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The Wear of Metals under Unlubricated ConditionsAuthor(s): J. F. Archard and W. HirstSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 236, No. 1206 (Aug. 2, 1956), pp. 397-410Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/99967 .

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The wear of metals under unlubricated conditions

BY J. F. ARCHARD AND W. HIRST

Research Laboratory, Associated Electrical Industries Limited, Aldermaston, Berks

(Communicated by T. E. Allibone, F.R.S.-Received 25 February 1956- Revised 3 April 1956)

[Plate 16]

The wear of a wide range of material combinations has been studied in unlubricated conditions. Loads of 50 g to 10 Kg and speeds of 2 to 660 cm/s have been used. A representative selection of the results is given. As a broad classification two contrasting mechanisms of wear have been observed. In nearly all experiments, and for all types of wear mechanism, once equilibrium surface conditions are established the wear rate is independent of the apparent area of contact. The wear rate is accurately proportional to the load for only a limited number of combinations but there are many other examples for which the relation between wear rate and load shows only a small deviation from direct proportionality. It is suggested that with the same surface conditions the wear rate is proportional to the load; in practice this simple relation is modified because the surface conditions depend on the load. These rules of wear may be derived, on a priori grounds, from the experimental results, or from more detailed theoretical calculations.

1. INTRODUCTION

Attempts have recently been made to develop a theoretical basis to explain the wear of materials, the ideas used being analogous to those on which the generally accepted theory of friction is founded (Bowden & Tabor I950). It is supposed that the real area of contact between two objects is far less than the apparent area and is determined by the extent of the deformation of the touching surface asperities under the applied load. There will be a number of local regions of true contact whose location will change during sliding and, in consequence, sliding gives rise to local encounters between small regions of the rubbing surfaces. The basis of these theories of wear is to relate the wear to the number and nature of the local encounters but in some theories the unit event leading to the production of a wear particle is regarded as an encounter between two atoms, one on each of the opposing surfaces (Holm I946, I953; Burwell & Strang I 92a, b; Burwell I953), whereas in another theory it is the encounter between two surface asperities (Archard I952,

I953 a, b). If the surface asperities deform plastically under the applied load and it is assumed that at each unit event there is a definite probability that a wear particle will be produced, the theories lead to the relation

W = KPlpm, (1)

where W is the worn volume, s is the sliding distance, P is the applied load, Pm is the flow pressure of the softer material, and K is a constant related to the probability per unit encounter of production of a wear particle. It will be seen that these theories predict that there should be two simple rules of wear, i.e. that the wear rate is independent of the apparent area of contact and that it is directly proportional to the applied load.

26 [ 397 ] Vo1. 236. A.



398 J. F. Archard and W. Hirst

These rules are analogous to Amonton's laws of friction, and there is now a certain amount of evidence that they are obeyed in simplified conditions of rubbing. Thus, Burwell & Strang (I 952 a, b) have measured the wear of steels and some other metals at slow speeds using cetane as lubricant. The dependence of wear rate upon load and pressure was determined and they concluded that the wear rate is proportional to the load and independent of pressure unless the mean surface stress exceeds a value equivalent to one-third of the hardness of the material. One of the authors (Archard I953 ) has also reported that the wear rates of some materials vary linearly with the applied load and are independent of pressure over a wide range. Because both K and p, may be expected to depend upon the material, the theory makes no direct prediction about the variation of wear rate with hardness. However, Hughes & Spurr (I955) have observed an inverse relationship between wear rate and hardness-which is predicted when K is a constant-when measuring the wear rate of a wax whose hardness they altered by changing its temperature. Krushchov & Babichev (I953) have measured the wear of a range of metals when rubbing against emery cloth, special precautions being taken to ensure reproducibility of the results. They find that, under these conditions, the wear rate of different materials is inversely proportional to their hardness, an exception to this general rule being found for heat-treated steels.

These simple results are in marked constrast to those of the majority of wear experiments reported in the literature; these suggest that wear is dependent on a large number of variables and there is no general agreement about how the wear depends on such quantities as the load, speed and apparent area of contact. It may be that some of these results can be discounted because the experiments were carried out under ill-defined conditions designed primarily to simulate the operating conditions of a particular piece of machinery. Moreover, the majority of experiments have been carried out using lubricated conditions where it is generally found that the wear rate decreases with time. This is usually because the condition of hydrodynamic lubrication is being approached so that in the limit the surfaces separate and wear, which is due to rubbing, ceases (Kenyon I946). However, even after considering these factors, one still gains the impression from the literature that rules of wear will not apply generally.

The present work was planned to extend the experimental work mentioned earlier. The experiments were made in unlubricated conditions and a wide range of materials, chosen largely at random, was examined to find out to what extent the same rules of wear apply to all materials. In this paper it is possible to quote only a limited selection of the results; these have been chosen to illustrate the conclusions drawn from several hundred experiments using different combinations of materials, loads and speeds.

It was found as a fairly general rule that the wear rate was independent of the apparent area of contact, and usually reasonable explanations could be advanced when this did not occur. Also, although the wear rate often increased roughly proportionally with the load, this was accurately true for only a limited number of cases. These results are discussed and an attempt made to define general rules of wear. These rules may be derived, on a priori grounds, from the experimental results,



Wear of metals 399

or from more detailed theoretical considerations. The first derivation requires few assumptions, whereas the latter involves theoretical postulates which require experimental verification.

2. APPARATUS

Two pin-and-ring machines have been used. The essential details, common to both machines, are shown in figure 1 (a). A ring B of us in. (2 38 cm) diameter was mounted on a shaft A and in the majority of the experiments it rotated at approxi- mately 1500 rev/min, the surface speed being about 180 cm/s (370 ft./min). A flat- ended 4 in. (0.635 cm) diameter pin C was pressed under a load P against the cir- cumference of the ring. Three such pins and rings were carried on each machine. On one machine it was possible to measure the frictional force and thus determine the coefficient of friction.

iP

(b)

FIGup.E 1. Schematic diagram of two arrangements of pin and ring wear machine. A, rotating shaft; B, ring 15 in. diam.; C, W in. diam. pin pressed under load P against ring.

The surfaces of the rings were usually prepared on a universal grinding machine; when a finer surface finish was required they were subsequently honed by the Superfinishing process. The ends of the pins were lapped with 240 Carborundum on a cast-iron lap and finished with 320 Carborundum on a lead lap. The pins and rings were cleaned by washing in petroleum ether and acetone followed by de- greasing in a Soxhlet apparatus containing petroleum ether or a mixture of acetone and isopropyl alcohol; any remaining traces of contaminant would be removed during the initial stages of the wear process.

For low-wear rates the wear was determined by measuring the wear scar on the pin with a travelling microscope. For higher wear rates the wear was measured by weighing. In a number of later experiments a different arrangement was used with the cylindrical pin loaded against the ring in a 'crossed cylinders' arrangement as shown in figure 1 (b). An elliptical wear scar developed on the pin, and this particular arrangement had the advantage that smaller amounts of wear could be measured. It should be noted that in these experimental arrangements the apparent area of contact is not constant; it increases with an increase in the dimensions of the wear scar. Therefore a linear wear-time relation implies that the wear rate is independent of the apparent area of contact between the rubbing members.

26-2




3. RESULTS

The most striking feature of the wear of metals in the conditions used is that they exhibit two forms of wear, one mild, the other severe. The mild form is usually observed at light loads, and the severe at heavier. It is often found, when the load is increased sufficiently after a period of mild wear, that the severe wear process is initiated as a patch of heavy damage. This creates the conditions for the con- tinuance of severe wear and the rough patch spreads to cover the whole of the rubbing surfaces. The difference between the scale of the damage in the two wear processes is very great and is illustrated by the profilometer records shown in figure 2. They were obtained using the Talysurf instrument. The records show the changes in surface profile of a mild steel ring during a period of mild wear and the changes when severe wear sets in after increasing the load. It can be seen that mild wear involves the slow removal of the tips of the higher asperities by a process on a scale too small to be reached by the Talysurf instrument. Severe wear occurs by a mechanism on a much larger scale of size and damage appears to take place by welding and plucking of the surfaces. The mechanism of severe wear is probably similar to the process of welding studied so extensively in investigations into the origin of friction (Bowden & Tabor I 950) but the mild wear process may be different in kind as well as in its scale of size. As an indication of the scale of size involved,

OOlin.

OOOO2ir.; Go A

0-01

0 0002in B

001

0 0002 c

0*01

0-000S a,, J JJ i D

Y d

FIGURE 2. Talysurf records showing wear of ring. Pin: silver steel (V.p. no. 320). Ring: mild steel (V.p. no. 186). Speed: 180 cm/s. A, original turned surface; B, surface after 0 75 h mild wear at a load of 150 g; C, after 2-25 h mild wear at load of 150 g. D, shortly after C, showing onset of severe wear at regions X and Y when the load was increased to 210 g. (Note that the vertical magnification is reduced in this record.) The diameter d of the equivalent area of true contact for the load used is shown for comparison.



Archard & Hirst Proc. fRoy. Soc. A, volume 236, plate 16

I.~~~~~~~~~~~~~~~~~~~~~~I

B

C

(b)

FIcGIRE 3. Motallographic sections of 70/30 brtass pins. (a) Mild wear after rubbing on hard- oend tool steel ring. Load 50 g, speed 175 cm/s3. (b) Severe wear after rubbing oln 70/30

brass ring. Load 240 g, speed 195 em/s. A, brass specimen; B, protective plating; C, transferred fragment.

(Facing p. 401)



Wear of metals 401

it may be seen from figure 2 that the surface wore by only about 10-4in. in the course of 105 revolutions of the ring.

The scale of the subsurface damage in the two types of wear process is also very different. Figures (3a) and 3 (b), plate 16, show photo-micrographs of sections* of a 70/30 brass pin taken after rubbing in the mild and the severe wear conditions. In severe wear the crystal structure of the surface layers becomes heavily distorted and deformation may extend to a considerable depth (up to about 0'01 cm for the relatively light load in the example shown), whereas after mild wear there is little indication of subsurface damage. It will also be noted that figure 3 (b) shows that in severe wear the surface regions may include fragments transferred from one rubbing member to the other. In the mild wear example shown, traces of subsurface damage are apparent, but this may have been due to an earlier period of severe wear; sections of pins of other materials after mild wear show no detectable deformation. The change from mild to severe wear is therefore associated with a change in the depth of deformation even though, as is explained later, the frictional force may not be increased. In severe wear the forces involved in rubbing cause plastic deformation well below the surface, whereas in mild wear any such deformation must be confined to regions very close to the rubbing interface.

In mild wear, however, a surface change of another kind often occurs. The surfaces develop a skin of appreciable electrical resistance and a contact resistance of several ohms, sometimes as high as 50 Q, is common; the surfaces often become visibly oxidized. If one assumes that the surface films are insulating and attributes the conductivity to direct metallic contact at an area where the film is locally broken down, the size of this contact area may be calculated by the spreading resistance method. The upper limit to the area of intermetallic contact is about I A2. This evidence shows that in mild wear intermetallic junctions between the two members can form only rarely. However, intermetallic junctions between metallic inclusions within the surface skin, or contacts between one of the underlying metals and the surface skin on the other, may occur more frequently.

The nature of the mild wear process is being examined in more detail and the results will be published subsequently. It is sufficient to remark here that these experiments confirm the thesis that the mild wear process concerns units whose scale of size is several orders of magnitude less than those involved in severe wear; for example, typical dimensions of the wear particles are some hundred angstroms. The bulk of the evidence therefore suggests that in mild wear the surface inter- actions are on so small a scale as to be confined within the surface skin generated during the course of rubbing. In contrast, in severe wear, extensive intermetallic contact occurs, the contact resistance is usually very low, the surfaces retain their metallic appearance and the wear particles are several orders of magnitude larger (typical dimensions being of the order of 10-2 cm).

As a general rule, severe wear is favoured by the use of similar materials and by high loads. Also, though this is not always true, soft materials tend to exhibit severe wear at lower loads than hard materials, and the harder materials examined did not show severe wear at the heaviest loads used (10 Kg). The existence of at

* We are indebted to Dr N. C. Welsh for preparing these sections.




least two types of wear in certain conditions of rubbing have been recognized by a number of workers (Holm 1946, I953; Mailander & Dies, I943; Dies I943), but they have not been fully described.

3 1. The relations between wear and time, and wear rate and load

The foregoing shows that, in general, when rubbing begins, changes in the condition and structure of the surface layers occur, and it is often found that the wear rate changes with time during the early stages of rubbing. However, after an initial period of running, the wear rate become constant and work by Hirst & Lancaster (i956) shows that this begins when the surface layers attain their equilibrium condition.

a) 4 X /3

4 - 12x

sldn ditnc010 m

2 -

~~~ Ax/

x A

0 12

sliding distance (106 cm) FIGURE 4. Graphs of wear against sliding distance for pins rubbing on rings of the same

material (speed 180 cm/s). (1) Mild steel, 50 g. (2) Ferritic stainless steel, 250 g. (3) 70/30 brass, 80g. (4) Stellite, 2500 g. (5) Hardened tool steel, 330g.

A constant wear rate after an initial transitional period is observed in a very wide range of circumstances and with a great number of materials. Figure 4 shows the variation of the wear with time for a number of materials when the pin and the ring were each of the same material, and figure 5 shows the same relation when the pin and ring were of different materials. Figure 6 shows the relationship between wear and time for ferritic stainless steel rubbing against hardened tool steel for a number of loads. Wear-time graphs which, after an initial transitional period, assume a linear form have been observed for speeds from 2 to 660 cm/s. It will be seen that for a wide range of materials, loads and speeds, the wear rate is independent of the apparent area of contact once the equilibrium surface condition is attained.

From the slopes of these graphs of wear against time, equilibrium wear rates may be obtained and the curves of wear rate against load so obtained have been plotted on a double logarithmic scale. The wear rate/load curve for ferritic stainless steel pins rubbing on hardened tool steel rings is given in figure 7. The fact that the wear rate is independent of the apparent area of contact clearly does not imply that a simple relationship between the wear rate and the load will be observed.



Wear of metals 403

5-

;2

4-

b / fI 3-~ ~ 7

0 1

sliding distance (106 cm)

FIGauRE 5. Graphs of wear against sliding distance for pins rubbing on rings of different materials (speed 180 cm/s). (1) Teflon on hardened tool steel, 150 g. (2) 60/40 brass on hardened tool steel, 120 g. (3) Ferritic stainless steel on sintered tungsten carbide, 1200 g. (4) Beryllium copper on hardened tool steel, 1000 g. (5) Stellite grade 1 on hardened tool steel, 750 g. (6) Sintered tungsten carbide on mild steel, 1000 g.

0 ~ ~ ~~~~~~~0

2-~~~~~~~~~~~~~

0 1 2 3 4 5 6


FIGuCE 6. Graphs of wear against sliding distance for ferritic stainless steel pins on hardened tool steel rings at various loads (g): (1) 2000, (2) 1500, (3) 930, (4) 580, (5) 330, (6) 80. Speed, 180 cm/s.




With this combination of ferritic stainless steel rubbing on hardened tool steel one observes a relatively sharp transition from mild to severe wear as the load is increased. With some other combinations the transition is not sharp and it is possible, over a range of loads, to observe mild wear, severe wear, or an intermediate condition in which the rubbing surfaces are patchy producing a mixture of the two types of wear. Annealed 70/30 brass rubbing on tool steel gives the wear-time graph shown in figure 8; some time after the start of the experiment severe wear occurs,

10 ~ ~ -- 1

-7 0

I 0~~~~~~~~~

I) _

10 to2 103 104

load (g)

FIGuRE 7. Graph of wear rate against load for ferritic stainless steel pins on high-speed tool steel rings. Speed 180 cm/s.

2-

- I

~~~~~~~~~~~~~~~~~I , I

0 1 2 3 4


FIGURE 8. Graph of wear against sliding distance for annealed 70/30 brass pins on hardened tool steel rings. Load 1000 g. Speed 180 cm/s.

and later there is a transition to mild wear. Despite the very different character of the wear processes, with both the wear increases linearly with time so that the wear rate is independent of the apparent area of contact for both types of wear process. In other experiments with this combination, the transition with time from severe to mild wear was more gradual, but in nearly all experiments where a transition occurred it was possible to obtain two distinct wear rates. The resulting graph of wear rate against load for this combination given in figure 9 indicates the range of loads (from A to B) between which the transition may occur. An experimental study of the factors influencing the transition from mild to severe wear is described in another paper (Hirst & Lancaster I956). A few combinations of materials gave a mixture of mild and severe wear over the full range of loads. Copper rubbing on Stellite was in this category; the wear rates were not reproducible and there was no simple relationship between the wear rate and the load.

Of the many combinations of materials examined only a few have a wear rate which is accurately proportional to the load, but examples have been found for



Wear of metals 405

both the mild and severe types of wear. 60/40 brass containing 2 0 of lead rubbing on hardened tool steel gave severe wear down to very low loads and the wear rates and the coefficient of friction were exceptionally reproducible. The slope of the graph of wear rate against load shown in figure 10 is 1O00 with a standard error of 0-015. The coefficient of friction had an average value of 0.24. Stellite grade 1 rubbing against high-speed tool steel exhibited mild wear over the full range of loads (50 g to 10 Kg). The results are also given in figure 10, and for this combination the slope of the line is 0-98 (standard error 0.015). Though the wear rate was reproducible,

10~~~~~~~~~ 6[.9

Q~~~~~~~~~~~~~~~~~~~~~

1-101 210 10 102 i03 104

load (g)

FIGURE 9. Graph of wear rate against load for 70/30 brass (annealed) pins rubbing on hardened tool steel rings. Speed 180 cm/s.

the coefficient of friction varied within the range 0 5 to 0 7. It will be observed that in severe wear where there is appreciable intermetallic contact the friction is not, excessively high nor is the friction very low in conditions of mild wear. This was found quite often, and as a further example the coefficient of friction for ferritic stainless steel against high-speed tool steel was observed to be from 0*48 to 0*58 in severe wear conditions and 0-65 to 0 75 during mild wear.

Though the wear rate is accurately proportional to load for only a few of the combinations examined, there are nevertheless many other examples for which the relation between wear rate and load shows only a small deviation from direct proportionality. The trend of the wear rate with load for a representative selection of material combinations is shown in figure 11.

3 2. The range of wear rates

Table 1 shows the wear rates of a range of materials (including some plastics) at a load of 400g. It will be observed that the range of wear rates is of the order 105-fold. The range of coefficients of friction for these materials was from 0 18 to 0'8, i.e. less than fivefold. The range of hardness of the materials (column 3 of the table) is from 17 to 1300 Kg/cm2.



406 J. F. Archard and W. Hirst -6

t 0 2,b aso| t 0~~~~~~1

h~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I lo f0-l'X

- -j brass__

A/ ~ ~ ~ ~ ~ 7 _9 _ _ _ _ -. v

10 102--- 3

to_ -2 10 o1 104

load (g) FIGURE I0 FIGURE 1I

FIGURE 10. Graphs of wear rate against load for brass and stellite pins rubbing on tool steel

rings. Speed 180 1m0s.

FIGFURE 11. G~raphs of wear rate against load for 'a representative selection of mnaterials. Speed 180 cm/s. (1) Mild steel on mild steel. (2) 60/40 brass on hardened tool steel. (3) Teflon on hardened tool steel. (4) Ferritic stainless steel on ferritic stainless steel. (5) 70/30 brass on hardened tool steel. (6) Hardened tool steel on hardened tool steel. (7) Ferritic stainless steel on hardened tool steel. (8) Stellite grade I on hardened tool steel. N.B. To avoid confusion, experimental points have been omitted. Each graph is based on 10 to 20 experimental points. Graphs 2, 5, 7 and 8 are shown elsewhere with their experimental points.

4. DISCUSSION

The experiments reported above have shown that it is relatively easy to obtain reproducible wear rates under unlubricated conditions and an estimated experimental error of a few units per cent has been obtained with many combinations of rubbing materials. This contrasts with experiments using a lubricant where results vary by as much as, or more than, 50 %/ and reproducible results are obtained only when special precautions are taken. Therefore, there is some justification in taking the experimental values of unlubricated wear rates as definite quantities and in attempting to provide a theoretical basis for their interpretation.

The second point which emerges is that, -once the equilibrium surface condition has been attained, the wear rate becomes independent of the apparent area of contact. It seems likely that this will prove. to be a general law of wear, for it has been found to be obeyed in several hundred experiments, which include a wide range



Wear of metals 407

of materials and a considerable range of speeds (2 to 660 cm/s) and loads (50 g to 1OKg). Exceptions to this law were observed when the surface conditions or the mechanism of wear were changing and during such periods the coefficient of friction altered also. Therefore this law appears to have the same general applicability as Amonton's corresponding law of friction. It is also important to note that the law holds for material combinations which have different wear mechanisms. Thus it holds in both mild and severe wear with their different scales of damage and for such varied combinations as those listed in table 1. The wear mechanisms for all those combinations have not been studied, but detailed investigations have been

TABLE 1. WEAR RATES OF PINS OF VARIOUS MATERTALS AT A LOAD OF 400g

(Speed 180 cm/s. Rings are hardened tool steel except where stated otherwise) wear rate hardness cale. value of K

combination of materials (10-10 cm3/cm) (106 g/cM2) (from (1)) mild steel on mild steel 1570 18.6 7 x 10-3 60/40 brass 240 9.5 6 x 10-4 Teflon 200 0 5 25 x 105 70/30 brass 100 6.8 1P7 x 10-4 Perspex 1465 2-0 7 x 10-6 moulded Bakelite x5073* 12*0 2-5 7-5 x 10-6 silver steel 7'5 32 6 x 10-5 beryllium copper 7-1 21 3'7 x 10-r hardened tool steel 6.0 85 1P3x 10-4

Stellite grade 1 3-2 69 5-5 x 10-5 ferritic stainless steel 2-7 25 1b7 x 10-5 laminated Bakelite 292/16* 1^8 3-3 1l5 x 10fi moulded Bakelite 11085/1* 1.0 3-0 7-5 x 10-7 sintered tungsten carbide on mild steel 09 18-6 4 x 10-6 laminated Bakelite 547/1* 0-4 2-9 3 x 10-7 polyethylene 0.3 0-17 1-3 x 10-7

sintered tungsten carbide on sintered 0 03 130 1 x 10-6 tungsten carbide

* The Bakelites quoted represent the best and worst laminated and moulded Bakelites of the range tested.

made of the wear of annealed tool steel on hardened tool steel (Kerridge I955), brass on hardened tool steel (Kerridge & Lancaster 1956), and hardened tool steel on hardened tool steel (Archard & Hirst I956). The mechanisms of wear for these combinations differ both in their scale of size and in the sequence of events leading to the production of a wear particle. However, in all these examples the wear rate is independent of the apparent area of contact and therefore this law does not seem to be restricted to any particular mechanism of wear.

The facts that the wear rate is reproducible and that it is independent of the apparent area of contact have the important consequence that the wear rate should be directly proportional to the load. Thus if n identical wear machines run simul- taneously the total wear rate is n times that produced in one. There is then n times the load and n times the apparent area of wearing surface. However, since the wear, rate is independent of the apparent area of contact, n times the load applied to the same area of contact should give n times the wear; i.e. the wear rate should be proportional to the load. Experiment shows, however, that this is not generally true,




and therefore the rule is not so widely applicable as the corresponding second law of friction.

A number of considerations help to explain this contrast between the general applicability of the rules of friction and wear. First, wear rates of material combinations range more widely than their coefficients of friction and thus it is to be expected that deviations from regular behaviour will be more noticeable for wear. Secondly, implicit in the statement of the second law of friction is the assumption that the surface conditions remain unchanged over the load range used. This proviso is even more vital when considering rules of wear because a major change in surface conditions such as a breakdown of a protective film changes the coefficient of friction at the most by a factor of 2 or 3, whereas the wear rate may change by one or two orders of magnitude. Therefore minor changes in surface conditions which produce no detectable change in friction may lead to a marked change in the wear rate. It should also be remembered that in most wear experiments, the surface conditions will depend on the load. In particular, at all but the slowest speeds of sliding, there will be an appreciable rise in surface temperature and the temperature of the rubbing surfaces will be load dependent.

This effect of temperature is probably one of the most important reasons why proportionality between wear rate and load is not generally observed. It is relevant to note that over a range of speeds from 10 to 200 cm/s Sata (I953) finds that the wear rate of cast iron depends on the load and the speed, but not in such a way as to indicate immediately any simple laws of wear. He shows, however, that when the wear rate is plotted against the load, the speed for each load being chosen to give the same surface temperature, then proportionality is observed.

The evidence therefore suggests that if the second rule of wear were to be for- mulated: 'With the same surface conditions, the wear rate is proportional to the load', it would be generally true and could be regarded as a law of wear. The most general expression for the wear then becomes

W = K1P8, (2)

where K1 is the wear per unit load per unit sliding distance. K1 may be described as the coefficient of wear and, in a series of experiments with the same combination of materials, changes in K1 denote changes in the surface conditions.

This is the only general expression for wear which can be deduced directly from experimental evidence. It has the limitation that it does not include a term related to material properties and to introduce one involves introducing assumptions requiring experimental verification. However, since experiment shows that the wear rate is independent of the apparent area of contact and since wear must be the result of localized damage of the rubbing members at the regions of true contact, it is natural to try to include the true area of contact in the expression for the wear. If it is postulated that the surface asperities deform plastically under the applied load, the true contact area (A) is given by A -P/pm, where pm is the flow pressure of the softer material. The wear is then proportional to the real area of contact and by re-writing equation (2) as W K(P/p.) s it will be seen that it reverts to the form given in equation (1).



Wear of metals 409

The results of table 1 show that values of K range more widely than values of Pm, and the explanation of the magnitude of K is therefore the most important problem in wear. All the experimental evidence about wear shows that wear occurs by the removal of lumps (that is, as distinct from the removal of individual atoms) and according to the theory of Archard (I953 b) the deduced values of K in table 1 mean that only one wear particle may be produced in the order of a million asperity encounters. In these circumstances, when two materials of comparable hardness rub together it is difficult to imagine how the surface asperities can continue to deform plastically. The first time they come together they may deform plastically but the relaxation would be elastic and thereafter the same load could be supported by elastic deformation. Dr Halliday of this laboratory has shown, using reflexion electron microscopy, that the surface asperities on carefully prepared specimens are, in fact, of such a shape as to support an appreciable load by elastic deformation (Halliday 1956). He has also shown (unpublished) that similar considerations apply to well run-in surfaces. If further work were to confirm this it would not be possible to assume that the true contact area could be expressed as Prpn nor could the expression W = K(P!prn) 8 be regarded as a general equation of wear.

In conclusion, to summarize, this survey shows that when equilibrium surface conditions are attained the wear rates of materials are independent of the apparent area of contact and suggests that the wear rate is proportional to the applied load unless a change in the load causes the surface conditions to change. These rules apply to both the mild and the severe forms of wear and have been observed for combinations of materials for which the wear mechanisms are known to be of different kinds. These rules are predicted by simple theories of wear, but the numerical application of these theories presents a paradox in that they are based on the assumption of plastic deformation of surface asperities, but yield values for the probability of surface damage which suggest that with some materials the asperities would, instead, deform elastically. Despite this apparent contradiction, it remains true that one of the most important problems in an understanding of wear is to explain the magnitude of the probability of the production of a wear particle at an asperity encounter. There is, at present, little experimental evidence to help do this and the most immediate need is for some detailed information about the mechanisms of wear and about how wear particles arise.

The authors are indebted to Mrs R. C. Jeffrey and Mr R. J. Tillen for their assist- ance with the experiments; they also thank Dr T. E. Allibone, F.R.S., Director of the Laboratory, for permission to publish this paper.

REFERENCES

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