G. M. BARTENEV
OF HIGH ELASTIC. MATERIALS
A. I. EL’KIN
Polymer Physics Laboratory, Lenin State Pedagogical Institute, Moscow (U.S.S.R.) (Keceived
The authors investigate the friction properties of crosslinked butadieneacrylonitrile, butadiene-styrene copolymers and natural rubber on polished steel in vacuum over a temperature range -1100~ to +xoo”C, which takes in the glassy and high-elastic states of rubbery polymers, and also the transition range between these states. A sharp difference is observed between the friction properties of these polymers below o°C, investigated in vacuum and under atmospheric conditions. Above the glass-transition temperature, i.e. in the range of high elasticity and in the transition range, the mechanical losses in friction play an insignificant part, and therefore they cannot be used to explain the maximum on the curves of the dependence of the friction force on temperature or on the logarithm of the rate of slip. The alteration in the friction properties on the transition from high to low temperatures and from low to high rates of slip is explained by the alteration in the elastic properties in the rubbery polymers in the glass-transition region, and also by the transition from the molecular-kinetic mechanism of friction to the mechanism of friction characteristic of rigid polymers (below the glass-transition temperature the coefficient of friction is practically independent of the rate of slip and the normal load). In the range of high elasticity the friction properties of polymers are explained by the adhesion molecular-kinetic theory, proposed in 1954 by one of the present authors. Working from this theory the authors introduce the critical rate of slip z)k and characteristic temperatures Tk and To, and an explanation is given for their physical meaning. An assessment is made of the influence, the type of polymer and of the normal load on the friction properties of vulcanised rubber. It is shown that the friction force alters in an analogous fashion on reduction in the temperature and raising of the logarithm of the rate of slip, which indicates the applicability of the principle of temperature-time equivalence to the friction properties of polymers. * The Editor of Wear wishes to express his appreciation Research
Wear, 8 (‘965)
to the staff of the Rubber and Plastic who were responsible for translating this paper.
FRICTION OF HIGH ELASTIC MATERIALS
There is a lack of systematic data on the friction of rubbery polymers over a wide range of temperatures. This is the result of the great experimental difficulties, since at low temperatures dry friction can be carried out only in vacuum or in an inert medium, where we exclude not only the corrosive influence of oxygen, but also condensation of atmospheric moisture and its freezing on the friction surfaces. As a result, for investigation of the nature of the friction of polymers at low and high temperatures, we developed a vacuum tribometerl, which makes it possible to carry out measurements in various media and in vacuum down to 10-5 mm mercury at temperatures from -200’ to +200°C. We investigated unfilled vulcanisates of various polymers : natural rubber, butadiene-styrene copolymers with IO%, 30% and 50% styrene (SKS-IO, SKS-30, SKS-50), butadiene-acrylonitriile copolymers with IS%, 26% and 40% of acrylonitrile (SKN-18, SKN-26, SKN-40) and other polymers. I. APPARATUS
RESULTS OF INVESTIGATION
The layout of the vacuum tribometer is shown in Fig. I. In a pressure-tight chamber a slide is housed with a sheet of metal or other test material. On this sheet there are placed three cylindrical polymeric specimens in a carriage, connected to a proof ring dynamometer. The investigation is carried out at constant rate of slip, this being applied by an electric motor with a reduction gear. The draw-bar linking the slide and the reduction gear is sealed by means of a metal bellows.
Fig. I. Layout of the vacuum tribometer. I. Vacuum chamber; z. base; 3. porcelain tubes; 4. cooling or heating element ; 5. slider ; 6. bar; 7. sheet of metal or polymer ; 8. carriage for specimens ; 9. vulcanised rubber specimens; IO. load; II. proof ring dynamometer with inductive transducer; 12. motor; 13. multi-stage reduction gear; 14. micrometer screw: 15. bellows; 16. drawbar of heatinsulating material; 17. circular scale; 18. stop. H’eav, 8 (1965)
G. M. BARTENEV, A. I. EL’KIK
The tribometer provides for two methods of testing at low temperatures: when the specimen is brought into contact with the sheet at 2oT and remains in contact with the hard surface during cooling to a given temperature; 2) when the specimens are brought into contact with the sheet after cooling to the given temperature. In the second method, during cooling and stabilisation of the thermal conditions, we provide for automatic separation of the friction surfaces, and then for bringing them into contact at the given temperature and normal load. For this purpose the slide 3 (Fig. I, b) is equipped with a bar 6, which when moving in the idling direction presses on the carriage 8. When this happens, the carriage with the specimens, sliding obliquely over the stop 18, is raised from the hard surface. As the carriage is raised, its end surface and the surface of the load IO lie on the tapered surfaces of the bar 0. In testing by the first method at each temperature of measurement the area of actual contact is that which has been created at 2o“C. In testing by the second method, at each temperature below zo”C, there is created a progressively smaller area of actual contact, corresponding to the mechanical properties of the polymer under these conditions. I)
Fig. 2. Curves of the temperature dependence of the friction force of vulcanisates of SKN-40 butadiene-acrylonitrile copolymer on polished steel in vacuum with drawbar movement at I mm/ min. Curve I, initial friction after cooling of the rubber from zo°C in contact with steel surface; curve 2, initial friction after cooling of the rubber without contact with steel surface; curve 3, steady-state friction.
This difference between the first and second methods is evident in the nonsteady state period of slip of the specimen. Thus, for instance, the friction force, occurring at the instant of start of movement of the specimen (the initial friction force) is different in testing by the two methods in vacuum, as may be seen from comparison of the diverging low-temperature portions of curves I and 2 in Fig. 2. At temperatures above 0°C both curves practically coincide, which indicates that the conditions of setting up a surface of actual contact are here approximately the same as at 2oT. The steady-state friction force* coincides in the two methods of measurement (curve 3 in Fig. z), since in the process of slip we are setting up one and the same final surface of actual contact. * In the glass-transition region in a certain narrow range of temperature the smooth slip of the specimen ceases and a stick-slip movement begins, which decreases and disappears at the glass-transition temperature and below. Where stick-slip takes place steady-state friction is regarded as being the average between the maximum and minimum values. Wear, 8 (1965) 8-21
FRICTION OF HIGH ELASTIC MATERIALS
In Fig. z we see also that the friction force at low temperatures, independently of the methods of testing, falls sharply as a result of the transition of the rubber to the glassy state. The main cause of the fall in the friction force in all cases is the reduction in the area of actual contact. This cause is obvious for curves z and 3. As for curve I, with lowering of the temperature it ought presumably to rise continuously, since it is assumed that at all low temperatures there is established the area of actual contact which had been set up at 2o“C, while the force of adhesion of the polymer to the metal increases as the temperature falls. Nevertheless we found that because of the difference in the coefficients of thermal expansion of vulcanised rubber and metal, when the temperature is lowered, internal stresses are set up in the specimen, which in the glassy state reach high values and lead to destruction of the original contact. As a result the initial friction force falls sharply (curve I in Fig. 2). If the friction surfaces are of identical materials, then in lowering the temperature the area of actual contact is not destroyed and we observe a continuous increase in the initial force of friction. Subsequently we investigated only steady-state friction of the vulcanisates at the various temperatures, normal pressures and slip rates along a smooth polished steel surface with a high degree of cleanliness. The nominal area of contact was 1.5 cm” in all the experiments. The accuracy of measurement of the friction force and the coefficient of friction was 2-3%. The steady-state friction was reached at all rates of slip after the specimen had travelled about 2-3 mm. Correspon~ngly the time of reaching steady-state friction is practically determined by the applied rate of slip.
Fig. 3, Temperature dependence of the friction force of natural rubber vulcanisates in steadystate friction at normal load of 0.65 kgf/cm* and rate of slip on smooth steel surface I mm/min. Curve I, in vacuum; curve z, in atmosphere of relative humidity of 50%.
When we compare the friction properties of vulcanisates in the low temperature range in vacuum (curve I, Fig. 3) and in natural atmospheric conditions (curve 2, Fig. 3) we observe a marked difference in the temperature dependencies of the friction force on account of condensation and subsequent freezing of atmospheric moisture on the friction surfaces. In the range of high temperatures these dependencies practically coincide. Curve 2 in Fig. 3 was obtained under atmospheric conditions with 50% relative humidity (at 2oT). The dew point corresponding to this humidity is about 9°C. Below this temperature the curves I and 2 clearly differ. The lower the humidity Wear, 8 (1965) 8--21
G. M. BARTENEV,
of the ambient
the lower the temperatures
force begins. Nevertheless we did not observe any coefficient of friction at 2oT and above. At temperatures below the dew point the fall in AB (Fig. 3) takes place because of the lubricant action and is not connected with the nature of the friction -5°C the friction force reaches its lowest value and
z\. I. EL’KIX
at which the fall in the friction influence
the friction force on the portion of the condensed water vapour surfaces. At a temperature of then begins to increase again,
passing through a low maximum. The cause of the occurrence of this maximum, which almost coincides with the maximum found in vacuum (curve I, Fig. 3), is evidently the same as that of the maximum in vacuum, with the difference that the friction force is lower because of the lubricant action of the ice film. In vacuum the friction force increases linearly as the temperature is lowered, and then falls, passing through a maximum at a certain low temperature (curve I, Fig. 3). Curves with a maximum were found by BULCIN et al.2 on tread rubber under atmospheric conditions. This is explained by the fact that they use relatively high rates of slip at which the maximum shifts towards high temperatures (above zo”C), where there is no condensation of atmospheric moisture. Thus, from the figures quoted it is sufficiently evident that dry friction of polymers can be brought about at low temperatures only by using a special procedure. The results given below are new, since investigation of friction of polymers in vacuum has not hitherto been carried out, with the exception of our previous communications and certain communications on the friction of hard polymers394. 2. INFLUENCE
In Fig. 4 we give a at an applied rate of slip experimental curves ABE tion AB the friction force
ON THE FRICTION PROPERTIES OF RUBBERY
picture of the temperature dependence of the friction force v and normal load N, analogous to curve I in Fig. 3. The consist of two portions. At high temperatures on the porincreases as the temperature is lowered, as is well-known
from previous work596. In the range of low temperatures on the portion BE the friction force falls on passing from the high-elastic to the glassy state. On portion AB we observe a linear relationship between the friction force F and the absolute temperature T, in conformity with the molecular-kinetic theory7: F=g.S(,-$)
where S is the area of actual contact; S, is the elementary area of actual contact, for one chain of the polymer network ; U is the activation energy of one chain in the friction process; ii is the average jump distance of a chain*; and TO is a constant with the dimension of temperature equal to TO =
U/k In (v$J)
where k is the Boltzmann constant, v the rate of slip, and * cf.
Transl. 925 (see ref. 7 of this paper)
Wear, 8 (1965) 8--21
FRICTION OF HIGH EI,ASTIC MATERIALS
vo a value close to the speed of sound in a glassy-state polymer ( Equation (I) corresponds to the single-term law of friction
F = cS where the coefficient c depends on the temperature, the rate of slip and the nature of the friction surfaces in accordance with eqn. (I), while S depends on the elastic properties of the rubber and the micro-geometry of the friction surfaces. From eqn. (I) we calculate the friction for an applied rate of slip, and conversely from the experimentally measured friction force we can calculate the rate of slip. Let us designate this theoretical rate of slip Q. From now on, to explain the friction properties at low temperatures, we must assume that the molecular-kinetic theory of friction of rubbery network polymers is correct in a given range of rate of slip z,vk. If we apply a rate of slip v = const., and the temperature is variable, as is the case in our experiment (Fig. 4), then it is desirable to introduce the concept of a critical temperature of friction Tk, at which the rate v = const. is the critical rate of slip. The temperature Tk corresponds approximately to the position of the maximum (Fig. 4).
Fig. 4. Schematic diagram of the temperature dependence of the friction force of crosslinked rubbery polymers on a smooth bard surface in steady-state friction. * In general no attempt has been made to anglicise the symbols and subscripts. Wear, 8 (1965)
G. M. BARTENEV,
A. I. EL'KIN
Below the critical temperature of friction Tk:, which depends upon the rate of slip ~1,the calculated value Ut # v, so that the coefficient c in eqn. (3) cannot be determined from eqn. (I).&orrespondingly at temperatures below TI, the law of friction (3) must be written in a different form, (4)
F = C’S
where E’ has a different physical meaning connected with the change in the mechanism of the friction of vulcanised rubber at low temperatures. The deviation of the temperature dependence of the friction force at low temperatures (BE on Fig. 4) from the theoretical (the extrapolated line BC) is explained by the reduction in the area of actual contact S, below the temperature corresponding to point B, as a consequence of the gradual transition of the polymer to the glassy state, and in addition, the transition to the different mechanism of friction, characteristic of rigid polymers. The fall in the friction force ought to be sharper (according to curve 2, Fig. 4) if there did not take place an increase in the coefficient c’, which forms part of eqn. (4), with the reduction in the temperature. Curve I (Fig. 4) represents the temperature dependence of the friction force according to eqn. (4), where instead of S we take Sn - the area of actual contact at a temperature corresponding to point B. Curve z represents the temperature dependence according to eqn. (I) or (3); the alteration in the area of actual contact at low temperatures being calculated according to the formula’proposed by BARTENEV AND LAVRENT'EV~ expressing the relationship between the area of actual contact and the static modulus of compression of vulcanised rubber. At temperatures above point B the modulus of compression of vulcanised rubber is of almost constant value ; at temperatures below point B it increases as the temperature falls. Therefore at high temperatures the area of actual contact is practically constant and in conformity with eqn. (I)we observe a linear dependence of the friction force on the temperature. At low temperatures the area of actual contact decreases until at the glass-transition temperature T, we reach the lowest value. In addition, below Tg the value c’ also reaches a practically constant value, characteristic of the friction of solid polymers. As a result of this, the friction force in the glassystate of vulcanised rubber is low and depends only slightly on the temperature. 3. INFLUENCE
One factor in setting up an area of actual contact is the compression modulus of the rubber, which depends markedly on the temperature and rate of deformation in the glass-transition range. Since at high rates of slip there is less time to establish the area of actual contact, the compression modulus is correspondingly higher than at lower rates of slip. In other words, as a result of the relaxation nature of the deformation of the polymer the range of transition from the high-elastic to the glassy state and the curve of the temperature dependence of the friction shift, with increasing rate of slip of the rubber, towards high temperatures; consequently, also, the transition to a different mechanism of friction is effected at higher temperatures. Thus on increasing the rate of slip of a vulcanisate of SKS-IO butadiene-styrene rubber by 5 Wear, 8 (196~) 8--2x
FRICTIONOF HIGH ELASTIC MATERIALS
times the maximum and the temperature Tk shift by IO~---I~‘C towards higher temperatures (Fig. 5). This phenomenon is observed in its pure form when the rate of slip is low and the temperature of the surface of the rubber is practically equal to the measured temperature in the apparatus. At higher rates of slip of the specimen, on account of the heating of the surfaces, the temperature of the surface of the rubber is higher than the measured temperature. As a result of this, the true curve of the temperature dependence of the friction force on changing to higher rates of slip will undergo an apparent shift to low temperatures. Since the data given in Fig. 5 show the opposite effect, this is reason to consider that our rates of slip are too low to cause a perceptible heating of the surfaces.
Fig. 5. Temperature dependence of the friction force of vulcanisate of SKS-IO with normal load 0.65 kgf/cms and two rates of slip. Curve I, 0.2 mm/min; curve 2, I mm/min.
In the temperature range below Tk we observe an increase, and above Ta a decrease, in the friction force, with rising temperature (Fig. 4). In the same way, in the range of slip lower than the critical value vk, we observe that the friction force increases with the rate of slip and that it decreases in the range of higher rates. This may be seen from the data given in Fig. 6 for a vulcanisate of SKS-50 butadienestyrene copolymer at 90, 40 and -30°C. Since at 40°C the critical rate is equal to 2.4 mm/min then at rates of slip lower than this we observe a rising portion of curve I, and at higher rates a falling portion (Fig. 6). At 90°C the critical rate of slip vk lies somewhat to the right of the range of the rates investigated, therefore we observe an increasing characteristic of friction (curve 2). Correspondingly at the temperature of -30°C we observe a falling characteristic of friction (curve 3). From a large number of friction curves at various temperatures, analogous to those given in Fig. 6, we can obtain by the method of WILLIAMS, LANDEL AND FERRY~, a dependence of the friction force over a very wide range of rates at any given temperature. For a vulcanisate of SK.%50 we took as our reference temperature 40°C and plotted a generalised curve for it (Fig. 7). This curve is plotted from individual curves at different temperatures by shifting them to the right or left (depending upon the temperature) parallel to the axis of the logarithm of the rate of slip until these lie on a single curve. This method of treating the results was used by BULGIN, HUBWear, 8 (1965) 8-21
(G.M. 13AHTESE\‘. A. I. EL’MS
BARD AND WALTERS~. A generalised
curve of this type was obtained recently 1~~. GROSCH~Ofor a vulcanisate of butadiene-acrylonitrile copolymer. On comparing the temperature dependence of the friction force (Fig. 3, curve I, or Fig. 5) with the dependence of the friction force on the logarithm of the rate of slip (Fig. 7) we see that the two dependencies are a mirror image of each other. This means that on reducing the temperature and on raising the logarithm of the rate of slip the course of the two curves is identical, i.e. for the friction of polymers the principle of temperature-time equivalence holds, the applicability of which has been demonstrated for many relaxation characteristics in polymers (viscosity, shear modulus, mechanical loss, etc.).
Fig. 6. Dependence of the friction force of vulcanisates of SKS-50 rubber on the logarithm of the rate of slip with normal load 0.65 kgf/cm* and temperatures of-40” (curve I) ; go’ (&n-v, z) ; - 30” (curve 3). At goT the critical rate of slip z)bis high, therefore curve 2 is to the left of ZIQ;at -3oT ok is low, therefore curve 3 lies to the right of zly. Fig. 7. Relationship between the friction force and the logarithm of the rate of slip (generalised curve) for vulcanisate of SKS-50 at 4oT and normal load 0.65 kgf/cmz.
In ref. 2 it was demonstrated that there is a definite coefficient of friction and the hysteresis losses of rubber.
Apparently, as a result of this, many writers”*10 connect the maximum of friction (Fig. 7) with the maximum of mechanical losses in rubber, regarding the friction of rubber as a process of dissipation of elastic energy in the volume of the rubber, for instance by the oscillations set up in the encounter and tearing away of the asperities of. the friction surfaces. The frequency of these oscillations depends upon the rate of slip of the rubber. This conception of the mechanism of friction of the rubber is found to be correct, particularly for very rough hard surfaces, but is not the only one. Another mechanism of friction of rubber may be purely adhesive, connected with the dissipation of energy, as a result of the process of the destruction and recovery of bonds wear, 8 (1965)
FRICTION OF HIGH ELASTIC MATERIALS
between the chains of rubber and the hard surface. According to theory’ and experimental data596 the adhesive mechanism of the friction of rubber, in its slip over a smooth hard surface, is the main one. The actual correlation between friction and mechanical losses in vulcanised rubbers at 2o”C, observed in many papers, is partially explained by the fact that the more polar the rubber the higher the mechanical losses in the rubber, on the one hand, and the greater the force of attachment of the rubber to the hard surface on the other hand, and consequently the higher also the friction force (cj. Fig. 8). The straight line portions of the curves AB in Fig. 4 and Fig. 7 are accurately described by the molecular-kinetic theory of the friction of rubber. At the same time it is impossible to explain by mechanical losses in the rubber the alteration in the friction force on the portion AB (Fig. 4), since it is known11 that in this temperature range the magnitude of the mechanical losses in vulcanised rubbers remains practically unchanged. In addition, in the glass-transition range we observe a clear and sharp maximum of mechanical losses11 which does not coincide with the markedly blurred maximum of the friction force (Fig. 4). Thus the maximum of friction (Fig. 7) cannot be explained by mechanical losses in the vulcanised rubber in friction on smooth and hard surfaces. As also in the case of the temperature dependence (Fig. 4)) the fall in the friction force with increasing rate of slip on portion BE (Fig. 7) is explained by the reduction in the area of actual contact and by the alteration in the mechanism of friction as a result of the glasstransition of the surface layer of the specimen of rubber on passing to high rates of slip, and consequently by the high frequency of oscillation of the roughnesses of the rubber (of course, if we exclude the heating of the surface layer of the rubber).
OF THE TYPE
ON THE FRICTION CHARACTERISTICS
OF THE VULCANISATES
Vulcanisates based on all rubbers give a temperature dependence of the friction force analogous to that shown in Fig. 4. A shift of this displacement on the temperature scale to the right or to the left depends upon the position of the glasstransition range of the vulcanisates and of the glass-transition temperature Tg. In addition to this characteristic temperature, the friction properties of vulcanised rubber are determined by the temperatures Tk: and TO. The friction properties of vulcanised rubber at temperatures below TO are the same as for hard polymers. The temperature range between T, and Tk: is a transition from one mechanism of friction to another; in the temperature range between Tk and TO we have a molecular-kinetic mechanism of friction. According to eqn. (I) at temperature TO the friction force becomes zero. In point of fact this result has no physical meaning, since extrapolation of eqn. (I) to low friction forces according to theory7 is not permissible. Therefore the temperature TO is a conventional value. For natural rubber vulcanisates there are more accurate data on the activation energy of the process of friction, according to whichbpe U = 18 kcal/mole. Bearing in mind that v = I mm/min and vo z IOOO mjsec, we find from eqn. (2) that TO = 51o”K, while the experimental value of TO = 4go’K (Fig. 3). Since for this vulcanisate Wear, 8 (1965) 8-21
G. M. BARTENEV,
A. I. EL'KIS
T, g zoo”K, the difference between T, and TO is 290°K. For the majority of the polymers this difference is 200°-3000K. The good agreement between the calculated and the experimental value of To for the natural rubber vulcanisates is somewhat fortuitous, since uo is not accurately determined, while the activation energy depends on the temperature, even if only slightly6. Calculation of TO for other vulcanisates gives a greater difference from the experimental values, although the order of values remains correct. Let us now consider the determination of the critical rates of slip of vulcanisecl rubber, working from the mechanism and theory for vulcanisecl rubberT. Let ;Zbe the mean distance between consecutive sites of attachment of a chain of the rubber network to the hard surface, while Z’ is the mean time of moving of the chain, which is attached to the hard surface, over a distance 1 along the direction of slip of the specimen, to which there is applied the tangential force F. Then the mean rate of movement of the chain, equal to the rate of slip of the rubber test piece, is v = njtt. The value z’ is calculated according to the theory, and it depends on the nature of the friction surfaces, the temperature and the magnitude of the tangential force. With increase in the tangential force t’ decreases, while the rate v increases. If t’ is greater than the time t*, which is necessary for movement of the chain into a new position after its separation from the surface, then the molecular-kinetic mechanism of friction of rubber takes effect. When we increase the rate of slip the time t’ may become shorter than t*, and the chain will no longer be capable of moving in time t’. Where r’
it being known that t* = to eU*‘/kT
where U* is the activation energy of the movement of a segment of the polymer chain from one equilibrium position to another in the process of thermal motion, and 70 a constant which is approximately 10-12 set for polymers. From the generalised curve for the SKS-50 vulcanisate at 4o°C (Fig. 7) we can clearly follow the transition with increasing rate of slip from the molecular-kinetic mechanism of friction of rubber (the straight-line portion AB) to the mechanism of friction of hard polymers, which is characterised by a low dependence of the friction force on the rate of slip (the horizontal portion E). The critical rate for this rubber at 40°C is 2.4 mm/min. For the natural rubber vulcanisates the critical rate was calculated from eqns. (5) and (6). According to ref. 6 1 = ~.Io-~ cm, while U* = IO/N* kcal/mole at 3oo”K, where NA is Avogadro’s number (from which it follows that t* = 10-5 set). Consequently vk = 30 mm/min at 300°K. With lowering of the temperature vk decreases and at the glass-transition temperature 200°K (U* = 13/N” kcal/mole and t* = 102 set according to the data of ref. 12) becomes equal to 3.10-6 mm/min. Wear,
FRICTION OF HIGH ELASTIC MATERIALS
Since the rates of slip used in the experiment are considerably higher than this, the observed friction properties of natural rubber vulcanisates at 200’K and below are analogous to those of the solids. If we apply a rate of slip v = const., then at the temperature Tk this rate of slip will be critical. From eqns. (5) and (6) it follows that Tk
kln(&v) For a natural rubber vulcanisate we calculate according to this formula Tk:= 252’K (at v = I mm/min and U* = IO/N~ kcal/mole), while the experimental value is 242OK (Fig. 3). For butadiene-styrene and butadiene-acrylonitrile rubbers the arrangement of the curves of the temperature dependence of the friction force depends in a definite way on the concentration of polar side groups on the polymer chain. For instance, from the data given in Fig. 8 we see that the temperatures TO and Tk are higher, the more styrene groups there are on the chain of the butadiene-styrene copolymer. This is explained by the corresponding increase in the activation energies U and Cl* on transition from a less to a more polar polymer.
Fig. 8. Temperature dependence of the friction force at normal load 0.65 kgf/cma at a rate of slip I mm/min for vulcanisates of butadiene-styrene copolymers. Curve I, SKS-IO; curve 2, SKS-30; curve 3. SKS-50.
With increase in the polarity of the butadiene-styrene copolymer the friction force in the high-elastic state increases, while in the glassy state it decreases (Fig. 8). This is explained on the one hand by the fact that with an increase in the number of styrene groups the modulus of elasticity of the polymer increases, and the area of actual contact and the force of friction decrease, and on the other hand by the fact that the activation energy of the process of friction, and consequently also the friction force, increase. In the high-elastic state the influence of the alteration of the activation energy is greater than that of the alteration in the elastic properties and in the glassy state on the other hand the influence of the adhesion forces with alteration in the polarity of the rubber is less than that of the elastic properties (in eqn. (4) the constant c’ is of less importance on changing from SKS-IO to SKS-50, while the area of actual contact decreases to a greater extent). Wear,
20 5. INFLUENCE
OF THE NORMAL LOAD
It is known that the friction force of rubber F increases with increasing normal load N, while the coefficient of friction ,LJdecreases. This property of vulcanised rubber is observed over the whole range of temperatures above the glass-transition tempersture (Fig. 9). Below T!, the coefficient of friction does not depend upon the load and the rubber obeys Amonton’s law.
Fig. 9. Temperature dependence of the coefficient of friction of vulcanisates of SKS-30 butadienestyrenc copolymers at rates of slip I mm/min and three normal loads. Curve I, 0.15 kgf/cms; curve 1, 0.65 kgf/cm 2; curve 3, z kgf/cm2.
From Fig. 9 it is seen that the temperature TO does not depend upon the normal load (or the area of actual contact), which ought to correspond also to eqn. (z), if the energy of activation U does not increase with increase in N. The correctness of the latter supposition has been demonstrated6 for a natural rubber vulcanisate in the range of normal loadings from 0.05-3 kgf/cmz. As already observed the deviation of friction force at low temperatures from a linear dependence (portion BE on Fig. 4) is explained by the alteration in the modulus of elasticity of the rubber E, in the glass-transition range. From Fig. 9 it is seen that the lower the normal load the earlier the deviation from the linear dependence. Probably this may be explained from the law of friction proposed by BARTENEV AND LAVRENT’EV~, where it was demonstrated that the friction force depends on the ratio NJE, in such a way that the most marked dependence of p on N is observed at low values of the ratio N/E. As a result of this the coefficient of friction is most sensitive to alteration in the modulus of rubber with lowering of the temperature in the range of low normal loads, which, probably, explains also the result given in Fig. 9. Wear, 8 (1965)
FRICTION OF HIGH ELASTIC MATERIALS
REFERENCES I G. M.
2 3 4
BARTENEV AND -4. I. EL'KIN,Zuvodska Lab., zg (2) (1963) 227; transl. Ind. Lab., 29 (2) (1963): Dokl. Akad. Nauk SSSR, 15r (2)(1963) 320;cover-to-covertransl. exists. D. BULGIN et al., 4th Rubber Technol. Conf., London, May. 1962, p. ‘73. R. F. KING AND D. TABOR, Proc. Phys. Sot. (London), B66 (1953) 728. K. G. MCLARENAND D. TABOR, Nature,rg7 (1963)856. 4. SCHALLAMACH,Proc. Phys. Sot., (London),B66 (1953) 386. G. M. BARTENEV AND 2.E. STYRAN, Vysokomolekul. Soedin., I (7) (1959) 978; RABRM Trawl.
784, reprinted in Rubber Chem. Technol., 33 (4) (1960) 1166. BARTENEV, Dokl. Akad.Nauk SSSR,96 (1954) 1161;translation available at RAPRA. Proc. 3rd All-U&on Conf. on Friction and Wear, Moscow, 1960, Vol. 2,7;RAPRA Transl. 925. 8 G.M. BARTENEVANDV.V.LAVRIZNT'EV, Dokl.Akad. Nauk SSSR,zqr (2)(1961)334; RAPRA Transl. 968. g M. L. WILLIAMS,R. F. LANDELAND J. D. FERRY, J. Am. Chem. Sot., 77 (1955) 3701. 7 G. M.
IO K. A. GROSCH, Nature,xg7 (1963)858. II G. M. BAR~ENEV AND Yu. V. ZELENEV, Vysokomolekul.
Soedin., 4 (I)(1962)66; RAPRA Transl. 991; Kauchuk. i. Rezina, 19 (8) (1960) 18; transl. Soviet Rubber Technol., 19 (8) (1960). 12 G. M. BARTENEV AND V. D. ZAITSEVA,Vysokomolekul. Soedin., I (9) (1939) 1309; transl. Rubber Chem. Tecknol., 34 (4) (rg6r) IZOI. Wear, 8 (1965) 8-2~