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Composites: Part A 65 (2014) 47–56

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Hybrid nanoreinforced carbon/epoxy composites for enhanced damage tolerance and fatigue life Joel S. Fenner, Isaac M. Daniel ⇑ Robert R. McCormick School of Engineering and Applied Science, 2137 Tech Drive, Evanston, IL 60208, United States

a r t i c l e

i n f o

Article history: Received 21 March 2014 Received in revised form 27 May 2014 Accepted 31 May 2014 Available online 6 June 2014 Keywords: A. Polymer–matrix composites Carbon nanotubes B. Damage tolerance D. Mechanical Testing

a b s t r a c t Hybrid nano/microcomposites with a nanoparticle reinforced matrix were developed, manufactured, and tested showing significant enhancements in damage tolerance properties. A woven carbon fiber reinforced polymer composite, with the polymer (epoxy) matrix reinforced with well dispersed carbon nanotubes, was produced using dispersant-and-sonication based methods and a wet lay-up process. Various interlaminar damage tolerance properties of this composite, including static strength, fracture toughness, fatigue life, and crack growth rates were examined experimentally and compared with similarly-processed reference material produced without nanoreinforcement. Significant improvements were obtained in interlaminar shear strength (20%), fracture toughness (180%), shear fatigue life (order of magnitude), and fatigue crack growth rate (factor of 2). Observations by scanning electron microscopy of failed specimens showed significant differences in fracture surface morphology between the two materials, related to the differences in properties and providing context for understanding of the enhancement mechanisms. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Composite materials reinforced by nanoparticles (nanocomposites) are a prominent topic of recent and ongoing composites research. The improvement of material properties that can be obtained from relatively small quantities of nanoparticles has been a strong motivation for further exploration, leading to optimistic predictions of greatly enhanced mechanical properties across the board for such materials. In general, these broad predictions have often failed to materialize, and there is some disparity in the results obtained to date. Various studies involving nanoparticle enhancement have shown specific increases in static strength [1–5], fracture toughness [4,6–10], and fatigue life [11–15], among other properties, confirming the notion that nanoparticles can have impressive benefits at low concentrations. The resulting enhancements can vary widely depending on the type of property under investigation, the choice of materials, nanoparticle type, concentration and dispersion, and processing methods. Static strength improvement can vary, for instance, from the results of Bekyarova et al. [2] with a 20% increase in tensile strength of a carbon fiber/CNT composite, to those of Iwahori et al. [1] where increased tensile and ⇑ Corresponding author. Tel.: +1 847 491 5649; fax: +1 847 491 5227. E-mail address: [email protected] (I.M. Daniel). http://dx.doi.org/10.1016/j.compositesa.2014.05.023 1359-835X/Ó 2014 Elsevier Ltd. All rights reserved.

compressive strengths from 2% to 10% came at the expense of stiffness reduction. Other properties more indicative of structural survivability, such as fatigue life, can vary from results by Manjunatha et al. [14] with an almost order-of-magnitude improvement through the addition of silica and elastomeric nanoparticles to a glass fiber composite (at rather high concentrations near 10%), to those of Grimmer and Dharan [12] with an improvement of 2.5 times in a similar composite with only 1% CNTs. Improvements in damage tolerance properties are expected from the introduction of nanoparticles due to additional energy absorbing mechanisms that arise [7]. Addition of carbon nanotubes, for example, provides an additional source of energy absorption through processes such as frictional nanotube pullout, nanotube fracture and microcrack bridging (Fig. 1). This behavior on the nanoscale is reflected on the macro-scale through increased fracture toughness, improved impact damage tolerance, higher residual compressive strength, and extended fatigue life. Despite these anticipated and attractive enhancements, the manufacture of composites containing nanoparticles remains a challenge, as it is often difficult to produce quantities of material with a good dispersion of nanoparticles [16,17], a reasonable volume fraction, and a small void content [7]. Small changes in processing or materials can cause wide variation in final material properties, exacerbating the debate over the overall effect of nanoparticles on bulk material properties [7,18–24].

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Fig. 1. Mechanisms of energy absorption in hybrid nano/microcomposites (a) nanotube pullout and fracture and (b) microcrack bridging by nanotubes [3].

Evaluation and quantification of the effects of nanoparticles is not always a consistent and definitive proposition. For example, improvement in basic strength (tensile, compressive, or shear), though relevant, is often quantitatively modest, and hence is not always a good measure of enhancement and should not be examined alone [1]. Fracture toughness is a more meaningful parameter to consider, as it describes more directly the ability of the material to tolerate sudden damage or absorb energy during destructive processes, and hence improve the survivability of the material in service [25]. Fatigue life, and related fatigue-fracture crack growth rate, are material properties associated with more long-term or progressive failure processes, and hence describe the ability of a material to survive in service over long periods [26]. Given these considerations, this study focuses on the development, processing, and testing of hybrid multi-scale nano/microcomposite materials to demonstrate and evaluate the enhancements in damage tolerance and energy absorbing properties. The work describes a comparative study with one basic material – a typical woven carbon/epoxy composite – and examines the effect on final properties of the introduction of short multi-walled carbon nanotubes into the matrix during manufacture. A discussion is given, with plausible explanations of the observed results. 2. Material processing The material investigated was a carbon fabric/epoxy composite with the matrix reinforced by multi-walled carbon nanotubes (CNTs). The major mechanical reinforcement was provided by a 5-harness satin weave carbon fabric preform (AS4 fibers, 6 k tows, Hexcel AGP370-5H). The matrix was a Bisphenol-A epoxy resin (DGEBA, Huntsman GY 6010) cured with an anhydride hardener (methyltetraphthalic anhydride, Huntsman HY 917) and an additional amine accelerator (1-Methylimidazole, Huntsman DY 070). The nominal mixture ratio was 100:90:1 (resin:hardener:accelerator) by weight. This particular epoxy resin chemistry was chosen for its ability to tolerate mild temperature excursions (60 °C), prior to introduction of the accelerator, without appreciable shortening of pot life, allowing greater flexibility in processing. The nanotube reinforcement was provided by short multi-wall carbon nanotubes (Helix Material Solutions) of 1–2 lm length and 10– 30 nm outer diameter. A polyester block copolymer supplied in solution with a weakly volatile organic solvent (Disperbyk-2150, BYK Chemie) was used to facilitate dispersion of the CNTs. This particular dispersant was chosen based on prior work that demonstrated its effectiveness in dispersing carbon nanotubes (Fig. 2) [27]. A nanotube particle loading of 0.5 wt% of the epoxy resin

Fig. 2. Enhancement of nanotube dispersion with copolymer dispersant [27]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

was chosen based on earlier evidence suggesting a near optimum enhancement of matrix dominated properties (compressive strength, interlaminar shear strength) for this material system (Fig. 3) [27]. A weighed amount of DGEBA was combined with 0.5 wt% of nanotubes and 0.5 wt% of copolymer solution. The materials were mixed together thoroughly, and then vacuum degassed at an elevated temperature (80 °C) to remove the organic solvent. The anhydride hardener was added and mixed thoroughly, followed by further vacuum degassing. The resulting mixture was then sonicated (90 W at 20 kHz for 30 min) to disperse the nanotubes. Just prior to composite infusion, the amine accelerator was added to spur the polymerization reaction, followed by a final degassing stage. Infusion of the resin mixture into the carbon fiber preform was carried out layer by layer in a wet layup process. The wetted preform stack was also subjected to final degassing and then placed into a mold for curing. The construction of the mold (Fig. 4) allowed for careful control of finished laminate thickness and controlled removal of excess resin during curing. This approach was developed and adapted to avoid previously encountered problems related to a marked increase in resin viscosity due to the presence of nanotubes and a filtration effect on nanotubes encountered in VARTM processing. Elevated temperature curing was carried out in a two-step cycle: 30 min at 80 °C, 60 min at 150 °C, with heating at a rate of 2 °C/min. The same procedure was used for the reference (without CNTs) and nano-reinforced (hybrid) composites. After curing, composite plates were rough cut into specimens by means of diamondabrasive cutting wheels, and wet-polished with SiC abrasive papers to final dimensions and smoothness.

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Fig. 3. In-plane compressive and interlaminar shear strengths of hybrid composite as a function of CNT concentration with and without block copolymer dispersant [27].

1 – Composite laminate 2 – PTFE-coated release layers 3 – Lower tool plate 4 – Pressure plate 5 – Vacuum bag 6 – Resin outlet gallery 7 – Tacky-tape seal 8 – External pressure plate 9 – Gauge block (for thickness control)

Fig. 4. Schematic diagram of composite fabrication mold.

3. Fracture toughness Fig. 5. Specimen geometry of fixed-width double cantilever beam specimen.

3.1. Matrix fracture toughness The neat and CNT-modified matrices were characterized initially by measuring their fracture toughness. The Mode-I toughness was determined by means of a notched beam specimen under three-point bending [28]. The measured critical stress intensity factor KIc (for plane strain conditions) was found to be

Showing an increase of approximately 30%. The listed values are averages of 10 tests of each type, with ranges (±) corresponding to one standard deviation. The elastic modulus was found to be nearly the same for both materials, giving corresponding strain energy release rates of 2

GIc = 106 J/m for the neat epoxy resin. GIc = 182 J/m2 for the nanotubes-reinforced resin. Showing an increase of approximately 70%. 3.2. Interlaminar fracture toughness The Mode I interlaminar strain energy release rate of the reference and hybrid composites was measured by means of double cantilever beam (DCB) tests. The typical fixed-width double-cantilever beam specimen (DCB) (Fig. 5) is often employed in fracture toughness testing of composites due to its general simplicity of fabrication [25,29,30]. In general, the strain-energy release rate is defined as the energy required per unit area increase of the crack

dW f dAc

where Wf is the work of fracture. Ac is the fracture surface area.

1 P2 dC 2 b da

G¼

ð2Þ

In the case of the DCB specimen shown in Fig. 3, the specimen compliance C is

KIc = 693 (±71) kPa m1/2 for the neat epoxy resin. KIc = 910 (±101) kPa m1/2 for the nanotube-reinforced resin.

G¼

For any uniaxially-loaded specimen, the strain energy release rate may be expressed in terms of the specimen compliance C as

ð1Þ

C¼

    d 24 1 a3 1 E1  a  8a3 ¼ þ ffi 3 P E1 b 3 h 10 G13 h E1 bh

ð3Þ

Then,

GI ¼

   12 P2 a2 1 E1 P 2 a2 ffi 12 þ 2 2 3 10 G31 E1 b h h E1 b h

ð4Þ

where d is the end deflection. P is the load. E1 is the tensile modulus along the beam axis. G13 is the shear modulus in the plane of beam bending. a is the crack length. b is the specimen width. 2h is the specimen thickness. The approximation in Eqs. (3) and (4) is reasonable for slender specimens where a  h, or where shear deformations can be neglected. Fixed-width DCB specimens were machined from cast plates of both reference and nano-reinforced composite, utilizing a segment of PTFE film cast into the plate during fabrication as an interlaminar ‘starter’ crack at the loaded end of the beam. Nominal specimen dimensions were b = 25 mm and 2h = 2.8 mm (8 plies). Tests conducted on multiple specimens under displacement control produced load–displacement curves such as those shown in Fig. 6. The significantly higher fracture toughness of the hybrid composite over that of the reference is apparent from the higher loads during crack extension. Also of note is the stepwise ‘‘zig-zag’’ form of the

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200 180 160

Load (N)

140 120 100 80 Hybrid

60 40 20

Reference

0 0

5

10

15

20

Displacement (mm) Fig. 6. Load–displacement curves from fixed-width double cantilever beam fracture toughness tests.

load–displacement curve, indicative primarily of crack propagation over woven fiber crimps (the advancing crack front follows the contour of the woven fabric surface rather than a straight path) resulting in local changes in coupon behavior. In addition, there is notably greater ‘step’ magnitude in these ‘‘zig-zag’’ features in the hybrid composite than in the reference material, which is consistent with a greater fracture energy measured. Fracture toughness for these fixed-width specimens was computed by two approaches: by the compliance method using Eq. (4) at points where crack length measurements were taken, and by numerically calculating the work of fracture from the load–displacement curves using Eq. (1). Measurement of the crack length in the above tests is not always easy or accurate. Numerous factors impede measurement of the crack length, such as the difficulty in observing the crack on a carbon composite (which is black in color) and the difficulty in confirming a perfectly orthogonal advancing crack front. For improved accuracy and testing confidence, a width-tapered DCB specimen was adopted for additional tests (Fig. 7) [29]. The specimen compliance in this case is given by

advantage of this type of test is that the crack grows in a stable manner, regardless of crack length. This obviates the need for close monitoring of the crack length. Multiple specimens of this type were prepared and tested similarly as the constant-width DCB specimens under displacement control, giving load–displacement curves such as those of Fig. 8. Nominal specimen dimensions were k = 2.33 and 2h = 2.8 mm (8 plies) with Vf = 0.55. As with the fixed-width specimens, the difference in load during crack extension is indicative of the higher fracture toughness in the hybrid composite than that of the reference material. The same stepwise ‘‘zig-zag’’ characteristics of the load displacement curve are also seen again, related to the woven structure of the material, as is the increase in ‘‘zig-zag’’ step height in the nanoreinforced material. Fracture toughness for these width-tapered specimens was computed by two approaches: by the compliance method using the mean load from the load– displacement curve during stable crack growth in Eq. (6), and by numerically calculating the work of fracture from the load– displacement curves using Eq. (1). Results from both fixed-width and width-tapered DCB tests were in good agreement within each specimen type and for both methods of strain-energy release rate calculation (6%). The values of interlaminar fracture toughness determined for the two materials were GIc = 176 (±14) J/m2 for the reference material. GIc = 498 (±61) J/m2 for the hybrid nano-reinforced material. Showing a significant increase of 180% in Mode-I fracture toughness for the nano-reinforced composite over that of the reference material. The listed values are averages of 8 tests for each material type (4 fixed-width and 4 width-tapered), with ranges (±) corresponding to one standard deviation. The above calculations of strain energy release rate are based on an implicit assumption of linear elastic behavior. This assumption is corroborated by the load–deflection loading/unloading curves for the two types of specimen used (Fig. 9).

4. Fatigue 2

C¼

d 12a k ¼ 3 P E1 h

ð5Þ

where k ¼ ba, the width taper ratio of the specimen. Then, the strain energy release rate for the width-tapered specimen is given by

4.1. Interlaminar shear fatigue Fatigue tests were conducted with short beams under cyclic load controlled three-point bending aimed at producing a cyclic

175

2

1 P2 dC 12P2 k ¼ 3 2 b da E1 h

ð6Þ

It is readily noted that this geometry removes the mathematical dependence of strain energy release rate on crack length a. The

150 125

Load (N)

GI ¼

100

Hybrid

75 50 Reference

25 0 0

20

40

60

80

100

Displacement (mm) Fig. 8. Load–displacement curves from width-tapered double cantilever beam fracture toughness tests. Fig. 7. Specimen geometry for width-tapered double cantilever beam specimen.

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70

100

60 50

80

Load (N)

Load (N)

120

60 40

30 20

20 0

40

10 0

5

10

15

20

25

30

35

40

45

Displacement (mm)

0

0

5

10

15

20

25

30

35

40

45

Displacement (mm)

Fig. 9. Loading/unloading displacement curves for the types of cantilever specimens used.

interlaminar shear stress. For such tests, the peak interlaminar shear stress at the center of the beam is

smax ¼

3P 4bh

ð7Þ

All cyclic loading was performed with stress ratio R = rmin/rmax = 0.1. Specimens were nominally 25 mm long, 10 mm wide and 5.5 mm thick (16 plies). Stress–life curves were produced for both the reference composite and the hybrid material containing CNTs (Fig. 10). Because the composite material is generally expected to behave elastically over the range of chosen applied stresses (60% to 80% of static shear strength), and with the intention of subjecting the material primarily to high-cycle fatigue, it is reasonable to assume that a form of the Basquin equation should fit the experimental data [31], hence

smax ¼ AN1=c

ð8Þ

where smax is the maximum cyclic shear stress. N is the number of cycles. A is a stress parameter related to the static strength. c is a parameter related to the rate of damage accumulation. The parameters for the two materials tested were found to be: A = 58.8 MPa and c = 20.47 for the reference composite. A = 66.2 MPa and c = 22.17 for the hybrid composite.

Max Shear Stress (MPa)

60

50

40

It can be seen that, at a given cyclic load amplitude, there is a significant difference of more than an order of magnitude in lifetimes between the two composite materials (Fig. 10). This can be attributed in part to the higher static interlaminar shear strength of the hybrid composite (20%) and in part to an expected increase in the Mode II interlaminar fracture toughness, although both of these increases are relatively moderate. The observed order of magnitude increase is the result of their amplified effect on the logarithmic lifetime. The difference in the stress parameter, A, is closely tied to the observed increase in static strength of the nanoparticle-enhanced material over the reference material. The difference in the slope parameter, c, is also significant, as it implies a slightly more gradual fatigue life rate, resulting in further separation of fatigue life curves between the reference and nanoparticle-enhanced materials at higher numbers of cycles. This, in turn, implies a slightly lesser sensitivity of the nanoreinforced composite to changes in applied stress amplitude. 4.2. Interlaminar fatigue crack growth In the case of the fixed-width DCB specimen, the ease of manufacture is offset by a more demanding protocol for data collection, namely the accurate measurement of crack length a during the test. This proved somewhat inconvenient in the case of static fracture-toughness tests, especially due to difficulty in observing the crack tip and accurately measuring the crack length along a deformed specimen. However, this would have proven more challenging in the case of fatigue-fracture tests, as it would have been necessary to periodically halt the test and make crack length measurements. To avoid such difficulties, as are still typically encountered in such experiments [25], width-tapered DCB specimens were employed exclusively [32]. To this end, the stress intensity factor for an applied load P may be calculated from Eq. (6) as

sffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 12 K I ¼ EGI ¼ Pk 3 h

Hybrid

ð9Þ

Hence, for the case of fatigue-fracture under load-control, 30

Reference

1

10

100

1,000

10,000

100,000

1,000,000 10,000,000

Cycles Fig. 10. Stress–life curves for interlaminar shear fatigue.

sffiffiffiffiffiffi 12 DK ¼ ðPmax  Pmin Þk 3 h

ð10Þ

where DK is the peak-to-peak magnitude of stress-intensity oscillation. Furthermore, the specimen end deflection amplitude is easily monitored during testing, and permits the calculation of the

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‘‘instantaneous’’ crack length from measured specimen compliance by rewriting Eq. (5) as

ð11Þ

The fatigue crack growth rate is typically described by the semiempirical Paris Law

da ¼ CðDKÞm dN

ð12Þ

80

Crack Length (mm)

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   3 d Eh a¼ P 12k

90

where N is the number of cycles. C and m are empirical parameters.

70 60 50 40 30 20 10 0 40,000 50,000 60,000 70,000 80,000 90,000 100,000 110,000

Cycles

C ¼ 2:049  107

Fig. 12. Representative plot showing comparison of directly measured crack length (points) and computed crack length from continuous record of deflection (curve) versus fatigue cycles.

Calculated Crack Length (mm)

Thus, it is possible to conduct a test under load-control at constant cyclic stress intensity amplitude DK and expect a constant crack growth rate da/dN. This is otherwise impossible with a fixed-width DCB. Fully automated and continuous monitoring of the crack length becomes possible from typical testing machine data in a fairly simple setup (Fig. 11). A representative plot of directly measured crack length and crack length computed from a continuous record of deflection amplitude is shown in Fig. 12. Fatigue tests were conducted on width-tapered DCB specimens at constant cyclic load (and stress intensity) amplitude and load amplitude ratio of Pmin/Pmax = 0.1, while monitoring (measuring and computing) crack length. Direct crack length measurements were used primarily to verify the computed crack length curves as in Fig. 12, showing agreement between the two approaches. Typical results of crack length versus fatigue cycles are shown in Fig. 13 for the reference and hybrid composites. It is noted that, once the crack extends sufficiently far beyond the tab and transitional fillet (where the hinges are attached, Fig. 7), the cyclic crack growth becomes essentially linear, allowing a simple linear fit to determine da/dN. The waviness in the curves, similar to the ‘‘zig-zag’’ behavior observed under static loading (Figs. 6 and 8), is again attributed to the crimps of the fabric weave. Results from many such tests at different cyclic load amplitudes produced were fitted to the Paris Law relation (Eq. (12)) as plotted in Figs. 14 and 15. The following parameters were determined

80 70 Reference

60 50 Hybrid

40 30 20 0

5000

10000

15000

20000

25000

30000

Cycles Fig. 13. Representative plot of computed crack length versus. cycles for reference and hybrid nano-reinforced composite, DK = 2.59 MPa m1/2 for both specimens.

for reference composite

m ¼ 10:55 C ¼ 4:89  108

90

0.008

for the hybrid nano  reinforced composite

0.007

1/2

with DK in MPa m and da/dN in mm/cycle. It is evident from the crack growth rate data and Paris Law parameters that the hybrid

da/dN (mm/cycle)

m ¼ 11:15

0.006 0.005 Reference

0.004 0.003

Hybrid

0.002 0.001 0.000 1.8

2

2.2

2.4

2.6

2.8

3

ΔK (MPa-m1/2 ) Fig. 14. Crack growth rate versus cyclic stress intensity for Mode-I interlaminar fatigue.

Fig. 11. Setup for Mode I fatigue testing of tapered double cantilever beams.

nanocomposite exhibits a lower crack growth rate than the reference material at a given cyclic loading. Furthermore, the onset of crack growth in the hybrid composite occurs at a higher value of DK and is somewhat delayed or shifted compared to the reference composite (Fig. 14) – implying the need for a greater minimum

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log (da/dN) ( log(mm/cycle) )

-1.50 -2.00 Reference

-2.50 Hybrid

-3.00 -3.50 -4.00 -4.50 0.25

0.30

0.35

0.40

0.45

0.50

53

CNTs, as shown in Fig. 17 (1.8 k versus 15 k magnification). Fatigue-fracture images also show a more sharply contoured or ‘fractal’ form of fracture surface than static fracture, further highlighting the effect of nanotubes on the composite properties. Nanotube pullout is evident in the pitting and protruding nanotube ends seen in the fatigue-fracture images in Fig. 17 (15 k magnification) but with a great deal more complex fracture morphology. This suggests that the mechanism of damage tolerance enhancement does not come purely from processes like nanotube pullout or fracture, but partially from modifying the crack surface at very small length scales. The more fractal surface of nanotube-enhanced material presents more total surface area, implying a greater number of chemical bonds in the matrix polymer being broken during crack propagation.

log (ΔK) ( log(MPa-m1/2 )) Fig. 15. Crack growth rate versus cyclic stress intensity (log–log scale).

stress intensity (or strain energy) in the nanoreinforced material for a nascent crack to begin propagating. The log–log plot of fatigue crack growth behavior (Fig. 15) is potentially more revealing by drawing comparisons with the interlaminar shear fatigue results (Fig. 10). The hybrid composite behavior in both cases exhibits a similar slope as the reference material, but there exists a considerable separation between the two lines. In general, for this material, it appears that nanoreinforcement primarily has the effect of imposing a ‘‘loading shift’’ on plots of fatigue behavior, implying a nearly constant reduction in rate of crack growth or increase in logarithmic lifetime independent of cyclic load amplitude.

5. Fractographic observations Failed specimens from interlaminar Mode-I static and fatigue fracture testing were abrasively machined into suitable samples for scanning electron microscopy. Surface conductivity for imaging was improved by plasma-deposition of metallic Osmium at a thickness of approximation 5 nm. Fig. 16 shows typical images of fracture surfaces of statically-tested width-tapered DCB specimens, while Fig. 17 shows typical images from fatigue crack growth specimens. The images show a noticeable difference in fracture morphology between the reference and hybrid nanotube-reinforced composite. The reference material with its neat epoxy matrix typically exhibits a smoother fracture surface than the hybrid material with nanotubes reinforcing the matrix. The apparent ‘haziness’ in the hybrid sample images comes from protruding

6. Fracture description and modeling To better illuminate the significance of the experimental results presented in this study, it is worthwhile to examine them in the context of rudimentary models and explanations. The results of Mode-I static fracture toughness tests are shown in Fig. 18 in a schematic presentation illustrating the degrees of enhancement introduced by the various material forms. Conventional explanations of nanoparticle reinforcement mechanisms in composites emphasize processes such as nanotube pullout. These processes are easy to envision, and on an individual basis have the potential to absorb significant amounts of energy. However, in the case of composites with a low nanotube content, as in this study, these explanations alone are not sufficient to account for the observed material behavior. In an approximation of energy absorption, a single CNT may be treated as an idealized rod bridging an advancing microcrack (Fig. 19). Assuming half the length of a nanotube ‘pulls out’, the equivalent local ‘‘surface fracture energy’’ absorbed by pullout of a CNT per unit crack surface may be estimated as

Gpullout ffi GCNT

1 2 1 4

pld l ¼ 2 GCNT d pd2

ð13Þ

where d is the nanotube diameter (nominally 20 nm). l is the nanotube length (nominally 1500 nm). It has been shown by experiment that a reasonable value of pullout surface energy for a single MWCNT is about GCNT = 20 J/m2 [33,34], which gives Gpullout ffi 3000 J/m2 locally at a single nanotube.

Fig. 16. Scanning electron micrographs of representative fracture surfaces from static fracture toughness tests: left: reference composite; right: hybrid nano-reinforced composite.

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Fig. 17. Scanning electron micrographs of representative fracture surfaces from fatigue-fracture tests. Left: reference composite; right: hybrid nano-reinforced composite (DK = 2.64 MPa m1/2 for both specimens, crack propagation is from top to bottom of image).

Fig. 19. Illustration of idealized single nanotube pullout during crack advance.

Fig. 18. Illustration of measured increases in Mode I fracture toughness in various material forms.

The volume fraction of the matrix polymer occupied by carbon nanotubes is given by

V CNT ¼

MCNT qm qCNT þ MCNT qm

ð14Þ

where MCNT is the CNT mass fraction (0.5%). qm is the density of the matrix polymer (1.20 g/cm3). qCNT is the average density of a carbon nanotube (approximation 1.50 g/cm3). The CNT volume ratio calculated from the above is VCNT = 0.4%. Using a rule-of-mixtures, the contribution of the CNTs to the overall matrix fracture toughness should then be 2

DGI;pullout ¼ V CNT Gpullout ffi ð0:004Þð3000 J=m Þ ¼ 12 J=m

2

ð15Þ

Clearly this value is well below the observed 92 J/m2 increase measured in this study (Fig. 18), even if one allows for some

improvement from nanotube waviness or nesting, so this mechanism alone is not sufficient to explain the large increase in fracture toughness. In practice, this value represents a lower-bound, as nanotubes are never perfectly straight or perfectly isolated from one another. In reality, nanotubes exhibit waviness and nesting as illustrated in Fig. 20. These irregularities greatly increase the pullout energy and divert the crack propagation. In addition, they may cause multifaceted matrix fractures or even CNT fractures. The SEM fractographs of Figs. 16 and 17 suggest a different picture of the failure process. The images show a change in fracture surface morphology in samples containing nanotubes. This resultant surface is not simply a flat, glassy plane with a ‘‘forest’’ of protruding nanotube ends, as a simple pullout model (Fig. 19) would suggest. Instead, the crack surface morphology in the resin matrix between fibers is more rugged because of the tortuous crack propagation through and around the CNTs (Fig. 20). This presents a larger true crack surface area. The irregular fracture surface observed in the SEM micrographs could be represented as a sinusoidal one,

y ¼ A sin

  2p x k

ð16Þ

A nominal ‘‘period’’ of k  3.5 lm and a peak-to-peak amplitude between one and two carbon fiber diameters (2A  10 lm) can be

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55

Fig. 20. Illustrations of realistic nanotube profiles and proposed effect on crack path. Left: nanotube waviness, right: nested nanotubes.

estimated from observation of the fractograph of Fig. 16. Taking a line integral over one period of this function and comparing it with the length of a straight path we obtain

S¼

1 k

Z 0

k

" 1þ

 2  #1=2 2p A 2px cos2 dx k k

ð17Þ

which represents a ratio between the larger crack ‘area’ of the tortuous crack compared to a perfect straight crack. For the given parameters, S  6.0, suggesting that a much larger crack surface area is formed in the matrix by the irregular crack path. Under this explanation, a significant portion of the increase in overall material fracture toughness comes in part from a micro-scale increase in matrix crack surface area. Considering the case of hybrid composite, weighting the contributions of the various proposed energy absorption mechanisms in a rule-of-mixtures approach gives an expected increase in GI of

DGI ¼ V CNT V m Gpullout þ SV m Gm ¼ ð0:004Þð0:45Þð3000 J=m2 Þ þ ð6:0Þð0:45Þð106 J=m2 Þ ffi 300 J=m2

It was demonstrated that such hybrid composites, with 0.5 wt% carbon nanotube reinforcement, show a modest increase of approximately 20% in static strength but a much larger enhancement of approximately 180% in interlaminar strain energy release rate. The combination of these effects manifests itself as an order of magnitude increase in interlaminar shear fatigue life. The interlaminar fatigue crack growth rate was also reduced by nearly a factor of 2 due to the presence of nanotubes in the composite matrix. These impressive enhancements to damage tolerance properties of the hybrid composite arise from a combination of energyabsorbing mechanisms derived from the nanotubes themselves (e.g. nanotube pullout) and from alterations to the morphology of the crack surface (e.g. fractal/textural roughness). Acknowledgments This work was supported in part by the Office of Naval Research (ONR) and by ISEN (Initiative for Sustainability and Energy at Northwestern). We are particularly grateful to Dr. Y.D.S. Rajapakse of ONR for his encouragement and cooperation.

ð18Þ

which is close to the value of 322 J/m2 increase measured experimentally (Fig. 18). It is therefore reasonable to conclude that the alteration to the crack surface geometry plays a significant role in the measured improvement in fracture toughness properties in the CNT-modified composites in this study. Therefore, while nanotube pullout does occur in fracture of nanocomposites, it is not the most significant mechanism by which nanotubes enhance fracture toughness. It appears that nanotubes, especially if they are wavy or nested, tend to blunt or re-direct the advancing crack, forcing it to follow a more tortuous path (Fig. 20), and greatly improve the macroscopic fracture toughness through an increase in total crack surface area. In addition, the presence of the continuous reinforcing fibers of the composite confines the crack to a more limited intra-tow or inter-tow path ‘‘band’’, augmenting the extent to which individual nanoparticles can blunt, re-direct, or arrest advancing microcracks. 7. Conclusions It was shown in this study that significant improvements in matrix dominated properties and energy absorption characteristics can be realized in hybrid nano/microcomposites by nanoparticle reinforcement of the matrix. While the presence of nanoparticles in the matrix offers modest improvements in strength and fracture toughness of the matrix alone, the overall enhancement of the hybrid composite is more dramatic.

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