**7. Nano-indentation**

Instrumented indentation testing, a test method where load and depth of indentation are continuously monitored, have become a common technique for characterizing mechanical behavior of a large variety of materials. Indentation testing is one of the few experimental techniques that can be performed at both large and small scales, thus allowing for the investigation of materials behavior across length scales from milli- to nanometers. The stress field induced by indenter in the specimen is highly localized, and the scale is proportional to the contact area. Thus by varying the indenter geometry, and size, as well as the applied load, one may obtain results representative for the material behavior on different scales. By using high-resolution testing equipment, the material properties can be measured at the micro- and nanometer level, thus allowing for a study of the variability in material properties across a specimen (Oliver & Pharr, 1992, 2003). Over the past 20 years, this technique has been used to investigate the linear elastic, viscoelastic and plastic properties of thin films, modified surfaces, individual phases in alloys and composites and other microscopic features. A detailed account of work done in this field has recently been given by (Gouldstone et al., 2007).

Recently number of attempts have been reported in the literature to use AFM in force mode to obtain elastic and viscoelastic properties of different materials, cf. e.g. (Tripathy & Berger, 2009; Gunter, 2009). AFM allows measurement of viscoelastic material properties with spatial resolution on the nanoscale; furthermore by performing the repetitive measurements at different temperatures or before and after oxidation it allows for the observance of different phases of the material. These data can be a key to understanding the governing mechanisms behind healing and ageing phenomena in bituminous binders.

The heart of any indentation testing is a method to extract the material parameters from the experimentally observed relation between indentation force *F* , and indentation depth, *h* . Modelling the indentation of viscoelastic solids thus forms the basis for analyzing the indentation experiments. Lee & Radok made substantial progress, by solving the problem of sphere indenting linear viscoelastic halfspace (Lee & Radok, 1960). Analogous results for the case of conical indenters were presented by (Graham, 1965), and for a flat punch by (Larsson & Carlsson, 1998). Huang & Lu (2007) developed a semi-empirical solution for viscoelastic indentation of the Berkovich indenter. In AFM, a probe consisting of a cone with a nominal tip radius on the order of 10 nm or higher is typically used. The accurate determination of the AFM tip shape is in fact one of the major sources of uncertainty, when performing nanoindentation testing with AFM, particularly at lower load levels. As it has been argued by many investigators, in indentation testing at micro- and nanoscales it is very difficult to make a valid assumption concerning the indenter geometry, cf. e.g. Korsunsky (2001) and Giannakopoulos (2006). Even the best attempts at preparing a perfectly round spherical or perfectly sharp conical shapes inevitably produce flattened imperfect shapes. These deviations of the indenter shapes from the assumed ideal shape will affect measurements performed at small scales. The AFM tip is normally considered to be of conical shape with round spherical tip. The contact geometry is thus dominantly controlled by the spherical indenter tip at low load levels and is switching to conical geometry at higher loads. The procedure to extract viscoelastic properties with spherical indentation is illustrated below (Larsson & Carlsson, 1998)

Using ordinary notation the stress-strain relations for linear viscoelastic solids can be formulated in relaxation form as:

$$s\_{ij}\left(t\right) = \int\_0^t G\_1\left(t - \tau\right) \frac{d}{d\tau} e\_{ij}\left(\tau\right) d\tau \tag{4a}$$

$$\sigma\_{ii}\left(t\right) = \Im \int\_0 G\_2\left(t - \tau\right) \frac{d}{d\tau} \varepsilon\_{ii}\left(\tau\right) d\tau \tag{4b}$$

where

224 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

0123456

Instrumented indentation testing, a test method where load and depth of indentation are continuously monitored, have become a common technique for characterizing mechanical behavior of a large variety of materials. Indentation testing is one of the few experimental techniques that can be performed at both large and small scales, thus allowing for the investigation of materials behavior across length scales from milli- to nanometers. The stress field induced by indenter in the specimen is highly localized, and the scale is proportional to the contact area. Thus by varying the indenter geometry, and size, as well as the applied load, one may obtain results representative for the material behavior on different scales. By using high-resolution testing equipment, the material properties can be measured at the micro- and nanometer level, thus allowing for a study of the variability in material properties across a specimen (Oliver & Pharr, 1992, 2003). Over the past 20 years, this technique has been used to investigate the linear elastic, viscoelastic and plastic properties of thin films, modified surfaces, individual phases in alloys and composites and other microscopic features. A detailed account

Recently number of attempts have been reported in the literature to use AFM in force mode to obtain elastic and viscoelastic properties of different materials, cf. e.g. (Tripathy & Berger, 2009; Gunter, 2009). AFM allows measurement of viscoelastic material properties with spatial resolution on the nanoscale; furthermore by performing the repetitive measurements at different temperatures or before and after oxidation it allows for the observance of different phases of the material. These data can be a key to understanding the governing

The heart of any indentation testing is a method to extract the material parameters from the experimentally observed relation between indentation force *F* , and indentation depth, *h* . Modelling the indentation of viscoelastic solids thus forms the basis for analyzing the indentation experiments. Lee & Radok made substantial progress, by solving the problem of sphere indenting linear viscoelastic halfspace (Lee & Radok, 1960). Analogous results for the case of conical indenters were presented by (Graham, 1965), and for a flat punch by (Larsson & Carlsson, 1998). Huang & Lu (2007) developed a semi-empirical solution for viscoelastic

of work done in this field has recently been given by (Gouldstone et al., 2007).

mechanisms behind healing and ageing phenomena in bituminous binders.

Loading cycle N

90

**7. Nano-indentation** 

95

No restperiod Restperiod VE Restperiod VE & PS

Fig. 19. Calculation of equivalent stiffness (Kringos et al., 2012)

100

105

110

Equivalent stiffness [MPa]

115

$$\varepsilon\_{i\dot{j}} = \sigma\_{i\dot{j}} - \frac{1}{3} \delta\_{i\dot{j}} \sigma\_{kk'} \qquad \qquad \varepsilon\_{i\dot{j}} = \varepsilon\_{i\dot{j}} - \frac{1}{3} \delta\_{i\dot{j}} \varepsilon\_{kk} \tag{5}$$

are the deviatoric components of stress and strain. In equations (4a) and (4b), *G*1 and *G*<sup>2</sup> are the so-called relaxation functions in shear and dilation, respectively. The viscoelastic Poisson's ratio, t , is related to the relaxation functions in equations (4a) and (4b) as:

$$\overline{\nu(s)} = \frac{1}{s} \frac{\left(\overline{G\_2(s)} - \overline{G\_1(s)}\right)}{\left(2\overline{G\_2(s)} - \overline{G\_1(s)}\right)}\tag{6}$$

using Laplace transformed quantities according to

$$\overline{f}\left(s\right) = \bigcap\_{0}^{\infty} f\left(t\right) e^{-st} \, dt \tag{7}$$

In principle, in order to completely characterize the viscoelastic material one needs to determine two independent viscoelastic functions <sup>1</sup> *G t*( ) and <sup>2</sup> *G t*( ) . However, these two functions cannot be determined uniquely from experimental force-displacement data. Thus in most conventional testing techniques a constant viscoelastic Poisson's ratio is assumed, and nanoindentation measures only the relaxation compliance in shear, cf. e.g. Giannakopoulos (2006) and Jäger et al. (2007). The shear relaxation function *G*1 is expressed then as Prony series and the introduced constants are then determined in order to best fit the experimental results.

The relaxation test with AFM is performed by programming the tip to indent the specimen to a specified depth, *h t*( ) , and then to hold the penetration depth constant for a specified time, i.e. *ht hH t* <sup>0</sup> , *H t*( ) being the Heaviside function. Provided that the indenter is stiff as compared to the sample, the relation between *G*1 and the indenter load measured as a function of time, *P t*( ) , is given than as:

$$G\_1(t) = \frac{6R(1 - \nu)P(t)}{8\,a\_0^3} \tag{8}$$

Atomic Force Microscopy to Characterize the Healing Potential of Asphaltic Materials 227

Huang & Lu (2007) suggested to use the semi-empirical force-displacement relations for the Berkovich indenter along with the analytical solution for the spherical indenters as two independent equations for establishing <sup>1</sup> *G t*( ) and <sup>2</sup> *G t*( ) . The relaxation functions may be then expressed as Prony series and their coefficients may be found as the best fit of the

It has to be pointed out however that both of these approaches appear to be questionable when applied to AFM indentation testing: instrumenting the specimens surface with additional sensors appears not to be practically feasible at the length scale in question; at the same time the approach presented in Huang & Lu (2007) would require AFM tips with two distinct well defined shapes. Furthermore, the possibility to accurately measure linear viscoelastic material behavior with sharp indenters, such as Berkovich or conical, has been questioned by several researches, cf. e.g. Vanlandingham et al. (2005). The reason is that sharp indenters inevitably introduce intense strains local to the indenter tip, thus making

It may be concluded from the above that using AFM in force mode provides a useful tool to obtain at least qualitative information regarding the bitumen properties at nano-scale and their evolution with temperature and oxidation. The use of AFM to obtain absolute quantitative estimates of viscoelastic properties of the bituminous binders appears however questionable at the present moment. One way to proceed is to complement AFM measurements by instrumented indentation measurements at microscale and macroscale, in order to obtain better initial quantitative estimates of the volumetric and shear relaxation

From simulations with the developed healing model, briefly described in the previous sections, it is evident that many different bitumen phase configurations can be formed from an initially homogeneous configuration. The initial configuration and the smallest local dispersions of the material can thereby have an important effect, as does the configurational and surface free energy potentials. The rate at which these changes occur is of great importance for the practical implications of this phenomenon relates to rest periods in the laboratory to assess the healing rates and the actual healing ability of the asphalt pavement. Mobility of the bitumen is thereby an important characteristic of the bitumen that affects the healing potential and should be determined. It can therefore be expected that enhancing the mobility of the bituminous phases will increase the healing

The configuration free energy potential of bitumen can be determined from the configuration free energy curves of the individual phases by assuming that in a certain composition only the phase with the lowest energy will exist. Equilibrium is then found when the chemical potential is homogeneous throughout the material. This does not, however, mean that the mass fraction has to be homogeneous. Inhomogeneous distribution of phase affects the ability for bitumen to transmit stresses through its matrix. Having knowledge about the bitumen configurational free energy potentials can therefore contribute to better predictions of the in-time evolution of its ability to transmit stresses and reduce damage propagation. Optimizing the bitumen phase diagrams to promote the

experimental data.

functions.

the assumption of linearity invalid.

**8. Discussion and recommendations** 

rates and thus the pavement life time.

where *R* is the radius of curvature of the spherical indenter tip and <sup>0</sup> *a* is the maximum radius of the contact area defined as:

$$a\_0^2 = \left(Dh\_0\right) / \,\, 2\tag{9}$$

Equation (8) may be used to obtain shear relaxation modulus, provided that constant Poisson's ration is known, the material response is linear and the contact geometry is spherical. Equation (9) provides a simple way to check the linearity of the material response. As it has been show by Larsson & Carlsson (1998), the size of the residual impression in the specimens surface is very close to the maximum size of the contact area. One may thus follow AFM indentation testing with AFM scanning in tapping mode to measure size of the residual impression and compare it with the maximum contact radius predicted by equation (9). The discrepancy between the measured and predicted contact radii would indicate the presence of non-linear material effects. The assumption of the constant Poisson's ratio may not be satisfactory for characterization of bituminous binders, as volumetric material response may also exhibit spatial variation. Researchers have been attempting to address this issue and distinguish dilation and shear compliances by using secondary sensors to measure circumferential strain at a small distance from the contact area, e.g. Larsson & Carlsson (1998) or by comparing force-displacement relations for indenters with different shapes, e.g. Huang & Lu (2007). In particular, Larsson & Carlsson (1998) derived the following relations between <sup>1</sup> *G t*( ) , 2 *G t*( ) and *P t* , :

$$\int\_{0}^{t} G\_{1}\left(\tau\right)d\tau = \frac{6R}{8a\_{0}^{3}} \Big| \mathop{P}\left(t - \tau\right) \left(1 - \nu\left(\tau\right)\right)d\tau \tag{10}$$

$$\int\_{0}^{t} \varepsilon\_{\theta} \left(r, t - \tau\right) \left(1 - \nu\left(\tau\right)\right) d\tau = -\frac{4a\_{0}^{3}}{6\pi R r^{2}} \int\_{0}^{t} \left(1 - 2\nu\left(\tau\right)\right) d\tau \tag{11}$$

Equations (10) and (11) are uncoupled Fredholm integral equations of first and second kind respectively. The technique required to solve such a system of equations numerically is well documented, cf. e.g. Andersson & Nilsson (1995).

Huang & Lu (2007) suggested to use the semi-empirical force-displacement relations for the Berkovich indenter along with the analytical solution for the spherical indenters as two independent equations for establishing <sup>1</sup> *G t*( ) and <sup>2</sup> *G t*( ) . The relaxation functions may be then expressed as Prony series and their coefficients may be found as the best fit of the experimental data.

It has to be pointed out however that both of these approaches appear to be questionable when applied to AFM indentation testing: instrumenting the specimens surface with additional sensors appears not to be practically feasible at the length scale in question; at the same time the approach presented in Huang & Lu (2007) would require AFM tips with two distinct well defined shapes. Furthermore, the possibility to accurately measure linear viscoelastic material behavior with sharp indenters, such as Berkovich or conical, has been questioned by several researches, cf. e.g. Vanlandingham et al. (2005). The reason is that sharp indenters inevitably introduce intense strains local to the indenter tip, thus making the assumption of linearity invalid.

It may be concluded from the above that using AFM in force mode provides a useful tool to obtain at least qualitative information regarding the bitumen properties at nano-scale and their evolution with temperature and oxidation. The use of AFM to obtain absolute quantitative estimates of viscoelastic properties of the bituminous binders appears however questionable at the present moment. One way to proceed is to complement AFM measurements by instrumented indentation measurements at microscale and macroscale, in order to obtain better initial quantitative estimates of the volumetric and shear relaxation functions.

## **8. Discussion and recommendations**

226 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

and nanoindentation measures only the relaxation compliance in shear, cf. e.g. Giannakopoulos (2006) and Jäger et al. (2007). The shear relaxation function *G*1 is expressed then as Prony series and the introduced constants are then determined in order to best fit

The relaxation test with AFM is performed by programming the tip to indent the specimen to a specified depth, *h t*( ) , and then to hold the penetration depth constant for a specified time, i.e. *ht hH t* <sup>0</sup> , *H t*( ) being the Heaviside function. Provided that the indenter is stiff as compared to the sample, the relation between *G*1 and the indenter load measured as

> 1 3

8 *R Pt*

6 1

where *R* is the radius of curvature of the spherical indenter tip and <sup>0</sup> *a* is the maximum

Equation (8) may be used to obtain shear relaxation modulus, provided that constant Poisson's ration is known, the material response is linear and the contact geometry is spherical. Equation (9) provides a simple way to check the linearity of the material response. As it has been show by Larsson & Carlsson (1998), the size of the residual impression in the specimens surface is very close to the maximum size of the contact area. One may thus follow AFM indentation testing with AFM scanning in tapping mode to measure size of the residual impression and compare it with the maximum contact radius predicted by equation (9). The discrepancy between the measured and predicted contact radii would indicate the presence of non-linear material effects. The assumption of the constant Poisson's ratio may not be satisfactory for characterization of bituminous binders, as volumetric material response may also exhibit spatial variation. Researchers have been attempting to address this issue and distinguish dilation and shear compliances by using secondary sensors to measure circumferential strain at a small distance from the contact area, e.g. Larsson & Carlsson (1998) or by comparing force-displacement relations for indenters with different shapes, e.g. Huang & Lu (2007). In particular, Larsson & Carlsson (1998) derived the

*G t*

2

0

 :

> 3 0 2

*Rr*

 (10)

(11)

 

<sup>1</sup> <sup>3</sup>

Equations (10) and (11) are uncoupled Fredholm integral equations of first and second kind respectively. The technique required to solve such a system of equations numerically is well

<sup>4</sup> , 1 1 2

 

*t t <sup>a</sup> r t <sup>d</sup> <sup>d</sup>*

*t t <sup>R</sup> G d Pt <sup>d</sup>*

<sup>6</sup> <sup>1</sup>

 

6

0 0 0

 

 

8

0 0

*a*

(8)

0 0 *a Dh* ( )/2 (9)

*a*

the experimental results.

a function of time, *P t*( ) , is given than as:

radius of the contact area defined as:

following relations between <sup>1</sup> *G t*( ) , 2 *G t*( ) and *P t* ,

 

documented, cf. e.g. Andersson & Nilsson (1995).

From simulations with the developed healing model, briefly described in the previous sections, it is evident that many different bitumen phase configurations can be formed from an initially homogeneous configuration. The initial configuration and the smallest local dispersions of the material can thereby have an important effect, as does the configurational and surface free energy potentials. The rate at which these changes occur is of great importance for the practical implications of this phenomenon relates to rest periods in the laboratory to assess the healing rates and the actual healing ability of the asphalt pavement. Mobility of the bitumen is thereby an important characteristic of the bitumen that affects the healing potential and should be determined. It can therefore be expected that enhancing the mobility of the bituminous phases will increase the healing rates and thus the pavement life time.

The configuration free energy potential of bitumen can be determined from the configuration free energy curves of the individual phases by assuming that in a certain composition only the phase with the lowest energy will exist. Equilibrium is then found when the chemical potential is homogeneous throughout the material. This does not, however, mean that the mass fraction has to be homogeneous. Inhomogeneous distribution of phase affects the ability for bitumen to transmit stresses through its matrix. Having knowledge about the bitumen configurational free energy potentials can therefore contribute to better predictions of the in-time evolution of its ability to transmit stresses and reduce damage propagation. Optimizing the bitumen phase diagrams to promote the

Atomic Force Microscopy to Characterize the Healing Potential of Asphaltic Materials 229

Jäger, A., Lackner, R., Eisenmenger-Sittner, Ch. & Blab, R. (2004). Identification of four

Jäger A., Lackner, R. & Stangl, K. (2007). Microscale Characterization of Bitumen–Back-

Kringos, N., Scarpas, A., Pauli, T. & Robertson, R. (2009b). A thermodynamic approach to

Kringos, N., Pauli, T., Schmets, A. & Scarpas, T. (2012). Demonstration of a New

Larsson, P.-L. & Carlsson, S. (1998). On Microindentation of Viscoelastic Polymers. *Polymer* 

Lee, E. H. & Radok, J. R. M. (1960). The contact problems for viscoelastic bodies. Journal of

Lesueur, D., Gerard, J.-F., Claudy, P., Létoffé, J.-M., Planche, J.-P. & Martin, D. (1996). A

Loeber, L., Sutton, O., Morel, J., Valleton, J.-M. & Muller, G. (1996). New direct observations

microscopy. *Journal of Microscopy*, Vol. 182, No. 1, pp. 32–39, ISSN 1365-2818 Loeber, L., Muller, G., Morel, J. & Sutton, O. (1998). Bitumen in colloidal science: a chemical,

Lu, X. & Redelius, P. (2006). Compositional and structural characterization of waxes isolated from bitumens. *Energy & fuels*, Vol. 20, No. 2, pp. 653-660, ISSN 0887-0624 Oliver, W. C. & Pharr, G. M. (1992). An Improved Technique For Determining Hardness and

*Journal of Materials Research*, Vol. 7, No. 6, pp. 1564-1583, ISSN 0884-2914 Oliver, W. C. & Pharr, G. M. (2003). Measurement of Hardness and Elastic Modulus by

Pauli, A.T. & Grimes, W. (2003). Surface morphological stability modeling of SHRP asphalts.

*ACS division of fuel chemistry preprints*, Vol. 48, No. 1, pp. 19-23

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*Pavement Design*. Vol. 5, pp. 9–24, ISSN 1468-0629

978-94-90284-04-6, Delf, The Netherlands, June 9-11, 2009

*Asphalt Paving Technologists*, Under review

Vol. 40, No. 5, pp. 813–836, ISSN 0148-6055

*preprints*, Vol. 46, No. 2, pp. 104-110

*Testing*, Vol. 17, No. 1, pp. 49-75, ISSN 0142-9418

415-55854-9, London

0016-2361

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Analysis of Viscoelastic Properties by Means of Nanoindentation. *International* 

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structural and rheological approach. *Fuel*, Vol. 77, No. 13, pp. 1443–1450, ISSN

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force microscopy investigation of SHRP asphalts. *ACS division of fuel chemistry* 

resilience for stress-endurance will therefore enhance the lifetime of the overall pavement. This means that molecular volumes, densities and solubility of the bitumen phases should be determined.

The surface free energy potential accounts for energy due to interfaces between the distinct phases. For diffuse interfaces this means that the free energy is dependent on both the local composition as well as its surroundings. In the developed healing model, the Cahn Hilliard approach is taken in which the generation and thicknesses of the interfaces depends on a gradient energy coefficient. Insight into the gradient energy coefficients of various bitumen would enable more accurate predictions into the evolution of damage and healing potential and would allow for an optimization of the long-term behaviour.

With the advent of more powerful experimental tools with better controlled environmental conditions, it is foreseen that future research will be able to accurately and more easily determine these parameter for bitumen. Research will continue to develop the predictive models and more insight into the fundamental parameters that influence the healing and damage resistance of bitumen will be generated. It can be envisioned that from this research, detailed databases with the most commonly used bitumen will be developed that can be included in future asphalt mixture and pavement design. Also, more detailed test procedures that would enable researchers and pavement engineers to measure these parameters for their own material will become available in the coming years.

## **9. References**


resilience for stress-endurance will therefore enhance the lifetime of the overall pavement. This means that molecular volumes, densities and solubility of the bitumen phases should

The surface free energy potential accounts for energy due to interfaces between the distinct phases. For diffuse interfaces this means that the free energy is dependent on both the local composition as well as its surroundings. In the developed healing model, the Cahn Hilliard approach is taken in which the generation and thicknesses of the interfaces depends on a gradient energy coefficient. Insight into the gradient energy coefficients of various bitumen would enable more accurate predictions into the evolution of damage and healing potential

With the advent of more powerful experimental tools with better controlled environmental conditions, it is foreseen that future research will be able to accurately and more easily determine these parameter for bitumen. Research will continue to develop the predictive models and more insight into the fundamental parameters that influence the healing and damage resistance of bitumen will be generated. It can be envisioned that from this research, detailed databases with the most commonly used bitumen will be developed that can be included in future asphalt mixture and pavement design. Also, more detailed test procedures that would enable researchers and pavement engineers to measure these

Andersson, M. & Nilsson, F. (1995). A perturbation method used for static contact and low

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de Moraes, M.B., Pereira, R.B., Simao, R.A., Leite, L.F.M. (2010). High temperature AFM

Giannnakopoulos, A. E. (2006). Elastic and Viscoelastic Indentation of Flat Surfaces by

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modeling. *Acta Materialia*, Vol. 55, No. 142, pp. 4015- 4039, ISSN 1359-6454 Graham, G. A. C. (1965). The contact problem in the linear theory of viscoelasticity. *International Journal of Engineering Sciences*, Vol. 3, No. 1, pp. 27-46, ISSN 0020-7225 Gunter, M. (2009). AFM Nanoindentation of Viscoelastic Materials with Large End-Radius

Hesp, S.A.M., Iliuta, S. & Shirokoff, J.W. (2007). Reversible aging in asphalt binders. *Energy* 

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velocity impact. *International Journal of Impact Engineering*, Vol. 16, No. 5, pp.759-

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and would allow for an optimization of the long-term behaviour.

parameters for their own material will become available in the coming years.

be determined.

**9. References** 

775, ISSN 0734-743X

46–53, ISSN 1365-2818

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**11** 

*France* 

**Atomic Force Microscopy – For Investigating** 

Textile fibers either natural or man-made (biodegradable and/or non biodegradable) are being increasingly used in non-traditional sectors such as technical textiles (automotive applications), medical textiles (e.g., implants, hygiene materials), geotextiles (reinforcement of embankments), agrotextiles (textiles for crop protection), and protective clothing (e.g., heat and radiation protection for fire fighter, bulletproof vests, and spacesuits).Textile structures (roving, knitted, woven or non woven) are also being increasingly used in textile

Surface treatments of textile fibers, yarns or fabrics play an important role in their processing and end-use. The AFM-Atomic Force Microscopy seems a very valuable tool for investigating the effect of different fiber surface treatments and their impact on the final textile material properties. The AFM probe has been used to understand the frictional behaviour of sized glass fibers, and to study the impact of an air-atmospheric plasma

Glass fibers, generally used to reinforce composite materials, readily suffer abrasion damage due to friction when glass filaments slide against each other. In manufacturing, glass fibers are coated with a size consisting of a coupling agent, a lubricant, a film former and other additives. While the coupling agent is used to increase adhesion between the fibers and the matrix, in glass fiber reinforced composite materials (P.Plueddeman, 1982), the complete size should improve the frictional performance of contacting fibers surfaces during their processing and their uses (e.g.: spinning, weaving...). With the increasing demand for good sizing agents which have low friction values, it is important to study the frictional behavior of sized fibers.

The frictional properties of polymer fibers deviate from the classical Amonton law. For polymers and fibers which are viscoelastic materials, the friction coefficient 'µ' depends on

**PART I: Use of AFM/LFM tool for friction analysis of sized glass fibers** 

**1. Introduction** 

reinforced composites.

**1. Introduction** 

treatment on polyethylene terephthalate fabrics

**1.1 Theoretical background of frictional properties of fibers** 

**Surface Treatment of Textile Fibers** 

*Univ Lille Nord de France, USTL, F-59655, Villeneuve d'Ascq Cedex* 

Nemeshwaree Behary and Anne Perwuelz *ENSAIT-GEMTEX : ENSAIT, GEMTEX, Roubaix* 

