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Frictional deformation of cobalt single crystals by high angle diamond indenters
Wear, 38 (1976) 361 - 370 0 Elsevier Sequoia S.A., Lausanne -Printed
361 in the Netherlands
FRICTIONAL DEFORMATION OF COBALT SINGLE CRYSTALS BY HIGH ANGLE DIAMOND INDENTERS
R. D. ARNELL Department of Mechanical Engineering, (G t. Britain) (Received
November
University of Salford, Salford M54WT
25, 1975)
summary The tribological properties of cobalt single crystals sliding against high angle pyramidal diamond indenters have been investigated. It has been found that the friction coefficient depends only on the indenter geometry and the coefficient of sliding friction at the cobalt-diamond interface; it does not vary either with the orientation of the crystal surface or the sliding direction. The width of the wear track formed is orientation dependent. However the actual form of the orientation dependence is not simply a property of the material but depends also on the shape of the indenter.
1. Introduction Tribological studies of metals have shown that there is a group of metals with hexagonal close-packed (h.c.p.) crystal structures which are intrinsically different in tribological behaviour from metals with other crystal structures. In particular, h.c.p. metals which deform almost exclusively by basal plane slip still exhibit relatively low friction adhesion and wear even when the contacting surfaces are perfectly clean, whereas under such conditions face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) metals and h.c.p. metals with multiple slip planes exhibit very high friction coefficients and, often, complete seizure. This advantage of h.c.p. metals is clearly not only relevant to behaviour in UHV but also to any rubbing situation where metal to metal contact is likely to occur. These materials are therefore potentially very useful for conditions of unlubricated sliding or boundary lubrication. This has been borne out in experiments by Rabinowicz [l] in which he showed that cobalt and rhenium had excellent friction and wear properties under normal laboratory conditions. As tribological properties vary with crystallographic orientation it should be possible, by preparing specimens with appropriate preferred
362 LEAF
SPRINGS
0.25mm
THICK
OF MOVEMENT
Fig. 1. Intermediate specimen stage for the microhardness tester.
orientations, to optimise these already favourable properties. A programme of work has therefore been carried out on the effects of crystal orientation on the tribological properties of cobalt when rubbed ag&nst indenters of different geometries. The present paper describes the results obtained with high angle pyramidal diamond indenters.
2. Experimental details The experiments were carried out on a Leitz microhardness tester with an intermediate stage mounted on the standard specimen stage. This intermediate stage is shown in Fig. 1 and was operated in the following way. A single-crystal slice was mounted in Piecin wax on a mild-steel plate which was located on the rotating table by dowels; the rotating table was clamped in the desired orientation to an accuracy of + 0.5”. An indenter was lowered onto the specimen surface and the specimen was traversed beneath the indenter by a 1 rev min- ’ motor attached to the appropriate micrometer of the standard specimen stage. This gave a sliding speed of 0.5 mm min- ‘. The frictional force between the crystal and the indenter caused a small deflection of the part of the stage mounted on the two leaf springs. This deflection was measured by the ,displacement transducer (a linear variable differential transformer) and displayed on a UV recorder. The sensitivity of this apparatus was adjustable both mechanically and electrically. For the present work the apparatus was set up to measure forces of 1 - 60 gf (10 600 mN) to an accuracy of 0.5 gf (5 mN) without adjustment. Friction tracks were made over distances of 100 - 300 pm, the friction force being measured continuously during each run. At the end of each run the track width was measured using the standard graticule eyepiece of the microhardness tester. Friction and track width were recorded on each crystal at intervals of 10” from a principal crystallographic direction. Three indenter geometries were used: (1) a Vickers diamond with a base diagonal parallel to the sliding direction;
363 TABLE
I
Indenter geometry
Coefficient of friction
Vickers diamond Knoop diamond sliding parallel to long diagonal Knoop diamond sliding parallel to short diagonal
0.37
?: 0.01
0.145 ?: 0.01 0.56
r 0.01
(2) a Knoop diamond with the long base diagonal parallel to the sliding direction; (3) a Knoop diamond with the short base diagonal parallel to the sliding direction. The standard loads used were 50 g (- 500 mN) on the Vickers diamond and on the Knoop diamond traversed parallel to the short diagonal, and 200 g (“2 N) on the Knoop diamond when traversed parallel to the long diagonal. These loads were chosen to give track widths of approximately 25 pm. In addition, for chosen orientations on each crystal, friction and track width were recorded as functions of the applied load.
3. Results 3.1. Friction The friction coefficients were found to be independent of surface orientation, sliding direction and load. Each indenter geometry exhibited a virtually constant friction coefficient as shown in Table 1. The slight variations in friction coefficient were not related in any systematic way to the orientation and for reasons which will emerge later are thought to be due to variations in slope on the specimen surface. 3.2. Track widths The width of the track formed by the Vickers diamond was found to be strongly direction dependent for sliding on the (lOiO), (1120) and (1122) planes, as shown in Fig. 2. There was little variation of track width on the (0001) plane. The width of the track formed by the Knoop diamond sliding parallel to the long diagonal was found to be direction dependent on all four planes, as shown in Fig. 3. The track widths for both these indenters were found to have a non-linear load dependence. The actual form of this load dependence is discussed later. It was not possible to get meaningful measurements of track width when sliding the Knoop indenter parallel to the short diagonal as the tracks were very shallow and extremely sensitive to small surface irregularities. One interesting observation on these tracks was that they became narrower during the initial part of the run and only became parallel after distances of
364
20
t
Ii231
c33r
I
[oooi]
I
[lioo]
Fig. 2. Variation of track width with sliding direction load.
I [0001] for the Vickers diamond;
50 g
approximately 100 pm. The final width of the track was typically a factor of two less than the corresponding width of the static indentation.
4. Discussion of results 4.1. Friction coefficients It has been shown that the friction coefficients for the indenters used in these experiments are virtually independent of load and specimen orientation, and have the constant values shown in Table 1. The friction coefficients are therefore not influenced by the high degree of anisotropy of the cobalt specimens. Each of the observed friction coefficients p can be taken to be the sum of a deformation or ploughing term ,.$, due to the force required to displace material ahead of the slider, and an adhesion term PA, due to the force required to shear the bonds at the diamond-metal interface. &, is given by the ratio of the projected areas of the indenter perpendicular to the sliding force and the normal force. For a pyramid with a base diagonal parallel to the sliding direction this gives a value for & of cot 0, where 0 is the angle between the leading edge of the pyramid and the vertical. Previous workers [ 21 have given the value of tin as (p’,/p,) cot 0 where p”,,, and p,,, were taken to be flow pressures perpendicular to the friction force and the normal force, respectively. In fact the frictional and normal forces are supported by the horizontal and vertical components of the same reaction at the interface
365
7
poioj
I
E1ZO-J
I
[orio’l
I If 2JOl
I IhO
I ml
Fig. 3. Variation of track width with sliding direction parallel to its long diagonal; 200 g load.
&Lj
for the Knoop diamond
traversed
and for the constant geometry of a diamond indenter these will always be in the ratio cot 8, regardless of hardness variations. In a situation where the geometry changes, e.g. with spherical indenters, variations in hardness must be taken into account (see, for example, ref. 3). This concept will be developed in a forthcoming paper. The values of y, Ho and by subtraction pA for the three sliding geometries are given in Table 2. It can be seen that within experimental error the VdUeS of PA for the three different geometries are all approximately 0.09, which is a reasonable value for the coefficient of sliding friction of diamond on metal. The spread in the measured values of p and hence the calculated values of C(Acould be accounted for by slight variations of slope on the metal surfaces, which would change the effective values of cot 0. This observed constancy of &, for the different indenters is in contrast to the theories of Goddard and Wilman [2] which predict a marked variation of p(Awith pyramid geometry. Recent experiments by Childs 141, in which he slid diamond cones over annealed silver flats under high adhesion conditions, have shown a similar trend. In this case the observed friction coeffi-
366 TABLE Indenter
2 geometry
Vickers diamond Knoop diamond sliding parallel to long diagonal Knoop diamond sliding parallel to short diagonal
P
PD
PA
-
0.37
c 0.01
0.27
0.10
f 0.01
0.145
f 0.01
0.065
0.08
? 0.01
0.56
+ 0.01
0.47
0.09
f 0.01
cients for a series of cones of different semi-angles were all approximately equal to the calculated deformation term plus approximately 0.5. Again, 0.5 is a reasonable value for the coefficient of sliding friction between diamond and an outgassed metal surface. 4.2. Orientation dependence of track width It has been shown in the previous section that for any applied load the total friction force under a particular indenter is constant and is determined by the indenter geometry and a constant coefficient of adhesive friction PA. The applied forces for a particular geometry have therefore to be balanced by a constant reaction at the interface. However, as microhardness measurements have shown very clearly [ 51, the yield stress of the material beneath the indenter varies with orientation. The area over which this stress acts will have to vary accordingly and the groove width anisotropy will therefore be related to the hardness anisotropy of the material. This is shown very clearly in Fig. 4 which relates track width and the reciprocal of (KDH)‘j2 (taken from ref. 5) for the Knoop diamond traversed parallel to the long diagonal. The arguments outlined above should apply equally well to other shapes of indenter. However it is not easy to correlate the track widths under the Vickers indenter with hardness anisotropy, owing to the high symmetry
Fig. 4. Relation between the track width and the Knoop parallel to its long diagonal; 200 g load.
hardness
for the Knoop
diamond
367
0
Fig. 5. Relation indenters.
between
(loi2) hIlo]
0
(0001) bliol
x
(,oio) Ii123
A
(IIIO)
[OOOj
A
(tljo)
Eo13]
m
(Ii52)
[eo”
mobt
ili3]
the normal load and the track width for Vickers and Knoop
*. 6oo
!
500
-
I
3i J *
400.
z x
300
*
I ?
200
-
1
100
.
Fig. 6. Variation of effective Vickers diamond.
hardness with width for different
orientations
of the
of the Vickers indenter and also perhaps to the marked topographical changes which occur near Vickers indentations. 4.3. Load dependence of track width It has already been stated that for all orientations there is a non-linear relation between load and track width and therefore, as friction force/load i!
368
,400
Fig. 7. Variation of microhardness of a Vickers diamond track.
constant, between the total applied force and the track width. By analogy with static tests this relation would be expected to be of the form L = kHw2
(1)
where L is the load, His the hardness, w the track width and kw2 the area of the interface. Graphs of log,, L uersus log,, w are plotted in Fig. 5 for several orientations and it can be seen that the actual relationship for both indenter geometries is of the form L = k1 w-
513
(2)
where kl is a different constant for each orientation. Equations (1) and (2) can only be compatible if the hardness H is proportional to w-‘j3, i.e. if the hardness of the material beneath the slider increases with decreasing track width. This is clearly shown in Fig. 6 in which there is a plot of effective hardness, i.e. 4L/w2, against w for several orientations. It should be noted that the effective hardness at very small track widths is several times greater than the static hardness calculated from the appropriate single diagonal of a static indentation and that the hardness tends asymptotically to the static value as the track width is increased. It is clear that the relation in eqn. (2) implies a breakdown in the principle of geometrical similarity during sliding experiments This is thought to be due to the higher strain immediately ahead of the leading edge of the diamond and the consequent higher hardening. To illustrate this, microhardness measurements under a 5 g load have been made at various positions ahead of some of the wider tracks. One example is shown in Fig. 7 and it can be seen that the hardness of the material immediately ahead of the cutting edge is considerably increased. No such effect is observed when similar measurements are made around static indentations. The dependence of effective hardness on track width as shown in Fig. 6 is quantitatively very similar to that found by Cane and Skinner [3] for
369
smaller paraboloidal indenters, The scale of the effect, however, is very much larger as the hardnesses found by Gane and Skinner were virtually constant for track widths greater than approximately 2 m. It is therefore thought to be very unlikely that the explanation invoked by Gane and Skinner, i.e. the difficulty of operating dislocation sources in very small volumes, can be applied to the present work. Hardening of material ahead of the slider accounts at least in part for the observation that the track width beneath the Knoop indenter traversed parallel to the short diagonal actually decreases over a considerable distance. Microhardness measurements of the material ahead of such tracks show high hardening over most of the track width, presumably because of the high strains which are needed to displace material from the path of the relatively blunt indenter. An alternative explanation of this effect is suggested by the work of Johnson et al. [6] who have shown that, during sliding, blunt wedges tend to form prows of material and rise to the level of the original surface. This effect is simply the most favourable way of accommodating the material movements which are necessary for sliding and does not require the material to become work hardened. It may be that the effect noted here is due to a combination of both these factors. 4.4. Comparison with previous work The work reported here shows that the friction coefficients between cobalt and various diamond pyramids are independent of crystallographic orientation. As cobalt is very anisotropic it would be surprising if similar results were not obtained on more isotropic materials. However Bailey and Gwathmey [ 71 and Flom [ 81 have described observed frictional anisotropy on single crystals of f.c.c. metals using diamond indenters and these results seem to be at variance with those found in the present work on cobalt. Bailey and Gwathmey, who used a three-sided pyramid, suggested that their observed anisotropies could be accounted for by changes in surface topography, but Flom pointed out that the anisotropies which he observed using a Vickers indenter on copper and aluminium were the opposite of those predicted from changes in surface topography. Flom therefore speculated that the effects could be due to surface films. In the present work marked variations in surface topography have been observed but these have had no effect on the frictional force. Furthermore, the theoretical explanation for the magnitude of P, which has been described earlier, should be valid for materials of all crystal structures. This has been supported by measuring I-(for a Vickers diamond sliding on polycrystalline specimens of hardened steel, zinc and brass, which all had y values in the range 0.36 and 0.38, and on a glass microscope slide which had a value of 0.33. The slight variations in the P values can be accounted for by slight differences in the values of PA. In an attempt to resolve the differences between the present work and that of previous workers some sliding experiments were therefore carried out on aluminium single crystals. It was again found that the P values were independent of orientation and were in the range 0.36 to 0.38.
370
It is suggested that the real differences between these results and those of other workers can be accounted for by differences in experimental technique. In the present work the indenters were loaded by dead-weight loading and the diamond was restrained to prevent it tilting, i.e. 0 was constant. In the experiments of Bailey and Gwathmey one specimen was mounted on leaf springs and both load and friction force were measured by the deflection of these springs. It is inevitable with this arrangement that the angle 0 between the indenter and the specimen will vary as other conditions are varied and, if the theory presented here is correct, this will lead to a change in friction force. This would be particularly noticeable in the experiments of Bailey and Gwathmey who used a right-ogled three-sided pyramid, that would give large changes in &, for relatively small changes in 0.
5. Conclusions The coefficient of friction between a cobalt single crystal and a high angle diamond indenter depends only on the geometry of the indenter and the coefficient of sliding friction at the cobalt/diamond interface. The friction coefficient is not significantly affected by the anisotropy of the material; this anisotropy is reflected in changes of track width with orientation. It should be noted, however, that the form of the orien~tion dependence of the track width is not a fund~ent~ property of the material but is also dependent on the geometry of the indenter.
Acknowledgments The author is indebted to Professor J. Halling, Professor D. Tabor and Dr. T. H. Childs for helpful discussion of this work. Financial support was provided by the Science Research Council and a cobalt single crystal was provided by the Cobalt Information Centre.
References 1 ‘2 3 4 5 6 7 8
E. Rabinowicz, Wear, 10 (1967) 313. J. Goddard and H. Wilman, Wear, 5 (1962) 114. N. Gane and J. Skinner, Wear, 24 (1973) 207. T. H. C. Childs, Int. J. Mech. Sci., 12 (1970) 393. R. D. Arnell, J. Phys. D, 7 (1974) 1225. K. L. Johnson, personal communication. J. M. Bailey and A. T. Gwathmey, ASLE Trans., 5 (1962) R. Flom, ASLE Trans., 5 (1962) 55.
45.
361 in the Netherlands
FRICTIONAL DEFORMATION OF COBALT SINGLE CRYSTALS BY HIGH ANGLE DIAMOND INDENTERS
R. D. ARNELL Department of Mechanical Engineering, (G t. Britain) (Received
November
University of Salford, Salford M54WT
25, 1975)
summary The tribological properties of cobalt single crystals sliding against high angle pyramidal diamond indenters have been investigated. It has been found that the friction coefficient depends only on the indenter geometry and the coefficient of sliding friction at the cobalt-diamond interface; it does not vary either with the orientation of the crystal surface or the sliding direction. The width of the wear track formed is orientation dependent. However the actual form of the orientation dependence is not simply a property of the material but depends also on the shape of the indenter.
1. Introduction Tribological studies of metals have shown that there is a group of metals with hexagonal close-packed (h.c.p.) crystal structures which are intrinsically different in tribological behaviour from metals with other crystal structures. In particular, h.c.p. metals which deform almost exclusively by basal plane slip still exhibit relatively low friction adhesion and wear even when the contacting surfaces are perfectly clean, whereas under such conditions face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) metals and h.c.p. metals with multiple slip planes exhibit very high friction coefficients and, often, complete seizure. This advantage of h.c.p. metals is clearly not only relevant to behaviour in UHV but also to any rubbing situation where metal to metal contact is likely to occur. These materials are therefore potentially very useful for conditions of unlubricated sliding or boundary lubrication. This has been borne out in experiments by Rabinowicz [l] in which he showed that cobalt and rhenium had excellent friction and wear properties under normal laboratory conditions. As tribological properties vary with crystallographic orientation it should be possible, by preparing specimens with appropriate preferred
362 LEAF
SPRINGS
0.25mm
THICK
OF MOVEMENT
Fig. 1. Intermediate specimen stage for the microhardness tester.
orientations, to optimise these already favourable properties. A programme of work has therefore been carried out on the effects of crystal orientation on the tribological properties of cobalt when rubbed ag&nst indenters of different geometries. The present paper describes the results obtained with high angle pyramidal diamond indenters.
2. Experimental details The experiments were carried out on a Leitz microhardness tester with an intermediate stage mounted on the standard specimen stage. This intermediate stage is shown in Fig. 1 and was operated in the following way. A single-crystal slice was mounted in Piecin wax on a mild-steel plate which was located on the rotating table by dowels; the rotating table was clamped in the desired orientation to an accuracy of + 0.5”. An indenter was lowered onto the specimen surface and the specimen was traversed beneath the indenter by a 1 rev min- ’ motor attached to the appropriate micrometer of the standard specimen stage. This gave a sliding speed of 0.5 mm min- ‘. The frictional force between the crystal and the indenter caused a small deflection of the part of the stage mounted on the two leaf springs. This deflection was measured by the ,displacement transducer (a linear variable differential transformer) and displayed on a UV recorder. The sensitivity of this apparatus was adjustable both mechanically and electrically. For the present work the apparatus was set up to measure forces of 1 - 60 gf (10 600 mN) to an accuracy of 0.5 gf (5 mN) without adjustment. Friction tracks were made over distances of 100 - 300 pm, the friction force being measured continuously during each run. At the end of each run the track width was measured using the standard graticule eyepiece of the microhardness tester. Friction and track width were recorded on each crystal at intervals of 10” from a principal crystallographic direction. Three indenter geometries were used: (1) a Vickers diamond with a base diagonal parallel to the sliding direction;
363 TABLE
I
Indenter geometry
Coefficient of friction
Vickers diamond Knoop diamond sliding parallel to long diagonal Knoop diamond sliding parallel to short diagonal
0.37
?: 0.01
0.145 ?: 0.01 0.56
r 0.01
(2) a Knoop diamond with the long base diagonal parallel to the sliding direction; (3) a Knoop diamond with the short base diagonal parallel to the sliding direction. The standard loads used were 50 g (- 500 mN) on the Vickers diamond and on the Knoop diamond traversed parallel to the short diagonal, and 200 g (“2 N) on the Knoop diamond when traversed parallel to the long diagonal. These loads were chosen to give track widths of approximately 25 pm. In addition, for chosen orientations on each crystal, friction and track width were recorded as functions of the applied load.
3. Results 3.1. Friction The friction coefficients were found to be independent of surface orientation, sliding direction and load. Each indenter geometry exhibited a virtually constant friction coefficient as shown in Table 1. The slight variations in friction coefficient were not related in any systematic way to the orientation and for reasons which will emerge later are thought to be due to variations in slope on the specimen surface. 3.2. Track widths The width of the track formed by the Vickers diamond was found to be strongly direction dependent for sliding on the (lOiO), (1120) and (1122) planes, as shown in Fig. 2. There was little variation of track width on the (0001) plane. The width of the track formed by the Knoop diamond sliding parallel to the long diagonal was found to be direction dependent on all four planes, as shown in Fig. 3. The track widths for both these indenters were found to have a non-linear load dependence. The actual form of this load dependence is discussed later. It was not possible to get meaningful measurements of track width when sliding the Knoop indenter parallel to the short diagonal as the tracks were very shallow and extremely sensitive to small surface irregularities. One interesting observation on these tracks was that they became narrower during the initial part of the run and only became parallel after distances of
364
20
t
Ii231
c33r
I
[oooi]
I
[lioo]
Fig. 2. Variation of track width with sliding direction load.
I [0001] for the Vickers diamond;
50 g
approximately 100 pm. The final width of the track was typically a factor of two less than the corresponding width of the static indentation.
4. Discussion of results 4.1. Friction coefficients It has been shown that the friction coefficients for the indenters used in these experiments are virtually independent of load and specimen orientation, and have the constant values shown in Table 1. The friction coefficients are therefore not influenced by the high degree of anisotropy of the cobalt specimens. Each of the observed friction coefficients p can be taken to be the sum of a deformation or ploughing term ,.$, due to the force required to displace material ahead of the slider, and an adhesion term PA, due to the force required to shear the bonds at the diamond-metal interface. &, is given by the ratio of the projected areas of the indenter perpendicular to the sliding force and the normal force. For a pyramid with a base diagonal parallel to the sliding direction this gives a value for & of cot 0, where 0 is the angle between the leading edge of the pyramid and the vertical. Previous workers [ 21 have given the value of tin as (p’,/p,) cot 0 where p”,,, and p,,, were taken to be flow pressures perpendicular to the friction force and the normal force, respectively. In fact the frictional and normal forces are supported by the horizontal and vertical components of the same reaction at the interface
365
7
poioj
I
E1ZO-J
I
[orio’l
I If 2JOl
I IhO
I ml
Fig. 3. Variation of track width with sliding direction parallel to its long diagonal; 200 g load.
&Lj
for the Knoop diamond
traversed
and for the constant geometry of a diamond indenter these will always be in the ratio cot 8, regardless of hardness variations. In a situation where the geometry changes, e.g. with spherical indenters, variations in hardness must be taken into account (see, for example, ref. 3). This concept will be developed in a forthcoming paper. The values of y, Ho and by subtraction pA for the three sliding geometries are given in Table 2. It can be seen that within experimental error the VdUeS of PA for the three different geometries are all approximately 0.09, which is a reasonable value for the coefficient of sliding friction of diamond on metal. The spread in the measured values of p and hence the calculated values of C(Acould be accounted for by slight variations of slope on the metal surfaces, which would change the effective values of cot 0. This observed constancy of &, for the different indenters is in contrast to the theories of Goddard and Wilman [2] which predict a marked variation of p(Awith pyramid geometry. Recent experiments by Childs 141, in which he slid diamond cones over annealed silver flats under high adhesion conditions, have shown a similar trend. In this case the observed friction coeffi-
366 TABLE Indenter
2 geometry
Vickers diamond Knoop diamond sliding parallel to long diagonal Knoop diamond sliding parallel to short diagonal
P
PD
PA
-
0.37
c 0.01
0.27
0.10
f 0.01
0.145
f 0.01
0.065
0.08
? 0.01
0.56
+ 0.01
0.47
0.09
f 0.01
cients for a series of cones of different semi-angles were all approximately equal to the calculated deformation term plus approximately 0.5. Again, 0.5 is a reasonable value for the coefficient of sliding friction between diamond and an outgassed metal surface. 4.2. Orientation dependence of track width It has been shown in the previous section that for any applied load the total friction force under a particular indenter is constant and is determined by the indenter geometry and a constant coefficient of adhesive friction PA. The applied forces for a particular geometry have therefore to be balanced by a constant reaction at the interface. However, as microhardness measurements have shown very clearly [ 51, the yield stress of the material beneath the indenter varies with orientation. The area over which this stress acts will have to vary accordingly and the groove width anisotropy will therefore be related to the hardness anisotropy of the material. This is shown very clearly in Fig. 4 which relates track width and the reciprocal of (KDH)‘j2 (taken from ref. 5) for the Knoop diamond traversed parallel to the long diagonal. The arguments outlined above should apply equally well to other shapes of indenter. However it is not easy to correlate the track widths under the Vickers indenter with hardness anisotropy, owing to the high symmetry
Fig. 4. Relation between the track width and the Knoop parallel to its long diagonal; 200 g load.
hardness
for the Knoop
diamond
367
0
Fig. 5. Relation indenters.
between
(loi2) hIlo]
0
(0001) bliol
x
(,oio) Ii123
A
(IIIO)
[OOOj
A
(tljo)
Eo13]
m
(Ii52)
[eo”
mobt
ili3]
the normal load and the track width for Vickers and Knoop
*. 6oo
!
500
-
I
3i J *
400.
z x
300
*
I ?
200
-
1
100
.
Fig. 6. Variation of effective Vickers diamond.
hardness with width for different
orientations
of the
of the Vickers indenter and also perhaps to the marked topographical changes which occur near Vickers indentations. 4.3. Load dependence of track width It has already been stated that for all orientations there is a non-linear relation between load and track width and therefore, as friction force/load i!
368
,400
Fig. 7. Variation of microhardness of a Vickers diamond track.
constant, between the total applied force and the track width. By analogy with static tests this relation would be expected to be of the form L = kHw2
(1)
where L is the load, His the hardness, w the track width and kw2 the area of the interface. Graphs of log,, L uersus log,, w are plotted in Fig. 5 for several orientations and it can be seen that the actual relationship for both indenter geometries is of the form L = k1 w-
513
(2)
where kl is a different constant for each orientation. Equations (1) and (2) can only be compatible if the hardness H is proportional to w-‘j3, i.e. if the hardness of the material beneath the slider increases with decreasing track width. This is clearly shown in Fig. 6 in which there is a plot of effective hardness, i.e. 4L/w2, against w for several orientations. It should be noted that the effective hardness at very small track widths is several times greater than the static hardness calculated from the appropriate single diagonal of a static indentation and that the hardness tends asymptotically to the static value as the track width is increased. It is clear that the relation in eqn. (2) implies a breakdown in the principle of geometrical similarity during sliding experiments This is thought to be due to the higher strain immediately ahead of the leading edge of the diamond and the consequent higher hardening. To illustrate this, microhardness measurements under a 5 g load have been made at various positions ahead of some of the wider tracks. One example is shown in Fig. 7 and it can be seen that the hardness of the material immediately ahead of the cutting edge is considerably increased. No such effect is observed when similar measurements are made around static indentations. The dependence of effective hardness on track width as shown in Fig. 6 is quantitatively very similar to that found by Cane and Skinner [3] for
369
smaller paraboloidal indenters, The scale of the effect, however, is very much larger as the hardnesses found by Gane and Skinner were virtually constant for track widths greater than approximately 2 m. It is therefore thought to be very unlikely that the explanation invoked by Gane and Skinner, i.e. the difficulty of operating dislocation sources in very small volumes, can be applied to the present work. Hardening of material ahead of the slider accounts at least in part for the observation that the track width beneath the Knoop indenter traversed parallel to the short diagonal actually decreases over a considerable distance. Microhardness measurements of the material ahead of such tracks show high hardening over most of the track width, presumably because of the high strains which are needed to displace material from the path of the relatively blunt indenter. An alternative explanation of this effect is suggested by the work of Johnson et al. [6] who have shown that, during sliding, blunt wedges tend to form prows of material and rise to the level of the original surface. This effect is simply the most favourable way of accommodating the material movements which are necessary for sliding and does not require the material to become work hardened. It may be that the effect noted here is due to a combination of both these factors. 4.4. Comparison with previous work The work reported here shows that the friction coefficients between cobalt and various diamond pyramids are independent of crystallographic orientation. As cobalt is very anisotropic it would be surprising if similar results were not obtained on more isotropic materials. However Bailey and Gwathmey [ 71 and Flom [ 81 have described observed frictional anisotropy on single crystals of f.c.c. metals using diamond indenters and these results seem to be at variance with those found in the present work on cobalt. Bailey and Gwathmey, who used a three-sided pyramid, suggested that their observed anisotropies could be accounted for by changes in surface topography, but Flom pointed out that the anisotropies which he observed using a Vickers indenter on copper and aluminium were the opposite of those predicted from changes in surface topography. Flom therefore speculated that the effects could be due to surface films. In the present work marked variations in surface topography have been observed but these have had no effect on the frictional force. Furthermore, the theoretical explanation for the magnitude of P, which has been described earlier, should be valid for materials of all crystal structures. This has been supported by measuring I-(for a Vickers diamond sliding on polycrystalline specimens of hardened steel, zinc and brass, which all had y values in the range 0.36 and 0.38, and on a glass microscope slide which had a value of 0.33. The slight variations in the P values can be accounted for by slight differences in the values of PA. In an attempt to resolve the differences between the present work and that of previous workers some sliding experiments were therefore carried out on aluminium single crystals. It was again found that the P values were independent of orientation and were in the range 0.36 to 0.38.
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It is suggested that the real differences between these results and those of other workers can be accounted for by differences in experimental technique. In the present work the indenters were loaded by dead-weight loading and the diamond was restrained to prevent it tilting, i.e. 0 was constant. In the experiments of Bailey and Gwathmey one specimen was mounted on leaf springs and both load and friction force were measured by the deflection of these springs. It is inevitable with this arrangement that the angle 0 between the indenter and the specimen will vary as other conditions are varied and, if the theory presented here is correct, this will lead to a change in friction force. This would be particularly noticeable in the experiments of Bailey and Gwathmey who used a right-ogled three-sided pyramid, that would give large changes in &, for relatively small changes in 0.
5. Conclusions The coefficient of friction between a cobalt single crystal and a high angle diamond indenter depends only on the geometry of the indenter and the coefficient of sliding friction at the cobalt/diamond interface. The friction coefficient is not significantly affected by the anisotropy of the material; this anisotropy is reflected in changes of track width with orientation. It should be noted, however, that the form of the orien~tion dependence of the track width is not a fund~ent~ property of the material but is also dependent on the geometry of the indenter.
Acknowledgments The author is indebted to Professor J. Halling, Professor D. Tabor and Dr. T. H. Childs for helpful discussion of this work. Financial support was provided by the Science Research Council and a cobalt single crystal was provided by the Cobalt Information Centre.
References 1 ‘2 3 4 5 6 7 8
E. Rabinowicz, Wear, 10 (1967) 313. J. Goddard and H. Wilman, Wear, 5 (1962) 114. N. Gane and J. Skinner, Wear, 24 (1973) 207. T. H. C. Childs, Int. J. Mech. Sci., 12 (1970) 393. R. D. Arnell, J. Phys. D, 7 (1974) 1225. K. L. Johnson, personal communication. J. M. Bailey and A. T. Gwathmey, ASLE Trans., 5 (1962) R. Flom, ASLE Trans., 5 (1962) 55.
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