Composites Science and Technology 84 (2013) 23–30
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Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
The effect of bulk-resin CNT-enrichment on damage and plasticity in shear-loaded laminated composites Isaac Aguilar Ventura, Gilles Lubineau ⇑ King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division, COHMAS Laboratory, Thuwal 23955-6900, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 31 January 2013 Received in revised form 30 April 2013 Accepted 2 May 2013 Available online 14 May 2013 Keywords: A. Carbon nanotubes A. Nanocomposites B. Mechanical properties C. Damage tolerance
a b s t r a c t One way to improve multi functionality of epoxy-based laminated composites is to dope the resin with carbon nanotubes. Many investigators have focused on the elastic and fracture behavior of such nanomodified polymers under tensile loading. Yet, in real structural applications, laminated composites can exhibit plasticity and progressive damage initiated mainly by shear loading. We investigated the damage and plasticity induced by the addition of carbon nanotubes to the matrix of a glass fiber/epoxy composite system. We characterized both the modified epoxy resin and the associated modified laminates using classical mesoscale analysis. We used dynamic mechanical analysis, scanning electron microscopy, atomic force microscopy and classical mechanical testing to characterize samples with different concentrations of nanofillers. Since the samples were prepared using the solvent evaporation technique, we also studied the influence of this process. We found that in addition to the global increase in elastic regime properties, the addition of carbon nanotubes also accelerates the damage process in both the bulk resin and its associated glass–fiber composite. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Traditionally, fiber reinforced polymers (FRPs) are used in structural applications due to their excellent mechanical behavior. Some applications also require that FRPs have outstanding electrical or thermal properties if they are intended to replace metallic materials with such properties. An example is the requirement of low electrical resistivity for electrical tomography based structural health monitoring [1] or the requirement of lightning protection in materials used to construct airplanes [2]. Glass fiber laminated composites are usually a poor conductor and these multifunctional properties must be introduced to the material. One promising option is through nano-enrichment. The addition of CNTs and other types of nanofillers to traditional composite materials has created a new type of composite referred to as multiscale or hierarchical composites. They are made of constituents embedded on the same matrix but whose dimensions are on completely different scales. Comprehensive reviews on multiscale and hierarchical composites were published by [3,4]. However, the introduction of CNTs in the matrix increases the complexity of the damage mechanisms observed in laminated composites. Here, we studied the damage and plasticity properties of CNT-enriched glass–fiber/epoxy laminated samples. First, we studied the behavior of the bulk matrix by preparing and testing CNT⇑ Corresponding author. Tel.: +966 (2) 808 2983. E-mail address:
[email protected] (G. Lubineau). 0266-3538/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2013.05.002
doped epoxy resin samples. Then, we used the vacuum infusion technique to impregnate glass–fiber plies into multiscale glass–fiber reinforced polymer (GFRP) samples. [±45]2s angle-ply specimens were then tested under loading/unloading tensile conditions to investigate the response of a single ply under shear loading. Indeed, very few investigations have been conducted on the shear response of CNT-doped laminates; those available focused on their elastic and ultimate strength behaviors [5]. We followed the framework of classical mesoscale damage mechanics based on the works of Ladevèze and co-workers [6]. This modeling approach has been demonstrated to be robust and popular in laminate design. We describe in Section 2 the materials, preparation procedures and characterization techniques. In Section 3, we provide comprehensive experimental observations on both the bulk resin and related laminates. It appears that although CNT-enrichment clearly improves the initial elastic stiffness of a composite system, it can also accelerate the damage process. We discuss this observation in terms of Dynamic Mechanical Analysis (DMA), mechanical testing, morphological analysis (including scanning electron microscopy (SEM) and Atomic Force Microscopy (AFM)). 2. Materials and methods 2.1. Description of raw constituents We prepared carbon nanotube-doped epoxy samples and carbon nanotube-doped glass–fiber reinforced polymer (GFRP)
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laminates using the following commercially available raw materials. –COOH functionalized MWCNTs are provided by CheapTubes and produced by catalyzed chemical vapor deposition. Per the supplier’s specifications, the purity was greater than 95 wt.% and the residual ash was less than 1.5 wt.%. The raw powder contained 2.56 wt.% of –COOH groups. The specified dimensions (outer diameter from 8 to 15 nm; inner diameter from 3 to 5 nm; length from 10 to 50 lm) were confirmed by transmission electron microscopy (TEM) observations. EPOLAM 2063, provided by AXSON Technologies is a blend of cycloaliphatic (CA) epoxy resin and a diglycidyl ether of bisphenol-A (DGEBA) resin. We mixed it with a compatible hardener, (anhydride 1,2,3,6-tetrahydromethyl-3, 6-methanophtalique), in equal parts by volume. According to the supplier’s specifications, the tensile strength and the Young’s modulus of this epoxy are 57 MPa and 3.1 GPa, respectively, at 23 °C. The glass transition temperature is expected to range from 180 °C to 200 °C depending on the curing cycle. Finally, for the laminated composites we used plain woven E-glass fiber cloth provided by HEXCEL (HEXTS92145) (surface weight: 220 g/m2). The warp, considered as the main renforcement direction, consists of bundles of 400 filaments (approximate diameter of the single filament: 9 lm); the weft is made of 200 filaments (approximate diameter of the single filament: 7 lm). Both warp and weft are present at 6 bundles per centimeter.
Material M2 (Fig. 1b) was our nano-doped material. Firstly, we dispersed MWCNTs into ethanol by sonication (Sonicator: CPX500 Cole-Parmer Instruments, frequency: 20 kHz) for 2 h in an ice bath. Then, we added the MWCNTs–ethanol solution to the epoxy (preheated to 80 °C); this mixture was stirred continuously using a magnetic stirrer for 2 h with the temperature maintained just above 80 °C until all the ethanol evaporated. Afterwards, the mixture was sonicated and stirred at the same time using a magnetic stirrer for 30 min at 80 °C. Finally, the required amount of hardener was added and the solution was thoroughly stirred for 15 min. We prepared M2 with three different MWCNT contents: 0.05 wt.%, 0.5 wt.% and 1.0 wt.% with respect to the total weight of the resin and hardener. We named the corresponding materials M2-0.05, M2-0.5 and M2-1.0. Material M3 (Fig. 1c) was made by repeating exactly the same steps used to make material M2, except that the MWCNTs were not introduced. The purpose of material M3 was to distinguish the effect of the addition of MWCNTs from the effect of processing. All bulk resin samples were prepared by molding the epoxy resin in a 80 °C preheated steel mold. The mold was kept at 80 °C for 6 h followed by a postcuring cycle of 6 h at 180 °C to ensure the complete curing of the samples (the extent of curing was checked by differential scanning calorimetry using a Netzsch DSC 204 F1 calorimeter; the results – not reported here – demonstrated complete crosslinking).
2.2. Sample preparation
2.2.2. Preparation of laminated samples Three laminated materials, called C1, C2-0.05 and C2-0.5, were prepared using the vacuum infusion technique. An E-glass fiber cloth was cut into 300 300 mm plies and then stacked together to form [±45]2s angle-ply laminates. The vacuum infusion was performed using the Infuplex system commercialized by Diatex (Fig. 2). Preheated resin at 80 °C flowed from an open container toward the inside of the vacuum-tight mold (also preheated to 80 °C), impregnating the fabric stack within. The plate was submitted to 1 bar of vacuum pressure at 80 °C for 6 h to ensure initial curing. Then, a post-curing cycle at 180 °C lasting 4 h
2.2.1. Preparation of bulk resin samples Three different material configurations designated as M1, M2 and M3 were investigated. The processing of these samples is illustrated in Fig. 1. Material M1 (Fig. 1a) was made from neat epoxy resin. Firstly, the epoxy resin was heated to 80 °C to lower the viscosity. Then, the hardener was added and blended using a magnetic stirrer for 15 min at 80 °C. The ratio of resin to hardener was 5:5.35 (by weight) as prescribed by the supplier.
MATERIAL M2
MATERIAL M1
MATERIAL M3
MWCNTs ETHANOL RESIN (pre-heated 80°C) HARDENER
Blending (MS - 80°C /15 mins)
Blending (US- ice bath / 2 hours) ETHANOL
ETHANOL + MWCNTs RESIN (pre-heated 80°C)
Blending (MS - 80°C /2 hour)
RESIN (pre-heated 80°C)
Blending (US+MS - 80°C / 30 mins)
Blending (US+MS - 80°C / 30 mins)
MWCNTs + RESIN HARDENER
BLENDED EPOXY READY FOR SAMPLE FABRICATION
(a)
(b)
Blending (MS - 80°C / 15 mins)
BLENDED MWCNTs/EPOXY READY FOR SAMPLE FABRICATION
Blending (MS - 80°C /2 hour)
RESIN HARDENER
Blending (MS - 80°C / 15 mins)
BLENDED EPOXY READY FOR SAMPLE FABRICATION
(c)
Fig. 1. Processing flow chart for the three material configurations, M1, M2 and M3 (MS: magnetic stirring, US: ultra-sonication).
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was run. The post-curing cycle was shorter for the laminates with respect to the bulk polymer samples since a systematic study of the polymer showed that 4 h of post-curing was enough to reach the complete polymerization. An E-glass fiber cloth was cut into 300 300 mm plies and then stacked together to form [±45]2s angle-ply laminates. The vacuum infusion was performed using the Infuplex system commercialized by Diatex (Fig. 2). Preheated resin at 80 °C flowed from an open container toward the inside of the vacuum-tight mold (also preheated to 80 °C), impregnating the fabric stack within. The plate was subjected to 1 bar of vacuum pressure at 80 °C for 6 h to ensure initial curing. Then, a post-curing cycle at 180 °C lasting 4 h was run. The post-curing cycle was shorter for the laminates with respect to the bulk polymer samples since a systematic study of the polymer showed that 4 h of post-curing was enough to reach the complete polymerization. Material C1 was infused with neat epoxy resin, which was processed in the same manner as in the M1 samples (see Fig. 1a). Similarly, Material C2 was made with MWCNT-doped epoxy resin, which was prepared using the same procedure used for the M2 samples (see Fig. 1b). The rapid increase in viscosity of the nano-enriched resin with increasing MWCNTs content is a limiting factor in the production of laminates via vacuum resin infusion. We found that the maximum achievable MWCNT concentration is around 0.75 wt.% for an eight-plies laminate. With higher MWCNT concentrations, the resin becomes too viscous for the impregnation of the laminate to be completed. Additionally, when this nano-doped epoxy resin flowed through the stack of glass– fiber plies, the inter- and intra-fiber bundle regions acted as a filter for the nanotubes and created heterogeneous zones with either concentration or depletion of carbon nanotubes. This effect is more pronounced with increased concentrations of MWCNTs. It was therefore impossible to achieve an infusion with reasonable quality with MWCNT concentrations equal to or greater than 1 wt.%. For this reason, two samples with MWCNTs were prepared: 0.05 wt.% and 0.5 wt.% and they were designated C2-0.05 and C20.5, respectively.
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the materials using molded samples according to the ASTM/ D638-03 type-I standard. All tests were performed using an Instron 8252 universal testing machine with a cross-head speed of 2 mm/ min. The load and longitudinal strains were monitored during the test using strain gauges and a Vishay 7000 StrainSmart acquisition system. X-ray inspection confirmed that the samples were free of processing defects (bubbles, inclusions, cracks) at the inspection scale (5 lm). The fractured surfaces of the MWCNT-epoxy composites were investigated using scanning electron microscopy (Nova Nano 630, FEI). The samples were coated with a thin layer of gold to reduce charging during analysis. The morphological feature of the cracked surface (typically the roughness) was investigated by atomic force microscopy, using an Agilent 5400 SPM (Agilent Technology, USA) operating in the intermittent contact mode. The surface of the fracture specimen was scanned at a scan speed of 0.7 Hz. with a silicon cantilever beam (resonance frequency: 150 kHz; force constant: 2.8 N/m). The measurement was performed at room temperature. 2.4. Characterization techniques for laminated samples We followed the ASTM D-3518 Standard to test the in-plane shear response of the [±45]2s laminated composites. Rectangular coupons (length: 200 mm, width: 20 mm) were cut from the infused plate using an automatic diamond saw (Struers Secotom10). Each sample was equipped with a transverse and a longitudinal strain gauge (Vishay Precision Group CEA 250UT) connected to a Vishay 7000 StrainSmart system. Aluminium tabs were used. As with the bulk resin samples, incremental loading/unloading tensile tests and monotonic tensile tests were performed with an Instron 8252 universal testing machine at a extension rate of 2 mm/min. We followed the damage characterization technique proposed by Ladevèze and Le Dantec [6]. 3. Experimental results and discussion 3.1. Characterization of the MWCNT-doped epoxy resin
2.3. Characterization techniques for the bulk resin samples The dynamic mechanical behavior was investigated using a dynamic mechanical analyzer (DMA 242 C Netzsch) in the bending mode. Rectangular specimens (50 15 2 mm) were subjected to load-controlled sinusoidal loading (peak load: 5 N, frequency: 1 Hz, span length: 50 mm) at a heating rate of 3 °C/min in the temperature range from 25 °C to 250 °C. To investigate the macroscopic plastic and damage behaviors, we conducted incremental loading/unloading tensile tests on all
3.1.1. Characterization of the elastic behavior DMA results (storage modulus and phase angle) for all the material configurations (M1, M2-0.05, M2-0.5, M2-1.0, M3) are reported in Fig. 3. First, it appears to be insignificant difference between materials M1 and M3. The storage modulus and the glass transition temperature are not affected by the processing or by the temporary introduction of ethanol. Second, a significant improvement is observed in the storage modulus of the M2 samples. Because the loss mod-
Fig. 2. Preparation of the laminated samples. (a) Stack of glass–fiber plies inside the vacuum bag. The Infuplex green layer is lying on top of the stack. (b) Infusion of the epoxy resin.
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0.6
M1 M2-0.05 .
4000
0.5
M2-0.5 M3
2000
M2-0.5 0.4
M2-1.0 3000
M1 M2-0.05
180• C 184• C 185.5• C
0.6
M2-1.0
0.4
tan (δ)
Storage Modulus (E’) (MPa)
5000
M3
0.2
0.3 0.0 150
165
180
195
0.2 1000
0.1
0
0.0 50
100
150
200
50
250
Temperature (ºC)
100
150
200
250
Temperature (ºC)
(a)
(b)
Fig. 3. (a) Storage modulus E0 in relation to temperature and (b) phase angle tan (d) in relation to temperature.
ulus can be neglected at room temperature, the storage modulus can be directly considered as a good approximation of the elastic Young’s modulus. Room temperature values are reported in Table 1. The storage modulus improves over the full temperature range up to 7% for M2-0.5 and up to 24% for M2-1.0 with respect to the original material. The effect becomes negligible at very low MWCNT content (M2-0.05). Our simple tensile tests showed that the stiffness improvements were globally smaller than the DMA results (see Table 1). Thus, it should be noted that DMA provides the correct trends in terms of stiffness improvements. Because DMA is performed at much lower amplitudes compared to macroscopic testing, the exact values of this improvement might differ. In polymeric materials, the storage modulus (and its stability during heating) is related to the displacement between polymer chains. In our previous study [7], we proposed a reaction mechanism in which the carboxilic groups present in functionalized carbon nanotubes react with the oxirane groups of the epoxy to create a covalent bond. This explains the increase in the Young’s modulus. It also affects the glass transition temperature (Tg) that can be observed in the phase angle curve (Fig. 3b) of the DMA analysis. Similarly, stronger crosslinking of the polymer chains will result in a higher glass transition temperature [8,9]. Thus, as expected, Tg is slightly shifted towards higher temperatures even in the presence of low concentrations of MWCNTs (see Table 1). 3.1.2. Characterization of damage and plastic behaviors The initial Young’s moduli (E0, see Fig. 4a) for all macroscopic tensile samples are reported in Table 1 and compared with the stiffness improvement measurements provided by DMA. We now consider the results of the incremental loading/unloading tests to understand the evolution of plasticity and damage in bulk nanodoped resin samples. Assuming an isotropic damage model for the bulk resin [10], its elastic strain energy density can be written:
ed ¼
h i kðdÞ ðtr½ee Þ2 þ lðdÞtr e2e 2
ð1Þ
where k(d) = k0(1 d) and l(d) = l0(1 d), l0 and k0 are the Lame parameters of the undamaged resin, ee is the elastic infinitesimal strain tensor and d is a scalar-valued damage indicator. At a given cycle i, the current damage level di can be evaluated as:
di ¼ 1
Ei E0
ð2Þ
Table 1 Storage modulus at room temperature, peak value of tan (d), glass transition temperatures and Young’s modulus for the M1, M2-0.05, M2-0.5, M2-1.0 and M3 samples. Material
E0 (MPa) (20 °C) (DMA)
tan(d) (peak value) (DMA)
Tg (°C) (DMA)
E0 (MPa) (20 °C) (tensile test)
M1 M2-0.05 M2-0.5 M2-1.0 M3
3440 3440 3680 4250 3440
0.54 0.54 0.53 0.41 0.54
180 184 184 185.5 180
3352 3471 3495 3646 3597
where Ei is the current secant Young’s modulus (see Fig. 4a). The evolution of the Young’s modulus in relation to the maximum strain achieved on every cycle is shown in Fig. 4b. The related damage evolution law, defined d and its as the relation between d dual damage force, Yd [10] Y d ¼ @e ¼ ed ðd ¼ 0Þ , is plotted in @d Fig. 4c. The residual plastic strain after each cycle (Fig. 4a) is reported in Fig. 4d. Although the initial elastic stiffness is increased in nano-enriched samples, it is interesting to note that the introduction of the MWCNTs does not change the damage behavior and that this addition can even have a detrimental effect. Indeed, as illustrated in Fig. 4c, the evolution of the damage is slightly higher when the concentration of MWCNTs is higher (the damage level is increased by 16% on average for M2-1.0). This can probably be attributed to the progressive degradation of all interfaces between MWCNTs and the bulk resin. The material now fully behaves as a composite in which interfaces between phases are a preferential locus for degradation. As far as the plastic behavior is concerned, the effect is less clear and it seems that there is no global modification of the plastic flow when the concentration of MWCNTs is low (Fig. 4d). This conclusion should be tempered by considering that the neat resin is itself very brittle and does not exhibit large plasticity. Thus, there is little room for any potential beneficial effects of MWCNTs on the plasticity. 3.1.3. Post-mortem observations Post-mortem SEM and AFM observations of the fractured surfaces are reported in Figs. 5 and 6. SEM (and additional,
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(a)
(b)
(c)
(d)
Fig. 4. (a) Definition of the initial Young’s modulus E0 and the secant Young’s modulus Ei for incremental loading. (b) Young’s modulus as a function of the maximum strain. (c) The evolution of damage as a function of the thermodynamic force Yd. (d) The residual plastic strain in every cycle.
non-reported TEM) images show that the MWCNTs were efficiently dispersed within the resin. No significant clusters of MWCNTs are visible even for the maximum load of 1 wt.%. In the M1 and M3 specimens (Fig. 5a and e), the smoothness of the fractured surfaces reveals a rather brittle process that is expected from an epoxy resin. The introduction of MWCNTs strongly modified the fracture morphology. Fig. 5d testifies to a transition toward a fragmentation process with an increase of the roughness of the fractured surface. The roughness parameters (Sq: root mean square height and Sa: arithmetic mean height) measured on the AFM scan (Fig. 6) increased up to (Sq) 79.8 nm and (Sa) 55.2 nm for M2-1.0 (compared to (Sq) 30.1 nm and (Sa) 18.8 nm for the neat epoxy). These results supports our observation of a much more progressive damage process in which interfaces and stress/strain redistribution play a major role. 3.2. Characterization of the laminated composite 3.2.1. Characterization of the elastic behavior The undamaged shear modulus G012 of the laminated ply was measured at the beginning of the cyclic tensile tests. We observed that the stiffness improvement in the modified epoxy resin (Section 3.1.1) was transferred to the laminates at the ply level. The G012 measurements were: 4.574 ± 0.151 GPa for C1,
4.892 ± 0.1 GPa for C2-0.05 and 5.060 ± 0.2 GPa for C2-0.5. These results correspond to increments of 6% for C2-0.05 and 10% for C2-0.5 when compared to the unmodified samples (C1). 3.2.2. Characterization of the damage and plastic behaviors During tensile tests in [±45]s laminates, the elementary ply at the mesoscale is mainly subjected to an in-the-plane shear-stress state. This shear loading is well known to activate degradation mechanisms at matrix/fiber interfaces, including diffused matrix damage and fiber/matrix debonding, which are responsible for the macroscopic stiffness reduction observed after every loop. In Fig. 7, we present the shear stress/shear strain curves at the ply level during incremental cyclic tensile tests that can be easily derived from macroscopic observations by lamination theory [6]. We characterized the linear stiffness reduction by using the damage meso-model proposed by Ladevèze and Le Dantec [6]. This model postulates the following evolution of the ply strain energy density with respect to the mesoscale damage variable, d (about the shear direction) and d0 (about the transverse direction) (1 denotes the fiber direction, 2 denotes the in-the-plane transverse direction, and 3 denotes the out-of-the-plane transverse direction):
ed ¼
r211 2E01
2m012 E01
r11 r22 þ
hr22 i2þ 2E02 ð1
0
dÞ
þ
hr22 i2 2E02
þ
r
2 12 0 2G12 ð1
dÞ
ð3Þ
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Fig. 5. SEM images of the fractured area for (a) M1, (b) M2-0.05, (c) M2-0.5, (d) M2-1.0 (e) M3.
(a)
(b)
(c)
(d)
Fig. 6. AFM observations of the fractured surfaces. (a) M1, (b) M2-0.05, (c) M2-0.5, (d) M2-1.0
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(a)
(d)
(c)
(d)
(e)
Fig. 7. The shear stress/shear strain cyclic curves for the [±45]2s multiscale laminates. (a) C1, (b) C2-0.5, (c) C2-0.05. (d) Shear damage master curves for samples C1, C2-0.05 and C2-0.5. (e) Plasticity master curve for the elementary ply of [±45]2s laminates.
where hi+ and hi are the positive and negative parts, respectively [6]. Following the developments presented in [6], from Eq. (3), we have: e 12
e ¼
r12 2G012 ð1 dÞ
f ¼ ð4Þ
where ee12 is only the elastic part of the shear strain at the ply level e12. The latter is a function of the macroscopic longitudinal and transverse strains, eL and eT as e12 ¼ eL 2eT . On the other hand, r12 is
the shear stress at the ply level and can be defined as r12 ¼ r2L , where rL is the macroscopic longitudinal stress. Then, the thermodynamic force, Yd, associated with the shear damage variable, d, becomes:
Yd ¼
@ed r212 ¼ @d 2G012 ð1 dÞ2
similar to [6]. p being the cumulated plastic strain, the pseudo-potential of dissipation is written:
ð5Þ
Finally, the shear damage d is identified in every cycle as: di ¼ 1 Gi12 =G012 . Using the data from Fig. 7a–c and Eqs. (3)–(6), the shear damage pffiffiffiffiffiffi master curves, d vs. Y d , were determined and are shown in Fig. 7d. It can be seen that the damage process is slightly accelerated (15% faster on average) in laminates with MWCNT-enriched resin. On one hand, this can be explained by greater diffused damage in the inter-fibers of the bulk resin as observed in Section 3.1.2. On the other hand, it is clear that there is no targeted reinforcement of the fiber/matrix interface even though it plays a major role in the shear damage of laminate composites. The damage process is not prevented in our nano-modified samples. In regard to plasticity in shear-loaded laminated plies, the apparent mesoscopic plasticity is generally induced by residual friction at the broken interfaces. To track any modification to this mechanism, we used a plasticity model with isotropic hardening
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r~ 212 þ a2 r~ 222 RðpÞ R0
ð6Þ
~ 12 and r ~ 22 are the effective shear and transverse stresses at where r the ply level, R0 is the initial elastic limit and R(p) is the hardening function. Identifying the evolution of the plasticity means identifying the evolution of the current plasticity limit, (R(p) + R0), in relation to the cumulated plastic strain, p. We refer to [6] for all corresponding analytical developments. We strictly follow this approach to derive the curve presented in Fig. 7e. Although no systematic conclusion can be drawn when the CNT content is low (C2-0.05), the plasticity limit is slightly higher for C20.5 samples. This increase in the plasticity limit could be attributed to two reasons. First, we could postulate an intrinsic modification of the plastic behavior of the matrix, but we found very little modification at this level in Section 3.1.2. Second, we could postulate that this increase in the plasticity limit comes from the modification of the roughness of broken surfaces (see Section 3.1.2). An increase in this residual friction due to an increase in the broken surface roughness would result in such a behavior. More investigations are needed to draw definitive conclusions about this point. 4. Conclusions We produced MWCNT-enriched glass–fiber/epoxy laminated composites using the vacuum resin infusion technique. A full characterization of the nanomodified resin system was performed, including observations on dispersion, elastic properties, damage and plastic behaviors. The shear damage and plasticity behavior of the laminates were studied through classical mesoscale damage mechanics and compared with non-nanoreinforced composites.
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Based on the experimental results and analyses, we draw the following conclusions: (1) the temporary addition of solvent and the solvent evaporation technique used for processing bulk resin and laminate samples did not affect the mechanical behavior, therefore all reported improvements or degradations can be confidently attributed to the nanoreinforcement (2) the addition of low concentrations of MWCNTs into the epoxy resin largely increased the elastic behavior but can speed up the damage process (up to 16% higher damage in 1 wt.% MWCNT content of the bulk resin). This downside was also observed in GFRP composites when the shear damage behavior was observed. This has been explained through morphological observations by the increase in the dissipation sites in the polymer at nanoreinforcement/resin interfaces. Finally, (3) CNT-enrichment did not significantly affect the plastic behavior of either the bulk resin or the laminated composites. The observed modifications of the meso and macroscopic behavior call for more investigations to completely understand the underlying damage process at the MWCNT-resin interface level. Acknowledgements Funding for this work was provided by KAUST baseline fund, the BOEING Company and SABIC. The authors are grateful for their financial aid.
References [1] Lubineau G, Nouri H, Roger F. On micro–meso relations homogenizing electrical properties of transversely cracked laminated composites. Composite Structures 2013. http://0-dx.doi.org.library.hct.ac.ae/10.1016/ j.compstruct.2013.05.001 [2] Kawakami H, Feraboli P. Lightning strike damage resistance and tolerance of scarf-repaired mesh-protected carbon fiber composites. Compos Part A: Appl Sci Manuf 2011;42(9):1247–62. [3] Qian H, Greenhalgh E, Shaffer M, Bismarck A. Carbon nanotube-based hierarchical composites: a review. J Mater Chem 2010;20(23):4751–62. [4] Lubineau G, Rahaman A. A review of strategies for improving the degradation properties of laminated continuous fiber/epoxy composites with carbon based nano reinforcements. Carbon 2012;50(7):2377–95. [5] Godara A, Mezzo L, Luizi F, Warrier A, Lomov S, Vuure AV, et al. Influence of carbon nanotube reinforcement on the processing and the mechanical behaviour of carbon fiber/epoxy composites. Carbon 2009;47(12): 2914–23. [6] Ladevèze P, LeDantec E. Damage modeling of the elementary ply for laminated composites. Compos Sci Technol 1992;43(3):257–67. [7] Ventura I.A, Rahaman A, Lubineau G. The thermal properties of a carbon nanotube-enriched epoxy: thermal conductivity, curing and degradation kinetics. Journal of Applied Polymer Science 2013. [8] Pérez AH, Avilés F, Pat AM, González AV, Herrera-Franco PJ, Bartolo-Pérez P. Effective properties of multiwalled carbon nanotube/epoxy composites using two different tubes. Compos Sci Technol 2008;68(6):1422–31. [9] Zhou Y, Pervin F, Lewis L, Jeelani S. Experimental study on the thermal and mechanical properties of multi-walled carbon nanotube-reinforced epoxy. Mater Sci Eng A 2007;452:657–64. [10] Edlung U, Klarbring A. A coupled elastic plastic damage model for rubbermodified epoxy adhesives. Int J Solids Struct 1993;30(19):2693–708.