The Role of Solid Lubricants for Brake Friction Materials

This review article comprises of three parts. Firstly, reports of brake manufacturers on the beneficial impact of solid lubricants for pad formulations are surveyed. Secondly, since tribofilms were identified to play a crucial role in friction stabilization and wear reduction, the knowledge about tribofilm structures formed during automotive braking was reviewed comprehensively. Finally, a model for simulating the sliding behavior of tribofilms is suggested and a review on modelling efforts with different model structures related to real tribofilms will be presented. Although the variety of friction composites involved in commercial brake systems is very broad, striking similarities were observed in respect to tribofilm nanostructures. Thus, a generalization of the tribofilm nanostructure is suggested and prerequisites for smooth sliding performance and minimal wear rates have been identified. A minimum of 13 vol % of soft inclusions embedded in an iron oxide based tribofilm is crucial for obtaining the desired properties. As long as the solid lubricants or their reaction products are softer than magnetite, the main constituent of the tribofilm, the model predicts smooth sliding and minimum wear.


Introduction
Solid lubricant nanoparticles like graphite, MoS 2 or WS 2 are frequently used as oil additives.Their beneficial role for friction and wear reduction under mixed lubrication regimes has been elucidated in several review articles recently [1][2][3].Since the particles from which tribofilms form are so small, the film thickness usually amounts to less than 100 nm.Whereas under mixed lubrication conditions using additive-free engine oil the coefficient of friction (COF) of steel-on-steel contacts approaches 0.15, it drops well below 0.05 under hydrodynamic lubrication conditions [4].The objective of using oil additives is to keep the ultra-low COF even under mixed lubrication conditions when asperities of the counter-bodies come into direct contact with each other [2].This usually is achieved by crystallographically aligned solid lubricant films of either graphite [5][6][7] or MoS 2 and WS 2 [8][9][10][11][12], or by amorphous films which can flow in a fluid-like manner [13,14].
Whereas the mechanisms of superlubricity caused by solid lubricant films are fairly well understood nowadays, the role of solid lubricants as friction stabilizers in typical dry friction applications like brakes and clutches is not so clear.Doubtlessly, the formation of solid lubricant films would reduce friction to an extent which cannot be accepted during braking.Therefore, other mechanisms must be responsible for the desired effect of friction force stabilization at a medium COF-level in the range 0.3-0.5.For decades, the challenge was to develop brake friction materials which, if rubbed against a cast iron rotor, provide smooth sliding and a stable COF within a wide range of stressing and environmental conditions.Therefore, it seems reasonable to start with a review on progress made with the addition of solid lubricants to brake pad formulations.A further literature review demonstrates how Godet's third body approach [15] is related to mechanisms occurring at the interface between the brake pad and disc.This section is dedicated to the characterization of tribofilms formed during automotive braking.Finally, modeling approaches enabling visualization of sliding mechanisms at the pad-disc interface, and providing an estimate of corresponding COF-evolution are reviewed.

Why Do We Need Solid Lubricants for Brake Applications?
According to a report prepared by P. Blau for the U.S. Department of Energy, the first resin-bonded friction composites were developed already around 1950 [16].From the beginning, brake pad materials were multiple composites and the number of ingredients increased continuously with the years.Complex materials are needed because of the multiple functionalities which have to be met.Constant friction within a wide range of stressing and environmental conditions is not the only criterion.Furthermore, the customer expects smooth pedal feel and noiseless braking operation.Especially the latter comfort requirements are a great challenge for brake and car manufacturers.The function of solid lubricant additions is to initiate smooth sliding conditions without impairing the frictional performance too much.Naturally, formulations become more and more complicated during an optimization procedure.This makes it almost impossible to assess the impact of one specific constituent on brake performance properties unless all stages of material development are known.Therefore, it makes sense to start the review while focusing on the literature describing systematic studies on more or less simple model materials, and then check whether the observed principles can be applied to more complex composites as well.

Addition of Graphite
Graphite is the most widely used solid lubricant for all kinds of applications including friction composites.Furthermore, it is present in almost every disc brake system in the form of graphite flakes as constituent of the cast iron rotor.As mentioned by Blau [16], its impact on tribological properties can be manifold, depending on structure variants, contaminants and environmental conditions.Pure graphite-like friction materials are applied as so-called C/C-brakes for aircraft braking.Since they always operate at elevated temperature, the problem of low friction at ambient conditions, especially under high humidity, can be neglected.Goudier et al. observed a low to high friction and wear transition at 300 ˝C which could be attributed to the onset of oxidation [17].Kasem et al. observed a similar transition already in the temperature range 130-180 ˝C [18].The same effect may also explain the results of Stadler et al. who reported on an increase of the COF and wear volume with increasing graphite content in the high temperature range, and an undesired low COF at ambient temperature in a metal matrix composite (MMC) pad rubbing against a C/C-SiC ceramic brake disc [19].Cho et al. performed thermogravimetric analysis of graphite showing signs of oxidation not until 700 ˝C [20].These authors also pointed out that flash temperatures at tribological contacts usually are much higher than average surface temperatures measured near the disc surface.Thus, tribooxidation of the graphite could have occurred readily under the applied conditions of testing.Nevertheless, in contrast to metal sulfide additions which will be discussed later, a positive effect of graphite towards friction stabilization at elevated temperatures was not proved in this case.This may be due to the fact that a graphite-free reference material was missing, or, that the composition of the friction material was already too complex.The same holds for a recent study by Ram Prabhu, who also could not elaborate a clear effect of graphite addition to a MMC friction material in contrast to MoS 2 addition [21].There are some other studies on copper-based MMCs which show clear effects of graphite additions on triboligical properties [22,23].The observed effect was a decrease of COF and wear with increasing graphite content.An interesting finding was that a major amount of the wear debris consisted of iron oxides [22].A systematic investigation considering well-defined powder mixtures of copper and graphite showed a transition from a high to a low friction regime with increasing graphite concentration [23].At 10% graphite, which is a common number of brake friction materials, the system was in the high friction regime corresponding to a COF of 0.5.However, even for pure graphite powder, the COF was still near to 0.3 which is much higher than the one observed for the C/C couple at ambient temperature (0.15) [17,18].Although not designed for brake application, it is interesting to look at the results obtained with epoxy coatings filled with graphite and MoS 2 particles [24,25].While rubbed against steel discs, the pure epoxy provided a COF of 0.5 and 0.55, according to [24] and [25], respectively.Epoxy filled with at least 10 wt % graphite provided a COF of 0.35 which remained constant with increasing graphite content [25] or decreased slightly to 0.25 [24].If we assume that the graphite particles are released from the film during the tribological test, forming a graphite particle layer at the interface, the COF should be lower.An explanation for the observed higher COF is that the released graphite particles mix with iron oxide particles formed by tribooxidation of the steel disc.The sliding behavior of iron oxide mixed with different concentrations of graphite was studied comprehensively by modelling, as described in Section 4.

Metal Sulfide Based Solid Lubricants
A number of metal sulfides are frequently applied in brake pad formulations, although rarely as single additives.The functionality of these constituents is to provide friction stability and to reduce wear at elevated temperatures.It was assumed that chemical reactions occurring at these elevated temperatures are responsible for the beneficial effects, and therefore Melcher and Faullant studied the thermo-physical properties of a comprehensive number of candidate materials and their oxides [26].Some of their findings are the following: Classical solid lubricants with a layer structure are besides graphite and hexagonal BN: SnS 2 , WS 2 , TiS 2 and MoS 2 .Other soft sulfides with Mohs hardness 2 or less but without layer structure are: Sb 2 S 3 , SnS, Bi 2 S 3 and CuS.Some of the latter are also frequently used as friction modifiers indicating that a layer structure is not a necessary prerequisite for obtaining the desired brake performance properties.According to Melcher and Faullant [26], such desired properties may be linked to phase transitions and/or chemical reactions and the properties of reaction products.The authors described some scenarios that could happen with the different additives during braking, but their experimental studies were not adequate for providing proof for their assumptions.Nevertheless, they compared a large number of different solid lubricant additions (6 wt % each) with a so-called base-formulation, and they could show impacts on wear and COF at 100 ˝C and 400 ˝C.Similar results were obtained by Hoyer et al. by adding 8 vol % of CuS 2 , PbS or Sb 2 S 3 to three different types of base compositions [27].Matejka et al. observed a chemical reaction of Sb 2 S 3 with iron [28] at 350 ˝C and correlated this with the observed decrease of the COF.According to these studies, each additive provided positive and negative effects.Therefore, a coherent conclusion is that single additives cannot fulfill all requirements, and that a combination of different ingredients is needed.Systematic approaches with different solid lubricant combinations were described by Jang and coworkers for graphite/Sb 2 S 3 [29] and graphite/Sb 2 S 3 /MoS 2 [20,30].There are some commercial products on the market promising smooth sliding without reducing the COF.One paper is pointing out that the perfect additive consists of graphite particles coated with molybdates, phosphates, sulfates or sulfides [31].The authors claim having obtained achievements by using such additives in a brake pad formulation, but such results cannot be generalized without knowing the mechanisms behind the observed effects.
As already mentioned above, it is almost impossible to predict the impact of single ingredients on brake performance properties of commercial friction materials, which further differ enormously in their base compositions.Nevertheless, we can learn from the experiences made by friction material compounders.Some of the numerous observations made during material development and dynamometer testing are compiled in Table 1.Only major components neglecting fillers are given in column 1.The term fade means decrease of COF at elevated temperatures.COF 1 indicates the COF-range obtained during moderate braking and COF 2 the friction behavior observed during typical fading cycles.If different material variants were considered within one study, the optimized composition in respect to overall brake performance was selected for displaying the COF data.Considering all observations together, the following general conclusions can be drawn.Solid lubricants are needed to provide a constant COF within a range of 0.3-0.5, irrespective of the applied load and sliding velocity at moderate and elevated temperatures.The concentration of solid lubricant additions must not exceed a certain limit of approximately 10 vol %, because otherwise the COF might drop below 0.3.Using only one type of a certain solid lubricant usually does not yield satisfactory results.Frequently, a combination of graphite and one of the soft metal sulfides is the best choice.Since the sulfides usually are oxidized at elevated temperatures during fading cycles, the evolving oxides should have similar mechanical strength as the original ingredients.In fact, this prerequisite is only fulfilled strictly for Sb 2 S 3 and PbS.Since both raw materials should be replaced in brake pad formulations because of health concerns [38], other soft metal sulfides have been tested comprehensively.Their oxides, like MoO 3 , SnO, Bi 2 O 3 and CuO, are harder than the corresponding sulfides, albeit still softer than the iron oxides [26].The latter finding will be important for the discussion in Section 5.Although most brake pad manufacturers have reduced or eliminated Sb 2 S 3 from their formulations, published reports on systematic studies with the other sulfides are still rare.As discussed during recent brake conferences [39][40][41], tin sulfides are currently regarded as the most promising candidates for antimony replacement in brake pad formulations.A recently published paper shows that good friction properties had been achieved with a solid lubricant blend consisting of tin sulfide, iron sulfide and potassium titanate [42].Certainly, tin sulfide is not the only alternative to Sb 2 S 3 .Yun et al. prepared an eco-friendly brake friction material without copper, lead, tin, antimony trisulfide and whisker materials [37].They used a small amount of MoS 2 in combination with graphite to reach this goal.
Most authors cited in Table 1 state that the formation of a stable tribofilm is responsible for achieving the desired brake performance properties.Exact knowledge about the structure and properties of such films seems to be the key for understanding the friction and wear behavior of the frictional brake system.Therefore, the state of the art of tribofilm characterization in conjunction with braking is reviewed in the next section.

Structure and Composition of Tribofilms Formed during Braking
Since almost 50 years, attempts were made to characterize and understand the material changes occurring at the interface between a rotating brake disc sliding against a fixed pad, the latter consisting of a friction composite.Whereas in at least 90% of considered studies the rotor material was the same, namely grey cast iron, the composition of the tested friction composites varied enormously.However, every commercial brake friction material has to fulfill similar requirements in terms of friction level, friction stability and wear with only slight differences in preferences according to the car manufacturers.This suggests that the composition and microstructure of wear products, which are partly released to the environment and partly forming tribofilms if compacted and bonded to the first body surfaces, should have similar microstructures which determine their friction and wear behavior while sliding against each other.Investigations performed by the authors during the last 15 years revealed a lot of details concerning tribofilm structures.In the following, the results are discussed in the context of a comprehensive, although certainly not complete, literature-review.The only restriction made during preparing the review was that the considered wear products were formed under real braking conditions leading to a COF level in the range of 0.3-0.5 (see also Table 1).The results of the review are compiled in Table 2. Naturally, the completeness of the derived information depends on the applied characterization methods.Therefore, usually only partial information was available within one study, which sometimes caused misinterpretation of the results by the authors.Therefore, whenever reasonable, an attempt was made to reinterpret the results in the light of the numerous new findings published in the meantime.The meanings of acronyms for the different methods are given in Table 3.
Table 2. Literature review on the characterization of tribofilms observed after brake dynamometer testing, and corresponding methods (chronological order).

Reference
Methods Observations Authors' Interpretation Comments [43] LM TEM Much less coarse and fine asbestos fibers observed, as expected.
Most asbestos converted to olivine and stored at surface as tribofilm.
Olivine mixed with other wear products has formed a tribofilm. [44] EA TGA PGC Thermal degradation of phenolic resin during braking.
Formation of a residual polymer which is aromatic hydrocarbon in nature.
Formation of a soft solid state wear product which is mixed with other wear debris. [45]

SEM EDS XRD
Mix of debris from pad and rotor forming tribofilms.Reduction of Fe and graphite grain size (XRD).Enrichment of inorganic species near pad surface.
No oxide observed at low temperature attributed to continuous removal.Plastically deformed layer and transferfilm at disc surface identified.
Almost all interpretations consistent with most recent findings.Exception: no iron oxide observed at low temp.This may be due to very thin tribofilm. [ X-LM TGA XRD XFA Changes of tribo-affected zone with increasing temperature: More inorganic, less asbestos, less polymer species.
Increasing wear with increasing temperature, complex material changes.Black tribofilm interpreted as carbonaceous material Black tribofilm at elevated temperatures consists of magnetite mixed with carbonaceous material. [47]

LM SEM EDS MH
Wear particles consisting of iron and iron oxide.Cu transfer to disc.
Formation of metallic iron and copper was attributed to hydrogen evolution during resin degradation.
Observations confirmed by later studies.Role of hydrogen not confirmed. [48]

LM SEM PGC
Incompletely oxidized metal and graphites.430 ˝C wear debris contained degraded resin.
Tribofilm continuously formed by compaction of wear debris, and sheared on both counterbodies.
This interpretation is up to date.
[49] XPS EDS MoS 2 and Ba SO 4 not stable but transformed to MoO 3 and BaO, respectively.
Although, transferfilm chemistry depends on abrasive addition, little effect on friction and wear.
MoO x confirmed [50] BaO not confirmed by additional studies.
Good coverage of surface with tribofilm formed from wear debris provides wear protection.
The general conclusion is correct.The role of aramid for tribofilm formation not confirmed by further studies.Not only the protruding plateaus, but also deeper areas may have been contacting areas.
This interpretation did not consider flow of 3rd body particles and the possibility of particle trapping in troughs.
[61] X-SEM ERM Transfer layers in a thickness range 10-50 µm were obtained by drag tests at elevated temperatures.
Solid lubricants exert great impact on transfer layer thickness.No effect on COF but smoother sliding.
The formation of such thick transfer layers is rarely observed in practice. [62]

SEM EDS XFA
Examples of binding solid lubricants to meso-scale pad constituents observed for commercial pad materials.
Distribution and retention of solid lubricants at the pad surface is an important issue.
Ingredients must be available everywhere at the rubbing interfaces for being incorporated into the 3rd body. [63] FIB/TEM GDOS RS Fe 3 O 4 -based tribofilm also contains amorphous and graphite-like C (RS).Ca-, Sand Cu-transfer to disc (GDOS).
Tribooxidation of Fe-constituents and mixing with graphite and other solid lubricants occurs on the nanometer scale.
Ca-enrichment at the disc surface not reported by other studies, except one [34]. [64]

TGA MS SEM
Oxidation of resin into volatile species at 300-600 ˝C.Mechanical activation lowers temperature range.
Good friction performance even at high temperatures attributed to 3rd body layers formed during degradation of resin.
Obviously, secondary plateaus were retained at elevated temperatures (SEM).
[34] SEM EDS EDS-maps suggest more material transfer from pad to disc for formulations with addition of sol.lubs.
The observed material transfer stabilized the COF and led to reduced wear.
Obviously an unconventional CaCO 3 -based film has formed, because of high CaCO 3 -content of the pad.
[65] FIB/SIM TEM/EDS Plastically deformed layer below tribofilm at disc surface.Nc Fe 3 O 4 -based tribofilm mixed with small amount of pad constituents.
Mixing of Fe 3 O 4 with soft nanoparticles from pad ingredients is a prerequisite for obtaining smooth sliding conditions.
This finding defined the basic structure for modelling the sliding behaviour of tribofilms, as discussed in Chapter 3. Since nanocrystalline wear particles were observed, their potential risks have to be considered in the future.
Identification of reaction products at disc surface by GA-XRD not confirmed by further studies.
[67] LM X-SEM EDS FIB EF-TEM Cross-section with pad still pressed against disc showed continuous 3rd body layer.Nasnoscale elemental mapping revealed C and Cu nanoparticles and submicron-sized Al 2 O 3 .
More 3rd body present at the interface while the pad is still pressed against the disc than usually observed during post mortem studies.
Complicated 3rd body structure with different submicron-or even micron-sized particles (depending on the thickness of the tribofilm) embedded in multi-phase nc-matrix.Final state of 3rd body formation leads to mixing of wear products on the nanometer scale [69] SEM Cavities formed around steel fibers which then were filled with wear debris under dry conditions and with water under wet conditions.
COF-increase with pressure attributed to increase of real contact area.COF-decrease under wet conditions attributed to wear debris removal and mixed lubrication.
The study shows that mechanisms taking place at the meso-and micro-scale have to be kept in mind.C-based ingredients (graphite, resin, coke . . . ) all transformed to amorphous C, thus explaining the high fraction of amorphous carbon in the wear product.
The high amount of amorphous carbon in the wear product was not corroborated by other studies.Actually the investigated formulation contained much C. On the other hand, TEM always considers only very small volumes, and thus uncloses the danger of over-interpretation.
[37] SEM EDS Different pad materials all covered with Fe-oxide based tribofilm.
Cu-and Sb-free pad forms similar tribofilm as conventional materials.Reaction of metal powders with solid lubricants considered as beneficial.
Reaction products could not be identified unambiguously with the applied methods. [42]

SEM X-SEM EDS XRD
Fe-Zr mixed oxides in films and wear debris.XRD: mainly Fe 2 O 3 , also metallic copper.
Released and fragmented hard particles from pad mixed with Fe-oxide from disc.Cu needed for binding constituents of the tribofilm together.
In principle in accord with previous findings, but hematite instead of magnetite is unlikely, because of the black colour of brake dust.At first, commonalities of the findings compiled in Table 2 are considered.Not a single case of a mono-phase solid lubricant film was observed.This clearly shows that the mechanism of friction stabilization at a medium COF-level is different compared to classical solid lubricant applications.In the latter case, the formation of a textured film providing easy shear planes leads to reduction of COF and wear.Furthermore, it was quite clear from the beginning that if films were observed at the surfaces of the first bodies, these were formed by compaction of wear products.Thus, it is quite clear that Godet's concept of a third body screening the surfaces of first bodies, pad and disc in our case, is valid [15].Naturally, wear debris is formed by fragmentation and mixing of first body materials, and eventually by chemical reactions between different species and the atmosphere.Almost all studies provide evidence that such processes have occurred, although the degree of fragmentation and mixing can differ considerably from site to site on a rubbed surface.The findings also depend on the applied characterization methods.Thus, LM and SEM will reveal fragments on the micrometer scale, while TEM is capable of revealing nanostructures but usually neglects or does not realize features on the micrometer scale.Since commercial brake pads generally consist of more than 10 ingredients, which furthermore differ in size, a large variety of different wear particles will be formed initially.The bigger particles cannot form stable films.Thus, they are either fragmented further or emitted to the environment.Under certain conditions several microns thick films were observed [61,75], although usually tribofilm thickness is in the sub-micron range.The latter films can only be formed from nanoparticles and, therefore, their structure can only be revealed by TEM-related methods.Nevertheless, SEM/EDS, XRD and some other bulk methods can provide information about third body composition and phase content provided that the third body material can be separated from its substrate.Considering these prerequisites, the majority of the studies of Table 2 led to the conclusion that the major phase of the third body, which finally is forming tribofilms, is iron oxide Fe 3 O 4 .Although Fe 2 O 3 may sometimes form as well [42,56], there is strong evidence that Fe 3 O 4 is the major phase for the following simple reason: If one touches a used brake pad or disc, the finger will turn black.Color is very sensitive to the type of oxide.Fe 3 O 4 (magnetite) is black and Fe 2 O 3 (hematite) is reddish or at least brown.Although, mostly only revealed by TEM-techniques, the nanocrystalline structure of the fully processed third body contains other species besides Fe 3 O 4 .Theoretically, all ingredients of the pad formulation or their chemical reaction products should be homogeneously mixed on the nanometer scale, provided the original ingredients are prone to nanostructure formation by mechanical processes like severe shear deformation or impact during particle collisions.The latter can be checked by ball milling experiments, as proved by several papers [70,[79][80][81].A special mechanism of nanostructure formation is tribooxidation of the cast iron disc providing the major constituent of the third body.Here, it is not only severe plastic deformation, but also the development of flash temperatures especially at the graphite lamellae which promote local magnetite formation and mixing with exfoliated graphite nanoflakes, as evidenced in [74].Taking into account that other pad constituents may also provide nanoparticles which can be incorporated into the magnetite-graphite blend, the complicated EDS-spectra usually obtained from third bodies prepared for TEM-investigations can be explained.Whereas some ingredients, like magnetite and graphite are milled down to crystal sizes <10 nm, others, like copper or zirconia, are not fragmented further beyond approximately 100 nm [76].The metal sulfides belong to the first category, because they never were observed as particles of the size class 100 nm within a fully processed third body.On the other hand, small but significant signals from Sb, Sn or other metal sulfides were frequently observed in EDS-spectra from third bodies indicating that species <10 nm containing such elements are present.This implies that the metal sulfides or their oxidation products are mixed with magnetite on the nanoscopic scale, similar to graphite.
Examples of the nanostructures described above can be viewed in previous articles [71][72][73]75,76].A further not yet published example of a TEM study of a typical third body formed during braking with a commercial pad is shown in Figure 1.The nanocrystalline nature of this tribofilm is revealed by the TEM micrograph in Figure 1a.The film is embedded between an artificially applied platinum layer at the top and the plastically deformed cast iron substrate appearing in dark contrast at the bottom.EDS-spectra were taken at the indicated points in Figure 1a.The spectrum shown in Figure 1b can be considered as representative for the tribofilm.Besides iron and oxygen, peaks of the elements Cu, Sn, Ba, Si and S are revealed.Since the latter elements were transferred from the pad to the disc, they provide evidence of the pad composition.It is very likely that the pad formulation contained Cu, BaSO 4 , SnS and or SnS 2 .Thus, the EDS-results show that the solid lubricant, tin sulfide in this case, is incorporated in the tribofilm.Graphite-like carbon was also observed, although unfortunately not by STEM-EDS but by HR-TEM [76] or RS [74].The high Cu signal is partly due to the usage of a copper grid for fixing the TEM lamella.Only the spectrum at point 004 (not shown here) is different compared to the others in the range 002-007.It reveals mainly Zr and O indicating a somewhat larger ZrO 2 particle, in accordance with the findings reported in [76].
the usage of a copper grid for fixing the TEM lamella.Only the spectrum at point 004 (not shown here) is different compared to the others in the range 002-007.It reveals mainly Zr and O indicating a somewhat larger ZrO2 particle, in accordance with the findings reported in [76].Finally, the following conclusions can be drawn.A fully processed third body formed during multiple braking events and trapped somehow at the interface between pad and disc consists of the following features: Nanocrystalline Fe3O4 as the major constituent, nanoparticles of graphite and other soft ingredients distributed homogeneously in the nc-magnetite and eventually submicron-sized abrasives like ZrO2 or Al2O3, also embedded in the magnetite-based matrix.A generalized description of the third body structure would be: A certain amount of soft nanoinclusions (d < 10 nm) and some bigger hard inclusions (50-100 nm) are homogeneously distributed in an agglomerate of brittle oxide nanoparticles.The terms soft and hard indicate whether the corresponding species are softer or harder than the embedding matrix.Copper particles need special consideration.Most investigators observed metallic copper and only rarely copper oxide particles were observed [42,55,59,67,73,76].In principle, soft metallic particles can adopt the Finally, the following conclusions can be drawn.A fully processed third body formed during multiple braking events and trapped somehow at the interface between pad and disc consists of the following features: Nanocrystalline Fe 3 O 4 as the major constituent, nanoparticles of graphite and other soft ingredients distributed homogeneously in the nc-magnetite and eventually submicron-sized abrasives like ZrO 2 or Al 2 O 3 , also embedded in the magnetite-based matrix.A generalized description of the third body structure would be: A certain amount of soft nanoinclusions (d < 10 nm) and some bigger hard inclusions (50-100 nm) are homogeneously distributed in an agglomerate of brittle oxide nanoparticles.The terms soft and hard indicate whether the corresponding species are softer or harder than the embedding matrix.Copper particles need special consideration.Most investigators observed metallic copper and only rarely copper oxide particles were observed [42,55,59,67,73,76].In principle, soft metallic particles can adopt the function of solid lubricants like graphite or the metal sulfides.More considerations on copper inclusions in tribofilms are presented in the next section.

Modelling of the Sliding Behavior of Tribofilms Formed during Braking
Since usually tribofilms are very thin, showing variation in thickness, incomplete surface coverage, and not well-defined chemical compositions, it is difficult to assess their impact on the frictional performance and sliding behavior.Material modelling can help obtain a better understanding of the impact of film composition and size effects of microstructural features on the sliding behavior.Unfortunately, only very few models are capable of describing processes taking place on the nanometer scale.Whereas Finite Element Modelling (FEM) usually provides only pressure distributions on the macroscopic [82] or, ultimately, on the microscopic scale [83], Molecular Dynamic modelling (MD) is restricted to very limited cases of well-known atomic structures, e.g., rolling of a Ni nanosphere on copper [84].Other authors applied a Cellular Automata (CA) approach for describing the dynamics of contact patch formation and destruction during automotive braking [85,86].A Discrete Element Model (DEM), which is well adapted to Godet's concept of the formation, mixing and flow of wear particles was suggested by Fillot et al. [87,88].The most important parameter of this model is adhesion between nanoparticles.Psakhie et al. proposed the Movable Cellular Automata (MCA) method which combines concepts of DEM, CA and FEM [89].The big advantage of this model is that it is not restricted by size, and thus can be adjusted to a large variety of technical as well as geological structures.
Since 2006, the authors have applied the MCA method for simulating the sliding behavior of model-tribofilms similar to the ones observed under real braking conditions.The principles of the approach and a possible combination with FEM modeling were described by Dmitriev et al. [90].The most up to date description of the model, although not its application to friction braking, can be found in [91].The most important features of the model are shown in Figure 2 and will be explained in the following.
Lubricants 2016, 4, x 14 of 23 function of solid lubricants like graphite or the metal sulfides.More considerations on copper inclusions in tribofilms are presented in the next section.

Modelling of the Sliding Behavior of Tribofilms Formed during Braking
Since usually tribofilms are very thin, showing variation in thickness, incomplete surface coverage, and not well-defined chemical compositions, it is difficult to assess their impact on the frictional performance and sliding behavior.Material modelling can help obtain a better understanding of the impact of film composition and size effects of microstructural features on the sliding behavior.Unfortunately, only very few models are capable of describing processes taking place on the nanometer scale.Whereas Finite Element Modelling (FEM) usually provides only pressure distributions on the macroscopic [82] or, ultimately, on the microscopic scale [83], Molecular Dynamic modelling (MD) is restricted to very limited cases of well-known atomic structures, e.g.rolling of a Ni nanosphere on copper [84].Other authors applied a Cellular Automata (CA) approach for describing the dynamics of contact patch formation and destruction during automotive braking [85,86].A Discrete Element Model (DEM), which is well adapted to Godet's concept of the formation, mixing and flow of wear particles was suggested by Fillot et al. [87,88].The most important parameter of this model is adhesion between nanoparticles.Psakhie et al. proposed the Movable Cellular Automata (MCA) method which combines concepts of DEM, CA and FEM [89].The big advantage of this model is that it is not restricted by size, and thus can be adjusted to a large variety of technical as well as geological structures.
Since 2006, the authors have applied the MCA method for simulating the sliding behavior of model-tribofilms similar to the ones observed under real braking conditions.The principles of the approach and a possible combination with FEM modeling were described by Dmitriev et al. [90].The most up to date description of the model, although not its application to friction braking, can be found in [91].The most important features of the model are shown in Figure 2 and will be explained in the following.The structure of first bodies and adhering tribofilms is built as two dimensional networks of linked particles, as shown in Figure 2a.Links to neighboring particles are displayed by lines.If we define a particles size of 10 nm, the width of a contact is 0.5 μm and the thickness of the tribofilm (orange or green) is approximately 100 nm.Different materials are depicted by different colors e.g., The structure of first bodies and adhering tribofilms is built as two dimensional networks of linked particles, as shown in Figure 2a.Links to neighboring particles are displayed by lines.If we define a particles size of 10 nm, the width of a contact is 0.5 µm and the thickness of the tribofilm (orange or green) is approximately 100 nm.Different materials are depicted by different colors, e.g., grey for the substrates, orange and green for lower and upper tribofilm, respectively, and magenta for soft inclusions in the tribofilms.During sliding simulation, a normal pressure is applied vertically and a sliding velocity, usually 10 m/s, is applied tangentially.This is done step by step while stresses and strains on each particle are calculated and new positions assigned.Furthermore, the state of linkage is checked by applying a fracture criterion.In the example shown in Figure 2, most of the links between particles were broken within zones at both sides of the interface.The two zones together represent the so-called Mechanically Mixed Layer (MML), because particles from both sides of the interface are mixed within this layer.Furthermore, since the particles within this layer are mostly not linked to their neighbors, they can move almost freely in tangential direction.This is an important feature, because such movement leads to smooth sliding with low friction and velocity accommodation between moving and fixed first bodies.Unlinked particles which are leaving the contact zone at one side are reintroduced on the other side.Thus, periodic boundary conditions are realized.
The main objective of many parameter studies performed during the last 10 years was to find conditions leading to MML-formation at a friction level which is still suitable for brake application.
Table 4 shows the progress made during previous systematic MCA-studies.

Discussion
The advantage of modelling is that the impact of structural as well as external parameters can be studied systematically.The disadvantage is that the complexity of structures is limited and mechanisms taking place at different length scales have to be treated separately.Here, only nanoscopic sliding mechanisms were considered.This is justified if sliding occurs within an approximately 100 nm thick surface film which is continuously screening the first bodies.Since wear cannot be neglected, it is necessary to assume that a dynamic equilibrium between film destruction and restitution is taking place.Conditions leading to MML-formation during modelling indicate that a steady state has been reached under which, at least for some time, sliding is determined by particle flow without further destruction of the tribofilm.During a period of particle flow, the COF-fluctuations between time steps are reduced considerably, although the mean COF is not changed.The situation is different for structures which do not show MML-formation.In that case, the tribofilm will be destroyed and removed completely during a sliding simulation within a modelling interval of typically 0.5 µs (2,000,000 time steps).This corresponds to higher wear rates and COF-instabilities not only between the time steps of modelling, but also during practically relevant time intervals of a tribological test procedure.
According to the modelling results shown in Table 4, neither pure metal-on-metal nor oxide-on-oxide contact situations provide MML-formation and corresponding smooth sliding.Only if the oxide is mixed with at least 13 vol % graphite sliding becomes smooth and the COF drops to 0.35 at ambient temperature and high normal pressure [92].Although most systematic studies have been made while assuming graphite as soft ingredient of the tribofilms, graphite must not be considered as the only species producing this effect.It has been shown that soft copper particles behave similar as graphite [73], and even copper clusters with diameters of 50 nm may substitute halve of the graphite and still provide smooth sliding of the corresponding tribofilm [93].These results imply that any other constituent will produce a similar effect provided it is significantly softer than the magnetite matrix of the tribofilm.Since all of the metal sulfide solid lubricants considered by Melcher et al. [26] are softer than the magnetite, they will show similar effects as the graphite during sliding simulations.The modelling results provide an explanation why the mixing of soft pad ingredients with magnetite, the major wear product from the brake disc, results in smooth sliding at a COF of at least 0.35.Furthermore, it was shown that the COF increases by adding approximately 5 vol % of a hard nanoconstituent, e.g., ZrO 2 , SiC or Al 2 O 3 [94,95], or by a decrease of the applied pressure [91,92].Thus, smooth sliding within a COF-range of 0.35-0.5 is predicted by the model for tribofilm nanostructures fulfilling the mentioned requirements.Velocity reduction from 10 to 1 m/s: no difference of final structure and COF.
[78] 2014 Summary of previous findings The increase of COF during a stop braking event can be explained by linking MCA-results with patch dynamics [85,86,102] Loose wear particles play an important role.
A further question is whether the effect of solid lubricants on smooth sliding behavior will also work at elevated temperatures.This can be expected as long as the magnetite is still hard and brittle and the oxides formed from the sulfides are still soft compared to the magnetite.The latter can be expected for Sb 2 O 3 and PbO, but it is not so clear for Sb 2 O 4 , SnO, SnO 2 , MoO 3 and Bi 2 O 3 [26].In the latter cases, the hardness of the oxides approaches that of magnetite.Thus, the effect of initiating smooth sliding conditions might get lost.On the other hand, the experience of many pad manufacturers, namely that metal sulfides provide good fade and wear resistance at elevated temperatures (Table 3), suggests that a similar mechanism may operate as at ambient temperature conditions.This implies that at least part of the metal oxides formed from the sulfides is softer than the magnetite in the temperature range usually responsible for fading effects (>400 ˝C, see references in Table 1).Hot hardness tests of pure magnetite and the relevant oxides formed from the sulfides at elevated temperatures would be necessary to check this hypothesis.
For the magnetite-graphite system, modelling with a wide range of hypothetical high temperature material properties showed that in principal similar mechanisms occur irrespective of temperature, although with slightly changed quantitative data of the pressure dependencies of COF [92].In the latter case, it was assumed that magnetite softens and undergoes a brittle-ductile transition while the strength of graphite was considered to be nearly independent of temperature.
A completely different explanation of increased fade resistance can be derived hypothetically if we assume that the oxides formed from the sulfides retain their hardness at elevated temperatures whereas the magnetite undergoes a brittle-ductile transition.Then, an inversion of the microstructure may occur with Sn-, Bi-or Mo-oxides forming hard inclusions within the softened magnetite matrix.Such a film would be comparable to the one studied theoretically in [101].Thus, smooth sliding at a reduced but stable COF-level can be expected.This is the behavior which frequently is observed while performing fading cycles during dynamometer testing of real brake couples.Although the role of soft inclusions in the sliding mechanism of thin nanostructured tribofilms provides a good explanation for many observations even quantitatively, other mechanisms operating at different length scales may play a role as well.Basically, in terms of size there are two types of particles which are present at the sliding interfaces and, thus, will somehow determine the sliding behavior.The first type corresponds to pad ingredients torn out from the composite due to degradation of the phenolic resin binder.They will still have their original size, usually 10-100 µm.If the gap between first bodies is large enough, such particles can flow along the interface until they are trapped in a surface depression or released to the environment.Unfortunately, we have no information about the impact of flowing micro-particles on the sliding behavior.On the other hand, it is not so unlikely to assume that they might behave similarly to the nanocrystalline multi-phase third body.Anyway, a certain fraction of particles is fragmented by multiple collisions and mixed with the nanocrystalline iron oxide formed by tribooxidation of the disc.Only the latter product can form the thin tribofilms which have the ability to screen the first body surfaces.Thus, the modeled contact sites represent only part of the global contact situation.Furthermore, it should be kept in mind that continuous formation, destruction and reformation of films as well as wear particle production, flow and fragmentation leads to permanent changes of local conditions with time.Thus, predictive modelling for the whole brake system as a function of time is not possible.Nevertheless, if tribofilm formation is considered as crucial for good brake performance properties, the modeling results help to understand the reasons and prerequisites for smooth sliding, wear reduction and COF-stabilization in a range which is suitable for brake applications.

Conclusions
Although using solid lubricants as additives for friction composites seems to be somehwhat conflicting, it is common practice.The objective of this review article was to find out why this is so.
A first literature review evaluated experiences of brake pad manufacturers.It turned out that usage of only one solid lubricant additive usually did not yield satisfactory results.In fact, it was necessary to find the right balance between two or more species during an optimization process.
A second review considered results of tribofilm characterization.The films were mostly formed during dynamometer testing simulating real braking conditions.Commercial brake pads were applied against cast iron discs.Thus, a broad variety of different pad formulations were taken into account.Striking similarities between the different systems were revealed.The films consisted mainly of iron oxide Fe 3 O 4 , but most of the pad ingredients could be identified as well, although usually only with minor amounts.Besides the magnetite-based films with nanocrystalline structure, micron-or submicron-sized particles of different pad constituents were frequently observed as well, especially in the form of dust particles.
A third review compiled modeling results related to sliding simulations of nanostructures resembling the ones observed for real tribofilms.Although only partial simple systems could be realized, the behavior of more complex systems could be assessed by stitching the results together.After generalization, the following conclusions were drawn: For providing smooth sliding in a COF range of 0.35-0.5, a volume fraction of at least 13% of soft nanoparticles should be embedded in the nanocrystalline magnetite film.If half of the particles are incorporated as clusters, the same effect is observed as for homogeneously embedded particles.Additional hard particle clusters do not disturb the smooth sliding behavior provided that they are completely embedded in the magnetite matrix.As long as solid lubricant additions are softer than the magnetite matrix, they will foster smooth sliding behavior.According to this model, the oxides formed from metal sulfides should be softer than the magnetite even at elevated temperatures, under conditions when the additives prevent fading (undesired COF-decrease) and excessive wear.Unfortunately, hot hardness data of the relevant oxides are not yet available in order to prove this hypothesis.
pad material to disc.FeO and C at the surface (AES).No tribofilm formed at low temperature, only at high temperature (SEM/EDS).Thin tribofilms not detected by SEM/EDS.FeO not confirmed.State of the art: Fe 3 O 4 .
Nanoparticle emissions correlated with fading cycles.Nanostructure of collected dust particles.Most pad constituents and Fe 3 O 4 observed in a single nanoparticle of approximately 300 nm diameter.
multiphase-structure of Fe 3 O 4 -based tribofilm revealed.Smooth sliding attributed to tribofilm structure, as shown by modelling.Contrary to [70], it was observed that Fe 3 O 4 is the matrix which contains C inclusions.[72] EEPS CI EF-TEM STEM EDS Airborne particles down to diameters of some few nanometers detected.Collected particles are agglomerates of nanoparticles of pad ingredients and Fe 3 O 4 .Differences of pad formulations mirrored in differences of composition of nanoparticle-agglomerates. Nanostructure and composition of airborne dust particles provide information of tribofilm structure.

Figure 1 .
Figure 1.(a) Cross-sectional TEM micrograph of a tribofilm at a brake disc surface formed during dynamometer testing against a commercial pad; (b) Typical STEM-EDS spectrum taken within the tribofilm at point 005 (without signals from the substrate).

Figure 1 .
Figure 1.(a) Cross-sectional TEM micrograph of a tribofilm at a brake disc surface formed during dynamometer testing against a commercial pad; (b) Typical STEM-EDS spectrum taken within the tribofilm at point 005 (without signals from the substrate).

Figure 2 .
Figure 2. (a) Arrangement of linked automata prior to sliding simulation; (b) Arrangement of automata after sliding simulation.For further explanations see text.Colors are displayed in the web-version of the article only.

Figure 2 .
Figure 2. (a) Arrangement of linked automata prior to sliding simulation; (b) Arrangement of automata after sliding simulation.For further explanations see text.Colors are displayed in the web-version of the article only.

Table 1 .
Literature review on the impact of solid lubricant additions to commercial brake pad formulations.

Table 3 .
Definition of acronyms used for the characterization methods mentioned in Table2

Table 4 .
MCA modelling results of model structures containing the essential constituents of real tribofilms formed during automotive braking (chronological order).