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Initial wear rates of soft metallic films
Wear, 54 (1979) 391 - 400 @ Elsevier Sequoia S.A., Lausanne
391 - Printed
in the Netherlands
INITIAL WEAR RATES OF SOFT METALLIC FILMS
M. G. EL-SHERBINY
and F. B, SALEM
deportment of ~eehanical Design and Production Cairo University, Cairo (Egypt) (Received
June 9, 1978; in final form November
engineering, Fuculty of engineering, 24,1978)
Summa~ A theoretical expression was derived for the initial wear rates of hard conical asperities ploughing a soft metallic film. The theory yields a wear equation similar to the well-known existing empirical formula, although the new wear coefficient K appears to be dominated by the surface topo~aphy of the system rather than by the material properties. The initial wear rates of the film appear to be determined by the system rather than by the material. The general characteristics of the model are confirmed by experimental results for the initial wear rates of ion-plated tin and lead films.
1. Introduction Surface coatings have been used extensively in sliding systems. Low shear strength (soft) coatings such as tin, lead and indium are recognized solid lubricants [ 1 - 41. Gold films are useful in sliding at high temperatures and in vacuum conditions [ 5,6] . When two metal parts, one of which is coated, are subjected to sliding under relatively mild conditions such that no gross galling occurs, the wear process of the surface film is usually characterized by high initial wear [‘7, 8 ] . The wear rate decreases to some steady value when the film thickness is reduced to the thin or ultrathin range [ 71. With thick films it is considered that the wear mechanism is essentially a microcutting process of the soft surface film. As the film thickness decreases many more contacts between the asperities and the hard substrate occur so that the mi~rocutt~g failures are reduced and a more moderate fatigue and possibly abrasive wear mechanism occurs at the substrate contacts. This has been revealed by scanning electron microscope examination of wear scars and tracks. Figure 1 shows the scratches (microtracks) produced during friction testing of an ion-plated tin film 6 pm thick. It is considered that the reliability of coated component depends on the initial wear rates. This paper describes a mathematical model for the prediction of the initial wear rates of surface films. The results are compared with exper-
392
Fig. 1. Scanning electron micrograph 6 pm thick.
showing
initial wear tracks in an ion-plated
tin film
imental values obtained for ion-plated tin and lead films sliding against an EN-31 steel rider. The experimental method involved repeat pass unidirectional sliding at low loads. The experimental results are in reasonable agreement with the predictions of the mathematical model. Thus the model is of interest in a number of engineering applications where solid surface films are used.
2. Theoretical It is generally agreed that the contact of two rough surfaces can be adequately represented by the contact of one rough surface, which has the superimposed roughness of the two basic surfaces, with a perfectly smooth surface [ 91. These arguments have been extended to coated surfaces [ 10 ] on the basis that the unique uniformity of the ion-plated coating does not alter the surface roughness. The present analysis assumes that the surface asperities are conical with rounded tips as shown in Fig. 2, though any other surface asperity shape can be analysed. Following an earlier method of analysis [lo] , a direct asperity penetration model was developed. At any instant the normal load P will be shared between the film and the substrate according to P=AfYc
+A,Y,
(1)
If it is assumed that both the asperity and the substrate metals are plastically deforming, the area of contact of the individual asperity is given by A, = rrhfld where h = 2 for plastic deformations asperities bedded into the film is
(2) [9]. The percentage
of surface
393
M.
U
222
.e , en
7
(b) Fig. 2. The contact surfaces: (a) real surfaces; (b) idealized surfaces. d+t
PV > 4 = $ N-q d2J
(3)
d
whilst the percentage of surface asperities penetrating the film and in contact with the substrate is p(Z>d+t)=J-$(Z)dZ
(4)
d+t
Although it is generally accepted that the distribution of surface asperities is Gaussian, it has been shown [lo] that an exponential distribution of the form (S = Z/o) = eCs
(5)
is more convenient as it provides an analytical solution in closed form and is a reasonable approximation to the upper decile of the distribution for many engineering components. Thus the area of contact with the film is d+t
Af = 2nflN $
(2 -d)@(Z)
dZ
(6)
d
and the area of contact with the substrate is
A, = 2n/3N f d+t
(2 -d
-
t)@(Z) dZ
(7)
394
Using the dimensionless
parameters
h = d/a
s = z/a and integrating
T = t/o
eqns. (6) and (7) yields
Af = %rpa2N e--h (1 - eeT(l A,
+ T)}
(8)
= 2nposN eeheeT
(9) The value of Y, will lie between Y, for negligible film thickness (t -+ 0) and Yr for a very thick film (t -+ -). Assume that the form of Y, can be presented by the exponential function Y, = Yr + (Ys - Yr) e-C’
(10)
where t is the film thickness and c is a constant defining the rate of transition from Y, to Yf. Substituting eqns. (8) - (10) into eqn. (1) and remembering that N = na2n yields P= n2pa2a2n eph[YS emT + Y,{l -emT(l + (Y, - Yf) eecf{l
-eeeT(l
+ T)} +
+ T)}]
(11) The individual asperities are assumed to plough the film by a microcutting process. The cross-sectional area x of the metal removed is defined by the shape and depth of penetration of the asperity. For a penetrating asperity (2 2 d + t) A
(Z-d)2
=
-((Z-d-t)2
f
(12)
tan 8
and A S
=(Z-d-t)2 -___tan 0
(13)
whilst the cross-sectional (@+t>Z>d)is A
=
f
V--d)2 tane
area of metal removed
by a bedded-in
A, = 0
asperity
(14)
Thus the total cross-sectional area of metal removed from the film owing to the ploughing action of the whole population of surface asperities is ((2 -d)2-
(2 -d
d+t +
J
(z -- d)2c#@) dz
d
and that of metal removed
- t)2}$(Z)
1
from the substrate
(2 -- d -
t)” $(Z) d2
dZ +
(15) is
(16)
395
An overlap factor (Y((Y< 1) is introduced to allow for the random distribution of surface asperities. Using dimensionless parameters and integrating eqns. (15) and (16) yields A,
au32(1
7ra2n
= -
aa3
- eeT) eeh
(17)
2e++T)
tan e Using the dimensionless parameter Y = Yf/YS and substituting eqn. (11) into eqns. (17) and (18) gives &
= ~
(1 -ePT)P
2aa
n/3 tan0
for eWh from
YS[{l-Y(l+T)}e-T+Y+(l-Y)e-CuT{l-ee-T(l+T)}]
(19) epTP 2CIcJ A, = _ ~0 tan 8 Y,[{l- Y(l + T)}eeT + Y + (I-- Y)e-C”T{l --+(I
Thus the total wear volume removed is
+T)}j
from the film within a pass of length L
v, = LXf 2Laa =_ n/3 tane
(1 - eCT)P
Y,[{l -Y(l+T)}ePT
+Y+(l-Y)e-cuT{l-ee-T(l+T)}] (21)
and the wear volume of the substrate v,
2Lao = @tan8
during the same sliding distance
is
eeTP Y,[{l-Y(l+T)}e-T
+Y+(l-Y)e-cuT{l-e-T(l+~))]
(22) Experimental determination of the effective hardness of the multilayer component (Fig. 3) showed that Y, = Yt for reasonably thick films; therefore eqns. (21) and (22) can be rewritten as v,
2LcJo = 77ptan e
v,
2Lolo = ~0 tan e
Further,
(1 - epT)P
Y,[{l- Y(1 + T)}ePT + Y]
(23)
ewTP
Y,[{l- Y(l + T)}eeT + Y]
(24)
when t = 0.0
v, = 0.0
(25)
396
film
ilm
I
1
0
2
1
Film
Fig. 3. Experimental (P = 5 N).
1
I
4
6
a
10
12
14
,
1 _m-
Thickness
values of the effective hardness H, of the multilayer component
When t + m 2ao Vf
= ~
77ptan 19
LP _=KL$
v, = 0.0
(26)
Yf
Thus eqns. (23) and (24) reduce to the expected solution for the extreme values of t.
3. Experimental A modified Leitz miniload microhardness tester was used for wear testing the ion-plated films. The basic modification to the tester was an electric drive coupled to the front micrometer. A d.c. motor with a speed of 1 rev mine1 was used; therefore the linear speed of the sliding table was 0.005 cm min-l. The coated specimen (a flat copper test specimen of dimensions 4 cm X 4 cm) was mounted rigidly on the sliding table of the tester. The spherical indenter, 2.36 mm in diameter, was made of EN-31 steel. The test specimens were first ground to an average surface finish of 0.133 I.tmstandard deviation followed by polishing with emery paper and ion etching to an average surface finish of u = 0.108 pm. The specimens were then coated in a conventional ion-plating apparatus. The ion-plating technique was particularly selected for its extremely good adhesion [ll] which eliminates other failure mechanisms (e.g. film plucking, detachment and peeling) which might affect the experimental results. The wear tests consisted of five unidirectional straight passes each of 6 mm length for a total sliding distance L of 30 mm. Wear was determined by both weight loss and the measurement of wear volume from the track width and depth.
397
A surface texture assessment was made for each specimen after each processing step. The surface roughness parameters (c.l.a., u, /3, nl, n2 and 0) were computed from the ordinates of the digitized surface trace, and the film thickness was measured on the sectioned test specimen. Table 1 shows the mean values of surface roughness parameters obtained from the 30 test specimens used. TABLE 1 The average surface roughness parameters of test specimens Surface
P (Pm)
(T (Pm)
e (rad)
n (mme2)
Ground Polished/etched Ion plated Rider
10.52 16.26 15.75 10.67
0.133 0.108 0.124 0.159
0.11 0.101 0.098 0.131
1.674 1.581 1.705 1.349
x x x x
lo4 104 104 104
4. Results and discussion Equations (21) - (24) reduce to the expected solutions (eqns. (25) and (26)) at extreme values of t. The general characteristics of these equations can be summarized as follows. (1) The overlap factor (Yis simply a scaling factor for the coordinate axis V and is expected to approach unity as the area of contact reduces to a point contact. (2) The total wear volume as t + 0 is the substrate wear volume only and is defined by both the substrate mean yield pressure Y, and the wear coefficient K = 2ao/np tan 0. (3) The total wear volume at t -+ 03 is the film wear volume only and is defined by both the film mean yield pressure Yr and the wear coefficient K. (4) The wear coefficient K appears to be a constant depending on surface texture parameters and independent of the mechanical properties. (5) The rate and form of variation of V with increasing values of t depend on the formulation of Y, (in this work the value of the constant c). Therefore the wear volume is a system property depending on the mechanical properties of the two metals involved (film and substrate). Figure 4 shows the total weight loss as predicted by the theoretical model for different tin films on copper substrates compared with the experimental weight loss of each specimen. The weight losses of both film and substrate calculated from eqns. (23) and (24) are plotted on the same graph for comparison with the experimental values obtained from measurements of track width and depth. Similar theoretical and experimental results were also obtained for lead films on copper substrates and are shown in Fig. 5.
398
11
I 2
, 4
I
1
I
6
8 Film
10
12
14
I 16
18
(fim
lhicknc$s
FIG (4)
Fig. 4. Comparison between the theoretical and experimental results of ion-plated tin films (P = 5 N). Material
Theoretical
Experimental
Measured
Film (Sn) Substrate (Cu) Total
--.._-.-
0 l
Volume Volume Weight
0
In both cases reasonable agreement is shown for the total weight loss and the general trendof the theory is justified. The discrepancy in the results is due to the simplified derivation of the area of contact from the normal approach of the individual asperities and the neglect of the change in the number of asperities bedded into the film as a result of asperity deformation under load.
5. Conclusion A simplified theoretical model for the initial wear rates of surface coatings has been developed. The general trend of the theoretical predictions shows reasonable agreement with experimental results obtained for tin and lead films of various thicknesses. According to this particular model the wear
399
2
L
6
10
8 Film
12
14
16
la
1
Am
thickness
Fig. 5. Comparison between theoretical and experimental results of ion-plated lead films (P = 5 N). Material
Theoretical
Experimental
Measured
Film (Pb) Substrate (Cu) Total
-.-
0
l
Volume Volume Weight
.. -
0
coefficient K appears to be dependent on the surface texture of the system rather than on material properties. The total wear volume of a multilayer system is dependent on the mechanical properties of the system (Y = Yf /Y,).
Nomenclature A
A ii K L t
z
area of contact cross-sectional area of asperity track constant defining effective hardness of the multilayer component separation between the mating pair of components wear coefficient pass length weight loss total number of asperities within the contact area density of surface asperities per unit area normal load
400
V
Y
z
film thickness wear volume mean yield pressure of the material asperity height overlapping factor average radius of asperities normal approach line density of surface apserities average slope of surface asperities density standard deviation of surface roughness asperity height distribution
Pp 23 P
;
Subscripts f film S substrate C film/substrate combination a asperity
References 1 F. Bowden and D. Tabor, Commun. 145, Australia Council for Scientific and Industrial Research, 1942, p. 39. 2 F. Bowden and D. Tabor, J. Appl. Phys., 14 (1943) 141. 3 Y. Tsuya and R. Takagi, Wear, 7 (1964) 131. 4 R. Burton and J. Russell, ASLE Trans., 8 (1965) 227. 5 M. Antler, ASLE Trans., 11 (1968) 248. 6 T. Spalvins and D. Buckley, J. Vacuum Sci. Technol., 3 (1966) 107. 7 M. El-Sherbiny and J. Hailing, Mech. Eng. Rep. USME/T/43/75, Univ. Salford; Wear, 45 (1977) 211. 8 E. Rabinowics, ASLE Trans., 10 (1967) 1. 9 J. Halling and K. Nuri, IUTAM Symp. on Contact of Deformable Bodies, Univ. Delft Press, Delft, 1976. 10 J. Halling and M. El-Sherbiny, Mech. Eng. Rep. USME/T/42/75, Univ. Salford; presented also in Tribology Convention, Swansea, 1978, Inst. Mech. Eng., London, 1978. 11 D. Teer, Tribol. Int., 8 (1975) 247.
391 - Printed
in the Netherlands
INITIAL WEAR RATES OF SOFT METALLIC FILMS
M. G. EL-SHERBINY
and F. B, SALEM
deportment of ~eehanical Design and Production Cairo University, Cairo (Egypt) (Received
June 9, 1978; in final form November
engineering, Fuculty of engineering, 24,1978)
Summa~ A theoretical expression was derived for the initial wear rates of hard conical asperities ploughing a soft metallic film. The theory yields a wear equation similar to the well-known existing empirical formula, although the new wear coefficient K appears to be dominated by the surface topo~aphy of the system rather than by the material properties. The initial wear rates of the film appear to be determined by the system rather than by the material. The general characteristics of the model are confirmed by experimental results for the initial wear rates of ion-plated tin and lead films.
1. Introduction Surface coatings have been used extensively in sliding systems. Low shear strength (soft) coatings such as tin, lead and indium are recognized solid lubricants [ 1 - 41. Gold films are useful in sliding at high temperatures and in vacuum conditions [ 5,6] . When two metal parts, one of which is coated, are subjected to sliding under relatively mild conditions such that no gross galling occurs, the wear process of the surface film is usually characterized by high initial wear [‘7, 8 ] . The wear rate decreases to some steady value when the film thickness is reduced to the thin or ultrathin range [ 71. With thick films it is considered that the wear mechanism is essentially a microcutting process of the soft surface film. As the film thickness decreases many more contacts between the asperities and the hard substrate occur so that the mi~rocutt~g failures are reduced and a more moderate fatigue and possibly abrasive wear mechanism occurs at the substrate contacts. This has been revealed by scanning electron microscope examination of wear scars and tracks. Figure 1 shows the scratches (microtracks) produced during friction testing of an ion-plated tin film 6 pm thick. It is considered that the reliability of coated component depends on the initial wear rates. This paper describes a mathematical model for the prediction of the initial wear rates of surface films. The results are compared with exper-
392
Fig. 1. Scanning electron micrograph 6 pm thick.
showing
initial wear tracks in an ion-plated
tin film
imental values obtained for ion-plated tin and lead films sliding against an EN-31 steel rider. The experimental method involved repeat pass unidirectional sliding at low loads. The experimental results are in reasonable agreement with the predictions of the mathematical model. Thus the model is of interest in a number of engineering applications where solid surface films are used.
2. Theoretical It is generally agreed that the contact of two rough surfaces can be adequately represented by the contact of one rough surface, which has the superimposed roughness of the two basic surfaces, with a perfectly smooth surface [ 91. These arguments have been extended to coated surfaces [ 10 ] on the basis that the unique uniformity of the ion-plated coating does not alter the surface roughness. The present analysis assumes that the surface asperities are conical with rounded tips as shown in Fig. 2, though any other surface asperity shape can be analysed. Following an earlier method of analysis [lo] , a direct asperity penetration model was developed. At any instant the normal load P will be shared between the film and the substrate according to P=AfYc
+A,Y,
(1)
If it is assumed that both the asperity and the substrate metals are plastically deforming, the area of contact of the individual asperity is given by A, = rrhfld where h = 2 for plastic deformations asperities bedded into the film is
(2) [9]. The percentage
of surface
393
M.
U
222
.e , en
7
(b) Fig. 2. The contact surfaces: (a) real surfaces; (b) idealized surfaces. d+t
PV > 4 = $ N-q d2J
(3)
d
whilst the percentage of surface asperities penetrating the film and in contact with the substrate is p(Z>d+t)=J-$(Z)dZ
(4)
d+t
Although it is generally accepted that the distribution of surface asperities is Gaussian, it has been shown [lo] that an exponential distribution of the form (S = Z/o) = eCs
(5)
is more convenient as it provides an analytical solution in closed form and is a reasonable approximation to the upper decile of the distribution for many engineering components. Thus the area of contact with the film is d+t
Af = 2nflN $
(2 -d)@(Z)
dZ
(6)
d
and the area of contact with the substrate is
A, = 2n/3N f d+t
(2 -d
-
t)@(Z) dZ
(7)
394
Using the dimensionless
parameters
h = d/a
s = z/a and integrating
T = t/o
eqns. (6) and (7) yields
Af = %rpa2N e--h (1 - eeT(l A,
+ T)}
(8)
= 2nposN eeheeT
(9) The value of Y, will lie between Y, for negligible film thickness (t -+ 0) and Yr for a very thick film (t -+ -). Assume that the form of Y, can be presented by the exponential function Y, = Yr + (Ys - Yr) e-C’
(10)
where t is the film thickness and c is a constant defining the rate of transition from Y, to Yf. Substituting eqns. (8) - (10) into eqn. (1) and remembering that N = na2n yields P= n2pa2a2n eph[YS emT + Y,{l -emT(l + (Y, - Yf) eecf{l
-eeeT(l
+ T)} +
+ T)}]
(11) The individual asperities are assumed to plough the film by a microcutting process. The cross-sectional area x of the metal removed is defined by the shape and depth of penetration of the asperity. For a penetrating asperity (2 2 d + t) A
(Z-d)2
=
-((Z-d-t)2
f
(12)
tan 8
and A S
=(Z-d-t)2 -___tan 0
(13)
whilst the cross-sectional (@+t>Z>d)is A
=
f
V--d)2 tane
area of metal removed
by a bedded-in
A, = 0
asperity
(14)
Thus the total cross-sectional area of metal removed from the film owing to the ploughing action of the whole population of surface asperities is ((2 -d)2-
(2 -d
d+t +
J
(z -- d)2c#@) dz
d
and that of metal removed
- t)2}$(Z)
1
from the substrate
(2 -- d -
t)” $(Z) d2
dZ +
(15) is
(16)
395
An overlap factor (Y((Y< 1) is introduced to allow for the random distribution of surface asperities. Using dimensionless parameters and integrating eqns. (15) and (16) yields A,
au32(1
7ra2n
= -
aa3
- eeT) eeh
(17)
2e++T)
tan e Using the dimensionless parameter Y = Yf/YS and substituting eqn. (11) into eqns. (17) and (18) gives &
= ~
(1 -ePT)P
2aa
n/3 tan0
for eWh from
YS[{l-Y(l+T)}e-T+Y+(l-Y)e-CuT{l-ee-T(l+T)}]
(19) epTP 2CIcJ A, = _ ~0 tan 8 Y,[{l- Y(l + T)}eeT + Y + (I-- Y)e-C”T{l --+(I
Thus the total wear volume removed is
+T)}j
from the film within a pass of length L
v, = LXf 2Laa =_ n/3 tane
(1 - eCT)P
Y,[{l -Y(l+T)}ePT
+Y+(l-Y)e-cuT{l-ee-T(l+T)}] (21)
and the wear volume of the substrate v,
2Lao = @tan8
during the same sliding distance
is
eeTP Y,[{l-Y(l+T)}e-T
+Y+(l-Y)e-cuT{l-e-T(l+~))]
(22) Experimental determination of the effective hardness of the multilayer component (Fig. 3) showed that Y, = Yt for reasonably thick films; therefore eqns. (21) and (22) can be rewritten as v,
2LcJo = 77ptan e
v,
2Lolo = ~0 tan e
Further,
(1 - epT)P
Y,[{l- Y(1 + T)}ePT + Y]
(23)
ewTP
Y,[{l- Y(l + T)}eeT + Y]
(24)
when t = 0.0
v, = 0.0
(25)
396
film
ilm
I
1
0
2
1
Film
Fig. 3. Experimental (P = 5 N).
1
I
4
6
a
10
12
14
,
1 _m-
Thickness
values of the effective hardness H, of the multilayer component
When t + m 2ao Vf
= ~
77ptan 19
LP _=KL$
v, = 0.0
(26)
Yf
Thus eqns. (23) and (24) reduce to the expected solution for the extreme values of t.
3. Experimental A modified Leitz miniload microhardness tester was used for wear testing the ion-plated films. The basic modification to the tester was an electric drive coupled to the front micrometer. A d.c. motor with a speed of 1 rev mine1 was used; therefore the linear speed of the sliding table was 0.005 cm min-l. The coated specimen (a flat copper test specimen of dimensions 4 cm X 4 cm) was mounted rigidly on the sliding table of the tester. The spherical indenter, 2.36 mm in diameter, was made of EN-31 steel. The test specimens were first ground to an average surface finish of 0.133 I.tmstandard deviation followed by polishing with emery paper and ion etching to an average surface finish of u = 0.108 pm. The specimens were then coated in a conventional ion-plating apparatus. The ion-plating technique was particularly selected for its extremely good adhesion [ll] which eliminates other failure mechanisms (e.g. film plucking, detachment and peeling) which might affect the experimental results. The wear tests consisted of five unidirectional straight passes each of 6 mm length for a total sliding distance L of 30 mm. Wear was determined by both weight loss and the measurement of wear volume from the track width and depth.
397
A surface texture assessment was made for each specimen after each processing step. The surface roughness parameters (c.l.a., u, /3, nl, n2 and 0) were computed from the ordinates of the digitized surface trace, and the film thickness was measured on the sectioned test specimen. Table 1 shows the mean values of surface roughness parameters obtained from the 30 test specimens used. TABLE 1 The average surface roughness parameters of test specimens Surface
P (Pm)
(T (Pm)
e (rad)
n (mme2)
Ground Polished/etched Ion plated Rider
10.52 16.26 15.75 10.67
0.133 0.108 0.124 0.159
0.11 0.101 0.098 0.131
1.674 1.581 1.705 1.349
x x x x
lo4 104 104 104
4. Results and discussion Equations (21) - (24) reduce to the expected solutions (eqns. (25) and (26)) at extreme values of t. The general characteristics of these equations can be summarized as follows. (1) The overlap factor (Yis simply a scaling factor for the coordinate axis V and is expected to approach unity as the area of contact reduces to a point contact. (2) The total wear volume as t + 0 is the substrate wear volume only and is defined by both the substrate mean yield pressure Y, and the wear coefficient K = 2ao/np tan 0. (3) The total wear volume at t -+ 03 is the film wear volume only and is defined by both the film mean yield pressure Yr and the wear coefficient K. (4) The wear coefficient K appears to be a constant depending on surface texture parameters and independent of the mechanical properties. (5) The rate and form of variation of V with increasing values of t depend on the formulation of Y, (in this work the value of the constant c). Therefore the wear volume is a system property depending on the mechanical properties of the two metals involved (film and substrate). Figure 4 shows the total weight loss as predicted by the theoretical model for different tin films on copper substrates compared with the experimental weight loss of each specimen. The weight losses of both film and substrate calculated from eqns. (23) and (24) are plotted on the same graph for comparison with the experimental values obtained from measurements of track width and depth. Similar theoretical and experimental results were also obtained for lead films on copper substrates and are shown in Fig. 5.
398
11
I 2
, 4
I
1
I
6
8 Film
10
12
14
I 16
18
(fim
lhicknc$s
FIG (4)
Fig. 4. Comparison between the theoretical and experimental results of ion-plated tin films (P = 5 N). Material
Theoretical
Experimental
Measured
Film (Sn) Substrate (Cu) Total
--.._-.-
0 l
Volume Volume Weight
0
In both cases reasonable agreement is shown for the total weight loss and the general trendof the theory is justified. The discrepancy in the results is due to the simplified derivation of the area of contact from the normal approach of the individual asperities and the neglect of the change in the number of asperities bedded into the film as a result of asperity deformation under load.
5. Conclusion A simplified theoretical model for the initial wear rates of surface coatings has been developed. The general trend of the theoretical predictions shows reasonable agreement with experimental results obtained for tin and lead films of various thicknesses. According to this particular model the wear
399
2
L
6
10
8 Film
12
14
16
la
1
Am
thickness
Fig. 5. Comparison between theoretical and experimental results of ion-plated lead films (P = 5 N). Material
Theoretical
Experimental
Measured
Film (Pb) Substrate (Cu) Total
-.-
0
l
Volume Volume Weight
.. -
0
coefficient K appears to be dependent on the surface texture of the system rather than on material properties. The total wear volume of a multilayer system is dependent on the mechanical properties of the system (Y = Yf /Y,).
Nomenclature A
A ii K L t
z
area of contact cross-sectional area of asperity track constant defining effective hardness of the multilayer component separation between the mating pair of components wear coefficient pass length weight loss total number of asperities within the contact area density of surface asperities per unit area normal load
400
V
Y
z
film thickness wear volume mean yield pressure of the material asperity height overlapping factor average radius of asperities normal approach line density of surface apserities average slope of surface asperities density standard deviation of surface roughness asperity height distribution
Pp 23 P
;
Subscripts f film S substrate C film/substrate combination a asperity
References 1 F. Bowden and D. Tabor, Commun. 145, Australia Council for Scientific and Industrial Research, 1942, p. 39. 2 F. Bowden and D. Tabor, J. Appl. Phys., 14 (1943) 141. 3 Y. Tsuya and R. Takagi, Wear, 7 (1964) 131. 4 R. Burton and J. Russell, ASLE Trans., 8 (1965) 227. 5 M. Antler, ASLE Trans., 11 (1968) 248. 6 T. Spalvins and D. Buckley, J. Vacuum Sci. Technol., 3 (1966) 107. 7 M. El-Sherbiny and J. Hailing, Mech. Eng. Rep. USME/T/43/75, Univ. Salford; Wear, 45 (1977) 211. 8 E. Rabinowics, ASLE Trans., 10 (1967) 1. 9 J. Halling and K. Nuri, IUTAM Symp. on Contact of Deformable Bodies, Univ. Delft Press, Delft, 1976. 10 J. Halling and M. El-Sherbiny, Mech. Eng. Rep. USME/T/42/75, Univ. Salford; presented also in Tribology Convention, Swansea, 1978, Inst. Mech. Eng., London, 1978. 11 D. Teer, Tribol. Int., 8 (1975) 247.