Role of fibre–matrix interface and fibre direction on dielectric behaviour of epoxy composites

COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 64 (2004) 1467–1475 www.elsevier.com/locate/compscitech

Role of fibre–matrix interface and fibre direction on dielectric behaviour of epoxy composites B. Kchaou

a,b

, C. Turki c, M. Salvia b, Z. Fakhfakh a, D. Treheux

b,*

a

b

Laboratoire des Materiaux Composites Ceramiques et Polymeres, Faculte des Sciences de Sfax(3018), Tunisia  Laboratoire Ingenierie et Fonctionnalisation des Surfaces, UMR 5621, Ecole Centrale de Lyon, 69134 Ecully Cedex, France c  LASEM, Ecole Nationale dÕIngenieurs de Sfax, 3018 Sfax, Tunisia Received 27 January 2003; received in revised form 27 October 2003; accepted 28 October 2003 Available online 23 January 2004

Abstract The aim of this paper is to show the influence of fibres and fibre orientation on dielectric behaviour of glass fibre reinforced polymer. The Scanning Electron Microscope Mirror Effect (SEMME) associated with the Ground Current measurement were used to determine the ability of trapping and motion of electric charges inside insulating materials. The role of the fibre/matrix interface nature seems to be essential for either trapping or diffusion of charges and consequently for localisation or spreading of stored polarisation energy which can induce, from the mechanical point of view, brittleness of interface.
2004 Elsevier Ltd. All rights reserved. Keywords: Glass Fibre Reinforced Polymer

1. Introduction Polymeric materials are widely used because of their good dielectric or mechanical properties. Nevertheless, the durability of insulating materials is linked to the presence of trapped electric charges. Storage and transport of these charges are related to their trapping and detrapping process [1]. Indeed, it was confirmed that the breakdown [2,3] fracture and wear [3–5] are the consequence of dielectric relaxation which follows charge detrapping. The concept of polaronic conduction introduced by Mott [6] allows us to explain the conduction of charge and the mechanisms of electric charges trapping in insulating materials. If the local variation of the dielectric susceptibility (caused by point defects, distortion of lattice, extended defects, etc.) is sufficiently large, charges could be trapped in the lattice which will be distorted *

Corresponding author. Present address: Ingenierie et Fonctionnalisation des Surfaces, UMR CNRS 5621, Ecole Centrale de Lyon, BP 163, 69131 Ecully Cedex, France. Tel.: +33-4-72186433; fax: +33-478331140. E-mail address: [email protected] (D. Treheux). 0266-3538/$ - see front matter
2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2003.10.016

and polarised [1,7]. The charge and the associated charge of polarisation are called polaron [6]. From the physical point of view, disorder in solid insulator produces a kind of localised states, called Anderson states [8,9], located in the conduction and valence band tails. In this way, topological disorders cause a weak localisation which results in the momentary capture of a charge in a given site. Energy bandwidth of localised states depends on the degree of disorder: the more considerable the disorder is, the wider the localised states bandwidth is. On the other hand, impurity or dopant can induce an impurity level in the band gap. Consequently, an impurity band of a certain width would be formed. A strong localisation, resulting from chemical species, interfaces and structural defects, causes the complete stabilisation of a charge on a site, i.e., trapping site. Only states lying in the impurity band can really trap charges. One of the important consequences of this localisation is that an electron can move from an impurity state to another only by exchanging energy (phonon). Typically, weak localisation affects the mobility of charges whereas strong localisation can affect the

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trapping properties of the dielectric. This hierarchy of localisation provides a way to understand both conduction and trapping properties of the dielectric [10]. The strong localisation of charge induced an increase in energy. The mechanical energy corresponding to the trapping was estimated to be 5 eV/trapped charge [1,10]. The release of this energy can induce catastrophic effects as breakdown, fracture, wear [2–5]. This approach has been applied successfully for ceramics or polymers, but, to our knowledge, this study is the first concerning polymer composites.

2. Materials In this work, two kinds of unidirectional (UD) epoxy composites were studied. These two materials differ only in the nature of the fibre/matrix interface. The materials were obtained from DGEBA/DDM (Epikote 828/HT 972) resin and continuous E glass fibres using Filament Winding at the VETROTEX International Company (Chambery, France) in collaboration with the Shell Research Laboratory (Amsterdam, Netherlands). Glass fibres were coated with an epoxy specific sizing (EP), (composite I), or with a multipurpose sizing suitable for use with epoxy, vinylester and polyester resins (MP), (composite II). The EP sizing contained a silane coupling agent and is specially designed for enhancing the fatigue behaviour. In the two cases, the sizing was in the range 0.5–0.8 of the whole mass of fibre, corresponding to a layer of about 80 nm [11–15]. The fibre volume fraction and density of composites were determined by matrix burn off method. These parameters are calculated using qf ¼ 2:56 g/cm3 , for fibre density and qm ¼ 1:24 g/cm3 for epoxy matrix density (Table 1). The fibre distribution is homogeneous as shown in Fig. 1. Torsion dynamic spectrometry (Metravib system) was performed on the neat epoxy resin and on the two composites at 1 Hz frequency, in the temperature range )180 C; +150 C (Fig. 2). For the three materials, the a relaxation associated with the glass transition more or less occurs at the same temperature (about 180 C). Nevertheless a light decrease, probably due to the subreticulation of the matrix in presence of fibres, is observed for the two composites in comparison with pure matrix. Other classical relaxations b (at about )50 C) and x (at 80 C) are observed too.

Table 1 density and fibre volume (Vf %) content of composites Reference

Density of composite

Vf (%)

Composite I ( EP) Composite II (MP)

1.86 1.83

47.0 45.6

Fig. 1. Micrographic observation (SEM) of the distribution of fibres for the two composites.

1

log(tang(δ))

0,1

Composite I ( EP) Neat matrix

0,01

Composite II (MP) 0,001 - 250

-200

-150

-100

-50

0

5

100

150

200

250

temperature (˚C)

Fig. 2. Torsion dynamic spectrometry: variation of the mechanical loss, log(tan (d)), for the neat matrix and the two composites versus temperature (f ¼ 1 Hz).

The main mechanical properties of the two composites were determined under three-point flexural testing with a constant cross-head speed of 2 mm/min (NFT 57–105 standard). The samples were about 100 mm long, 10 mm width, and 2 mm thick. The span to depth ratio is equal to about 20 in order to minimize shear contribution. Table 2 gives the values of the YoungÕs modulus E, flexural failure stress (rf ) and flexural failure strain (ef ) for the two composites.

B. Kchaou et al. / Composites Science and Technology 64 (2004) 1467–1475 Table 2 Mechanical properties of tested composites materials (scattering 5%) Materials

E (Gpa)

rf (MPa)

ef (%)

Composite I (EP) Composite II (MP)

34.1 34.6

1200 1170

3.70 3.50

E, apparent flexural modulus, rf , flexural failure stress, ef , flexural failure strain.

Fig. 3. Failure feature micrograph (SEM) after flexural testing. (a) Composite I EP; (b) composite II MP.

While the monotonic mechanical properties are slightly higher for composite I, the failure feature SEM analysis shows better fibre–matrix interface strength (si ) for the EP sizing. In this case the failure process involves mainly cohesive phenomena. This is indicated by matrix debris on the fibre (Fig. 3(a)). For MP sizing, the failure feature displays many bare fibres (Fig. 3(b)). This difference is confirmed and quantified by micro-indentation technique; so the shear stress ratio si (composite I EP) to si (composite II MP) is equal to 1.14 [15]. This improved interface shear strength led to a significantly better fatigue behaviour as shown previously using three-point bending fatigue tests performed under deflection control. For the composite EP, the fatigue-life expectancy is about a decade greater than that of composite MP [13].

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based on two complementary methods using a SEM (LEO 440): the Scanning Electron Microscope Mirror Effect (SEMME) method [16] and the absorbed current method [17]. These methods have been applied to any insulating material, that is ceramic and polymer and allow us to know the ability of insulator to trap or diffuse electric charges. The principle is the following: the insulating sample is irradiated in a SEM at high voltage (30 kV). The total amount of electrons Qi injected in the sample is perfectly controlled by using a beam blanking device. Injection times (tinj ) are about 50, 100 and 200 ms corresponding, respectively, to Qi ¼ 50, 100, 200 pC injected electrons. In our experiments, using a focused electron beam, the analysed volume corresponds to about 1 lm laterally and 8 lm deep. During injection of electrons, ground current Ig can be recorded (Fig. 4). In fact, during injection, according to the electromagnetic laws, a positive electric charge appears in all conductor pieces of the SEM chamber (mainly in gun and in the sample holder). This induction charge QIC vary with the charges trapped or distributed in the sample. The created positive charge corresponds to an electron flux going from conductor pieces towards the ground. The corresponding ground current Ig can be collected using a pico-ammeter. It is directly related to the evolution of the quantity of charges: Ig ¼ aðdQIC =dtÞ, where a is a corrective factor depending on the SEM chamber characteristics, including induction charges in other metallic pieces of the SEM chamber [17]. In our experimental conditions a can be estimated to be 0.93. The evolution of Ig during injection (Fig. 5) gives information on the different steps of diffusion or trapping of charges present in the insulating sample. Different parameters can be deduced from this curve (Fig. 5): Imax , initial current, informs on the response of material without any perturbation; QIC , quantity of charges distributed in the sample. Sometimes, relaxation of charges (Fig. 5(b)), associated with secondary electron emission, occurs giving information on: Qr , quantity of charges distributed in

3. SEMME technique The use of electron beam inside Scanning Electron Microscope (SEM) can exhibit different aspects of the material properties and particularly among them trapping properties. Our dielectric characterisation was

Fig. 4. Schematic representation of the induction charge measurement: Ip , primary intensity; Ir , secondary electron emission; Ig , ground current due to induction charges.

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Imax 100 0

1300

Ig(pA)

Imax

Qr Ig(pA) 50 0

800

0 -20 0

300

0 -50 0

-50

(a)

-200

0

50

QIC

100

150

200

40 0

tr

600

time (ms)

200

time (ms)

(b)

-100 0

Fig. 5. Different parameters deduced from the ground current curve Ig ¼ f(times) (a) curve without relaxation, (b) curve presenting a lot of charge relaxations associated with secondary emission.

the sample before the first relaxation; tr , time of the first relaxation. The second step is the formation of the mirror image. Negative charges Qt locally trapped and stabilised in the insulator during the injection produce an electrical field in the vacuum chamber of the SEM. If the sample is observed later with a lower energy electron beam (V ¼ 100–1500 eV), the electrical field can be strong enough to deflect the electrons in the same manner as a convex mirror does with light. Consequently, a mirror image is given on the screen which displays a distorted view of the SEM chamber (Fig. 6(a) and (b)). The amount Qt of trapped and stabilized charges is calculated using an electrostatic law, established by Vallayer [16,18], relating the real diameter dÕ of the last output diaphragm and the apparent one d measured on the mirror image (Fig. 6(b)):

1 4L V ¼ 0 d d AQt

ð1Þ

with L, the working distance of the SEM; A, parameter dependent on SEM chamber and permittivity of the sample and V, acceleration potential of the electron beam. For low potentials the curve 1=d ¼ f ðV Þ (Fig. 7) shows a quasi linear part (part 1) and a curved part for higher potentials (part 2). The quantity of trapped charge Qt can be deduced from the slope of the linear part. For higher values of potential V (part 2), two types of deviation from the initial straight line were observed. A curvature directed downwards proves a lateral spreading of charges and an opposite curvature proves a deep spreading of charges [16,19]. The mirror image disap-

Fig. 6. SEMME method: (a) Schematic diagram of the principle of SEM measurement. First charges are injected in the insulating sample; second, the sample is observed with a low energetic electron beam whose electrons are deviated by the electrostatic field due to the stabilised trapped charges (Qt ). Electrons 1 go back in the electron beam and give the central black disk in (b). Electrons 2 are reflected by the microscope chamber and give an image of its walls (mirror image, (b)). Electrons 3 are just deviated by the trapped charge and give a distorted image of the sample.

B. Kchaou et al. / Composites Science and Technology 64 (2004) 1467–1475

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Fig. 7. Curve 1=d vs. lecture potential V . The curve presents a linear part I which permits to determine the quantity of trapped charges Qt .

4. Results and discussion 4.1. Experimental procedure Samples were parallelepipedic, (10
10 mm and 3 mm thick). The injection of electrons is performed at high voltage (30 kV), at room temperature, during 50, 100 and 200 ms, corresponding to 50, 100, 200 pC injected electrons. Each sample has been ultrasonic washed in ethanol and dried before its introduction in vacuum chamber. Ig (pA)

1500

M

tinj = 100 ms

CI

1000

Fig. 8. Orientation of the electron beam in relation to fibre direction: (1) perpendicular injection noted ð?Þ; (2) Parallel injection.

To understand the role of fibres and fibre/matrix interfaces, the injection of electron was achieved following two different orientations (Fig. 8). 1. In the first case: electron beam was perpendicular to the fibre direction (?Þ. 2. In the second case: electron beam was parallel to the fibre direction (k). To evaluate the reproducibility, each experiment was carried out at least three times. The experimental scattering concerning the determination of quantities of charges (Qt , QIC ) is less than 5%. 4.2. Dielectric behaviour of matrix and composite I and II (perpendicular injection) Ground current curves Ig ¼ f(time) are presented in Fig. 9, for the three studied sample. The duration of the Ig(pA)

pears for a potential Vd and charges could be detrapped by the electron beam. To conclude, both evolutions of the ground current curves and ‘‘Mirror effect’’ give informations about localisation, diffusion, and stability of trapped charges into the dielectric material. Especially, the ratio Qt /QIC represents the capacity of material to diffuse the charges in the bulk: if Qt /QIC tends toward 1, the charges are stabilised and the trapping is total; if Qt /QIC tends toward 0, the charges distributed in the sample during the injection diffuse and consequently are not stabilised.

1500

M 1000

500

0 0

50

100

150

200

-500

-100

0

-1500

100

200

300

400

500

-500 times (ms)

-1000

CI

500

0 -50

tinj = 200 ms

C II

times (ms) -1000 -1500

Fig. 9. Ground current curves Ig vs. time for neat matrix, composite I and II recorded during 100 and 200 ms injection times. Relaxations are observed at 72 ms for composite II, 113 ms for composite I and 168 ms for matrix.

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injection is fixed first at 100 ms then at 200 ms, for the given examples. The response of samples facing the injected charges only is similar at the beginning of the injection (t < 50 ms) but changes later. The ground current is decreasing more for the two composites compared to the pure matrix, and relaxation phenomenon occurs at 72 ms for (CII), at 113 ms for (CI) and at 168 ms for matrix (M). At that time the material reaches a critical density of trapped charges and electrons will be re-emitted in the vacuum. The relaxation time can be explained by the aptitude of material to spread trapped charges, inducing the decrease in the polarisation field which is linked to the local polarisation energy. This field seems to be responsible for detrapping phenomenon. Observation of specimen at low voltage, after a short injection time (tinj ¼ 50 ms), presents a mirror effect and confirms the high quantity of stabilised trapped charges. Mirror curve 1=d ¼ f ðV Þ for two injection times (50 and 100 ms), for the same samples, are shown in Fig. 10. The rapid disappearance of mirror effect for composite II (Vd ¼ 300 V for 50 ms), in accordance with a rapid relaxation at 72 ms, is due to the instability of trapped charges, contrary to composite I and epoxy matrix.

In addition, lateral spreading of trapped charges in pure matrix is proved by the appearance of down concave of the mirror curve (Fig. 10) while composites I and II give linear law as far as the detrapping of trapped charges. Table 3 summarizes the main parameters deduced from the different ground current curves and mirror experiments for ? injection. For 50 ms injection time, the QIC and stabilised trapped charges Qt are of the same order. Consequently it is interesting that the majority of charges (QIC ) distributed in the sample are trapped: Qt /QIC is roughly equal to one. For all materials a large part of electrons is immediately kept in the sample (Imax : high). This phenomenon blocks the incoming electrons and the ground current decreases progressively. At the beginning (t < 50 ms), for the three materials, the decrease is low but the trapping is high (Qt /Qi ¼ 0.8, Qt /QIC ¼ 1). For longer times, the trapping remains high for matrix, but decreases for composite I (Qt /Qi ¼ 0.57; Qt /QIC ¼ 0.87) and composite II which presents relaxations confirming a tendency to a significant diffusion of charges in the composite samples.

tinj = 50 ms

300

M

CI

CI

200 -1

1/d (mm )

CII

200

-1

1/d (mm )

250

tinj = 100 ms

250

M

150 100

150 100 50

50 0

0

0

2000 4000 potential (V)

6000

0

2000

4000 potential (V)

6000

8000

Fig. 10. Curve 1=d vs. lecture potential V for matrix and composite I and II. Only a linear part is observed for composites, contrary to the matrix which presents a deviation in the part II. No mirror has been measured for composite II, at 100 ms injection time, because relaxation of charges at 72 ms.

Table 3 Main parameters deduced from the different ground current curves and mirror experiments tinj (ms)

Samples

Imax (pA)

QIC (pC)

Qr (pC)

tr (ms)

Qt (pC)

Vd (V)

Qt /QIC

50

Matrix Composite I (EP) Composite II (MP)

822 837.5 877

44 43 46

– – –

– – –

42 37 39

4500 2500 800

0.95 0.85 0.84

100

Matrix Composite I (EP) Composite II (MP)

831 801 785

85 76 –

– – 56

– – 72

75 57 –

6500 1800 –

0.88 0.75 –

200

Matrix Composite I (EP)

848 807

– –

120 75

168 113

– –

– –

– –

B. Kchaou et al. / Composites Science and Technology 64 (2004) 1467–1475 Ig (pA)

Ig (pA)

Composite I

100 0

⊥ 800 600

600 400

//

400

//

200

200

0 -20

Composite II

1000

⊥

800

1473

0

0

20

40

60

80

100

-20

0

20

40

60

80

1 00

time (ms)

time (ms)

Fig. 11. Ground current curves Ig vs. time for two injection directions ? and k (tinj ¼ 50 ms). 140 120

//

100

( ⊥) (⊥

Composite II tinj = 50 ms

-1

1/d (mm )

Consequently, the difference of dielectric behaviour of pure matrix and composites shows the role of fibres on trapping and diffusion phenomenon. To summarise: • The presence of fibre modifies the responses of epoxy beside the injection of charges. • The fibres induce instability of trapped charges: lower potential Vd , occurrence of the first relaxation tr early and lower ratio Qt /QIC . This effect is more pronounced for composite II compared to composite I. • Therefore, the two composites I and II only differ in their sizing. All different behaviours may be attributed to the sizing. • The role of interface nature obviously plays a role in the flow and trapping along interface. In fact, in perpendicular injection, the superficial layer of epoxy is first concerned with the electron beam and traps a high quantity of charges as shown by the pure matrix behaviour, which is similar to composite behaviour at the beginning of injection (t < 50 ms). Afterwards injected electrons reach fibres which favours both trapping and diffusion along matrix/fibre interface in a dynamical way dependent on the sizing type.

80 60 40 20 0 0

400 800 potential (V)

1200

Fig. 12. Curve 1=d vs. lecture potential V for two injection directions ? and k (composite II). No mirror was observed for composite I.

Conversely, for composite II, parallel injection leads to a stable mirror effect (Fig. 12) but the mirror curve presents a curvature directed upwards, proving diffusion and trapping of charges parallel to the injection direction, that is along the fibres. When the injection time increases (100 ms) the relaxation phenomenon only occurs at tr ¼ 73 ms for

To confirm the precedent results, injection of charges can be performed parallel (k) to the fibres (see Fig. 8). In this case, the electron beam impacts both matrix and fibres. The Fig. 11 presents the curve Ig ¼ f(time) for the two injection modes. The injection time is 50 ms (Qi ¼ 50 pC). In parallel injection (k) to the glass fibres, the slope of curve is very pronounced at the beginning, compared to (?Þ injection, for which a plateau is obvious. On the other hand, for composite I, mirror effect disappears speedily for parallel injection (Vd < 0300 V) compared to (?Þ injection which presents a stable mirror effect (see Fig. 10).

Ig (pA)

4.3. Effect of fibre orientation 900 C II (//)

500 100 -50 -300 0 -700

50

100

150 C I (//)

200

times (ms)

-1100 -1500 Fig. 13. Ground current curves Ig vs. time (tinj ¼ 100 ms) for composites (k injection). Relaxation occurs at 73 ms for composite I.

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Table 4 Main parameters deduced from the different ground current curves and mirror experiments for composites (k and ? injection comparison) tinj (ms) Composite CI (EP)

Composite CII (MP)

Injection

Imax (pA)

QIC (pC)

Qr (pC)

tr (ms)

Qt (pC)

Vd (V)

Qt /QIC

50

Perpendicular Parallel

837.5 552

43 19

– –

– –

36.5 –

2500 300

0.85 –

100

Perpendicular Parallel

801 743

76

– 32

– 73

57.5 –

1800 –

0.76 –

50

Perpendicular Parallel

877 635

46 26

– –

– –

39 25.5

800 1000

0.84 0.98

100

Perpendicular Parallel

785 615

51

56 –

72 –

– 51

– 1000

– 1.00

composite I, in parallel injection. Whereas no relaxation is detectable for composite II (Fig. 13) From Imax and QIC values (Table 4), it is obvious that the capacity to retain the charges is lower in the case of parallel injection. In fact, for perpendicular injection, the electron beam impacts primarily the matrix which presents a high capacity to trap charges (see Table 3), contrary to parallel injection for which injection concerns both matrix and glass fibres. In comparison, for k injection both composite I and II present a driving of charges along fibres. But, for composite I, diffusion takes place, linked to a low trapping (unstable mirror, Vd < 300 V and/or relaxation of charges at tr ¼ 73 ms), contrary to composite II which is characterised by a strong and stable trapping (Qt / QIC ¼ 1, Vd ¼ 1000 V, Qt /Qi ¼ 0.5) without relaxation for t < 100 ms. Relaxation observed for perpendicular injection at 72 ms for composite II can be explained by a high localisation of charges in both matrix and fibre/ matrix interfaces inducing high polarisation field favouring sudden spreading of charges (see Table 4).

5. Conclusion This study brings to the fore the role of fibre–matrix interface nature on dielectric properties of composite materials. Intrinsically, epoxy matrix presents an high capacity to trap charges and fibres permit a diffusion of charges along fibre/matrix interface. For composite I this diffusion is not accompanied by significant trapping of charges along interfaces: the trapping, essentially remains located in the matrix. The injected charges spread more rapidly in the whole composite. In other words, the trapping sites are either filled or with a short life and polarisation energy is dispersed. From the mechanical s of view, this behaviour corresponds to higher interfacial shear stress si . and greater fatigue-life expectancy. On the opposite, for composite II, the trapping is effective both in matrix and in fibre/matrix interfaces,

inducing high localisation of polarisation energy along interfaces. The relaxation of the trapped charges can induce a ‘‘breakdown’’ close to the interface leading to fibre/matrix damaging (see Fig. 3). The same mechanism has been observed along grain boundaries of ceramics [2,4]. Consequently, the interfacial zone plays a considerable role in the trapping or diffusion of charges. High interface strength contributing to diffusion of charges in order to reduce the field of polarisation, linked to local polarisation energy, have to be prefer to obtain high properties by the dispersing of energy stored in the materials.

References [1] Blaise G, Le Gressus C. Charge trapping–detrapping processes on related breakdown phenomena. In: Latham RV, editor. HV vacuum insulation, basic concepts and technological practice. New York: Academic Press; 1995. p. 330–8. [2] Blaise G, Le Gressus C. Mise en evidence dÕun claquage des isolants associe a la destabilisation dÕune charge dÕespace localisee. C R Acad Sci Paris 1992;314(II):1017–24. [3] Le Gressus C. Flashover triggered by charge detrapping at dielectric at dielectric–vacuum interface. Supplement a la Revue Le Vide: science technique et application 1995;275:568–72. [4] Berriche Y, Vallayer J, Trabelsi R, Treheux D. Severe wear mechanisms in Al2 O3 –AlON ceramic composite. J Eur Ceram Soc 2000;20:1311–8. [5] Vallayer J, Pauhle O, Juve D, Vernet JM, Treheux D. Endommagement des materiaux isolants par effet de charges electriques. Materiaux et techniques 2000;7–8:15–9. [6] Mott NF. Metal–insulator transitions. London: Taylor & Francis; 1974. [7] Stoneham AM. Electronic and defect process in oxides, the polaron action. IEEE Trans Dielectr Electr Ins 1997;4:604–13. [8] Blaise G. Charge localisation and transport in disordered dielectric materials. J Electrostat 2001;50:69–89. [9] Blaise G. Fields and polarisation, conduction and charge trapping in insulating materials. Supplement de la revue- Le vide: science technique et application 1998;287:25–37. [10] Coudray C, Blaise G. Description microscopique de lÕenergie interne dÕun reseau cubique polarise par une charge piegee. Supplement de la revue- Le vide: science, technique et application 1995;275:170–6. [11] Turki C, Salvia M, Vincent L. Fretting maps of glass fiberreinforced composites. In: Chandra T, Dhingra AK, editors.

B. Kchaou et al. / Composites Science and Technology 64 (2004) 1467–1475

[12]

[13]

[14]

[15]

Proceedings of the Internatonal Conference on Advanced Composite materials 93, Wollolong, Australia. TMS: Warrendale, PA; 1993. p. 1419–24. Turki C, Chateauminois A, Salvia M, Vincent L. In: Miravete A, Lim TB, Velocity accommodation during GFRP/ metal fretting contacts, ICCM9, Madrid. Woodhead Publications: Cambridge, UK; 1993. p. 695–702. Salvia M, Vincent L. Modelling of flexural fatigue behaviour of UD glass fibre reinforced polymer (GFRP). Compos Sci Technol 1996;56:797–802. Veelen A. van Stamhuis J. Fracture behaviour of unidirectional glass fibre reinforced composites based on toughened epoxy resin systems. In: 1st International Conference on Deformation and Fracture of Composites, ed PRI. UMIST: Manchester, UK. 1991. p. 3/1–3/6. Toumi B, Salvia M, Carpentier L, Veauville O, Kapsa P, Vincent L. Microindentation technique for characterisation of fibre/matrix interfaces of fibre reinforced polymers. ECCM 6, Bordeaux 1993:145–50.

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[16] Vallayer B, Blaise G, Le Gressus C, Treheux D. Space charge measurement in a dielectric material after irradiation with a 30 kV electron beam: application to single-crystals oxide trapping properties. Rev Sci Instr 1999;70:3102–12. [17] Berroug A, Bigarre J, Fayeulle S, Treheux D. Charging effect under electron beam injection on sapphire implanted with zirconium ions. In: Conference on Electrical Insulation and Dielectric Phenomena CEIDP, IEEE annual report, 1997. p. 97–100. [18] Vallayer B. Modelisation of both electronic trajectories and electrical field distribution in the vacuum near a trapped charge implanted with an electron beam. Distribution in an insulating target and its relaxation in an electrostatic mirror experiment. Supplement revue- Le vide: science technique et application 1995;275:619–25. [19] Attard C, Damamme G, Ganachaud JP, Renoud R, Vicario E. Monte-Carlo simulation of the building up of a charge distribution in an insulating target and its relaxation in an electrostatic mirror experiment. Supplement revue- Le vide science, technique et application 1998;287:215–23.