Accepted Manuscript
Friction between single aramid fibres under pre-tension load
Nurhidayah Ismail, Matthijn B. de Rooij, Erik G. de Vries, Nurul Hilwa Mohd Zini, Dik
J. Schipper
PII:
S0301-679X(19)30207-5
DOI:
https://doi.org/10.1016/j.triboint.2019.04.013
Reference:
JTRI 5729
To appear in:
Tribology International
Received Date: 23 November 2018
Revised Date:
26 March 2019
Accepted Date: 4 April 2019
Please cite this article as: Ismail N, de Rooij MB, de Vries EG, Hilwa Mohd Zini N, Schipper DJ,
Friction between single aramid fibres under pre-tension load, Tribology International (2019), doi: https://
doi.org/10.1016/j.triboint.2019.04.013.
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1
Friction between single aramid fibres under pre-tension load
Nurhidayah ISMAIL
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, Matthijn B. de ROOIJ , Erik G. de VRIES , Nurul Hilwa MOHD ZINI
J. SCHIPPER
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1,2,3
,and Dik
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Laboratory for Surface Technology and Tribology, Department Mechanics of Solids, Surfaces and
Systems (MS3), Faculty of Engineering Technology, University of Twente, Drienerlolaan 5, 7522 NB,
Enschede, The Netherlands.
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8
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1,2,3*
Fakulti Kejuruteraan Mekanikal, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian
Tunggal, Melaka, Malaysia.
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Centre for Advanced Research on Energy, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100
Durian Tunggal, Melaka, Malaysia.
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Abstract
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Understanding the friction mechanism at microscale of fibrous material is important as it
16
is one of the key roles in governing the behaviour of fibre assemblies at meso and
17
macroscale. However, mechanical stress such as tension may also influence the
18
frictional behaviour. In this study the frictional behaviour between fibres under pre-
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tension is explored. A new experimental setup was successfully developed to measure
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the friction force between two single aramid fibres at perpendicular contact. Although
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pre-tension influences the bending stiffness of the fibre, the results show that the effect
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of pre-tension on the contact length is relatively small. The elastic deformation of the
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contact dominates over the ‘wrapping effect’, generating the contact area over which the
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interfacial shear takes place.
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1
Introduction
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Aramid fibres are often found in high-performance applications such as in some
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composites, ballistics, aerospace, protective clothing, ropes and cables applications.
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This is due to its combination of high strength and high stiffness properties as well as
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the high strength-to-weight ratio, about five times higher than steel. Unfortunately, the
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fibre may expose to a series of mechanical stresses for instance friction during
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processing or handling stages, which lead to its structural deformation and deteriorate
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the physical and mechanical performance of a final product.
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In general, the fibre is produced in the form of individual continuous filaments which are
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bundled together forming the tows. These yarns are then interlaced to form a woven
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fabric. The processes show that the individual continuous filaments, are basically the
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contacting and interacting bodies and subjected to frictional effects. Therefore, a
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thorough understanding of the frictional behaviour between fibres at filament level is
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necessary, especially for the complex structures like woven fabrics.
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It is important to note that, the friction plays a dual role. An excessive frictional force,
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either fibre against fibre or fibre against tool, can deteriorate the physical characteristics
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of the fibre itself, e.g., defibrillation that lead to fibre breakage. This breakage is crucial
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as it influences the strength properties of the fibre yarns and fabric [1-3]. On the
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contrary, for the spun yarn, a higher inter-fibre friction will increase the yarn strength,
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but if the tension exceeds the friction level, a high possibility of rupturing and slipping of
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fibres exists. For example, in some dynamically loaded applications such as in mooring
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lines, the friction between fibres may cause a premature failure of the fibre ropes and
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hence influence the mechanical properties and the ropes lifespan [4,5]. Vertical tension
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because of the rope weight as well as a dynamic response which is excited by
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longitudinal oscillation due to wave motion will generate the internal friction in fibres
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ropes. Thus, understanding the friction and tension between fibres at microscale level is
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needed as it has a great influence on the structural and properties of a final product
53
such as a rope and a woven fabric.
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Many researchers have developed various methods to study the friction between fibres
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and have been reviewed by several authors [6,7]. One of the fundamental methods is to
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measure friction based on the principle of rubbing fibre against another fibre in linear
57
motion [8-12]. This method is commonly used for concentrated point, line and disperse
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contacts between fibres, yarns (tows) and fabrics. For example, this method has been
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adapted in measuring the friction force between single fibres of different materials such
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as carbon [13], polyamide [14], polyester [14] and polyethylene [15], and tow against
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tow or metal contact [16,17]. Meanwhile, Gralen, Olofsson and Lindberg [18-20] have
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used a twist method to study the frictional behaviour in textile materials. In their
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experiments, two fibres were twisted together by a certain number of turns, and the
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friction force would be only measured during slippage. If measuring at high velocities or
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when a lubricant is present at the fibre interface, a capstan method is the most common
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way to measure friction between fibres. In this method, a fibre is wrapped over a
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cylindrical body and the frictional force that is developed is calculated based on a
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normal force generated by the tension exerted at both fibres end. Roselman and Tabor
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[21] have used this method to study friction behaviour at microscale level, while
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Cornelissen et al. [22] and Chakladar et al. [23] used this method to study at mesoscale
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level. Other factors that affecting the friction such as surface roughness [22], tow angle
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and tow size [23] have been also investigated through this method.
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There are many papers on the friction between fibres, however, to the best of the
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author’s knowledge, the effect of pre-tension loads on the frictional behaviour at
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microscale has not yet been discussed in detail even though it is a relevant issue in
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many applications. For example, in a continuous composite manufacturing process, low
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and high pre-tension during winding may result in poor mechanical properties and
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catastrophic failure, respectively. Therefore, this study aims at investigating the frictional
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behaviour between single fibres in contact with the influence of pre-tension. The ‘fibre-
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on-fibre’ term that will be used hereafter is representing the interactions between two
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single fibres. A new experimental setup has been developed to measure the dynamic
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friction of two single fibres sliding onto each other at 90° (perpendicular) contact under
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the influence of pre-tension and other parameter conditions such as normal load and
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elastic modulus.
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2
Material and Method
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2.1
Materials used
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Two types of aramid fibres used in this study was provided by Teijin Aramid B.V. The
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properties of the fibres are listed in Table 1. In this study, a low Young’s modulus fibre
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type and a high Young’s modulus fibre type are called as LM and HM, respectively.
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Initially, the fibres were in the form of tow bundle (see Figure 1(a)), with each tow
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consists of thousand single filaments. Then, the fibres were manually separated into a
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single filament with its Scanning Electron Microscope (SEM) image is shown in Figure
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1(b).
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2.2
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The surface texture of the Twaron aramid fibres was examined using atomic force
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microscopy (AFM). The FlexAFM from Nanosurf was used to observe the surface
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topography and measure the roughness of the fibre surface. The ACTA cantilever form
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AppNano was used with a stiffness in the range of 13-77 N/m. The scanning area was
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set at a size of 3 µm x 3 µm.
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Surface characterization
2.3
Experimental setup
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An experimental setup has been developed to measure friction between two single
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fibres crossing each other at angle of 90°. Figure 2 shows the schematic description of
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the experimental setup. The setup consists of fibre holder (one to hold top fibre and
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the other one is to hold bottom fibre), an XY linear stage and a set of two capacitive
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sensors mounted and a force measuring mechanism (FMM). The resolution of the
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capacitive sensor is 1 nm with a measuring range up to 50 µm. Using this setup the
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forces (normal and friction) are calculated based on the spring stiffness concept, in
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which the deflection of the FMM is measured in x and z direction. A detailed explanation
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of the FMM can be found in Yaqoob [24]. With this load controlled setup, the maximum
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normal load can be applied is 100 mN with an accuracy of 8 µN.
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In this study, the tension of the fibre during gluing is only controlled at the bottom fibre,
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while for the top fibre a minimal pre-tension is applied just to prevent the fibre from
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slacking.. A low viscosity glue type, Loctite 401 was used for gluing the fibre at fibre
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holders. For bottom fibre, the first end of the fibre is initially glued to a holder, then the
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other end is connected to a cable lug. The function of the cable lug is to clamp the end
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of the fibre into a loop shape so that the dead weight can be hooked to it to induce the
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pre-tension to the fibre. Once the dead weight is loaded to the fibre , the other end is
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then glued. The dead weight is removed after the glue at both ends is cured.
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To conduct the friction measurement, both fibres need to be brought into an initial
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contact. The top fibre is moved downwards approaching the bottom fibre at two different
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speeds; v = 0.01 mm s-1 to find the contact and v = 0.001 mm s-1 to find a few microns
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before the contact. During this procedure, no initial load is applied (Figure 3(a)).
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Therefore, the normal and friction forces are assumed zero just before contact is made.
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As there is no deformation in the FMM system before contact, the measured normal
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load is close to represent the true value. Once the final normal load is applied to the
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contact, the fibres start to bend as shown in Figure 3(b). The friction force measurement
127
is taken as the bottom fibre is sliding against the top fibre in x direction with the help of
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the stage. Multi-pass friction loops are executed to determine the repeatability and
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running-in effects. Table 2 shows the parameters that are used for the friction force
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measurements. The measurements are repeated five times for data producibility and
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repeatability.
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Results and discussion
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3.1
Surface roughness
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AFM measurements were performed to obtain the roughness of the fibre surface in
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three-dimensional (3D) analysis. The Sq parameter, represents the root mean square of
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the roughness within the measured area and is calculated using the following formula
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[25]:
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=
1
( , )
(1)
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where
is the roughness measured area and
is the height surface profile. To observe
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the effect of the pre-tension on the fibre surface, a roughness measurement is
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performed before and after applying the pre-tension load on the fibre. The fibre sample
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that has been confronted with pre-tension is prepared separately from the sample for
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friction tests. The pre-tension fibre sample has the same length as for the friction test
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sample, which is cut, stretched with load for about 2 hours. Then, the load is released
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from the fibre and a roughness measurement is carried out using the AFM. Here, it is
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assumed that at a very small length, the pre-tension load would play a role on the
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roughness surface. Then, the fibre is placed vertically parallel to the AFM tip (see Figure
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4). The fibre is scanned along the x direction within the scan size are of 3 µm x 3 µm
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with a resolution of 512 x 512 points and thus the influence of fibre orientation on the
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roughness measurement is therefore eliminated.
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Figure 5 shows the AFM images of HM fibre type before and after applying pre-tension
154
loads. The lines and treated particles on the surface prove that at microscale level, the
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fibre surface is quite rough with Sq ≈ 15.1 nm as in Fig. 5(a). With 50 mN of pre-tension
156
load, the surface roughness is found to be reduced to Sq ≈ 11.3 nm, the AFM image is
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shown in Figure 5(b). By increasing the pre-tension load to 100 mN, the fibre surface
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changes to be even smoother, as shown in Figure 5(c) with Sq ≈ 5.6 nm. Note that the
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Sq value decreases asymptotic when the pre-tension load is more than 50% of the fibre
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breaking strength. For each pre-tension load, the roughness measurements are
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performed at three different locations. Figure 6 shows the overall results of the Sq value
162
of the fibre surface measured at different pre-tension loads. The result shows that the
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Sq values reduced as the pre-tension increases. Note that, in one single fibre consists
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hundreds of fibrils. With pre-tension this fibril elongates and hence reduce the contour
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peaks.
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3.2
Friction measurements
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Figure 7 shows the friction force measurement signal, which measured on the HM fibre
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type under 10 mN normal load and a pre-tension load of 50 mN. The fibre is set to slide
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with a stroke of 100 µm both in forward and backward direction to complete one friction
171
cycle. At the first 10 µm of sliding distance, the friction force signal shows a transient
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response when the normal load is applied to the contacting fibres. This is due to the
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lateral stiffness of the friction force mechanism (FFM) and the deformation of the
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contact. After reaching the desired normal load, the fibre starts sliding and the friction
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signal becomes stable. The pattern of the friction curve during forward and backward
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direction is similar, showing that a same value of the force is measured in both
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directions. Also, it is observed that the friction force values for the first cycle is slightly
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different from the other four cycles. This may be explained by the presence of the
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impurities on the fibre surface and these impurities are removed as the fibre slides. To
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complete one friction experiment, the friction cycle is repeated five times. The same
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trends can be observed in all friction tests. The friction force is calculated based on the
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average value of the friction force of five cycles both during forward and backward
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sliding. It is also can be seen from Figure 7, that the variation between each cycle is
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very small showing a good reproducibility, with a standard deviation, SD ≤ 0.1 mN.
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3.2.1 Geometrical analysis on the contact length due to pre-tension and the effect on
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friction
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The contact length between the fibres is totally governed by the fibre deflection. The
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theory of taut wire [26] was used to have a clear view on the relationship between
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deflection,
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and pre-tension load, T. The taut wire equation is given by:
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193
.
+
−
4
=0
(2)
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where
is the fibre deflection (m), L is the fibre length (m), A is the fibre cross-sectional
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area (m2), E is the Young’s modulus (Pa), T is the pre-tension load (N) and N is the
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normal load (N). There are two assumptions that were made in the analysis; (a) the
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contact length could be influenced by the deflection of the fibre and (b) the contact
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geometry is triangular as shown in Figure 8. This latter assumption is due to the very
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small contact length as compared to the fibre diameter. Also, note that a higher pre-
200
tension will result in a lower deflection, which reduces the contact length. By using the
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taut wire equation (Eq. 2), the length of the contact could be determined by solving the
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equations in the half-plane axis that represents the fibres in the system (see Figure 8).
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Due to the normal load, both fibres that are in contact start to deform at certain
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deflection . Thus, the behaviour of the bottom fibre can be mathematically expressed
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as;
=
−
(3)
and the circumference of the top fibre that touch the bottom fibre is represented by;
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( −
!)
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+( −
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!)
="
!
!
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where m is the line gradient,
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of the top fibre and R is the fibre radius. By solving both equations (3) and (4), the half-
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plane axis of the crossing point in coordinates x and z between two fibres can be
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determined. If it is assumed that the contact geometry is triangular and the negative
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sign represent the direction of the fibre deflection moving downward (see Figure 8), the
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is the centre coordinates
D
load can be calculated as;
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+(
&
− )
(5)
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and
wrapping length #$ between two fibres in contact at a certain pre-tension and normal
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is the fibre deflection,
(4)
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From the calculation using the geometrical analysis above, the results of HM and LM
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fibre deflection (of the bottom fibre) under the influence of pre-tension and normal loads
220
are plotted in Figure 9 (a) and (b) respectively. The calculation (theoretical model) are
221
validated by comparing the results with the experiment data. The results of HM and LM
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fibres show a similar trend where the deflection of the fibre decreases with the pre-
223
tension load. However, it is must be noted that the experimental values represent the
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total deflection of both top and bottom fibre, meanwhile the theoretical value only
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represent the deflection of the bottom fibre. Therefore, the deflection of the top fibre is
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the difference between the experimental and theoretical values. Interestingly, the
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difference between the experimental and theoretical values are found to be in the same
228
range at least for the high normal loads at N = 5 mN and 10 mN, regardless of the fibre
229
types. This result shows that the pre-tension of the top fibre is constant. From equation
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(2), we know that if the pre-tension is constant, the only factor that contribute to the
231
deflection is the fibre length. Moreover, as the top fibre length is only 2 mm, so it is
232
considered as stiff, which resulting in lower values of deflection than for the bottom fibre.
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Figure 10 shows the experimental results of the friction force as a function of the pre-
234
tension load for both the LM and HM fibre type. It can be observed that there is a
235
gradual decrease in friction as the pre-tension load is increased, regardless of the
236
normal load. A high pre-tension load could reduce the conformability and intimacy of the
237
contact, which results in the decrease of the contact size and the friction force.
238
Assuming the contact behaviour between fibres follows the Hertzian theory [27], the
239
radius of the elastic contact deformation is compared with the calculated contact length
240
(taut wire model). The contact radius between fibre-fibre at perpendicular contact is
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calculated using the equation as follows:
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#' =
*
3 "∗
4 ∗
(6)
where N is the normal load, R* is the effective radius and E* is the contact modulus.
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The contact modulus is calculated from the elastic modulus of the fibre,
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Poisson ratios ,+ and , [27];
1
∗
=
1 − ,+
+
+
+
and
1−,
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and the effective radius is calculated from the radius of the fibre, R1 and R2 [27];
and
(7)
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"∗ =
"+ "
"+ + "
(8)
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From calculations, at 1 mN, 5 mN and 10 mN normal loads, the contact radius is about
252
1.3 µm, 2.3 µm and 2.9 µm, respectively. Obviously, this contact radius is larger than
253
the contact length that is due to the ‘wrapping effect’ between fibres which are found
254
only 0.1 µm, 0.5 µm, 0.8 µm, respectively. Thus, in this case, the elastic deformation in
255
fibre-fibre contact is found more significant over the ‘wrapping effect’ in influencing the
256
contact area and friction force (see Figure 11). However, the role of pre-tension cannot
257
be neglected as our result (see Figure 6) shows that the Sq values could be reduced by
258
increasing the pre-tension load. This shown that although the influences of pre-tension
259
on the fibre ‘wrapping effect’ is small, it does play a small role in changing the physical
260
surface of the fibres and indirectly influences the size of the elastic deformation of the
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contact area.
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3.2.2 Effect of elastic modulus on friction
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Figure 12 shows the friction force of the low and high modulus fibre with similar sizing
265
under 50 mN pre-tension at varying normal load. The friction force of low modulus (LM)
266
fibre type is found to be slightly higher than the high modulus (HM) fibre type under
267
similar conditions. The fibre with low elastic modulus has a low bending stiffness and
268
therefore during loading, the LM fibre have a higher deflection and generate a larger
269
contact length between the fibres that increase the friction force as shown in Figure 12
270
(a). With respect to the elastic modulus values, one would expect that the friction force
271
of LM fibre will be two times higher than the HM fibre. However, according to Gupta, the
272
resistance to bending is determined by [7]:
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"-./.0#12- 03 4-1 /15 = 6
1 ;
:
4789 <
(9)
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where ; is the shape factor, E is the modulus, d is linear density, < is the density
and 89 is a constant which depend on the units in which ,
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and < are expressed. So,
although the elastic modulus of the LM fibre is half of the HM fibre, the size of the fibre
278
in terms of linear density also need to be considered in influencing the contact intimacy
279
and friction between fibres. Due to this effect the friction forces are found to differ by
280
34%.
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3.2.3 Effect of normal load on friction
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In order to study the effect of normal load on friction, the friction forces are also
285
measured for the HM fibre with varying normal load in the range of 1 to 10 mN at
286
various pre-tension loads. The same normal load range has been used by Tourlonias et
287
al. [13] in tests with single carbon fibres. The friction force as a function of normal load
288
is shown in Figure 13. In the range of normal load tested, the friction force is found to be
289
proportional with the normal load. These results are in agreement with [13], as the
290
friction force is found to approximately follow the Coulomb’s law.
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The frictional behaviour between two single aramid fibres in contact under the influence
294
of pre-tension loads have been successfully studied. An experimental setup was
295
developed to measure the friction force of single fibres sliding perpendicular against
296
each other in linear reciprocating motion. The friction measurements data of the single
297
aramid fibres obtained show a good reproducibility. Also, the friction force obtained
298
using this experimental setup and the contact length model are in agreement. As a high
299
pre-tension load is induced to the fibre, the friction force decreases as a result of high
300
resistance to bending of the fibre and as a consequence a reducing contact length
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between the fibres. However, this contact length is found to be very small compared to
302
the contact radius of the elastic deformation of the fibre-fibre contact. It can be
303
concluded that the elastic deformation in contact dominates the contact area and friction
304
force significantly. On average, for normal loads ranging from 1 to 10 mN, the friction
306
force increased ~ 34% as the elastic modulus of the fibre increased.Also,the friction
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force increases linear with the normal load.
Knowing that at tow and fabric level the contact configuration is in complex
308
arrangement, therefore understanding the friction mechanism at the microscale level
309
enables the engineers to predict the friction and contact model of the fibre assemblies at
310
meso (tow level) and macroscale (fabric level).
311
Acknowledgement
312
The authors would like to thank Universiti Teknikal Malaysia Melaka and Ministry of
313
Education Malaysia for providing financial support of the first author and Teijin Aramid
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B.V, The Netherlands for supplying the material.
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Table 1 Manufacturer data of the material properties of the aramid fibres used in the friction
experiments.
HM
Elongation at break [%]
4.4
2.9
Linear density [dtex]
1.2
1.6
Young’s modulus [GPa]
60
115
Tensile stress [GPa]
3.2
Breaking strength [N]
0.26
Fibre diameter [µm]
10.8
alkyl-phosphate salt
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Finishing material
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LM
3.5
0.4
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Description [unit]
11.9
alkyl-phosphate salt
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Table 2 Parameters for friction measurements.
symbol
value
units
Normal load
N
1- 10
mN
Pre-tension load
T
50 - 200
mN
Sliding speed
v
0.002
mm/s
Crossing angle
θ
90
degree
Sliding distance
d
100
Fibre length
Top fibre: 2
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µm
mm
Bottom fibre: 6
mm
5
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Number of friction cycles
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Description
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Figure 1 Aramid fibres (a) Scanning electron microscope (SEM) images of the fibre tow bundle , (b)
close-up image of the fibre surface.
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(a)
(c)
Figure 2 (a) Schematic description of friction experiment between fibres, (b) Schematic of the fibreon-fibre contact, and (c) Experimental setup.
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Figure 3 (a) Finding initial contact between the fibres, and (b) Fibres under loading.
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Figure 4 Illustration of the roughness measurement using AFM.
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Figure 5 AFM images of HM fibre type (a) without pre-tension, (b) 50 mN pre-tension load, (c) 100
mN pre-tension load, and (d) 200 mN pre-tension load.
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2
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After applying pretension (T= 50 mN)
After applying pretension (T= 100mN)
After applying pretension (T= 200 mN)
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Before applying pretension
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Figure 6 The effect of pre-tension on the Sq value of the fibre surface, scan area
3 µm x 3 µm.
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Sq [nm]
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Figure 7 Typical friction force measured, N = 10 mN and T = 50 mN.
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Figure 8 Fibre deflection due to the presence of pre-tension and normal load.
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(a)
300
Experiment, N = 1 mN
Experiment, N = 5 mN
Experiment, N = 10 mN
Model, N = 1 mN
Model , N = 5 mN
Model , N = 10 mN
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0
50
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deflection, δ (µm)
250
150
200
250
pre-tension load, T (mN)
(b)
300
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deflection, δ (µm)
250
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Experiment, N = 1 mN
Experiment, N = 5 mN
Experiment, N = 10 mN
Model, N = 1 mN
Model , N = 5 mN
Model , N = 10 mN
0
50
100
150
200
250
pre-tension load, T (mN)
Figure 9 Comparison of the theoretical and experimental results on fibre deflection: (a) HM fibre,
and (b) LM fibre.
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(a)
3.00
N = 5 mN
2.50
N = 10 mN
2.00
1.50
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Friction force, F [mN]
N= 1 mN
1.00
0.50
0
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50
100
150
200
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Pre-tension load, T [mN]
(b)
2.50
N = 5 mN
N = 10 mN
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N= 1 mN
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Friction force, F [mN]
3.00
1.00
0.00
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200
250
Pre-tension load, T [mN]
Figure 10 Friction force as a function of pre-tension load: (a) LM fibre type, and (b) HM fibre type.
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Figure 11 Illustration of the contact length due to ‘wrapping effect’ and elastic deformation in fibrefibre contacts.
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LM fibre type with E = 60 GPa
2.00
HM fibre type with E = 115 GPa
1.50
1.00
0.50
0.00
N= 5 mN
(b)
[um]
1.20
LM fibre type with E = 60 GPa
1.00
HM fibre type with E = 115 GPa
0.80
0.60
0.40
0.20
0.00
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N= 10 mN
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Friction force, F [mN]
(a)
2.50
N= 5 mN
N= 10 mN
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Figure 12 The effect of elastic modulus on (a) Friction force, and (b) Contact length two different
fibre types under 50 mN pre-tension load.
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
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Pre-tension load, T= 50 mN
Pre-tension load, T= 80 mN
Pre-tension load, T= 100 mN
Pre-tension load, T= 200 mN
5
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7
8
9
10
Normal load, N [mN]
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Figure 13 Friction force as a function of normal load for the HM fibre type.
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Friction force, F [mN]
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Highlights:
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The frictional behaviour between two single aramid fibres in contact under the
influence of pre-tension loads.
A newly developed experimental setup to measure friction force in contact at
microscale level.
The effect of pre-tension load on the fibre bending stiffness, contact intimacy and
friction force.
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