Wear, 40 (1976) 23 - 35 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands

23

WEAR OF SOME F.C.C. METALS DURING UNLUBRICATED SLIDING PART III: A MECHANICAL ASPECT OF WEAR

N. SODA

The Institute of Physical and Chemical Research, Wak6, Saitama (Japan)

Y. KIhIURA aad A. TANAKA

Institute of Space and Aeronautical Science, The University of Tokyo, Tokyo (Japan)

(Received September 8, 1975; in final form December 1,1975)

Summary

The relations between the size of wear fragments and the sliding velocity or normal load were studied from a mechanical point of view for the unlubricated wear of nickel. It was found that the size of mean wear frag- ments has a definite quantitative correlation with the thickness of the plastically deformed substrate layer, irrespective of the experimental condi- tions. The thickness of the deformed layer is determined by the actual forces working on real contact points, which are dependent on the dynamic properties of the specific sliding system. These mechanical factors govern wear-velocity and wear-normal load characteristics.

1. Introduction

A change in the volume of wear fragments can be the critical factor which governs wear behaviour, though it does not appear explicitly in the adhesion theory.

The wear of nickel, copper and gold was determined with varying load, sliding velocity and atmospheric pressure [l] . The results were interpreted in terms of the volume and the formation rate of wear fragments [2]. It was found that the change in wear with sliding velocity or normal load was predo- minantly due to a change in the volume of individual fragments.

Few studies are available in which factors determining the volume of fragments are discussed. An important contribution was made by Rabinowicz, who proposed an energy criterion [ 31. The diameter of a loose wear fragment was shown to be essentially dependent on the ratio of the surface energy to the hardness of the surfaces. However, it was also shown that this law was not obeyed at moderate and high loads or velocities [4]. Some further explanation is required even though such an energy criterion is applicable.

24

Fig. 1. A micrograph of a vertical section of a worn Ni pin specimen (etched): sliding velocity 335 mm s-l, nominal load 0.26 kg, sliding distance 50 m, atmospheric pressure 760 Torr; sliding direction left to right.

As suggested previously [ 21, a mechanical approach is made in the present paper. With nickel, the volume of wear fragments, which was deter- mined earlier [ 21, is correlated with the thickness of the deformed layer in the substrate, and the thickness is compared with the stress field around the contact points.

2. Thickness of the deformed layer and size of a wear fragment

From the observation of vertical sections of worn pin specimens, a process of wear fragment removal was postulated [l] : friction causes plastic deformation or flow of the substrate.and cracks extend along the flow to lead eventually to the separation of a candidate wear fragment from the bulk material. If this is the case, some quantitative correlation may be expected between the dimensions of the deformed layer and the wear fragments. As a characteristic dimension, the thickness of the plastically deformed layer is compared with that of the mean wear fragments*.

Figure 1 shows an etched vertical section of a worn Ni pin specimen. Similar deformed layers may also be observed in disk specimens. Figure 2 shows an increase in the hardness of the substrate caused by sliding contact. The thickness of the hardened layer coincides fairly closely with that of the deformed layer determined from micrographs. The thickness of the deformed layer in a specimen increases slightly from the leading to the trail-

*A fragment can be approximated by a flattened ellipsoid [ 21 with the principal axes a, b and c. The ratio a:b:c is assumed to be 12:5:1, and the thickness c is calculated from the results given in Part II [ 21.

600

Depth (m-n)

0’15 I-T E

0 .lO .

ii c” .

P -E f 0.05

.

0

25

0 100 200 300

Stiding vetoaty Imm s-11

Fig. 2. Variation of hardness in the substrate: sliding velocity 168 mm s-l, nominal load 0.26 kg, sliding distance 50 m; q 5 x 10m2 Torr, n 760 Torr.

Fig. 3. The thickness of the deformed layer (m) and that of the mean fragments (0) us. sliding velocity: nominal load 0.26 kg, atmospheric pressure 760 Torr, sliding distance 50 m.

ing edge, and the value is determined as the average of several measurements in the sliding direction.

Figure 3 shows the effect of sliding velocity on the thickness of the deformed layer; the mean thickness of the wear fragments is also plotted. The thickness of the deformed layer increases with sliding velocity, in a similar manner to that of the wear fragments. When the normal load or the atmospheric pressure is varied, the correlation still holds.

The thickness of the deformed layer is replotted against the mean thickness of the wear fragments in Fig. 4. Although some scatter is observed, all points appear to fall on a straight line, irrespective of the wide variety of experimental conditions. This result indicates that a quantitative correlation exists between the thickness of the deformed layer and the thickness of the wear fragments, i.e. the size of the fragments. The ratio of the mean thickness of the wear fragments to that of the deformed layer is calculated to be about 0.25. This correlation means that one of the following three hypotheses must be valid : (a) the thickness of the deformed layer determines the size of the wear fragments; (b) the size of the fragments determines the thickness of the layer; or (c) some other factor simultaneously affects both. Hypothesis (b) is physically meaningless. The factor determining the thickness of the deformed layer, therefore, must govern the size of the wear fragments whether (a) or (c) is valid.

26

0 20

r E 015

& ”

1 0.10

$

8 3 0.05

E .Y f

0 0 C I 002 0.03 O.OL 0.05

Thickness of mean wear fragments (mm)

Normal force 0.26 kg

Fractbmal force

1 L Imml

Fig. 4. Correlation between the thickness of the deformed layer and that of the mean wear fragments: sliding distance 50 m; o pressure is varied, q velocity is varied in vacuum, m velocity is varied in air, A load is varied in vacuum, A load is varied in air.

Fig. 5. Shearing stress contours.

3. Shearing-stress field and the thickness of the deformed layer

Plastic deformation in the substrate is considered to be caused by the repetitive action of normal and frictional forces. Many types of micro- structural change take place in this layer: disolocations pile up, crystals are distorted, fragmentation of grains occurs. Macroscopically they are perceived as work-hardening. It is difficult to describe fully the plastically deformed layer, but the critical condition for deformation to occur may be predicted by the theory of elasticity.

It is well known that two surfaces do not touch over the whole apparent area of contact but only at some discrete contact points. This enables the stress field in the substrate to be calculated as that induced by a concentrated force on each contact point.

First, the number of real contact points is estimated by a statistical method developed by Kimura [ 51. Surface profiles of the specimens, along and perpendicular to the sliding direction, are analyzed. As the distributions of the heights around a reference plane and the slopes can be characterized as Gaussian, the expected number of contact points in a unit apparent area is given by a simple function of variances of the distributions; calculated results are listed in Table 1. Irrespective of the experimental conditions, the expected number is always less than unity. This implies that the apparent area of contact is too small to give a stationary contact condition with the expected separation between the two reference planes; the actual separation between them fluctuates, even under static loading, to form a single contact point. Apparently, this single contact point migrates over the apparent area of contact during sliding.

27

TABLE 1

Number of contact points

Sliding_;elocity Expected number of contact Expected number of

(mms ) points in a unit apparent area (X 1 0e2 mm- )

contact points in the apparent area

21 7.7 0.09 63 5.1 0.09

168 6.7 0.18 250 3.9 0.11 335 4.5 0.12

I I, I I I 0.02 0.04 0.06 0.08

Depth (mm)

Fig. 6. Maximum T,, le=~ in the substrate: normal load 0.26 kg, coefficient of friction 1.3.

The stress’field around a contact point is calculated as that produced in a semi-infinite body by a concentrated force on its boundary plane. It is obtained by superposing the stress field by a normal force [6] and by a tangential force [ 71.

Cylindrical coordinates are defined, where the cylinder axis z is taken in the direction of the normal load and 13 is measured from the sliding direc- tion (Fig. 5). Among six stress components, the shearing-stress component on a plane parallel to the surface in the direction of sliding is considered. Further, only rrz 10 = e in the quarter plane (z 2. 0 and 6 = 0) is calculated since the maximum of the absolute value of the shearing-stress component appears in this plane.

The stress component can be written as

7rz I0 = e = -(3P/2n)zr(z + pr) (z2 + r2)-5/2

in which P is the normal load and ~1 is the coefficient of friction.

(1)

28

capacit pickup

, disk

- pin

ante

\ arm

Fig. 7. Device to measure the vertical displacement of the pin specimen (seen through a peep-window).

At a low sliding velocity, where vertical oscillation of the pin specimen is not observed, the nominal load and the coefficient of friction [l] can be used as P and ~1 in eqn. (1). Contours for the shearing stress r,, I0 = e due to such static forces are shown in Fig. 5. The maximum stress a point at any depth undergoes when the contact point moves on the surface is plotted as a function of the depth (Fig. 6). In this condition the observed thickness of the deformed layer is about 0.027 mm, which coincides with the depth where the material undergoes its critical shearing stress for yielding (70 kg mme2).

4. Shearing-stress fields and the thickness of the deformed layer under inter- mittent sliding

As the sliding velocity was observed to have little effect on the coeffi- cient of friction, a change in the thickness of the deformed layer with sliding velocity is no longer interpreted in terms of the nominal forces. This suggests that it is necessary to take account of the effect of the vertical oscillation of the pin specimen against the surface of the disk specimen [2] ; such an oscillation must instantaneously produce a much greater force than the nominal force. This actual force is analyzed below.

29

4.1. Measurements of vertical oscillation Figure 7 shows the device used to measure the vertical displacement of

the pin specimen. A change of clearance between the pick-up and the arm on which the pin is mounted was detected as a change of capacitance and was recorded with an electromagnetic oscillograph (Fig. 8). The upper trace corresponds to the displacement of the pin and the lower trace shows the intermittent nature of the sliding [ 21.

4.2. Estimation of actual forces The sliding system is idealized in Fig. 9. Here m is the equivalent total

mass of the moving part which includes the pin, the collet and a part of the arm; k, is the reduced stiffness of the loading spring and k, is the surface stiffness at the contact point. If plastic crushing of asperities is considered, the load-displacement relation at the contact point becomes nonlinear. As shown in the Appendix, when the load-displacement curve is divided into two sections and approximated by a straight line in each section, an expression for the actual normal force P*(t) is developed from Suzuki’s linear solution [ 81 as

p*(t) = $ff$ (1 -A,, cos (w,,t + 0,)) 0 5 ts tI, t& t 8 1

(2)

for the smaller-displacement section, and

k&d P*(t) k, + k2

= - (1 -AI cos (qt + 6,)) -

- (’ - kl)kS’ (1 -A0 cos (wotl + 0,)) tI 5 t 5 h 12, +h

(2’)

F^“^^“““““““” cmtar. s 0 0.1 0.2

t-l-UVT zb LO 6b

Fig. 8. Electromagnetic oscillogram (redrawn). The upper trace shows the displacement of the pin and the lower trace the intermittent nature of the sliding contact as stated in Part II [ 21. The natural frequency of the instrument ia 400 Hz.

Fig. 9. Idealization of the sliding system.

30

for the larger-displacement section; tl or tz is the time at which the displace- ment at the cur&et point passes frcrm one section to the other, fn this

ks +- k2 Al = (a” + b2)lf2 -

and

where g is the reduced static deflection of the toading sprigs FV is the mean vertical impinging velocity at the onset of contact (t = O), and kl and kz ttre the approximate values of k, in each section, Since m, { and kS are directly measurable, P(t) can now be determined.

The normal force during each actual contact P(t) is characterized by a wsitive part of P*(t) and the successive nom&G load (Rg, 10), For the analysis of the thickness of the deformed layer, the average values of the m~~mum P, of SW& a normal force are considered as the normal fo%ee component. Figure 11 shows the dependence’of P, on sliding velocity; Pm in- creases ~ot~&e~ly with velocity*.

Another force component a&mg on a cm&a& point is the ~~~t~on~ force. The nominal coefficient of friction under experimental conditions has been defined f13 as the ratio of the mew optional force over the high friction stage to the nominal load, and its dependence on experimental variables has been shown. hen the detailed behatiour of the normal force is now revealed, it seems necessary to make some modification. The actual coefficient of friction pS is defined by

*Even under these actual lo&ibs, the expect& men-n&r of real contact points is less than unity; the assumption of single contact still holds.

P*lt)

nominal load I

-0 loo 200 300

Sliding velocity (mm se’)

Fig. 10. Change of the normal force during each actual contact.

Fig. 11. Actual load us. sliding velocity: nominal load 0.26 kg.

where F is the mean frictional force and T is the corresponding sliding dura- tion; this value becomes a little larger than the nominal one [l] . The tangential force component is given by the product of c(a and P,.

4.3. Shearing-stress fields and the thickness of the deformed layer The averaged maximum force components P, and PJ’~ are obtained

and are used to calculate the shearing-stress field around a contact point at higher sliding velocities where vertical oscillation is present. By following the earlier procedure, the relation between sliding velocity and the maximum stress that a point at any depth undergoes is obtained (Fig. 12); earlier results are included. The observed thickness of the deformed layer (Fig. 3) is again shown by a continuous line.

When the sliding velocity is changed, the thickness of the deformed layer and the depth at which the material is subjected to a certain level of the maximum stress vary in a similar manner. The solid curve lies very close to the points representing the critical shear stress of the material, i.e. 70 kg mm-‘. A similar analysis is made for the case where the nominal load is varied (Fig. 13); the agreement is again satisfactory.

These results suggest that the stress distribution induced by real contacts determines the thickness of the deformed layer and the size of the wear fragments. This conclusion is supported in part by the fact that the thicknesses of the deformed layer and of the wear fragments remain constant during an experiment.

32

0.20 0.20

0.15 0.15

E E F

z O’O E 0.10

8 L x

0”

0 05 005

0 0 0 100 200 300 0 0.3 06 09 1.2

Sliding velocity (mm se11 Nomrnl load (kg)

Fig. 12. Relation between the sliding velocity and the depth at which the material is subjected to a certain maximum stress level: nominal load 0.26 kg; q -50 kg mmm2, o -70 kg mmM2, A -90 kg mmT2. The continuous line shows the observed thickness of the deformed layer.

Fig. 13. Relation between the nominal load and the depth at which the material is _2 subjected to a certain maximum stress level: sliding velocity 168 mm s-l ; q -50 kg mm o -70 kg mmm2, A -90 kg mme2. The continuous line shows the observed thickness of thi deformed layer.

5. Discussion

Unlubricated wear of metals changes markedly with experimental varia- bles. The change of wear with sliding velocity or normal load was found to be predominantly due to a change in the size of the individual wear fragments, which was affected by some mechanical factors [2]. However, it was not made clear which factors governed the size of fragments.

In the present paper, the correlation between the size of the wear fragments and the thickness of the deformed layer in the substrate is clarifi- ed. The size of the wear fragments is distributed over a wide range under a single condition. When the thickness of the wear fragments of the mean volume is considered, it measures about one-fourth of that of the corresponding deformed layer irrespective of the experimental conditions. The existence of this definite quantitative correlation suggests that the mechanisms of wear fragment formation should be discussed in relation to a change in or accumulation of damage in the substrate. This has received little attention.

The thickness of the deformed layer was analyzed from a mechanical point of view. Plastic flow takes place when a condition of yielding is satisfied in the material. Actual forces on a real contact point, which are affected by vertical oscillation at higher velocities, were taken into account and the shear- ing-stress fields were determined around the contact point. When the shear-

33

ing stress obtained is compared with the critical value of the material, the dependence of the thickness of the deformed layer on the sliding velocity and the nominal load can be interpreted reasonably. This result confirms that the thickness of the deformed layer and therefore that of the wearfrag- ments is governed by the actual forces on real contact points. These actual forces determine the wear behaviour when the sliding velocity or the nominal load is varied since the rate of fragment formation changes little with these variables. Cracks must extend over longer distances to form larger fragments, and their propagation rate must be higher for larger fragments to maintain constant formation rates. Though the details are not revealed, this effect may be compensated by increased actual forces.

Experimental results by Rabinowicz and Foster [4] on the effects of velocity or load on the size of wear fragments may be explained similarly. However, the apparent relation between sliding velocity or normal load and the size of the fragments may depend on the dynamic properties of specific sliding systems. The effects of vertical oscillation predominated in the expe- riments; this is common to unlubricated sliding. When liquid lubricants were used, the so-called partial hydrodynamic lubricating effect made the actual forces smaller and the deformed layer. thinner at higher velocities [ 91.

That the shearing-stress component 7rt I0 = ,-, is used as a criterion of plastic flow warrants comment. As an alternative, the distribution of maximum shearing stress was calculated for a few cases and compared with the results shown in Fig. 5. It was found that they show analogous distribu- tions and similar dependences on experimental variables, though the maxi- mum shearing stress is a little larger in every case. Hence 7rZ I0 = ,, is conveniently used in the discussion of the thickness of the deformed layer.

The suggested process of wear fragment formation [l] is made somewhat clearer in its quantitative aspect by the present findings. However, a qualitative description of phenomena occurring in the deformed layer, which eventually result in detachment of the fragments, is still required. Observations of microstructural changes would furnish useful information. For example, Suh [lo] proposed a process in which dislocations, piled up at a finite depth, lead to the formation of voids or cracks. He discussed the depth at which cracks or other faults initiate in relation to the surface energy and the drag stress on dislocations. Combined with such investigations, the present analysis is expected to contribute to a more accurate assessment of the wear process.

6. Conclusion

A close quantitative correlation exists between the mean size of the wear fragments and the thickness of the plastically deformed substrate layer. The mean thickness of wear fragments is about one-fourth of that of the deformed layer in all cases examined. Moreover, it was shown that the

34

thickness of the deformed layer may be predicted from a simplified analysis of the stress field around contact points, where the dynamics of the sliding system are taken into consideration.

Adetailed picture of the suggested process of wear fragment formation [l] is now available. As a result of the repetitive action of normal and frictional forces, plastic flow of the material occurs in the substrate; the thickness of the deformed layer is determined by the actual magnitude of the forces. Cracks extend to a depth propo~ional to the thickness of the deformed layer to liberate wear fragments eventually.

The mechanical factor suggested earlier [ 1, 2) to govern the size of wear fragments and wear behaviour is shown to be the actual force acting at real contact points. Its value is influenced not only by the nominal load and the coefficient of friction, but also by the dynamic properties of the specific sliding system.

Acknowledgments

The authors thank Professor S. Ohno for his considerable assistance in the analysis of the oscillation.

References

1 N. Soda, Y. Kimura and A. Tanaka, Wear, 33 (1975) 1. 2 N. Soda, Y. Kimura and A, Tanaka, Wear, 35 (1975) 331. 3 E. Rabinowicz, J. Appl. Phys., 32 (1961) 1440. 4 E. Rabinowicz and R. G. Foster, Trans. ASME, D86 (1964) 306. 5 Y. Kimura, Wear, 15 (1970) 47. 6 S. Timoshenko and J. N. Goodier, Theory of Elasticity, 2nd edn., McGraw-Hill,

New York, 1951, p. 362. 7 R. Muki, Trans. Jpn. Sot. Mech. Eng., 22 (1956) 466. 8 T. Suzuki, Sci. Rep. Res. Inst. Tohoku Univ., 4 (1952) 313. 9 Y. Kimura and K. Yamaguchi, Prepr. Jpn. Sot. Lubr. Eng. Meeting, Hamamatsu,

Japan, February, 1974, JSLE, Tokyo, p. 49. 10 N. P. Suh, Wear, 25 (1973) 111.

Appendix

Surface stiffness at a contact point The surface stiffness at a contact point is estimated on the basis of the

following idealization. The contact of two rough surfaces can be substituted by the contact

between a perfectly smooth surface and a surface with combined roughness. A contact point is assumed to be formed between a plastic quadrangular pyramid and an elastic smooth surface (Fig. Al). The apex angles CQ and a2 of the pyramid are approximated by the use of slopes along and

35

Displacement z 4

Fig. Al. Idealization of the contact point.

Fig. A2. Normal load us. displacement.

perpendicular to the sliding direction, respectively, which are the average values obtained for individual specimens.

The amount of crush z1 of the pyramid is given by the equilibrium bet- ween a normal load Q and the product of the yield pressure p and the project- ed area AA of the crushed pyramid (AA = 4 tan e1 tan c& ) :

( Q )

112 2, =

4ptan 01~ tan e2 (Al)

For the estimation of the elastic displacement z, of the smooth surface it is further assumed that the load Q is uniformly distributed over a circular area AA on the boundary of a semi-infinite solid. Then,

1 -v2 Q 22 =

fiE (tan 0~~ tan CX~)~‘~Z~ (W

where E is Young’s modulus and v is Poisson’s ratio of the solid. From eqns. (Al) and (A2), the load-displacement relation at the con-

tact point is expressed as

I 4p (1 -us)

t

-2

Q=4ptanarl tana l+ fiE

(tan (Yl tan C#s z2

where z = zl + zs is the total displacement. Further, this quadratic relation is conveniently approximated by two

straight lines with slopes kl and k2 (Fig A2); suitable values for the critical displacement z* are chosen for particular cases. The values of kl and k2 are used in eqn. (2). Since plastic crushing is considered, this displacement has an irreversible part. However it does not cause serious error in the estima- tion of P, or p,.