Reciprocating sliding wear behaviour of PEEK-based hybrid composites

Reciprocating sliding wear behaviour of PEEK-based hybrid composites

Author’s Accepted Manuscript RECIPROCATING SLIDING BEHAVIOUR OF PEEK-BASED COMPOSITES WEAR HYBRID V. Rodriguez, J. Sukumaran, A.K. Schlarb, P. De Ba...

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Author’s Accepted Manuscript RECIPROCATING SLIDING BEHAVIOUR OF PEEK-BASED COMPOSITES

WEAR HYBRID

V. Rodriguez, J. Sukumaran, A.K. Schlarb, P. De Baets www.elsevier.com/locate/wear

PII: DOI: Reference:

S0043-1648(16)30109-0 http://dx.doi.org/10.1016/j.wear.2016.05.024 WEA101702

To appear in: Wear Received date: 29 January 2016 Revised date: 16 May 2016 Accepted date: 29 May 2016 Cite this article as: V. Rodriguez, J. Sukumaran, A.K. Schlarb and P. De Baets, RECIPROCATING SLIDING WEAR BEHAVIOUR OF PEEK-BASED HYBRID COMPOSITES, Wear, http://dx.doi.org/10.1016/j.wear.2016.05.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

RECIPROCATING SLIDING WEAR BEHAVIOUR OF PEEK-BASED HYBRID COMPOSITES 1

1

2

V. Rodriguez , J. Sukumaran , A.K. Schlarb , P. De Baets 1

2

1

Ghent University, Laboratory Soete, Technologiepark, 9052 Zwijnaarde, Belgium

Lehrstuhl für Verbundwerkstoffe, University of Kaiserslautern, Kaiserslautern, Germany.

*Corresponding author: Vanessa Rodriguez Tel.: +32 9 331 04 80; fax: +32 9 331 04 90 E-mail: [email protected]

Abstract: The present research deals with the effects of fillers in Polyetheretherketone (PEEK) based hybrid composites from the view point of mechanical and tribological properties. In this background, nanosized silica (SiO2), short carbon fiber (SCF), graphite, titanium dioxide (TiO2) and zinc sulphide (ZnS) were added as the additives. Reciprocating sliding wear tests (flat-on-flat) against AISI 52100 bearing steel were performed at contact pressures ranging from 4 MPa to 10 MPa and with sliding velocities of 20 mm/s and 50 mm/s. Under most test conditions, the nanoparticles reduced the friction coefficient. The morphologies of the worn surfaces and the transfer films, were observed by surface topography (ST), optical microscopy (OM) and scanning electron microscopy (SEM). A dimensional analysis was used to evaluate the influence of nanoparticles on transfer film formation on bearing steel counter surface. It is evident that the effect of nanoparticles on wear rate depended on the contact pressure and sliding speed. Results indicated a limited wear resistance for neat PEEK, but PEEK filled with nano-sized silica exhibited superior wear resistance at the highest contact pressure for both sliding speeds. The nanoparticles seem to have a polishing effect on the steel counter surface. The nanoparticle additives may account for their lower friction coefficient and improved wear resistance in comparison to micro-particle-filled and unfilled PEEK. The output from the dimensional analysis based on transfer layer characteristics is in good agreement with the friction result. Keywords: nano-particles, friction coefficient, fillers, micro-particles, short carbon fibre

1. Introduction In recent years, polymer composites have been increasingly used as machine components such as e.g. gears, bearings, cams, seals, etc. [1] because of their particular properties such as low weight and good corrosion resistance as compared with the traditional metallic materials. These applications are often also related with friction, wear and lubrication which are the three main components of tribology. Friction and wear are important in machine components because they determine their efficiency and operating life. Polymer based composites consists of one or more fillers that have been added to a polymer matrix as a reinforcing and/or lubricating agent. The main objective is to improve the structural and tribological properties of the polymer. However, there are still many challenges remaining for the effective and economic use of polymers in specific tribological applications. E.g., the wear rate can be extremely high when the contact pressure is slightly raised, and low friction is not necessarily associated with low wear rate [1]. Those disadvantages sometimes limit the application of neat polymers. For a better control of the performance, fillers are added to improve strength, wear

resistance and friction. The type and concentration of filler materials is often a closely guarded secret of the manufacturer [1]. The use of polymer matrix and its composites for tribological behaviour has been studied by several researches [1-3] in the last decades. The replacement of metals by polymer composites have gained much attention. One of the major reasons is that polymer composites are lighter and capable of resisting relatively loads and speeds. Additionally, advantages of self-lubricating behaviour in polymer matrix has been reported in the literature [4-6]. Several authors have reported the beneficial tribological characteristics of the addition of fillers in polymer composites. Bahadur and Sunkara [7] found that TiO2 nanoparticles effectively reduces the wear rate of PPS (polyphenylenesulfide). Zhang et al. [8] showed that a composite of epoxy with carbon fibres, graphite and TiO2 shows reduced wear rate compared to pure epoxy. Friedrich et al. reported that PEEK with 30% of carbon fibres at increased temperature shows a higher wear rate but lower friction [9]. Bahadur and Tabor [10] found that using graphite in a PTFE polymer considerably reduces the wear rate. Recently, tribological studies of polymer filled with nano and micro- composites have been increasing because of their interesting results. In some cases the fillers contribute to enhanced wear resistance, while in some case they result into the deterioration of wear resistance [11]. In order to better understand the role of nanocomposites in a polymer matrix, the present work will investigate the effects of nano and micro-composites in the tribological behaviour of polyetheretherketone (PEEK) based hybrid composites. The fillers comprise short carbon fibres (SCF), graphite, TiO2, ZnS and SiO2. PEEK known as a high performance engineering polymer that can be used at high-temperature is used as a matrix in the present investigation. Despite its relatively high friction PEEK has a good wear-resistance. In this study the PEEK-based hybrid composites have been compared to neat PEEK as a reference. Tests were performed under a variety of loads and sliding velocities in controlled ambient conditions of temperature and humidity. Dimensional analysis was performed to relate the formation of transfer film on the counter surface to the tribological behaviour. This was done by taking into account the terms of operating conditions, compositions and counter surface roughness. Dark field photomacrography was used to reveal the transfer film formation on the steel counter surface. In short the purpose of this work is to utilize the understanding of the role of fillers in designing high performance tribo-composites.

2. Experimental procedure In this investigation a commercially available polyetheretherketone (PEEK) (Vestakeep 2000 G) was used as a polymer matrix. Short carbon fibres (SCFs), three different micro- and nano-particles, and one type of graphite were applied as fillers. The detailed production procedure is described elsewhere [12] and the nomenclature and composition of the different PEEK-based hybrid composites are given in the Table 1. The neat PEEK, which was prepared by extrusion and injection moulding, was used as a reference material. The mixture of the PEEK with various fillers was achieved by injection moulding in twin-screw-extruders with standard screw configurations. The polymers samples were moulded in sizes of 70 x 70 x 4 mm plates and consequently cut to the size of 40 x 40 x 4 mm. Mechanical properties of the different composites are shown in Table 2. Table 1: Nomenclature and composition (weight %) of PEEK-based hybrid composites and information on fillers [12]. Particle Filament Fibre Constituent PEEK-S00 PEEK-S02 PEEK-S05 diameter diameter length (nm) (µm) (µm) PEEK 100 60 60 Graphite 0 10 10 7 6 SCF 0 10 10 340 TiO 0 10 5 2

ZnS

0

10

5

SiO2

0

0

10

300 12

-

-

Table 2: Mechanical and thermal properties of the PEEK-based hybrid composites [12]. Properties Tensile strength (MPa) Young’s modulus (GPa) 2

Impact strength (KJ/m ) Fracture toughness (MPa *m1/2) 3

Density (g/cm ) Melting point (°C)

PEEK-S00

PEEK-S02

PEEK-S05

102.20 2.49

136.20 7.27

139.40 6.58

12 8.40

6.60 4.40

6.80 4.80

1.34

1.61

1.53

342.40

343.30

342.50

Reciprocating linear sliding friction and wear tests of PEEK composites were performed against hardened and polished carbon steel AISI 52100 (100Cr6, DIN 1.3505) as a counter material. Having the following mechanical properties: yield strength of 304 MPa, hardness of 147 HB, modulus of elasticity of 211 GPa, Poisson ratio of 0.4, tensile strength of 609 MPa and an elongation of 19.7%. Counter plate specimens sized 200 mm x 80 mm x 19 mm. Before each tests the steel counter plates were cleaned with a solvent (petroleum ether) under ultrasonic vibrations for 10 minutes. Then the same was immersed also in acetone under ultrasonic vibration for 5 minutes and further were atmospherically dried with cleaning paper. The surfaces were grounded perpendicular to the sliding direction to a surface roughness Ra = 0.20 µm (measured according to DIN 4768). A so-called large-scale flat-on-flat tribotester was used in the present investigation. The advantage of this set-up is that it has sample sizes that are closer to real applications, compared to traditional tribotesters. The large-scale reciprocating apparatus was designed at Soete Laboratory (Ghent University) and is schematically illustrated in Figure 1. The polymer samples are positioned in holders that are fixed in vertical position by a reaction force. The polymers samples are put in contact with (two) steel counter plates mounted on a central sliding block. The machine has two pistons: one in the horizontal direction to apply the normal load and another in the vertical direction to provide the vertical sliding motion of the central sliding block relatively to the statically mounted polymer samples. This vertical motion is continuously measured by means of an LVDT displacement transducer. During the test the friction forces are continuously recorded in order to calculate the friction coefficient. The largescale tests were done at normal loads of 6.5 kN, 13 kN and 16 kN, corresponding to a contact pressured of 4 MPa, 8 MPa and 10 MPa and at two sliding speeds: 20 mm/s and 50 mm/s. No lubricant was applied. All tests were performed in controlled ambient conditions: a temperature of 25 °C and relative humidity of 50%. The total sliding distance was chosen 1080 m with a sliding stroke of 80 mm. The duration of the tests was approximately 15 hours and 6 hours using a sliding velocity of 20 mm/s and 50 mm/s, respectively. The tests at a sliding velocity of 20 mm/s ran over 15 hours or 6750 sliding cycles. The velocity of the linear reciprocating motion is kept constant at the middle of the stroke length. Wear was measured as a thickness reduction, and post mortem wear rate was calculated from weight loss of the polymer samples. A preconditioning procedure prior the actual sliding wear test was performed in order to align the polymer specimens with their counter plates. The force and displacement signals are logged at a sample rate of 200 Hz for a period of 8 seconds out of every minute. From the results of every logged cycle the static and dynamic coefficient of friction are calculated. Independent tests were performed in neat PEEK and PEEK composites for at least 3 times under identical test conditions where a relative standard deviation of 10 % and 15 % was found for friction and wear rate, respectively.

3 4

6

Figure 1: Large-scale flat tribotester: 1) screw connection to load frame actuator, 2) central sliding block, 3) countersurface plate, 4) specimen holder, 5) clamp: normal load, 6) polymer samples.

Before the sliding tests, the polymers samples were cleaned with Isopropanol and some drops of distilled water to remove any contamination. Additionally, a drying procedure was implemented to remove the moisture in the polymer. This was carried out in the oven at 150 °C during a period of 2 hours. Subsequently, the specimens mass was measured in a weighing balance (OHAUS explorer, capacity 210 g, accuracy 0.1 mg). The same procedure was repeated after testing. With the difference in mass (mass loss ) on each test the wear volume was calculated using the following equation: (1) Where represents the density of the polymer specimen. Finally, according to Archard’s equation [13] -6 3 specific wear rate (x10 mm /Nm) was derived as the ratio of wear volume and the product of normal contact load “ ”and the total sliding distance “ ”, see equation 2. (2) It is well known the wear behaviour of polymer materials depends on many factors such as interacting bodies, operating parameters and the working environment. To correlate these factors with the observed wear mechanisms we used an equation which has been developed in this work. Further details can also be found in section 3.4. This wear equation, based on dimensional analysis theory, has been expressed as a function of operated conditions, materials properties and surfaces characteristics. It is worth mentioning that in such equation the thermal and mechanical characteristics play an important role: a threshold for wear is based on the transfer film appearances on the contacting surfaces.

3. Results and Discussion 3.1 Coefficient of friction The evolution of dynamic coefficient of friction as a function of sliding distance is illustrated in Figure 2. Moreover, the static and dynamic coefficients of friction as well as corresponding wear rates (based on the weight loss measurement) are summarized in Table 3.

One of the objectives in this study is to determine the effect of nano- and micro-particles on tribological behaviour of PEEK, in comparison to neat PEEK (PEEK-S00). Figure 2 shows the coefficient of friction against sliding distance of the three composite materials. It can be observed that the coefficient of friction is reduced from 0.5 for neat PEEK to 0.24 for PEEK filled with silica (SiO2). This is a reduction of around 50 %. It means that the incorporation of nano-particles into the polymermatrix leads to a significant decrease of the coefficient of friction. In the friction curves of Figure 2 a maximum can be observed at the beginning of the test followed by a constant regime. This is the case for both neat PEEK (PEEK-S00) and filled PEEK (PEEK-S02 and PEEK-S05). Pooley and Tabor reported [14] that in some cases the decrease in friction depends on the formation of a transfer film in relation to the levels of roughness of the counter plate. They evidenced this by means of visual inspection of the steel counter plates, revealing the formation of polymer transfer film on the steel.

Table 3: Friction and wear results of three polymer composites against steel counter plates Normal Contact µstatic µdyn W Velocity load pressure Material (mm/s) -6 3 FN (kN) (MPa) (-) (-) (10 mm /Nm) 6.5 4 0.60 0.44 4.81 13.0 8 0.55 0.49 12.06 PEEK-S00 16.0 10 0.49 0.43 42.50 6.5 4 0.45 0.34 3.31 20 13.0 8 0.34 0.32 15.71 PEEK-S02 16.0 10 0.32 0.30 10.74 6.5 4 0.41 0.36 4.57 13.0 8 0.36 0.24 15.10 PEEK-S05 16.0 10 0.31 0.26 9.13 6.5 4 0.56 0.43 12.10 13.0 8 0.52 0.39 18.45 PEEK-S00 16.0 10 0.52 0.37 19.32 6.5 4 0.38 0.33 15.87 50 13.0 8 0.36 0.27 17.29 PEEK-S02 16.0 10 0.34 0.27 16.28 6.5 4 0.40 0.32 43.36 13.0 8 0.37 0.28 22.82 PEEK-S05 16.0 10 0.33 0.23 11.99

It is known that multiple fillers play important role on improving the tribological performance of the matrix. As it was mentioned earlier the fillers used in this study were short carbon fibre (SCF), graphite, TiO2, ZnS and SiO2. Those fillers have to a certain extent been investigated in combination with other polymer matrices. Short carbon fibres have been reported to improve wear behaviour of PEEK matrix composites [8] [15]. Additionally, SCF are less abrasive than many other reinforcements and are favourable with respect to bearing capacity. In the present research internal lubricant, such as graphite, is shown to reduce the coefficient of friction. Additionally, the incorporation of solid lubricants, i.e. submicron-particles of TiO2 were used to enhance the wear resistance. These particles are known to increase both hardness and strength of the polymer matrix. Another reason for the observed reduction in the coefficient of friction is the increase of the surface temperature associated with increased sliding speed and contact pressure (pv-factor). The temperature increase results into softening the interface at the sliding contact. Therefore, the shear strength of the interfacial surfaces decreases hence reduced coefficient of friction [16]. The main conclusion drawn from literature [17] is that nanocomposites do form a uniform transfer film which will also be called from here on primary

transfer film on the counter surface, contributing to a significant decrease in the coefficient of friction. Additionally, some authors [2, 18] have mentioned that together with a decrease of the coefficient of friction a decrease of wear rate is observed. 4 MPa 20 mm/s 50 mm/s

(b)

(a)

8 MPa 20 mm/s

50 mm/s

(d)

(c)

10 MPa 20 mm/s

(e)

50 mm/s

(f)

Figure 2: Dynamic coefficient of friction as a function of the sliding distance against steel counterplate (100 Cr6) at sliding velocity of 20 mm/s and 50 mm/s and contact pressure of 4, 8 and 10 MPa.

3.2 Specific wear rate The effect of nano- and micro-particles on the wear behaviour of polymers is compared in figure 3 at two sliding speeds and three contact pressures. It can be seen that the wear rate of the neat PEEK increases with the contact pressure at both sliding speeds. At low and intermediate contact pressures (4 and 8 MPa) and at both speeds (20 and 50 mm/s), the wear rate of nano-reinforced PEEK (PEEKS02 and PEEK-S05) is not significantly different from neat PEEK. At 10 MPa, both reinforced PEEKs (PEEK-S02 and PEEK-S05) have shown a more favourable wear performance. In fact, a noticeable improvement on the wear resistance of filled PEEK-S05 (SiO2), by approximately one order of magnitude, has been observed at the highest contact pressure of 10 MPa and low speed 20 mm/s, as compared to its neat PEEK polymer matrix. This behaviour is also observed at 50 mm/s but at a lower extent. It is evident that the addition of nanocomposite filler, i.e. SiO2, TiO2 and ZnS, is beneficial for the wear performance at high contact pressure of the studied tribosystem. These results are in full agreement with the literature [15, 16]. It has indeed been reported that the addition of nanoparticles enhances the wear resistance of the polymer material. Such addition of nanoparticles does not only increase the stiffness but also the strength of the polymer composite. Nano-reinforcement also produces less stress concentration at its interface with the matrix compared to micro- and macroreinforcements. Hence it is less prone to debonding at the matrix interface. It is known that during sliding fragments of the polymer matrix generated by wear can result into the formation of a transfer film on the counter surface asperities [19]. This process initiates the formation of discrete patches of polymeric material which are augmented by cohesion between mutually compatible polymer fragments produced during sliding and the polymeric material initially transferred to the counter surface. Those patches on the counter surfaces can be beneficial. It has been demonstrated that the presence of a uniform or primary transfer film and sometimes also patches can lead to a reduction on the wear rate. On the contrary, the wear rate increases when the transfer film is thick and discontinuous [3], which is also called secondary transfer film [20]. Evidences of both primary (uniform) and secondary (thick and discontinuous) transfer film can be confirmed with electron microscopy observations on the worn surface, as described in section 3.3.

Sliding speed 20 mm/s

Sliding speed 50 mm/s

Figure 3: Specific wear rate of PEEK (neat and nanocomposites) at sliding velocity of 20 mm/s and 50 mm/s and contact pressure of 4, 8 and 10 MPa.

3.3 Surface morphological analysis The worn surfaces were observed by optical microscopy (OM) for wear mechanisms characterisation and to quantify the wear model. Generally speaking, two main wear mechanisms were observed as shown in the Figures 4 and 5. These were adhesion and abrasion, which are normally found in sliding contact with polymer materials. In the Figurers 4 and 5 with PEEK-S00 the worn surface mostly exhibits adhesion mechanism and plastics deformation that leads to the formation of wear debris. Adhesion is characterized by material transfer between contacting surface. A transfer film of wear debris is visible over the surface. The presence of a secondary transfer film is pronounced at lower speed of 20 m/s and higher loading conditions of 8 MPa and 10 MPa. For nanocomposites PEEK-S02 and PEEK-S05 a uniform or primary transfer film was observed having abrasion as the predominant wear mechanism. This phenomenon leads to geometrical changes on the surface topography (grooves and cracks) with or without material loss. Parallel groves in the wear scar caused by ploughing or cutting and characteristic for abrasion are clearly observed in the figures 4 and 5. Additionally, loose wear particles or debris were observed in the vicinity of the counter surface which relative amount increased with the loading condition.

20 mm/s 8 MPa

10 MPa

PEEK-S00

4 MPa

Adhesion

100 µm

100 µm

100 µm

100 µm

100 µm

100 µm

100 µm

100 µm

Adhesion

PEEK-S05

PEEK-S02

100 µm

Figure 4: Optical microscopy of worn PEEK surfaces sliding velocity at 20 mm/s.

50 mm/s 8 MPa

PEEK-S00

4 MPa

10 MPa Adhesion

Abrasion

Adhesion

Abrasion

100 µm

Abrasion

100 µm

PEEK-S02

100 µm

100 µm

100 µm

100 µm

100 µm

100 µm

PEEK-S05

100 µm

Figure 5: Optical microscopy of worn PEEK surfaces at sliding velocity at 50 mm/s. Further topographic characteristics of the PEEK surfaces and steel counter plates were assessed. This was done by means of a digital microscope (VHX-200 Keyence) using the 3D and 2D profile with a magnification lens of 300X. Adhesion as wear mechanism was validated from the contour analysis of the transferred layer (secondary transfer film) on the steel counter surface and PEEK surface, as shown in Figure 6. From Figure 6, it can be seen that the transfer film (secondary layer) on both, steel counter surface and PEEK surface, can have a thickness up to approximately 40 µm. a)

b)

Figure 6: Topographic characteristics of secondary transfer film on: a) PEEK surface and b) steel counter surfaces at contact pressure of 10 MPa and sliding speed of 20 mm/s.

To better identify wear mechanisms and the effect of the fillers, the contact surfaces were investigated by scanning electron microscopy (SEM) at higher magnification. Figure 7a shows the plastic deformed wear zone of neat PEEK (PEEK-S00), in which also particle debris can be observed and may be critical for the formation of the transfer film. It is know that transfer film formation it is a usual cause for changes in wear rate observed during repeated sliding [21]. Figure 7b shows a magnified detail around the fibres in PEEK-S02 (carbon fibres, graphite and submicron TiO2 and ZnS). Debonding and micro-cracking of the carbon fibres and wear debris can be observed. In the case of nano-SiO2-filled composites (PEEK-S05), Figure 7c, some agglomerates in the polymer due to the abrasion mechanism can be observed. The presence of agglomerates is promoted by circulating and trapping of debris, which comes from the abraded polymer surface, into the sliding contact. Those agglomerates contribute in increasing the wear rate as shown by Figure 3. Also, looking at the details of Figure 7d it can be noticed that some of the fibres were polished by the nanoparticles and showed very smooth surface. Mild damage occurred, and the incorporation of nano-SiO2 significantly protects the carbon fibres and PEEK matrix during the sliding process. No obvious interfacial failure is noticed. This can be the main reason why the wear resistance improved with the incorporation of these nanoparticles. Previous studies [15] have described that with the incorporation of the nanoparticles the stiffness of PEEK increases and the stress concentration on the short carbon fibres is reduced. 8 MPa – 20 mm/s (a)

(b)

Debris

Fiber

PEEK –S00

Micro-cracks

PEEK- S02

(c)

(d)

Fiber Fiber Agglomerates

Debris

PEEK-S05 Figure 7: SEM micrographs of the worn surfaces of neat and filled-PEEK against steel counter plate (100 Cr6) at contact pressure of 8 MPa and sliding velocity of 20 mm/s.

3.4 Dimensional analysis and linear classifier method The wear mechanisms of the materials used in this investigation were quantified. The secondary transfer film on the steel counter surface was observed from digital photomacrographs and micrographs. The thick and discontinuous transfer film (secondary transfer film) was revealed using an enhanced dark field imaging technique. Post-processing of the images was done using Image J program and segmentation method which allowed the quantification of the area “ ” of the secondary transfer film. This area was further used as an input in the dimensional analysis. In the literature, researchers have used dimensional analysis to express a wear equation of polymers [20, 22, 23]. It is known that in polymers basically two main wear mechanisms (abrasion and adhesion) are found and related to material properties and the tribological system. In this paper a wear equation has been developed by means of a dimensional analysis. Different constants and/or parameters among them: 3 material properties (thermal conductivity “ ”, density “ ” and Young’s modulus “ ”) and 5 operational conditions (temperature “ ”, roughness “ ”, sliding distance “ ”, velocity “ ” and contact pressure “ ”) were considered to correlate the transfer film formation “ ”. It is expressed as follows: (

)

(3)

Four fundamental units were considered as “M” for mass, “L” for distance, “T” for time and “t” for temperature. These were assigned to each variable to determine the dimensional formula as show in Table 4. Table 4. Dimensional variables and fundamental units of the wear equation. Variable Symbol Fundamental unit -1 -2 Contact pressure ML T -1 Sliding Velocity LT Sliding distance L -1 -2 Young’s modulus ML T -3 Density ML Roughness L -3 -1 Thermal conductivity MLT t Temperature t

To compute the dimensional parameters, the Buckingham Pi theorem has been implemented. According to the Buckingham Pi theorem, the number of dimensionless Pi parameters is calculated subtracting the number of fundamental units (r = 4) from the total number of variables (N = 8). Therefore, the number of dimensionless Pi parameters is π = N - r = 4. Repeating variables or core group were selected based on the r = 4 variables. For such core group formation, it has been considered the following: the variables should not have the same dimensions and should not be dimensionless. The selected repeating variables are , , , while the remaining variables are named as non-repeating variables. Four product groups are formed with both repeating and nonrepeating variables. For each product group dimension formulae are applied and arbitrary exponents are assigned for each variable. ( )

( )

( )

()

( )

(4)

( )

( )

( )

()

( )

(5)

( )

( )

( )

()

(

( )

( )

( )

()

( )

)

(6) (7)

By making the four product groups dimensionless, arbitrary exponents are solved. The resulting dimensionless group are: (8) (9) (10) (11) Afterwards, the four group can be put together and a constant K is added. In such a way, the proportionality between the transfer film and the four dimensionless groups can be expressed as: [( ) (

) ( )(

)]

(12)

The idea of this model is to understand the relation between the discontinuous (secondary) transfer film formation and the tribosystem variables (material properties and operational conditions). Solving the equation 12 results in: (13) Where K is the wear dependent constant. (14) From equation (14) a K-value was obtained and plotted in Figure 7 as a function of the pv-factor applied in this study. Two distinct regions can clearly be observed. The two regions were segregated by means of a statistical analysis with Linear Support Vector Machines (LSVM) using a linear classifier. The statistical method separates the original data in two classes of points and maximizes both the limits or margins and the distance between the nearest points from the two data groups or classes. The original data has been randomly segregated and resampled in a K equal size of subsamples using k-fold cross classification technique. From the resampling, one sample is used for testing the model as well as validating the data and the reaming samples (k-1) are used as training data. 10-fold cross validation was implemented, which is an often used iteration practice in this type of analysis, with an accuracy of 94.45. From the data of the present work, the solution for Linear Support Vector Machine can be found as follows: ( ) (15) ( )

(16) (17) (18) (19) (20)

Adhesion

Abrasion

Figure 8: Wear response K-value based on the dimensional analysis with linear classification algorithm. As it can be observed in Figure 8 that the two highest points above of the linear classifier correspond to neat PEEK (PEEK-S00) and characterize the adhesion wear mechanism observed in Figures 4 and 7. For the others two materials (PEEK-S02 and PEEK-S05) the primary wear mechanism appeared to be abrasion, with clear wear tracks and grooves parallel to the sliding direction. It can be concluded that the surface morphology plays an important role in the dimensional analysis that reveals the dominant wear mechanism on this study.

4. Conclusions The effects of several types of fillers in a PEEK polymer matrix were studied. Tribological tests were performed under three contact pressures 4 MPa, 8 MPa and 10 MPa at sliding velocity of 20 mm/s and 50 mm/s. Unlubricated reciprocating sliding conditions with a flat-on-flat contact configuration were used. Friction coefficients and wear rates were evaluated and worn surfaces were examined by optical and scanning electron microscopy. Following conclusions can be drawn from the present work: 1. Nano- and micro-particle reduces the coefficient of friction of PEEK-based hybrid composites and this effect becomes more significant at higher contact pressure (10 MPa). A reduction of the coefficient of friction with 50% could be noticed for PEEK composites. 2. Neat PEEK polymer showed with poor wear resistance at high pressures of 8 and 10 MPa at both sliding velocities. However, by adding nano-fillers (PEEK-S02 and PEEK-S05) the wear resistance could be improved, at both speeds 20 and 50 mm/s and contact pressure of 10 MPa. Such improvement is more pronounced in composite grade PEEK-S05 at 20 mm/s and 10 MPa (wear rate approximately one order of magnitude lower). Generally, for all studied materials, no significant changes on the wear resistances are observed at low sliding velocity (under 20 mm/s). 3. The influence of nano-SiO2-particles on the wear rate is strongly dependent on the apparent contact pressure. Positive effects such as lower friction and higher wear resistance are more pronounced at increased contact pressure and sliding velocity. 4. The formation of a secondary transfer film on the counter plate during sliding affects the wear behaviour of polymers and in some cases improves or degrades the quality of these transfer films. In the case that it is degraded, the wear resistance of the polymer matrix decreases due to the abrasive action of the counter plate and agglomerates. 5. The dominant wear mechanism was adhesion for the neat PEEK and abrasion for the PEEK based nanocomposites. Theses wear mechanisms were properly modelled and segregated by means of a dimensional and statistical analysis.

5. Acknowledgements The authors wish to thank the participating partners, Lehrstuhl für Verbundwerkstoffe, University of Kaiserslautern, Kaiserslautern, Germany for supplying test and performing mechanical characterisation. The conducted research is financially supported by the Foundation for Scientific Research of the Flemish Community (FWO grant number: 3G070108).

6. References 1. 2. 3. 4. 5.

6. 7.

8.

9.

10. 11.

12. 13. 14. 15.

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Highlights

The tribological behaviour of PEEK hybrid composites in sliding contact was studied.

Transfer film formation was examined by dark field imaging and optical microscopy.

Transfer film area was calculated by segmentation technique.

The calculated area was used in the analytical model.

A mathematical model was developed based on a dimensional analysis.