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Investigation of tribological behavior of Styrene-Butadiene Rubber compound on asphalt-like surfaces
Tribology International 136 (2019) 487–495
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Tribology International journal homepage: www.elsevier.com/locate/triboint
Investigation of tribological behavior of Styrene-Butadiene Rubber compound on asphalt-like surfaces
T
Anahita Emamia,∗, Seyedmeysam Khaleghianb a b
Virginia Polytechnic Institute and State University, 460 Old Turner St., Blacksburg, VA, USA Texas State University, 601 University Dr. San Marcos, TX, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Rubber friction Surface roughness Wear rate Tribo-modified layer
Tribological behavior of Styrene-Butadiene Rubber (SBR) compound reinforced by silica and carbon-black fillers on two different asphalt-like surfaces is studied using theoretical and experimental approaches. Linear sliding friction and wear tests were performed on two different roofing asphalt papers. The surface roughness power spectra of asphalts and the master curves of the large-strain viscoelastic modulus of SBR compound were used to model the contact area and friction coefficient theoretically. The theoretical results are in good agreement with experiment providing the tribochemical degradation is not the dominant wear mechanism. When the formation of a tribo-modified layer prevails the mechanical abrasion, the wear rate, in terms of mass loss, does not necessarily increase with the increase of frictional work as expected theoretically.
1. Introduction
surface is substituted by sandpaper [24–27]. Although the value of the friction coefficient of a rubber compound on specific sandpaper might be similar to the rubber-pavement friction coefficient, the dominant mechanism of the friction and wear might be completely different. Most of the asphalt surfaces are less abrasive compared to various sandpapers since the asphalt asperities are typically not as sharp as the ones on the sandpapers. Therefore, the dominant mechanisms of rubber friction and wear on sandpaper are controlled by sharp tips of asperities that penetrate and abrade the rubber surface. Sharp asperities typically contribute to rubber friction and wear by cutting, plowing, and scratching the rubber surface. In a recent study, Salehi et al. [19] measured the friction coefficient of four different compounds on four different electro-corundum discs of various grain sizes using LAT100. They found that the best correlation coefficient between the results of lab tests and tire-road data was about 0.93 for a disc with an average particle size of 60 μm. Although their test setup is able to simulate different working conditions of a real tire and provide a good correlation with tire data [28], whether the grip mechanism between rubber and the disc is the same as the rubber-road grip mechanism still remained an open question. In some other studies [29–31], a blade abrasion tester was used to study friction and abrasion pattern formation on the rubber specimen due to a single abrader. A spherical indenter sliding on a rubber disk was also used to study mild wear and formation of a tribo-modified film on the rubber surface [32–34]. Although these studies provide very
Friction and wear of rubber on asphalt surfaces are important topics in many practical applications such as engineering of tire treads and shoe soles. However, rubber-pavement interaction has not been completely understood despite extensive theoretical [1–8] and experimental [9–19] investigations. When a rubber block slides on a rough surface, the interaction between two surfaces involves complex processes. These processes include viscoelastic energy dissipation due to the pulsating deformations applied by asperities, adhesion through van der Waals forces, surface crack propagation due to oscillating loading excreted by roughness profile, scratching and plowing of the rubber surface by sharp asperities, and material degradation as a result of frictional heating. In addition, any surface contaminations such as dust and wear particles also contribute to rubber friction and wear mechanisms and increase the complexity of the problem. Another challenge in the characterization of friction and wear performance of rubber materials is conducting experiments on a realistic condition. Typically, in-field tests are expensive and very time-consuming. Moreover, some of the effective parameters such as environmental conditions of in-field tests are not controllable. Therefore, laboratory testings are more reliable and popular among scientists and engineers. The conventional lab-based test setups include Lambourn abrader [20], Lat-100 [21], Akron abrader [22], and DIN abrader [23], just to name a few. In many lab-based experimental studies, the asphalt
∗
Corresponding author. E-mail address: [email protected] (A. Emami).
https://doi.org/10.1016/j.triboint.2019.04.002 Received 15 November 2018; Received in revised form 17 February 2019; Accepted 1 April 2019 Available online 05 April 2019 0301-679X/ © 2019 Elsevier Ltd. All rights reserved.
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of partial contact which typically occurs when the squeezing force is not too large, and it needs further correction [39]. Therefore, the overestimation of elastic energy in the original theory was later addressed by Persson as he introduced a correction factor based on the comparison of the theoretical results with calculations obtained from Molecular Dynamics (MD) simulation [40]. This correction factor is calculated using the following equation:
useful insight into a specific mechanism of rubber friction and wear, they are not a good representative of the actual condition for the surface to surface contact. Therefore, despite the development of various laboratory test setups and numerous experimental results in the literature, characterization of friction and wear performance of rubber compounds on realistic working condition is challenging. In this study, a portable sliding friction and wear test set-up capable of running on a large substrate surface was used to study rubber friction and wear mechanism on different asphalt-like surfaces. Two different types of roofing asphalt were used in an indoor controlled condition to study friction and wear rate of a Styrene-Butadiene Rubber (SBR) compound filled with 60 parts per hundred rubber (phr) silica and 20phr carbon black that typically used as tire tread compound. Moreover, a modified version of Persson's contact theory was used to calculate the real contact area between rubber and asphalt surfaces. The friction coefficient was also modeled theoretically using a modified version of the extended Persson's theory of rubber friction, and the theoretical results were compared with the experimental data. Rest of this paper is structured as follows: in section 2, the theoretical models used in this work to calculate the real contact area and friction coefficient are briefly reviewed. Section 3 presents the material and experimental methods used in this study. In section 4, the results and discussion are presented, and finally, section 5 presents the conclusions.
2
A (q) ⎞ S (q) = γ + ⎛⎜1 − γ ⎞⎟ ⎛ ⎝ ⎝ ⎠ A0 ⎠ ⎜
and γ is an empirical parameter in the where A (q) = A (ζ ) at ζ = range of 0.4–0.5 [35]. This factor in the model enhances the real contact area by a factor of γ −0.5 at small load. In order to better estimate γ for each surfaces at applied normal load and velocities, a physics-based approach was used in this study. This approach is applicable for selfaffine fractal surfaces in which the roughness pattern repeats itself at different length scales providing it is scaled appropriately different along parallel and perpendicular directions to the surface plane. Many asphalt surfaces have self-affine characteristics over a wide range of length scales [41], and they can be described using fractal parameters. The surface roughness power spectrum of a fractal surface for spatial frequency larger than a short wavenumber cutoff q0 can be analytically described as: 2
A (ζ ) 1 ⎛ ⎞ = erf ⎜ ⎟ A0 2 G ( ζ ) ⎝ ⎠
(1)
hT (x ) =
where 2π
⎧
∫ ⎨q3S (q) C (q) ⎧⎨∫ q0
⎩
⎩
0
E (vq cos φ) (1 − ϑ2) σ0
2
dφ
⎫⎫ dq ⎬⎬ ⎭⎭
(4)
where H is Hurst exponent, h 0 is the Root Mean Square (RMS) of the surface roughness. In this approach, an affine transformation with a fixed maximum height of z max is used to shift the height profile of the rough surface (z = h(x)) to the upper region of the surface where the rubber has complete contact on the large (macroscale) asperities. Using this approach, the large valleys between high asperities that have no contact with the deformed material and do not contribute to the displacement field is eliminated, and the partial contact problem is converted to the complete contact problem where the Persson's original theory is exact. This affine transformation does not change the fractal parameters of the surface and only shift the height profile towards the upper region using the following affine transformation:
In this study, Persson theory of contact mechanics is used to calculate the real contact area between the rubber block and the rough substrate surface. The rubber block is modeled as a linear viscoelastic material with isotropic properties and a smooth contact surface. Considering that the stiffness of the substrate surface is much higher than the rubber, it is reasonable to model it as a rigid rough surface. Persson contact theory models the contact between the rubber and randomly rough surface using surface roughness power spectrum C (q) , where q is the spatial frequency (wavenumber), using the following equation:
ζq0
−2(H + 1)
h H ⎛q⎞ C (q) = ⎜⎛ 0 ⎟⎞ ⎜ ⎟ q 2 ⎝ 0 ⎠ π ⎝ q0 ⎠
2.1. Contact mechanics
1 8
(3) q q0
2. Theory
G (ζ ) =
⎟
h (x ) − z max + z max pT
(5)
where pT is an affine shift parameter and hT (x ) is the transformed height profile that can be approximated as the vertical displacement in the original model. After this transformation, the mean of height profile
(2)
(
shifts from zero to hT = z max 1 −
and A0 and σ0 are nominal contact area and pressure, respectively. The function A (ζ ) denotes the apparent contact area as a function of the magnification ζ at which the contact area is studied. The short cutoff wavenumber q0 is the magnitude of the smallest wave vector that contributes to the contact area. E (ω) is the viscoelastic modulus of the rubber which is a function of the loading frequency applied by the surface asperities along the sliding direction so that ω = vq cos φ , where v is the sliding velocity. The dependency of Poisson ratio ϑ on the loading frequency is assumed to be negligible. S (q) is the correction factor which was not considered in the original theory [3] and it was added later [35]. In the original theory [3], it is assumed that the vertical displacement of the rubber on the contact area can be approximated by the height profile of the rough surface while deriving the diffusion equation for multiscale contact pressure distribution. Although partial contact is considered by imposing a boundary condition on the solution of the equation, the initial assumption of displacement field results in an overestimation of deformation and accordingly the elastic energy in the rubber by about 20% [36]. Therefore, the original model tends to underestimate the real contact area [37,38] in the case
1 pT
) and this becomes the new nom-
inal contact plane and coordinate system. This transformation from full contact to partial contact for a single scale roughness is shown in Fig. 1. After eliminating the offset of the transformed profile by zeroing the new mean hT , the mean square of transformed height profile can be calculated as:
→ h (→ x ) h( 0 ) → hT (→ x ) hT ( 0 ) = 2 pT
(6)
which is assumed to be equal to the mean square of vertical displacement. Therefore, it can correct the displacement assumption for partial contact similar to the correction factor S (q) by reducing the effective surface roughness power spectrum. Consequently, the transformed power spectrum becomes:
CT (q) =
C (q) pT 2
(7)
where CT (q) should be equal to S (q) C (q) as q approaches the large cutoff wavenumber at small normal load and accordingly pT ≈ γ −0.5 . This 488
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Fig. 1. Schematic of transformation from (a) full contact to (b) partial contact.
hysteresis friction is important at high velocities when the energy loss due to deformation of the rubber is significant while the adhesion component of friction is dominant at low sliding velocities and sufficiently clean surfaces. The exact contribution of adhesion to the friction under different conditions is still a controversial subject. Persson [43] believes that adhesion does not have a significant contribution to rubber-pavement friction, especially at high velocity, due to the high roughness of the asphalt surfaces. On the other hand, as Wagner et al. [44] compared the results of a multiscale finite element model with experiments, they suggested that adhesive interaction even contributes to the friction between rubber and a wet rough surface covered with water and soup at low sliding velocity. Makhovskaya [8] also developed an analytical multiscale model to calculate the sliding friction for a viscoelastic material considering both adhesion and hysteresis friction at different length scale. Based on his model, he concluded that implementing the effect of adhesion shifts the hysteresis peak of friction towards higher velocities. In a recent paper, Myshkin and Kovalev [45] reviewed various mechanisms and models for adhesion mechanisms in polymers. Lorenz et al. [14]. also argued that at low sliding velocities, other shearing processes on the real contact area might also have a significant effect on the rubber friction, including the interfacial crack propagation, abrasion, interaction with contaminations on the substrate surface and so on. The two components of the friction coefficient can be superimposed to obtain a master curve for the rubber friction over a wide range of velocities. Therefore, the total friction coefficient can be written as:
shift factor can be determined using the separation distance between two nominal contact planes which can be calculated using GreenwoodWilliamson contact theory [42] expressed as the following equation:
σ0 =
4 E (ωmin ) 1 R 2 na 3 1 − ϑ2
∞
∫ (z − d)3/2ϕ (z ) dz d
(8)
where d is the separation distance without considering the interaction between asperities, na is the number of asperities per unit area, R is the effective mean radius of asperities, and ϕ (z ) is the distribution of asperity heights denoted by z. If the surface height profile has a normal 1
2 − z
distribution, then ϕ (z ) = σ˜ 2π e 2σ˜ 2 where σ˜ is the standard deviation. Since in this theory, a single scale roughness is considered, the viscoelastic modulus of rubber at the minimum loading frequency (ωmin = q0 v ), which is applied by the macro-asperities with a wave length of 2π / q0 must be used. Equation (8) has to be solved implicitly for the separation distance d. Then, the effect of interaction between neighboring asperities can be included in an approximate way by introducing the effective separation distance as:
(1 − ϑ2) Aa d˜ (σ0) = d + σ0 E (ωmin )
(9)
where Aa is the compact area. The number of asperities per unit area can be estimated as follows:
na ≈
q02 2π 2 3
(10)
μ (v ) = μH (v ) + μA (v )
where it is assumed that the asperities have a disordered hexagonal-like 2π distribution [41] with a lattice constant λ 0 = q . 0 If the large-scale roughness is modeled by a sinusoidal function as z = h (x ) = hA cos(q0 x ) , then, the amplitude of this function is hA = 2 h 0 . Then, the average radius of macro-asperities can be calculated as:
d 2z R = ⎜⎛ 2 ⎝ dx
−1
⎞
⎟
≈
x=0 ⎠
1 q02 2 h 0
where μH and μA are hysteresis and adhesive components of the friction coefficient, respectively. The hysteresis component of friction can be calculated using a modified version of Persson theory of rubber friction which is formulated as:
μH (v ) =
(11)
Using equations (10) and (11) in equation (8) to solve d, and using the solution in equation (9), finally the shift factor can be calculated using the following equation:
2 h0 pT = d˜ (σ0) − z max
(13)
1 2
ζm q0
∫ q0
q3
A (q) ⎧ S (q)C(q) ⎨ σ0 A0 ⎩
2π
∫ cos φIm ⎧⎨ E (1(vq−cosϑ2)φ) ⎫⎬ dφ⎫⎬ dq ⎩
0
⎭
⎭
(14) where the magnification ζ m is the maximum magnification that contributes to the hysteresis friction. Due to the complexity involved in the adhesive component of friction, a semi-empirical model proposed by Lorenz et al. [14] is used to model the adhesive friction coefficient which is expressed as:
(12)
where z max is the maximum height of the surface profile. Calculations based on nominal pressure, material properties of the rubber sample, and the roughness profile of two surfaces gives pT in the range of 1.4–1.6 and results in γ in the mentioned range of 0.4–0.5.
μA (v ) =
2.2. Rubber friction
2 τ fm A(v, ζm) v ⎛ ⎞ exp ⎜−c ⎡log ⎛ ⎞ ⎤ ⎟ ⎢ σ0 A0 v ⎥ ⎝ ⎣ ⎝ 0 ⎠⎦ ⎠ ⎜
⎟
(15)
where v0 ≈ 6 mm / s and c = 0.1 are empirical parameters which have approximately constant values, and τ fm is the maximum shear stress on the real contact area when v = v0 . The value of τ fm varies with rubber compounds and substrate surface roughness, but it is in the order of few megapascal [14,46] and must be obtained from experiment.
Rubber friction is a result of complex processes occurring at the interface. Grosch [10] attributed the rubber friction on dry surfaces to two competing mechanisms of adhesion and hysteresis loss. The 489
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3. Material and experimental methods 3.1. Viscoelastic modulus The viscoelastic modulus of the filled Styrene Butadiene Rubber (SBR) compound used in the experiments was measured using the Dynamic Mechanical Analysis (DMA) technique. Since the frequency range of the DMA test is typically limited between 0.1 and 100 Hz, the temperature-frequency superposition method was used to obtain the viscoelastic modulus at a broader range of frequencies. The temperature was varied between −25 °C and 80 °C, and the Williams-Landel-Ferry (WLF) shift factor with a reference temperature of 20 °C was used to superimpose the master curve segments. Initially, the measurement was performed at a low strain of 0.5% which is in the linear viscoelastic region. However, the applied strain was increased at lower frequencies (corresponding to higher temperatures) so that the detected force remains higher than the lower limit of the transducer. The glass temperature was found to be −21.7 °C corresponding to the frequency of about 62.5 KHz. When rubber is sliding on a rough substrate surface, the rubber contact area can undergo very large strain, about 100% or even more [47], and the viscoelastic modulus at high strain amplitude must be used in modeling of the contact area and rubber friction. Therefore, strain sweep tests were performed at a constant frequency of 1 Hz and varied temperature from −25 °C to 80 °C. The strain was increased from about 0.095% to the breakpoint of the specimen or maximum force limit of the equipment. In the range of temperatures between 20 °C and 80 °C, the maximum strain could reach up to 96% while at lower temperatures the maximum strain was smaller e.g. about 20%. The same WLF shift factor was used to calculate the master curve for large strain values. The storage modulus and loss modulus of the rubber for low strain and approximated high strain values were shown in Fig. 2. The loss factor and the WLF shift factor are shown in Fig. 3 and Fig. 4, respectively.
Fig. 3. Loss factor of filled SBR compound.
Fig. 4. WLF shift factor of filled SBR compound.
recording the friction and wear measurements, it can be assumed that the substrate surface already went through the initial transition region of the abrasion and reached a steady state condition. The three-dimensional sample profiles of both surfaces are shown in Fig. 5. Before calculating the surface roughness power spectrum from the measured height profiles, it was ensured that the measurement is valid. The profile measurement is considered to be valid only if the drop-out rate for the height signal is less than 10% [48]. After assuring the validity of the measurement, a linear interpolation was used to replace each invalid sample point. Moreover, the offset, slop, and any curvature of the sample surface relative to the flat reference plane was eliminated. The one-dimensional height profiles with height distribution functions of two surfaces are shown in Fig. 6. The Discrete Fourier Transform (DFT) was used to calculate the surface rough power spectrum. The DFT analysis assumes a periodic repetition of the measured signal, which is the height profile in this study, and this can result in a jump between the end and beginning of periodic lengths. This spectral leakage was eliminated using a Split Cosine Bell (SCB) window, which is suitable for short length signals because it retains 80% of the original signal unaltered as it smoothly goes from unity to zeros at two edges of the signal. The SCB is defined as:
3.2. Surface height profile Two roofing asphalt surfaces with different roughness were used to study rubber friction and wear. The first surface, referred to as surface A, consists of larger grains and has similar texture and roughness as a typical asphalt road. The second surface, referred to as surface B, has smaller grains and smoother macrotexture similar to concrete surfaces. The height profiles of the surfaces were measured using an optical profilometer with excellent accuracy and precision with a resolution of sub-micron. The surfaces were sampled from the middle section of the sliding path, and the surface measurements were carried out after the experiments. Since several running-in tests were conducted before
⎧ cos2 ⎪ WSCB (n) =
⎨ ⎪ cos2 ⎩
(
5πn N
−
π 2
)
1
(
5πn N
−
9π 2
)
0≤n<
N 10
N 10
≤n≤
9N 1
9N 10
N 10
(16)
where N is the number of sample points. The height profile was sampled over a square area with dimensions of L × L by measuring equally spaced points with a constant distance L of N along perpendicular directions of x and y. The height values are
Fig. 2. Viscoelastic modulus of filled SBR compound for low strain and high strain. 490
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Fig. 6. One dimensional height profile and height distribution function of the surfaces after offset and slope suppression.
Fig. 5. A section of three-dimensional surface profiles. L
L
denoted by h (x, y) where = N n x , y = N n y , and both n x and n y vary from 0 to N. Consequently, the Fourier Transform of height profile was calculated using the following equation:
h (→ q)=
L2 (2π )2N 2
N
N
∑ ∑ ny = 0 nx = 0
2π L L WSCB (n x , n y ) h ⎛ n x , n y ⎞ e−i N (mx nx + my ny) N ⎠ ⎝N
(17)
→ where q = (qx , qy ) =
(
)
2π 2π m x , L m y is the discretized wave vector and L N+1 from 0 to N or 2 depending on which one is an 2
both m x and m y vary integer value. After calculating equation (18) using the Fast Fourier Transform (FFT) algorithm, the surface roughness power spectrum was calculated using the following equation [43]:
C (q) =
(2π )2 2 hA ( → q) L2
(18)
The average surface roughness power spectra of several samples for both surfaces are shown in Fig. 7. The power spectra of both surfaces can be approximately modeled using equation (4) between the short cutoff wavenumber q0 and the large cutoff wavenumber q1. The slopes of the log-log plot of the power spectra were measured to calculate the Hurst exponent using the following equation:
Slope H = −⎛ + 1⎞ ⎠ ⎝ 2
Fig. 7. Surface roughness power spectra of two roofing asphalt surfaces.
(19) 491
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Table 1 Surface roughness parameters. H
h 0 (μm )
q0 (m−1)
q1 (m−1)
Surface A
0.84
204.8
2000
106
Surface B
0.93
139.7
3000
106
The surface parameters of both surfaces are presented in Table 1. 3.3. Friction and wear test procedure
Fig. 9. Measured data points for friction coefficient at velocity 0.5 m/s over a sliding distance of 3.4 m on surface A.
A linear sliding friction and wear test set-up developed at Center for Tire Research (CenTiRe) was used in the experiments. In this test-setup, a cubic rubber specimen with a nominal contact area of 25.4 mm by 25.4 mm was dragged on each substrate surface using a six-wheel robot for a maximum distance of 3.5 m. The sliding velocity was accurately measured by encoders attached to the wheels, and it was controlled using a real-time control algorithm. The friction force was measured using a load cell, and a constant normal load was applied using dead weights on the rubber block. The nominal contact pressure remained 81 KPa in each experiment. All the tests were conducted at room temperature 23 ± 3°C on dry surfaces. The substrate surfaces were also cleaned using a brush to reduce the contaminations as much as possible. On each surface, the friction and wear rate were measured for four different sliding velocities. A new sample was used for each velocity, and before recording the data, the sharp edges of the rubber contact surface was abraded in several running-in tests by sliding the rubber block on the same substrate surface. After reaching a steady state condition, friction and mas loss were recorded. Then, the experiment for each velocity was repeated between 10 and 15 times. The average sliding friction coefficient was calculated from data in the steady state region, after passing the initial transition region between the static and the kinematic friction. The mass of the specimen was measured using a weighing scale with an accuracy of 1 mg after sliding over a sufficiently large distance, which is typically about 5 m.
surfaces. The theoretical results indicated that the real contact area between rubber block and both surfaces is about 1% of the nominal contact area. The contact area predicted by the modified version of Persson theory is slightly larger than the value that the original theory predicts since the modified model approximately corrects for the displacement assumption of full contact by considering displacement for partial contact. As it is expected from roughness parameters of both surfaces, the real contact area on surface A is smaller than on surface B due to its larger macroasperities and roughness indicating by higher RMS and smaller Hurst exponent values. The theoretical real contact area also decreases with the increase of sliding velocity, as the rubber stiffness increases with the increase of the frequency of loading exerted by the substrate asperities. 4.2. Experimental and theoretical rubber friction Fig. 9 shows the recorded signals of the friction coefficient measured using the load cell during one sliding test period. The average friction coefficient for each test was calculated over the steady state region after the initial peak due to static friction and inertia. The average value is shown by the dashed line. The average friction coefficient measured in each sliding test for surface A and surface B is shown as a green dot in Fig. 10. The average friction coefficients for each velocity for both surfaces are shown as red pentagon stars. The theoretical model for adhesive friction coefficient was calculated using the semi-empirical model presented in equation (15) and shown as a dot-dashed line with a peak value at a very low sliding velocity. This adhesive component of friction theoretically decreases with the increase of velocity until it vanishes at very high velocity. When the sliding velocity is very low, the rubber molecules at the interface have sufficient time to adjust themselves to the substrate surface and form adhesive bonds through van der Waals interaction with molecules of the substrate surface. As the sliding velocity increases, few molecules can form adhesive bonds and the strength of adhesion between two surfaces decreases. It is found that the maximum shear stress of τf m = 4.8 MPa and τf m = 3.2 MPa match the peaks in experimental results for surface A and surface B, respectively. These values of maximum shear stress are smaller than the ones found in other studies [14,46] because the modification made to the Persson contact theory predicts a larger real contact area compared to the original theory used in those studies. Assuming a constant maximum shear force, when the contribution of real contact area increases, the value of maximum shear stress decreases. In the range of sliding velocities used in the experiment, the dominant mechanism of friction is hysteresis friction which was calculated using equation (14). The superposition of adhesive and hysteresis friction results in the total theoretical friction coefficient which is shown by a solid blue line for each surface in Fig. 10. The theoretical model could successfully predict the average friction coefficient on surface A over the entire range of velocities used in the experiment. On the other hand, the theoretical model could not predict the rapid increase of friction coefficient at high sliding velocities on
4. Results and discussion 4.1. Theoretical contact area The ratio of apparent contact area to the nominal contact area for different length scales was calculated using the modified version of Persson contact theory for both surfaces. The comparison between the numerical results for the minimum and maximum velocities used in the experiment is shown in Fig. 8. The magnification here is defined as the ratio of wavenumber to the minimum cutoff wavenumber of two
Fig. 8. The logarithm of the ratio of apparent contact area to the nominal contact area as a function of magnification for two different asphalt surfaces and velocities. 492
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Fig. 12. Measured mass of rubber blocks vs sliding distance for different velocities. Fig. 10. Experimental and theoretical friction coefficient vs sliding velocity.
4.3. Rubber wear rate The measured weights vs sliding distance for steady-state wear condition on both surfaces are shown in Fig. 12. The average wear rate for each sliding velocity was calculated from the slope of the corresponding regression line. At the sliding velocity of 0.5 m/s on surface B, the rubber mass was measured after removing the decomposed rubber attached to the side of the specimen (as shown in Fig. 11) in order to keep the geometry of the contact surface consistent during the experiment. Therefore, the measured mass loss is significantly larger compared with the results of other velocities. However, before removing the degraded piece of rubber manually, the weight loss of the rubber block was not measurable using a scale with a resolution of 1 mg. Therefore, the real wear rate for this velocity is expected to be very small until the accumulated tribo-modified rubber is ruptured by a sharp asperity, and results in a sudden large mass loss. The abrasion pattern was developed on the rubber surface, as it was sliding on surface A, and the pattern was detected for all the sliding velocities used in the experiment. The abrasion pattern is referred to parallel ridges that develop perpendicular to the sliding direction which have saw-tooth shapes with tips pointing to the rubber sliding direction. The abrasion pattern was initially discovered by Shallamach [49,50] on the rubber surface abraded by various rough surfaces such as different types of concrete roads and sandpapers. On the other hand, the abrasion pattern was detectable on the rubber specimens sliding on surface B only at low velocities, and it disappeared as sliding velocity increased. At velocity 0.5 m/s, the abrasion pattern could not be detected as shown in Fig. 11 because the tribo-modified layer on the rubber surface acts as a protective film that prevents material loss due to abrasive wear and reduces the total wear rate. This type of material degradation has been referred to as smearing or oily abrasion in the literature [51,52], and is the product of thermochemical process on the contact area due to
Fig. 11. Rubber surface after running on smooth roofing asphalt at v = 0.5 m/s.
surface B. On the contrary, the theory of friction that considers the role of flash temperature [5] predicts a decrease of friction coefficient with the increase of velocity as a result of the elastic softening of the rubber due to high flash temperature. However, it was found that elastic softening is not the only process occurring on the rubber surface at high temperature. Inspecting the rubber surface revealed that the rapid increase of friction coefficient at high velocities is the result of the formation of a thin sticky layer on the rubber surface due to thermochemical degradation. This degraded layer has inferior mechanical properties and it is softer than the bulk material [34]. As the degraded layer forms on the rubber surface, the deformation of rubber at the interface increases resulting in the increase of the real contact area and the adhesion between two surfaces. The material characterization of the thermos-modified layer under different tribological conditions will be carried out in the future study. Fig. 11 shows the viscous liquid-like layer, referred to as the tribo-modified layer, which had been accumulated at the side of the contact area while it is still bonded to the rubber block.
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surfaces [9,21,53,54]. On the other hand, the wear rate vs friction coefficient on surface B does not follow the same trend. In this case, most of the energy dissipated due to friction results in chemical degradation and the formation of the tribo-modified layer rather than surface crack propagation and wear particle detachment. This can result in an inverse relation between mass loss and friction coefficient, which is desired for many rubber-based products such as tires. On the contrary, Mokhtari and Schipper [34] found that the formation of tribomodified layer reduces the friction coefficient under a different experimental condition. They studied the friction of a rubber sample using a ball-on-disk setup and found that the formation of the tribo-modified layer decreases the friction coefficient between the SBR disk and the granite ball by altering the shear stress. In their case, the modified layer might have acted as a lubricant to decrease the friction between the rubber and granite surface. It can be concluded that based on the chemical structure of the tribo-modified layer and contact condition, the smearing of rubber might have different effects on the friction coefficient. Therefore, further investigations on the formation of the tribo-modified layer and its effect on the friction coefficient under different conditions are required.
Fig. 13. Wear rate vs sliding velocity – data points in dashed ellipse were obtained after detachment of the modified accumulated layer artificially.
frictional heating on the rubber surface. Since surface B is smoother than surface A, the macroscale contact regions tend to be more clustered and closer to each other. Therefore, the overlap of temperature field around the hot contact regions results in higher temperature rise on the contact area leading to a thermally activated chemical reaction of the rubber molecules with oxygen (oxidation), and chemical decomposition of the surface layer of the rubber sample. As the flash temperature increases, the formation rate of the tribo-modified layer also increases and becomes greater than the rate of its removal by abrasion. The effect of thermochemical degradation is significant and visibly detectable at a sliding velocity of 0.5 m/s. The effect of the tribomodified layer, possibly at a smaller length scale, on friction coefficient can be also found when sliding velocity is 0.4 m/s as shown in Fig. 10. Wear rate in terms of mass loss per unit sliding distance at different sliding velocity is shown in Fig. 13 for both surface A and B. The data separated by a dashed ellipse in the plot for surface B corresponds to the condition where the accumulated tribo-modified layer was removed by hand before mass measurement. On surface A, the wear rate increases with the increase of sliding velocity, while on surface B the wear rate decreases with the increase of sliding velocity until the accumulation of degraded layer is so significant that could be removed as a big wear particle. The scattered measurement of the wear rate at velocity 0.5 m/s is due to artificial detachment of tribo-modified piece of rubber from the side of the contact area. As previously mentioned, if the tribo-modified chunk of rubber was not removed during the mass measurement, the wear rate in terms of mass loss would be so small that could not be measured precisely. On the other hand, after several tests, a large amount of tribomodified rubber would be finally detached from the rubber surface by the asperities and results in a large mass loss. The relation between wear rate and friction coefficient on each substrate surface is also demonstrated in Fig. 14. On surface A, a power law equation, compared to a linear equation, provides slightly better representation for the relation between wear rate and friction coefficient of rubber samples. A similar relation was also observed and reported by other researches on different abrasive
5. Conclusions Friction and wear of a SBR compound filled with 60 phr silica and 20 phr carbon black on two different types of roofing asphalts, referred to as surface A and B, were studied. Surface A has a texture and roughness parameters similar to real asphalt roads, while surface B has a smoother surface similar to concrete pavements with finer grain size. The profiles of both surfaces were measured using an optical profilometer with sub-micron resolution, and the surface profiles were used to calculate the surface roughness power spectra. The master curve of the large-strain viscoelastic modulus of the rubber was measured using DMA tests and strain sweep data. The data of surface roughness power spectra and viscoelastic modulus were used to model the real contact area of rubber sample on both surfaces using an improved version of Persson's contact theory. The friction coefficient as a function of sliding velocity was also calculated using an improved and extended version of Persson's rubber friction theory. The results of the theoretical model for surface A were in good agreement with the experimental results. However, the theoretical results for surface B underestimated the friction coefficient at high velocities. Inspection the rubber surface after sliding with velocity 0.5 m/s on surface B, it was found that the top layer on the rubber surface was significantly altered due to thermochemical degradation as a result of high flash temperature at the contact interface. Since the tribo-modified layer is sticky and softer than the bulk material, it affects the dominant mechanism of friction and wear by increasing the real contact area in addition to preventing the rubber surface from surface crack propagation and pattern abrasion. It was found that when the rubber wear mechanism is controlled by mechanical abrasion, in the absence of significant tribo-modified layer, there is a power law relation between wear rate, measured as mass loss per sliding distance, and friction coefficient. On the other hand, when the thermochemical degradation and smearing abrasion occur on the rubber surface, the wear rate in terms of mass loss does not necessarily increase with the friction unless the accumulation of degraded rubber detaches from the surface by a sudden rupture, causing a significant material loss. Therefore, when the tribo-modified layer forms on the rubber surface, the mass loss does not sufficiently represent the wear rate of the rubber sample, and change in chemical composition and molecular weight of the rubber material need to be considered in the evaluation of wear rate. In the future study, the material characterization will be conducted for rubber samples to elucidate the mechanism of thermochemical abrasion and its effect on the friction mechanism.
Fig. 14. Wear rate vs friction coefficient. 494
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Acknowledgments
[23] Pal K, Das T, Rajasekar R, Pal SK, Das CK. Wear characteristics of styrene butadiene rubber/natural rubber blends with varying carbon blacks by DIN abrader and mining rock surfaces. J Appl Polym Sci 2009;111:348–57. [24] Ramakrishnan R, Donovan J, Medalia A. The effect of abrading surfaces on the wear of rubber tread compounds. Rubber Chem. Technol. 1995;68:609–22. [25] Vieira T, Ferreira R, Kuchiishi A, Bernucci L, Sinatora A. Evaluation of friction mechanisms and wear rates on rubber tire materials by low-cost laboratory tests. Wear 2015;328:556–62. [26] Motamedi M, Taheri S, Sandu C. Rubber–road contact: comparison of physics-based theory and indoor experiments. Tire Sci Technol 2016;44:150–73. [27] Morozov A, Bukovskiy P. Method of constructing a 3D friction map for a rubber tire tread sliding over a rough surface. J Frict Wear 2018;39:129–36. [28] Riehm P, Unrau H-J, Gauterin F. A model based method to determine rubber friction data based on rubber sample measurements. Tribol Int 2018;127:37–46. [29] Fukahori Y, Yamazaki H. Mechanism of rubber abrasion. Part I: abrasion pattern formation in natural rubber vulcanizate. Wear 1994;171:195–202. [30] Fukahori Y, Yamazaki H. Mechanism of rubber abrasion: Part 2. General rule in abrasion pattern formation in rubber-like materials. Wear 1994;178:109–16. [31] Fukahori Y, Yamazaki H. Mechanism of rubber abrasion part 3: how is friction linked to fracture in rubber abrasion? Wear 1995;188:19–26. [32] Mané Z, Loubet J-L, Guerret C, Guy L, Sanseau O, Odoni L, et al. A new rotary tribometer to study the wear of reinforced rubber materials. Wear 2013;306:149–60. [33] Mokhtari M, Schipper DJ, Vleugels N, Noordermeer JW. Existence of a tribo-modified surface layer on SBR elastomers: balance between formation and wear of the modified layer. Tribol Lett 2015;58:22. [34] Mokhtari M, Schipper DJ. Existence of a tribo-modified surface layer of BR/S-SBR elastomers reinforced with silica or carbon black. Tribol Int 2016;96:382–8. [35] Afferrante L, Bottiglione F, Putignano C, Persson B, Carbone GJTL. Elastic contact mechanics of randomly rough surfaces: An Assessment of Advanced Asperity Models and Persson’s Theory. Tribol. Lett. 2018;66:75. [36] Persson B. On the elastic energy and stress correlation in the contact between elastic solids with randomly rough surfaces. J Phys Condens Matter 2008;20:312001. [37] Manners W, Greenwood J. Some observations on Persson's diffusion theory of elastic contact. Wear 2006;261:600–10. [38] Bugnicourt R, Sainsot P, Lesaffre N, Lubrecht A. Transient frictionless contact of a rough rigid surface on a viscoelastic half-space. Tribol Int 2017;113:279–85. [39] Scaraggi M, Persson B. Friction and universal contact area law for randomly rough viscoelastic contacts. J Phys Condens Matter 2015;27:105102. [40] Yang C, Persson B. Contact mechanics: contact area and interfacial separation from small contact to full contact. J Phys Condens Matter 2008;20:215214. [41] Persson BN. Contact mechanics for randomly rough surfaces. Surf Sci Rep 2006;61:201–27. [42] Ciavarella M, Greenwood J, Paggi M. Inclusion of “interaction” in the Greenwood and Williamson contact theory. Wear 2008;265:729–34. [43] Persson B, Albohr O, Tartaglino U, Volokitin A, Tosatti E. On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J Phys Condens Matter 2004;17:R1. [44] Wagner P, Wriggers P, Veltmaat L, Clasen H, Prange C, Wies B. Numerical multiscale modeling and experimental validation of low speed rubber friction on rough road surfaces including hysteretic and adhesive effects. Tribol Int 2017;111:243–53. [45] Myshkin N, Kovalev A. Adhesion and surface forces in polymer tribology—a review. Friction 2018;6:143–55. [46] Tiwari A, Miyashita N, Espallargas N, Persson B. Rubber friction: the contribution from the area of real contact. J Chem Phys 2018;148:224701. [47] Iwai T, Uchiyama Y. The strain generated on a rubber surface in the course of pattern abrasion. Tire Sci Technol 2000;28:96–105. [48] Motamedi M. Road surface measurement and multi-scale modeling of rubber road contact and adhesion. Virginia Tech; 2015. [49] Schallamach A. On the abrasion of rubber. Proc Phys Soc B 1954;67:883. [50] Schallamach A. Abrasion pattern on rubber. Rubber Chem. Technol. 1953;26:230–41. [51] Zhang S. Mechanisms of rubber abrasion in unsteady state. Rubber Chem. Technol. 1984;57:755–68. [52] Zhang S-W. Tribology of elastomers. Elsevier; 2004. [53] Gent A, Pulford C. Mechanisms of rubber abrasion. J Appl Polym Sci 1983;28:943–60. [54] Zhang S. Investigation of abrasion of nitrile rubber. Rubber Chem. Technol. 1984;57:769–78.
The authors would like to thank the Industry Advisory Board (IAB) members of Center for Tire Research (CenTiRe) for their financial support and Sumitomo Rubber Industries (SRI) for providing the rubber samples and their dynamic modulus master curves. The authors are also gratefully thankful to the academic advisor, Dr. Saied Taheri. This work (Project Code: MODL-2015-B4-4) was financially supported by the Industry Advisory Board of the Center for Tire Research (CenTiRe), an Industry/University Cooperative Research Center (NSF-I/UCRC) program led by Virginia Tech. References [1] Schallamach A. A theory of dynamic rubber friction. Wear 1963;6:375–82. [2] Kluppel M, Heinrich G. Rubber friction on self-affine road tracks. Rubber Chem. Technol. 2000;73:578–606. [3] Persson BN. Theory of rubber friction and contact mechanics. J Chem Phys 2001;115:3840–61. [4] Le Gal A, Yang X, Klüppel M. Evaluation of sliding friction and contact mechanics of elastomers based on dynamic-mechanical analysis. J Chem Phys 2005;123. 014704. [5] Persson BN. Rubber friction: role of the flash temperature. J Phys Condens Matter 2006;18:7789. [6] Le Gal A, Klüppel M. Investigation and modelling of rubber stationary friction on rough surfaces. J Phys Condens Matter 2007;20. 015007. [7] Persson B. Theory of powdery rubber wear. J Phys Condens Matter 2009;21:485001. [8] Makhovskaya Y. Modeling sliding friction of a multiscale wavy surface over a viscoelastic foundation taking into account adhesion. Lubricants 2019;7:13. [9] Schallamach A. Friction and abrasion of rubber. Rubber Chem. Technol. 1958;31:982–1014. [10] Grosch K. The relation between the friction and visco-elastic properties of rubber. Proceedings of the royal society of London A: mathematical, physical and engineering sciences. The Royal Society; 1963. p. 21–39. [11] Mofidi M, Prakash B, Persson B, Albohr O. Rubber friction on (apparently) smooth lubricated surfaces. J Phys Condens Matter 2008;20. 085223. [12] Besdo D, Heimann B, Klüppel M, Kröger M, Wriggers P, Nackenhorst U. Elastomere friction: theory, experiment and simulation. Springer Science & Business Media; 2010. [13] Lorenz B, Persson B, Dieluweit S, Tada T. Rubber friction: comparison of theory with experiment. Eur. Phys. J.E 2011;34:129. [14] Lorenz B, Oh Y, Nam S, Jeon S, Persson B. Rubber friction on road surfaces: experiment and theory for low sliding speeds. J Chem Phys 2015;142:194701. [15] Kärkimaa J, Tuononen A. Experimental study on velocity and temperature dependency of rubber-asphalt friction. The dynamics of vehicles on roads and tracks: proceedings of the 24th symposium of the international association for vehicle system dynamics (IAVSD 2015), graz, Austria, 17-21 august 2015. CRC Press; 2016. 453. [16] Lang A, Klüppel M. Influences of temperature and load on the dry friction behaviour of tire tread compounds in contact with rough granite. Wear 2017;380:15–25. [17] Wu Y, Zhou Y, Li J, Zhou H, Chen J, Zhao H. A comparative study on wear behavior and mechanism of styrene butadiene rubber under dry and wet conditions. Wear 2016;356:1–8. [18] Huang M, Guibert M, Thévenet J, Fayolle C, Chaussée T, Guy L, et al. A new test method to simulate low-severity wear conditions experienced by rubber tire materials. Wear 2018;410:72–82. [19] Salehi M, Noordermeer JW, Reuvekamp LA, Dierkes WK, Blume A. Measuring rubber friction using a Laboratory Abrasion Tester (LAT100) to predict car tire dry ABS braking. Tribol Int 2019;131:191–9. [20] Adams J, Reynolds J, Messer W, Howland L. Abrasion resistance of GR-S vulcanizates. Rubber Chem. Technol. 1952;25:191–208. [21] Grosch K, Schallamach A. The load dependence of laboratory abrasion and tire wear. Rubber Chem. Technol. 1970;43:701–13. [22] Heinz M, Grosch K. A laboratory method to comprehensively evaluate abrasion, traction and rolling resistance of tire tread compounds. Rubber Chem. Technol. 2007;80:580–607.
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Tribology International journal homepage: www.elsevier.com/locate/triboint
Investigation of tribological behavior of Styrene-Butadiene Rubber compound on asphalt-like surfaces
T
Anahita Emamia,∗, Seyedmeysam Khaleghianb a b
Virginia Polytechnic Institute and State University, 460 Old Turner St., Blacksburg, VA, USA Texas State University, 601 University Dr. San Marcos, TX, USA
A R T I C LE I N FO
A B S T R A C T
Keywords: Rubber friction Surface roughness Wear rate Tribo-modified layer
Tribological behavior of Styrene-Butadiene Rubber (SBR) compound reinforced by silica and carbon-black fillers on two different asphalt-like surfaces is studied using theoretical and experimental approaches. Linear sliding friction and wear tests were performed on two different roofing asphalt papers. The surface roughness power spectra of asphalts and the master curves of the large-strain viscoelastic modulus of SBR compound were used to model the contact area and friction coefficient theoretically. The theoretical results are in good agreement with experiment providing the tribochemical degradation is not the dominant wear mechanism. When the formation of a tribo-modified layer prevails the mechanical abrasion, the wear rate, in terms of mass loss, does not necessarily increase with the increase of frictional work as expected theoretically.
1. Introduction
surface is substituted by sandpaper [24–27]. Although the value of the friction coefficient of a rubber compound on specific sandpaper might be similar to the rubber-pavement friction coefficient, the dominant mechanism of the friction and wear might be completely different. Most of the asphalt surfaces are less abrasive compared to various sandpapers since the asphalt asperities are typically not as sharp as the ones on the sandpapers. Therefore, the dominant mechanisms of rubber friction and wear on sandpaper are controlled by sharp tips of asperities that penetrate and abrade the rubber surface. Sharp asperities typically contribute to rubber friction and wear by cutting, plowing, and scratching the rubber surface. In a recent study, Salehi et al. [19] measured the friction coefficient of four different compounds on four different electro-corundum discs of various grain sizes using LAT100. They found that the best correlation coefficient between the results of lab tests and tire-road data was about 0.93 for a disc with an average particle size of 60 μm. Although their test setup is able to simulate different working conditions of a real tire and provide a good correlation with tire data [28], whether the grip mechanism between rubber and the disc is the same as the rubber-road grip mechanism still remained an open question. In some other studies [29–31], a blade abrasion tester was used to study friction and abrasion pattern formation on the rubber specimen due to a single abrader. A spherical indenter sliding on a rubber disk was also used to study mild wear and formation of a tribo-modified film on the rubber surface [32–34]. Although these studies provide very
Friction and wear of rubber on asphalt surfaces are important topics in many practical applications such as engineering of tire treads and shoe soles. However, rubber-pavement interaction has not been completely understood despite extensive theoretical [1–8] and experimental [9–19] investigations. When a rubber block slides on a rough surface, the interaction between two surfaces involves complex processes. These processes include viscoelastic energy dissipation due to the pulsating deformations applied by asperities, adhesion through van der Waals forces, surface crack propagation due to oscillating loading excreted by roughness profile, scratching and plowing of the rubber surface by sharp asperities, and material degradation as a result of frictional heating. In addition, any surface contaminations such as dust and wear particles also contribute to rubber friction and wear mechanisms and increase the complexity of the problem. Another challenge in the characterization of friction and wear performance of rubber materials is conducting experiments on a realistic condition. Typically, in-field tests are expensive and very time-consuming. Moreover, some of the effective parameters such as environmental conditions of in-field tests are not controllable. Therefore, laboratory testings are more reliable and popular among scientists and engineers. The conventional lab-based test setups include Lambourn abrader [20], Lat-100 [21], Akron abrader [22], and DIN abrader [23], just to name a few. In many lab-based experimental studies, the asphalt
∗
Corresponding author. E-mail address: [email protected] (A. Emami).
https://doi.org/10.1016/j.triboint.2019.04.002 Received 15 November 2018; Received in revised form 17 February 2019; Accepted 1 April 2019 Available online 05 April 2019 0301-679X/ © 2019 Elsevier Ltd. All rights reserved.
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A. Emami and S. Khaleghian
of partial contact which typically occurs when the squeezing force is not too large, and it needs further correction [39]. Therefore, the overestimation of elastic energy in the original theory was later addressed by Persson as he introduced a correction factor based on the comparison of the theoretical results with calculations obtained from Molecular Dynamics (MD) simulation [40]. This correction factor is calculated using the following equation:
useful insight into a specific mechanism of rubber friction and wear, they are not a good representative of the actual condition for the surface to surface contact. Therefore, despite the development of various laboratory test setups and numerous experimental results in the literature, characterization of friction and wear performance of rubber compounds on realistic working condition is challenging. In this study, a portable sliding friction and wear test set-up capable of running on a large substrate surface was used to study rubber friction and wear mechanism on different asphalt-like surfaces. Two different types of roofing asphalt were used in an indoor controlled condition to study friction and wear rate of a Styrene-Butadiene Rubber (SBR) compound filled with 60 parts per hundred rubber (phr) silica and 20phr carbon black that typically used as tire tread compound. Moreover, a modified version of Persson's contact theory was used to calculate the real contact area between rubber and asphalt surfaces. The friction coefficient was also modeled theoretically using a modified version of the extended Persson's theory of rubber friction, and the theoretical results were compared with the experimental data. Rest of this paper is structured as follows: in section 2, the theoretical models used in this work to calculate the real contact area and friction coefficient are briefly reviewed. Section 3 presents the material and experimental methods used in this study. In section 4, the results and discussion are presented, and finally, section 5 presents the conclusions.
2
A (q) ⎞ S (q) = γ + ⎛⎜1 − γ ⎞⎟ ⎛ ⎝ ⎝ ⎠ A0 ⎠ ⎜
and γ is an empirical parameter in the where A (q) = A (ζ ) at ζ = range of 0.4–0.5 [35]. This factor in the model enhances the real contact area by a factor of γ −0.5 at small load. In order to better estimate γ for each surfaces at applied normal load and velocities, a physics-based approach was used in this study. This approach is applicable for selfaffine fractal surfaces in which the roughness pattern repeats itself at different length scales providing it is scaled appropriately different along parallel and perpendicular directions to the surface plane. Many asphalt surfaces have self-affine characteristics over a wide range of length scales [41], and they can be described using fractal parameters. The surface roughness power spectrum of a fractal surface for spatial frequency larger than a short wavenumber cutoff q0 can be analytically described as: 2
A (ζ ) 1 ⎛ ⎞ = erf ⎜ ⎟ A0 2 G ( ζ ) ⎝ ⎠
(1)
hT (x ) =
where 2π
⎧
∫ ⎨q3S (q) C (q) ⎧⎨∫ q0
⎩
⎩
0
E (vq cos φ) (1 − ϑ2) σ0
2
dφ
⎫⎫ dq ⎬⎬ ⎭⎭
(4)
where H is Hurst exponent, h 0 is the Root Mean Square (RMS) of the surface roughness. In this approach, an affine transformation with a fixed maximum height of z max is used to shift the height profile of the rough surface (z = h(x)) to the upper region of the surface where the rubber has complete contact on the large (macroscale) asperities. Using this approach, the large valleys between high asperities that have no contact with the deformed material and do not contribute to the displacement field is eliminated, and the partial contact problem is converted to the complete contact problem where the Persson's original theory is exact. This affine transformation does not change the fractal parameters of the surface and only shift the height profile towards the upper region using the following affine transformation:
In this study, Persson theory of contact mechanics is used to calculate the real contact area between the rubber block and the rough substrate surface. The rubber block is modeled as a linear viscoelastic material with isotropic properties and a smooth contact surface. Considering that the stiffness of the substrate surface is much higher than the rubber, it is reasonable to model it as a rigid rough surface. Persson contact theory models the contact between the rubber and randomly rough surface using surface roughness power spectrum C (q) , where q is the spatial frequency (wavenumber), using the following equation:
ζq0
−2(H + 1)
h H ⎛q⎞ C (q) = ⎜⎛ 0 ⎟⎞ ⎜ ⎟ q 2 ⎝ 0 ⎠ π ⎝ q0 ⎠
2.1. Contact mechanics
1 8
(3) q q0
2. Theory
G (ζ ) =
⎟
h (x ) − z max + z max pT
(5)
where pT is an affine shift parameter and hT (x ) is the transformed height profile that can be approximated as the vertical displacement in the original model. After this transformation, the mean of height profile
(2)
(
shifts from zero to hT = z max 1 −
and A0 and σ0 are nominal contact area and pressure, respectively. The function A (ζ ) denotes the apparent contact area as a function of the magnification ζ at which the contact area is studied. The short cutoff wavenumber q0 is the magnitude of the smallest wave vector that contributes to the contact area. E (ω) is the viscoelastic modulus of the rubber which is a function of the loading frequency applied by the surface asperities along the sliding direction so that ω = vq cos φ , where v is the sliding velocity. The dependency of Poisson ratio ϑ on the loading frequency is assumed to be negligible. S (q) is the correction factor which was not considered in the original theory [3] and it was added later [35]. In the original theory [3], it is assumed that the vertical displacement of the rubber on the contact area can be approximated by the height profile of the rough surface while deriving the diffusion equation for multiscale contact pressure distribution. Although partial contact is considered by imposing a boundary condition on the solution of the equation, the initial assumption of displacement field results in an overestimation of deformation and accordingly the elastic energy in the rubber by about 20% [36]. Therefore, the original model tends to underestimate the real contact area [37,38] in the case
1 pT
) and this becomes the new nom-
inal contact plane and coordinate system. This transformation from full contact to partial contact for a single scale roughness is shown in Fig. 1. After eliminating the offset of the transformed profile by zeroing the new mean hT , the mean square of transformed height profile can be calculated as:
→ h (→ x ) h( 0 ) → hT (→ x ) hT ( 0 ) = 2 pT
(6)
which is assumed to be equal to the mean square of vertical displacement. Therefore, it can correct the displacement assumption for partial contact similar to the correction factor S (q) by reducing the effective surface roughness power spectrum. Consequently, the transformed power spectrum becomes:
CT (q) =
C (q) pT 2
(7)
where CT (q) should be equal to S (q) C (q) as q approaches the large cutoff wavenumber at small normal load and accordingly pT ≈ γ −0.5 . This 488
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A. Emami and S. Khaleghian
Fig. 1. Schematic of transformation from (a) full contact to (b) partial contact.
hysteresis friction is important at high velocities when the energy loss due to deformation of the rubber is significant while the adhesion component of friction is dominant at low sliding velocities and sufficiently clean surfaces. The exact contribution of adhesion to the friction under different conditions is still a controversial subject. Persson [43] believes that adhesion does not have a significant contribution to rubber-pavement friction, especially at high velocity, due to the high roughness of the asphalt surfaces. On the other hand, as Wagner et al. [44] compared the results of a multiscale finite element model with experiments, they suggested that adhesive interaction even contributes to the friction between rubber and a wet rough surface covered with water and soup at low sliding velocity. Makhovskaya [8] also developed an analytical multiscale model to calculate the sliding friction for a viscoelastic material considering both adhesion and hysteresis friction at different length scale. Based on his model, he concluded that implementing the effect of adhesion shifts the hysteresis peak of friction towards higher velocities. In a recent paper, Myshkin and Kovalev [45] reviewed various mechanisms and models for adhesion mechanisms in polymers. Lorenz et al. [14]. also argued that at low sliding velocities, other shearing processes on the real contact area might also have a significant effect on the rubber friction, including the interfacial crack propagation, abrasion, interaction with contaminations on the substrate surface and so on. The two components of the friction coefficient can be superimposed to obtain a master curve for the rubber friction over a wide range of velocities. Therefore, the total friction coefficient can be written as:
shift factor can be determined using the separation distance between two nominal contact planes which can be calculated using GreenwoodWilliamson contact theory [42] expressed as the following equation:
σ0 =
4 E (ωmin ) 1 R 2 na 3 1 − ϑ2
∞
∫ (z − d)3/2ϕ (z ) dz d
(8)
where d is the separation distance without considering the interaction between asperities, na is the number of asperities per unit area, R is the effective mean radius of asperities, and ϕ (z ) is the distribution of asperity heights denoted by z. If the surface height profile has a normal 1
2 − z
distribution, then ϕ (z ) = σ˜ 2π e 2σ˜ 2 where σ˜ is the standard deviation. Since in this theory, a single scale roughness is considered, the viscoelastic modulus of rubber at the minimum loading frequency (ωmin = q0 v ), which is applied by the macro-asperities with a wave length of 2π / q0 must be used. Equation (8) has to be solved implicitly for the separation distance d. Then, the effect of interaction between neighboring asperities can be included in an approximate way by introducing the effective separation distance as:
(1 − ϑ2) Aa d˜ (σ0) = d + σ0 E (ωmin )
(9)
where Aa is the compact area. The number of asperities per unit area can be estimated as follows:
na ≈
q02 2π 2 3
(10)
μ (v ) = μH (v ) + μA (v )
where it is assumed that the asperities have a disordered hexagonal-like 2π distribution [41] with a lattice constant λ 0 = q . 0 If the large-scale roughness is modeled by a sinusoidal function as z = h (x ) = hA cos(q0 x ) , then, the amplitude of this function is hA = 2 h 0 . Then, the average radius of macro-asperities can be calculated as:
d 2z R = ⎜⎛ 2 ⎝ dx
−1
⎞
⎟
≈
x=0 ⎠
1 q02 2 h 0
where μH and μA are hysteresis and adhesive components of the friction coefficient, respectively. The hysteresis component of friction can be calculated using a modified version of Persson theory of rubber friction which is formulated as:
μH (v ) =
(11)
Using equations (10) and (11) in equation (8) to solve d, and using the solution in equation (9), finally the shift factor can be calculated using the following equation:
2 h0 pT = d˜ (σ0) − z max
(13)
1 2
ζm q0
∫ q0
q3
A (q) ⎧ S (q)C(q) ⎨ σ0 A0 ⎩
2π
∫ cos φIm ⎧⎨ E (1(vq−cosϑ2)φ) ⎫⎬ dφ⎫⎬ dq ⎩
0
⎭
⎭
(14) where the magnification ζ m is the maximum magnification that contributes to the hysteresis friction. Due to the complexity involved in the adhesive component of friction, a semi-empirical model proposed by Lorenz et al. [14] is used to model the adhesive friction coefficient which is expressed as:
(12)
where z max is the maximum height of the surface profile. Calculations based on nominal pressure, material properties of the rubber sample, and the roughness profile of two surfaces gives pT in the range of 1.4–1.6 and results in γ in the mentioned range of 0.4–0.5.
μA (v ) =
2.2. Rubber friction
2 τ fm A(v, ζm) v ⎛ ⎞ exp ⎜−c ⎡log ⎛ ⎞ ⎤ ⎟ ⎢ σ0 A0 v ⎥ ⎝ ⎣ ⎝ 0 ⎠⎦ ⎠ ⎜
⎟
(15)
where v0 ≈ 6 mm / s and c = 0.1 are empirical parameters which have approximately constant values, and τ fm is the maximum shear stress on the real contact area when v = v0 . The value of τ fm varies with rubber compounds and substrate surface roughness, but it is in the order of few megapascal [14,46] and must be obtained from experiment.
Rubber friction is a result of complex processes occurring at the interface. Grosch [10] attributed the rubber friction on dry surfaces to two competing mechanisms of adhesion and hysteresis loss. The 489
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3. Material and experimental methods 3.1. Viscoelastic modulus The viscoelastic modulus of the filled Styrene Butadiene Rubber (SBR) compound used in the experiments was measured using the Dynamic Mechanical Analysis (DMA) technique. Since the frequency range of the DMA test is typically limited between 0.1 and 100 Hz, the temperature-frequency superposition method was used to obtain the viscoelastic modulus at a broader range of frequencies. The temperature was varied between −25 °C and 80 °C, and the Williams-Landel-Ferry (WLF) shift factor with a reference temperature of 20 °C was used to superimpose the master curve segments. Initially, the measurement was performed at a low strain of 0.5% which is in the linear viscoelastic region. However, the applied strain was increased at lower frequencies (corresponding to higher temperatures) so that the detected force remains higher than the lower limit of the transducer. The glass temperature was found to be −21.7 °C corresponding to the frequency of about 62.5 KHz. When rubber is sliding on a rough substrate surface, the rubber contact area can undergo very large strain, about 100% or even more [47], and the viscoelastic modulus at high strain amplitude must be used in modeling of the contact area and rubber friction. Therefore, strain sweep tests were performed at a constant frequency of 1 Hz and varied temperature from −25 °C to 80 °C. The strain was increased from about 0.095% to the breakpoint of the specimen or maximum force limit of the equipment. In the range of temperatures between 20 °C and 80 °C, the maximum strain could reach up to 96% while at lower temperatures the maximum strain was smaller e.g. about 20%. The same WLF shift factor was used to calculate the master curve for large strain values. The storage modulus and loss modulus of the rubber for low strain and approximated high strain values were shown in Fig. 2. The loss factor and the WLF shift factor are shown in Fig. 3 and Fig. 4, respectively.
Fig. 3. Loss factor of filled SBR compound.
Fig. 4. WLF shift factor of filled SBR compound.
recording the friction and wear measurements, it can be assumed that the substrate surface already went through the initial transition region of the abrasion and reached a steady state condition. The three-dimensional sample profiles of both surfaces are shown in Fig. 5. Before calculating the surface roughness power spectrum from the measured height profiles, it was ensured that the measurement is valid. The profile measurement is considered to be valid only if the drop-out rate for the height signal is less than 10% [48]. After assuring the validity of the measurement, a linear interpolation was used to replace each invalid sample point. Moreover, the offset, slop, and any curvature of the sample surface relative to the flat reference plane was eliminated. The one-dimensional height profiles with height distribution functions of two surfaces are shown in Fig. 6. The Discrete Fourier Transform (DFT) was used to calculate the surface rough power spectrum. The DFT analysis assumes a periodic repetition of the measured signal, which is the height profile in this study, and this can result in a jump between the end and beginning of periodic lengths. This spectral leakage was eliminated using a Split Cosine Bell (SCB) window, which is suitable for short length signals because it retains 80% of the original signal unaltered as it smoothly goes from unity to zeros at two edges of the signal. The SCB is defined as:
3.2. Surface height profile Two roofing asphalt surfaces with different roughness were used to study rubber friction and wear. The first surface, referred to as surface A, consists of larger grains and has similar texture and roughness as a typical asphalt road. The second surface, referred to as surface B, has smaller grains and smoother macrotexture similar to concrete surfaces. The height profiles of the surfaces were measured using an optical profilometer with excellent accuracy and precision with a resolution of sub-micron. The surfaces were sampled from the middle section of the sliding path, and the surface measurements were carried out after the experiments. Since several running-in tests were conducted before
⎧ cos2 ⎪ WSCB (n) =
⎨ ⎪ cos2 ⎩
(
5πn N
−
π 2
)
1
(
5πn N
−
9π 2
)
0≤n<
N 10
N 10
≤n≤
9N 1
9N 10
N 10
(16)
where N is the number of sample points. The height profile was sampled over a square area with dimensions of L × L by measuring equally spaced points with a constant distance L of N along perpendicular directions of x and y. The height values are
Fig. 2. Viscoelastic modulus of filled SBR compound for low strain and high strain. 490
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Fig. 6. One dimensional height profile and height distribution function of the surfaces after offset and slope suppression.
Fig. 5. A section of three-dimensional surface profiles. L
L
denoted by h (x, y) where = N n x , y = N n y , and both n x and n y vary from 0 to N. Consequently, the Fourier Transform of height profile was calculated using the following equation:
h (→ q)=
L2 (2π )2N 2
N
N
∑ ∑ ny = 0 nx = 0
2π L L WSCB (n x , n y ) h ⎛ n x , n y ⎞ e−i N (mx nx + my ny) N ⎠ ⎝N
(17)
→ where q = (qx , qy ) =
(
)
2π 2π m x , L m y is the discretized wave vector and L N+1 from 0 to N or 2 depending on which one is an 2
both m x and m y vary integer value. After calculating equation (18) using the Fast Fourier Transform (FFT) algorithm, the surface roughness power spectrum was calculated using the following equation [43]:
C (q) =
(2π )2 2 hA ( → q) L2
(18)
The average surface roughness power spectra of several samples for both surfaces are shown in Fig. 7. The power spectra of both surfaces can be approximately modeled using equation (4) between the short cutoff wavenumber q0 and the large cutoff wavenumber q1. The slopes of the log-log plot of the power spectra were measured to calculate the Hurst exponent using the following equation:
Slope H = −⎛ + 1⎞ ⎠ ⎝ 2
Fig. 7. Surface roughness power spectra of two roofing asphalt surfaces.
(19) 491
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Table 1 Surface roughness parameters. H
h 0 (μm )
q0 (m−1)
q1 (m−1)
Surface A
0.84
204.8
2000
106
Surface B
0.93
139.7
3000
106
The surface parameters of both surfaces are presented in Table 1. 3.3. Friction and wear test procedure
Fig. 9. Measured data points for friction coefficient at velocity 0.5 m/s over a sliding distance of 3.4 m on surface A.
A linear sliding friction and wear test set-up developed at Center for Tire Research (CenTiRe) was used in the experiments. In this test-setup, a cubic rubber specimen with a nominal contact area of 25.4 mm by 25.4 mm was dragged on each substrate surface using a six-wheel robot for a maximum distance of 3.5 m. The sliding velocity was accurately measured by encoders attached to the wheels, and it was controlled using a real-time control algorithm. The friction force was measured using a load cell, and a constant normal load was applied using dead weights on the rubber block. The nominal contact pressure remained 81 KPa in each experiment. All the tests were conducted at room temperature 23 ± 3°C on dry surfaces. The substrate surfaces were also cleaned using a brush to reduce the contaminations as much as possible. On each surface, the friction and wear rate were measured for four different sliding velocities. A new sample was used for each velocity, and before recording the data, the sharp edges of the rubber contact surface was abraded in several running-in tests by sliding the rubber block on the same substrate surface. After reaching a steady state condition, friction and mas loss were recorded. Then, the experiment for each velocity was repeated between 10 and 15 times. The average sliding friction coefficient was calculated from data in the steady state region, after passing the initial transition region between the static and the kinematic friction. The mass of the specimen was measured using a weighing scale with an accuracy of 1 mg after sliding over a sufficiently large distance, which is typically about 5 m.
surfaces. The theoretical results indicated that the real contact area between rubber block and both surfaces is about 1% of the nominal contact area. The contact area predicted by the modified version of Persson theory is slightly larger than the value that the original theory predicts since the modified model approximately corrects for the displacement assumption of full contact by considering displacement for partial contact. As it is expected from roughness parameters of both surfaces, the real contact area on surface A is smaller than on surface B due to its larger macroasperities and roughness indicating by higher RMS and smaller Hurst exponent values. The theoretical real contact area also decreases with the increase of sliding velocity, as the rubber stiffness increases with the increase of the frequency of loading exerted by the substrate asperities. 4.2. Experimental and theoretical rubber friction Fig. 9 shows the recorded signals of the friction coefficient measured using the load cell during one sliding test period. The average friction coefficient for each test was calculated over the steady state region after the initial peak due to static friction and inertia. The average value is shown by the dashed line. The average friction coefficient measured in each sliding test for surface A and surface B is shown as a green dot in Fig. 10. The average friction coefficients for each velocity for both surfaces are shown as red pentagon stars. The theoretical model for adhesive friction coefficient was calculated using the semi-empirical model presented in equation (15) and shown as a dot-dashed line with a peak value at a very low sliding velocity. This adhesive component of friction theoretically decreases with the increase of velocity until it vanishes at very high velocity. When the sliding velocity is very low, the rubber molecules at the interface have sufficient time to adjust themselves to the substrate surface and form adhesive bonds through van der Waals interaction with molecules of the substrate surface. As the sliding velocity increases, few molecules can form adhesive bonds and the strength of adhesion between two surfaces decreases. It is found that the maximum shear stress of τf m = 4.8 MPa and τf m = 3.2 MPa match the peaks in experimental results for surface A and surface B, respectively. These values of maximum shear stress are smaller than the ones found in other studies [14,46] because the modification made to the Persson contact theory predicts a larger real contact area compared to the original theory used in those studies. Assuming a constant maximum shear force, when the contribution of real contact area increases, the value of maximum shear stress decreases. In the range of sliding velocities used in the experiment, the dominant mechanism of friction is hysteresis friction which was calculated using equation (14). The superposition of adhesive and hysteresis friction results in the total theoretical friction coefficient which is shown by a solid blue line for each surface in Fig. 10. The theoretical model could successfully predict the average friction coefficient on surface A over the entire range of velocities used in the experiment. On the other hand, the theoretical model could not predict the rapid increase of friction coefficient at high sliding velocities on
4. Results and discussion 4.1. Theoretical contact area The ratio of apparent contact area to the nominal contact area for different length scales was calculated using the modified version of Persson contact theory for both surfaces. The comparison between the numerical results for the minimum and maximum velocities used in the experiment is shown in Fig. 8. The magnification here is defined as the ratio of wavenumber to the minimum cutoff wavenumber of two
Fig. 8. The logarithm of the ratio of apparent contact area to the nominal contact area as a function of magnification for two different asphalt surfaces and velocities. 492
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Fig. 12. Measured mass of rubber blocks vs sliding distance for different velocities. Fig. 10. Experimental and theoretical friction coefficient vs sliding velocity.
4.3. Rubber wear rate The measured weights vs sliding distance for steady-state wear condition on both surfaces are shown in Fig. 12. The average wear rate for each sliding velocity was calculated from the slope of the corresponding regression line. At the sliding velocity of 0.5 m/s on surface B, the rubber mass was measured after removing the decomposed rubber attached to the side of the specimen (as shown in Fig. 11) in order to keep the geometry of the contact surface consistent during the experiment. Therefore, the measured mass loss is significantly larger compared with the results of other velocities. However, before removing the degraded piece of rubber manually, the weight loss of the rubber block was not measurable using a scale with a resolution of 1 mg. Therefore, the real wear rate for this velocity is expected to be very small until the accumulated tribo-modified rubber is ruptured by a sharp asperity, and results in a sudden large mass loss. The abrasion pattern was developed on the rubber surface, as it was sliding on surface A, and the pattern was detected for all the sliding velocities used in the experiment. The abrasion pattern is referred to parallel ridges that develop perpendicular to the sliding direction which have saw-tooth shapes with tips pointing to the rubber sliding direction. The abrasion pattern was initially discovered by Shallamach [49,50] on the rubber surface abraded by various rough surfaces such as different types of concrete roads and sandpapers. On the other hand, the abrasion pattern was detectable on the rubber specimens sliding on surface B only at low velocities, and it disappeared as sliding velocity increased. At velocity 0.5 m/s, the abrasion pattern could not be detected as shown in Fig. 11 because the tribo-modified layer on the rubber surface acts as a protective film that prevents material loss due to abrasive wear and reduces the total wear rate. This type of material degradation has been referred to as smearing or oily abrasion in the literature [51,52], and is the product of thermochemical process on the contact area due to
Fig. 11. Rubber surface after running on smooth roofing asphalt at v = 0.5 m/s.
surface B. On the contrary, the theory of friction that considers the role of flash temperature [5] predicts a decrease of friction coefficient with the increase of velocity as a result of the elastic softening of the rubber due to high flash temperature. However, it was found that elastic softening is not the only process occurring on the rubber surface at high temperature. Inspecting the rubber surface revealed that the rapid increase of friction coefficient at high velocities is the result of the formation of a thin sticky layer on the rubber surface due to thermochemical degradation. This degraded layer has inferior mechanical properties and it is softer than the bulk material [34]. As the degraded layer forms on the rubber surface, the deformation of rubber at the interface increases resulting in the increase of the real contact area and the adhesion between two surfaces. The material characterization of the thermos-modified layer under different tribological conditions will be carried out in the future study. Fig. 11 shows the viscous liquid-like layer, referred to as the tribo-modified layer, which had been accumulated at the side of the contact area while it is still bonded to the rubber block.
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surfaces [9,21,53,54]. On the other hand, the wear rate vs friction coefficient on surface B does not follow the same trend. In this case, most of the energy dissipated due to friction results in chemical degradation and the formation of the tribo-modified layer rather than surface crack propagation and wear particle detachment. This can result in an inverse relation between mass loss and friction coefficient, which is desired for many rubber-based products such as tires. On the contrary, Mokhtari and Schipper [34] found that the formation of tribomodified layer reduces the friction coefficient under a different experimental condition. They studied the friction of a rubber sample using a ball-on-disk setup and found that the formation of the tribo-modified layer decreases the friction coefficient between the SBR disk and the granite ball by altering the shear stress. In their case, the modified layer might have acted as a lubricant to decrease the friction between the rubber and granite surface. It can be concluded that based on the chemical structure of the tribo-modified layer and contact condition, the smearing of rubber might have different effects on the friction coefficient. Therefore, further investigations on the formation of the tribo-modified layer and its effect on the friction coefficient under different conditions are required.
Fig. 13. Wear rate vs sliding velocity – data points in dashed ellipse were obtained after detachment of the modified accumulated layer artificially.
frictional heating on the rubber surface. Since surface B is smoother than surface A, the macroscale contact regions tend to be more clustered and closer to each other. Therefore, the overlap of temperature field around the hot contact regions results in higher temperature rise on the contact area leading to a thermally activated chemical reaction of the rubber molecules with oxygen (oxidation), and chemical decomposition of the surface layer of the rubber sample. As the flash temperature increases, the formation rate of the tribo-modified layer also increases and becomes greater than the rate of its removal by abrasion. The effect of thermochemical degradation is significant and visibly detectable at a sliding velocity of 0.5 m/s. The effect of the tribomodified layer, possibly at a smaller length scale, on friction coefficient can be also found when sliding velocity is 0.4 m/s as shown in Fig. 10. Wear rate in terms of mass loss per unit sliding distance at different sliding velocity is shown in Fig. 13 for both surface A and B. The data separated by a dashed ellipse in the plot for surface B corresponds to the condition where the accumulated tribo-modified layer was removed by hand before mass measurement. On surface A, the wear rate increases with the increase of sliding velocity, while on surface B the wear rate decreases with the increase of sliding velocity until the accumulation of degraded layer is so significant that could be removed as a big wear particle. The scattered measurement of the wear rate at velocity 0.5 m/s is due to artificial detachment of tribo-modified piece of rubber from the side of the contact area. As previously mentioned, if the tribo-modified chunk of rubber was not removed during the mass measurement, the wear rate in terms of mass loss would be so small that could not be measured precisely. On the other hand, after several tests, a large amount of tribomodified rubber would be finally detached from the rubber surface by the asperities and results in a large mass loss. The relation between wear rate and friction coefficient on each substrate surface is also demonstrated in Fig. 14. On surface A, a power law equation, compared to a linear equation, provides slightly better representation for the relation between wear rate and friction coefficient of rubber samples. A similar relation was also observed and reported by other researches on different abrasive
5. Conclusions Friction and wear of a SBR compound filled with 60 phr silica and 20 phr carbon black on two different types of roofing asphalts, referred to as surface A and B, were studied. Surface A has a texture and roughness parameters similar to real asphalt roads, while surface B has a smoother surface similar to concrete pavements with finer grain size. The profiles of both surfaces were measured using an optical profilometer with sub-micron resolution, and the surface profiles were used to calculate the surface roughness power spectra. The master curve of the large-strain viscoelastic modulus of the rubber was measured using DMA tests and strain sweep data. The data of surface roughness power spectra and viscoelastic modulus were used to model the real contact area of rubber sample on both surfaces using an improved version of Persson's contact theory. The friction coefficient as a function of sliding velocity was also calculated using an improved and extended version of Persson's rubber friction theory. The results of the theoretical model for surface A were in good agreement with the experimental results. However, the theoretical results for surface B underestimated the friction coefficient at high velocities. Inspection the rubber surface after sliding with velocity 0.5 m/s on surface B, it was found that the top layer on the rubber surface was significantly altered due to thermochemical degradation as a result of high flash temperature at the contact interface. Since the tribo-modified layer is sticky and softer than the bulk material, it affects the dominant mechanism of friction and wear by increasing the real contact area in addition to preventing the rubber surface from surface crack propagation and pattern abrasion. It was found that when the rubber wear mechanism is controlled by mechanical abrasion, in the absence of significant tribo-modified layer, there is a power law relation between wear rate, measured as mass loss per sliding distance, and friction coefficient. On the other hand, when the thermochemical degradation and smearing abrasion occur on the rubber surface, the wear rate in terms of mass loss does not necessarily increase with the friction unless the accumulation of degraded rubber detaches from the surface by a sudden rupture, causing a significant material loss. Therefore, when the tribo-modified layer forms on the rubber surface, the mass loss does not sufficiently represent the wear rate of the rubber sample, and change in chemical composition and molecular weight of the rubber material need to be considered in the evaluation of wear rate. In the future study, the material characterization will be conducted for rubber samples to elucidate the mechanism of thermochemical abrasion and its effect on the friction mechanism.
Fig. 14. Wear rate vs friction coefficient. 494
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Acknowledgments
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