Author's Accepted Manuscript

Indentation of hairy surfaces: role of frictionand entanglement

Brigitte Camillieri, Marie-Ange Bueno

PII: S0301-679X(14)00411-3DOI: http://dx.doi.org/10.1016/j.triboint.2014.11.009Reference: JTRI3484

To appear in: Tribology International

Received date: 25 August 2014Revised date: 10 November 2014Accepted date: 13 November 2014

Cite this article as: Brigitte Camillieri, Marie-Ange Bueno, Indentation of hairysurfaces: role of friction and entanglement, Tribology International, http://dx.doi.org/10.1016/j.triboint.2014.11.009

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Indentation of hairy surfaces: role of friction and entanglement

Brigitte CAMILLIERI, Marie-Ange BUENO

Univ. Haute Alsace, Laboratoire de Physique et Mécanique Textiles, École Nationale Supérieure

d’Ingénieurs Sud-Alsace, 11 rue Alfred Werner, 68093 Mulhouse Cedex, France.

*All correspondence should be addressed to: Marie-Ange Bueno - ENSISA - 11 rue Alfred Werner -

68093 Mulhouse Cedex - France, marie-ange.bueno@uha.fr, Tel: 00 33 (0)3 89 33 63 20, Fax: 00 33

(0)3 89 33 63 39

Abstract:

The present paper is focused on loading-unloading features and hysteresis during indentation of

surfaces having a superficial hairiness. Friction between the pile and the indenter and between bristles

constituting the pile has been modified in experimental and modelling approaches. The results

highlight the influence on stiffness and hysteresis of the friction between the bristles and between the

indenter and the bristles. For an oriented straight pile with a fixed length, the indentation behaviour is

strongly influenced by the friction between bristles. For a pseudo-random structure in terms of bristles

orientation and length, the inter-bristles friction has a lower influence than the friction with the

indenter.

Keywords:

Fibre, indentation, friction, textile fabrics.

1. INTRODUCTION

Many surfaces are characterised by emergent fibres, i.e. superficial hairiness, like textile fabrics for

garments, carpets or seat upholstery, and some leather or paper surfaces. It is well known that

hairiness plays an important role in the frictional and tactile properties of such surfaces. This study

focuses on highly hairy surfaces. The objective is to identify, understand and quantify the features

influencing the tactile feeling in order to get the desired tactile properties before manufacture.

2

Indentation tests are conducted. In the textile field, these tests are often called compression tests, i.e.

lateral compression, although the entire surface of the sample is not subjected to the test. The authors

noticed that the word compression is currently used instead of indentation, due to the misuse of

language, even for a semi-infinite material for which the border effect can be neglected. Cyclic tests of

textile indentation load and unload are conducted. These tests reflect what happens for example when

you press a soft surface with a finger, when you walk on a carpet or when you sit in a seat. For de

Jong, the measurement of the lateral compression of fabrics forms an integral part of the objective

measurements currently being considered internationally for wool fabrics [1]. The compressional

property of a fabric is closely related to fabric handle [2]. Treatments, for example finishing (singeing,

pressing, raising, coating, etc.), have effects on the lateral compression of fabrics; therefore, many

studies use the compression test as a means of quality control [3,4]. Specific devices measure the

compressibility of fabrics (KES-F, Fast ...); Huang has developed an online measurement system for

fabric compressional behaviour to control various relevant textile manufacturing processes like

finishing [5]. Measuring means therefore exist, but understanding of this is still partial.

Hairy surfaces are composed of elements on two different scales: a structure and a superficial

hairiness. Even if the hairiness has a low density compared to the underlying structure, it strongly

influences the compressibility and the properties of the surface like softness and warmth of touch [6-

8]. In the literature, few studies on lateral compression have been found regarding highly hairy

surfaces. For these materials, this is the surface hairiness which starts by being deformed and then the

fabric bulks [9-11]. Finch examined several widely different materials and showed a good

understanding of the deformation mechanism including bending, pile height, stiffness and density, as

well as buckling and relaxation of the foundation [12]. For a plush fabric with high pile of fine fibres

with a three-phase load curve, he expected that the initial resistance to compression was the buckling

of pile followed by its bending and then the compression of the bent pile into the fabric. For a mohair

upholstery fabric with a pile that was not particularly dense but with coarse and stiff fibres, the first

cycle shows a particular behaviour (strong load growth followed by a decrease before the normal

growing) due to the behaviour of the hairs and of the foundation: bristles suddenly buckle resulting in

3

a significant compression of the foundation, then they bend and the foundation relaxes and recovers

from the heavy loads.

If one looks at studies performed on low hairy fabrics, the compression curves show three distinct

regions: the first one corresponds to bending of the bristles emerging from the surface, the second is

the suppression of spaces between the fibres and the yarn, the last region corresponds to the lateral

compression of the fibres [1,2,7,9,13,14]. Matsudaira tested various fabrics to a pressure of 25 kPa [2].

The first zone is a linear (elastic) region and ends with a pressure ranging from 50 to 500 Pa according

to the fabric. In the second area, the force increases exponentially with the penetration of the indenter

into the fabric because of inter-fibre or inter-yarn friction. It ends at a pressure between 4 and 6 kPa.

The last region is a linear region but is not elastic with a high slope, because the pressure increases

rapidly as the thickness changes little. De Jong developed a 3-layer model consisting of a relatively

incompressible core layer (a dense assembly of fibres/yarns with air spaces in between) flanked by

two much more compressible surface layers (mainly air with some projecting fibres) [1]. Based on

both scanning electron microscopy and optical measurements, he showed that at a pressure of 5 kPa,

the emerging fibres are fully bent and the core fibres are displaced without compression. He evaluated

the mass of emerging fibres to an average of 2% of the total fabric mass per unit area for woollen

samples. For information, this percentage of hairiness for a pile fabric is much higher (of the order of

15% for our fabric). Taylor announced that pressures up to 1 kPa deform only the outer surfaces layers

for woven and knitted materials with a small percentage of protruding fibres [15]. Shaving the hair

surface of a wool fabric allowed him to state that the surface layer makes a large contribution to the

compressibility. Hu proposed a five-layer model suitable for all woven fabrics, even for those whose

pile is very weak [16]. The inner layer was the same as in de Jong’s model; he divided each outer layer

into two: the first contained protruding hairs and also the crimp crowns above the average geometrical

thickness.

Another avenue investigated is carpets that have a vertical or near-vertical pile consisting of closed

loops of yarns or open-ended lengths of yarns. The scale is larger for the fabrics considered before. In

fact, for carpet bristles or loops, these are constituted by yarn portions which are much larger than

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fibres. Carpets, however, may be laid on an underlay which will have an influence on behaviour. In

1949, Barach published an interesting study with static loads [17]. The carpet was placed in

unpolymerised plastic with a weight on top of it and was left; after polymerisation, the carpet was cut

through the middle of the load area. One interesting finding was that the backing yarns provided a stiff

enough structure to hold the lower portion of the pile in an almost vertical position. Barach showed

that the effect of the back of the carpet may be noticeable, except at low loads.

Quasi-static indentation tests exhibit non-linearity and irreversibility of at least the first cycles and

hysteresis (distinct loading and unloading curves).

Nonlinearity has been extensively studied in the textile field for loose wads or fabrics in particular,

because it is difficult to determine the thickness of a textile material. The thickness of material

changes with pressure applied on it; if the law of evolution is known, extrapolation to zero pressure

yields the thickness. For fabrics, Hoffmann retains the relationship [11]:

( )aTTkP −= 0 (E1)

where: T0 is the thickness under no pressure, T the thickness under pressure P, and k and a are

constants to be determined.

The exponent a increases suddenly from a value of about 5/4 at low pressures to a value of about 3 at

medium and high pressures. According to Hoffmann, this change could reflect a fundamental change

in the compression process: bending of superficial hairs to a real compression of the fabric.

Bogaty chose a hyperbolic relationship between thickness T and pressure P [9]:

cP

baT

++= (E2)

in which a, b and c are constants.

Equation (2) may be written in the form of the van der Waals’ equation and the constants a and c may

be considered a “correction” of thickness and pressure. Matsudaira, who cut the load curve of fabrics

5

into three zones, estimated that in the two extremes, the pressure is proportional to the thickness, while

in the central area, the pressure varies exponentially with the pressure foot displacement [2]. Kothari

characterised the compressional and recovery properties of non-woven fabrics where fibres are linked

together with two independent parameters: α, the compressional parameter, and β, the recovery one

[18]. For needle-punched non-woven fabrics, the equations of loading and unloading are:

β

α

=−=

ff

eP

P

T

T

P

P

T

T

00

log1

(E3)

where subscript 0 and f for initial and final respectively, P range is 2-200 kPa.

For a coarse linear fibre assembly, named a sliver, the following relationship for wool fibres was

reported by Schofield in 1938 [19]:

3TP

α=

(E4)

with α being a constant, and P ranging from 0 to 170 kPa.

In 1946, Van Wyk offered the first theoretical study for an arrangement of fibres with random

orientations, mainly considering the bending of the fibres in the case of small displacements [20]. For

fibres with ρ density, the pressure P required to compress a mass m is of the form:

−

××=

30

33

3 11

VV

mEKP

ρ (E5)

where E is the Young’s modulus of the fibres and V is the volume of the fibre mass (V0 at zero

pressure).

Van Wyk introduced a constant K because of a number of assumptions (neglecting slippage, friction,

extension, twisting…, straight beam, constant length between contacts, number of fibre-fibre contacts

increases linearly with charge…).

6

Using the mass volume fraction φ, this law is written in the form:

( )30

3 φφ −= KEP (E6)

Van Wyk suggested a correction for large pressures and introduced V' as the limiting volume of the

fibres (incompressible volume) [21]:

( ) ( )

−−

−=

30

3'

1

'

1

VVVV

aP

(E7)

with a being a constant

This law, with three parameters, may be used for fabrics and can be simplified again into two

parameters if V0 is higher than V and V' [1,22]:

( )

−=

3'

1

VV

aP

(E8)

However, this simplification seems to be convenient for high pressures [15] but not in other cases [23].

Despite the many assumptions and simplifications, this model (modified or not) is suitable for many

fibrous assemblies (oriented or not), woven, knitted or non-woven fabrics, and yarns and is currently

widely used for example to fit the compression curve and sometimes the discharge curve [15,16,24]

[22]. In 2009, Allaoui found that tangles of nanotubes follow the law of van Wyk during loading [25].

In 2013, Tran investigated highly porous wood-based fibreboards [24]. At the macroscopic scale, the

response of the material during compression respects the van Wyk model. The evolution of the

microstructure was observed under compression by X-ray micro-tomography. Digital volume

correlation showed that the pore size decreased during compression while the diameters of fibres did

not change. Sometimes, another power law is used; Larose found that the value 2.5 is more

appropriate than 3 for pile fabrics, but he used the law with 2 parameters (E5) [10]; for Sebestyen, for

high pressures (2.5 MPa), greasy wool, scoured wool and man-made fibres, the power ranged from 2.8

to 6.2 [26].

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Van Wyk developed his model assuming that fibres undergo bending stress only (no twisting,

slippage, extension); worse, the original equation was obtained by considering small displacements.

However, his model also depended on the length between two contacts, therefore on the number of

contacts, this assumption probably makes his model so perform. Indeed, Toll, based on a statistical

analysis of the distribution of fibre-fibre contact points, showed a similar model to describe the full

range of fibre network structures [27]:

nKEP φ= (E9)

with φ denoting the volume fraction of fibres, and n indicating the single adjustable parameter of the

model.

He found that n is 3 for 3D fibre wads, but n is not constant with the structure for bundles and weaves;

for aligned fibres, n ranges from 7 to 15.5. The non-linearity is directly connected with creation of

contacts [27-29]. When a fibre assembly is compressed, the number of contacts of a fibre with others

increases and the length of segment between contacts decreases; since a short segment is stiffer than a

long one, the compression force is a nonlinear function of φ [27]. The interactions at contact points

also have an influence on the curve (slippage, jamming, adhesion) [25,30]. Durville found better

agreement with van Wyk’s model for nine randomly generated samples of entangled materials as the

crimp of fibres was higher [29].

If we focus on multiple load-release cycles, the cycles do not overlap, showing a plastic behaviour. A

softening exists; the force required to reach the same thickness decreases with each subsequent loading

cycle. A great difference exists, especially between the first cycle and the next. Some researchers

found that cycles stabilise; for example Dunlop found a stabilisation between 5 or 10 cycles depending

on the fabrics (woven or knitted), while Kelly quoted 20 cycles or more for certain materials,

depending on the tolerance and accuracy [31-33]. To obtain reproducibility of the tests, preparation is

recommended because the first cycle is very sensitive to the sample preparation [12,32]. Stabilisation

is explained by the fact that irreversible slippage no longer exists (but reversible slippage remains)

[32]. Stankovic [22] submitted plain knitted fabrics to five compression-release cycles to achieve

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stabilisation. Rees [34] carried out a more complex procedure consisting of sixteen cycles for kapok

fibres. Sometimes, the viscous nature of the material is also invoked more [5,35-37].

The hysteresis may be attributed to either viscous damping or frictional loss. Since the late seventies,

hysteresis has been primarily related to the fibre-to-fibre friction and slippage which generates the

reorganisation of the fibres in the arrangement which may well have a viscous behaviour, even if a

fibre has an elastic behaviour [30,38,39]. In 1979, Dunlop demonstrated the importance of slippages

between fibres using acoustic measurements; in 1983, he scanned the assumption of viscosity as the

hysteresis was independent of the rate of compression. Later he carried out dynamic measurements on

carpets and used a conventional model for the textile: a spring in parallel with a damper [40,41]. He

found that the damping loss remained constant with frequency, indicating that the damping mechanism

is friction-controlled rather than viscoelastic. For entangled materials or mats, the hysteresis is

explained by the friction between fibres and the instability of the contacts between fibres rather than

by the non-elastic behaviour of fibres [31,42,43].

Friction, other than that between fibres, is rarely mentioned, even if precautions are taken to limit

them, for example with the use of polytetrafluoroethylene. Curiskis performed compression tests with

and without a chamber to hold the fibres for which the difference is obvious; for the same transverse

strain, it was necessary to apply a greater transverse stress with a chamber than without [30]. Rees

showed that friction between the fibres and the cylinder wall introduce errors into the determination of

resilience (ability of the fibres mass to recover from compression), even if the cylinder wall is polished

[44]. Earlier, he showed that the measurement of the overall specific volume is not distorted by

friction between fibres and the cylinder if the fibres are arranged in a cylinder whose cross-section is

large than its thickness [34]. Another effect arises when the diameter of the piston is less than the

diameter of the cylinder. In 1955, DeMaCarty compressed cylindrical wads of wool fibres with pistons

of different diameters [45]. These wads were placed or not in a cylinder. The diameter of the piston

was always smaller than the diameter of the fibre wad. He found that there was no difference between

the walled and wall-less experiments and concluded that frictional effects caused by the proximity of

the outer edge of a compressing piston to the inner surface of a confining wall are unimportant. He did

9

not mention nor study the fibres’ friction on the inner wall of the cylinder. Sebestyen used three

cylinders with three different diameters (1, 2 or 3 inch) [26]. He filled the cylinders with a fibre mass

proportional to the cylinder section (15, 60 or 135g). The regression lines have the same slope. Since

the gap is smaller between the two larger diameters compared to two smaller ones, he concluded that

the edge effect is almost negligible for a 3-inch diameter cylinder.

In this paper, we consider pile textile fabrics. A fundamental difference with entangled materials is

that all of the bristles in hairy surfaces are embedded in the structure, as for carpets. We show by

experiments and finite element modelling, the influence of inter-fibre friction but also the influence of

indenter-fibre friction, which is rarely considered during experiments. Modelling, although taking into

account the compression of a few bristles, allows a better understanding the origin of the non-linearity

and hysteresis.

2. MATERIALS AND METHODS

2.1. Investigated pile fabrics

Two different kinds of pile fabrics were tested: velvet and polar fabrics (Fig. 1). A pile fabric consists

of a woven or knitted structure, which provides dimensional stability, and an extra yarn going out

structure in order to give the pile. This yarn, i.e. an assembly of fibres or filaments, is cut to the

desired length during the manufacture of the fabric. The released bristles make up the hairiness and are

in the form of a fibre bundle held on the side of the structure. In the case of velvet, the length and

orientation of the bristles are regular. In the case of polar fabrics, treatments include scraping tangled

hairs, which is named the raising process; the bristles have variable lengths and the bristle orientation

is random; pile is over the two sides of the fabric. For both velvet and polar fabrics, the pile yarns are

made of polyester material. For information, the carpet pile is similar to velvet except for the scale. In

fact, a bristle is a fibre in a velvet fabric (10-20 microns in thickness) and a cable, i.e. an assembly of

yarns, in a carpet (few millimetres in diameter).

In order to change the coefficient of friction between bristles, the fabrics were subjected to two

chemical treatments: a hydrophilic or a hydrophobic treatment. These treatments, in contrast to

10

mechanical treatments, change the surface tension of the fibres but should not alter the stiffness of the

bristles. The links, firstly between friction and adhesion and lastly between adhesion and surface

tension, are well-attested, and were extended to solids by Rabinowicz [46-48]. In the case of a contact

between two bodies, no 1 and 2, the work Wad for separating two bodies in contact because of adhesion

forces is:

( ) ( )21ad 1W γ+γ⋅ξ−≈ (E10)

with

γ1 and γ2 : surface tension in air for the materials 1 and 2 (N.m).

2

1 =ξ for insoluble materials and

4

1 =ξ for soluble materials.

The effect of hydrophilic and hydrophobic treatments is to increase and decrease fibre surface tension,

respectively.

Before treatment, the fabric is washed at 90°C in order to remove superficial treatment due to

manufacturing processes and then it is rinsed and drained. It is dipped in the hydrophobic or

hydrophilic treatment bath and expressed and finally dried at 150°C. The hydrophobic agent is

Clariant Nuva 2110 (emulsion of fluorocarbon resin commonly used as water- and oil-repellent agent)

and the hydrophilic one is Huntsman Ultravon CN (non-ionic surfactant).

The wettability of the fabrics is verified by measuring the contact angle with the use of the

DropAnalysis plugin (Biomedical Imaging Group, EPFL, Lausanne, Switzerland) of ImageJ 1.46r

software (National Institute of Health, USA). For the hydrophilic treated fabrics, the hydrophilicity is

such that the drops spread completely on the fabric. Figure 2 shows the hydrophobic character of the

fabrics after hydrophobic treatment.

Because of the pile on the surface, it is quite difficult to see the base of the drop, but we can estimate

in both cases that the drop angle exceeds 140°.

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2.2. Friction experiments

A reciprocating pin-plane linear tribometer described elsewhere was used to measure sliding friction

force [49]. Tangential force was acquired in order to determine the whole force induced by the friction

between the slider and the investigated surfaces during dynamic friction contacts. The measurement

conditions consisting of the pressure, the slider apparent contact area, the sliding distance and the

velocity were chosen relative to fabric tactile conditions [49,50]. The normal load was applied by

means of dead weights in order to have a nominal contact pressure of 6.5 kPa. The frequency of the

reciprocating movement was 0.05 Hz, corresponding to nominal sliding velocities of 5 mm.s-1. The

sliding distance was 50 mm. The slider used was cuboid-shaped and was in aluminium with an

apparent surface area of 150 mm². As we sought to determine the coefficient of friction between the

fibres, the slider was covered with fabric. To avoid the interlocking of fibre surfaces, the friction

measurement proceeded with the fabric back side against back side.

All measurements were carried out in a standard atmosphere of 20°C and 65% RH. The friction

experiments comprised six measurements on each kind of fabric. The average friction force and the

coefficient of friction are given in both directions.

2.3. Indentation/compression measurement

The indentation tests were performed with an Anton Paar MCR500 rheometer (Fig.3). This was fitted

with two concentric cylinders: the lower fixed cylinder supports the fabric sample and the upper

movable cylinder is the indenter. It was controlled by the software RheoPlus V3.40. A force sensor at

the upper end of the indenter monitored the force as a function of the position of the indenter. Usually,

the position of the indenter is given relative to the upper surface of the lower cylinder, but we

developed a procedure to detect the upper surface of a fabric. This change of origin allowed us to

compare fabrics that would not have the same thickness. The indentation curves used in the following

provide the pressure (all indenters have a diameter of 15 mm, i.e. a 177 mm² surface area) as a

function of the penetration depth in the fabric. The results can be expressed in absolute penetration

depth in millimetres or relative to the initial thickness in percent. An indentation test is a load at

12

constant speed of displacement of the indenter and a release at the same rate. A preliminary study on

hairy fabrics showed that the speed of indentation in a range of 0.02 to 0.2 mm.s-1 does not have any

influence [51]. The following tests will be carried out at a speed of 0.1 mm.s-1. Similarly, preliminary

tests have shown that successive cycles of load and release overlapped after two or three cycles. The

analysed cycles were those obtained after three preliminary rounds. To take into account the

dispersion of textile products, several measures (at least six) were performed on each fabric and an

average cycle was calculated.

A maximal loading force of 10N was chosen in order to indent essentially the pile and not the knitted

or woven structure.

In order to change the coefficient of friction between piles and indenter, different materials for the

indenter (stainless steel, aluminium, polyvinylchloride, polytetrafluoroethylene) were used. These

coefficients were related to the surface tension of materials. The surface tension measurement was

carried out with various solvents using the Owens & Wendt’s model [52]. The results which are

consistent with those found in the literature [53-55] are shown in table 1.

The roughness of the different indenters used was also determined with a mechanical profilometer

(Subtronic 3, Taylor Hobson) and is shown in table 1.

3. FINITE ELEMENT MODELLING

Modelling was carried out under Abaqus/CAE 6.11 (Dassaults Systems, France). Only the velvet

fabric was modelled. In fact, the tortuosity of polar fibres, I.e. their 3D arrangement, is unknown at

present.

The goal was to understand the impact of piles on the overall behaviour of the fabric, with modelling

focused on each bristle. First, a single bristle was considered and then the number of bristles was

increased. The bristles were assumed to have an elastic and isotropic behaviour and the indenter was

assumed to be infinitively rigid. Each bristle was modelled as a volume element (hexahedral mesh).

The features (Table 2) provided to the finite element software were those of the previously tested

13

velvet. The fibre morphological characteristics were measured by optical methods [51] and the

Young’s modulus by modal analysis [56].

Figure 4 shows the modelling of two bristles. The free end of the hair was completed by a curvature to

facilitate the calculations; the indenter began by pressing on this end. The other end was clamped.

A vertical movement was imposed on the indenter down and up.

Abaqus allows the inclusion of the non-linear behaviour of the bristles as well as friction between the

indenter and bristles and between the bristles (friction surface area). From each computation, a curve

similar to the experimental indentation curve is obtained: normal force was exerted by the indenter as

a function of the penetration depth.

4. EXPERIMENTAL RESULTS

4.1. Friction experiments

The coefficients of friction obtained with the hydrophilic (HI) or hydrophobic (HO) fabrics are

summarised in figure 5. As the relationship between friction, adhesion and surface tension led us to

assume, the friction coefficient increases from a hydrophobic to a hydrophilic fabrics.

4.2. Indentation/compression measurements

The experimental results are summarised in the following figures.

When the objective was to compare the indentation effect between the velvet and the polar fabrics, the

penetration depth was expressed relative to the initial thickness. In the other cases, the penetration

depth was expressed in millimetres.

Figure 6 includes the indentation cycles for both hydrophilic and hydrophobic fabrics with an

aluminium indenter. The influence of the indenter material is shown in figure 7 for the hydrophobic-

treated velvet and the hydrophobic-treated polar fabrics. The influence of the indenter roughness is

illustrated in figure 8 for both hydrophobic fabrics.

14

We note that for a given penetration depth of the indenter, the normal force decreases (so it is easier to

indent) when:

- The coefficient of friction between the bristles decreases (the case of hydrophobic versus

hydrophilic),

- The coefficient of friction between the indenter and the bristles decreases, or

- The roughness of the indenter decreases (velvet case only).

The indentation behaviour of the polar was not influenced by a change in the indenter roughness,

unlike velvet fabric.

When comparing indenters in stainless steel such as polytetrafluoroethylene and polyvinylchloride,

which have a similar roughness, the order of the indentation curves corresponded to the order of

surface tensions.

Hydrophilic and hydrophobic treatments (Fig. 6) led to a much more important shift for the velvet

(6.5%) than for the polar fabric (1.3%). The two extreme curves in the case of a change in material of

the indenter (Fig. 7) were displaced by 0.07 mm in the case of velvet (this corresponds to 2.8%

because the initial thickness was 2.61 mm), whereas the gap was 0.16 mm, namely 4.2%, in the case

of polar fabrics (initial thickness was 3.96 mm).

The velvet fabric was more influenced by inter-fibre friction and less influenced by friction between

the indenter and the pile than the polar fabric.

15

4.3. Finite Element Model results

The modelling only concerned the velvet fabric because the experimental results showed that the

influence of the different parameters was higher for this kind of fabric than for the polar material.

Figure 9 shows the shape of the load curve for a single bristle. The unloading curve is similar to the

loading curve. There are two areas: one area where linearity can be admitted and a second

substantially non-linear zone.

The deformation of the bristle at different steps of the load (including start and end zones) is shown.

The influence of the variation of the coefficient of friction µi between the indenter and the bristle is the

same as that plotted in Figure 10 for two bristles.

The following curves show the influence of the friction during the indentation of two bristles. Two

cases were treated: the coefficient of friction between the bristles µp is kept constant, when the

coefficient of friction between the indenter and the bristles µ i varies (Fig. 10), or µi is set to a constant

value and µp varies (Fig. 11).

The same trends as in the experiments can be obtained by Finite Element Modelling (FEM).

Moreover, when there is no friction, there is no hysteresis. In fact, the loading and unloading curves

are superposed. When there is friction, hysteresis exists; the greater the friction, the larger the

hysteresis is.

5. DISCUSSION

The finite element modelling confirmed the experimental results. In fact, for a given penetration depth

of the indenter, the normal force decreases (so it is easier to indent) when:

- The coefficient of friction between the bristles decreases (the case of hydrophobic versus

hydrophilic), or

- The coefficient of friction between the indenter and the bristles decreases.

16

Simulation of the roughness of the indenter was not performed with Abaqus but other researchers

found similar results. Poquillon observed the same phenomenon as a result of testing of entangled

polyamide or aluminium fibres, whose roughness was increased by mechanical or chemical treatment

[57,58].

The simulation was performed on a limited number of bristles (up to four but this leads to significant

computing time or a shutdown calculation at the beginning of unload), but allows extrapolation to find

the magnitude of the experimental results. If we consider the curve of figure 9 obtained by indenting a

single bristle, the calculated strength was close to 130 µN for a penetration depth of 1 mm. Taking into

account the surface of our indenter and the density of the bristles, a force of 1.75N was obtained

versus a force of approximately 5N obtained experimentally (fig. 7 top). This calculation was made

without considering the frictional forces that should be added.

Despite the limitations of our modelling, this simulation should help to understand the mechanisms at

a microscopic scale governing the indentation of pile fabrics. The finite element modelling shows that

for an elastic material, hysteresis only exists if friction occurs. Other simulations show hysteresis

during cycles, both when friction is considered or not and a shift of cycle to lower deformation with

friction [42,59]. This performance model can simulate successive cycles and detects irreversible

rearrangements of fibres that were eliminated experimentally by preparing our samples (successive

cycles overlap). In our stabilised case, when friction exists, the hysteresis can be explained only by the

different shape of the bristles during load and unload. Figure 12 shows a fibre during the load and

unload for the same position of the indenter assuming the existence of friction. When the indenter goes

down, friction limits the fibre sliding and causes increased curvature, whereas during the ascent of the

indenter, the slippage limitation causes a reduction of the curvature. A different form of fibre causes a

different normal force.

The model allows studying the influence of various parameters of the fabric as the material (Young's

modulus) and characteristics of pile (diameter, pitch, length). This study is not presented here, but

when the bristles are implanted more vertically, buckling becomes very clear (Fig. 13) [60].

17

When comparing the experimental behaviour of velvet and polar fabrics, differences exist: the polar

material is not sensitive to the roughness of the indenter, while for the velvet, roughness shifts the

cycle and especially changes the load curve. Velvet hairiness, which is relatively straight, probably

also undergoes buckling when compared to the roughness of the indenter, while the bristles of polar,

which are curly (Fig. 14) and go in all directions, are not trapped in the lumps of the indenter.

The influence of the variation of inter-fibre friction is higher for velvet fabric, where hair is almost

straight and parallel, than for polar fabric, as the surfaces of fibres which will come into contact during

the indentation are larger for velvet than for polar. On the contrary, the influence of friction between

indenter and pile is slightly more important for polar than for velvet fabric (relative to the fabric

thickness). This trend can be due to the tortuosity of the fibre of polar fabric; the contact with the

indenter does not only occur at the free end. In addition, for velvet fabric, all of the bristles do not

come into contact with the indenter because they have not exactly the same length and they are not

perfectly parallel to each other.

6. CONCLUSIONS

Pile fabrics with bristles embedded in the structure of the fabric are experimentally tested in

indentation. Two kinds of fabrics have been tested with regular hairiness in length and spatial

orientation, i.e. velvet fabrics and fabrics with irregular hairiness, i.e. polar fabrics. With the help of a

Finite Element Model of bristles, the mechanisms involved during a load-unload cycle have been

identified; in particular, the role of friction between fibres and between the indenter and the fibres has

been identified. In fact, there is no hysteresis without at least one of these two mechanisms.

When the friction between fibres or the friction between fibres and the indenter decreases, the

penetration depth becomes higher for the same strength.

A decrease in the fibre/fibre friction is more efficient with the velvet fabric, which presents regular

hairiness, than with the polar fabric. For the velvet fabric, the fibres are almost straight, therefore the

contact area between fibres is larger than for non-oriented bristles.

18

A decrease in the fibre/indenter friction is slightly more efficient with the polar fabric than with the

velvet fabric. For the polar fabric, the bristles are curly and pseudo-randomly oriented; therefore, the

contact area with the indenter can be larger than with the velvet fabric.

Moreover, the higher the indenter roughness, the lower the penetration depth for the same strength is.

This effect exists only if the hairiness is straight. In fact, in that case, bristles can buckle.

If one wants to make a hairy fabric from fibres of fixed characteristics (length, diameter, pitch,

material, density of hair ...) more flexible in its compression, that is to say with low resistance during

the indentation, the strategy can be different relative to the kind of hairiness. For a regular pile, i.e.

with fixed bristle orientation and length, the friction between bristles significantly influences the

indentation curve. In the case of tactile exploration, the indenter is the finger. The inconvenient factor

is that finger roughness can induce bristle buckling, which is not pleasant, especially for coarse fibres.

On the other hand, for a pseudo-random hairiness, the friction between the finger and the fabric has to

be reduced. A perspective of this study is to work with an indenter with shape, hardness, roughness

closed to human finger. Moreover a comparison with a psychophysical study is planned.

References

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Figure and table caption

Fig. 1: The investigated fabrics: velvet (a), polar (b).

Fig. 2: Water drop on velvet (a) and polar fabrics (b).

Fig. 3: The MCR500 rheometer (a) and zoom the plane-plane system with a fabric sample (b).

Tab. 1 – Surface free energy and roughness of the different indenters.

Tab. 2 – Characteristics of the bristles.

Fig. 4: Modelling of two bristles and the indenter.

Fig. 5: Coefficient of friction for polar (a) and velvet (b) fabrics with hydrophobic (HO) and

hydrophilic (HI) treatments.

Fig. 6: Experimental loading-unloading cycle for the hydrophilic and hydrophobic velvet and polar

fabrics. Example with aluminium indenter

Fig. 7: Experimental loading-unloading cycle for the different materials of indenter for velvet (a) and

polar fabrics (b). Example with hydrophobic treated fabrics.

Fig. 8: Experimental loading-unloading cycle for two different roughness of materials of

polytetrafluoroethylene indenter for velvet (a) and polar fabrics (b). Example with hydrophobic treated

fabrics.

Fig. 9: Simulated loading curve for one bristle with the corresponding deformed shape of the bristle.

There is no friction between bristle and indenter.

Fig. 10: Simulated loading-unloading curve for different values of the coefficient of friction µ i

between the indenter and the bristles. Two bristles are considered. There is no friction between the

bristles. The same trend is obtained when the friction between bristles exists.

Fig. 11: Simulated loading curve for different values of the coefficient of friction for two bristles: a)

total curve; b) zoom on the end of the curve. There is no friction between the indenter and the bristles.

The same trend is obtained when the friction between bristle and indenter exists.

Fig. 12: Shape and position of a bristle during load and unload to the same height of the indenter.

Fig. 13: Buckling and bending coupled on a bristle. The angle between the bristle axis and the vertical

line is 15°.

Fig. 14: Top view of the investigated fabrics: velvet (left), polar (right).

Figure 1

a)

b)

22

Figure 2

a)

b)

23

24

Figure 3

a)

b)

25

Table 1

Stainless steel Aluminium PVC* PTFE**

γS (10-3 N.m-1) 40.0 40.4 34.1 21.5 (smooth) 24.5 (rough)

Ra (µm) 0.54 ± 0.10 0.22 ± 0.03 0.46 ± 0.15 0.62 ± 0.28 (smooth) 4.77 ± 1.29 (rough)

*PVC is polyvinylchloride **PTFE is polytetrafluoroethylene

26

Table 2

Material Polyester; E = 8 GPa; ν = 0.22

Fibre length 2.11 ± 0.01 mm

Fibre diameter 31 ± 2 microns

Angle of hair inclination/vertical 41° ± 2°

Number of bristles per mm2 76 ± 8

27

Figure 4

Figure 5

a)

b)

28

Figure 6

29

Figure 7

a)

b)

30

Figure 8

a)

b)

31

32

Figure 9

Figure 10

33

34

Figure 11

35

Figure 12

0.1 mm

0.1 mm

36

Figure 13

0.1 mm

0.1 mm

37

Figure 14

38

Highlights:

• Mechanisms involved in indentation of pile surfaces are identified and described.

• Hysteresis is due to friction between fibres or between fibres and indenter.

• The influence of both kinds of friction depends on fibre orientation and length.

• The indenter roughness has an influence if the pile is straight: buckling occurs.