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A model for the friction of multiphase materials in abrasion
Tribology International Vol. 29, No. 6, pp. W-475,
ELSEVIER SCIENCE:
1996 Copyright @ 1996 Ekevier Science Ltd Printed in Great Britain. All rights reserved 0301-679X/%/$15.00 +O.OO
0301-679X(95)00104-2
A model for the friction of multiphase materials in abrasion N. Axhn*,
I. M. Hutchingsf
and S. Jacobson*
A model is presented for the sliding friction of multiphase materials in abrasion. The friction is described in terms of the load distribution between the phases. Different load distribution modes are used with Amontons’ first law of friction to derive both the friction force and the coefficient of friction as functions of the area fractions of the phases, their individual coefficients of friction and their wear resistance. It is shown that the coefficient of friction of a multiphase material should depend on the load distribution mode and that the upper and lower limits for the coefficient of friction expected from composites or multiphase materials can be identified. For most pressure distribution modes, the friction depends on the wear resistance of the phases. The model is compared with results from abrasion tests on a silicon carbide reinforced aluminium alloy (AlSi7Mg) over a wide range of loads and with different fixed abrasive particles. The experimental results are described and interpreted in terms of the model. Copyright 0 1996 Elsevier Science Ltd Keywords: phase
friction, material
abrasion,
composite,
meta/ matrix
Introduction Materials used in situations where good wear and friction properties are desired, are very often multiphase. Traditional multiphase materials often used in tribological applications mclude tool steels, cast irons and cemented carbides. Composites form a sub-group of multiphase materials, and can be described as artificially manufactured multiphase materials containing phases from different material groups. The competition from new composites increases as new manufacturing techniques come into use and today a variety of light metal and polymer matrix composites are
* Department of Technology, Materials Science Division, Uppsala University, 60x 534, S-751 21 Uppsala, Sweden f Department of Materiuls Science and Metallurgy, University of Cambridge, Pembroke Street, CB2 3QZ, UK Received 9 May 1995; revtied 3 October 1995; accepted 9 October 1995
Tribology
composite,
mdti-
availablel. The understanding of the wear and friction properties of multiphase materials is thus an important topic in tribology. The wear and friction behaviour of multiphase materials is complex. Not only the tribological behaviour of the constituents of a multiphase material, but also the extension and distribution of the phases, as well as the inter-phase bonding, are important2-4. The kinetic friction force is the tangential force necessary to slide one body over the surface of another. The friction force is sometimes described as the sum of two contributions: one caused by surface asperities deforming the counter surface and the other due to the shearing of adhesive contacts. This view was largely developed by Bowden and Tabor in their work on friction in the 1950~~. Since then numerous papers have been published on the origin of friction in terms of the interaction between surface asperities in sliding contact. An overview has been provided by LarsenInternational
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A large number of papers have also been published on the frictional properties of composites8-14. Many ,deal with polymer matrix composites8-lo, but also carbon fibre reinforced glass matricesi and light metal matrix composites with ceramic reinforcements have been studiedlz-14. The number of works on the friction properties of ceramic matrix composites is relatively smalps. The sliding friction of composites has been more systematically studied than friction associated with abrasion. Nevertheless, friction in abrasion is an important feature, e.g. in grinding and for applications such as brake disc materialsi6. There have been few fundamental works published on the friction of multiphase materials during abrasion. Zhang et al. l2 reported an increased friction coefficient caused by alumina and silicon carbide particulate reinforcements in a 6061 aluminium matrix as measured in single-point scratch tests. They explain the increased friction by an additional particle fracture contribution to the adhesion and ploughing components. Amontons’ first law of friction implies that the friction force should be proportional to the normal load. This statement has been shown to be valid for many material combinations under both unlubricated and lubricated sliding, It has also been found to be a good approximation for steady-state abrasion1’,14. For a multiphase material the friction force can therefore be expected to be related to the load on each phase, i.e. the distribution of the load between the phases. Recent work by Axen, Jacobson and Lundberg has shown how the load carried by each phase in a multiphase material subjected to abrasion depends on the wear resistance and area fractions of the phases18-20. In that work the load on each phase was described in terms of load (or pressure) distribution modes. Equal pressure (EP), equal wear (EW) and intermediate (I) pressure distribution modes were defined. It was shown that the EP and EW modes describe load distribution limits above or below which, respectively, the pressure distribution cannot fall. The types of surface interactions that fulfil the EP and EW modes are described in Reference 18. In fact, all possible surface interactions correspond to a certain pressure distribution (necessarily falling between EW and EP) between the phases. The I mode results from intermediate pressure distributionszo. This paper presents a model for the abrasive friction of a multiphase material. The model is based on Amontons’ law and the distribution of the load between the phases. The model is compared with experimental data from a SiC particle reinforced aluminium alloy abraded by fixed SiC and flint abrasives under various loads.
Theory It is assumed that the tangential friction force F is proportional to the applied normal load L: F= pL 468
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This implies that independent of L.
the coefficient
of friction
F is
As a multiphase material is slid over a counter-surface, each phase i exposed at the sliding interface exhibits its own coefficient of friction t~,~in contact with the counter-material and each phase carries a load Li. The friction force on each phase Fi is then: Fi = FiLi from equation (1). The total friction force F is the sum of the contributions from each phase, for ‘a total of N different phases: F= i
FiLi
i=l
To derive the total friction force for a multiphase material, the friction coefficient of each phase against the counter-material and the load carried by each phase, must be known. It must also be assumed that the phases retain their individual friction properties when part of the composite, and that the area fractions remain constant. The friction coefficient is of course material pair specific and must be measured individually for each case. The loads Li can be derived from the pressure distribution mode model presented in References 18-20. This model is based on Archard’s equation (i.e on the assumption that the volumetric wear rate is proportional to the load) and on two pressure distribution modes describing how much of the total applied load each phase carries: equal normal pressures on the phases (EP) and equal linear wear rates of the phases (EW). It is assumed in the model that the phases do not influence the specific wear resistance or coefficient of friction of each other and that the area fractions remain known. For example one phase must not become smeared out over the other to an unpredictable extent. From the pressure distribution mode model it follows that the load Li carried by phase i with area fraction cq is given by: Li ZZLOli in EP mode and:
n=l
in EW mode, where the specific wear resistance of each phase is denoted by ai. For the intermediate (I) mode the load on each phase can be expressed as:
where 0 represents the proportion of EW mode pressure distribution. f3 = 1 for pure EW and 0 = 0 for pure EP mode. Equation (6) provides a mathematical formalism for intermediate load distributions and includes EP and EW as special cases. However, since the EP and EW modes represent the fundamental
(11 29 Number 6 1996
Friction
assumptions of the model they will be treated separately below. C$)mgbining equation Ives:
(3) with equations (4), (5) and
N
f’Ep = x
PiLai,
(7)
i=l N fli FEW=
2 i=l
PiL
N Ix n=l
anfin
ai
and
for the friction forces in the EP, EW and I modes, respectively. The coefficient of friction is derived by dividing the appropriate friction force from equations (7), (8) or (9) by the total load L. Thus:
materials:
N. Ax&
er a/.
Materials and test procedures Materials
The metal matrix composites studied in this work were based on a hypoeutectic aluminium-silicon alloy (AlSi7Mg; 7% Si, 0.3% Mg, 0.18% Fe, 0.05% Cu, 0.15% Ti) reinforced with 0, 10 or 30 vol. % of 20 pm silicon carbide particles (hardness 2500 HV). The particle composites were fabricated by Sintef Produktionsteknikk, Norway by a rheocasting technique. A typical example of the structure is shown in Fig 1. The distribution of the particles was uniform, although some isolated pores were observed. A pure sintered polycrystalline silicon carbide (>99%, solid state sintered, 2500 HV) was also tested. The composites were heat treated to two different hardnesses, referred to as annealed and quenched. All specimens were first soft annealed at 4OO’C for 1 h and slowly furnace cooled to room temperature (annealed). Some specimens were then hardened by solution treatment at 52O’C for 20 min followed by rapid quenching in turbulent cool water, followed by ageing at 140°C for two hours (quenched). The hardnesses of the composites and the unreinforced alloy in the annealed and quenched states are shown in Fig 2. Friction
For a two-phase composite material consisting of a matrix m and a reinforcing phase p, equations (lo), (11) and (12) become
of multiphase
and wear tests
A pin-on-drum abrasion apparatus was used to evaluate the friction and wear properties of the materials. A rotating cylindrical drum (0 200 mm) was covered with silicon carbide (25OO HV) or flint (900 HV) abrasive papers with grit sizes of 4OO, 220 or 80 mesh corresponding to about 20,75 or 200 Km, respectively. The specimens had square cross-sections of 5 x 5 mm and were pressed radially against the drum by means of dead weights acting via a lever mechinism, with forces ranging from 0.9 to 39.1 N, corresponding to nominal surface pressures of 0.04 to 1.56 MPa. The
and
for the EP, EW and I modes, respectively. The model permits an estimate of the friction coefficient resulting from combining a number of materials with known friction coefficients into a multiphase or composite material. It should be noted that the wear resistance of the individual phases also influences the resulting friction, except in the special case of the EP mode load distribution. Tribology
Fig 1 Scanning electron micrograph of polished and etched surface of AlSi7Mg aluminium composite containing 10 vol. % silicon carbide particles of 20 pm size International
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1 I-J 0% SiCparticles ;m 10%
0 Annealed
’
0 0.2 0.4 0.6 Area fraction of reinforcing
0.8 1 phase, aP
0
0.8
Quenched
Fig 2 Bulk hardness of the unreinforced and reinforced aluminium alloys after heat treatment
sliding speed was 0.08 m s-l in all experiments. The pins were continuously moved parallel to the axis of rotation of the drum, to form a helical wear track, so that the samples were always tested against fresh abrasives. The wear rate and friction force were continuously measured by a linear displacement transducer and a load cell, respectively, for the whole test which lasted 10 revolutions corresponding to 6.3 m sliding distance. Before each test the pins were runin using the appropriate conditions of load and abrasive. The tests were run until the pins had formed a steady contact against the drum and the friction value had stabilised, which was achieved after a few revolutions of the drum (i.e. after a sliding distance of = lm). After the running-in period, the friction was stable with time, since the pin continuously slides against fresh abrasives. Only steady-state values of friction and wear resistance are considered in this work. The friction and wear results each represent the average of at least two measuremens. The deviation of the measured friction values from the averages were not more than 5% of the quoted values.
Results Consequences
of the friction
In the EW mode the relative loads on the phases depend on both their area fractions or, and am and their wear resistances flp and &. A phase carries a higher part of the total load, the more wear resistant it is. Consequently, the more wear resistant phase dominates the friction coefficient of a binary composite, as illustrated in Figs 3b and 3c. If the reinforcing phase has a higher wear resistance and a lower coefficient of friction than the matrix, then the coefficient of friction of the’composite stays close to Tribology
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0.4
0.6
Ama fraction of reinforcing
3 g 8
phase,
1
ap
i?i1.8 1.6
2 .i
1.4
)j
1.2 1.0
w
0
0.2
Am
fraction of reinforcing
0.4
0.6
0,8 phase,
1
ap
Fig 3 Coefficient of friction versus the area fraction of reinforcing phase ap in (a) EP mode and in (b) and (c) EW mode. The friction coefficient of the matrix and the reinforcing phase are set to p,,,, = 2 and p,,, = 1 in (a and b) and p,,, = 1 and b = 2 in (c)
model
In the EP mode both the phases of a composite carry load in proportion to their area fractions op and a,,, and independently of their wear resistance. The friction coefficient should therefore vary linearly according to equation (10) from the matrix value p,,, to the value of the reinforcing phase I+, as illustrated in Fig 3a for the case where F,,, = 2.
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the lower y,, value, except when oi, is very low (Fig 3b). Also, m the opposite case of the matrix having the lower friction, the composite’s friction coefficient p,Ew stays close to the value of the more wear resistant reinforcing phase p,, (Fig 3~). Consequently, a second phase in a composite contributes most to a low friction coefficient if it has low friction as well as high wear resistance. In the intermediate I pressure distribution mode, i.e. 0 < 0 < 1, the values of the friction coefficient fall between the EP and EW mode curves, as shown in Figs 4a and 4b. The I mode curves distribute evenly between EP and EW for both high and low wear resistance ratios fi&,,. It is also seen in Fig 4 that the EW curve falls further away from the EP line as the wear resistance ratio rises. This means that the 6 1996
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0.2
Area fraction
0.4
0.6
of reinforcing
0.8
1
The friction tests typically showed a load dependence of the coefficient of friction as shown in Figs 5 and 6. There was almost no load dependence for loads above -5 N, whereas at lower loads the friction coefficient fluctuated somewhat, often rising slightly. However, at any load the ranking of the materials was always the same.
phase, ctP
Pure sintered SiC exhibited lower coefficients of friction than any other materials tested, against both SiC and flint abrasives. The friction coefficient for the SiC was slightly lower against flint than against SiC abrasives of equal grit size, as seen by comparing Figs 5a and 5b.
1.0 0
0.2 Awa fnwioo
0.4
0.6
of reinforcing
0.8
1
phase, czP
Fig 4 Coeficient of friction versus area fraction of reinforcing phase op in EW, EP and I modes for wear resistance ratios (a) 0JLI,,, = 100, and (b) L$l Q,, = 10. The pressure coefficient 13 ranges from 0 (EP) to 1 (EW) in steps of 0.2
For the same matrix hardness, the coefficient of friction for the unreinforced alloy was nearly the same against both SiC and flint abrasives at high loads. The friction of the composites showed the same type of load dependence as the unreinforced alloy and the SiC (Fig 6). The coefficient of friction was higher
reinforcing phase dominates the friction at lower area fractions if the wear resistance ratio is higher. Friction phases
coacients
and wear resistances
N. Axbn et a/.
materials:
of the hard bulk SiC against the much softer flint abrasives was very high, leading to the high tip/&,, ratios for flint abrasives, especially at the high (39 N) load. Since the wear resistances of the phase materials do not conform perfectly to the proportionality predicted by Archard’s equation, the wear resistance was measured separately at each load. Comparisons between composites are then made only with wear resistance and friction values measured at the same load. The wear resistance of the same composites has been discussed in more detail in Reference 19.
2.0
@)
of multiphase
2.0
AlSi7Mg. AlSi7Mg.
of the
In order to compare the theoretical predictions of equations (13) to (15) with the experimental results, not only the friction coefficients of the individual phases but also their wear resistances must be known. The abrasive wear resistances of the unreinforced alloy, the pure sintered SiC and the composites were therefore measured. The results are presented as ratios between the wear resistance of the reinforcing phase and the matrix L$,/&, in Table 1. The wear resistance
0
IO
20
annealed quenched
30
40
30
40
Load. N
Table 1 Wear resistance ratios between reinforcing phase and matrix $I,,/&,, for the composites Abrasive
20 pm SiC 75 pm SiC
Heat treatment Q :
200 pm SiC t 75 km flint
f$~Q-Il; 0.9 N
&Jfk 39 N
13.3 20.6 14.6 20.0 13.2 89.1 71.6
29.7 38.1 38.1 24.0 20.4 435 488
0AU-J 0
10
@)
20 Load, N
Fig 5 Coefficient of friction versus applied load for pure silicon carbide and the annealed and quenched unreinforced AlSi7Mg alloy tested against (a} 75 um SiC and (b) 75 um flint abrasives Tribology
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, , ,
A. 1.6 #E! 1.2
-
% E aa 0.8 i 0.4
12
N. Ax&
ef d.
, , , , , , , , , l,, , , Abrasive: 75 pm SiC Reinfotcemenc 30% SiC OAtlIUkd
0
Qltenched
0
g
QEI
G
64
~ i
0 0.2 0.4 0.6 Area fkaction of reinforcing
0.8 1 phase, uP
0
0.8
0.8 0.6
% g 0.4
0 0
~~~~‘~~~fi’~~~~‘s~a~ 10 20
0)
30
40 CW
Load, N
Fig 6 Coeficient of friction versus load for annealed and quenched composites containing 30 vol. YO silicon carbide tested against (a) 75 um silicon carbide and (b) 75 urn pint abrasives against SiC than against flint abrasives. Both the unreinforced alloy and the composites showed a somewhat higher coefficient of friction for the low alloy hardness. Comparison experimental
between results
model
predictions
and
Figures 7 to 10 show the coefficients of friction for the composites together with the EP and EW mode curves, as calculated from the a&&,, values from Table 1, from the tests against the SiC and flint abrasives at 0.9 N and 39 N loads. The majority of the tests resulted in coefficients of friction for the composites that fell between the EP and EW curves. At the low load (0.9 N) the difference between the coefficients of friction of the matrix P,~ and the reinforcing phase l.i,r was larger than at the high load. The difference between the EP and EW mode curves was also smaller for higher matrix hardnesses. For the low load tests against 200 pm SiC the coefficients of friction for the composites with the harder matrix fell close to the EW curve. For the softer matrix, however, the coefficient of friction rose towards the EP line (Fig 7a). At the higher load, the coefficients of friction of the composites tested against 200 pm SiC abrasives, lay close to the EP lines (Fig 7b). For the smaller 75 pm SiC abrasives the coefficients of friction fell further away from the EP lines (Figs 8a and 8b). This was especially clear at the lower load 472
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0.2 Am
0.4
0.6
fmction of reinforcing
1
phase,
Fig 7 Model predictions (lines) and experimentally measured (points) coefficients of friction plotted against area fraction of reinforcing phase (20 pm SC) for annealed and quenched composites tested against 200 urn SC abrasives at a load of (a) 0.9 N and (b) 39 N
where some of the data points even fell beneath the EW curve. Also with the 75 pm abrasives the low load and hard matrix resulted in behaviour closer to the EW mode. For the smallest abrasives (20 pm) the coefficients of friction lay very close to the EW curves at both low and high load (Fig 9). In the tests with 75 Frn flint abrasives, the coefficients of friction fall between the EP and EW curves at both loads (Fig 10). No strong influence of matrix hardness or load could be seen. The very large gap between the EP and EW curves for the flint results is due to the high Qr/&,, ratios (Table 1) for flint, especially at the higher load. Discussion The model presented here predicts that the friction coefficient of a composite or multiphase material can depend not only on the friction coefficients of the constituents and their area fractions, but also on the wear resistances of the phases. The influence of the wear resistance on the friction depends on the pressure distribution mode in which the wear proceeds. The phase carrying the larger proportion of the applied load will contribute more to the total coefficient of friction. In pure EP mode, where the pressure on each phase is by definition equal, the total friction depends only on the coefficients of friction and area fractions of each phase. However, when the load is 6 1996
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Am
0.2
0.4
0.6
!iaetion of zrinforcing
0.8
1
0
phase,ap
(a)
0.2
Ama ffaeth
? g
0.8
2
0.6
0.4
0.6
of reinforcing
0.8
1
phase, UP
%
0 @I
Am
0.2 tiaetion
0.4
0.6
of reinhrcing
0.8
,g
0.4
j
0.2
1
0 @J
phase, aP
0.2
Area fraction
0.4
0.6
of nk&rcing
0.8
I
phase, aP
Fig 8 Modei predictions (lines) and experimentaliy measured (points) coefficients of friction plotted against area fraction of reinforcing phase (20 pm SC) for annealed and quenched composites tested against 75 pm SiC abrasives at a /oad of (a) 0.9 N and (b) 39 N
Fig 9 Model predictions (lines) and experimentaily measured (points) coeficients of friction versus area fraction of reinforcing phase (20 pm SC) for quenched composites tested against 20 urn SC abrasives at a load of (a) 0.9 N and (b) 39 N
unevenly distributed, i.e. in the I and EW modes, the wear resistances of the constituents are also important. It follows from equations (13) to (15) that, unless the load distribution mode is purely EP, the reinforcing phase must exhibit both a low coefficient of friction and a high wear resistance in order to reduce the coefficient of friction of the composite.
simple friction theory in Reference 5). In the results presented here the coefficient of friction was relatively independent of the load. There was a tendency towards slightly higher friction coefficients at low loads (~5 N), though sometimes it remained constant or even decreased. One explanation for the behaviour at low loads could be the higher sensitivity of the coefficient of friction to fixed errors in the measured friction force. It is also possible that effects of contact with continuously fresh abrasive grits make a larger difference at low loads. At higher loads these effects are small compared with the friction force caused by ploughing or adhesion. As a consequence of this load dependence, the coefficients of friction of the matrix and reinforcing phase differ depending on the load (Figs 7 to lo), in contradiction to Amontons’ law.
The results presented here show that friction tends to follow the EP mode predictions in situations involving high loads, large abrasives and soft matrices. This is in agreement with the load distribution modells, which predicts an even load distribution (EP mode) whenever the abrasive wear grooves are large in comparison with the reinforcing particle size. In contrast, the reinforcing particles carry the largest proportion of the load (and thus have the greatest influence on the wear resistance and friction coefficient) with the smallest abrasive particles (Fig 9). In this case, the abrasive particle tracks are small enough to allow the matrix and the reinforcing particles to wear down gradually without much fragmentation or detachment of individual particles, a situation typical for EW mode. The influence of parameters such as matrix hardness or type and size of the abrasive grits, which do affect both the wear resistance and friction values, is not directly predictable with the model. They would influence the model through changed lo or fl values or through 6. In many practical situations the coefficient of friction is found to be load dependent (in contradiction to the Tribology
Nevertheless, it is possible to compare the friction force with the predictions of the mode1 for a certain composite tested under specific conditions. It must, however, be borne in mind that the value of the coefficient of friction measured at one load may not be applicable at another load. The model was more successful in predicting the influence of material parameters on the friction than the influence of load. It is further assumed in the model that both the wear resistance and the friction coefficient of the constituents of a multiphase material do not interact. The model would not be applicable in its present form if the wear resistance or friction properties of a phase are changed when they are incorporated into a composite. International
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N. Ax&
et a/. relative wear resistances of the phases would be expected to have no influence on the friction of the composite. The validity of the model has been explored by measuring the friction against fixed abrasives of an aluminium alloy containing different volume fractions of silicon carbide particle reinforcement. Most friction values fell between the theoretical EP and EW curves as predicted by the model. Any parameter change leading to larger abrasive grooves (e.g. high load, larger abrasives, soft matrices) tended to move the friction level closer to the EP line. In the mildest case examined (20 pm abrasive particles) the friction fell very close to the predicted EW curve.
00 GG
Am
0.2
0.4
0.6
fraction of reinforcing
0.8
1
phase,as
The model is thus able to explain why the friction coefficient of composites generally does not follow a linear rule of mixtures, but is rather dominated by the friction coefficient of the most wear resistant phase. With the exception of pure EP mode, in which the reinforcing phase does not carry any extra load, a reinforcing phase must exhibit both a low coefficient of friction and a high wear resistance in order to reduce the overall friction of a composite.
0.2 0 0
@I
0.2
0.4
0.6
0.8
1
Area fraction of reinturcing phase, ar
Fig 10 Model predictions (lines) and experimentally measured (points) coefjkients of friction versus area fraction of reinforcing phase (20 m SC) for annealed and quenched composites tested against 75 pm pint abrasives at a load of (a) 0.9 N and (b) 39 N
The model presented above describes a simplified situation. The input parameters must be known and remain at least relatively constant as wear proceeds for the model to be useful. In many practical cases, this will not be true, and the expressions given here would not be directly applicable. It would nevertheless be essential to take account of the distribution of load between the phases in the manner outlined above. The experimental results show that in an idealized laboratory test, especially designed to simulate abrasion, the friction obeys the model reasonably well, although it should be recognized that under more complex circumstances that may not be the case.
The model presented requires further evaluation and has limitations, but appears to be valuable in analysing and understanding the friction behaviour of composites and multiphase materials. It may also be a useful tool for estimating the frictional behaviour of composite materials under development. Due to the complex nature of friction and wear the model should not, however, be expected to produce exact friction values, but rather to give useful estimates and predictions of trends.
Acknowledgements The work has been supported by the Human Capital and Mobility Programme of the EC. The Swedish Institute and the Wennergren foundations are also gratefully acknowledged for their financial support to N. Axen during the course of this work.
References
2.
Conclusions The pressure distribution mode model, previously applied to wear resistance, has been demonstrated also to be valuable in modelling the coefficient of friction during abrasion of multiphase materials. The model predicts that the friction of a composite is influenced not only by the relative amounts and friction coefficients of the constituent phases, but also in most cases by their individual wear resistances. In most wear situations (corresponding to the EW and I load distributions) the more wear resistant phases carry a disproportionately high part of the load, and hence have a larger influence on the friction of the composite than the phases with low wear resistance. In situations where the load is evenly distributed (EP mode) the 474
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P.K., Liu Y. and Ray S. ASM Handbook, Volume 18. Friction, Lubrication and Wear Technology, ASM International, USA, 1992, 693-820 Hutchings I.M. Tribological properties of metal matrix composites. Mater. Sci. TechnoZ. 1994, 10, 513-517 Zum Gahr K.-H. Microstructure and Wear of Materials, EIsevier, Amsterdam, 1987 Ax6n N. and Zum Gahr K.-H. Verschleip von TaC- turd TicLaserdispersions-schichten durch weiche und harte Abrasivstoffe. Mat.-wiss. u. Werkstofftech. 1992, 23, 360-367 Bowden F.P. and Tabor D. The Friction and Lubrication of Solids, Clarendon Press, Oxford, 1950 Larsen-Basse J. ASM Handbook, Friction, Lubrication and Wear Technology, Volume 18, ASM ZnternationaZ, USA, 1992,
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25-38 LL. and Pollock ELM. (eds), Fundamentals of Friction: Macroscopic and Microscopic Processes, Proceedings of the NATO ASI, Braunlage, Harzp Germany, 1991 8. Zum Gahr K.-H. Einfluss des Makroaufbaus von StahbPolymerfaserverbundwerkstoffen auf den Abrasiwerschleiss, Z. Werkstoflech. 1985, 16, 2%-305
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15. Lui II., Fhw M.E., Cheng H.S. and Geiir A.L. Lubricated rolling and sliding wear of a Sic-whisker-reinforced SisN4 composite against M2 tool steel. J. Amer. Ceram. Sot. 1993, 76, 1, 105-121 16. Anderson A.E. ASM Handbook, Volume 18. Friction, Lubrication and Wear Technology, ASM International, USA, 1992, 569-577 17. Wang A. Abrasive wear of metal matrix composites, Ph D thesis, University of Cambridge, October 1988
9. Sung NH. and Sub N.P. Effect of fibre orientation on friction and wear of fibre reinforced polymeric composites. Wear 1979, 53, 129-141 10. Kapoor A. and Bahadur S. Transfer film bonding and wear studies on CuS-nylon composite sliding against steel. Tribal. Intern. 1994, 27, 5, 323-329 11. Minford E. and Prewo K. Friction and wear of graphite-fibrereinforced glass matrix composites. Wear 1985, 102, 253-264 12. Zhang Z., Zhang L. and Mai Y.-W. Modelling friction and wear of scratching ceramic particle reinforced metal composites. Wear 1994, 176, 231-237 13. Saks N. and Haraiekas D.P. Friction and wear of particlereinforced metal-ceramic composites. In Wear of Materials 8.5 (Ed. K.C. Ludema) Vancouver, 784-793
18. Ax& N. and Jacobson resistance of multiphase 19. Ax& N. and Jacobson resistance of fibre and 1994, 178, l-7
14. Ax& N., Alahelisten A. and Jacobson S. Abrasive wear of alumina fibre reinforced aluminium. Wear 2994, 173, 95-104
20. Ax& N. and Lundberg B. Abrasive wear in intermediate mode of multiphase materials. Tribal. Intern. 1995, 28, 523-529
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S. A model for the abrasive wear materials. Wear 1994, 174, 187-199 S. Transitions in the abrasive wear particle reinforced aluminium. Wear
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1996 Copyright @ 1996 Ekevier Science Ltd Printed in Great Britain. All rights reserved 0301-679X/%/$15.00 +O.OO
0301-679X(95)00104-2
A model for the friction of multiphase materials in abrasion N. Axhn*,
I. M. Hutchingsf
and S. Jacobson*
A model is presented for the sliding friction of multiphase materials in abrasion. The friction is described in terms of the load distribution between the phases. Different load distribution modes are used with Amontons’ first law of friction to derive both the friction force and the coefficient of friction as functions of the area fractions of the phases, their individual coefficients of friction and their wear resistance. It is shown that the coefficient of friction of a multiphase material should depend on the load distribution mode and that the upper and lower limits for the coefficient of friction expected from composites or multiphase materials can be identified. For most pressure distribution modes, the friction depends on the wear resistance of the phases. The model is compared with results from abrasion tests on a silicon carbide reinforced aluminium alloy (AlSi7Mg) over a wide range of loads and with different fixed abrasive particles. The experimental results are described and interpreted in terms of the model. Copyright 0 1996 Elsevier Science Ltd Keywords: phase
friction, material
abrasion,
composite,
meta/ matrix
Introduction Materials used in situations where good wear and friction properties are desired, are very often multiphase. Traditional multiphase materials often used in tribological applications mclude tool steels, cast irons and cemented carbides. Composites form a sub-group of multiphase materials, and can be described as artificially manufactured multiphase materials containing phases from different material groups. The competition from new composites increases as new manufacturing techniques come into use and today a variety of light metal and polymer matrix composites are
* Department of Technology, Materials Science Division, Uppsala University, 60x 534, S-751 21 Uppsala, Sweden f Department of Materiuls Science and Metallurgy, University of Cambridge, Pembroke Street, CB2 3QZ, UK Received 9 May 1995; revtied 3 October 1995; accepted 9 October 1995
Tribology
composite,
mdti-
availablel. The understanding of the wear and friction properties of multiphase materials is thus an important topic in tribology. The wear and friction behaviour of multiphase materials is complex. Not only the tribological behaviour of the constituents of a multiphase material, but also the extension and distribution of the phases, as well as the inter-phase bonding, are important2-4. The kinetic friction force is the tangential force necessary to slide one body over the surface of another. The friction force is sometimes described as the sum of two contributions: one caused by surface asperities deforming the counter surface and the other due to the shearing of adhesive contacts. This view was largely developed by Bowden and Tabor in their work on friction in the 1950~~. Since then numerous papers have been published on the origin of friction in terms of the interaction between surface asperities in sliding contact. An overview has been provided by LarsenInternational
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A large number of papers have also been published on the frictional properties of composites8-14. Many ,deal with polymer matrix composites8-lo, but also carbon fibre reinforced glass matricesi and light metal matrix composites with ceramic reinforcements have been studiedlz-14. The number of works on the friction properties of ceramic matrix composites is relatively smalps. The sliding friction of composites has been more systematically studied than friction associated with abrasion. Nevertheless, friction in abrasion is an important feature, e.g. in grinding and for applications such as brake disc materialsi6. There have been few fundamental works published on the friction of multiphase materials during abrasion. Zhang et al. l2 reported an increased friction coefficient caused by alumina and silicon carbide particulate reinforcements in a 6061 aluminium matrix as measured in single-point scratch tests. They explain the increased friction by an additional particle fracture contribution to the adhesion and ploughing components. Amontons’ first law of friction implies that the friction force should be proportional to the normal load. This statement has been shown to be valid for many material combinations under both unlubricated and lubricated sliding, It has also been found to be a good approximation for steady-state abrasion1’,14. For a multiphase material the friction force can therefore be expected to be related to the load on each phase, i.e. the distribution of the load between the phases. Recent work by Axen, Jacobson and Lundberg has shown how the load carried by each phase in a multiphase material subjected to abrasion depends on the wear resistance and area fractions of the phases18-20. In that work the load on each phase was described in terms of load (or pressure) distribution modes. Equal pressure (EP), equal wear (EW) and intermediate (I) pressure distribution modes were defined. It was shown that the EP and EW modes describe load distribution limits above or below which, respectively, the pressure distribution cannot fall. The types of surface interactions that fulfil the EP and EW modes are described in Reference 18. In fact, all possible surface interactions correspond to a certain pressure distribution (necessarily falling between EW and EP) between the phases. The I mode results from intermediate pressure distributionszo. This paper presents a model for the abrasive friction of a multiphase material. The model is based on Amontons’ law and the distribution of the load between the phases. The model is compared with experimental data from a SiC particle reinforced aluminium alloy abraded by fixed SiC and flint abrasives under various loads.
Theory It is assumed that the tangential friction force F is proportional to the applied normal load L: F= pL 468
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This implies that independent of L.
the coefficient
of friction
F is
As a multiphase material is slid over a counter-surface, each phase i exposed at the sliding interface exhibits its own coefficient of friction t~,~in contact with the counter-material and each phase carries a load Li. The friction force on each phase Fi is then: Fi = FiLi from equation (1). The total friction force F is the sum of the contributions from each phase, for ‘a total of N different phases: F= i
FiLi
i=l
To derive the total friction force for a multiphase material, the friction coefficient of each phase against the counter-material and the load carried by each phase, must be known. It must also be assumed that the phases retain their individual friction properties when part of the composite, and that the area fractions remain constant. The friction coefficient is of course material pair specific and must be measured individually for each case. The loads Li can be derived from the pressure distribution mode model presented in References 18-20. This model is based on Archard’s equation (i.e on the assumption that the volumetric wear rate is proportional to the load) and on two pressure distribution modes describing how much of the total applied load each phase carries: equal normal pressures on the phases (EP) and equal linear wear rates of the phases (EW). It is assumed in the model that the phases do not influence the specific wear resistance or coefficient of friction of each other and that the area fractions remain known. For example one phase must not become smeared out over the other to an unpredictable extent. From the pressure distribution mode model it follows that the load Li carried by phase i with area fraction cq is given by: Li ZZLOli in EP mode and:
n=l
in EW mode, where the specific wear resistance of each phase is denoted by ai. For the intermediate (I) mode the load on each phase can be expressed as:
where 0 represents the proportion of EW mode pressure distribution. f3 = 1 for pure EW and 0 = 0 for pure EP mode. Equation (6) provides a mathematical formalism for intermediate load distributions and includes EP and EW as special cases. However, since the EP and EW modes represent the fundamental
(11 29 Number 6 1996
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assumptions of the model they will be treated separately below. C$)mgbining equation Ives:
(3) with equations (4), (5) and
N
f’Ep = x
PiLai,
(7)
i=l N fli FEW=
2 i=l
PiL
N Ix n=l
anfin
ai
and
for the friction forces in the EP, EW and I modes, respectively. The coefficient of friction is derived by dividing the appropriate friction force from equations (7), (8) or (9) by the total load L. Thus:
materials:
N. Ax&
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Materials and test procedures Materials
The metal matrix composites studied in this work were based on a hypoeutectic aluminium-silicon alloy (AlSi7Mg; 7% Si, 0.3% Mg, 0.18% Fe, 0.05% Cu, 0.15% Ti) reinforced with 0, 10 or 30 vol. % of 20 pm silicon carbide particles (hardness 2500 HV). The particle composites were fabricated by Sintef Produktionsteknikk, Norway by a rheocasting technique. A typical example of the structure is shown in Fig 1. The distribution of the particles was uniform, although some isolated pores were observed. A pure sintered polycrystalline silicon carbide (>99%, solid state sintered, 2500 HV) was also tested. The composites were heat treated to two different hardnesses, referred to as annealed and quenched. All specimens were first soft annealed at 4OO’C for 1 h and slowly furnace cooled to room temperature (annealed). Some specimens were then hardened by solution treatment at 52O’C for 20 min followed by rapid quenching in turbulent cool water, followed by ageing at 140°C for two hours (quenched). The hardnesses of the composites and the unreinforced alloy in the annealed and quenched states are shown in Fig 2. Friction
For a two-phase composite material consisting of a matrix m and a reinforcing phase p, equations (lo), (11) and (12) become
of multiphase
and wear tests
A pin-on-drum abrasion apparatus was used to evaluate the friction and wear properties of the materials. A rotating cylindrical drum (0 200 mm) was covered with silicon carbide (25OO HV) or flint (900 HV) abrasive papers with grit sizes of 4OO, 220 or 80 mesh corresponding to about 20,75 or 200 Km, respectively. The specimens had square cross-sections of 5 x 5 mm and were pressed radially against the drum by means of dead weights acting via a lever mechinism, with forces ranging from 0.9 to 39.1 N, corresponding to nominal surface pressures of 0.04 to 1.56 MPa. The
and
for the EP, EW and I modes, respectively. The model permits an estimate of the friction coefficient resulting from combining a number of materials with known friction coefficients into a multiphase or composite material. It should be noted that the wear resistance of the individual phases also influences the resulting friction, except in the special case of the EP mode load distribution. Tribology
Fig 1 Scanning electron micrograph of polished and etched surface of AlSi7Mg aluminium composite containing 10 vol. % silicon carbide particles of 20 pm size International
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1 I-J 0% SiCparticles ;m 10%
0 Annealed
’
0 0.2 0.4 0.6 Area fraction of reinforcing
0.8 1 phase, aP
0
0.8
Quenched
Fig 2 Bulk hardness of the unreinforced and reinforced aluminium alloys after heat treatment
sliding speed was 0.08 m s-l in all experiments. The pins were continuously moved parallel to the axis of rotation of the drum, to form a helical wear track, so that the samples were always tested against fresh abrasives. The wear rate and friction force were continuously measured by a linear displacement transducer and a load cell, respectively, for the whole test which lasted 10 revolutions corresponding to 6.3 m sliding distance. Before each test the pins were runin using the appropriate conditions of load and abrasive. The tests were run until the pins had formed a steady contact against the drum and the friction value had stabilised, which was achieved after a few revolutions of the drum (i.e. after a sliding distance of = lm). After the running-in period, the friction was stable with time, since the pin continuously slides against fresh abrasives. Only steady-state values of friction and wear resistance are considered in this work. The friction and wear results each represent the average of at least two measuremens. The deviation of the measured friction values from the averages were not more than 5% of the quoted values.
Results Consequences
of the friction
In the EW mode the relative loads on the phases depend on both their area fractions or, and am and their wear resistances flp and &. A phase carries a higher part of the total load, the more wear resistant it is. Consequently, the more wear resistant phase dominates the friction coefficient of a binary composite, as illustrated in Figs 3b and 3c. If the reinforcing phase has a higher wear resistance and a lower coefficient of friction than the matrix, then the coefficient of friction of the’composite stays close to Tribology
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0.4
0.6
Ama fraction of reinforcing
3 g 8
phase,
1
ap
i?i1.8 1.6
2 .i
1.4
)j
1.2 1.0
w
0
0.2
Am
fraction of reinforcing
0.4
0.6
0,8 phase,
1
ap
Fig 3 Coefficient of friction versus the area fraction of reinforcing phase ap in (a) EP mode and in (b) and (c) EW mode. The friction coefficient of the matrix and the reinforcing phase are set to p,,,, = 2 and p,,, = 1 in (a and b) and p,,, = 1 and b = 2 in (c)
model
In the EP mode both the phases of a composite carry load in proportion to their area fractions op and a,,, and independently of their wear resistance. The friction coefficient should therefore vary linearly according to equation (10) from the matrix value p,,, to the value of the reinforcing phase I+, as illustrated in Fig 3a for the case where F,,, = 2.
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the lower y,, value, except when oi, is very low (Fig 3b). Also, m the opposite case of the matrix having the lower friction, the composite’s friction coefficient p,Ew stays close to the value of the more wear resistant reinforcing phase p,, (Fig 3~). Consequently, a second phase in a composite contributes most to a low friction coefficient if it has low friction as well as high wear resistance. In the intermediate I pressure distribution mode, i.e. 0 < 0 < 1, the values of the friction coefficient fall between the EP and EW mode curves, as shown in Figs 4a and 4b. The I mode curves distribute evenly between EP and EW for both high and low wear resistance ratios fi&,,. It is also seen in Fig 4 that the EW curve falls further away from the EP line as the wear resistance ratio rises. This means that the 6 1996
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Area fraction
0.4
0.6
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0.8
1
The friction tests typically showed a load dependence of the coefficient of friction as shown in Figs 5 and 6. There was almost no load dependence for loads above -5 N, whereas at lower loads the friction coefficient fluctuated somewhat, often rising slightly. However, at any load the ranking of the materials was always the same.
phase, ctP
Pure sintered SiC exhibited lower coefficients of friction than any other materials tested, against both SiC and flint abrasives. The friction coefficient for the SiC was slightly lower against flint than against SiC abrasives of equal grit size, as seen by comparing Figs 5a and 5b.
1.0 0
0.2 Awa fnwioo
0.4
0.6
of reinforcing
0.8
1
phase, czP
Fig 4 Coeficient of friction versus area fraction of reinforcing phase op in EW, EP and I modes for wear resistance ratios (a) 0JLI,,, = 100, and (b) L$l Q,, = 10. The pressure coefficient 13 ranges from 0 (EP) to 1 (EW) in steps of 0.2
For the same matrix hardness, the coefficient of friction for the unreinforced alloy was nearly the same against both SiC and flint abrasives at high loads. The friction of the composites showed the same type of load dependence as the unreinforced alloy and the SiC (Fig 6). The coefficient of friction was higher
reinforcing phase dominates the friction at lower area fractions if the wear resistance ratio is higher. Friction phases
coacients
and wear resistances
N. Axbn et a/.
materials:
of the hard bulk SiC against the much softer flint abrasives was very high, leading to the high tip/&,, ratios for flint abrasives, especially at the high (39 N) load. Since the wear resistances of the phase materials do not conform perfectly to the proportionality predicted by Archard’s equation, the wear resistance was measured separately at each load. Comparisons between composites are then made only with wear resistance and friction values measured at the same load. The wear resistance of the same composites has been discussed in more detail in Reference 19.
2.0
@)
of multiphase
2.0
AlSi7Mg. AlSi7Mg.
of the
In order to compare the theoretical predictions of equations (13) to (15) with the experimental results, not only the friction coefficients of the individual phases but also their wear resistances must be known. The abrasive wear resistances of the unreinforced alloy, the pure sintered SiC and the composites were therefore measured. The results are presented as ratios between the wear resistance of the reinforcing phase and the matrix L$,/&, in Table 1. The wear resistance
0
IO
20
annealed quenched
30
40
30
40
Load. N
Table 1 Wear resistance ratios between reinforcing phase and matrix $I,,/&,, for the composites Abrasive
20 pm SiC 75 pm SiC
Heat treatment Q :
200 pm SiC t 75 km flint
f$~Q-Il; 0.9 N
&Jfk 39 N
13.3 20.6 14.6 20.0 13.2 89.1 71.6
29.7 38.1 38.1 24.0 20.4 435 488
0AU-J 0
10
@)
20 Load, N
Fig 5 Coefficient of friction versus applied load for pure silicon carbide and the annealed and quenched unreinforced AlSi7Mg alloy tested against (a} 75 um SiC and (b) 75 um flint abrasives Tribology
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, , ,
A. 1.6 #E! 1.2
-
% E aa 0.8 i 0.4
12
N. Ax&
ef d.
, , , , , , , , , l,, , , Abrasive: 75 pm SiC Reinfotcemenc 30% SiC OAtlIUkd
0
Qltenched
0
g
QEI
G
64
~ i
0 0.2 0.4 0.6 Area fkaction of reinforcing
0.8 1 phase, uP
0
0.8
0.8 0.6
% g 0.4
0 0
~~~~‘~~~fi’~~~~‘s~a~ 10 20
0)
30
40 CW
Load, N
Fig 6 Coeficient of friction versus load for annealed and quenched composites containing 30 vol. YO silicon carbide tested against (a) 75 um silicon carbide and (b) 75 urn pint abrasives against SiC than against flint abrasives. Both the unreinforced alloy and the composites showed a somewhat higher coefficient of friction for the low alloy hardness. Comparison experimental
between results
model
predictions
and
Figures 7 to 10 show the coefficients of friction for the composites together with the EP and EW mode curves, as calculated from the a&&,, values from Table 1, from the tests against the SiC and flint abrasives at 0.9 N and 39 N loads. The majority of the tests resulted in coefficients of friction for the composites that fell between the EP and EW curves. At the low load (0.9 N) the difference between the coefficients of friction of the matrix P,~ and the reinforcing phase l.i,r was larger than at the high load. The difference between the EP and EW mode curves was also smaller for higher matrix hardnesses. For the low load tests against 200 pm SiC the coefficients of friction for the composites with the harder matrix fell close to the EW curve. For the softer matrix, however, the coefficient of friction rose towards the EP line (Fig 7a). At the higher load, the coefficients of friction of the composites tested against 200 pm SiC abrasives, lay close to the EP lines (Fig 7b). For the smaller 75 pm SiC abrasives the coefficients of friction fell further away from the EP lines (Figs 8a and 8b). This was especially clear at the lower load 472
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0.2 Am
0.4
0.6
fmction of reinforcing
1
phase,
Fig 7 Model predictions (lines) and experimentally measured (points) coefficients of friction plotted against area fraction of reinforcing phase (20 pm SC) for annealed and quenched composites tested against 200 urn SC abrasives at a load of (a) 0.9 N and (b) 39 N
where some of the data points even fell beneath the EW curve. Also with the 75 pm abrasives the low load and hard matrix resulted in behaviour closer to the EW mode. For the smallest abrasives (20 pm) the coefficients of friction lay very close to the EW curves at both low and high load (Fig 9). In the tests with 75 Frn flint abrasives, the coefficients of friction fall between the EP and EW curves at both loads (Fig 10). No strong influence of matrix hardness or load could be seen. The very large gap between the EP and EW curves for the flint results is due to the high Qr/&,, ratios (Table 1) for flint, especially at the higher load. Discussion The model presented here predicts that the friction coefficient of a composite or multiphase material can depend not only on the friction coefficients of the constituents and their area fractions, but also on the wear resistances of the phases. The influence of the wear resistance on the friction depends on the pressure distribution mode in which the wear proceeds. The phase carrying the larger proportion of the applied load will contribute more to the total coefficient of friction. In pure EP mode, where the pressure on each phase is by definition equal, the total friction depends only on the coefficients of friction and area fractions of each phase. However, when the load is 6 1996
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Am
0.2
0.4
0.6
!iaetion of zrinforcing
0.8
1
0
phase,ap
(a)
0.2
Ama ffaeth
? g
0.8
2
0.6
0.4
0.6
of reinforcing
0.8
1
phase, UP
%
0 @I
Am
0.2 tiaetion
0.4
0.6
of reinhrcing
0.8
,g
0.4
j
0.2
1
0 @J
phase, aP
0.2
Area fraction
0.4
0.6
of nk&rcing
0.8
I
phase, aP
Fig 8 Modei predictions (lines) and experimentaliy measured (points) coefficients of friction plotted against area fraction of reinforcing phase (20 pm SC) for annealed and quenched composites tested against 75 pm SiC abrasives at a /oad of (a) 0.9 N and (b) 39 N
Fig 9 Model predictions (lines) and experimentaily measured (points) coeficients of friction versus area fraction of reinforcing phase (20 pm SC) for quenched composites tested against 20 urn SC abrasives at a load of (a) 0.9 N and (b) 39 N
unevenly distributed, i.e. in the I and EW modes, the wear resistances of the constituents are also important. It follows from equations (13) to (15) that, unless the load distribution mode is purely EP, the reinforcing phase must exhibit both a low coefficient of friction and a high wear resistance in order to reduce the coefficient of friction of the composite.
simple friction theory in Reference 5). In the results presented here the coefficient of friction was relatively independent of the load. There was a tendency towards slightly higher friction coefficients at low loads (~5 N), though sometimes it remained constant or even decreased. One explanation for the behaviour at low loads could be the higher sensitivity of the coefficient of friction to fixed errors in the measured friction force. It is also possible that effects of contact with continuously fresh abrasive grits make a larger difference at low loads. At higher loads these effects are small compared with the friction force caused by ploughing or adhesion. As a consequence of this load dependence, the coefficients of friction of the matrix and reinforcing phase differ depending on the load (Figs 7 to lo), in contradiction to Amontons’ law.
The results presented here show that friction tends to follow the EP mode predictions in situations involving high loads, large abrasives and soft matrices. This is in agreement with the load distribution modells, which predicts an even load distribution (EP mode) whenever the abrasive wear grooves are large in comparison with the reinforcing particle size. In contrast, the reinforcing particles carry the largest proportion of the load (and thus have the greatest influence on the wear resistance and friction coefficient) with the smallest abrasive particles (Fig 9). In this case, the abrasive particle tracks are small enough to allow the matrix and the reinforcing particles to wear down gradually without much fragmentation or detachment of individual particles, a situation typical for EW mode. The influence of parameters such as matrix hardness or type and size of the abrasive grits, which do affect both the wear resistance and friction values, is not directly predictable with the model. They would influence the model through changed lo or fl values or through 6. In many practical situations the coefficient of friction is found to be load dependent (in contradiction to the Tribology
Nevertheless, it is possible to compare the friction force with the predictions of the mode1 for a certain composite tested under specific conditions. It must, however, be borne in mind that the value of the coefficient of friction measured at one load may not be applicable at another load. The model was more successful in predicting the influence of material parameters on the friction than the influence of load. It is further assumed in the model that both the wear resistance and the friction coefficient of the constituents of a multiphase material do not interact. The model would not be applicable in its present form if the wear resistance or friction properties of a phase are changed when they are incorporated into a composite. International
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N. Ax&
et a/. relative wear resistances of the phases would be expected to have no influence on the friction of the composite. The validity of the model has been explored by measuring the friction against fixed abrasives of an aluminium alloy containing different volume fractions of silicon carbide particle reinforcement. Most friction values fell between the theoretical EP and EW curves as predicted by the model. Any parameter change leading to larger abrasive grooves (e.g. high load, larger abrasives, soft matrices) tended to move the friction level closer to the EP line. In the mildest case examined (20 pm abrasive particles) the friction fell very close to the predicted EW curve.
00 GG
Am
0.2
0.4
0.6
fraction of reinforcing
0.8
1
phase,as
The model is thus able to explain why the friction coefficient of composites generally does not follow a linear rule of mixtures, but is rather dominated by the friction coefficient of the most wear resistant phase. With the exception of pure EP mode, in which the reinforcing phase does not carry any extra load, a reinforcing phase must exhibit both a low coefficient of friction and a high wear resistance in order to reduce the overall friction of a composite.
0.2 0 0
@I
0.2
0.4
0.6
0.8
1
Area fraction of reinturcing phase, ar
Fig 10 Model predictions (lines) and experimentally measured (points) coefjkients of friction versus area fraction of reinforcing phase (20 m SC) for annealed and quenched composites tested against 75 pm pint abrasives at a load of (a) 0.9 N and (b) 39 N
The model presented above describes a simplified situation. The input parameters must be known and remain at least relatively constant as wear proceeds for the model to be useful. In many practical cases, this will not be true, and the expressions given here would not be directly applicable. It would nevertheless be essential to take account of the distribution of load between the phases in the manner outlined above. The experimental results show that in an idealized laboratory test, especially designed to simulate abrasion, the friction obeys the model reasonably well, although it should be recognized that under more complex circumstances that may not be the case.
The model presented requires further evaluation and has limitations, but appears to be valuable in analysing and understanding the friction behaviour of composites and multiphase materials. It may also be a useful tool for estimating the frictional behaviour of composite materials under development. Due to the complex nature of friction and wear the model should not, however, be expected to produce exact friction values, but rather to give useful estimates and predictions of trends.
Acknowledgements The work has been supported by the Human Capital and Mobility Programme of the EC. The Swedish Institute and the Wennergren foundations are also gratefully acknowledged for their financial support to N. Axen during the course of this work.
References
2.
Conclusions The pressure distribution mode model, previously applied to wear resistance, has been demonstrated also to be valuable in modelling the coefficient of friction during abrasion of multiphase materials. The model predicts that the friction of a composite is influenced not only by the relative amounts and friction coefficients of the constituent phases, but also in most cases by their individual wear resistances. In most wear situations (corresponding to the EW and I load distributions) the more wear resistant phases carry a disproportionately high part of the load, and hence have a larger influence on the friction of the composite than the phases with low wear resistance. In situations where the load is evenly distributed (EP mode) the 474
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P.K., Liu Y. and Ray S. ASM Handbook, Volume 18. Friction, Lubrication and Wear Technology, ASM International, USA, 1992, 693-820 Hutchings I.M. Tribological properties of metal matrix composites. Mater. Sci. TechnoZ. 1994, 10, 513-517 Zum Gahr K.-H. Microstructure and Wear of Materials, EIsevier, Amsterdam, 1987 Ax6n N. and Zum Gahr K.-H. Verschleip von TaC- turd TicLaserdispersions-schichten durch weiche und harte Abrasivstoffe. Mat.-wiss. u. Werkstofftech. 1992, 23, 360-367 Bowden F.P. and Tabor D. The Friction and Lubrication of Solids, Clarendon Press, Oxford, 1950 Larsen-Basse J. ASM Handbook, Friction, Lubrication and Wear Technology, Volume 18, ASM ZnternationaZ, USA, 1992,
1. Rohatgi
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25-38 LL. and Pollock ELM. (eds), Fundamentals of Friction: Macroscopic and Microscopic Processes, Proceedings of the NATO ASI, Braunlage, Harzp Germany, 1991 8. Zum Gahr K.-H. Einfluss des Makroaufbaus von StahbPolymerfaserverbundwerkstoffen auf den Abrasiwerschleiss, Z. Werkstoflech. 1985, 16, 2%-305
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15. Lui II., Fhw M.E., Cheng H.S. and Geiir A.L. Lubricated rolling and sliding wear of a Sic-whisker-reinforced SisN4 composite against M2 tool steel. J. Amer. Ceram. Sot. 1993, 76, 1, 105-121 16. Anderson A.E. ASM Handbook, Volume 18. Friction, Lubrication and Wear Technology, ASM International, USA, 1992, 569-577 17. Wang A. Abrasive wear of metal matrix composites, Ph D thesis, University of Cambridge, October 1988
9. Sung NH. and Sub N.P. Effect of fibre orientation on friction and wear of fibre reinforced polymeric composites. Wear 1979, 53, 129-141 10. Kapoor A. and Bahadur S. Transfer film bonding and wear studies on CuS-nylon composite sliding against steel. Tribal. Intern. 1994, 27, 5, 323-329 11. Minford E. and Prewo K. Friction and wear of graphite-fibrereinforced glass matrix composites. Wear 1985, 102, 253-264 12. Zhang Z., Zhang L. and Mai Y.-W. Modelling friction and wear of scratching ceramic particle reinforced metal composites. Wear 1994, 176, 231-237 13. Saks N. and Haraiekas D.P. Friction and wear of particlereinforced metal-ceramic composites. In Wear of Materials 8.5 (Ed. K.C. Ludema) Vancouver, 784-793
18. Ax& N. and Jacobson resistance of multiphase 19. Ax& N. and Jacobson resistance of fibre and 1994, 178, l-7
14. Ax& N., Alahelisten A. and Jacobson S. Abrasive wear of alumina fibre reinforced aluminium. Wear 2994, 173, 95-104
20. Ax& N. and Lundberg B. Abrasive wear in intermediate mode of multiphase materials. Tribal. Intern. 1995, 28, 523-529
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S. A model for the abrasive wear materials. Wear 1994, 174, 187-199 S. Transitions in the abrasive wear particle reinforced aluminium. Wear
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