Model systems for thermo-oxidised epoxy composite matrices

Composites: Part A 39 (2008) 1522–1529

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Model systems for thermo-oxidised epoxy composite matrices N. Rasoldier a, X. Colin a,*, J. Verdu a, M. Bocquet a, L. Olivier b, L. Chocinski-Arnault b, M.C. Lafarie-Frenot b a b

Arts et Métiers Paritech (UMR 8006), LIM, 151 Boulevard de l’Hopital, 75013 Paris, France ENSMA (UMR 6617), Laboratoire de Mécanique et Physique des Matériaux, BP 40109, 86961 Futuroscope-Chasseneuil Cedex, France

a r t i c l e

i n f o

Article history: Received 31 January 2008 Received in revised form 26 May 2008 Accepted 30 May 2008

Keywords: A. Epoxide resins D. Thermal oxidation B. Elastic properties A. Model networks B. Antiplasticization

a b s t r a c t This paper deals with the thermal oxidation of organic matrix composites, more precisely aromatic amine crosslinked epoxy resins (977-2 DGEBF-TGPAP-DDS) reinforced by carbon fibers. In this first part, it is tried to understand the effects of thermal oxidation on mechanical properties, emphasis being put on elastic and viscoelastic properties. It is shown that oxidation decreases the glass transition temperature, that results from predominant chain scission, but increases the glassy state elastic modulus. From quasistatic tensile testing, flexural and torsional dynamic testing (DMA) and ultrasonic measurement (5 MHz, 20 °C), it is shown that degradation affects essentially the amplitude of high temperature component of the sub-glass transition (internal antiplasticization). Model networks have been synthesized from amine and epoxy but in non-stoichiometric ratio. It is clearly shown that they display the same behaviour, that confirms the precedent interpretation. For the same crosslink density, the dangling chains concentration is higher in model than in degraded networks, but it remains of the same order of magnitude. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction It is now well established that, when exposed in air, at temperatures lower than the glass transition temperature (Tg), organic matrix composites (OMC) perish by thermo-oxidation of the matrix [1,2]. A key feature of this ageing process is that degradation is non-uniform in the sample thickness because oxidation is diffusion controlled. In the last years, there were many attempts to model degradation gradients in order to obtain a realistic description of OMC thermal ageing [3–7]. Certain of us contributed to this research with a kinetic model derived from a radical chain oxidation mechanism, including reaction–diffusion coupling [8–10]. In its present form, this model predicts, at every time t, for every elementary thickness layer at the distance x from the surface, various quantities among which: weight variation (even in cases where it is non-monotonic) [9] and atomic composition from which the density variation can be estimated [10]. The knowledge of weight change and density variation allows to determine the volume change (generally, oxidation induces a shrinkage [11]), which is expected to generate a stress state. But this latter can be predicted only if local mechanical properties are known. The objective of this work is to try to establish a relationship between the local structural state of a degradation network and the corresponding mechanical properties. Two directions will be

* Corresponding author. Tel.: +33 1 44 24 61 47; fax: +33 1 44 24 62 90. E-mail address: [email protected] (X. Colin). 1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2008.05.016

simultaneously investigated: (i) The mechanical characterisation of oxidized epoxy networks, (ii) the physical and mechanical characterization of networks of well-controlled structure, modelling oxidized ones. In the case where both investigations would lead to converging results, it would become possible to extend the kinetic model to the prediction of local mechanical properties, i.e., to make a decisive step towards the prediction of OMC failure. In this paper, the investigation field will be limited to unreinforced aromatic diepoxide–aromatic diamine matrices of the diglycicyl ether of bisphenol A (DGEBA)–diaminodiphenylsulfone (DDS) type and to viscoelastic properties. Thermal oxidation of such aromatic epoxide–amine networks is localized on the propanol moeity of which the radical reactivity is considerably higher than aromatic ones. According to Korcek et al. [12], the relative reactivities represented by the propagation rate constant would be at 30 °C: 4  102 l mol1 s1 for aliphatic CH bonds belonging to the propanol unit, 6  104 l mol1 s1 for CH bonds belonging to methyl groups of the DGEBA isopropyledene unit and 2  108 l mol1 s1 for CH bonds of aromatic nuclei. Since the activation energies vary in the same way, the reactivity ratios are expected to increase with temperature. In other words, oxidative attack is highly selective and concerns only the propanol unit. In DGEBA–DDS systems, where the electron density on nitrogen is relatively low, owing to the electron withdrawing effect of the sulfone bridge [13], the a amino methylene (Cc) is expected to be relatively stable, so that most of the propagation events are expected to occur essentially on the Ca or Cb carbons:

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Fig. 2. Schematization of a dangling chain in a network based on epoxide excess (e, unreacted epoxide group).

Their oxidation must lead to hydroperoxides:

Both hydroperoxides are relatively unstable owing to the presence of an electronegative heteroatom in a position (oxygen in both cases). Their decomposition leads to an alkoxy radical of which the ability to undergo b scission, i.e., here chain scission, is well known. Crosslinking would result only from radical coupling but even in conditions (radiochemical initiation at low temperature) where it would be favoured it is negligible relatively to chain scission [14]. Finally, the oxidation effect on network structure can be schematized by Fig. 1. Each chain scission leads to the disappearance of three elastically active chains [15] and gives one bulky and one short dangling chains. The scheme of Fig. 1 suggests that epoxide–amine networks with an epoxide excess could be interesting models of degraded stoichiometric networks since the concentration of elastically active chains is a decreasing function of the concentration of excess epoxides, these latter being the terminal groups of bulky dangling chains (Fig. 2). After a short investigation aimed to establish the trends of the effect of thermal oxidation on viscoelastic properties of stoichiometric epoxide–amine networks of the DGEBA–DDS type, we will try to determine if samples based on same monomers but with various values of epoxide excess, can be considered as good models of stoichiometric network with various degrees of oxidative degradation. 2. Experimental 2.1. Materials The experiments were performed using DGEBA (diglycidylether of bisphenol A) and DDS (diamino diphenyl sulfone) with various ratios of those monomers (especially epoxy excess) for simulating the consequence of oxidation. The specimens were made as follows: The monomers were blended at 150 °C in an oil bath during a half an hour. Then the mixture was degassed under vacuum at the same temperature. Afterwards, it was cast into a mould and cured during one hour at 170 °C and then during 2 h (maximum

Fig. 1. Schematization of a chain scission occurring on a propanol unit.

duration) at 210 °C in a ventilated oven. Finally, the specimens were striped and corrected by machining and polishing. Besides, the moulds had different shapes: (i) Bars for DMA testing: 3  10  40 mm3 for torsion testing and 1  10  35 mm3 for flexural testing. (ii) Plates for ultrasonic testing: 5  30  60 mm3. (iii) Little samples were cut to realise DSC testing: 15 mg. (iv) Dogbone specimens for tensile testing (Fig. 3).

2.2. Test conditions and characterization We proceeded at two kinds of DMA testing: torsiometry with a Rheometric Scientific RDA III and single cantilever flexural mode with a TA Instruments Q800. Both tests were performed at 1 Hz. Torsiometry measurements were done with a 0.05% strain amplitude between 30 and 250 °C with a 5 °C min1 temperature ramp. Flexural tests were done with a 0.02% strain amplitude, between 150 and 250 °C and with a temperature ramp of 2 °C min1. The curves gave loss and storage moduli and allowed to measure transition temperatures: Ta (associated to the glass transition temperature T g to which it will be assimilated in the following) and Tb. Tg values will be reported in the ‘‘results” section (Table 2). Torsion values are slightly lower than ‘‘flexural” ones. This difference (1.8% in average) is not surprising owing to multiple causes: difference in strain amplitude, temperature ramp, distinct sample series, etc. Tg was also obtained by using DSC thermograms obtained with a TA Instruments Q10-0553. DSC values are very close to DMA flexural values, the difference being generally of the order of measurement incertitudes. In all the cases, Tg is taken at the inflection point of the curve. Ultrasonic measurements were made on specimens immersed in a tank containing water at room temperature (20 °C). The transducers (transmitter one and receiver one) have a frequency of 5 MHz. Elastic properties (Young’s modulus Eu, shear modulus Gu, bulk modulus Ku, Poisson’s ratio lu, u subscript standing for ultrasonic method of identification) were calculated from the following equations [16]:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eu ð1  lu Þ VL ¼ ; q ð1 þ lu Þð1  2lu Þ

Fig. 3. Tensile specimen.

ð1Þ

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VT ¼

N. Rasoldier et al. / Composites: Part A 39 (2008) 1522–1529

sffiffiffiffiffiffi Gu

;

ð2Þ

Gu ¼

Eu ; 2ð1 þ lu Þ

ð3Þ

Ku ¼

Gu Eu ; 9Gu  3Eu

ð4Þ

q

where VL and VT were the longitudinal and the shear wave velocities measured with an oscilloscope and q the density measured by pycnometry. Besides, tensile testing was conducted by using an Instron 4502 device at room temperature with a 1.67  102 s1 strain rate. An extensometer with an initial length of 10 mm was used to measure the longitudinal strain. 3. Results 3.1. Oxidation effect on viscoelastic properties Parallelepipedic samples of 17.5  10  1 mm3 of fully cured stoichiometric 977-2 resin (preliminarily dried under vacuum 15 days at 100 °C) have been exposed at 150 °C under 0.5 MPa pure oxygen pressure ie at an O2 pressure about 25 times higher than in air, in order to increase the thickness of the oxidized layer. After ageing, the samples were analyzed by dynamic mechanical analysis (DMA) at 1 Hz frequency, with a temperature ramp of 2 °C min1, in single cantilever flexural mode, in order to have the maximum sensitivity to modulus changes in superficial layers. For the exposure conditions under consideration, especially the high oxygen pressure, the kinetic analysis [8–11] predicts the existence of quasi homogeneously oxidized, superficial layers separated by a thin, less oxidized, core zone. The fact that no splitting and, even, no significant broadening of the glass transition interval was observed, indicates that the curves of Fig. 4 are characteristic of superficial layers and can be reasonably related to the extent of oxidation. Indeed, these assumptions would lack their validity for thicker samples or for exposures at lower oxygen pressures. These latter cases are now under investigation.

The modulus–temperature curves are shown in Fig. 4. Two ‘‘isobestic” points: T1 at 60 °C and T2 at 170 °C allow to define three temperature domains. At T < T1, i.e., below the b transition, the modulus decreases with ageing time. This domain will be called domain (I). At T1 < T < T2, i.e., schematically between Tb and Tg, the modulus increases with ageing time. This domain will be called domain (II). At T > T2, i.e., in domain (III), the most striking feature is the decrease of the transition temperature Tg with ageing time. Tg has been plotted against exposure time at 150 °C in Fig. 5. The curve displays a pseudo-hyperbolic shape with an asymptote close to Tg1  450 K. A noticeable scatter can be observed in its initial part. Extreme values of the initial slope estimated from the points at 20 and 50 h, would be respectively 0.15 and 0.45 K h1. However, assuming a monotonic character for the curve, the true value would be closer to 0.45 K h1 than to 0.15 K h1. We will provisionally retain the value of 0.33 K h1 corresponding to the fit of Fig. 5, having in mind the need for a more precise determination. The decrease of Tg reveals the existence of a chain scission process. For a network having trifunctional crosslinks, the number m of elastically active strands varies with the number of chain scissions s according to

dm ds ¼ 3 dt dt

ð5Þ

(at low conversion when chain scissions in dangling chains are negligible). The Di Marzio’s theory [17] offers a relationship between Tg and the crosslink density x:

Tg ¼

T gl ; 1  KFx

ð6Þ

where Tgl represents the Tg of the linear polymer (without crosslink), K is an universal constant and F is a flex parameter. Since x ¼ 23 m and K  3

Tg ¼

T gl T gl ¼ : 1  23 KF m 1  2F m

ð7Þ

For a network of the DGEBA–DDS m0 = 3.1 mol kg1; F = 37 g mol1 [17], so that

7000 unoxidized 977-2 resin 18h 48h 96h 430h

Storage Modulus (MPa)

6000

5000

4000

3000

2000

1000

0 -150

(I)

-100

(II)

T1

-50

0

50

Temperature (ºC)

(III)

100

150

T2

200

Fig. 4. Flexural storage modulus (1 Hz) against temperature for the unoxidized and aged samples (see text).

250

type:

Tgl = 364 K,

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Glass transition temperature (K)

480

470

460

450

440 0

50

100

150

200

250

300

350

400

450

500

Exposure time in oxygen (h) Fig. 5. Glass transition temperature (assimilated to Ta (1 Hz)) against exposure time in oxygen (0.5 MPa) at 150 °C.

2FT gl dT g ðT g Þ2 ¼ ¼ 2F : dm T gl ð1  2F mÞ2 Thus,



dT g dm



0

ð8Þ

1

 46 K kg mol

dT g dT g dm dT g ds ¼ ¼ 3 dt dm dt dm dt ¼ 2:4  103 mol kg

1

thus 1

h :

  ds dt 0 ð9Þ

Then, linearizing s evolution for low exposure duration, after 18 h, the number of broken chains is: Ds  4.3  102 mol kg1, i.e., about 1.4% of initially present elastically active chains. Eqs. (7)–(9) loose their validity at higher conversions because: (i) Di Marzio’s relationship has been established for ideal networks, its validity for non-ideal networks of the type of degraded ones is not demonstrated. (ii) Anyhow, degradation must change the parameters Tgl and F. The hyperbolic shape of the curve Tg = f(t) results from at least three causes: (i) The mathematical form of Di Marzio’s equation (6). As a matter of fact, in the case where the rate of chain scission would be constant (s = kt), all the other parameters being unchanged, the curve would have the same shape but with an asymptote at Tg ? Tgl when t ? 1. (ii) The autoretardated character of chain scission kinetics, first because the whole oxidation process is autoretardated due to substrate consumption, second, because when the conversion increases, the probability to have chain scissions on dangling chains (i.e., without effect on Tg) increases. (iii) The probable increase of Tgl (which represents the copolymer effect of network strands [17]. As a matter of fact, oxidation destroys the softer segments of network and creates branched chains, that is expected to increase both Tgl and F. In domain (I), i.e., below Tb, elasticity is essentially governed by cohesion. The modulus decrease can be explained by the disappearance of group having an important contribution to cohesion. The first group which comes in mind is, indeed, the alcohol group which plays a key role through hydrogen bonding. It can disappear from direct attack, to be transformed into ketone, or from an indirect attack, for instance

Domain (II) is the most intriguing because the modulus increases whereas the crosslink density decreases. This phenomenon can be called ‘‘internal antiplasticization”. It is observed when a structure change induces a Tg decrease, for instance incomplete cure for a stoichiometric system [18], shift of the amine/epoxide ratio from stoichiometry [19,20] (see below), incorporation of monoamines as chain extenders [21], etc. The temperature variation of Young’s (or shear) modulus can be ascribed [22]:

  X T  EðTÞ ¼ E0 1  a DEi ; Tg i

ð10Þ

P where E0 is the modulus at 0 K, a is of the order of 0.5 and i DEi is the sum of modulus gaps corresponding to the transitions at temperatures lower than T. Here, considering that there is no other significant sub-glass transition than Tb:

  T  DEb EðTÞ ¼ E0 1  a Tg

at T b < T < T g :

ð11Þ

It can be checked that this relationship works well, in the vicinity of ambient temperature, taking E0 = 7000 MPa, a = 0.56 and

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DEb = 1300 MPa, for the unoxidized sample. In Fig. 4, the upper dashed line corresponds to the unrelaxed modulus:

  T E ¼ E0 1  a Tg and the lower dashed line corresponds to the relaxed modulus E(T), both for the unoxidized sample. A kinetic curve of modulus change, from the dynamic flexural test at ambient temperature, is shown in Fig. 6. DMA modulus values can carry noticeable systematic errors but the shape of the curve is, no doubt, well representative of ageing antiplasticization effects. After 430 h of exposure, the modulus at 20 °C attains 3843 MPa, whereas the unrelaxed modulus is of the order of 4120 MPa. b relaxation is not completely suppressed but, since E0 continues to decrease, E(Tamb) cannot go beyond far from 3843 MPa and, perhaps decreases at long term. 3.2. Model networks of degraded networks As proposed in the introduction, we will study the elastic and viscoelastic properties of DGEBA–DDS networks with various r = amine/epoxide ratio values ranging from 0.8 (epoxide excess) to 1.2 (amine excess).

It can be checked that an infinite network can be obtained connecting male and female functions. These CRU are valid, in principle, only for r values not very far from unity, where each unreacted epoxide (E0 ) or secondary amine (NH) is isolated from the others by many network strands. This representation can be considered sufficient to establish the global trends of structure–property relationships. It can be shown that, in case of epoxide excess (r < 1), the number i of repeat units in one network branch (Fig. 7) is given by

i¼

3r  2 : 4ð1  rÞ

And in case of amine excess (r > 1):

i¼

2r : 4ð1  rÞ

All the network elements can be counted, that leads to Table 1. Crosslink density values can be checked using rubber elasticity measurements made at 225 °C using the dynamic torsiometer at 1 Hz frequency and density measurement made at 20 °C by pycnometry. It is assumed that





q ¼ q0 exp AT 2g ½1 þ al ðT  T g Þ1

ð12Þ

with A = 27.6  108 K2, al = 6  104 K1 [23] so that

qð498 KÞ  0:96: qð293 KÞ

4. Network characteristics The network characteristics have been calculated from the constitutive repeat units (CRU) shown in Fig. 7.

ð13Þ

Small variations of A with r are neglected in a first approach.

3900

Storage Modulus at 293 K (Mpa)

3800

3700

3600

3500

3400

3300 0

50

100

150

200

250

300

350

400

450

Exposure time in oxygen (h) Fig. 6. Modulus obtained from a dynamic flexural test at 1 Hz, 20 °C against exposure time.

Fig. 7. CRU of diamine–diepoxide networks with an epoxide excess (left) or a diamine excess (right).

500

1527

N. Rasoldier et al. / Composites: Part A 39 (2008) 1522–1529 Table 1 Parameter (i), crosslink density (x), concentration of dangling chains (b), concentration of elastically active chains (m), molar mass of elastically active chains (Me) for the networks under study, as a function of the amine/epoxide (r) ratio r

i

x (mol kg1)

b (mol kg1)

m (mol kg1)

Me (kg mol1)

0.8 0.85 0.9 0.95 1 1.05 1.1 1.2

0.50 0.92 1.75 4.25 1 4.75 2.25 1.00

0.88 1.20 1.50 1.80 2.09 1.96 1.83 1.59

0.881 0.652 0.429 0.212 0 0 0 0

1.32 1.79 2.25 2.70 3.13 2.94 2.75 2.38

0.76 0.56 0.44 0.37 0.32 0.34 0.36 0.42

Glass transition temperatures Tg determined by DSC and a transition temperature (closely linked to Tg) determined by DMA (in torsion) are given in Table 2. Both values are in reasonable agreement. Tg is maximum at r = 1.05. We have calculated Tg using Di Marzio’s equation. The theoretical values are in agreement with DMA ones but the maximum lies at r = 1.00 rather than 1.05. There are many possible reasons to this small shift from theoretical stoichiometry, for instance the loss of a small DDS quantity by evaporation during the cure operations.

machined parallelepipedic plates. They were used with density values of Table 2 to calculate the unrelaxed elastic properties: bulk (Ku), shear (Gu) and Young’s (Eu) moduli, and Poisson’s ratio lu. The cohesive energy density ec was calculated from CRU, using Fedors group increments [24]. It is probably slightly underestimated for amine excess samples where the contribution of –NH– groups was considered equal to the ones, but the incidence of the error is negligible. The results are summarized in Table 3. Those results call for the following comments: (v) Elastic properties are close to previously reported ones [21]. (vi) The moduli increase slightly with r, as the cohesive energy density. (vii) The ratio bulk modulus/cohesive energy density is constant at ±2.5%. It is close to 11.0 against 11.5 previously found for a wide series of epoxy networks. (viii) According to Eqs. (10) and (11), the unrelaxed modulus is expected to be equal to about 4.62 GPa at 20 °C, which is not very far from the value of 5.20 GPa for the ultrasonic modulus.

6. Relaxed moduli

5. Unrelaxed (ultrasonic) elastic properties Propagation rates of ultrasonic (5 MHz) longitudinal and transversal waves were measured at ambient temperature on carefully

The strains were measured with a mechanical extensometer. The tensile Young’s modulus ET values are given in Table 4, where ultrasonic values are recalled.

Table 2 Rubbery shear modulus (G0 ), density (q), calculated and theoretical values of the concentration of elastically active network strands (mexp and mth), experimental (Tg DSC, Tg DMA in torsion, Tg DMA in flexion) and theoretical Tg as a function of the amine/epoxide ratio (r) r

G0 (498 K) (MPa)

q (293 K) (kg m3)

q (498 K) (kg m3)

mexp (mol kg1)

mth (mol kg1)

TgDSC (K)

TgDMAtorsion(K)

TgDMAflexural (K)

Tgth (K)

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.20

5.9 7.9 12.5 12.5 16.8 25.9 23.7 16.8

1233 1233 1234 1234 1235 1236 1237 1238

1121 1127 1141 1143 1152 1154 1153 1154

1.2 1.6 2.6 2.6 3.4 5.3 4.8 3.4

1.3 1.8 2.3 2.7 3.1 2.9 2.8 2.4

418 434 469 472 495 497 493 492

410 427 454 467 478 488 487 484

424 432 461 469 491 496 498 493

409 428 447 468 491 484 477 466

Table 3 Density (q), cohesive energy density (ec), unrelaxed elastic properties (lu, Gu, Eu, Ku measured at 5 MHz, 20 °C), and ratio bulk modulus/cohesive energy density (Ku/ec) as a function of the amine/epoxide ratio (r) r

q (kg m3)

ec (MPa)

lu

Gu (GPa)

Eu (GPa)

Ku (GPa)

Ku/ec (GPa)

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.20

1233 1233 1234 1234 1235 1236 1237 1238

568 575 584 592 599 600 600 601

0.37 0.37 0.37 0.37 0.37 0.36 0.36 0.37

1.8 1.9 1.9 1.9 1.9 1.9 2.0 1.9

5.0 5.1 5.2 5.2 5.3 5.3 5.3 5.3

6.4 6.4 6.4 6.5 6.5 6.5 6.4 6.5

11.3 11.1 11.0 10.9 10.8 10.8 10.7 10.9

Table 4 Tensile Young modulus ET, ultrasonic Young modulus Eu, E0DMA and G0DMA storage moduli (obtained in flexural and torsion mode, respectively), and viscoelasticity ratio uT as a function of the amine/epoxide ratio (r) r

ET (GPa)

Eu (GPa)

E0DMA flexural (GPa)

G0DMAtorsion (GPa)

Gu (GPa)

uT

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.20

3.4 3.4 3.3 3.2 3.1 3.1 3.0 3.0

5.0 5.1 5.2 5.2 5.3 5.3 5.3 5.3

3.8 3.6 3.4 3.2 3.0 3.1 3.1 3.1

1.3 1.2 1.1 1.2 1.1 1.1 1.1 0.9

1.8 1.9 1.9 1.9 1.9 1.9 2.0 1.9

0.33 0.34 0.37 0.38 0.41 0.42 0.43 0.43

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8000 7000

r = 0,8

Storage Modulus (MPa)

r = 0,9 6000

r =1 r = 1,1

5000

r = 1,2

4000 3000 2000 1000 0 -150

-100

-50

0

50

100

150

200

250

Temperature (ºC) Fig. 8. Flexural storage modulus E0DMA (1 Hz) against temperature for DGEBA–DDS samples for various amine/epoxide ratio (r).

Dynamic testing was performed at 1 Hz frequency in single cantilever mode. The flexural storage modulus–temperature curves are shown in Fig. 8. The storage modulus values at 20 °C determined from dynamic torsional testing at 1 Hz frequency are also given in Table 4. The most striking fact is that the quasi static (or low frequency) and ultrasonic moduli vary in opposite ways with r. This is, no doubt, a result of antiplasticization in non-stoichiometric samples, at least those containing an epoxide excess (r < 1). This effect, i.e., the inhibition of b motions and the resulting reduction of the modulus gap at Tb, can be characterized by the dimensionless ratio

uT ¼

Eu  Et ; Eu

u decreases regularly from r = 1.00 to r = 0.80, when the crosslink density (i.e., also Tg) decrease and the concentration of dangling chains increases. In the case of amine excess (r > 1), the effect of structural changes is less obvious. It is noteworthy that networks with a small amine excess are quasi ideal networks. The amine excess works as a chain extender, which is not the case for epoxide excess. 7. Discussion Thermally oxidised epoxy networks of the 977-2 resin undergo changes of their viscoelastic spectrum which can be clearly attributed to predominant chain scission (Tg decrease). This latter induces an internal antiplasticization phenomenon responsible for modulus increase at ambient temperature. Below the b transition (210 K at 1 Hz), the modulus decreases, that can be attributed to a decrease of cohesive energy density presumably due to the oxidative destruction of alcoholic groups. It seemed to us interesting to try to study model networks of oxidised ones starting from a well-known DGEBA–DDS system in which the structure can be relatively well controlled. Chain scissions are replaced by amine lack. The crosslink density can be varied in a controlled way from epoxide excess. Bulky dangling chains are introduced in concentrations increasing with the number of virtual chain scissions, as in degraded networks. Starting from a stoichiometric DGEBA–DDS system (r = 1, m = m0 = 3.13 mol kg1), we have calculated the number of chain scissions (sD) needed to obtain the same concentration of elasti-

Table 5 Characteristics of the model networks (mM) and (bM) r

mM (mol kg1)

bM (mol kg1)

sD (mol kg1)

bD (mol kg1)

0.80 0.85 0.90 0.95 1.00

1.3 1.8 2.3 2.7 3.1

0.88 0.65 0.43 0.21 0

0.60 0.45 0.29 0.14 0.00

0.60 0.45 0.29 0.14 0.00

Number of chain scissions on a stoichiometric network (sD) to obtain the same m value and corresponding bD value.

cally active strands as in non-stoichiometric, undegraded samples (mD = mM), and the corresponding concentration of dangling chains (bD), using the following relationships [25]:

m ¼ m0  3s; b ¼ s: The results are given in Table 5 The concentration in dangling chains (bD) would be lower, at same crosslink density, in degraded than in model networks (bM), but it remains of the same order (the ratio is 0.67 ± 0.01). The elastic and viscoelastic properties of model and degraded polymers are very similar. In fact, they depend essentially on three factors: cohesion, which affects essentially the low temperature behaviour, local (b) mobility, which affects essentially elastic properties between Tb and Tg, and crosslink density, which affects the high temperature behaviour: Tg and the rubber elasticity. All these factors vary in the same trend with the number of chain scissions in aged samples and virtual chain scissions in model networks. It remains now to establish the relationship between the number of chain scissions and elastic properties. In a first approach, empirical relationships could be established from above results. However, it would be better to have a non-empirical approach through a detailed analysis of antiplasticization phenomenon. This point is under investigation in our laboratories. 8. Conclusion The thermal oxidation, at 150 °C under 0.5 MPa oxygen pressure of a commercial (977-2) amine cured epoxy resin was studied by DMA. The main consequences of ageing were a decrease of Tg linked to predominant chain scission, and an increase of the glassy

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modulus at ambient temperature, attributed to an internal antiplasticization effect. It was tried to simulate these phenomena using model networks based on diepoxide (DGEBA)–diamine (DDS) combinations with various amine/epoxide molar ratios ranging from 0.8 to 1.2. Here, chain scissions are simulated by amine lack. These networks were characterized by DSC, DMA (1 Hz), tensile testing (20 °C, 1.67  102 s1) and ultrasonic measurements (5 MHz). these networks behave in the same way as degraded ones: their Tg decreases and their glassy modulus at 20 °C increases with the number of virtual chain scissions. It can be concluded that model networks are well representative of homogeneously degraded ones. Then, a theoretical correlation has been made between oxidized stoichiometric model resin and unoxidized non-stoichiometric model resin, via the concentration of elastically active strands. This result is all the more important than it will help to understand and model the effect of chain scissions induced by thermo-oxidation on elastic modulus variations. In the end, this should lead to a non-empirical model useful for modeling thermo-oxidation inside carbon/epoxy composites with finite element codes, and help to understand the damage initiation processes due to thermo-oxidation. Acknowledgements This work is part of the COMEDI program supported by the French Research National Agency (ANR), Dr. J. Cinquin from EADS IW is gratefully acknowledge for sample furniture.

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References [1] Favre JP, Levadoux H, Ochin T, Cinquin J. In: Baptiste D, Vautrin A, editors. Proceedings of JNC-10, vol. 1. Paris: AMAC; 1996. p. 205. [2] Lafarie-Frenot MC, Rouquie S, Ho NQ, Bellenger V. Composites A 2006;37(4):662. [3] Nelson JB. In: O’Brien TK, editor. ASTM-STP-813, 1983. p. 206. [4] Bowles KJ, Meyers A. In: Proceedings of the 31st international SAMPE symposium; 1986. p. 1285. [5] Salin JR, Seferis JC. J Appl Polym Sci 1996;62:1023. [6] Skontorp A, Wong MS, Wang SS. In: Proceedings of ICCM-10, vol. 4, Canada; 1995. p. 375. [7] Cunningham RA, Mc Manus HL. In: Proceedings of ASME-52; 1996. p. 353. [8] Colin X, Marais C, Verdu J. J Appl Polym Sci 2001;82:3918. [9] Colin X, Marais C, Verdu J. Polym Deg Stab 2002;78:545. [10] Colin X, Verdu J. Compos Sci Technol 2005;65:411. [11] Rouquie S, Lafarie-Frenot MC, Cinquin J, Colombaro AM. Compos Sci Technol 2005;65(3–4):403. [12] Korcek S, Chenier JBH, Howard JA, Ingold KU. Can J Chem 1972;50:2285. [13] Eichler J, Mleziva J. Makromol Chem 1971;19:31. [14] Devanne T, Bry A, Audouin L, Verdu J. Polymer 2005;46:229. [15] Pascault JP, Sautereau H, Verdu J, Williams RJJ. Thermosetting polymers. New York: Marcel Dekker; 2002. p. 436 [chapter 14]. [16] Stanford EG, Fearon JH. Progress in non-destructive testing, vol. 1. London: Heywood; 1958. [17] Di Marzio EA. J Res NBS 1964;68A:611. [18] Bellenger V, Morel E, Verdu J. J Polym Sci Polym Phys Ed 1987;B25:1219. [19] Venditti R, Gillham JK. J Appl Polym Sci 1996;56:1687. [20] Bellenger V, Dhaoui W, Verdu J, Boye J, Lacabanne C. Polymer Eng Sci 1990;30:321. [21] Morel E, Bellenger V, Bocquet M, Verdu J. J Mater Sci 1989;24:69. [22] Gilbert DG, Ashby MF, Beaumont PWR. J Mater Sci 1986;21:3194. [23] Tcharkhtchi A, Gouin E, Verdu J. J Polym Sci Polym Phys Ed 2000;38:537. [24] Van Krevelen DJ. Properties of polymers. 3rd ed. Amsterdam: Elsevier; 1990. [25] Pascault JP, Sautereau H, Verdu J, Williams RJJ. Thermosetting polymers. New York: Marcel Dekker; 2002. p. 316 [chapter 10].