shear strength increases. The relationship between shear strength and pressure is a simple one involving two constants r. and (11.r. is an intrinsic strength property of the polymer and aris a pressure coefficient. Both constants are a function of velocity of sliding (or strain rate) and temperature. However (II shows less dependence in this respect than ro. It turns out that the coefficient of friction of these films when they are deposited on hard plastically deforming substrates is almost equal to the pressure coefficient, (II. This shear strength behaviour has been compared with data obtained for the shear of bulk polymers under hydrostatic stresses; while the values of Q in the two experiments are similar, the values of r. for the bulk material, at similar strain rates, are between 5 and 10 times larger than for the thin
37
films. This is probably due to the fact that in the thin film experiments shearing is constrained to a narrow very well defined plane. This both affects the shear process and produces a high degree of o~en~tion in the polymer film. It is significant that in the sliding of the corresponding polymer over a clean smooth hard surface the shear strength in the frictional interface corresponds closely to the shear strength observed in the thin film experiments. It is of the same order as, but appreciably iessthan, the bulk shear strength of the polymer. With PMMA the shear strength of thin films shows a marked reversible decrease at a critical temperature of about 125 “C. This is close to the bulk “glass-transition” temperature of the polymer. Increasing the contact pressure produces a rise in this critical temperature. This is similar to the effect of pressure on the glass-transition temperature of the bulk material but the increase with the thin films is appreciably less than for the bulk. This may be due to the fact that the bulk experiments involve very small strains and very small strain rates. Or again it may be due to the high degree of orientation in the thin film produced by the shearing process itself. Such material will have a smaller free volume than the bulk and its glass transition temperature will be less affected by pressure. It is evident that the shear properties of thin polymeric films trapped between hard surfaces closely resemble the properties of the interfacial region which is sheared when the polymer itself is slid over a hard substrate. These shear properties also resemble, in a qualitative way, those of the bulk polymer although there is an appreciable quantitative difference. The shear behaviour of these thin polymeric films sheds light on the action of organic boundary lubricants as well as on the frictional properties of polymers themselves. Acknowledgements The authors wish to acknowledge those members of their laboratory who have participated fully in the areas of work described in this presentation. In particular Dr. B. Scruton and Mr. J. K. A. Amuzu. They also thank General Electric (Schenectady) for the provision of the research funds which allowed parts of this work to be carried out. References 1 2 3 4 5 6 7 8 9
H. S. Furey, Wear, 26 (1973) 369. K. L. Johnson and A. D. Roberts, Proc. Roy. Sot. (London), A337 (1974) 217. R. C. Bowers, W. C. Clinton and W. A. Zisman, Lubric. Eng., 9 (1953) 204. C. M. Pooley and D. Tabor, Proc. Roy. Sot. (London), A329 (1972) 251. B. J. Briscoe, B. Scruton and R. F. Willis, Proc. Roy. Sot. (London), A333 (1973) B. J. Briscoe and D. Tabor, Trans. ASLE, July (1974). P. W. Bridgman, Rev. Mod. Phys., 18 (1946) 1. R. C. Bowers, J. Appl. Phys., 39 (1968) 5385. L. C. Towle, J. Appl. Phys., 42 (1971) 2368.
99.
33 10 11 12 13 14 15 16 17 18
S. Rabinowitz, I. M. Ward and J. S. C. Parry, J. Mater. Sci., 5 (1970) 29. I. M. Ward, Polymer Sci. Symp., 32 (1971) 195. R. A. Duckett, S. Rabinowitz and I. M. Ward, J. Mater. Sci., 5 (1970) 909. P. B. Bowden and J. A. Dukes, J. Mater. Sci., 7 (1972) 52. J. A. Sauer, D. R. Mears and R. D. Pae, Europ. Polymer J., 6 (1970) 1015. J. K. A. Amuzu, B. J. Briscoe and D. Tabor, unpublished data. P. R. Billinghurst and D. Tabor, Polymer, 12 (1971) 101. R. S. Fein, Trans. ASME, F 89 (1967).127. E. G. Trachman and G. Harrison, Trans. ASME, F 94 (1972) 306.
THE EFFECT OF PRESSURE ON THE FRICTIONAL POLYMERS*
29
PROPERTIES OF
B. J. BRISCOE and D. TABOR Physics and ~hern~t~ (Ct. Britain)
of Solids, Caue~dish LQ&orato~, ~n~ue~ity of Cambridge
(Received February 20,1975)
Summary
This paper describes a study of the effect of pressure on the shear properties of very thin polymeric films. It is found that pressure increases the shear yield stress, the increase being approximately proportional to the applied pressure. These results are compared with those obtained (by other workers) on bulk polymer specimens. They aiso find a marked increase in shear strength with pressure. The results qu~i~~vely resemble those obtained with thin polymeric films but there is a rather large quantitative discrepancy. It is suggested that this is due, at least in part, to the fact that the thin film is constrained to shear in a very narrow well defined plane. The effect of temperature on the shear strength of thin polymethyimethacrylate (PITA) films is also described. The shear strength falls markedly at a critical temperature which corresponds to the glass transition temperature of the polymer. This critical temperature is affected by the sliding speed and is increased if the contact pressure is increased.
Many areas of tribology may be considered as the shearing of polymeric films or the sliding of such films over each other. For example, when sliding metallic surfaces are separated by a layer of lubricating oil, organic material may be either absorbed or chemically formed at the metal surfaces. In many cases these layers may be regarded as thin ,films of organic polymers. If the oil contains polymeric viscosity-improvers these additives may well adsorb at the interface. Alternatively the polymer may form from degradation products. Here we may include the classical “friction polymer” or “friction resin”. Recent work by Furey [l] has also described the lubricating action of in situ formed polymers where monomer polymerises on the hot surfaces of the contacting metals. It may also be useful to regard the *Paper presented at the Tribology Session of the Eighth Israel Conference on Mechanical Engineering, Technion, Haifa, 23 - 24 September, 1974.
30
liquid oil as a polymer when it is subjected to high hydrostatic stresses in the sliding contact. Johnson and Roberts [ 21 speculate that under sliding contact hydrocarbon oils behave as viscoelastic solids rather than viscous fluids. Under fully fluid lubricating conditions the polymer films play no part in the sliding process. However when the fluid film thickness decreases asperity contact takes place and the surfaces are then protected by the polymeric layers. Further a high proportion of the sliding friction is dissipated within these thin surface layers. The present paper presents data which may be used in the calculation of this frictional energy. A range of polymers is considered and as a first step these materials may be regarded as model surface films. Their mechanical properties are studied under those conditions which might exist at contacting asperities: that is at high pressure (up to 5 X 10’ Pa, 50 k Bar, 8 X lo5 p.s.i., 5 X lo4 atm), high temperatures (reaching 200 “C) and at high strain rates and large strains. Finally we may note here that polymers are used either as bulk materials or as thin films in dry bearings. The data described may also be useful in these applications. The present paper deals mainly with the effects of pressure although reference is made to certain aspects of the temperature and velocity dependences. Most of the data were obtained by depositing the polymers as thin films on hard smooth substrates and then sliding the films over each other under a range of contact pressures, temperatures and sliding velocities. These data are compared with the observed properties of bulk specimens under comparable pressures and tested at similar strain rates but at much lower strains. The materials
and sample preparations
The polymers fall into three groups: (a) typical semicrystalline polymers; the polymer studied was low density polythene (LDPE) supplied by ICI, grade WNC71 density 0.92 g cm-‘; (b) two “low friction” polymers; high density polythene (HDPE) B.P. grade Marlex 6001, density 0.96 g cm-‘, average molecular weight cu. 30,000; polytetrafluorethylene (PTFE) 60% crystallinity; (c) an amorphous polymer, polymethylmethacrylate (PMMA) ICI commercial grade, additive free. Low density polythene and polymethylmethacrylate were deposited as thin films from dilute solutions of p-xylene and chloroform respectively. The films were then annealed at 80 “C!for 6 h in vacuum before use. The films were typically between 150 nm and 200 nm in thickness. The low friction polymers were repeatedly rubbed over the surfaces of the supports at 20 “C for PTFE and 50 “C for HDPE. It was shown many years ago by Bowers, Clinton and Zisman [3] that this procedure deposits thin layers of highly drawn polymer on the substrate. This has been confirmed in a later, more detailed study by Pooley and Tabor [4] who also showed that the film
31
is only about 10 nm thick. The molecular chains appear to be orientated in the direction of rubbing and the layer comprises at most twenty, or perhaps fewer, orientated chains. Experimental technique The apparatus and experimental procedure has been described elsewhere in detail [ 5,6] . The substrates were a flamed glass flat and flamed glass spherical indenters. Glass has the advantage that it can be prepared with a good surface finish and it deforms almost wholly in an elastic manner. The films-were deposited on the glass flat. The indenter was loaded against the film and repeated traversals of the indenter were made over the “lubricated” flat. The area of contact was estimated from the Hertz elastic deformation analysis of the substrate material and it was assumed that this calculated area was the area of the film undergoing deformation in shear. Further it was assumed that no glass-glass contact occurred and all the energy was dissipated within the polymer. Careful optical and electron microscopic examination of the glass surfaces both before and after sliding indicated this was generally the case. By varying the contact load (IV) from 10 mg to 20 g and by the use of a range of indenters the radii of which varied from 4 pm to 2.5 mm the calculated contact pressure (P) could be varied from about 10’ Pa to over 10’ Pa. This pressure range covers the flow stresses of most engineering materials. During the sliding experiments the frictional force was monitored. Simply dividing this force by the calculated area of contact gives the critical shear stress or a flow stress (7) for the polymer film. The temperature of the film as well as the sliding velocity were also varied. Results Figure 1 shows the calculated shear flow stress (subsequently denoted as shear strength) against the mean calculated pressure at 20 “C for the four polymers described earlier. The sliding speed was approximately 0.03 mm s-’ which, assuming that the thickness of polymer undergoing shear was the same as the initial film thickness, corresponded to a strain rate of approximately lo3 s-l (for HDPE and PTFE) and lo2 s-l for LDPE and PMMA. (Experiments were not carried out at significantly higher sliding velocities (or strain rates) since this introduces the complication of frictional heating.) We note that without exception increasing the contact pressure causes an increase in the shear strength although the absolute magnitude of the shear strength varies from one polymer to another. This data is similar to that reported many years ago by Bridgman [ 71 and his collaborators using opposed anvils. More recently Bowers [8] and Towle [9] have published similar data on polymers over limited ranges of pressure. Bowers used essentially the same technique as that described here. Figure 2 shows the same data as those in Fig. 1 but plotted on linear coordinates over a limited range of pressure. It is apparent that in most cases the shear strength is linearly dependent on the pressure, P:
32
I PMMA
Pp
lo6
1 IO7 Moan
I
I
lo8
IO3
calculated
pressure
/ Pa
Fig. I. The effect of pressure on the shear strength of polymeric films. Although the absolute values of the calculated shear strength differ, all the polymers show similar increases in strength with increasing pressure.
r=ro
-tap
(1)
where r. and (Yare constants*. The two constants are functions of temperature and strain rate and the polymer. 7. appears to be critically dependent upon temperature and strain rate whilst LYis less so. From a knowledge of (Y and r. and the mechanical properties of the substrates as well as the contact conditions, it is therefore possible in principle to estimate the sliding friction of ductile solids lubricated with thin polymeric or similar organic films. Assume that the true area A supporting the normal load W is determined solely by the plastic yield pressure 23 of the solid. (This quantity is essentially the same as the indentation hardness of the solid.) Then A = W/H. If no penetration of the polymeric film occurs during sliding the frictional force F is simply the force to shear the film trapped between the surfaces over the area A. Thus F = AT. But this film is subjected to a pressure H so that T = r. + 0rH. Consequently the coefficient of friction p may be written ,+LL2+,
w
(21
HH
For most metals H % r. so that the first term is small compared with (Y. Consequently w is very nearly equal to the pressure coefficient 01of the lubricant film under the contact conditions. Within certain ranges of temperature and strain rate orappears not to be critically dependent on these *In the case of PTFE we observe a phase change at about 5 tion has been noted previously by Bowers [ 81.
X
lo8 Pa. This transi-
33
-
Moan
calculated
prossuro
--,PTFE
/Pa
Fig. 2. Plot showing the linear dependence of the shear strength with contact pressure.
variables. A complete analysis of a real lubricated system would require an estimate of the amount of asperity (solid-solid) contact through the lubricant film as well as any resistance arising from the fluid or hydrodynamic friction. The present shear results on thin films may be compared with those obtained by Ward et al. [lo - 121 on bulk specimens. Their experiments were carried out in torsional shear under various hydrostatic pressures and their data has to be extrapolated to a similar strain-rate to that estimated to apply in the thin-film work described above. The comparison for PMMA is shown in Fig. 3. The shear strength for the bulk specimen is five to ten times larger than for the thin film over the pressure range considered. On the other hand the variation of shear strength with pressure is similar in both types of experiment. This is shown in Table 1 which summarises these data as well as other results on PMMA and HDPE. It may be concluded that whilst r. differs by a large factor in the two types of experiments the value of OLis almost the same. There are at least two possible explanations for this discrepancy. First the strain in the bulk experiments did not exceed about 30% at failure whereas in the thin film experiments the strains are presumably very much larger. Secondly in the thin film experiments the shear process is constrained to a very narrow zone. This not only changes the conditions of shear: it also
lo8
lo9
Prossure/Pa Fig. 3. Comparison of current data (A) for PMMA with that obtained by Ward et al. [ 111 on bulk specimens (B). The present high strain data are a factor of ten or less, in some cases. than the low strain data observed for the bulk materials.
TABLE 1 Comparison of present data with data obtained from measurements on bulk specimens at 20 “C
Bulk
Polymer
ToPa)
HDPE HDPE HDPE
1.4 1.7 2.8
a
P-(Pa)
x 10’ x 10’ x 10’
0.034 0.05 0.09
5x
lo8
(a)
r(s-l)
Ref. No.
5 x lo-* 2 x 1O-3
10, 11,12 13 (b) 14 (c)
Film
HDPE
0.3
x 10’
0.09
2 x log
lo3
Present paper
Buhk
PMMA PMMA
5.03 x 10’ 1.4 x 1oa
0.20 0.16
5 x lo8
5 x lo-*
lO,ll, 11 (d)
Film
PMMA
1.2
0.24
5x
102
Present paper
(a) (b) (c) (d)
x 10’
log
12
maximum pressure obtained in plain strain compression obtained in tensile tests data of Ward extrapolated to lo2 s-l strain rate.
tends to produce a high degree of molecular orientation in the polymer. In some cases this may be the major factor. For example, if a hemisphere of HDPE is slid over a clean smooth glass plate a very thin film of highly oriented polymer is laid down on the glaS8surface. From the width (d) of the film the area of contact being sheared (nd2/4) may be estimated. From the frictional force the shear strength at the interface may be calculated [4]. The value obtained at room temperature is about 4 X lo6 Pa. The contact pressure is determined by the yield pressure of the polymer, about 3 X 10’ Pa.
35
Tg 26-
16
I
I
I
I
I
I
I
I
20
40
60
00
100
120
140
160
Temperature
I
/“C
Fig, 4. Shear strength as a function of temperature for PMMA films at a contact pressure of 2 X 10’ Pa and a sliding velocity of 0.03 mm s-l. The glass transition temperature, Tg,is marked at 125 “C.
TABLE 2 Shear strength comparisons: Polymer
HDPE PMMA
thin film, friction and bulk at 20 “C
Contact pressure (Pa)
Shear strength (Pa)
(Amox. 1
Thin film
Friction
Bulk
3 x 10’ 3 x 10’
4 x106 1.1 x 10’
4 x106 0.8 x 10’
14 - 28 X lo6 15 x 10’
Figure 2 shows that at this contact pressure the shear strength of a thin film of HDPE is also about 4 X lo6 Pa: whereas the bulk shear strength lies between 14 and 28 X lo6 Pa (see Table 1). Evidently the shearing of the interface in the polymer-glass friction experiments reproduces interfacial material with the same shear properties as in the thin-film experiments. With PMMA a similar comparison cannot be made with the same confidence since in the sliding of a PMMA hemisphere over clean glass at room temperature there is often no detectable transfer: sliding appears to occur truly at the polymer glass interface [ 41. However an estimate of the inter-facial shear strength can be made and a value of about 0.8 X 10’ Pa is deduced. This occurs at a contact pressure of 3 X 10’ Pa. From Fig. 3 this may be compared with the shear strength, at the same pressure, of a thin film of PMMA -1.1 X 10’ Pa and with the bulk polymer -15 X 10’ Pa. Here again (although in this case orientation of the polymer at the interface is not established) when shearing is confined to a narrow plane the shear properties of the polymer resemble those in the thin-film experiments rather than those of the bulk material (see Table 2).
36
There is another type of experiment with PMMA which again provides a comparison of the shear properties of a thin film deposited on a hard substrate and those of the bulk polymer; the effect of temperature on the shear strength. This is shown in Fig. 4 for a PMMA film at a constant contact pressure of 2 X lo8 Pa and a sliding velocity of 0.03 mm s-l (a nominal strain rate of about 1 s-l). The shear strength remains effectively constant up to 125 “C but above this temperature there is a marked fall in the shear strength. The phenomenon is reversible and is ascribed to the transition from a “glassy” to a “rubbery” material. Further, as the contact pressure is increased the transition temperature increases by about 3 “C per 1000 atm [15]. These results may be compared with the bulk properties of PMMA. Experiments carried out in a torsion-pendulum apparatus where the strain rate and the total strains are very small and where the pressure can be applied hydrostatically show that a true glass-transition occurs at 115 “C [16] thus resembling the transition observed in the friction experiments. On the other hand in the torsion-pendulum experiments pressure increases the glass transition temperature by about 30 “C!per 1000 atm [16] compared with 3 “C per 1000 atm in the friction experiments. The difference in the pressure coefficients may be due to a real difference in the action of the compressive stresses or to the large difference in the strain-rates and total strains in the two types of experiment compared. It does not appear to be due to viscoelastic retardation effects [17, 181 which could conceivably operate in the thin film experiment [ 21. On the other hand, as pointed out above, the thin film is constrained to shear in a very restricted direction: if this produces well oriented polymer chains the free volume will be less than in the bulk experiments: consequently the effect of pressure on the glass transition temperature will be less. Although none of these explanations is proven the main conclusion is that the shear behaviour of thin films qualitatively resembles that of bulk polymer: quantitatively the differences are appreciable. Conclusions This paper has described some of the effects of contact pressure on the shear strength of polymeric films. As contact pressure is increased the shear strength increases. The relationship between shear strength and pressure is a simple one involving two constants r. and (11.r. is an intrinsic strength property of the polymer and aris a pressure coefficient. Both constants are a function of velocity of sliding (or strain rate) and temperature. However (II shows less dependence in this respect than ro. It turns out that the coefficient of friction of these films when they are deposited on hard plastically deforming substrates is almost equal to the pressure coefficient, (II. This shear strength behaviour has been compared with data obtained for the shear of bulk polymers under hydrostatic stresses; while the values of Q in the two experiments are similar, the values of r. for the bulk material, at similar strain rates, are between 5 and 10 times larger than for the thin
37
films. This is probably due to the fact that in the thin film experiments shearing is constrained to a narrow very well defined plane. This both affects the shear process and produces a high degree of o~en~tion in the polymer film. It is significant that in the sliding of the corresponding polymer over a clean smooth hard surface the shear strength in the frictional interface corresponds closely to the shear strength observed in the thin film experiments. It is of the same order as, but appreciably iessthan, the bulk shear strength of the polymer. With PMMA the shear strength of thin films shows a marked reversible decrease at a critical temperature of about 125 “C. This is close to the bulk “glass-transition” temperature of the polymer. Increasing the contact pressure produces a rise in this critical temperature. This is similar to the effect of pressure on the glass-transition temperature of the bulk material but the increase with the thin films is appreciably less than for the bulk. This may be due to the fact that the bulk experiments involve very small strains and very small strain rates. Or again it may be due to the high degree of orientation in the thin film produced by the shearing process itself. Such material will have a smaller free volume than the bulk and its glass transition temperature will be less affected by pressure. It is evident that the shear properties of thin polymeric films trapped between hard surfaces closely resemble the properties of the interfacial region which is sheared when the polymer itself is slid over a hard substrate. These shear properties also resemble, in a qualitative way, those of the bulk polymer although there is an appreciable quantitative difference. The shear behaviour of these thin polymeric films sheds light on the action of organic boundary lubricants as well as on the frictional properties of polymers themselves. Acknowledgements The authors wish to acknowledge those members of their laboratory who have participated fully in the areas of work described in this presentation. In particular Dr. B. Scruton and Mr. J. K. A. Amuzu. They also thank General Electric (Schenectady) for the provision of the research funds which allowed parts of this work to be carried out. References 1 2 3 4 5 6 7 8 9
H. S. Furey, Wear, 26 (1973) 369. K. L. Johnson and A. D. Roberts, Proc. Roy. Sot. (London), A337 (1974) 217. R. C. Bowers, W. C. Clinton and W. A. Zisman, Lubric. Eng., 9 (1953) 204. C. M. Pooley and D. Tabor, Proc. Roy. Sot. (London), A329 (1972) 251. B. J. Briscoe, B. Scruton and R. F. Willis, Proc. Roy. Sot. (London), A333 (1973) B. J. Briscoe and D. Tabor, Trans. ASLE, July (1974). P. W. Bridgman, Rev. Mod. Phys., 18 (1946) 1. R. C. Bowers, J. Appl. Phys., 39 (1968) 5385. L. C. Towle, J. Appl. Phys., 42 (1971) 2368.
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S. Rabinowitz, I. M. Ward and J. S. C. Parry, J. Mater. Sci., 5 (1970) 29. I. M. Ward, Polymer Sci. Symp., 32 (1971) 195. R. A. Duckett, S. Rabinowitz and I. M. Ward, J. Mater. Sci., 5 (1970) 909. P. B. Bowden and J. A. Dukes, J. Mater. Sci., 7 (1972) 52. J. A. Sauer, D. R. Mears and R. D. Pae, Europ. Polymer J., 6 (1970) 1015. J. K. A. Amuzu, B. J. Briscoe and D. Tabor, unpublished data. P. R. Billinghurst and D. Tabor, Polymer, 12 (1971) 101. R. S. Fein, Trans. ASME, F 89 (1967).127. E. G. Trachman and G. Harrison, Trans. ASME, F 94 (1972) 306.