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Deformation of single and multiple asperities on metal surfaces
Wear Elsevier Sequoia
381 S.A., Lausanne
- Printed
DEFORMATION OF SINGLE METAL SURFACES
A. H. UPPAL
and
in the Netherlands
AND MULTIPLE
ASPERITIES
ON
S. D. PROBERT
Department of Mechanical Engineering, University College of Swansea, Swansea (ct. Britain) (Received
January
18, 1972)
SUMMARY
Single and multi-asperity models were separately deformed by being pressed against a relatively hard flat surface. Prolilometric studies using a relocation technique indicate that a movement of material occurred around the base of the single asperity when the deformation ratio exceeded 0.5. At higher loads there was a lateral movement as well as a rise of material near the asperity base. Under loadings approaching the indentation hardness the peaks of the multi-asperity model became flattened and a rise of the valley floors ensued, the latter being more pronounced for the originally shallow valleys. All valleys became narrower as the material was pushed outwards from the flattened peaks. Hence the assumption made in “prolilometric” theories that the relation between contact area and separation could be directly inferred from the bearing area curve can be in error by up to 20%.
INTRODUCTION
Profilometric and microscopic studies of bead-blasted surfaces show that the irregularities or protrusions on a metal surface resemble circular domes’ or circular cones with rounded tips. The sizes of these asperities depend upon the dimensions of the beads used for the blasting operation as well as upon the hardness of the metal’. For aluminium bead-blasted surfaces, these asperities vary in height from 0.25 to 7.5 pm, with base diameters ranging from 1.25 to 75 pm’ and asperity slopes lying between 5” and 25”. If a hard flat surface is pressed against a soft rough surface, the asperities deform plastically to an extent dependent upon : (i) the applied load, (ii) their individual size, and (iii) their location with respect to neighbouring asperities3. Bowden and Tabor proposed for fully plastic deformations that the real area of contact A, equals W/M, where M is the indentation hardness. This has until recently been used by most investigators5 : it was corroborated by Hill6 who showed by a theoretical analysis using slip-line theory that compressing an infinite wedge was identical with the indentation process, and gave the same value for M. Williamson’ in his work on “plastic contact of surfaces” has also used the identation process to show the mode of surface deformation. However, from recent measurements undertaken by the authors it appears that the phenomenon of infinite wedge compression or indentation differs Wear, 20
(1972)
382
A. H. UPPAL,
S. D. PROBER’1
fundamentally from compressing or deforming a minute cone or dome shaped asperity on the surface. The strength of the asperity while undergoing deformation, is in fact greatly enhanced by the interaction of the base of the asperity with the surrounding material. Previous investigators 8*9have ignored this interaction. Therefore, for this study it was desirable to devise an idealized model of an asperity on a real surface, of size comparable with that found on bead-blasted surfaces, and to consider the stages of deformation. The flow pressure of the llattened part of the asperity varied as the deformation progressed3, the movement of material around the asperity base being shown by relocation pro~lometry’~. MATERIALS
Relatively soft materials were selected for the single and multi-asperity models (see Table If. The copper, silver, aluminium and tin chosen were all of 99.9 % purity. and cold drawn in the shape of 6.25 mm diameter rods. Micro-hardnesses were measured with a Vickers micro-indenter in conjunction with a M-55 projection microscope, at loads of 5, 10 and 20 grammes. TABLE
I
SPECIMEN
DETAILS ..- ~..~_-_______-.
Material
Mean
prqjected
hardness
M
(kg mm~- ‘)
Tin Aluminium Silver Copper Silver-steel
11.8 38.4 1 15.2 152.0 310.0
Roughness surfhce
qf’
bt@re
~~
_. _..._..____~_
Roughness surfnce
after
lapping and polishing
lapping und polishing
(CLU. (&)
(C.i.Lf. (urn))
0.30 0.55 0.65 0.85 0.80
0.070 0.032 0.040 0.035 0.030
of’
. PeriodJtir su$~~
which was
beud-blasted (sect
1 2 2.5-3 2.5-3
In all deformation experiments, the single and multi-asperity models were pressed by a lapped and polished silver-steel nominally flat surface. PREPARATION
OF A SINGLE
ASPERITY
MODEL
Considerable machining skill was needed to manufacture a model of an asperity in the shape of a right circular cone of about 10 to 1.5times the size of a typical asperity which would occur on a bead-blasted surface of the same material. A small telescope attached to the tool post was first used to locate the exact centre of the crosssection through the 6.25 mm diam. rod. The size of the asperity was then dictated by appropriately setting the angle of the facing tool, and judiciously stopping its traverse just short of the centre. The smallest asperity which could be accurately produced by this technique was of base diameter approximately 0.1 mm and this involved halting the traverse-carrying facing tool 0.05 mm short of the centre. For the series of experiments reported here, comparatively larger asperity Weur,20(19721
DEFORMATION
models
having
OF ASPERITIES
0.3 mm
6 06
ON
METAL
0.5 mm and
383
SURFACES
120” 6 4~
when deformed perity bases.
by the anvil, gave clearly discernable
EXPERIMENTAL
PROCEDURE
150”, were prepared. material
flows around
These, the as-
Relocation projilometry A three-point kinematic rig, developed from that of Williamson and Hunt lo, was employed to relocate (to 0.1 pm) the track made by a 50 mg stylus attached to the Talysurf-4 (Fig. 1). The specimen assembly (a) carrying a single asperity model was locked in position in the relocation table (b) by three grub screws. The table was placed gently on the rollers in the relocating rig and then lifted to its position by slowly inflating an airbag (c) to an overpressure of 150 torr. The Talysurf stylus was then lowered on to the asperity tip by a tine nylon thread tied to the hoist (d). The relocating block was aligned by means of the adjustable gear(f) so that the tip of the stylus passed over the apex of the cone asperity during its traverse. As the asperity was so small, a telescope (g) was needed to confirm that proper location had occurred. Once aligned the block was locked in position and a Talysurf trace taken across the asperity model. The profile of the asperity gave a two dimensional representation of the model and enabled estimates for C#Jand D to be obtained. The first traverse across the model was termed the original trace, and all subsequent ones, taken after various deformations, were with the Talysurf stylus relocated in the original track. This was confirmed by observing under high magnification ( x 300) with the Vickers Projection Microscope-55. Any misalignments in the relocation of the tracks made by the stylus exceeding 0.2 pm could be detected and only observations with smaller deviations were recorded. The areas of the truncated cones were also measured so providing an estimate of the local flow pressures at the deformed asperity flat.
Fig. 1. Relocation
rig in position
Fig. 2. Apparatus
for statically
on Talysurf-4. loading
single and multi-asperity
models.
Loading arrangement The relocating table (Fig. 2 (a)) together with the specimen model (b) was locked in position on the loading rig. The pressure was applied by lowering the flat anvil (c) by means of a screw arrangement (d) which was loaded by a 3 cm coil spring (e). A Kistler piezo-electric transducer type 9311 (f) which was interposed between the two Wear, 20 (1972)
384
A. H. UPPAL.
S. D. PROBER.1
ends of the anvil, gave an indication on the oscilloscope (g) linked through a Kistler charge amplifier (h) of the applied static load. With this arrangement, static loads of between 5 and 1000 N could be accurately imposed upon the single and multi-asperity models. However, in order to apply smaller loads in a reproducible and measurable manner a dead weight system (i-m) was adopted. A steel cylinder (k) whose lower end had been lapped and polished, was then lowered through a precision bored bush (I) on to the asperity model, and the cylinder subsequently loaded with weights (m) in small increments of 0.1 N. The total load was that due to the added weight plus that of the cylinder (0.03 N). It was desirable that the steel cylinder should be brought into contact with the model with the least impact. Once the contact had been achieved no rotary movement between the contacting surfaces was permitted. The loads could be increased in small increments, ten seconds being allowed to lapse between the application of each increment. The total load was removed after a minimum lapse of 20 set so that the effects of plastic yielding could be seen (e.6~.see Fig. 3).
Fig. 3. Plan view of a single asperity model after it had been deformed by a hard flat surface. material : tin. II = 20 mm, A series of four relocated tracks, made by a SO mg stylus of a Talysurf-4. cross the photograph.
DEFORMATION
OF A SINGLE
ASPERITY
MODtL
Figure 4(a) shows a Talysurf trace of an aluminium asperity profile with D = 0.38 mm, and $= 130”. The profiles, Figs. 4(b)-(h), are the relocated traces taken across the asperity model after it had been partly flattened by the “flat” silver steel surface under several static loads. Figures 5 (at(h) d escribe the same surface tracks as those shown in Fig. 4, but with the Talysurf vertical magnification now being 5,000, Werrr.20 (I 973
VARIOUS STAGES OF SINOLE ASPERITY DEFORMATION
(i)
_____...-...--.._.. -_____-_-_.___ ________.-
-----I_----.__~---____-~____-
L--Fig. 4. Single asperity Model profile
-
model of aluminium
Applied static load (N)
--0
8.38mm
------I
: D=O.38 mm and @= 130”
Dejiirmation ratio
Flow pressure (MN m-‘)
Zero g;
1.1
0.22
204
;I$
4.4 2.2
0.28 0.43
208 240
I; (9) (h)
26.7 13.4 53.5 107
0.70 0.97 1.10 1.23
252 239 395 610
In (i) the asperity profiles(b) to (h) have been superimposed of the material during the deformation.
on the original
profile (a) to show the movement
386
A. H. UPPAL.
S. D. PROBERT
i.e. ten times greater, so that it is easier to discern the movement of the asperity base and the rise of the material around the base at higher loads. The deformation of the asperity model can be considered in three stages. (1) rb 0.5. During this plastic deformation the material displaced from the apex of the cone accumulates in the shoulders (Figs. 4 (b)-(d)). As expected the measurements indicate that the total volume of the material remains unchanged3. Also the projected apex angle of the truncated cones was always less than 4. Tabor” showed from geometric considerations that
Fig. 5. Series of Talysurf profiles across the same asperity dicular to the surface is in this case ten times greater. Wear, 20 ( 1Y72)
as in Fig. 4. However,
the magnification
perpen-
DEFORMATION
Wear,20(1972)
OF ASPERITIES
ON
METAL
SURFACES
387
388
A. H. UPPAL. S. D. PROBERT
co+ - p)=~~~~ The slip-line plane strain theory of Hill6 for the deformation of an infinite wedge by a hard flat surface is applicable only during this stage of deformation. (2) 0.5 < r < 1. When the deformation ratio exceeded 0.5, an outward movement of the base of the asperity (see Fig. 5(e)) ensued3. This movement was followed by a “filling” of the valleys nearest the base (see Fig. 6(c)), a process which appears similar to the rise of the bottom of the shaflow valleys experienced with the multi-asperity model. (3) 1.0 < r < 1.25. As r increased the base continued to move outwards, filling some of the valleys completely (Fig. 5(f)). At Y= 1.1 (Fig. 5(g)) the surface around the base of the asperity began to rise without affecting the relative topography. This upward movement of the surface influenced a zone of radius 30 when the deformation ratio equalled 1.25. Even at such high loads (104 N) the asperity was not compietely flattened (see Fig. 5(h)). While the indentation hardness obtained at the flattened asperity remained constant (which also indicated no work hardening), the local flow pressure of the deformed asperity increased with the deformation ratio (see Fig. 7). During the first stage the average flow pressure was approximately half of the indentation hardness.
5. 600Ll
VICKERS
INDENTATION
HARDNESS -2i
-1.
-1.’
I
!
0.2
O-4
O-6
MFGfWATlON
1 ,o
O-6
RAT0
12
14
t if b---W
Fig. 7. Difference between the local flow pressure and the indentation hardness of the flattened asperity described in Fig. 4. Wear, 20 (1972)
DEFORMATION
OF ASPERITIES
ON
METAL
SURFACES
389
As the base of the asperity began to move outwards there was a gradual rise in the flow pressure, The high value exhibited by the asperity in the third stage could only be due to the interaction of the asperity base with the surrounding material and this may be the explanation for the persistence of the asperities under very high loads”. The right-hand ordinate axis of Fig. 7 shows the mean yield pressure in units of the yield stress of the material. (The Vickers indentation hardness in this example corresponded to 2.8Y.j MULTI-ASPERITY
MODEL
When comparing the deformation of the large idealized model for a single asperity with that for asperities on real surfaces, it should be remembered that asperities never occur alone on surfaces. The behaviour depends upon the interaction occurring between asperities, and it is this aspect of contact between solids that has hitherto been somewhat neglected. Williamson’ in his constrained specimen experiment observed a rise of the non-contacting surface under large static loads. It was feared’, however, that the large hoop stresses in the sleeve surrounding his specimen led to the observed rise of the surface. A multi-asperity model was developed by imprinting a small area of rough surface (0.25 pm2 to 0.5 pm’) on a nominally flat semi-inmate surface. A rise of the bottom of the valleys was observed when the peaks were flattened, but this occurred at much higher loads than suggested by Williamsoni. PREPARATION
OF MULTI-ASPERITY
MODEL
This was achieved by blasting small glass beads (2.5 pm to 3.75 ,um average diameter) through an aperture (0.5 mm to 0.8 mm in diam.) on to a nominally flat, lapped and polished surface. A localized roughened region (see Fig. 8) was produced, the surface peaks being formed of the metal displaced from the valleys by the impact of the glass beads. The most suitable durations of blast for the tin, aluminum, silver and copper surfaces were found empirically (see Table I) and satisfied the following three criteria : (1) A uniform blast must be produced over the whole surface exposed to the glass beads (see Fig. 8(a)). (2) Within the exposed area all parts of the original surface suffered changes due to the impact of the beads. (3) The bead-blasted surface should have an almost gaussian topography, with the original level of the surface forming the mean line for the height distribution (see Fig. 9). The number of craters or valleys formed per square millimetre by the impact of the glass beads was about 100. Protilometric representation of the models (Figs. 9 (a) and (b)) shows a uniform distribution of peaks and valleys above and below the original level of the flat surface. The number of peaks and valleys on a diametral (Dm= 0.8 mm) trace across the model was either seven or eight. The average height of the peaks and depth of the valleys from the mean surface of the model depended upon the hardness of the specimen material. The tallest peaks for the softer aluminium and tin models had heights of 5.0 pm and 5.5 pm respectively, whereas those for silver and Wear,20
(1972)
A. H. UPPAL,
S. D. PROBER-f
Fig. 8. Multi-asperity models viewed with the scanning electron microscope. (a) This micrograph, taken at 6.5” tilt, to the surface, is of a polished tin surface which had been subjected to a blast of glass beads through a 0.5 mm aperture for one second. (b) Tin model (D,=OS mm) after it had been subjected to 40 N. The relocated tracks of the Talysutfstylus can be seen running across the model. (c) Silver model (D, =0.5 mm) after the imposition of 210 N. (d) Magnified \;iew of part of the surface shown in (c).
copper were smaller. The values of mean deviation (0) deduced from these profiles closely resembled (within 8 ‘A) those values obtained from many separate surface traces in several directions over the surface and evaluated with a digital analyzer. The bearing area curves for the models are similar to the “Abbot Curves”, 1‘, showing a gaussian height distribution. The per;centage bearing length at mean surface varied between the ideal of 0.5 D, and 0.57 D,, Surfaces exposed to longer periods of beadblasting showed at the mean surface level greatly reduced bearing lengths, namely 0.35 D, and 0.40 D,. Wear,20
( 1972)
bearing
the gaussian
MOOEL Of i4LUMlNtUM
area curves showing
MULlI - ASPERITY
Fig. 9. Typical
iat
distribution
of the undeformed
multi-asperity
BEARING
models.
AREA
CURVES
fff
RFACE
WAN
SURFACE
_-_--MEAN
---I
392 RESULTS
t’t. H. UPPAL.. S. I). PROBER-1 AND
DISCUSSION
: MULTI-ASPERITY
MODELS
Figures 8(b)-(d) show some scanning electron micrographs of multi-asperity mod& of tin and silver which had been deformed by the flat anvil. The deep valleys persisted after the peaks had been fully flattened, as indicated by the flat areas around the craters.
ftM
WW&CE
____l-_&--l
Fig. 10. Multi-asperity model of aluminium (0,=0.80 mm). (a) Undeformed subjected to a load of 275 N: (c) profiles (a) and (b) superimposed. W’ecrr, 20 (1972)
^_----
profile;
(b) after it had been
DEFORMATION
OF ASPERITIES
ON METAL
393
SURFACES
The material rose around the periphery of the silver model (Fig. S(c)) but not in the case of the softer tin model (Fig. 8(b)). Thi s corresponds to the “piling-up” and “sinking-in” noticed by Tabor during the indentation produced by a spherical indenter on highly worked materials (e.g. silver) and annealed materials (e.g. tin) respectively. Figure 8(d) shows how the true area of contact (i.e. the flat areas) could be clearly distinguished from the surrounding non-contacting areas (i.e. the craters). The efficacy of the model to depict the changes as a result of the surface being deformed is shown in Fig. 10 ; the mean surface of the model being used as the reference line. Because the model rough surface is implanted on a relatively large flat extending around it, it was reasonable to assume that the mean surface did not register any measurable rise as a consequence of the peaks being flattened. To some extent the behaviour was similar to that of the “constrained model” of Williamson without the complication of hoop stresses ‘. Using the mean surface as the datum, the heights of peaks and the depths of valleys could be measured directly to an accuracy of 0.1 pm. It was expected that when the peaks of the multi-asperity model became flattened the displaced material from the truncated peaks would fill the valleys, and the surfaces would become a homogeneous flat (as before bead-blasbng). However, Fig. 10 shows that this was not quite so. The upward movement of the valley floors corresponded to only a small fraction (8%) of the flattening suffered by the peaks. For example the maximum rise in valley V, was 0.4 pm while peak P, moved downwards by 5.3 pm.
Fig. 11. Multi-asperity model of silver (D, =0.5 mm). (a) Undeformed been imposed; (c) profiles (a) and (b) superimposed.
profile;(b) after
a load of 210 I? had
The silver model (Fig. 11) consisted of four peaks (P), five valleys (V), four lower peaks (LP) and one upper valley (UV). The tin model (Fig. 12) had five peaks (P), six valleys (V), four lower peaks (LP) and one upper valley (UV). For both models D, equafled 0.5 mm. When the flat anvil approached the mean surface of the model, the peaks were deformed as they came into contact. The peaks of the tin model tended to sink downwards at higher loads besides being flattened (see P,, P,, P,, P,, in Fig. 12) whereas those of the silver model exhibited greater rigidity and the flattening led to pronounced “shouldering” (see P,, P,, P,, P, in Fig. 11). Wear,20
(1972)
-- om i F8g. 12. Multi-asperity model of tin (D,=OS 40 N; (c) profiles (a) and (b) superimposed.
Smm
mm). (a) Original
-
-
-.-
--
*
profile; (b) after surface had been loaded to
Under a static load of P/M 3 1.0, there was a tendency for the bottoms of all the valleys to rise. However, deep valleys (such as V, and V, for the silver model) rose minutely (< 0.1 pm and 0.2 pm respectively) compared with the shallower valleys (V, and V,), which experienced rises of as much as 0.9 pm (V,). For the tin model, the rise of the deep valleys (V,, V,, V,) was comparatively greater (0.3 pm to 1.2 pm). Flattening of the peaks resulted in a decrease of valley widths at mean surface levels. The nearer the base of the valley was to this level, the greater was the filling effect (see e.g. UV for the silver model). The static loading also resulted in the lower peaks such as LP, and LP, (i.e. those not touching the anvil) rising. This confirmed Williamson’s hypothesis7 that parts of the surfaces not touching the anvil, whether valleys or peaks rise due to the imposition of the load. In the case of the tin model (Fig. 12) the upper valley (UV) moved downwards as it followed the sinking of the peaks according to the “sinking-in” phenomenon’ ‘. The envelope of the flattened peaks on each deformed surface was a curved surface, convex upwards, despite the hard steel anvil being absolutely flat. This phenomenon is due to partial elastic recovery and hence it occurred least for the softest material considered i.e. the tin model. The separation between the anvil and the mean surface of the tin model decreased successively from 5.0 /irn to 1.0 pm as the load increased (see Fig. 13). The narrowing of the valleys due to a flattening of peaks is apparent by the shift of the curves, the bearing length fraction at the mean surface increasing from 0.56 to 0.61 and 0.63 at respective loads of 2.5 N and 5 N. At much higher loads the tendency of the topography was to sink downwards (see curvea). The filling of the valleys is shown by the lateral shift of the curve below the level of the mean surface. The bearing area curves do not demonstrate the rise of the base of the valleys, which was usually of the order of 0.1 ,um under the considered loads. However, the curves do show the narrowing and the “tilling” of shallower valleys by the material displaced from the apex of the peaks. This factor could add 15-20”/: to the contact area calculated from prolilometric theoriess using the Abbot curve. Weur, 20 ( 1972)
DEFORMATION
-5
OF ASPERITIES
20
0
LO ‘/.
395
ON METAL SURFACES
BEARING
60 AREA
60
1
Fig. 13. Bearing area curves for a multi-asperity tin model (DR1 = 0.80 mm). A, undeformed model ; 0, V, [I1, after being deformed by 2.5 N, 5.0 N and 40 N respectively. TABLE II DEPTHS OF VALLEYS (FROM MEAN SURFACE) AND RISE OF VALLEY BOTTOMS (IN pm) AS A RESULT OF THE SURFACE BEING LOADED TO P/M= 1. The negative sign indicates the sinking of the valley with respect to the mean surface. Tin model Valley
Silver model
Aiuminium model Valley Depth
Valley Rise
Valley
Valley Depth
Vulley Rise
Valley
Valley Depth
1.50
V6
1.40
V, V, V, V, V, V, V, V* V, V Fifgq15
5.40 5.05 4.80 4.30 3.85 2.30 1.15 2.80 2.00 0.65
0.10 0.20 0.15 0.05 0.60 -0.70 - 0.60 -0.20 0.25 0.50
4.35 3.40 1.55 2.00 0.70
V,
0.25 1.00 0.30 0.55 0.20 0.00 0.30 -0.10 0.00 0.10
Vi V2
V6
4.90 4.60 4.30 2.50 2.25 2.10
V, V2 v3 V4 V5
V9 v
1.00 0.55
F;; 14
V3 V4 VS
V6 V7 V6 v9
V -&!?--Fig. 16
0.10 1.75 1.70 1.60 0.30
Valley Rise 0.75
0.10 0.00 -0.22 0.60 -0.30 0.00 0.00 0.90 0.95
Figures 14,15 and 16 show the rises of the valley bottoms for the multi-asperity models (having D, = 0.8 mm) of tin, aluminium and silver, after each model had been loaded to P/M= 1.0. Owing to the high resoiution (i.e. vertical magni~cation x 104) some of the peaks are not displayed. Although a consistent load was applied (P/M- 1.0) to the models, the rise of the valleys (see Table II) was not systematic-it did not solely depend on their depth (see V, or V, for the tin and silver model). Similarly shallower Continued on page 399 Wear, 20 (1972)
A. H. UPPAL, S.D. PROHtRI
3EFORh4ATION
OF ASPERITIES
ON METAL
397
SURFACES
”
--...._
.----I
20
.G rr’ ?. ~
A
b U
Wear, 20 ( 1972)
h
CI
A U
t) V
._...?-----~-
398
Weur, 20 (I 972)
A. H. UPPAL.
S. D. PROBER7
DEFORMATION
OF ASPERITIES
ON
METAL
SURFACES
399
valleys near each other could show either a rise or fall (e.g. V, and V, for the aluminium model) in one vicinity. It would be premature to attempt to explain from a single topographic profile why certain areas below the mean surface rise more than others as a result of the static loading. Even using vertical magnification ofthe Talysurf profile of x 104, it was difficult to detect rises in the deep valleys at loadings of 0.1~ P/M < 0.5 with the present instrumentation. The shallower valleys did register rises of approximately 0.1 to 0.3 pm for the softer materials such as tin and aIuminium, but the deeper valleys, i.e. those 3 to 5 pm deep did not exhibit any detectable rise. CONCLUSIONS
Deformation studies of an idealized asperity show that material from the apex is displaced to the shoulders. At a specific loading, dependent upon the apex angle, material from the asperity base begins to move outwards, and thereafter plane strain slip-line theory of infinite wedge compression does not apply. The neighbouring valleys then begin to fill, a process which resembles the rise of the bottoms of shallow valleys of the multi-asperity model. For deformation ratios exceeding unity the material around the base of the single asperity moves laterally and rises upward, the magnitude of the effects decreasing to zero at about three times the base diameter from the centre of the asperity. This movement is followed by the high ffow pressures (exceeding the Vickers hardness for the material) being exhibited by the flattened part of the asperity. Existing plasticity theories fail to explain this phenomenon. The persistence of the asperity at very high pressures is due to an interaction of the asperity base with the surrounding material. The multi-asperity model experiments indicate that at high loads (P/M- 1.0) there was a tendency for the bottoms of all valleys to rise. However, the deep valleys rose very little compared with the shallower valleys. At light loads the deep valleys did not register any change. The rise of the shallower valleys was probably due to an overspill of the flattened peaks. ACKNOWLEDGEMENTS
The authors thank Dr. T. R. Thomas of Teesside Polytechnic for advice with this project, and the Science Research Council for financial support. The specimens were supplied by Messrs. Johnson Matthey Limited. NOMENCLATURE
d D D, M P
diameter of the flattened part of asperity, original diameter of single asperity model, diameter of bead-blasted area defining the extent of the multi-asperity indentation hardness of the specimen material, nominal applied pressure,
P,
flowpressure[W/(td:)],
Y
deformation
lVeur, 20 (1972)
ratio for a single asperity (=-d/D),
model,
400
W Y # B (5
A. H. LIPPAL.
S I). PROBER-1
applied load, yield stress. apex angle of the asperity, projected apex angle of the flattened asperity. standard deviation of surface roughness..
REFERENCES 1 J. B. P. Williamson, Topography of solid surfaces, Proc. Symp. Jnterdisciplinary Approach to Friction und Wear, NASA, Washington, 1968, 88-142. 2 A. H. Uppal and S. D. Probert, Topographic changes resulting from surfaces being in contact under static and dynamic loads, M/cur, 16 (1970) 261-271. 3 T. R. Thomas, A. H. Uppal and S. D. Probert, Hardness of rough surfaces, Nature (Phys. Sci.). 229 (3) (197 1) 86-87. 4 F. P. Bowden and D. Tabor. Friction and Lubrication a/‘Solids, Part 1. Oxford Univ. Press, London, 1954, pp. 19920. 5 7. Tsukizoe and T. Hisakado, On the mechanism ofcontact between solid surfaces; Part 2, Truns. Am. Sac. Mech. Engrs., 90F (1968) 81.--88. 6 R. Hill, The mathernarical theory ofplasticity, Oxford Univ. Press, London, 19.50, p. 215. 7 J. B. P. Williamson, J. Pullen and R. T. Hunt, Plastic contact of surfaces, Eurndy Res. Rep. Nos. 78 and 79, 1970. 8 A. Mallock, Hardness, Nature, 117 (2034) (1926) 117. 9 G. H. H. Williams and H. O’Neill, The Mallock cone hardness test and its relation to indentation mcthods, J. Iron Sreel Inst., 189 (1958) 29-37. IO J. B. P. Wiil~mson and R. T. Hunt, Relocation profi~om~try. f. Sci. Ittstrum., Ser. 7, I (1968) 749-752. 11 D. Tabor, The ~nrdness qf Metals, Oxford Univ. Press, London, 1951, pp. 64-65. I2 G. W. Rowe and J. A. Greenwood, Deformation of surface asperities during bulk plastic flow. J. Appl. Ph_vs., 36 (2) (1965) 667-668. 13 E. J. Abbot and F. A. Firestone, Specifying surface quality, Mech. Eng., 55 (1933) 569. M;‘rrrr..20
{ 1972)
381 S.A., Lausanne
- Printed
DEFORMATION OF SINGLE METAL SURFACES
A. H. UPPAL
and
in the Netherlands
AND MULTIPLE
ASPERITIES
ON
S. D. PROBERT
Department of Mechanical Engineering, University College of Swansea, Swansea (ct. Britain) (Received
January
18, 1972)
SUMMARY
Single and multi-asperity models were separately deformed by being pressed against a relatively hard flat surface. Prolilometric studies using a relocation technique indicate that a movement of material occurred around the base of the single asperity when the deformation ratio exceeded 0.5. At higher loads there was a lateral movement as well as a rise of material near the asperity base. Under loadings approaching the indentation hardness the peaks of the multi-asperity model became flattened and a rise of the valley floors ensued, the latter being more pronounced for the originally shallow valleys. All valleys became narrower as the material was pushed outwards from the flattened peaks. Hence the assumption made in “prolilometric” theories that the relation between contact area and separation could be directly inferred from the bearing area curve can be in error by up to 20%.
INTRODUCTION
Profilometric and microscopic studies of bead-blasted surfaces show that the irregularities or protrusions on a metal surface resemble circular domes’ or circular cones with rounded tips. The sizes of these asperities depend upon the dimensions of the beads used for the blasting operation as well as upon the hardness of the metal’. For aluminium bead-blasted surfaces, these asperities vary in height from 0.25 to 7.5 pm, with base diameters ranging from 1.25 to 75 pm’ and asperity slopes lying between 5” and 25”. If a hard flat surface is pressed against a soft rough surface, the asperities deform plastically to an extent dependent upon : (i) the applied load, (ii) their individual size, and (iii) their location with respect to neighbouring asperities3. Bowden and Tabor proposed for fully plastic deformations that the real area of contact A, equals W/M, where M is the indentation hardness. This has until recently been used by most investigators5 : it was corroborated by Hill6 who showed by a theoretical analysis using slip-line theory that compressing an infinite wedge was identical with the indentation process, and gave the same value for M. Williamson’ in his work on “plastic contact of surfaces” has also used the identation process to show the mode of surface deformation. However, from recent measurements undertaken by the authors it appears that the phenomenon of infinite wedge compression or indentation differs Wear, 20
(1972)
382
A. H. UPPAL,
S. D. PROBER’1
fundamentally from compressing or deforming a minute cone or dome shaped asperity on the surface. The strength of the asperity while undergoing deformation, is in fact greatly enhanced by the interaction of the base of the asperity with the surrounding material. Previous investigators 8*9have ignored this interaction. Therefore, for this study it was desirable to devise an idealized model of an asperity on a real surface, of size comparable with that found on bead-blasted surfaces, and to consider the stages of deformation. The flow pressure of the llattened part of the asperity varied as the deformation progressed3, the movement of material around the asperity base being shown by relocation pro~lometry’~. MATERIALS
Relatively soft materials were selected for the single and multi-asperity models (see Table If. The copper, silver, aluminium and tin chosen were all of 99.9 % purity. and cold drawn in the shape of 6.25 mm diameter rods. Micro-hardnesses were measured with a Vickers micro-indenter in conjunction with a M-55 projection microscope, at loads of 5, 10 and 20 grammes. TABLE
I
SPECIMEN
DETAILS ..- ~..~_-_______-.
Material
Mean
prqjected
hardness
M
(kg mm~- ‘)
Tin Aluminium Silver Copper Silver-steel
11.8 38.4 1 15.2 152.0 310.0
Roughness surfhce
qf’
bt@re
~~
_. _..._..____~_
Roughness surfnce
after
lapping and polishing
lapping und polishing
(CLU. (&)
(C.i.Lf. (urn))
0.30 0.55 0.65 0.85 0.80
0.070 0.032 0.040 0.035 0.030
of’
. PeriodJtir su$~~
which was
beud-blasted (sect
1 2 2.5-3 2.5-3
In all deformation experiments, the single and multi-asperity models were pressed by a lapped and polished silver-steel nominally flat surface. PREPARATION
OF A SINGLE
ASPERITY
MODEL
Considerable machining skill was needed to manufacture a model of an asperity in the shape of a right circular cone of about 10 to 1.5times the size of a typical asperity which would occur on a bead-blasted surface of the same material. A small telescope attached to the tool post was first used to locate the exact centre of the crosssection through the 6.25 mm diam. rod. The size of the asperity was then dictated by appropriately setting the angle of the facing tool, and judiciously stopping its traverse just short of the centre. The smallest asperity which could be accurately produced by this technique was of base diameter approximately 0.1 mm and this involved halting the traverse-carrying facing tool 0.05 mm short of the centre. For the series of experiments reported here, comparatively larger asperity Weur,20(19721
DEFORMATION
models
having
OF ASPERITIES
0.3 mm
6 06
ON
METAL
0.5 mm and
383
SURFACES
120” 6 4~
when deformed perity bases.
by the anvil, gave clearly discernable
EXPERIMENTAL
PROCEDURE
150”, were prepared. material
flows around
These, the as-
Relocation projilometry A three-point kinematic rig, developed from that of Williamson and Hunt lo, was employed to relocate (to 0.1 pm) the track made by a 50 mg stylus attached to the Talysurf-4 (Fig. 1). The specimen assembly (a) carrying a single asperity model was locked in position in the relocation table (b) by three grub screws. The table was placed gently on the rollers in the relocating rig and then lifted to its position by slowly inflating an airbag (c) to an overpressure of 150 torr. The Talysurf stylus was then lowered on to the asperity tip by a tine nylon thread tied to the hoist (d). The relocating block was aligned by means of the adjustable gear(f) so that the tip of the stylus passed over the apex of the cone asperity during its traverse. As the asperity was so small, a telescope (g) was needed to confirm that proper location had occurred. Once aligned the block was locked in position and a Talysurf trace taken across the asperity model. The profile of the asperity gave a two dimensional representation of the model and enabled estimates for C#Jand D to be obtained. The first traverse across the model was termed the original trace, and all subsequent ones, taken after various deformations, were with the Talysurf stylus relocated in the original track. This was confirmed by observing under high magnification ( x 300) with the Vickers Projection Microscope-55. Any misalignments in the relocation of the tracks made by the stylus exceeding 0.2 pm could be detected and only observations with smaller deviations were recorded. The areas of the truncated cones were also measured so providing an estimate of the local flow pressures at the deformed asperity flat.
Fig. 1. Relocation
rig in position
Fig. 2. Apparatus
for statically
on Talysurf-4. loading
single and multi-asperity
models.
Loading arrangement The relocating table (Fig. 2 (a)) together with the specimen model (b) was locked in position on the loading rig. The pressure was applied by lowering the flat anvil (c) by means of a screw arrangement (d) which was loaded by a 3 cm coil spring (e). A Kistler piezo-electric transducer type 9311 (f) which was interposed between the two Wear, 20 (1972)
384
A. H. UPPAL.
S. D. PROBER.1
ends of the anvil, gave an indication on the oscilloscope (g) linked through a Kistler charge amplifier (h) of the applied static load. With this arrangement, static loads of between 5 and 1000 N could be accurately imposed upon the single and multi-asperity models. However, in order to apply smaller loads in a reproducible and measurable manner a dead weight system (i-m) was adopted. A steel cylinder (k) whose lower end had been lapped and polished, was then lowered through a precision bored bush (I) on to the asperity model, and the cylinder subsequently loaded with weights (m) in small increments of 0.1 N. The total load was that due to the added weight plus that of the cylinder (0.03 N). It was desirable that the steel cylinder should be brought into contact with the model with the least impact. Once the contact had been achieved no rotary movement between the contacting surfaces was permitted. The loads could be increased in small increments, ten seconds being allowed to lapse between the application of each increment. The total load was removed after a minimum lapse of 20 set so that the effects of plastic yielding could be seen (e.6~.see Fig. 3).
Fig. 3. Plan view of a single asperity model after it had been deformed by a hard flat surface. material : tin. II = 20 mm, A series of four relocated tracks, made by a SO mg stylus of a Talysurf-4. cross the photograph.
DEFORMATION
OF A SINGLE
ASPERITY
MODtL
Figure 4(a) shows a Talysurf trace of an aluminium asperity profile with D = 0.38 mm, and $= 130”. The profiles, Figs. 4(b)-(h), are the relocated traces taken across the asperity model after it had been partly flattened by the “flat” silver steel surface under several static loads. Figures 5 (at(h) d escribe the same surface tracks as those shown in Fig. 4, but with the Talysurf vertical magnification now being 5,000, Werrr.20 (I 973
VARIOUS STAGES OF SINOLE ASPERITY DEFORMATION
(i)
_____...-...--.._.. -_____-_-_.___ ________.-
-----I_----.__~---____-~____-
L--Fig. 4. Single asperity Model profile
-
model of aluminium
Applied static load (N)
--0
8.38mm
------I
: D=O.38 mm and @= 130”
Dejiirmation ratio
Flow pressure (MN m-‘)
Zero g;
1.1
0.22
204
;I$
4.4 2.2
0.28 0.43
208 240
I; (9) (h)
26.7 13.4 53.5 107
0.70 0.97 1.10 1.23
252 239 395 610
In (i) the asperity profiles(b) to (h) have been superimposed of the material during the deformation.
on the original
profile (a) to show the movement
386
A. H. UPPAL.
S. D. PROBERT
i.e. ten times greater, so that it is easier to discern the movement of the asperity base and the rise of the material around the base at higher loads. The deformation of the asperity model can be considered in three stages. (1) rb 0.5. During this plastic deformation the material displaced from the apex of the cone accumulates in the shoulders (Figs. 4 (b)-(d)). As expected the measurements indicate that the total volume of the material remains unchanged3. Also the projected apex angle of the truncated cones was always less than 4. Tabor” showed from geometric considerations that
Fig. 5. Series of Talysurf profiles across the same asperity dicular to the surface is in this case ten times greater. Wear, 20 ( 1Y72)
as in Fig. 4. However,
the magnification
perpen-
DEFORMATION
Wear,20(1972)
OF ASPERITIES
ON
METAL
SURFACES
387
388
A. H. UPPAL. S. D. PROBERT
co+ - p)=~~~~ The slip-line plane strain theory of Hill6 for the deformation of an infinite wedge by a hard flat surface is applicable only during this stage of deformation. (2) 0.5 < r < 1. When the deformation ratio exceeded 0.5, an outward movement of the base of the asperity (see Fig. 5(e)) ensued3. This movement was followed by a “filling” of the valleys nearest the base (see Fig. 6(c)), a process which appears similar to the rise of the bottom of the shaflow valleys experienced with the multi-asperity model. (3) 1.0 < r < 1.25. As r increased the base continued to move outwards, filling some of the valleys completely (Fig. 5(f)). At Y= 1.1 (Fig. 5(g)) the surface around the base of the asperity began to rise without affecting the relative topography. This upward movement of the surface influenced a zone of radius 30 when the deformation ratio equalled 1.25. Even at such high loads (104 N) the asperity was not compietely flattened (see Fig. 5(h)). While the indentation hardness obtained at the flattened asperity remained constant (which also indicated no work hardening), the local flow pressure of the deformed asperity increased with the deformation ratio (see Fig. 7). During the first stage the average flow pressure was approximately half of the indentation hardness.
5. 600Ll
VICKERS
INDENTATION
HARDNESS -2i
-1.
-1.’
I
!
0.2
O-4
O-6
MFGfWATlON
1 ,o
O-6
RAT0
12
14
t if b---W
Fig. 7. Difference between the local flow pressure and the indentation hardness of the flattened asperity described in Fig. 4. Wear, 20 (1972)
DEFORMATION
OF ASPERITIES
ON
METAL
SURFACES
389
As the base of the asperity began to move outwards there was a gradual rise in the flow pressure, The high value exhibited by the asperity in the third stage could only be due to the interaction of the asperity base with the surrounding material and this may be the explanation for the persistence of the asperities under very high loads”. The right-hand ordinate axis of Fig. 7 shows the mean yield pressure in units of the yield stress of the material. (The Vickers indentation hardness in this example corresponded to 2.8Y.j MULTI-ASPERITY
MODEL
When comparing the deformation of the large idealized model for a single asperity with that for asperities on real surfaces, it should be remembered that asperities never occur alone on surfaces. The behaviour depends upon the interaction occurring between asperities, and it is this aspect of contact between solids that has hitherto been somewhat neglected. Williamson’ in his constrained specimen experiment observed a rise of the non-contacting surface under large static loads. It was feared’, however, that the large hoop stresses in the sleeve surrounding his specimen led to the observed rise of the surface. A multi-asperity model was developed by imprinting a small area of rough surface (0.25 pm2 to 0.5 pm’) on a nominally flat semi-inmate surface. A rise of the bottom of the valleys was observed when the peaks were flattened, but this occurred at much higher loads than suggested by Williamsoni. PREPARATION
OF MULTI-ASPERITY
MODEL
This was achieved by blasting small glass beads (2.5 pm to 3.75 ,um average diameter) through an aperture (0.5 mm to 0.8 mm in diam.) on to a nominally flat, lapped and polished surface. A localized roughened region (see Fig. 8) was produced, the surface peaks being formed of the metal displaced from the valleys by the impact of the glass beads. The most suitable durations of blast for the tin, aluminum, silver and copper surfaces were found empirically (see Table I) and satisfied the following three criteria : (1) A uniform blast must be produced over the whole surface exposed to the glass beads (see Fig. 8(a)). (2) Within the exposed area all parts of the original surface suffered changes due to the impact of the beads. (3) The bead-blasted surface should have an almost gaussian topography, with the original level of the surface forming the mean line for the height distribution (see Fig. 9). The number of craters or valleys formed per square millimetre by the impact of the glass beads was about 100. Protilometric representation of the models (Figs. 9 (a) and (b)) shows a uniform distribution of peaks and valleys above and below the original level of the flat surface. The number of peaks and valleys on a diametral (Dm= 0.8 mm) trace across the model was either seven or eight. The average height of the peaks and depth of the valleys from the mean surface of the model depended upon the hardness of the specimen material. The tallest peaks for the softer aluminium and tin models had heights of 5.0 pm and 5.5 pm respectively, whereas those for silver and Wear,20
(1972)
A. H. UPPAL,
S. D. PROBER-f
Fig. 8. Multi-asperity models viewed with the scanning electron microscope. (a) This micrograph, taken at 6.5” tilt, to the surface, is of a polished tin surface which had been subjected to a blast of glass beads through a 0.5 mm aperture for one second. (b) Tin model (D,=OS mm) after it had been subjected to 40 N. The relocated tracks of the Talysutfstylus can be seen running across the model. (c) Silver model (D, =0.5 mm) after the imposition of 210 N. (d) Magnified \;iew of part of the surface shown in (c).
copper were smaller. The values of mean deviation (0) deduced from these profiles closely resembled (within 8 ‘A) those values obtained from many separate surface traces in several directions over the surface and evaluated with a digital analyzer. The bearing area curves for the models are similar to the “Abbot Curves”, 1‘, showing a gaussian height distribution. The per;centage bearing length at mean surface varied between the ideal of 0.5 D, and 0.57 D,, Surfaces exposed to longer periods of beadblasting showed at the mean surface level greatly reduced bearing lengths, namely 0.35 D, and 0.40 D,. Wear,20
( 1972)
bearing
the gaussian
MOOEL Of i4LUMlNtUM
area curves showing
MULlI - ASPERITY
Fig. 9. Typical
iat
distribution
of the undeformed
multi-asperity
BEARING
models.
AREA
CURVES
fff
RFACE
WAN
SURFACE
_-_--MEAN
---I
392 RESULTS
t’t. H. UPPAL.. S. I). PROBER-1 AND
DISCUSSION
: MULTI-ASPERITY
MODELS
Figures 8(b)-(d) show some scanning electron micrographs of multi-asperity mod& of tin and silver which had been deformed by the flat anvil. The deep valleys persisted after the peaks had been fully flattened, as indicated by the flat areas around the craters.
ftM
WW&CE
____l-_&--l
Fig. 10. Multi-asperity model of aluminium (0,=0.80 mm). (a) Undeformed subjected to a load of 275 N: (c) profiles (a) and (b) superimposed. W’ecrr, 20 (1972)
^_----
profile;
(b) after it had been
DEFORMATION
OF ASPERITIES
ON METAL
393
SURFACES
The material rose around the periphery of the silver model (Fig. S(c)) but not in the case of the softer tin model (Fig. 8(b)). Thi s corresponds to the “piling-up” and “sinking-in” noticed by Tabor during the indentation produced by a spherical indenter on highly worked materials (e.g. silver) and annealed materials (e.g. tin) respectively. Figure 8(d) shows how the true area of contact (i.e. the flat areas) could be clearly distinguished from the surrounding non-contacting areas (i.e. the craters). The efficacy of the model to depict the changes as a result of the surface being deformed is shown in Fig. 10 ; the mean surface of the model being used as the reference line. Because the model rough surface is implanted on a relatively large flat extending around it, it was reasonable to assume that the mean surface did not register any measurable rise as a consequence of the peaks being flattened. To some extent the behaviour was similar to that of the “constrained model” of Williamson without the complication of hoop stresses ‘. Using the mean surface as the datum, the heights of peaks and the depths of valleys could be measured directly to an accuracy of 0.1 pm. It was expected that when the peaks of the multi-asperity model became flattened the displaced material from the truncated peaks would fill the valleys, and the surfaces would become a homogeneous flat (as before bead-blasbng). However, Fig. 10 shows that this was not quite so. The upward movement of the valley floors corresponded to only a small fraction (8%) of the flattening suffered by the peaks. For example the maximum rise in valley V, was 0.4 pm while peak P, moved downwards by 5.3 pm.
Fig. 11. Multi-asperity model of silver (D, =0.5 mm). (a) Undeformed been imposed; (c) profiles (a) and (b) superimposed.
profile;(b) after
a load of 210 I? had
The silver model (Fig. 11) consisted of four peaks (P), five valleys (V), four lower peaks (LP) and one upper valley (UV). The tin model (Fig. 12) had five peaks (P), six valleys (V), four lower peaks (LP) and one upper valley (UV). For both models D, equafled 0.5 mm. When the flat anvil approached the mean surface of the model, the peaks were deformed as they came into contact. The peaks of the tin model tended to sink downwards at higher loads besides being flattened (see P,, P,, P,, P,, in Fig. 12) whereas those of the silver model exhibited greater rigidity and the flattening led to pronounced “shouldering” (see P,, P,, P,, P, in Fig. 11). Wear,20
(1972)
-- om i F8g. 12. Multi-asperity model of tin (D,=OS 40 N; (c) profiles (a) and (b) superimposed.
Smm
mm). (a) Original
-
-
-.-
--
*
profile; (b) after surface had been loaded to
Under a static load of P/M 3 1.0, there was a tendency for the bottoms of all the valleys to rise. However, deep valleys (such as V, and V, for the silver model) rose minutely (< 0.1 pm and 0.2 pm respectively) compared with the shallower valleys (V, and V,), which experienced rises of as much as 0.9 pm (V,). For the tin model, the rise of the deep valleys (V,, V,, V,) was comparatively greater (0.3 pm to 1.2 pm). Flattening of the peaks resulted in a decrease of valley widths at mean surface levels. The nearer the base of the valley was to this level, the greater was the filling effect (see e.g. UV for the silver model). The static loading also resulted in the lower peaks such as LP, and LP, (i.e. those not touching the anvil) rising. This confirmed Williamson’s hypothesis7 that parts of the surfaces not touching the anvil, whether valleys or peaks rise due to the imposition of the load. In the case of the tin model (Fig. 12) the upper valley (UV) moved downwards as it followed the sinking of the peaks according to the “sinking-in” phenomenon’ ‘. The envelope of the flattened peaks on each deformed surface was a curved surface, convex upwards, despite the hard steel anvil being absolutely flat. This phenomenon is due to partial elastic recovery and hence it occurred least for the softest material considered i.e. the tin model. The separation between the anvil and the mean surface of the tin model decreased successively from 5.0 /irn to 1.0 pm as the load increased (see Fig. 13). The narrowing of the valleys due to a flattening of peaks is apparent by the shift of the curves, the bearing length fraction at the mean surface increasing from 0.56 to 0.61 and 0.63 at respective loads of 2.5 N and 5 N. At much higher loads the tendency of the topography was to sink downwards (see curvea). The filling of the valleys is shown by the lateral shift of the curve below the level of the mean surface. The bearing area curves do not demonstrate the rise of the base of the valleys, which was usually of the order of 0.1 ,um under the considered loads. However, the curves do show the narrowing and the “tilling” of shallower valleys by the material displaced from the apex of the peaks. This factor could add 15-20”/: to the contact area calculated from prolilometric theoriess using the Abbot curve. Weur, 20 ( 1972)
DEFORMATION
-5
OF ASPERITIES
20
0
LO ‘/.
395
ON METAL SURFACES
BEARING
60 AREA
60
1
Fig. 13. Bearing area curves for a multi-asperity tin model (DR1 = 0.80 mm). A, undeformed model ; 0, V, [I1, after being deformed by 2.5 N, 5.0 N and 40 N respectively. TABLE II DEPTHS OF VALLEYS (FROM MEAN SURFACE) AND RISE OF VALLEY BOTTOMS (IN pm) AS A RESULT OF THE SURFACE BEING LOADED TO P/M= 1. The negative sign indicates the sinking of the valley with respect to the mean surface. Tin model Valley
Silver model
Aiuminium model Valley Depth
Valley Rise
Valley
Valley Depth
Vulley Rise
Valley
Valley Depth
1.50
V6
1.40
V, V, V, V, V, V, V, V* V, V Fifgq15
5.40 5.05 4.80 4.30 3.85 2.30 1.15 2.80 2.00 0.65
0.10 0.20 0.15 0.05 0.60 -0.70 - 0.60 -0.20 0.25 0.50
4.35 3.40 1.55 2.00 0.70
V,
0.25 1.00 0.30 0.55 0.20 0.00 0.30 -0.10 0.00 0.10
Vi V2
V6
4.90 4.60 4.30 2.50 2.25 2.10
V, V2 v3 V4 V5
V9 v
1.00 0.55
F;; 14
V3 V4 VS
V6 V7 V6 v9
V -&!?--Fig. 16
0.10 1.75 1.70 1.60 0.30
Valley Rise 0.75
0.10 0.00 -0.22 0.60 -0.30 0.00 0.00 0.90 0.95
Figures 14,15 and 16 show the rises of the valley bottoms for the multi-asperity models (having D, = 0.8 mm) of tin, aluminium and silver, after each model had been loaded to P/M= 1.0. Owing to the high resoiution (i.e. vertical magni~cation x 104) some of the peaks are not displayed. Although a consistent load was applied (P/M- 1.0) to the models, the rise of the valleys (see Table II) was not systematic-it did not solely depend on their depth (see V, or V, for the tin and silver model). Similarly shallower Continued on page 399 Wear, 20 (1972)
A. H. UPPAL, S.D. PROHtRI
3EFORh4ATION
OF ASPERITIES
ON METAL
397
SURFACES
”
--...._
.----I
20
.G rr’ ?. ~
A
b U
Wear, 20 ( 1972)
h
CI
A U
t) V
._...?-----~-
398
Weur, 20 (I 972)
A. H. UPPAL.
S. D. PROBER7
DEFORMATION
OF ASPERITIES
ON
METAL
SURFACES
399
valleys near each other could show either a rise or fall (e.g. V, and V, for the aluminium model) in one vicinity. It would be premature to attempt to explain from a single topographic profile why certain areas below the mean surface rise more than others as a result of the static loading. Even using vertical magnification ofthe Talysurf profile of x 104, it was difficult to detect rises in the deep valleys at loadings of 0.1~ P/M < 0.5 with the present instrumentation. The shallower valleys did register rises of approximately 0.1 to 0.3 pm for the softer materials such as tin and aIuminium, but the deeper valleys, i.e. those 3 to 5 pm deep did not exhibit any detectable rise. CONCLUSIONS
Deformation studies of an idealized asperity show that material from the apex is displaced to the shoulders. At a specific loading, dependent upon the apex angle, material from the asperity base begins to move outwards, and thereafter plane strain slip-line theory of infinite wedge compression does not apply. The neighbouring valleys then begin to fill, a process which resembles the rise of the bottoms of shallow valleys of the multi-asperity model. For deformation ratios exceeding unity the material around the base of the single asperity moves laterally and rises upward, the magnitude of the effects decreasing to zero at about three times the base diameter from the centre of the asperity. This movement is followed by the high ffow pressures (exceeding the Vickers hardness for the material) being exhibited by the flattened part of the asperity. Existing plasticity theories fail to explain this phenomenon. The persistence of the asperity at very high pressures is due to an interaction of the asperity base with the surrounding material. The multi-asperity model experiments indicate that at high loads (P/M- 1.0) there was a tendency for the bottoms of all valleys to rise. However, the deep valleys rose very little compared with the shallower valleys. At light loads the deep valleys did not register any change. The rise of the shallower valleys was probably due to an overspill of the flattened peaks. ACKNOWLEDGEMENTS
The authors thank Dr. T. R. Thomas of Teesside Polytechnic for advice with this project, and the Science Research Council for financial support. The specimens were supplied by Messrs. Johnson Matthey Limited. NOMENCLATURE
d D D, M P
diameter of the flattened part of asperity, original diameter of single asperity model, diameter of bead-blasted area defining the extent of the multi-asperity indentation hardness of the specimen material, nominal applied pressure,
P,
flowpressure[W/(td:)],
Y
deformation
lVeur, 20 (1972)
ratio for a single asperity (=-d/D),
model,
400
W Y # B (5
A. H. LIPPAL.
S I). PROBER-1
applied load, yield stress. apex angle of the asperity, projected apex angle of the flattened asperity. standard deviation of surface roughness..
REFERENCES 1 J. B. P. Williamson, Topography of solid surfaces, Proc. Symp. Jnterdisciplinary Approach to Friction und Wear, NASA, Washington, 1968, 88-142. 2 A. H. Uppal and S. D. Probert, Topographic changes resulting from surfaces being in contact under static and dynamic loads, M/cur, 16 (1970) 261-271. 3 T. R. Thomas, A. H. Uppal and S. D. Probert, Hardness of rough surfaces, Nature (Phys. Sci.). 229 (3) (197 1) 86-87. 4 F. P. Bowden and D. Tabor. Friction and Lubrication a/‘Solids, Part 1. Oxford Univ. Press, London, 1954, pp. 19920. 5 7. Tsukizoe and T. Hisakado, On the mechanism ofcontact between solid surfaces; Part 2, Truns. Am. Sac. Mech. Engrs., 90F (1968) 81.--88. 6 R. Hill, The mathernarical theory ofplasticity, Oxford Univ. Press, London, 19.50, p. 215. 7 J. B. P. Williamson, J. Pullen and R. T. Hunt, Plastic contact of surfaces, Eurndy Res. Rep. Nos. 78 and 79, 1970. 8 A. Mallock, Hardness, Nature, 117 (2034) (1926) 117. 9 G. H. H. Williams and H. O’Neill, The Mallock cone hardness test and its relation to indentation mcthods, J. Iron Sreel Inst., 189 (1958) 29-37. IO J. B. P. Wiil~mson and R. T. Hunt, Relocation profi~om~try. f. Sci. Ittstrum., Ser. 7, I (1968) 749-752. 11 D. Tabor, The ~nrdness qf Metals, Oxford Univ. Press, London, 1951, pp. 64-65. I2 G. W. Rowe and J. A. Greenwood, Deformation of surface asperities during bulk plastic flow. J. Appl. Ph_vs., 36 (2) (1965) 667-668. 13 E. J. Abbot and F. A. Firestone, Specifying surface quality, Mech. Eng., 55 (1933) 569. M;‘rrrr..20
{ 1972)