friction and wear processes – thermodynamic approach

8/10/2019 Friction and wear processes Thermodynamic approach

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Vol. 36, No. 4 (2014) 341347

Tribology in Industry www.tribology.fink.rs

Friction and Wear Processes Thermodynamic Approach

M. Banjac a, A. Vencl a, S. Otovi a

a University of Belgrade Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia.

Keywords:

Friction Wear Energy dissipation Entropy generation Non equilibrium thermodynamics

A B S T R A C T

Tribology, as the scientific and professional discipline within the mechanical engineering, studies phenomena and processes on the interacting surfaces, in direct and indirect contact and in relative motion. It includes the study and application of the principles of friction, wear and lubrication, as well as phenomena connected with these processes. Given that a process involving friction is always accompanied by transformation of energy, more precisely an energy dissipation process which generates entropy, the concept of thermodynamic entropy production analysis

represents one of appropriate tools for studying and analysing the behaviour of complex friction and wear processes. This paper presents a review of published works in which the thermodynamic approach was used in analysing the friction and wear processes in tribosystems.

2014 Published by Faculty of Engineering

Corresponding author:

M. Banjac University of Belgrade Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia E mail: [email protected]

1. INTRODUCTION

Analysis of the literature may bring us toconclude that most of the published papers thatinvestigate the processes of friction and wearare using a heuristic approach, which thusbecame not the exception, but the rule forstudying these processes [1]. At the same time,although they represent differentmanifestations of the same physical processes,due to historical separation of their research,models developed for describing the frictionand wear have mostly remained without clearcorrelation and defined mutual dependence oftheir manifestations [2,3]. Consequently, it can

be said that, regardless of the large number ofproposed models that describe these processesin available literature, their applicability is still

considerably restricted and does not have thedesired level of generality.

On the other hand, although there is no doubt thatfriction and wear essentially represent typicalenergy processes, thermodynamic analyses ofthese processes are very rarely present in theliterature on tribology. During these processesoccurs the conversion of mechanical work orkinetic energy into other types of work, energy andheat, like the work of friction, the work for plasticdeformation, the work for wear, i.e. conversion ofworks into internal (thermal), chemical, potentialand other forms of energy. The amount of heatresulting from dissipation of the work of friction

force is around 80 to 90% of that work [21].Therefore, it can be said that the analysis of theseprocesses can not be considered complete, unless

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performed also from the aspect of the law ofconservation of energy, i.e. from the aspect of theFirst law of thermodynamics.

Besides their energyrelated character, theseprocesses occur with a prominent dissipation ofenergy, as well as in the temperature and chemicalnon equilibrium, often with the occurrence ofchemical reactions. That is why these processesmust unavoidably be also classified in the group ofirreversible thermodynamic processes. Hence, it isclear that in order to obtain a complete picture ofthese processes, their analysis should be madethrough the Second law of thermodynamics, i.e.through the balance of entropy (property of statethat describes the degree of irreversibility of allphysical processes).

Due to all above mentioned, this paper presentsan attempt to describe the friction and wearprocesses through a typical thermodynamicapproach. Because of their nature and the need toinclude in the description processes of exchangeof material between the contact surfaces, that isthe loss of material in the form of wear products, atribological system that includes the twocontacting bodies with their contact surfaces, wastreated as an open thermodynamic system. That iswhy it is described through three basic lawsdefined for open thermodynamic systems: the lawof conservation of mass (continuity equation) andthe First and Second law of thermodynamics.Unlike the approach used so far [48], definingthese balances based on the Prigogine theory ofirreversible processes and the Gibbs EntropyFormula [9,10], which combines the First andSecond law of thermodynamics, this paper usesthe forms of these three laws which are used inthe conventional technical thermodynamics. Thiswas done primarily because of identified

shortcomings of the Prigogine theory ofirreversible processes in defining balances.Namely, the balances defined in this way either donot recognize energy and entropy effects of theexchange of material between contact surfaces orinclude them in a too complicated way.

2. MODEL

2.1 The physical model

Wear has been defined as the progressive loss ofsubstance from the operating surface of a body

occurring as a result of relative motion at thesurface, while friction has been defined as theresisting force tangential to the commonboundary between two bodies when, under theaction of an external force, one body moves ortends to move relative to the surface of the other[22]. This definition of friction refers mostly tothe external friction and do not specificallyinclude the internal friction (viscosity). Externalfriction, and wear occurring in this case, will bethe subject of this analysis.

Thus, a considered physical model is made up oftwo solid bodies in direct or indirect contactwhich are in relative motion against each other.Each body, viewed from a thermodynamic pointof view, is a thermodynamically open system

(subsystem), where the boundaries of each ofthe subsystems include the outer contours of thecorresponding body and pass through theircontact surface. Exchange of material betweenthese bodies through this contact surface isexactly the reason that these systems have to betreated as open (Fig. 1).

Body I

Controlboundaryof body I

F n F f = F n

Sliding directionBody II

Zoneof tribologicaleffects Control

boundaryof body II

Fig. 1. Physical model of the tribological system andthe areas of mechanical action ( F f friction force; F n normal force; coefficient of friction).

2.2 The thermodynamical model

Thermodynamics is based on two fundamentallaws; the first law implies conservation of energyand the second implies that, for any process totake place, the change in entropy has to be zero orpositive. Entropy therefore can only be created,never destroyed. The first law is independent ofthe type of the process [21].

With the previously defined conditions, the massbalance of the subsystem which makes the body I(Fig. 2a), i.e. overall change in mass of the first

body can be defined by the equation:in I cv out d = d( ) +dm m m , (1)


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where: d( m I)cv is change of mass of the body I(body into control volume) in a differentiallysmall moment of time d t , dm in is the mass ofmaterial of the body II, which is to betransferred to the body I in a differentially smallmoment of time d t , dmout is the mass of materialof the body I which is separated by wear fromthe body I in a differentially small moment oftime, and cv is the control volume.

The second main balance equation for thecontrol volume of the body I represents thebalance of energy or the First law ofthermodynamics. For the so defined controlvolume (Fig. 2b) this balance in differential form,i.e. for a differentially small moment of time d t ,is as follows:

in in cv=1

+ + d = d( )m

j j

Q W u m U

out out =1 =1 =1

productsreactants

d d + d + d p n r

k k l l ik l i

n n E u m

, (2)

where: Q is the elementary quantity of heattransferred to the body I in a differentially smallmoment of time, W j is the different type ofelementary work done on the body I (work forovercoming adhesion forces, work for creatingplastic deformation, etc.), d( U )cv is the differentialchange of internal (thermal) energy of the body I(body into control volume), u in is the specificinternal (thermal) energy of the mass d m in, uout isthe specific internal (thermal) energy of the massdmout , k dnk and l dn l are the elementarychemical work or elementary energy of chemicalreaction of the k th and l th component, k and l are the chemical potentials of chemical reactionof the k th and l th component, d nk and d n l arethe moles of substance k and l with the

chemical potential k and l transported from thesystem to its surroundings, d E i is the change ofother forms of its internal energy, e.g.electrochemical, photochemical, etc.

Opposite to the aforementioned approach basedon Prigogine theory of irreversible processesand Gibbsons relation, two new terms u indm in and uout dmout , appear in the equation (2), andrepresent the energy transferred into the controlvolume of body I with mass transfer d m in andout of the control volume of body I by weardmout , respectively. The u in and uout denote

specific internal energy of supplied and specificinternal energy of removed material.

d( U ) cv dn + dE

Body I

Body I

u out dm out

Body I

d( m I) cv

dm out dm in

u in dm in

s in dm in

d( S ) cv dS gen

W Q

sout dm out cscs

dq AT

Fig. 2. Schematic view of the balance of mass, energyand entropy of a tribological system.

Finally, the third main balance equation for thecontrol volume of the body I is the balance ofentropy equation or the Second law ofthermodynamics (Fig. 2c). This law indifferential form, i.e. for a differentially smallmoment of time d t is:

gen in in cv out out cscs

dd + + d = d( ) + dq AS s m S s mT

, (3)

where: d S gen is the entropy generation thatoccurs in the control volume of the body I causedby irreversible processes within the controlvolume (processes of dissipation of mechanicalwork, chemical reactions, nonequilibriumprocesses of heat and mass transfer, etc.);

cscs

dq A T is an increment of entropy originating

from the transfer of heat to the body I (where q isthe specific heat flow, d A is the elementarysurface of the control surface and T cs is thetemperature of that elementary surface), d( S )cv isthe differential change of entropy of the body Iand sin and sout are the specific entropy of massdm in and d mout , respectively.

(a)

(b)

(c)


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3. CAUSES OF ENTROPY GENERATION

Unfortunately, balances written in this way aretoo general and have no practical use regardlessof their universality. Just because of that, allattempts in defining the models of tribologicalsystems with laws of thermodynamics, definedin this and similar way, had a very limitedsuccess [5,6,1114]. In addition, all attempts oftheoretical elaboration of particular terms madeso far, because of the extreme complexity of thederived equations and the accompanyinginability of their solution, did not lead to thedesired result.

For this reason, in order to make balanceequations more applicable for practical use, the

existing phenomenological (empirical)relationships that define specific processes whichoccur during wear and friction were used fordefining the particular terms which exist in them.These processes are connected by the samecauses of irreversibility. Since Klamecki [5] andthen also Bryant [8] proposed their classification,some of the mathematical relations alreadyproposed by these authors will be used.

As identified causes of irreversibility the authorsspecify: the dissipation of work for overcomingthe adhesion forces, the dissipation of work forabrasion (plastic deformation) process, thedissipation of work for fracture (creating cracksand fissures), the processes of change in state ofmaterial, chemical reactions, heat conductionand diffusion processes. Each of these causes ofentropy increase will be explained in detail.

3.1 Dissipation of mechanical work used for overcoming the adhesion forces

Dissipation of mechanical work used forovercoming the forces of adhesion is the workthat is being spent for overcoming theelectromagnetic intermolecular forces ofattraction of solids at small distances. Thesesmall distances occur between the contactsurfaces of the tribological system elements inthe process of friction and wear. During theseprocesses work dissipates and turns into otherforms of energy, first heat and then into theinternal (thermal) energy.

Since this work is defined as the product of theinterface surface energy (the surface tension of

fluids in the case of fluids) and the newly createdsurface area d As, its energy value can be defined as:

ad S = dW A . (4)

Using the general expression that correlates the

transferred amount of heat Q, the change ofentropy substance d S and its temperature T

d = QS T

, (5)

under the assumption of complete dissipation ofmechanical work into heat when mastering theadhesion forces, entropy change caused by thisirreversible process can be written as:

adgen, ad S

m m

d = = d

W S AT T

, (6)

where T m is the local temperature of the body I.

It is important to note that under the influenceof these types of electromagnetic intermolecularforces the adhesive wear of materials occurs.This type of wear is manifested by the transferof material between the two contact surfaces, aswell as by creation of wear products. The partsof energy and the parts of entropy, exchanged inthat way between the control volumes arecovered by the appropriate terms in equations

(2) and (3) i.e. u indm in and uout dmout and sindm in and sout dmout , respectively. Therefore, the termssindm in and sout dmout do not belong to the part ofgenerated entropy, but to the part of entropyexchanged along with the exchange ofsubstances.

3.2 Dissipation of mechanical work used for abrasion (plastic deformation) process

The process of abrasion, which is happening

during the mutual movement of contactsurfaces, as a result of penetration of asperitiesof harder material into the surface layers ofsofter material is accompanied by ploughingand/or cutting (plastic deformation) of bothcontact surfaces. Thus, the work used forabrasion of the surface could be defined as theproduct of the work for abrasion reduced to unitvolume (work per volume) w pl and elementarychange of the body volume d V :

ab ab = dW w V . (7)

Extensive studies on the relationship betweenabrasion, i.e. plastic deformation of the surface,


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and dissipation of energy were conducted byFouvry at all. [1517]. They found that there is alinear function between the volume of the wornmaterial and dissipation of the energy usedduring this process. They have presented thislinear relationship by defining the appropriatecoefficients for a large number of testedmaterials. One of the analysed cases, with a welldefined linear dependence, is shown in Fig. 3.

Fig. 3. Linear relationship between the dissipatedenergy during the process of fretting wear and wornmaterial volume [4].

Generation of entropy caused by irreversibleprocess of abrasion in accordance with equation(5) can be determined as:

gen, ab abgen, ab

m m

d = = d

W w S V

T T , (8)

where T m is the local temperature of the body.

3.3 Dissipation of mechanical work used for creating cracks and fissures

Work that is used for creating of cracks orfissures on the surface, as well as for theprocesses associated with the surface fatiguewear, i.e. pitting and to some extent erosivewear, is defined by the empirical expression:

cr cr = ( 2 )dW G A , (9)

where G is the energy release rate during theprocess of creating cracks, reduced to a unitcrack area, is the surface energy, and Acr is thearea of cracks surface. So, the energy releaserate is defined as:

crcr

= U

G A , (10)

where U cr is internal energy of crack growth.

Based on the foregoing and in accordance with theequation (5), the generation of entropy caused bythis irreversible process can be determined as:

crgen, cr cr

cr cr

( 2 )d = = dW G S AT T

, (11)

where T cr is the local temperature of the crackedmaterial at the crack tip.

3.4 Dissipation of energy used for phase transition process

The energy required for a phase transition, i.e.that is consumed during the process of meltingand subsequent recrystallization of the metalsurface can be determined as the product of thespecific energy or latent heat absorbed or lostduring the phase change from a liquid to a solidstate r sol and mass of molten metal m liq:

phase sol liqd = dE r m . (12)

According to equation (5) and in the case ofcomplete dissipation of that energy, generationof entropy caused by this irreversible processcan be determined as [8]:

sol solgen, phase liqphase phase

dd = = d

E r S mT T , (13)

where T phase is the local temperature of thematerial in the place of phase change.

3.5 Change of entropy caused by the chemical reactions

Due to its special significance, the energy ofchemical reactions, associated with corrosive andoxidative wear, was singled out from other energy

influences in the equation of energy balance (2)and presented by the following expression:

hem=1 =1

reactants products

d = d d p n

k k l l k l

E n n

. (14)

Appropriate change in entropy caused bydifferent chemical reactions, in accordance withthe expression (5) can be defined as:

=1 =1ch

ch, ch,

d d

d =

p nk k l l

k l

k l

n n

S T T

, (15)


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where T ch,k and T ch, l are the local temperature atthe place of chemical reaction for reactants andfor products.

3.6 Change of entropy caused by the heat conduction process

The process of conduction of the heatthroughout the body, released during friction Q occurs in the temperature imbalance betweenthe temperature at the boundary surface T s andthe temperature inside the body T b. Because ofthat temperature imbalance, this processinevitably causes an increase of entropy, whichcan be defined as [9]:

gen,s b

1 1d = QS QT T

. (16)

In considering the amount of released heat Q, itshould be noticed that it is only a part of the totaldissipation of mechanical energy. As mentioned,a part of that energy is spent on the overcomingthe adhesion, abrasive wear, formation of cracksand fissures, etc. The determination of allocationof mechanical energy and the share of itsconversion into heat have studied by Chen and Li[18,19] and Elalem et al. [20]. Figure 4 shows thedistribution of generated heat during sliding, for

different loads, as a function of distance from thecontact surface.

Fig. 4. Share of heat in the total dissipated energydepending on the distance from contact surface [4].

3.7 Generation of entropy due to diffusion processes

Although the assumed physical model does not

anticipate a third body (lubricating fluid), in thecase that it exists, generation of entropy causedby the process of diffusion of that fluid into

structure of the body I or into the body II shouldbe also taken into account.

4. CONCLUSION

Although the thermodynamic approach offersthe possibility of a systematic analysis ofbehaviour of tribological systems, it is not yetsufficiently developed to have the practical use.For that approach to reach practical use, itshould be improved and completed by thecorresponding constitutive equations, which willconnect the main physical processes with theirenergetic and entropic effects. Their creationwill certainly require additional, dedicatedexperimental studies of individual processes.

However, despite its shortcomings, thisapproach based on using main laws of physics:mass balance, energy balance and entropybalance, to reach a universal tribological model,still remains very promising, due to itsmethodical feature.

Acknowledgement

The authors are grateful to the Ministry ofEducation, Science and Technological Developmentof the Republic of Serbia, which has financiallysupported this paper through the projects TR33018, TR 33047, TR 34028 and TR 35021.

REFERENCES

[1] K.C. Ludema: The state of modelling in friction and wear and a proposal for improving that state ,Journal of Korean Society of Tribologist andLubrication Engineers, Vol. 11, No. 5, pp. 1014,1995.

[2] I.V. Kragelskii: Friction and Wear , Butterworthand Co., Bath, 1965.

[3] E. Rabinowicz: Friction and Wear of Materials ,John Wiley and Sons, New York, 1965.

[4] H.A. AbdelAal: Thermodynamic modeling of wear , in: Q.J. Wang, Y.W. Chung (Eds.):Encyclopedia of Tribology , Springer, New York,2013, pp. 36223636.

[5] M. Amiri, M.M. Khonsari: On the thermodynamics of friction and wear A review , Entropy, Vol. 12,No. 5, pp. 10211049, 2010.

[6] B.E. Klamecki: Wear An entropy production model , Wear, Vol. 58, No. 2, pp. 325330, 1980.


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[7] B.E. Klamecki: A thermodynamic model of friction ,Wear, Vol. 63, No. 1, pp. 113120, 1980.

[8] M.D. Bryant, M.M. Khonsari, F.F. Ling: On the thermodynamics of degradation , Proceedings ofthe Royal Society A, Vol. 464, No. 2096, pp. 20012014, 2008.

[9] M.D. Bryant: Entropy and dissipative processes of friction and wear , FME Transactions, Vol. 37, No.2, pp. 5560, 2009.

[10] I. Prigogine: Etude Thermodynamique des Processus Irreversibles , Desoer, Liege, 1967.

[11] D. Kondepudi, I. Prigogine: Modern Thermodynamics from Heat Engines to Dissipative Structures , John Wiley & Sons, Inc., New York,1998.

[12] OECD Research Group on Wear of Engineering

Materials: Glossary of Terms and Definitions in the Field of Friction, Wear and Lubrication: Tribology , Organisation for Economic Cooperation and Development, Paris, 1969.

[13] B.E. Klamecki: An entropy based model of plastic deformation energy dissipation in sliding , Wear,Vol. 96, No. 3, pp. 319329, 1984.

[14] A. Zmitrowicz: A thermodynamical model of contact, friction and wear: I governing equations ,Wear, Vol. 114, No. 2, pp. 135168, 1987.

[15] A. Zmitrowicz: A thermodynamical model of contact, friction and wear: II constitutive equations for materials and linearized theories ,Wear, Vol. 114, No. 2, pp. 169197, 1987.

[16] A. Zmitrowicz: A thermodynamical model of contact, friction and wear: III Constitutive equations for friction, wear and frictional heat ,Wear, Vol. 114, No. 2, pp. 199221, 1987.

[17] S. Fouvry, P. Kapsa, H. Zahouani, L. Vincent: Wear analysis in fretting of hard coatings through a dissipated energy concept , Wear, Vol. 203204,pp. 393403, 1997.

[18] S. Fouvry, T. Liskiewicz, Ph. Kapsa, S. Hannel, E.Sauger: An energy description of wear mechanisms and its applications to oscillating sliding contacts ,Wear, Vol. 255, No. 16, pp. 287298, 2003.

[19] S. Fouvry, C. Paulin, T. Liskiewicz: Application of an energy wear approach to quantify fretting contact durability: Introduction of a wear energy capacity concept , Tribology International, Vol.40, No. 1012, pp. 14281440, 2007.

[20] Q. Chen, D.Y. Li: A computational study of frictional heating and energy conversion during sliding processes , Wear, Vol. 259,No. 712, pp.13821391, 2005.

[21] Q. Chen, D.Y. Li: Computer simulation of solid particle erosion of composite materials , Wear, Vol.255, No. 16, pp. 7884, 2003.

[22] K. Elalem, D.Y. Li, M.J. Anderson, S. Chiovelli:Modeling abrasive wear of homogeneous and heterogeneous materials , in: G.E. Totten, D.K.Wills, D.G. Feldmann (Eds.): Hydraulic Failure

Analysis: Fluids, Components, and System Effects ,ASTM, West Conshohocken, 2001, pp. 90104.

friction and wear processes – thermodynamic approach

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