EDITORIAL

Predicting the behaviour of frictional interfaces: a ‘grand challenge’ in mechanics

There can be few mechanical or civil engineering systems that

do not make use of friction in some form or another.

Obvious examples include friction drives (such as the tyre/

road or wheel/rail interface), brakes on vehicles and threa-

ded fasteners. As engineers, we are so familiar with these

applications that we barely give them a second thought. Yet,

if we look in more detail at these systems, it is often sur-

prising how poorly understood they are. Of course, we have

classical ‘laws’ of friction, which most of us must have come

across in school science lessons, yet these rely on empirical

constants such as the friction coefficient, which must be

experimentally determined and which are subject to a con-

siderable degree of uncertainty. We are also well aware of

situations where these ‘laws’ do not really give a good

approximation to physical reality. It is sometimes instructive

to ask a group of engineering students why formula one

racing cars have such wide tyres. The answer received will

typically (and not unreasonably) be along the lines of ‘to give

more grip when cornering’. If one then follows the question

up with ‘how does the limiting frictional force depend on

apparent area of contact?’, they will often resort to the

classical Coulomb model without appreciating that this is

completely at variance with their answer to the first question.

Our classical concepts of friction date back at least to Leo-

nardo da Vinci, who noted ‘The friction made by the same

weight will be of equal resistance at the beginning of its

movement although the contact will be of different breadths

and lengths’, together with ‘friction produces double the

amount of effort if the weight be doubled’ [1]. These state-

ments are readily recognisable as part of what we would now

regard as Coulomb’s (or Amontons’) laws of friction. It was

not, however, until 200 years later in 1699, when Guillaume

Amontons published his article reporting the results of careful

measurements of frictional force between a range of surfaces

[2]. Amontons’ principal observation essentially restated what

Leonardo had observed: (i) that frictional resistance increased

in proportion to the normal load and (ii) that it was indepen-

dent of the apparent area of contact. It is also interesting to

note that Amontons appreciated, at least to some extent, the

importance of surface roughness in frictional behaviour of

interfaces. A further 86 years passed before Charles Coulomb

published his well-known article, which essentially confirmed

the observations of Leonardo and Amontons [3]. In addition,

Coulomb also investigated the behaviour of kinetic friction (i.e.

once rigid body sliding had commenced). He found that this

was generally less than the static value and is frequently quoted

as having said that kinetic friction is independent of velocity,

although he was almost certainly aware that this was less

generally true than is sometimes supposed. These scientists

helped lay the foundations of our classical understanding of

friction, and the reader interested in finding out more of

the background to their discoveries is referred to Duncan

Dowson’s comprehensive history of tribology [1].

The experiments and theories described earlier chiefly con-

cern the transmission of forces between what are, essentially,

rigid bodies. However, at the end of the nineteenth century,

scientistsandengineersbeganto look ina littlemoredetail at the

precise way in which these forces were transmitted between

contacting components. In part, their investigations were

motivated by service failures, such as those involving fretting

betweenrailwaywheelsandaxles.Hertz[4] laid the foundations

forwhatwewouldnowregardas thefieldof contactmechanics,

by investigating the distribution of normal pressure within an

elastic contact, and this work was followed up by Cattaneo [5]

and Mindlin [6], who independently looked at solutions for

transmission of a frictional force within a contact by the estab-

lishment of shear tractions. Implicit within these solutions is the

assumption that the concept of Coulomb friction can be applied

at length scales significantly smaller than those at which it had

beenmeasured. Initiallyat least,evidence for thiswassomewhat

circumstantial, although Ken Johnson’s celebrated experiment

[7] showed that the stick and stick zones found in practice were

very similar to those predicted by Mindlin and Cattaneo.

Hence, the classical ‘laws’ of friction were well established,

and by the mid-twentieth century, they were being used at

length scales significantly smaller than that of the overall

� 2010 Blackwell Publishing Ltd j Strain (2010) 46, 213–214 213

contact. However, fundamental understanding of the origins

of friction was more limited until the 1940s and 1950s, when

a substantial body of work by Bowden and Tabor, amongst

others, shed considerable light on the mechanisms of friction

at a microscopic scale [8]. In particular, it was shown that

adhesion plays a significant role in determining the level of

friction experienced by metal surfaces in contact. Green-

wood and Williamson’s model of rough elastic contact pro-

vided further insight by showing that the real area of contact

between two contacting surfaces could be proportional to

the normal load [9]. Development of new instruments such

as the atomic force microscope and new techniques such as

molecular dynamics simulations have further developed our

understanding, but there is still little to guide the practicing

engineer beyond the concept of a friction coefficient (which

must be determined experimentally), little changed from the

approach suggested by Leonardo da Vinci 500 years ago.

We have reached the stage in the first decade of the

twenty-first century where finite element analysis and similar

numerical tools allow us to simulate the performance of large

and complex mechanical engineering systems. Our under-

standing of solid mechanics is so good that it is generally

possible to predict the natural frequencies of vibration of a

component such as a turbine blade with an accuracy which is

better than the variation between nominally identical com-

ponents which arises from manufacturing tolerances. How-

ever, when a number of such components are assembled

into a system the frictional interfaces present introduce

compliance and damping. These introduce significant uncer-

tainty and our predictions of system behaviour will be far less

accurate than those for individual components. It is not

possible to predict the influence of the frictional joints in the

system from fundamental properties and geometry of the

contacting bodies and experimentally measured properties

such as ‘friction coefficient’ and ‘contact stiffness’ are

required as inputs to the model. Similar considerations occur

when considering the structural integrity of the system as well

as its dynamic performance. The fretting fatigue performance

of an interface will depend strongly on the precise manner in

which the frictional forces are transferred between the

contacting components. In particular, the friction coefficient

will vary both spatially and temporally in a complex way. Even

if we accept that friction measurements are likely to be

required as inputs to our models, there is little agreement on

how these should be carried out, and how the results should

be interpreted. An ASTM standard does exist [10] and gives

useful guidance, but its recommendations are relatively high

level and not always adhered to. Further, it is found that

frictional interface behaviour can be highly variable so that

the response of an interface when disassembled and

reassembled can be significantly different from its original

behaviour. Hence, it can be difficult to obtain reliable data

that are relevant to service conditions.

A series of workshops have been organised over the past

decade, most recently by Prof. Larry Bergman at the Uni-

versity of Illinois and Prof. David Ewins at Imperial College.

These have started to map out the challenges that need to be

overcome to improve our predictive capability for frictional

joint performance. These include [11] (i) Progress towards

standardisation of experimental techniques so as to provide

more reliable data for a ‘top down’ model of contact

behaviour; (ii) Development and validation of physics-based

understanding of interface response and (iii) Development of

consistent multi-scale models of friction, from the atomic

level to the scale of the whole contact. These challenges

define the landscape in which future research will take place.

The requirement is for research groups to come forward and

address them. It is hoped that the readership of Strain will

play their part in this and that we can look forward to some

interesting publications in this area over the next decade.

REFERENCES

1. Dowson, D. (1998) History of Tribology. Professional

Engineering Publishing, London.

2. Amontons, G. (1699) De la resistance causee dans les

machines. Memoires de l’Academie Royale, A 257–282.

3. Coulomb, C. A. and Coulomb, C. A. (1785) Theorie des

machines simples, en eyant egard au frottement de leurs

parties et a la roideur des cordages. Memoires de Math-

ematique et de Physique de l’Academie Royale 161–342.

4. Hertz, H. (1882) Uber die Beruhrung fester elasticher

Korper. Jnl. reine und angewandte Mathematik. 92, 156–171.

5. Cattaneo, C. (1938) Sul contatto di due corpi elastici:

distribuzion locale degli sforzi. Reconditi dell Accademia

nazionale dei Lincei 27, 342–348, 434-436, 474-478.

6. Mindlin, R. D. (1949) Compliance of elastic bodies in

contact. J. Appl. Mech. 16, 259–268.

7. Johnson, K. L. (1955) Surface interaction between elasti-

cally loaded bodies under tangential forces. Proc. R. Soc. A

320, 531–548.

8. Bowden, F. P. and Tabor, D. (1942) The mechanism of

metallic friction. Nature 150, 197–199.

9. Greenwood, J. A. and Williamson, J. P. B. (1966) Contact

of nominally flat surfaces. Proc. R. Soc. A 295, 300–319.

10. ASTM G115 – 04. (2004) Standard Guide for Measuring

and Reporting Friction Coefficients. ASTM, West Cons-

hohocken, PA.

11. Segalman, D. J., Bergman, L. A. and Ewins, D. J. (2007) Re-

port on the SNL/NSF International Workshop on Joint

Mechanics, Arlington Virginia, 16-18 October 2006, Sandia

Report2007-7761.SandiaNationalLabs,Albuquerque,NM.

David NowellDepartment of Engineering Science,

University of Oxford, Oxford, UK

E-mail: david.nowell@eng.ox.ac.uk

Editorial

214 � 2010 Blackwell Publishing Ltd j Strain (2010) 46, 213–214