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carbon microfiber hybrid composites
Composites Science and Technology 72 (2012) 1711–1717
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Application of continuously-monitored single fiber fragmentation tests to carbon nanotube/carbon microfiber hybrid composites Noa Lachman a, Brent J. Carey b, Daniel P. Hashim b, Pulickel M. Ajayan b, H. Daniel Wagner a,⇑ a b
Department of Materials & Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Department of Mechanical Engineering & Materials Science, Rice University, Houston, TX 77005, USA
a r t i c l e
i n f o
Article history: Received 17 October 2011 Received in revised form 21 May 2012 Accepted 4 June 2012 Available online 18 June 2012 Keywords: A. Carbon fibers A. Carbon nanotubes B. Interfacial strength B. Fragmentation
a b s t r a c t To assess the effect of carbon nanotube (CNT) grafting on interfacial stress transfer in fiber composites, CNTs were grown upon individual carbon T-300 fibers by chemical vapor deposition. Continuously-monitored single fiber composite (SFC) fragmentation tests were performed on both pristine and CNT-decorated fibers embedded in epoxy. The critical fragment length, fiber tensile strength at critical length, and interfacial shear strength were evaluated. Despite the fiber strength degradation resulting from the harsh CNT growth conditions, the CNT-modified fibers lead to a twofold increase in interfacial shear strength which correlates with the nearly threefold increase in apparent fiber diameter resulting from CNT grafting. These observations corroborate recently published studies with other CNT-grafted fibers. An analysis of the relative contributions to the interfacial strength of the fiber diameter and strength due to surface treatment is presented. It is concluded that the common view whereby an experimentally observed shorter average fragment length leads to a stronger interfacial adhesion is not necessarily correct, if the treatment has changed the fiber tensile strength or its diameter. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The discovery of carbon nanotubes (CNTs) in the 1990s almost immediately triggered the exploration of their potential use in composites. Indeed, nano-reinforcements, especially CNTs, were found to exhibit exceptional mechanical properties including very high elastic modulus and strength combined with high flexibility, low density and negligible thermal expansion [1–8]. Moreover, since nano-scale objects have a great deal more surface area (thus, for the case of composites, significantly more interfacial area) massive stress transfer and energy dissipation was expected to potentially lead to very high strength and toughness in these materials [9]. Indeed, it was observed that the addition of tiny amounts of CNTs to polymer matrices could result in improved mechanical properties [10–13]. Unfortunately, the improvements are almost always limited by a ‘critical mixing threshold’ of particle content, above which severe particle aggregation and drastic viscosity increases arose. As a result, it is currently impossible to manufacture CNT-based composites with CNT loadings that would be comparable to those of microfibers used in conventional composites (60–70% or so). This current state of affairs also contrasts with the existence in nature of nanocomposites with very high nanofiller content, up to 95 wt.% and sometimes even more [14,15]. Faced with such a ⇑ Corresponding author. Tel.: +972 89342594; fax: +972 89344137. E-mail address: [email protected] (H.D. Wagner). 0266-3538/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2012.06.004
challenge, composite material scientists are thus attempting to develop simple preparation techniques leading to high-content nanocomposites with superior mechanical properties. The road to high-performance synthetic nanocomposites requires that a fourfold set of structural parameters be optimized. These include (1) the particle aspect ratio, (2) particle dispersion, (3) particle packing (i.e. alignment), and (4) polymer-to-particle interfacial stress [9]. A recent review by Qian et al. [16] suggests two different routes for combining CNTs with conventional fiberreinforcements in polymer composites: either by dispersing CNTs throughout the composite matrix or by attaching CNTs directly onto primary reinforcing fibers (see Fig. 1 in Ref. [16]) using either chemical vapor deposition (CVD) [16–18] or electrophoretic deposition (EPD) [19,20]. By focusing here on the second route and using CVD to grow CNTs directly on the surface of fibers, we deal mainly with points 3 and 4 above while avoiding the problems of controlling the CNT dispersion in the bulk of the matrix as well as the CNT aspect ratio (a non-trivial task). Such an approach, wherein CNTs are vertically grown over specific fibers or over fabric layers, might lead to well-controlled, high CNT content, high toughness nanocomposites [15]. Perhaps more importantly, the presence of well-ordered CNTs at the fiber–matrix interface might enhance interfacial adhesion and stress transfer, and positively affect the mechanical properties of such hierarchical composites. In the present work, CNTs were synthesized and grown on carbon fibers by chemical vapor deposition (CVD). Single-fiber
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Fig. 1. Custom-made support bridge ensuring full CNT-coating of the individual fibers when held horizontally in the growth environment during synthesis.
fragmentation tests, of the continuously-monitored type [21,22], were then performed on both the CNT-grafted and reference (pristine) single fiber composites using a relatively soft epoxy matrix. The fragmentation phenomenon, in its continuously-monitored version, is a rich source of micromechanical information [21,22] as it simultaneously enables the rapid measurement of (i) the Weibull shape and scale parameters of the single fiber (within the matrix), (ii) the effect of fiber length on strength and thus the strength of fiber fragments having reached the saturation length, and (iii) the interfacial shear strength, a crucial factor in determining the strength and toughness of a composite. 2. Materials and specimen preparation The substrate fiber used in this work was an intermediate-modulus PAN-based carbon, T-300 from Cytex, untreated and sized. Its Young’s modulus is 157 GPa and its nominal diameter is 7 lm. For the CNT growth, a well-documented vapor-phase chemical vapor deposition (CVD) synthesis procedure [18] was employed, using xylene and ferrocene as the carbon and catalyst precursors, respectively. Individual fibers were loaded into a custom-made support bridge (Fig. 1) which held the suspended fibers horizontally in the growth environment during synthesis. The CNTs grow normal to the surface, thus suspension was necessary to keep the individual fibers separated and to prevent them from disturbing each other’s radial, ‘‘pipe-cleaner-like’’ structure during synthesis. The copper foil bridge suspended individual fibers across two slits separated by a distance of 50 mm, while excess fiber length hung over the outside of the bridge support to help prevent excessive drooping. Many slits were made for the possibility of loading multiple fibers in parallel. The fiber-loaded bridge was placed into a 50 mm-in-diameter quartz tube to act as the transfer boat, which was then positioned at the center of the 70 mm-in-diameter quartz tube which served as the growth environment. The chamber was held at atmospheric pressure conditions and set to a temperature of 780 °C, while at the same time Ar flowed at a rate of 1.00 L/ min to purge the growth environment. A 1 mm-in-diameter quartz tube was used as a nozzle tip to transport the precursor solution into the reaction zone, and was positioned into the furnace at 300 °C. When the synthesis temperature was achieved, the carrier gas was changed to a gas mix (15% H2/balance Ar) and was set to a flow rate of 4.00 L/min. A 3 mm-in-diameter steel tube concentric to the 1 mm-in-diameter quartz tube carried the identical gas mix at a rate of .64 L/min to promote the nozzle tip spray pyrolysis of the chemical precursor. A 5 min synthesis time resulted in 10 lm-long MWCNTs grown outwardly from the fiber surface. Typical CNT grafting results can be seen in Fig. 2. Epoxy films containing a single fiber were prepared according to a procedure now routinely used in our laboratory and described in our previous works [21,22]. The matrix was EP-502 from Polymer Gvulot, a bisphenol-A based (DGEBA) liquid epoxy resin, mixed with the curing agent EPC-9, triethylenetetramine (TETA). The Young’s modulus of the cured matrix is 1.34 GPa. Curing, film forming and sample cutting were performed according to the pro-
Fig. 2. SEM views of (a) CNT-grafted fibers prior to embedment in epoxy. Inset: High magnification (5000). (b) pulled-out CNT-grafted fibers from the epoxy specimens following final rupture of the fragmentation test specimen. The fiber diameter is approximately 17 lm before and after pull-out (Table 1), an indication of the strength of the fiber-CNT interface.
cedure described in previous work [9]. The resulting single fiber composite samples had typical cross-sectional dimensions of 3.1 0.15 mm2, and a gauge length of 12 mm. 3. Continuously monitored single-fiber fragmentation tests Mechanical testing of single fiber composites of each type was carried out using a computer-controlled MiniMat tensile tester fitted to a microscope possessing video recording capability. Four pristine specimens and five CNT-coated specimens were tested at a deformation rate of 50 lm/min. The continuously monitored version of the single filament composite test (CM-SFC) developed in our laboratory [21,22] and further validated along the years [23,24] was used. During a fragmentation test, under increasing levels of applied stress the fiber gradually breaks into shorter and shorter fragments. The rising stress–strain curve, as well as a magnified digital version of both the stress and the strain, was recorded simultaneously with the individual fracture events which were counted sequentially from real-time color video monitoring. Birefringent gaps under polarized light helped identify the fiber break sites while the specimen was under load, see Fig. 3. When a break occurred, the corresponding stress was recorded, and the average length of the fragments present was calculated by dividing the initial gauge length by the number of breaks plus one. The
N. Lachman et al. / Composites Science and Technology 72 (2012) 1711–1717
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Fig. 3. Typical fragmentation patterns by optical polarized light microscopy, showing birefringence around the fragment ends under load: (a) pristine T-300 fibers and (b) CNT-grafted T-300 fibers. Scale bars: 500 lm.
average fragment length s progressively decreased, first linearly with the applied stress until a deviation from linearity occurred as the fragments eventually ceased to break down into shorter fragments (Fig. 4). The latter situation is termed the saturation limit. The procedure is fully discussed in Ref. [22]. In the early stages of the fragmentation test, under low loads and far below the saturation limit, the probability of interaction between rare and distant (on average) breaks along a fiber is extremely low and the fragmentation test may be viewed as a ‘‘multiple tensile test’’ with independent samples, each of slightly different length, for which Weibull statistics applies. Assuming that the
strength of a fiber obeys the Weibull/weakest link model, the mean f of fibers of length L is [21,22]: tensile strength r
r f ¼ aL½1=b C 1 þ
1 ; b
where a and b are the Weibull scale and shape parameters for strength, respectively, and C(.) is the Gamma function, which is tabulated. If indeed the fragmentation test is viewed as a tensile test in which fiber samples (of varying lengths) in a series arrangement are submitted simultaneously to an (average) applied stress, we may adopt Eq. (1) (in reverse form) to obtain the desired relationship bef : tween the average fragment length s and the average fiber stress r
b 1 s ¼ ab r b C 1 þ : f b
Fig. 4. Typical output data from a continuously monitored single fiber fragmentation test with pristine and CNT-grafted T-300 fibers, showing the decreasing average fragment length resulting from increasing applied load. CNT-grafted fibers break under lower stress than pristine fibers, and their final fragment length is smaller. The lines are linear fits to the experimental data, with slopes of b, and intercept of b(ln a + ln C(1 + b1)).
ð1Þ
ð2Þ
This reverse form is preferred because it better fits the experimental reality, where a test yields a set of fragment lengths as a function of the applied stress. Closer to the saturation limit Eq. (2) ceases to be applicable because as the fragment lengths reach their saturation limit they cannot divide any further, whatever the stress increase, and therefore the average fragment length becomes insensitive to the applied stress. This means that in lnðsÞ vs f Þ coordinates, deviations relative to the straight line predicted lnðr from Eq. (2) occur as the saturation limit is approached. Note that f is (approximately) r f ¼ ðEf =Ea Þra , where Ef and the fiber stress r Ea are the fiber and matrix moduli, respectively, and ra is the applied stress (which is the output information in the experimental setup). This is valid as long as strain continuity at the fiber–matrix interface is maintained. The CM-SFC approach, which was also considered separately by Figueroa et al. at the same time [25], has significant advantages over the classical fragmentation test. First, as long as the fragment does not become too small (thus, away from the saturation limit and within the limits of validity of Eq. (2)), a plot of Eq. (2) in a ln–ln form yields a straight line with slope equal to the Weibull shape parameter (b) of the (embedded) fiber. This may be seen in Fig 4. The Weibull scale parameter a of the fiber is readily obtained from the intercept, given by b½lnðaÞ þ lnfCð1 þ b1 Þg. In other words, there is no need for large amounts of separate single fiber tests as commonly performed to obtain the strength vs length dependence and the relevant Weibull parameters. Second, the interfacial shear strength can be calculated by adapting the classical Kelly–Tyson approach to the fiber continuous fragmentation framework employed here, as follows. As long as a fragment length
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remains greater than the critical length, it can still break into smaller pieces, thus at saturation a range of fragment lengths exists, 0.5‘c < ‘sat < ‘c, the average of which is ‘sat ¼ 075‘c (assuming the length distribution is Gaussian). From this saturation state length, assuming a constant interfacial shear stress, one can calculate the interfacial shear strength si through the simple force balance [22]
si ¼
f ð‘c Þ f ð‘c Þ rr rr ¼ 0:75 ; ‘c ‘sat
ð3Þ
f ð‘c Þ is the ultimate strength of where r is the fiber diameter, and r the fiber (or rather the fiber fragment) at the critical length, as obtained from Eq. (1):
r f ð‘c Þ ¼ a‘c½1=b C 1 þ
intercept 1 ¼ ‘½1=b e b : c b
ð4Þ
A last advantage of the CM-SFC test is that since the fibers are embedded in a matrix, the proposed testing method inherently accounts for the effect of matrix on the fibers performance, so that the in situ results (Weibull scale and shape parameters, or fiber strength and variability) are closer to real-life performance. More rigorous analyses also exist for the fragment length distribution [26,27] and have recently been assessed experimentally [28]. Note also that the resin was cured at 80 °C and that resulting residual stresses are easily calculated [29] to be comparatively small, of the order of 50–100 MPa (compressive) in the fiber and 15– 35 kPa (tensile) in the matrix. This indeed is too small to be of significance since the strength of the T-300 carbon fiber is of the order of (at least) 3 GPa and the strength of the epoxy matrix is 35– 100 MPa. 4. Results and discussion The experimental observations and data are presented in Fig. 4 and 5, and the ensuing mechanical parameters are summarized in Table 1. This is followed by a critical discussion of the results. First, we observe that the strength of an embedded fiber deduced from CM-SFC measurements is higher than the strength of typical intermediate modulus carbon/graphite fibers tested in air, as reflected from the scale parameter (the manufacturer data indicates strength of 3–3.5 GPa for the intermediate modulus carbon fiber used here). This is likely because in a fragmentation test the fiber is embedded in the matrix which serves as a protective layer whereby fiber surface defects are comparatively ‘de-activated’. Moreover, the strength variability of the embedded fiber is definitely lower than the corresponding variability of the same fiber tested in air, as reflected from the higher shape parameter (b 1/(coefficient of variation)), which is typically only 4–6 for an intermediate modulus carbon fiber tested in air. Second, and significantly, we find here that the tensile strength (and scale parameter) of carbon fibers covered with a CNT layer is significantly lower compared to the sized, pristine fiber. Literature data for CNT-coated single fiber strength is hard to find, but two sets of papers concur with our results. Sager et al. [30] observe a similar strength decrease using both sized and unsized Thornel T650 carbon fibers, and explain this decrease as a result of thermal degradation and surface oxidation, causing surface flaws. Qian et al. [31,32] observe that the strength of several fiber types (silica [31], IM7 carbon [32] and C320 carbon [33]) significantly decreases following CNT-growth, an effect they also attribute to surface damage. Third, Fig. 2b shows the fracture surface of a fragmentation test following specimen rupture and fiber eventual pull-out from the matrix. As seen, the average diameter of the pulled-out fiber has significantly increased from 7 lm for a pristine sized fiber, to about 17 lm for the CNT treated fiber. This observation has, in fact, never
Fig. 5. Plot of Eq. (A1). Increases (decreases) in fiber–matrix adhesion do not necessarily translate into shorter (longer) critical lengths. ‘Strange’ cases are predicted to occur on the upper-right and lower-left boxes on the plot. See detailed explanations in the text.
been presented elsewhere (most papers on CNT grafted fibers show that the fiber diameter remains the same after grafting [30–33]), and probably implies that the adhesion of the fiberCNT interface is better than that of the CNT-epoxy interface. This could be considered a ‘‘coated fiber’’ problem, where the ‘‘coating’’ in this case is very thick – comparable to the fiber radius – and stiffer than the matrix but less stiff than the fibers. Exactly how load transfer happens in this system is yet unclear, since the effect should depend on the CNT/epoxy ratio in the ‘‘coating’’, the direction of the CNTs, and the adhesion between all three components (namely: fiber-epoxy, fiber-CNT and CNT-epoxy). However, since the pulled out fiber seems to possess quite uniform a diameter and a relatively smooth surface (in all fibers that have undergone pull-out), it seems reasonable to treat this three-components system as a one ‘‘composite fiber’’ with a thicker diameter. Taking into account the increase in diameter, the decrease in fiber strength and the smaller critical length, following CNT growth, using Eq. (3), the interfacial shear strength of CNT-coated carbon fiber based composites is found here to be about twice higher than that of pristine fiber based ones (Table 1). The observed increase in interfacial shear strength due to CNT grafting is generally consistent with recent work in the literature for silica and carbon fibers, using either the SFC test [30–33] or the droplet test [34], as summarized in Table 2. Increases in fracture toughness due to CNT grafting are also observed [35]. Diameter change effects on toughness have been recently examined using simple theoretical models; see Wagner and Lustiger [36], who showed that increasing the fiber diameter can enhance the available pull-out energy, and thus the maximum composite toughness. It is also likely that additional physical parameters such as surface energy and surface roughness, or even different compressive residual stresses caused
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N. Lachman et al. / Composites Science and Technology 72 (2012) 1711–1717 Table 1 Mechanical properties of the fibers and the fiber–matrix interfacial shear strength, as obtained from CM-SFC tests. Fiber type
T-300 Pristine T-300 CNTcoated
Average diameter d = 2r (lm) 7±0 17.1 ± 0.4
Shape parameter b
Scale parameter a (GPa)
Strength at critical f ð‘c Þ length r (GPa)
13.1 ± 5.7
6.8 ± 0.6
6.8 ± 0.7
6.7 ± 1.2
3.2 ± 0.5
Average saturation length, ‘sat [mm] 0.5 ± 0.09
3.3 ± 0.35
0.36 ± 0.06
c
Average critical length, ‘c (mm)
Interface shear strength si (MPa)
# of specimens
0.66 ± 0.12
36.9 ± 8.3d
8a
0.48 ± 0.08
70.0 ± 12.5
d
5b
a
Three specimens were tested at 50 lm/min, and five specimens at 250 lm/min. A t-test shows no significant difference between results at both strain-rates. One specimen did not reach saturation. Average excludes unsaturated specimen. d f ð‘c Þ, ‘c ) for each specimen, which somewhat differs from the (less This calculation of the interfacial shear strength is based on the exact values of all parameters (r, r accurate) calculation based on their average values presented in the table. b
c
Table 2 Effect of geometrical and material parameters on the normalized fiber–matrix interfacial shear strength. Normalization (or comparison) is performed relative to the corresponding non-coated fiber. Fiber type
a
Fiber strength ratio
Fiber radius ratio qr
Critical length
qr T-300: CNT-coated (compared to sized fiber)
0.49
2.44
0.73
1.64 [1.9]a
Thornel T650: unsized with aligned CNT (compared to unsized fiber) Thornel T650: unsized with random CNT (compared to unsized fiber) Silica With CNT (12 min) (compared to sized fiber) Silica With CNT (15 min) (compared to sized fiber) IM7 CNT-grafted (compared to oxidized fiber)
0.84
0.99
1.07
0.78 [1.11]a
Present work [25]
0.97
0.89
0.68
1.27 [1.72]a
[25]
0.42 0.45 0.79
a
[26] [26] [27]
0.95 0.75 0.92
1 1 1
ratio
‘Tr c ‘Pr c
Interfacial shear strength
Refs.
Tr ratio ssPr
2.26 [2.56] 1.67 [1.79]a 1.17 [1.21]a
The figures within brackets are based on the ratios calculated from the experimental data in Table 1, and in Refs. [25–27].
by the presence of CNT, plays a role in altering the interfacial shear strength. These were recently examined by Qian and Bismarck [33] via contact angle measurements and conveniently correlated with droplet test mechanical data. More research along these lines is necessary. These observations are critically important because the Kelly– Tyson model used to evaluate the adhesion level from the measured fragmentation length at saturation (or from the corresponding critical length) includes the shortest (average) fragment strength and the fiber diameter as parameters. Both of these usually remain constant following fiber surface treatments (such as sizing, functionalization by amination, and carboxylation). In such case the critical fiber length obtained at the saturation state is an unequivocal measure of the degree of interfacial adhesion: the shorter the critical fiber length, the better the interfacial adhesion. However, if the surface treatment leads to either a change in the fiber diameter, in the fiber strength, or in both as observed in the present work, the degree of interfacial adhesion has no straightforward correlation with the critical length. In other words, an increase (decrease) in fiber–matrix adhesion will not necessarily translate into a shorter (longer) critical length (See Appendix A). Note that the fiber strength as well as the CNT-fiber adhesion can be very sensitive to the CNT deposition conditions. For example, Bekyarova et al. [37] point out that high-temperature processing with CVD removes any sizing that may be applied to the fiber during manufacturing, and the CVD reaction may also significantly degrade the fiber strength. Zhang et al. [38] investigated the tensile strength properties as a function of time under different temperatures and atmospheric conditions and found high strength sensitivity between 750 °C and 800 C. As seen from Eqs. (A1) and (A2), a shorter critical length does not necessarily imply that the fiber–matrix interface is stronger, and vice versa. Indeed, the relative contributions of the fiber diam-
eter and the fiber strength are critically important. For example, a look at the T650 sized fiber data (Table 2) reveals that the sized fiber has better adhesion than the unsized fiber even though its critical length is slightly longer. As another example, had we not accounted for the diameter increase following CNT-coating in the present T-300 carbon fiber – thus had we used a fiber diameter ratio of 1 instead of 2.44 – the interfacial shear strength ratio would have become equal to 0.67 instead of 1.64, thus a decrease in interfacial strength instead of an increase. Thostenson et al. [39] correctly state that the critical length of the fibers can only be used as a relative measure of interfacial shear strength, when the shorter fragment lengths imply a stronger fiber/matrix interface, at a constant fiber diameter and fiber strength. They add, importantly, that fiber degradation can also result in smaller strength as well as shorter fragment lengths. Overall it appears that CNT grafting of carbon and silica fibers improves the fiber–matrix adhesion provided, however, that the Kelly–Tyson approach is assumed to remain physically valid when drastic changes in fiber diameter (such as those brought about by coatings or grafting) occur. This issue is of importance because of the well-known implications of interfacial adhesion on properties such as composite toughness and compressive strength.
5. Conclusions CNTs were CVD-grown upon individual carbon T-300 fibers and continuously monitored single-fiber fragmentation tests were performed on both the pristine and the CNT-grown fibers embedded in epoxy, to assess the effect of the treatment on the interfacial stress transfer. The critical fragment lengths, fiber tensile strengths at critical length, in situ fiber Weibull scale and shape parameters, and interfacial shear strength were evaluated. We observe a
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significant strength degradation of the CNT-grown carbon fibers compared to pristine fibers, due to the CNT growth conditions. Nevertheless, the CNT-grown fibers show an improvement in interfacial shear strength in epoxy, most probably due to the increase in apparent fiber diameter resulting from CNT grafting. A simple criterion for interfacial strength improvement in a SFC test was proposed, which addresses the most critical issue regarding direct CNT growth onto fiber surfaces, namely, by how much to limit the reduction of strength degradation of the fibers. More work is underway along these lines so as to yield CNT-grafted fibers suitable for improving critical engineering composite properties, including interlaminar toughness and compression strength. Acknowledgements This research was supported by a grant from the United StatesIsrael Binational Science Foundation (BSF), Jerusalem, Israel, and by the NES MAGNET program of the Israel Ministry of Trade and Industry. The generosity of the Harold Perlman family and the G.M.J. Schmidt Minerva Centre of Supramolecular Architectures is acknowledged. H.D. Wagner is the recipient of the Livio Norzi Professorial Chair in Materials Science.
Improved adhesion accompanied by a longer critical length; Worse adhesion accompanied by a (much) longer critical length. (iii) qr qr < 1. In this final case there are again three possibilities: Improved adhesion accompanied by a shorter critical length (the classical case); Worse adhesion accompanied by a shorter critical length (thus, a shorter critical length following treatment does not necessarily mean a better adhesion if this particular product of qr and qr leads to a value that is smaller than 1); And worse adhesion accompanied by a longer critical length. Thus the ‘strange’ (meaning: rarely observed) cases are predicted to occur on the upper-right and lower-left boxes on the plot. All other occurrences are traditionally observed in those fragmentation experiments where neither the fiber diameter nor the strength are affected by the surface treatment. The (1, 1) locus is the pristine reference point. The ‘strange’ cases involve fiber modifications due to surface treatment: a change in the fiber diameter (for example, through transcrystalline growth in thermoplastic matrices [40], or to CNT growth such as observed here); or a change in the fiber strength due to the treatment.
Appendix A Following a given fiber surface treatment, an observed increase (decrease) in fiber–matrix adhesion does not necessarily translate into a shorter (longer) critical length. Indeed, if ‘Tr’ and ‘Pr’ designate treated and pristine fibers respectively, we have
rTr ð‘Tr c Þ rPr ð‘Pr c Þ
s ¼ sPr Tr
Tr
r Tr r Pr
‘c ‘Pr c
q q
¼ rTr r ; ‘c ‘Pr c
ðA1Þ
where
qr ¼
!
r Tr ‘Trc ; r Pr ‘Prc
qr ¼
r Tr : r Pr
In other words, following treatment, the interfacial shear Tr strength sTr increases if ssPr > 1 or, using Eq. (A1), if
‘Tr c < qr qr : ‘Pr c
ðA2Þ
Eq. (A1) is plotted in Fig. 5, and as seen, several cases are possible: (i) qr qr ¼ 1, which occurs if (a) both the fiber strength and diameter are unaffected by the surface treatment (which is often the case when fibers are chemically treated), or if (b) the fiber strength and diameter are both affected by the treatment in a precisely compensating way (for example, an increase in qr by a factor of f is exactly compensated by a decrease in qr by a factor of 1/f, so that the product equals 1). The latter is a rare but nevertheless possible occurrence. Thus, if qr qr ¼ 1, Fig. 5 shows that there are only 2 unequivocal possibilities, because the hyperbolic line crosses the (1, 1) coordinate on the plot: better adhesion if a treated fiber exhibits a shorter critical length lc or worse adhesion if the fiber treatment results in a longer critical length. (ii) qr qr > 1. In this case, referring again to Fig. 5, there are three possibilities following treatment: Improved adhesion accompanied by a shorter critical length (the classical case);
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N. Lachman et al. / Composites Science and Technology 72 (2012) 1711–1717 [22] Yavin B, Gallis HE, Scherf J, Eitan A, Wagner HD. Continuous monitoring of the fragmentation phenomenon in single fiber composite materials. Polym Compos 1991;12:436–46. [23] Zhao FM, Okabe T, Takeda N. The estimation of statistical fiber strength by fragmentation tests of single-fiber composites. Compos Sci Tech 2000;60:1965–74. [24] Curtin WA. Stochastic damage evolution and failure in fiber reinforced composites. Adv Appl Mech 1999;36:163–253. [25] Figueroa JC, Carney TE, Schadler LS, Laird C. Micromechanics of single filament composites. Compos Sci Tech 1991;42:77–101. [26] Curtin WA. Exact theory of fibre fragmentation in a single-filament composite. J Mater Sci 1991;26:5239–53. [27] Hui CY, Phoenix SL, Kogan L. Analysis of fragmentation in the single filament composite: roles of fiber strength distributions and exclusion zone models. J Mech Phys Solids 1996;44:1715–37. [28] Kim J, Leigh S, Holmes G. E-Glass/DGEBA/m-PDA single fiber composites: new insights into the statistics of fiber fragmentation. J Polym Sci: Part B: Pol Phys 2009;47:2301–12. [29] Wagner HD. Residual stresses in microcomposites and macrocomposites. J Adhes 1995;52(1):131–48. [30] Sager RJ, Klein PJ, Lagoudas DC, Zhang Q, Liu J, Dai L, et al. Effect of carbon nanotubes on the interfacial shear strength of T650 carbon fiber in an epoxy matrix. Comput Sci Tech 2009;69:898–904. [31] Qian H, Bismarck A, Greenhalgh ES, Shaffer MSP. Carbon nanotube grafted silica fibres: characterising the interface at the single fibre level. Comput Sci Tech 2010;70:393–9.
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[32] Qian H, Bismarck A, Greenhalgh ES, Shaffer MSP. Carbon nanotube grafted carbon fibres: a study of wetting and fibre fragmentation. Composites: A 2010;41:1107–14. [33] Qian H, Bismarck A, Greenhalgh ES, Kalinka G, Shaffer MSP. Hierarchical composites reinforced with carbon nanotube grafted fibers: the potential assessed at the single fiber level. Chem Mater 2008;20:1862–9. [34] Zhang F, Wang R, He X, Wang C, Ren L. Interfacial shearing strength and reinforcing mechanisms of an epoxy composite reinforced using a carbon nanotube/carbon fiber hybrid. J Mater Sci 2009;44:3574–7. [35] Kepple KL, Sanborn GP, Lacasse PA, Gruenberg KM, Ready WJ. Improved fracture toughness of carbon fiber composite functionalized with multi walled carbon nanotubes. Carbon 2008;46:2026–33. [36] Wagner HD, Lustiger A. Optimized toughness of short fiber-based composites: the effect of fiber diameter. Comput Sci Tech 2009;69:1323–5. [37] Bekyarova E, Thostenson ET, Yu A, Kim H, Gao J, Tang J, et al. Multiscale carbon nanotube-carbon fiber reinforcement for advanced epoxy composites. Langmuir 2007;23:3970–4. [38] Zhang QH, Liu JW, Sager R, Dai LM, Baur J. Hierarchical composites of carbon nanotubes on carbon fiber: influence of growth condition on fiber tensile properties. Comput Sci Tech 2009;69:594–601. [39] Thostenson ET, Li WZ, Wang DZ, Ren ZF, Chou TW. Carbon nanotube-carbon fiber hybrid multiscale composites. J Appl Phys 2002;91(9):6034–7. [40] Gati A, Wagner HD. Stress transfer efficiency in semicrystalline-based composites comprising transcrystalline interlayers. Macromolecules 1997;30:3933–5.
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Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Application of continuously-monitored single fiber fragmentation tests to carbon nanotube/carbon microfiber hybrid composites Noa Lachman a, Brent J. Carey b, Daniel P. Hashim b, Pulickel M. Ajayan b, H. Daniel Wagner a,⇑ a b
Department of Materials & Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Department of Mechanical Engineering & Materials Science, Rice University, Houston, TX 77005, USA
a r t i c l e
i n f o
Article history: Received 17 October 2011 Received in revised form 21 May 2012 Accepted 4 June 2012 Available online 18 June 2012 Keywords: A. Carbon fibers A. Carbon nanotubes B. Interfacial strength B. Fragmentation
a b s t r a c t To assess the effect of carbon nanotube (CNT) grafting on interfacial stress transfer in fiber composites, CNTs were grown upon individual carbon T-300 fibers by chemical vapor deposition. Continuously-monitored single fiber composite (SFC) fragmentation tests were performed on both pristine and CNT-decorated fibers embedded in epoxy. The critical fragment length, fiber tensile strength at critical length, and interfacial shear strength were evaluated. Despite the fiber strength degradation resulting from the harsh CNT growth conditions, the CNT-modified fibers lead to a twofold increase in interfacial shear strength which correlates with the nearly threefold increase in apparent fiber diameter resulting from CNT grafting. These observations corroborate recently published studies with other CNT-grafted fibers. An analysis of the relative contributions to the interfacial strength of the fiber diameter and strength due to surface treatment is presented. It is concluded that the common view whereby an experimentally observed shorter average fragment length leads to a stronger interfacial adhesion is not necessarily correct, if the treatment has changed the fiber tensile strength or its diameter. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The discovery of carbon nanotubes (CNTs) in the 1990s almost immediately triggered the exploration of their potential use in composites. Indeed, nano-reinforcements, especially CNTs, were found to exhibit exceptional mechanical properties including very high elastic modulus and strength combined with high flexibility, low density and negligible thermal expansion [1–8]. Moreover, since nano-scale objects have a great deal more surface area (thus, for the case of composites, significantly more interfacial area) massive stress transfer and energy dissipation was expected to potentially lead to very high strength and toughness in these materials [9]. Indeed, it was observed that the addition of tiny amounts of CNTs to polymer matrices could result in improved mechanical properties [10–13]. Unfortunately, the improvements are almost always limited by a ‘critical mixing threshold’ of particle content, above which severe particle aggregation and drastic viscosity increases arose. As a result, it is currently impossible to manufacture CNT-based composites with CNT loadings that would be comparable to those of microfibers used in conventional composites (60–70% or so). This current state of affairs also contrasts with the existence in nature of nanocomposites with very high nanofiller content, up to 95 wt.% and sometimes even more [14,15]. Faced with such a ⇑ Corresponding author. Tel.: +972 89342594; fax: +972 89344137. E-mail address: [email protected] (H.D. Wagner). 0266-3538/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2012.06.004
challenge, composite material scientists are thus attempting to develop simple preparation techniques leading to high-content nanocomposites with superior mechanical properties. The road to high-performance synthetic nanocomposites requires that a fourfold set of structural parameters be optimized. These include (1) the particle aspect ratio, (2) particle dispersion, (3) particle packing (i.e. alignment), and (4) polymer-to-particle interfacial stress [9]. A recent review by Qian et al. [16] suggests two different routes for combining CNTs with conventional fiberreinforcements in polymer composites: either by dispersing CNTs throughout the composite matrix or by attaching CNTs directly onto primary reinforcing fibers (see Fig. 1 in Ref. [16]) using either chemical vapor deposition (CVD) [16–18] or electrophoretic deposition (EPD) [19,20]. By focusing here on the second route and using CVD to grow CNTs directly on the surface of fibers, we deal mainly with points 3 and 4 above while avoiding the problems of controlling the CNT dispersion in the bulk of the matrix as well as the CNT aspect ratio (a non-trivial task). Such an approach, wherein CNTs are vertically grown over specific fibers or over fabric layers, might lead to well-controlled, high CNT content, high toughness nanocomposites [15]. Perhaps more importantly, the presence of well-ordered CNTs at the fiber–matrix interface might enhance interfacial adhesion and stress transfer, and positively affect the mechanical properties of such hierarchical composites. In the present work, CNTs were synthesized and grown on carbon fibers by chemical vapor deposition (CVD). Single-fiber
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Fig. 1. Custom-made support bridge ensuring full CNT-coating of the individual fibers when held horizontally in the growth environment during synthesis.
fragmentation tests, of the continuously-monitored type [21,22], were then performed on both the CNT-grafted and reference (pristine) single fiber composites using a relatively soft epoxy matrix. The fragmentation phenomenon, in its continuously-monitored version, is a rich source of micromechanical information [21,22] as it simultaneously enables the rapid measurement of (i) the Weibull shape and scale parameters of the single fiber (within the matrix), (ii) the effect of fiber length on strength and thus the strength of fiber fragments having reached the saturation length, and (iii) the interfacial shear strength, a crucial factor in determining the strength and toughness of a composite. 2. Materials and specimen preparation The substrate fiber used in this work was an intermediate-modulus PAN-based carbon, T-300 from Cytex, untreated and sized. Its Young’s modulus is 157 GPa and its nominal diameter is 7 lm. For the CNT growth, a well-documented vapor-phase chemical vapor deposition (CVD) synthesis procedure [18] was employed, using xylene and ferrocene as the carbon and catalyst precursors, respectively. Individual fibers were loaded into a custom-made support bridge (Fig. 1) which held the suspended fibers horizontally in the growth environment during synthesis. The CNTs grow normal to the surface, thus suspension was necessary to keep the individual fibers separated and to prevent them from disturbing each other’s radial, ‘‘pipe-cleaner-like’’ structure during synthesis. The copper foil bridge suspended individual fibers across two slits separated by a distance of 50 mm, while excess fiber length hung over the outside of the bridge support to help prevent excessive drooping. Many slits were made for the possibility of loading multiple fibers in parallel. The fiber-loaded bridge was placed into a 50 mm-in-diameter quartz tube to act as the transfer boat, which was then positioned at the center of the 70 mm-in-diameter quartz tube which served as the growth environment. The chamber was held at atmospheric pressure conditions and set to a temperature of 780 °C, while at the same time Ar flowed at a rate of 1.00 L/ min to purge the growth environment. A 1 mm-in-diameter quartz tube was used as a nozzle tip to transport the precursor solution into the reaction zone, and was positioned into the furnace at 300 °C. When the synthesis temperature was achieved, the carrier gas was changed to a gas mix (15% H2/balance Ar) and was set to a flow rate of 4.00 L/min. A 3 mm-in-diameter steel tube concentric to the 1 mm-in-diameter quartz tube carried the identical gas mix at a rate of .64 L/min to promote the nozzle tip spray pyrolysis of the chemical precursor. A 5 min synthesis time resulted in 10 lm-long MWCNTs grown outwardly from the fiber surface. Typical CNT grafting results can be seen in Fig. 2. Epoxy films containing a single fiber were prepared according to a procedure now routinely used in our laboratory and described in our previous works [21,22]. The matrix was EP-502 from Polymer Gvulot, a bisphenol-A based (DGEBA) liquid epoxy resin, mixed with the curing agent EPC-9, triethylenetetramine (TETA). The Young’s modulus of the cured matrix is 1.34 GPa. Curing, film forming and sample cutting were performed according to the pro-
Fig. 2. SEM views of (a) CNT-grafted fibers prior to embedment in epoxy. Inset: High magnification (5000). (b) pulled-out CNT-grafted fibers from the epoxy specimens following final rupture of the fragmentation test specimen. The fiber diameter is approximately 17 lm before and after pull-out (Table 1), an indication of the strength of the fiber-CNT interface.
cedure described in previous work [9]. The resulting single fiber composite samples had typical cross-sectional dimensions of 3.1 0.15 mm2, and a gauge length of 12 mm. 3. Continuously monitored single-fiber fragmentation tests Mechanical testing of single fiber composites of each type was carried out using a computer-controlled MiniMat tensile tester fitted to a microscope possessing video recording capability. Four pristine specimens and five CNT-coated specimens were tested at a deformation rate of 50 lm/min. The continuously monitored version of the single filament composite test (CM-SFC) developed in our laboratory [21,22] and further validated along the years [23,24] was used. During a fragmentation test, under increasing levels of applied stress the fiber gradually breaks into shorter and shorter fragments. The rising stress–strain curve, as well as a magnified digital version of both the stress and the strain, was recorded simultaneously with the individual fracture events which were counted sequentially from real-time color video monitoring. Birefringent gaps under polarized light helped identify the fiber break sites while the specimen was under load, see Fig. 3. When a break occurred, the corresponding stress was recorded, and the average length of the fragments present was calculated by dividing the initial gauge length by the number of breaks plus one. The
N. Lachman et al. / Composites Science and Technology 72 (2012) 1711–1717
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Fig. 3. Typical fragmentation patterns by optical polarized light microscopy, showing birefringence around the fragment ends under load: (a) pristine T-300 fibers and (b) CNT-grafted T-300 fibers. Scale bars: 500 lm.
average fragment length s progressively decreased, first linearly with the applied stress until a deviation from linearity occurred as the fragments eventually ceased to break down into shorter fragments (Fig. 4). The latter situation is termed the saturation limit. The procedure is fully discussed in Ref. [22]. In the early stages of the fragmentation test, under low loads and far below the saturation limit, the probability of interaction between rare and distant (on average) breaks along a fiber is extremely low and the fragmentation test may be viewed as a ‘‘multiple tensile test’’ with independent samples, each of slightly different length, for which Weibull statistics applies. Assuming that the
strength of a fiber obeys the Weibull/weakest link model, the mean f of fibers of length L is [21,22]: tensile strength r
r f ¼ aL½1=b C 1 þ
1 ; b
where a and b are the Weibull scale and shape parameters for strength, respectively, and C(.) is the Gamma function, which is tabulated. If indeed the fragmentation test is viewed as a tensile test in which fiber samples (of varying lengths) in a series arrangement are submitted simultaneously to an (average) applied stress, we may adopt Eq. (1) (in reverse form) to obtain the desired relationship bef : tween the average fragment length s and the average fiber stress r
b 1 s ¼ ab r b C 1 þ : f b
Fig. 4. Typical output data from a continuously monitored single fiber fragmentation test with pristine and CNT-grafted T-300 fibers, showing the decreasing average fragment length resulting from increasing applied load. CNT-grafted fibers break under lower stress than pristine fibers, and their final fragment length is smaller. The lines are linear fits to the experimental data, with slopes of b, and intercept of b(ln a + ln C(1 + b1)).
ð1Þ
ð2Þ
This reverse form is preferred because it better fits the experimental reality, where a test yields a set of fragment lengths as a function of the applied stress. Closer to the saturation limit Eq. (2) ceases to be applicable because as the fragment lengths reach their saturation limit they cannot divide any further, whatever the stress increase, and therefore the average fragment length becomes insensitive to the applied stress. This means that in lnðsÞ vs f Þ coordinates, deviations relative to the straight line predicted lnðr from Eq. (2) occur as the saturation limit is approached. Note that f is (approximately) r f ¼ ðEf =Ea Þra , where Ef and the fiber stress r Ea are the fiber and matrix moduli, respectively, and ra is the applied stress (which is the output information in the experimental setup). This is valid as long as strain continuity at the fiber–matrix interface is maintained. The CM-SFC approach, which was also considered separately by Figueroa et al. at the same time [25], has significant advantages over the classical fragmentation test. First, as long as the fragment does not become too small (thus, away from the saturation limit and within the limits of validity of Eq. (2)), a plot of Eq. (2) in a ln–ln form yields a straight line with slope equal to the Weibull shape parameter (b) of the (embedded) fiber. This may be seen in Fig 4. The Weibull scale parameter a of the fiber is readily obtained from the intercept, given by b½lnðaÞ þ lnfCð1 þ b1 Þg. In other words, there is no need for large amounts of separate single fiber tests as commonly performed to obtain the strength vs length dependence and the relevant Weibull parameters. Second, the interfacial shear strength can be calculated by adapting the classical Kelly–Tyson approach to the fiber continuous fragmentation framework employed here, as follows. As long as a fragment length
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remains greater than the critical length, it can still break into smaller pieces, thus at saturation a range of fragment lengths exists, 0.5‘c < ‘sat < ‘c, the average of which is ‘sat ¼ 075‘c (assuming the length distribution is Gaussian). From this saturation state length, assuming a constant interfacial shear stress, one can calculate the interfacial shear strength si through the simple force balance [22]
si ¼
f ð‘c Þ f ð‘c Þ rr rr ¼ 0:75 ; ‘c ‘sat
ð3Þ
f ð‘c Þ is the ultimate strength of where r is the fiber diameter, and r the fiber (or rather the fiber fragment) at the critical length, as obtained from Eq. (1):
r f ð‘c Þ ¼ a‘c½1=b C 1 þ
intercept 1 ¼ ‘½1=b e b : c b
ð4Þ
A last advantage of the CM-SFC test is that since the fibers are embedded in a matrix, the proposed testing method inherently accounts for the effect of matrix on the fibers performance, so that the in situ results (Weibull scale and shape parameters, or fiber strength and variability) are closer to real-life performance. More rigorous analyses also exist for the fragment length distribution [26,27] and have recently been assessed experimentally [28]. Note also that the resin was cured at 80 °C and that resulting residual stresses are easily calculated [29] to be comparatively small, of the order of 50–100 MPa (compressive) in the fiber and 15– 35 kPa (tensile) in the matrix. This indeed is too small to be of significance since the strength of the T-300 carbon fiber is of the order of (at least) 3 GPa and the strength of the epoxy matrix is 35– 100 MPa. 4. Results and discussion The experimental observations and data are presented in Fig. 4 and 5, and the ensuing mechanical parameters are summarized in Table 1. This is followed by a critical discussion of the results. First, we observe that the strength of an embedded fiber deduced from CM-SFC measurements is higher than the strength of typical intermediate modulus carbon/graphite fibers tested in air, as reflected from the scale parameter (the manufacturer data indicates strength of 3–3.5 GPa for the intermediate modulus carbon fiber used here). This is likely because in a fragmentation test the fiber is embedded in the matrix which serves as a protective layer whereby fiber surface defects are comparatively ‘de-activated’. Moreover, the strength variability of the embedded fiber is definitely lower than the corresponding variability of the same fiber tested in air, as reflected from the higher shape parameter (b 1/(coefficient of variation)), which is typically only 4–6 for an intermediate modulus carbon fiber tested in air. Second, and significantly, we find here that the tensile strength (and scale parameter) of carbon fibers covered with a CNT layer is significantly lower compared to the sized, pristine fiber. Literature data for CNT-coated single fiber strength is hard to find, but two sets of papers concur with our results. Sager et al. [30] observe a similar strength decrease using both sized and unsized Thornel T650 carbon fibers, and explain this decrease as a result of thermal degradation and surface oxidation, causing surface flaws. Qian et al. [31,32] observe that the strength of several fiber types (silica [31], IM7 carbon [32] and C320 carbon [33]) significantly decreases following CNT-growth, an effect they also attribute to surface damage. Third, Fig. 2b shows the fracture surface of a fragmentation test following specimen rupture and fiber eventual pull-out from the matrix. As seen, the average diameter of the pulled-out fiber has significantly increased from 7 lm for a pristine sized fiber, to about 17 lm for the CNT treated fiber. This observation has, in fact, never
Fig. 5. Plot of Eq. (A1). Increases (decreases) in fiber–matrix adhesion do not necessarily translate into shorter (longer) critical lengths. ‘Strange’ cases are predicted to occur on the upper-right and lower-left boxes on the plot. See detailed explanations in the text.
been presented elsewhere (most papers on CNT grafted fibers show that the fiber diameter remains the same after grafting [30–33]), and probably implies that the adhesion of the fiberCNT interface is better than that of the CNT-epoxy interface. This could be considered a ‘‘coated fiber’’ problem, where the ‘‘coating’’ in this case is very thick – comparable to the fiber radius – and stiffer than the matrix but less stiff than the fibers. Exactly how load transfer happens in this system is yet unclear, since the effect should depend on the CNT/epoxy ratio in the ‘‘coating’’, the direction of the CNTs, and the adhesion between all three components (namely: fiber-epoxy, fiber-CNT and CNT-epoxy). However, since the pulled out fiber seems to possess quite uniform a diameter and a relatively smooth surface (in all fibers that have undergone pull-out), it seems reasonable to treat this three-components system as a one ‘‘composite fiber’’ with a thicker diameter. Taking into account the increase in diameter, the decrease in fiber strength and the smaller critical length, following CNT growth, using Eq. (3), the interfacial shear strength of CNT-coated carbon fiber based composites is found here to be about twice higher than that of pristine fiber based ones (Table 1). The observed increase in interfacial shear strength due to CNT grafting is generally consistent with recent work in the literature for silica and carbon fibers, using either the SFC test [30–33] or the droplet test [34], as summarized in Table 2. Increases in fracture toughness due to CNT grafting are also observed [35]. Diameter change effects on toughness have been recently examined using simple theoretical models; see Wagner and Lustiger [36], who showed that increasing the fiber diameter can enhance the available pull-out energy, and thus the maximum composite toughness. It is also likely that additional physical parameters such as surface energy and surface roughness, or even different compressive residual stresses caused
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N. Lachman et al. / Composites Science and Technology 72 (2012) 1711–1717 Table 1 Mechanical properties of the fibers and the fiber–matrix interfacial shear strength, as obtained from CM-SFC tests. Fiber type
T-300 Pristine T-300 CNTcoated
Average diameter d = 2r (lm) 7±0 17.1 ± 0.4
Shape parameter b
Scale parameter a (GPa)
Strength at critical f ð‘c Þ length r (GPa)
13.1 ± 5.7
6.8 ± 0.6
6.8 ± 0.7
6.7 ± 1.2
3.2 ± 0.5
Average saturation length, ‘sat [mm] 0.5 ± 0.09
3.3 ± 0.35
0.36 ± 0.06
c
Average critical length, ‘c (mm)
Interface shear strength si (MPa)
# of specimens
0.66 ± 0.12
36.9 ± 8.3d
8a
0.48 ± 0.08
70.0 ± 12.5
d
5b
a
Three specimens were tested at 50 lm/min, and five specimens at 250 lm/min. A t-test shows no significant difference between results at both strain-rates. One specimen did not reach saturation. Average excludes unsaturated specimen. d f ð‘c Þ, ‘c ) for each specimen, which somewhat differs from the (less This calculation of the interfacial shear strength is based on the exact values of all parameters (r, r accurate) calculation based on their average values presented in the table. b
c
Table 2 Effect of geometrical and material parameters on the normalized fiber–matrix interfacial shear strength. Normalization (or comparison) is performed relative to the corresponding non-coated fiber. Fiber type
a
Fiber strength ratio
Fiber radius ratio qr
Critical length
qr T-300: CNT-coated (compared to sized fiber)
0.49
2.44
0.73
1.64 [1.9]a
Thornel T650: unsized with aligned CNT (compared to unsized fiber) Thornel T650: unsized with random CNT (compared to unsized fiber) Silica With CNT (12 min) (compared to sized fiber) Silica With CNT (15 min) (compared to sized fiber) IM7 CNT-grafted (compared to oxidized fiber)
0.84
0.99
1.07
0.78 [1.11]a
Present work [25]
0.97
0.89
0.68
1.27 [1.72]a
[25]
0.42 0.45 0.79
a
[26] [26] [27]
0.95 0.75 0.92
1 1 1
ratio
‘Tr c ‘Pr c
Interfacial shear strength
Refs.
Tr ratio ssPr
2.26 [2.56] 1.67 [1.79]a 1.17 [1.21]a
The figures within brackets are based on the ratios calculated from the experimental data in Table 1, and in Refs. [25–27].
by the presence of CNT, plays a role in altering the interfacial shear strength. These were recently examined by Qian and Bismarck [33] via contact angle measurements and conveniently correlated with droplet test mechanical data. More research along these lines is necessary. These observations are critically important because the Kelly– Tyson model used to evaluate the adhesion level from the measured fragmentation length at saturation (or from the corresponding critical length) includes the shortest (average) fragment strength and the fiber diameter as parameters. Both of these usually remain constant following fiber surface treatments (such as sizing, functionalization by amination, and carboxylation). In such case the critical fiber length obtained at the saturation state is an unequivocal measure of the degree of interfacial adhesion: the shorter the critical fiber length, the better the interfacial adhesion. However, if the surface treatment leads to either a change in the fiber diameter, in the fiber strength, or in both as observed in the present work, the degree of interfacial adhesion has no straightforward correlation with the critical length. In other words, an increase (decrease) in fiber–matrix adhesion will not necessarily translate into a shorter (longer) critical length (See Appendix A). Note that the fiber strength as well as the CNT-fiber adhesion can be very sensitive to the CNT deposition conditions. For example, Bekyarova et al. [37] point out that high-temperature processing with CVD removes any sizing that may be applied to the fiber during manufacturing, and the CVD reaction may also significantly degrade the fiber strength. Zhang et al. [38] investigated the tensile strength properties as a function of time under different temperatures and atmospheric conditions and found high strength sensitivity between 750 °C and 800 C. As seen from Eqs. (A1) and (A2), a shorter critical length does not necessarily imply that the fiber–matrix interface is stronger, and vice versa. Indeed, the relative contributions of the fiber diam-
eter and the fiber strength are critically important. For example, a look at the T650 sized fiber data (Table 2) reveals that the sized fiber has better adhesion than the unsized fiber even though its critical length is slightly longer. As another example, had we not accounted for the diameter increase following CNT-coating in the present T-300 carbon fiber – thus had we used a fiber diameter ratio of 1 instead of 2.44 – the interfacial shear strength ratio would have become equal to 0.67 instead of 1.64, thus a decrease in interfacial strength instead of an increase. Thostenson et al. [39] correctly state that the critical length of the fibers can only be used as a relative measure of interfacial shear strength, when the shorter fragment lengths imply a stronger fiber/matrix interface, at a constant fiber diameter and fiber strength. They add, importantly, that fiber degradation can also result in smaller strength as well as shorter fragment lengths. Overall it appears that CNT grafting of carbon and silica fibers improves the fiber–matrix adhesion provided, however, that the Kelly–Tyson approach is assumed to remain physically valid when drastic changes in fiber diameter (such as those brought about by coatings or grafting) occur. This issue is of importance because of the well-known implications of interfacial adhesion on properties such as composite toughness and compressive strength.
5. Conclusions CNTs were CVD-grown upon individual carbon T-300 fibers and continuously monitored single-fiber fragmentation tests were performed on both the pristine and the CNT-grown fibers embedded in epoxy, to assess the effect of the treatment on the interfacial stress transfer. The critical fragment lengths, fiber tensile strengths at critical length, in situ fiber Weibull scale and shape parameters, and interfacial shear strength were evaluated. We observe a
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significant strength degradation of the CNT-grown carbon fibers compared to pristine fibers, due to the CNT growth conditions. Nevertheless, the CNT-grown fibers show an improvement in interfacial shear strength in epoxy, most probably due to the increase in apparent fiber diameter resulting from CNT grafting. A simple criterion for interfacial strength improvement in a SFC test was proposed, which addresses the most critical issue regarding direct CNT growth onto fiber surfaces, namely, by how much to limit the reduction of strength degradation of the fibers. More work is underway along these lines so as to yield CNT-grafted fibers suitable for improving critical engineering composite properties, including interlaminar toughness and compression strength. Acknowledgements This research was supported by a grant from the United StatesIsrael Binational Science Foundation (BSF), Jerusalem, Israel, and by the NES MAGNET program of the Israel Ministry of Trade and Industry. The generosity of the Harold Perlman family and the G.M.J. Schmidt Minerva Centre of Supramolecular Architectures is acknowledged. H.D. Wagner is the recipient of the Livio Norzi Professorial Chair in Materials Science.
Improved adhesion accompanied by a longer critical length; Worse adhesion accompanied by a (much) longer critical length. (iii) qr qr < 1. In this final case there are again three possibilities: Improved adhesion accompanied by a shorter critical length (the classical case); Worse adhesion accompanied by a shorter critical length (thus, a shorter critical length following treatment does not necessarily mean a better adhesion if this particular product of qr and qr leads to a value that is smaller than 1); And worse adhesion accompanied by a longer critical length. Thus the ‘strange’ (meaning: rarely observed) cases are predicted to occur on the upper-right and lower-left boxes on the plot. All other occurrences are traditionally observed in those fragmentation experiments where neither the fiber diameter nor the strength are affected by the surface treatment. The (1, 1) locus is the pristine reference point. The ‘strange’ cases involve fiber modifications due to surface treatment: a change in the fiber diameter (for example, through transcrystalline growth in thermoplastic matrices [40], or to CNT growth such as observed here); or a change in the fiber strength due to the treatment.
Appendix A Following a given fiber surface treatment, an observed increase (decrease) in fiber–matrix adhesion does not necessarily translate into a shorter (longer) critical length. Indeed, if ‘Tr’ and ‘Pr’ designate treated and pristine fibers respectively, we have
rTr ð‘Tr c Þ rPr ð‘Pr c Þ
s ¼ sPr Tr
Tr
r Tr r Pr
‘c ‘Pr c
q q
¼ rTr r ; ‘c ‘Pr c
ðA1Þ
where
qr ¼
!
r Tr ‘Trc ; r Pr ‘Prc
qr ¼
r Tr : r Pr
In other words, following treatment, the interfacial shear Tr strength sTr increases if ssPr > 1 or, using Eq. (A1), if
‘Tr c < qr qr : ‘Pr c
ðA2Þ
Eq. (A1) is plotted in Fig. 5, and as seen, several cases are possible: (i) qr qr ¼ 1, which occurs if (a) both the fiber strength and diameter are unaffected by the surface treatment (which is often the case when fibers are chemically treated), or if (b) the fiber strength and diameter are both affected by the treatment in a precisely compensating way (for example, an increase in qr by a factor of f is exactly compensated by a decrease in qr by a factor of 1/f, so that the product equals 1). The latter is a rare but nevertheless possible occurrence. Thus, if qr qr ¼ 1, Fig. 5 shows that there are only 2 unequivocal possibilities, because the hyperbolic line crosses the (1, 1) coordinate on the plot: better adhesion if a treated fiber exhibits a shorter critical length lc or worse adhesion if the fiber treatment results in a longer critical length. (ii) qr qr > 1. In this case, referring again to Fig. 5, there are three possibilities following treatment: Improved adhesion accompanied by a shorter critical length (the classical case);
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