- Email: [email protected]
Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes
Composites Science and Technology 71 (2011) 1486–1494
Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes Shafi Ullah Khan, Chi Yin Li, Naveed A. Siddiqui, Jang-Kyo Kim ⇑ Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
a r t i c l e Article history: Received 9 October Received in revised Accepted 23 March Available online 23
i n f o 2010 form 4 March 2011 2011 June 2011
Keywords: A. Carbon nanotubes A. Carbon fibres B. Vibration
a b s t r a c t Vibration damping characteristic of nanocomposites and carbon fiber reinforced polymer composites (CFRPs) containing multiwall carbon nanotubes (CNTs) have been studied using the free and forced vibration tests. Several vibration parameters are varied to characterize the damping behavior in different amplitudes, natural frequencies and vibration modes. The damping ratio of the hybrid composites is enhanced with the addition of CNTs, which is attributed to sliding at the CNT–matrix interfaces. The damping ratio is dependent on the amplitude as a result of the random orientation of CNTs in the epoxy matrix. The natural frequency shows negligible influence on the damping properties. The forced vibration test indicates that the damping ratios of the CFRP composites increase with increasing CNT content in both the 1st and 2nd vibration modes. The CNT–epoxy nanocomposites also show similar increasing trends of damping ratio with CNT content, indicating the enhanced damping property of CFRPs arising mainly from the improved damping property of the modified matrix. The dynamic mechanical analysis further confirms that the CNTs have a strong influence on the composites damping properties. Both the dynamic loss modulus and loss factor of the nanocomposites and the corresponding CFRPs show consistent increases with the addition of CNTs, an indication of enhanced damping performance. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Carbon fiber reinforced polymer composites (CFRPs) are widely used in aerospace, automotive and other high performance structural applications due to their high stiffness and strength to weight ratio. Besides various mechanical properties and fracture resistance, vibration damping capability is very important as it affects system performance, safety and reliability [1–6]. Many engineering structures made from CFRPs, including military equipment, automobiles, aircrafts, wind turbine blades and spacecrafts, often suffer from the menace of vibrations during their normal operations. Micro-cracks present in these structures propagate rapidly due to fatigue caused by vibrations, resulting in premature failure. Materials with high stiffness values generally have a low damping ability and so does CFRPs. Widespread applications of CFRPs in new areas are often limited due to their low damping factor resulting from poor viscoelastic nature of carbon fibers and poor damping at the CFRP interface [2]. A few methods have been suggested to improve the damping properties of CFRPs, e.g. addition of high damping polymer layers in prepreg lay-up [3,4] and use of hybrid rubber particle reinforced composites [5]. However, the improvements in
⇑ Corresponding author. Tel.: +852 2358 7207; fax: +852 2358 1543. E-mail addresses: shafi[email protected] (S.U. Khan), [email protected] (J.-K. Kim). 0266-3538/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2011.03.022
damping properties arising from these methods are at the expense of reduced mechanical properties of the composites. With the development of carbon nanotubes (CNTs) and their composites in the last two decades, significant attention has been paid to improve the damping properties of polymers, especially epoxy, in terms of loss modulus [6–8] or damping ratio [9,10]. The combination of extremely large specific surface area along with large interfacial area, week interfacial adhesion with the polymer, and low mass density offered by carbon nanotubes implies that frictional sliding of nanotubes with the polymer matrix can cause dissipation of a large amount of energy with minimal weight penalty, providing the nanocomposites with a high damping capability. While a high damping capability is achieved by taking advantage of large interfacial friction between the CNTs and resin [6–8], reinforcement of strong and stiff CNTs means simultaneous improvements of various important mechanical properties of nanocomposites [11,12]. The ‘‘stick–slip’’ mechanism is known to be responsible for the improvement of energy dissipation capability of CNT nanocomposites [8–10]. When the nanocomposite is subjected to an external stress, a shear stress is generated between the nanotube wall and the surrounding matrix resin due to the elastic mismatch according to the well-known shear lag theory. The nanotubes will elongate together with the matrix if they are bonded, but once the external load exceeds a critical value, the nanotubes will stop
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
elongate together with the matrix [13]. Further increasing the load will result in the deformation of the matrix, which would start flowing over the nanotube surface, allowing the deformation energy to be dissipated through the slippage between the nanotubes and the matrix. If the load is released below the critical value, the deformation of CNTs will resume together with the matrix and the interfacial sliding will be vanished. The energy dissipation capability of CNT nanocomposites is dependent on the strain amplitude of applied load [9,10]. It is because the CNTs are randomly dispersed into the matrix without particular orientation, and thus the tube walls will be subject to varying shear stresses although a uniform stress is applied from the vibration source. In general, the higher is the external load, the more is the CNT-matrix interfacial slippage and so is the more energy dissipation. Most previous studies on the above damping properties are limited to epoxy-based nanocomposites containing CNTs, but it can also be well expected that use of a CNT–modified epoxy matrix may also improve the damping characteristics of CFRP laminates. We hereby report a study on the effects of CNT on vibration damping characteristics of CNT–CFRP hybrid composites. The CNT–CFRP hybrid composites are produced based on a prepreg process using a CNT reinforced resin as the composite matrix. Flexural testing mode was selected because most of the structures that are prone to damping suffer bending loads. As such, a flexural test as specified in ASTM Standard was used for measuring vibration damping properties using damped cantilever beam theory. The damping behavior of CNT–CFRP hybrid composites are characterized in terms of damping ratio and natural frequency in both free and forced vibration tests. 2. Relationship between applied load, 1st vibration amplitude and beam length The relationship between the initial vibration amplitude, x1, and the initial vibration load, P, is presented in the following. Consider a single cantilever beam of a total length L, shown in Fig. 1. When an initial vibration load, P, is applied to the beam, there will generate an initial elastic deflection, V(z), and an initial vibration amplitude, x1, assuming the beam vibrates in the 1st mode. The bending moment M(z) is given by:
MðzÞ ¼ EI
@2V z ¼ PL 1 @z2 L
ð1Þ
where EI is the flexural rigidity of the beam. Thus, the displacement V(z) is given by:
VðzÞ ¼
Z
z
z¼0
Z
z
z¼0
MðzÞdz ¼
PL z2 z3 ¼ EI 2 6L
Z
z
z¼0
Z
z PL 1 dz L z¼0 z
ð2Þ
At the free end of the beam, z = L, the deflection V(L) is given:
VðLÞ ¼
PL3 3EI
ð3Þ
1487
In the case of free vibration of a cantilever beam, the 1st vibration amplitude is equivalent to the deflection, i.e. V(L) = x1. Thus, P can be written as:
P¼
3EI L
3
x1 ¼ a
x1 L3
ð4Þ
where the flexural rigidity coefficient a = 3EI is a consistant for a given specimen with a constant cross-sectional shape. Eq. (4) implies that the ratio of initial vibration amplitude to cube of beam length, x1/L3, is directly proportional to the applied vibration load. 3. Experiments 3.1. Materials and fabrication of prepregs of CFRP–CNT hybrid composites The multi-walled carbon nanotubes (MWCNT Hollow-NK 50, supplied by Finetex Technology) used in this study (Fig. 2) were produced by a chemical vapor deposition (CVD) method. They had an outer diameter ranging between 40 and 60 nm and an average length of about 20 lm. The as-received CNTs were functionlized by a UV–ozone treatment for 30 min to create the oxygen containing functional groups on the CNT surface, which in turn helped uniform dispersion of CNT agglomerates into individual CNTs [14,15]. The oxidized CNTs were further functionalized in a mixture of acetone and a nonionic surfactant, polyoxyethylene octyl phenyl ether (Triton X-100, supplied by VWR International) with the critical micelle concentration (CMC) value of 10CMC for 2 h to improve the interfacial interactions with the epoxy matrix [16]. The epoxy resin (LY556 supplied by Huntsman) was added into the solution and the mixture was further sonicated for 1 h to improve the dispersion of CNTs in the epoxy. The epoxy-CNT mixture was degassed in a vacuum oven to evaporate acetone for 2 h, followed by high speed shear mixing (ROSS) at 4000 rpm for 30 min. Both the neat epoxy resin and the epoxy-based nanocomposites containing CNTs of varying contents were used to produce carbon fiber reinforced composite (CFRP) prepregs via a solventless prepregging process. The epoxy resin with and without dispersed CNTs was mixed with a hardener system (consisting of Aradure 5021 and hardener XB3041, supplied by Huntsman) at a mixing ratio of 100:25:12 before filling into the prepregger resin pot. The CNT contents were varied between 0 and 1.0 wt%. Carbon fiber rovings (Pyrofil TR 30 S, from Mitsubishi Raynon) with a filament count of 6 K were impregnated to produce prepreg sheets of thickness about 0.4 mm on a lab-scale prepregger (Model 40 Research Tool Corp.). The temperature of the resin bath was set at 37 °C, which was optimised to maintain the viscosity of the CNT-resin mixture within the required range of 1.5–2.5 Pa s and thus to achieve good wetting of carbon fiber tows. 3.0 mm thick laminates consisting of nine layers of unidirectional prepregs [0]9 were fabricated by hand lay-up and curing in a vacuum hot press (CARVER No. 4122) at 90 °C for 8 h. In addition to CFRP laminates, plates made from neat epoxy resin as well as CNT nanocomposites without carbon fibers were also produced using the same CNT functionalization and dispersion processes. 3.2. Measurements of vibration damping properties
Fig. 1. Cantilever beam subject to an external load P at fixed end L.
Rectangular specimens of 10 mm wide 3.0 mm thick 230 mm long were cut from the CFRP laminates and nanocomposite plates for vibration tests according to the ASTM standard E756. The specimens were tested in both the free vibration and forced vibration modes and the corresponding configurations are given Fig. 3. The free beam length is defined as the distance between
1488
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 2. SEM (a) and TEM (b) images of MWCNTs used in this study.
Fig. 3. Schematics of experimental set-up for (a) free vibration test and (b) forced vibration test.
the clamp and the specimen tip. In the free vibration test, cantilever beam specimens were used with one end clamped and the other end deflected to a desired displacement before release. The resulting vibration response was continuously monitored using the accelerometer attached to the tip of the specimen, which was stored in a digital storage cathode ray oscilloscope (CRO). The vibration data were processed to determine the damping ratio, n, based on the logarithmic decrement method [10]:
n¼
1 x1 ln xn ðn 1ÞT d xn
ð5Þ
where xn is the fundamental natural frequency in radian, n is the number of cycle of free vibration, Td is the period of the 1st vibration cycle, and xn is the amplitude of the nth vibration cycle. n = 11 was chosen for the calculation of damping ratio in this study so that the system error from the CRO reading can be minimized.
Several important material and geometric parameters were varied to study the damping characteristics of materials affected by different CNT contents, damping amplitudes and dampted natural frequencies. There is a critical shear stress above which interfacial sliding of CNTs initiates against the epoxy matrix. Because the CNTs were randomly dispersed in the matrix, the shear stress components acting on the CNTs with different orientations were all different. Moreover, the flexural vibration test means that the strain varies though the beam thickness. Thus, while flexural vibrations at sufficiently high amplitudes may activate certain CNT–epoxy slippage mechanism near the surface of the beam where strains are concentrated, a large proportion of the volume of the beam near the beam mid-plane will have little or no slippage. This means that when an external vibration load is applied to the specimen, not all the shear stress component on CNTs can reach the critical value to initiate interfacial sliding at the same vibration load. In
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
other words, the damping ratio given by Eq. (5) increases with increasing the vibration load, P, according to Eq. (4), allowing more CNTs to undergo interfacial sliding. Thus, to study the amplitudedependent damping characteristics of the materials, the specimens were placed to maintain a constant free length, L = 185 mm, while the initial tip amplitudes, x1, were varied between 10 and 40 mm with an increment of 10 mm. The damped natural frequencies of specimens were also varied by modifying the beam length, L, from 120 mm to 170 mm with an increment of 10 mm. The natural frequency is a system property and is independent of applied vibration load, P. Thus, the vibration amplitude was selected to keep the ratio of initial vibration amplitude to cubic of beam length, x1/L3, constant, as indicated by Eq. (4), such that P remained constant regardless of the change in natural frequency. An approximately constant ratio, x1/L3 = 200,000 was chosen in this study to determine the corresponding initial vibration amplitude as given in Table 1. To study the damping behavior of CNT nanocomposites and CFRP composites under different vibration modes, the forced vibration tests were also carried out as shown in Fig. 3b. The specimen having a free length of 180 mm was fixed at one end. The beam was excited sinusoidally using a mini shaker with an input voltage of 0.3 V for CFRP laminates, and 0.1 V for neat epoxy or nanocomposite specimens in order to create similar vibration amplitudes at the 1st resonance frequency, or the damped natural frequency, xn. An accelerometer was used to monitor the tip displacement data as in the free vibration test. The damping ratio was calculated based on the half-bandwidth method as shown in Fig. 4, according to the following equation,
n¼
Dx 2xn
ð6Þ
where Dx is the difference between frequencies x1 and x2 corresponding to half power points around the fundamental damped natural frequency, xn. 3.3. Dynamic mechanical analysis Dynamic mechanical analysis was employed using a dynamic mechanical analyzer (DMA-7, Perkin Elmer), according to the specification, ASTM Standard D4065. The samples with dimensions 20 mm long 3 mm wide 1.0 mm thick were tested in a three point bending mode from 25 to 150 °C at a heating rate of 10 °C/ min and a frequency of 1.0 Hz. 4. Results and discussion
1489
Fig. 4. Definitions of x1, x2 and xn according to the half-band width method.
capabilities of epoxy and CFRP improved significantly with the addition of CNTs as evidenced by the increasingly rapid decaying of the vibration amplitudes. As can be envisaged from the comparison of waveforms in Figs. 5 and 6, the natural frequency, xn of CFRPs was much higher than that of neat epoxy or nanocomposites for a given initial vibration load amplitude because as the square of natural frequency is proportional to the flexural stiffness to mass ratio of the beam, EI/m. Damping ratios of these materials were determined for a fixed cycle number, n = 11, according to Eq. (5). Fig. 7 plots the damping ratios of the composites with varying CNT contents as a function of vibration amplitude. The CFRP laminates had a slightly lower damping ratio than the neat epoxy or nanocomposite due to the poor viscoelastic nature of carbon fiber and poor energy dissipation through the fiber and matrix interface [2]. It is interesting noting that for the neat epoxy and CFRP without CNT reinforcement, the damping ratios were almost constant independent of the initial vibration amplitude applied between 10 mm and 40 mm. A further increase in the initial vibration amplitude may result in inaccuracy of calculated damping ratios because the logarithmic decrement method represented by Eq. (5) can only be used for small vibration amplitudes. In contrast, the damping ratios of the nanocomposites and CFRPs containing CNTs increase almost linearly with the initial vibration amplitude, the higher was the CNT content the more prominent was the increase. The CFRP laminates in general showed a higher degree of increase in damping ratio than the nanocomposites for a given increment of vibration amplitude.
4.1. General waveform and damping ratio in free vibration The damped natural frequency of CFRP became lower after the incorporation of CNTs into the matrix due to the enhancement of damping ratio. Similar to the damping behavior of CNT reinforced nanocomposite, the CNT–CFRP hybrid composites showed an amplitude dependent vibration characteristic, which indicates that the CNT modified matrix material was responsible for the improvement in damping characteristics. Figs. 5 and 6 show the free vibration time histories of nanocomposites and CFRP laminates containing varying CNT contents at the same initial vibration amplitude. It can be seen that the damping
Table 1 Cantilever beam free length and the corresponding initial vibration amplitude. Beam free length, L (mm) Initial vibration amplitude, x1 (mm)
170 24
160 21
150 17
140 14
130 11
120 9
4.2. Effects of beam length and natural frequency on damping ratio The free vibration tests were further performed at different natural frequencies by varying the beam length and thus the flexural stiffness, EI. The damped natural frequency xd, depends both on the natural frequency, xn and the damping ratio, n according to the following equation,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
xd ¼ xn ð1 n2 Þ
ð7Þ
For a given material, its damped natural frequency, xd is normally lower than the undamped natural frequency or resonance frequency, xn but in many cases the damping ratio is relatively small and so is the difference. Indeed, the results in Fig. 8 indicate that there were negligible changes in damped natural frequency of CFRP composites due to the incorporation of CNTs for all beam
1490
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 5. Vibration amplitude vs. time history of (a) neat epoxy, (b) nanocomposite with 0.5 wt% CNT, and (c) nanocomposite with 1.0 wt% CNT.
Fig. 6. Vibration amplitude vs. time history of CFRP composites containing (a) neat epoxy, (b) 0.5 wt% CNT, and (c) 1.0 wt% CNT.
lengths studied. In contrast, the CNT nanocomposites in general had marginally higher damped natural frequency than the neat epoxy, showing ameliorating effects of CNT reinforcement. These conflicting observations indicate that the damped natural frequency depended more on how the matrix properties, especially the stiffness, were modified by CNT reinforcements than how the damping ratios were enhanced by CNTs. It is obvious that the presence of CNTs in epoxy enhanced the stiffness of nanocomposites far more than that of CFRPs because the overall stiffness of CFRPs is dominated by the properties of the major reinforcement, carbon fibers. The marginally steeper increase in damping ratio for the CFRP composites with CNTs (Fig. 7b) than the CNT nanocomposites (Fig. 7a) did not play a significant role because the overall damping
ratios for all materials studied here remained lower than about 0.013, hardly affecting the damped natural frequency. In summary, the stiffness or the undamped natural frequency was the dominant factor that determined the damped natural frequency of the nanocomposites and CFRPs. The damping ratios were determined for different beam lengths, and damped natural frequency was transformed into fundamental natural frequency by Eq. (7). The damping ratio is plotted as a function of fundamental natural frequency in Fig. 9. It is obvious that the natural frequency had only negligible effects on damping ratio of both the nanocomposites and CFRP laminates. The initial vibration amplitudes were selected so that the initial vibration loads were maintained constant for all frequency values.
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
1491
Fig. 7. Damping ratio of (a) nanocomposites and (b) CFRP composites containing different CNT contents as a function of initial vibration amplitude.
Neat 0.5 % CNT 1 % CNT
26 24
100 90
22 CFRP composites
20
80 70
18
Nanocomposites
16
60
14
50
12 120
130
140
150
160
Damped Natural Frequancey (Hz)
Damped Natural Frequancey (Hz)
28
170
Beam Free Length (mm) Fig. 8. Damped natural frequency of (a) nanocomposites and (b) CFRP composites containing different CNT contents as a function beam free length.
Therefore, the energy dissipation due to initiation of CNT-matrix interfacial sliding depended only on the applied load, independent of the fundamental natural frequency of the material. 4.3. Damping behavior in forced vibration The accelerometer reading at different exciting frequencies in forced vibration was collected and transformed into the vibration amplitude. Fig. 10 shows the general frequency response of the nanocomposite and CFRP composites in the excitation frequency from 5 Hz to 600 Hz. For the neat epoxy and CNT nanocomposites,
two prominent peaks were identified at around 16 Hz and 150 Hz, corresponding to the 1st and the 2nd modes of beam vibration, respectively. The corresponding frequencies were much higher, i.e. about 60 Hz and 370 Hz respectively, for the CFRP composites than for the nanocomposites because of the much higher stiffness for the former. The damping ratios calculated according to Eq. (6) based on the half bandwidth method are presented in Fig. 12. As expected, the damping ratios for both the nanocomposites and CFRP composites consistently showed a similar increasing trend with increasing CNT content. It is worth noting that both the materials had higher damping ratios in the 2nd mode than in the 1st mode. This observation can be attributed to the potentially very large vibration amplitude near the beam center in the 2nd mode, see Fig. 11. The damping ratio of nanocomposites was in general higher than the CFRP composites in the 1st vibration mode, consistent with the free vibration test, Fig. 7, whereas it was higher for the CFRP composites than the nanocomposites in the 2nd mode. This observation may be attributed to the additional damping mechanisms that take place in the CFRP laminate composites, but not in the nanocomposites, such as (i) Coulomb friction due to slip in unbounded or debonded region of the fiber/matrix interface; and (ii) relative slip along the laminar interfaces [17–19]. These mechanisms appear to be more prominent in the 2nd mode than in the 1st mode especially when there is a large vibration amplitude near the beam center. Nevertheless, the degree of contributions by these mechanisms may vary depending on the nature and strength of the fiber/matrix interfacial adhesion, as well as the orientations, stacking sequence and number of layers in the laminate composites. In summary, the 1st mode is dominated by the inherent damping characteristics of materials, such as viscoelasticity, whereas the
Fig. 9. Damping ratio of (a) nanocomposites; (b) CFRP composites containing different CNT contents as a function of natural frequency of material.
1492
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 10. Exciting frequency response of (a) nanocomposites and (b) CFRP composites containing different CNT contents.
Fig. 11. Modal vibration in (a) the 1st vibration mode and (b) the 2nd vibration mode.
0.05
Damping Ratio
0.04 0.03
Nanocomposites CFRP composites
2
nd
vibration mode
st
1 vibration mode
0.012
0.008
0.004 0.0
0.2
0.4
0.6
0.8
1.0
CNT Content (wt %) Fig. 12. Damping ratio of nanocomposites and CFRP composites obtained from (a) the 1st vibration mode and (b) the 2nd vibration mode.
2nd mode is dominated by the structural response. Further studies are required to draw any conclusion regarding the relative importance of the damping arising from the 1st and 2nd modes of vibration.
4.4. Dynamic mechanical analysis The results obtained from the DMA analysis are plotted as a function of temperature in Figs. 13 and 14. The incorporation of the CNTs to epoxy resin induced a positive influence on storage
modulus both in the glassy region and in the vicinity of the glass transition temperature, Tg confirming improved elastic properties of epoxy due to addition of CNTs. The loss modulus, which reflects the energy dissipation capacity, was also significantly higher for the CNT nanocomposites than the neat epoxy over the whole temperature range studied, the increment being maximum at around Tg. Loss factor or tan d, defined as the ratio of loss modulus to storage modulus, is an important parameter that presents the macromolecular viscoelasticity and the damping capacity of a material, which is an ability to convert the mechanical energy to heat energy when the material is subjected to an external load [20–22]. The nanocomposites modified with CNTs showed a consistently higher tan d than the neat epoxy over the whole temperature range, and the difference becoming more pronounced with increasing CNT content, consistent with the improved energy dissipation observed from the vibration tests. The increase in loss factor of the CNT– epoxy nanocomposites compared to the neat epoxy was becoming more pronounced with increasing temperatures toward Tg, which could be attributed to the added effect of thermally induced/activated frictions by the CNT particle boundary sliding (filler–filler) and interfacial sliding (filler–matrix). For polymers composites, the loss factor varies with temperature and becomes a maximum at Tg because their intrinsic damping originates from the viscoelasticity of the polymer matrix [21–23]. The enhanced damping capacity was achieved without sacrificing the elastic (storage) modulus. The results of the CNT–CFRP hybrid composites showed essentially similar tendencies as for the CNT–epoxy nanocomposites. A major difference is that the increases in storage and loss moduli
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
1493
Fig. 13. Storage modulus, loss modulus and tan d obtained from the dynamic mechanical analysis of CNT–epoxy nanocomposites.
Fig. 14. Storage modulus, loss modulus and tan d obtained from the dynamic mechanical analysis of CNT–CFRP hybrid composites.
Maximum tan delta
0.9
shown in Fig. 15, confirmed that the former nanocomposites had better damping capacity than the latter hybrid composites due to the dominance of the polymer matrix in determining the damping capacity. This observation also agreed with the vibration test results.
Nanocomposites CFRP composites
0.8
0.7
5. Conclusions The vibration damping properties of nanocomposites and CFRP hybrid composites containing CNTs were studied based on the free and forced vibrations tests. The following results can be highlighted from the study.
0.6
0.5 0.0
0.2
0.4
0.6
0.8
1.0
CNT content (wt %) Fig. 15. Maximum tan d values obtained at Tg of corresponding nanocomposites and CNT–CFRP hybrid composites as a function of CNT content.
were not as significant as for the CNT nanocomposites because of the large presence of fiber phase which dominates the elastic properties of the composites. The inclusion of a small CNT content in the matrix material had only negligible overall effect on the properties of hybrid composites. As such, the Tg remained practically unchanged, also indicating that the presence of CNTs did not significantly affect the cure chemistry of matrix material [24]. The comparison of the loss factors obtained at Tg of the corresponding nanocomposites and the CNT–CFRP hybrid composites,
(i) The free vibration test indicated that the damping ratio of the CFRP-CNT hybrid composites increased with increasing CNT content, consistent with the previous hypothesis of sliding at the CNT–matrix interfaces. (ii) Although the CFRP composites had an inherently lower damping ratio than the neat epoxy, the former composites showed a higher rate of increase in damping ratio than the epoxy nanocomposites. (iii) The forced vibration test confirmed the beneficial effect of CNTs on improving the damping ratio of both nanocomposites and CFRP composites, in both the 1st and 2nd vibration modes. (iv) The damping ratios of nanocomposites were in general higher than the CFRP hybrid composites in the 1st vibration mode. Additional damping mechanisms arising from the slip
1494
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
at the fiber/matrix interface and laminar structure may contribute significantly to the 2nd vibration mode in CFRP laminate composites. (v) The DMA results indicated ameliorating effects of CNTs on damping properties of composites. Both the loss modulus and tan delta of nanocomposites and CFRP composites exhibited consistent increases with CNT content, the increase being more pronounced in the nanocomposites than the CFRP hybrid composites due to different degrees of influence by CNTs on the stiffness of the materials.
Acknowledgments This project was supported by the Research Grant Council of Hong Kong SAR (Project No. 614607). Technical assistances from the Materials Characterization and Preparation Facilities (MCPF) and Advanced Engineering Materials Facility (AEMF) of HKUST are appreciated. References [1] Smith PA. Carbon fiber reinforced plastics—properties. Compr Compos Mater 2003:107–50. [2] Chandra R, Singh SP, Gupta K. Damping studies in fiber-reinforced composites – a review. Compos Struct 1999;46:41–51. [3] Saravanos DA, Pereira JM. Effects of interply damping layers on the dynamic characteristics of composite plates. AIAA J 1992;30(12):2906–13. [4] Liao FS, Su AC, Hsu TC. Vibration damping of interleaved carbon fiber-epoxy composite beams. J Compos Mater 1994;28(18):1840–54. [5] Moser K, Lumassegger M. Increasing the damping of flexural vibration of laminated FPC structures by incorporation of soft intermediate plies with minimum reduction of stiffness. Compos Struct 1988;10:321–33. [6] Koratkar NA, Wei BQ, Ajayan PM. Multifunctional structural reinforcement featuring carbon nanotube films. Compos Sci Technol 2003;63(11):1525–31. [7] Koratkar NA, Wei BQ, Ajayan PM. Carbon nanotube films for damping applications. Adv Mater 2002;14(13–14):997–1000.
[8] Koratkar NA, Suhr J, Joshi A, Kane RS, Schadler LS, Ajayan PM, et al. Appl Phys Lett 2005;87:063102. [9] Zhou X, Shin E, Wang KW, Bakis CE. Interfacial damping characteristics of carbon nanotube composites. Compos Sci Technol 2004;64:2425–37. [10] Rajoria H, Jalili N. Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites. Compos Sci Technol 2005;65:2079–93. [11] Sham ML, Kim JK. Surface functionalities of multi-wall carbon nanotubes after UV/ozone and TETA treatments. Carbon 2006;44:768–77. [12] Ma PC, Kim JK, Tang BZ. Effects of silane functionalization on the properties of carbon nanotube/epoxy nanocomposites. Compos Sci Technol 2007;67:2965–72. [13] Buldum A, Lu JP. Atomic scale sliding and rolling of carbon nanotubes. Phys Rev Lett 1999;83:5050–3. [14] Sham ML, Li J, Ma PC, Kim JK. Cleaning and functionalizaton of polymer surfaces and nanoscale carbon fillers by UV/ozone treatment: a review. J Compos Mater 2009;43:1537–64. [15] Ma PC, Siddiqui NA, Marom G, Kim JK. Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: a review. Composites: Part A 2010;41:1345–67. [16] Geng Y, Liu MY, Li J, Shi XM, Kim JK. Effects of surfactant treatment on mechanical and electrical properties of CNT/epoxy nanocomposites. Composites: Part A 2008;39:1876–83. [17] Mahi AE, Assarar M, Sefrani Y, Berthelot JM. Damping analysis of orthotropic composites materials and laminates. Composites: Part B 2008;39:1069–76. [18] Berthelot JM, Sefrani Y. Damping analysis of unidirectional glass and kevlar fibre composites. Compos Sci Technol 2004;64:1261–78. [19] Yam LH, Wei Z, Cheng L. Non destructive detection of internal delamination by vibration-based method for composite plates. J Compos Mater 2004;38:2183. [20] Liang JZ, Li RKY, Tjong SC. Effects of glass bead size and content on the viscoelasticity of filled polypropylene composites. Polym Test 2000;19:213–20. [21] Ma M, Wang X. Preparation, microstructure and properties of epoxy-based composites containing carbon nanotubes and PMN-PZT piezoceramics as rigid piezo-damping materials. Mater Chem Phys 2009. [22] Gu J, Wu G, Zhang Q. Effect of porosity on the damping properties of modified epoxy composites filled with fly ash. Scripta Mater 2007;57:529–32. [23] Tsantzalis S, Karapappas P, Vavouliotis A, Tsotra P, Paipetis A, Kostopoulos V. Enhancement of the mechanical performance of an epoxy resin and fiber reinforced epoxy resin composites by the introduction of CNF and PZT particles at the microscale. Composites: Part A 2007;38:1076–81. [24] Suhr J, Koratkar N, Keblinski P, Ajayan PM. Viscoelasticity in carbon nanotubes composites. Nat Mater 2005;4:134–7.
Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech
Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes Shafi Ullah Khan, Chi Yin Li, Naveed A. Siddiqui, Jang-Kyo Kim ⇑ Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
a r t i c l e Article history: Received 9 October Received in revised Accepted 23 March Available online 23
i n f o 2010 form 4 March 2011 2011 June 2011
Keywords: A. Carbon nanotubes A. Carbon fibres B. Vibration
a b s t r a c t Vibration damping characteristic of nanocomposites and carbon fiber reinforced polymer composites (CFRPs) containing multiwall carbon nanotubes (CNTs) have been studied using the free and forced vibration tests. Several vibration parameters are varied to characterize the damping behavior in different amplitudes, natural frequencies and vibration modes. The damping ratio of the hybrid composites is enhanced with the addition of CNTs, which is attributed to sliding at the CNT–matrix interfaces. The damping ratio is dependent on the amplitude as a result of the random orientation of CNTs in the epoxy matrix. The natural frequency shows negligible influence on the damping properties. The forced vibration test indicates that the damping ratios of the CFRP composites increase with increasing CNT content in both the 1st and 2nd vibration modes. The CNT–epoxy nanocomposites also show similar increasing trends of damping ratio with CNT content, indicating the enhanced damping property of CFRPs arising mainly from the improved damping property of the modified matrix. The dynamic mechanical analysis further confirms that the CNTs have a strong influence on the composites damping properties. Both the dynamic loss modulus and loss factor of the nanocomposites and the corresponding CFRPs show consistent increases with the addition of CNTs, an indication of enhanced damping performance. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Carbon fiber reinforced polymer composites (CFRPs) are widely used in aerospace, automotive and other high performance structural applications due to their high stiffness and strength to weight ratio. Besides various mechanical properties and fracture resistance, vibration damping capability is very important as it affects system performance, safety and reliability [1–6]. Many engineering structures made from CFRPs, including military equipment, automobiles, aircrafts, wind turbine blades and spacecrafts, often suffer from the menace of vibrations during their normal operations. Micro-cracks present in these structures propagate rapidly due to fatigue caused by vibrations, resulting in premature failure. Materials with high stiffness values generally have a low damping ability and so does CFRPs. Widespread applications of CFRPs in new areas are often limited due to their low damping factor resulting from poor viscoelastic nature of carbon fibers and poor damping at the CFRP interface [2]. A few methods have been suggested to improve the damping properties of CFRPs, e.g. addition of high damping polymer layers in prepreg lay-up [3,4] and use of hybrid rubber particle reinforced composites [5]. However, the improvements in
⇑ Corresponding author. Tel.: +852 2358 7207; fax: +852 2358 1543. E-mail addresses: shafi[email protected] (S.U. Khan), [email protected] (J.-K. Kim). 0266-3538/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2011.03.022
damping properties arising from these methods are at the expense of reduced mechanical properties of the composites. With the development of carbon nanotubes (CNTs) and their composites in the last two decades, significant attention has been paid to improve the damping properties of polymers, especially epoxy, in terms of loss modulus [6–8] or damping ratio [9,10]. The combination of extremely large specific surface area along with large interfacial area, week interfacial adhesion with the polymer, and low mass density offered by carbon nanotubes implies that frictional sliding of nanotubes with the polymer matrix can cause dissipation of a large amount of energy with minimal weight penalty, providing the nanocomposites with a high damping capability. While a high damping capability is achieved by taking advantage of large interfacial friction between the CNTs and resin [6–8], reinforcement of strong and stiff CNTs means simultaneous improvements of various important mechanical properties of nanocomposites [11,12]. The ‘‘stick–slip’’ mechanism is known to be responsible for the improvement of energy dissipation capability of CNT nanocomposites [8–10]. When the nanocomposite is subjected to an external stress, a shear stress is generated between the nanotube wall and the surrounding matrix resin due to the elastic mismatch according to the well-known shear lag theory. The nanotubes will elongate together with the matrix if they are bonded, but once the external load exceeds a critical value, the nanotubes will stop
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
elongate together with the matrix [13]. Further increasing the load will result in the deformation of the matrix, which would start flowing over the nanotube surface, allowing the deformation energy to be dissipated through the slippage between the nanotubes and the matrix. If the load is released below the critical value, the deformation of CNTs will resume together with the matrix and the interfacial sliding will be vanished. The energy dissipation capability of CNT nanocomposites is dependent on the strain amplitude of applied load [9,10]. It is because the CNTs are randomly dispersed into the matrix without particular orientation, and thus the tube walls will be subject to varying shear stresses although a uniform stress is applied from the vibration source. In general, the higher is the external load, the more is the CNT-matrix interfacial slippage and so is the more energy dissipation. Most previous studies on the above damping properties are limited to epoxy-based nanocomposites containing CNTs, but it can also be well expected that use of a CNT–modified epoxy matrix may also improve the damping characteristics of CFRP laminates. We hereby report a study on the effects of CNT on vibration damping characteristics of CNT–CFRP hybrid composites. The CNT–CFRP hybrid composites are produced based on a prepreg process using a CNT reinforced resin as the composite matrix. Flexural testing mode was selected because most of the structures that are prone to damping suffer bending loads. As such, a flexural test as specified in ASTM Standard was used for measuring vibration damping properties using damped cantilever beam theory. The damping behavior of CNT–CFRP hybrid composites are characterized in terms of damping ratio and natural frequency in both free and forced vibration tests. 2. Relationship between applied load, 1st vibration amplitude and beam length The relationship between the initial vibration amplitude, x1, and the initial vibration load, P, is presented in the following. Consider a single cantilever beam of a total length L, shown in Fig. 1. When an initial vibration load, P, is applied to the beam, there will generate an initial elastic deflection, V(z), and an initial vibration amplitude, x1, assuming the beam vibrates in the 1st mode. The bending moment M(z) is given by:
MðzÞ ¼ EI
@2V z ¼ PL 1 @z2 L
ð1Þ
where EI is the flexural rigidity of the beam. Thus, the displacement V(z) is given by:
VðzÞ ¼
Z
z
z¼0
Z
z
z¼0
MðzÞdz ¼
PL z2 z3 ¼ EI 2 6L
Z
z
z¼0
Z
z PL 1 dz L z¼0 z
ð2Þ
At the free end of the beam, z = L, the deflection V(L) is given:
VðLÞ ¼
PL3 3EI
ð3Þ
1487
In the case of free vibration of a cantilever beam, the 1st vibration amplitude is equivalent to the deflection, i.e. V(L) = x1. Thus, P can be written as:
P¼
3EI L
3
x1 ¼ a
x1 L3
ð4Þ
where the flexural rigidity coefficient a = 3EI is a consistant for a given specimen with a constant cross-sectional shape. Eq. (4) implies that the ratio of initial vibration amplitude to cube of beam length, x1/L3, is directly proportional to the applied vibration load. 3. Experiments 3.1. Materials and fabrication of prepregs of CFRP–CNT hybrid composites The multi-walled carbon nanotubes (MWCNT Hollow-NK 50, supplied by Finetex Technology) used in this study (Fig. 2) were produced by a chemical vapor deposition (CVD) method. They had an outer diameter ranging between 40 and 60 nm and an average length of about 20 lm. The as-received CNTs were functionlized by a UV–ozone treatment for 30 min to create the oxygen containing functional groups on the CNT surface, which in turn helped uniform dispersion of CNT agglomerates into individual CNTs [14,15]. The oxidized CNTs were further functionalized in a mixture of acetone and a nonionic surfactant, polyoxyethylene octyl phenyl ether (Triton X-100, supplied by VWR International) with the critical micelle concentration (CMC) value of 10CMC for 2 h to improve the interfacial interactions with the epoxy matrix [16]. The epoxy resin (LY556 supplied by Huntsman) was added into the solution and the mixture was further sonicated for 1 h to improve the dispersion of CNTs in the epoxy. The epoxy-CNT mixture was degassed in a vacuum oven to evaporate acetone for 2 h, followed by high speed shear mixing (ROSS) at 4000 rpm for 30 min. Both the neat epoxy resin and the epoxy-based nanocomposites containing CNTs of varying contents were used to produce carbon fiber reinforced composite (CFRP) prepregs via a solventless prepregging process. The epoxy resin with and without dispersed CNTs was mixed with a hardener system (consisting of Aradure 5021 and hardener XB3041, supplied by Huntsman) at a mixing ratio of 100:25:12 before filling into the prepregger resin pot. The CNT contents were varied between 0 and 1.0 wt%. Carbon fiber rovings (Pyrofil TR 30 S, from Mitsubishi Raynon) with a filament count of 6 K were impregnated to produce prepreg sheets of thickness about 0.4 mm on a lab-scale prepregger (Model 40 Research Tool Corp.). The temperature of the resin bath was set at 37 °C, which was optimised to maintain the viscosity of the CNT-resin mixture within the required range of 1.5–2.5 Pa s and thus to achieve good wetting of carbon fiber tows. 3.0 mm thick laminates consisting of nine layers of unidirectional prepregs [0]9 were fabricated by hand lay-up and curing in a vacuum hot press (CARVER No. 4122) at 90 °C for 8 h. In addition to CFRP laminates, plates made from neat epoxy resin as well as CNT nanocomposites without carbon fibers were also produced using the same CNT functionalization and dispersion processes. 3.2. Measurements of vibration damping properties
Fig. 1. Cantilever beam subject to an external load P at fixed end L.
Rectangular specimens of 10 mm wide 3.0 mm thick 230 mm long were cut from the CFRP laminates and nanocomposite plates for vibration tests according to the ASTM standard E756. The specimens were tested in both the free vibration and forced vibration modes and the corresponding configurations are given Fig. 3. The free beam length is defined as the distance between
1488
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 2. SEM (a) and TEM (b) images of MWCNTs used in this study.
Fig. 3. Schematics of experimental set-up for (a) free vibration test and (b) forced vibration test.
the clamp and the specimen tip. In the free vibration test, cantilever beam specimens were used with one end clamped and the other end deflected to a desired displacement before release. The resulting vibration response was continuously monitored using the accelerometer attached to the tip of the specimen, which was stored in a digital storage cathode ray oscilloscope (CRO). The vibration data were processed to determine the damping ratio, n, based on the logarithmic decrement method [10]:
n¼
1 x1 ln xn ðn 1ÞT d xn
ð5Þ
where xn is the fundamental natural frequency in radian, n is the number of cycle of free vibration, Td is the period of the 1st vibration cycle, and xn is the amplitude of the nth vibration cycle. n = 11 was chosen for the calculation of damping ratio in this study so that the system error from the CRO reading can be minimized.
Several important material and geometric parameters were varied to study the damping characteristics of materials affected by different CNT contents, damping amplitudes and dampted natural frequencies. There is a critical shear stress above which interfacial sliding of CNTs initiates against the epoxy matrix. Because the CNTs were randomly dispersed in the matrix, the shear stress components acting on the CNTs with different orientations were all different. Moreover, the flexural vibration test means that the strain varies though the beam thickness. Thus, while flexural vibrations at sufficiently high amplitudes may activate certain CNT–epoxy slippage mechanism near the surface of the beam where strains are concentrated, a large proportion of the volume of the beam near the beam mid-plane will have little or no slippage. This means that when an external vibration load is applied to the specimen, not all the shear stress component on CNTs can reach the critical value to initiate interfacial sliding at the same vibration load. In
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
other words, the damping ratio given by Eq. (5) increases with increasing the vibration load, P, according to Eq. (4), allowing more CNTs to undergo interfacial sliding. Thus, to study the amplitudedependent damping characteristics of the materials, the specimens were placed to maintain a constant free length, L = 185 mm, while the initial tip amplitudes, x1, were varied between 10 and 40 mm with an increment of 10 mm. The damped natural frequencies of specimens were also varied by modifying the beam length, L, from 120 mm to 170 mm with an increment of 10 mm. The natural frequency is a system property and is independent of applied vibration load, P. Thus, the vibration amplitude was selected to keep the ratio of initial vibration amplitude to cubic of beam length, x1/L3, constant, as indicated by Eq. (4), such that P remained constant regardless of the change in natural frequency. An approximately constant ratio, x1/L3 = 200,000 was chosen in this study to determine the corresponding initial vibration amplitude as given in Table 1. To study the damping behavior of CNT nanocomposites and CFRP composites under different vibration modes, the forced vibration tests were also carried out as shown in Fig. 3b. The specimen having a free length of 180 mm was fixed at one end. The beam was excited sinusoidally using a mini shaker with an input voltage of 0.3 V for CFRP laminates, and 0.1 V for neat epoxy or nanocomposite specimens in order to create similar vibration amplitudes at the 1st resonance frequency, or the damped natural frequency, xn. An accelerometer was used to monitor the tip displacement data as in the free vibration test. The damping ratio was calculated based on the half-bandwidth method as shown in Fig. 4, according to the following equation,
n¼
Dx 2xn
ð6Þ
where Dx is the difference between frequencies x1 and x2 corresponding to half power points around the fundamental damped natural frequency, xn. 3.3. Dynamic mechanical analysis Dynamic mechanical analysis was employed using a dynamic mechanical analyzer (DMA-7, Perkin Elmer), according to the specification, ASTM Standard D4065. The samples with dimensions 20 mm long 3 mm wide 1.0 mm thick were tested in a three point bending mode from 25 to 150 °C at a heating rate of 10 °C/ min and a frequency of 1.0 Hz. 4. Results and discussion
1489
Fig. 4. Definitions of x1, x2 and xn according to the half-band width method.
capabilities of epoxy and CFRP improved significantly with the addition of CNTs as evidenced by the increasingly rapid decaying of the vibration amplitudes. As can be envisaged from the comparison of waveforms in Figs. 5 and 6, the natural frequency, xn of CFRPs was much higher than that of neat epoxy or nanocomposites for a given initial vibration load amplitude because as the square of natural frequency is proportional to the flexural stiffness to mass ratio of the beam, EI/m. Damping ratios of these materials were determined for a fixed cycle number, n = 11, according to Eq. (5). Fig. 7 plots the damping ratios of the composites with varying CNT contents as a function of vibration amplitude. The CFRP laminates had a slightly lower damping ratio than the neat epoxy or nanocomposite due to the poor viscoelastic nature of carbon fiber and poor energy dissipation through the fiber and matrix interface [2]. It is interesting noting that for the neat epoxy and CFRP without CNT reinforcement, the damping ratios were almost constant independent of the initial vibration amplitude applied between 10 mm and 40 mm. A further increase in the initial vibration amplitude may result in inaccuracy of calculated damping ratios because the logarithmic decrement method represented by Eq. (5) can only be used for small vibration amplitudes. In contrast, the damping ratios of the nanocomposites and CFRPs containing CNTs increase almost linearly with the initial vibration amplitude, the higher was the CNT content the more prominent was the increase. The CFRP laminates in general showed a higher degree of increase in damping ratio than the nanocomposites for a given increment of vibration amplitude.
4.1. General waveform and damping ratio in free vibration The damped natural frequency of CFRP became lower after the incorporation of CNTs into the matrix due to the enhancement of damping ratio. Similar to the damping behavior of CNT reinforced nanocomposite, the CNT–CFRP hybrid composites showed an amplitude dependent vibration characteristic, which indicates that the CNT modified matrix material was responsible for the improvement in damping characteristics. Figs. 5 and 6 show the free vibration time histories of nanocomposites and CFRP laminates containing varying CNT contents at the same initial vibration amplitude. It can be seen that the damping
Table 1 Cantilever beam free length and the corresponding initial vibration amplitude. Beam free length, L (mm) Initial vibration amplitude, x1 (mm)
170 24
160 21
150 17
140 14
130 11
120 9
4.2. Effects of beam length and natural frequency on damping ratio The free vibration tests were further performed at different natural frequencies by varying the beam length and thus the flexural stiffness, EI. The damped natural frequency xd, depends both on the natural frequency, xn and the damping ratio, n according to the following equation,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
xd ¼ xn ð1 n2 Þ
ð7Þ
For a given material, its damped natural frequency, xd is normally lower than the undamped natural frequency or resonance frequency, xn but in many cases the damping ratio is relatively small and so is the difference. Indeed, the results in Fig. 8 indicate that there were negligible changes in damped natural frequency of CFRP composites due to the incorporation of CNTs for all beam
1490
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 5. Vibration amplitude vs. time history of (a) neat epoxy, (b) nanocomposite with 0.5 wt% CNT, and (c) nanocomposite with 1.0 wt% CNT.
Fig. 6. Vibration amplitude vs. time history of CFRP composites containing (a) neat epoxy, (b) 0.5 wt% CNT, and (c) 1.0 wt% CNT.
lengths studied. In contrast, the CNT nanocomposites in general had marginally higher damped natural frequency than the neat epoxy, showing ameliorating effects of CNT reinforcement. These conflicting observations indicate that the damped natural frequency depended more on how the matrix properties, especially the stiffness, were modified by CNT reinforcements than how the damping ratios were enhanced by CNTs. It is obvious that the presence of CNTs in epoxy enhanced the stiffness of nanocomposites far more than that of CFRPs because the overall stiffness of CFRPs is dominated by the properties of the major reinforcement, carbon fibers. The marginally steeper increase in damping ratio for the CFRP composites with CNTs (Fig. 7b) than the CNT nanocomposites (Fig. 7a) did not play a significant role because the overall damping
ratios for all materials studied here remained lower than about 0.013, hardly affecting the damped natural frequency. In summary, the stiffness or the undamped natural frequency was the dominant factor that determined the damped natural frequency of the nanocomposites and CFRPs. The damping ratios were determined for different beam lengths, and damped natural frequency was transformed into fundamental natural frequency by Eq. (7). The damping ratio is plotted as a function of fundamental natural frequency in Fig. 9. It is obvious that the natural frequency had only negligible effects on damping ratio of both the nanocomposites and CFRP laminates. The initial vibration amplitudes were selected so that the initial vibration loads were maintained constant for all frequency values.
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
1491
Fig. 7. Damping ratio of (a) nanocomposites and (b) CFRP composites containing different CNT contents as a function of initial vibration amplitude.
Neat 0.5 % CNT 1 % CNT
26 24
100 90
22 CFRP composites
20
80 70
18
Nanocomposites
16
60
14
50
12 120
130
140
150
160
Damped Natural Frequancey (Hz)
Damped Natural Frequancey (Hz)
28
170
Beam Free Length (mm) Fig. 8. Damped natural frequency of (a) nanocomposites and (b) CFRP composites containing different CNT contents as a function beam free length.
Therefore, the energy dissipation due to initiation of CNT-matrix interfacial sliding depended only on the applied load, independent of the fundamental natural frequency of the material. 4.3. Damping behavior in forced vibration The accelerometer reading at different exciting frequencies in forced vibration was collected and transformed into the vibration amplitude. Fig. 10 shows the general frequency response of the nanocomposite and CFRP composites in the excitation frequency from 5 Hz to 600 Hz. For the neat epoxy and CNT nanocomposites,
two prominent peaks were identified at around 16 Hz and 150 Hz, corresponding to the 1st and the 2nd modes of beam vibration, respectively. The corresponding frequencies were much higher, i.e. about 60 Hz and 370 Hz respectively, for the CFRP composites than for the nanocomposites because of the much higher stiffness for the former. The damping ratios calculated according to Eq. (6) based on the half bandwidth method are presented in Fig. 12. As expected, the damping ratios for both the nanocomposites and CFRP composites consistently showed a similar increasing trend with increasing CNT content. It is worth noting that both the materials had higher damping ratios in the 2nd mode than in the 1st mode. This observation can be attributed to the potentially very large vibration amplitude near the beam center in the 2nd mode, see Fig. 11. The damping ratio of nanocomposites was in general higher than the CFRP composites in the 1st vibration mode, consistent with the free vibration test, Fig. 7, whereas it was higher for the CFRP composites than the nanocomposites in the 2nd mode. This observation may be attributed to the additional damping mechanisms that take place in the CFRP laminate composites, but not in the nanocomposites, such as (i) Coulomb friction due to slip in unbounded or debonded region of the fiber/matrix interface; and (ii) relative slip along the laminar interfaces [17–19]. These mechanisms appear to be more prominent in the 2nd mode than in the 1st mode especially when there is a large vibration amplitude near the beam center. Nevertheless, the degree of contributions by these mechanisms may vary depending on the nature and strength of the fiber/matrix interfacial adhesion, as well as the orientations, stacking sequence and number of layers in the laminate composites. In summary, the 1st mode is dominated by the inherent damping characteristics of materials, such as viscoelasticity, whereas the
Fig. 9. Damping ratio of (a) nanocomposites; (b) CFRP composites containing different CNT contents as a function of natural frequency of material.
1492
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
Fig. 10. Exciting frequency response of (a) nanocomposites and (b) CFRP composites containing different CNT contents.
Fig. 11. Modal vibration in (a) the 1st vibration mode and (b) the 2nd vibration mode.
0.05
Damping Ratio
0.04 0.03
Nanocomposites CFRP composites
2
nd
vibration mode
st
1 vibration mode
0.012
0.008
0.004 0.0
0.2
0.4
0.6
0.8
1.0
CNT Content (wt %) Fig. 12. Damping ratio of nanocomposites and CFRP composites obtained from (a) the 1st vibration mode and (b) the 2nd vibration mode.
2nd mode is dominated by the structural response. Further studies are required to draw any conclusion regarding the relative importance of the damping arising from the 1st and 2nd modes of vibration.
4.4. Dynamic mechanical analysis The results obtained from the DMA analysis are plotted as a function of temperature in Figs. 13 and 14. The incorporation of the CNTs to epoxy resin induced a positive influence on storage
modulus both in the glassy region and in the vicinity of the glass transition temperature, Tg confirming improved elastic properties of epoxy due to addition of CNTs. The loss modulus, which reflects the energy dissipation capacity, was also significantly higher for the CNT nanocomposites than the neat epoxy over the whole temperature range studied, the increment being maximum at around Tg. Loss factor or tan d, defined as the ratio of loss modulus to storage modulus, is an important parameter that presents the macromolecular viscoelasticity and the damping capacity of a material, which is an ability to convert the mechanical energy to heat energy when the material is subjected to an external load [20–22]. The nanocomposites modified with CNTs showed a consistently higher tan d than the neat epoxy over the whole temperature range, and the difference becoming more pronounced with increasing CNT content, consistent with the improved energy dissipation observed from the vibration tests. The increase in loss factor of the CNT– epoxy nanocomposites compared to the neat epoxy was becoming more pronounced with increasing temperatures toward Tg, which could be attributed to the added effect of thermally induced/activated frictions by the CNT particle boundary sliding (filler–filler) and interfacial sliding (filler–matrix). For polymers composites, the loss factor varies with temperature and becomes a maximum at Tg because their intrinsic damping originates from the viscoelasticity of the polymer matrix [21–23]. The enhanced damping capacity was achieved without sacrificing the elastic (storage) modulus. The results of the CNT–CFRP hybrid composites showed essentially similar tendencies as for the CNT–epoxy nanocomposites. A major difference is that the increases in storage and loss moduli
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
1493
Fig. 13. Storage modulus, loss modulus and tan d obtained from the dynamic mechanical analysis of CNT–epoxy nanocomposites.
Fig. 14. Storage modulus, loss modulus and tan d obtained from the dynamic mechanical analysis of CNT–CFRP hybrid composites.
Maximum tan delta
0.9
shown in Fig. 15, confirmed that the former nanocomposites had better damping capacity than the latter hybrid composites due to the dominance of the polymer matrix in determining the damping capacity. This observation also agreed with the vibration test results.
Nanocomposites CFRP composites
0.8
0.7
5. Conclusions The vibration damping properties of nanocomposites and CFRP hybrid composites containing CNTs were studied based on the free and forced vibrations tests. The following results can be highlighted from the study.
0.6
0.5 0.0
0.2
0.4
0.6
0.8
1.0
CNT content (wt %) Fig. 15. Maximum tan d values obtained at Tg of corresponding nanocomposites and CNT–CFRP hybrid composites as a function of CNT content.
were not as significant as for the CNT nanocomposites because of the large presence of fiber phase which dominates the elastic properties of the composites. The inclusion of a small CNT content in the matrix material had only negligible overall effect on the properties of hybrid composites. As such, the Tg remained practically unchanged, also indicating that the presence of CNTs did not significantly affect the cure chemistry of matrix material [24]. The comparison of the loss factors obtained at Tg of the corresponding nanocomposites and the CNT–CFRP hybrid composites,
(i) The free vibration test indicated that the damping ratio of the CFRP-CNT hybrid composites increased with increasing CNT content, consistent with the previous hypothesis of sliding at the CNT–matrix interfaces. (ii) Although the CFRP composites had an inherently lower damping ratio than the neat epoxy, the former composites showed a higher rate of increase in damping ratio than the epoxy nanocomposites. (iii) The forced vibration test confirmed the beneficial effect of CNTs on improving the damping ratio of both nanocomposites and CFRP composites, in both the 1st and 2nd vibration modes. (iv) The damping ratios of nanocomposites were in general higher than the CFRP hybrid composites in the 1st vibration mode. Additional damping mechanisms arising from the slip
1494
S.U. Khan et al. / Composites Science and Technology 71 (2011) 1486–1494
at the fiber/matrix interface and laminar structure may contribute significantly to the 2nd vibration mode in CFRP laminate composites. (v) The DMA results indicated ameliorating effects of CNTs on damping properties of composites. Both the loss modulus and tan delta of nanocomposites and CFRP composites exhibited consistent increases with CNT content, the increase being more pronounced in the nanocomposites than the CFRP hybrid composites due to different degrees of influence by CNTs on the stiffness of the materials.
Acknowledgments This project was supported by the Research Grant Council of Hong Kong SAR (Project No. 614607). Technical assistances from the Materials Characterization and Preparation Facilities (MCPF) and Advanced Engineering Materials Facility (AEMF) of HKUST are appreciated. References [1] Smith PA. Carbon fiber reinforced plastics—properties. Compr Compos Mater 2003:107–50. [2] Chandra R, Singh SP, Gupta K. Damping studies in fiber-reinforced composites – a review. Compos Struct 1999;46:41–51. [3] Saravanos DA, Pereira JM. Effects of interply damping layers on the dynamic characteristics of composite plates. AIAA J 1992;30(12):2906–13. [4] Liao FS, Su AC, Hsu TC. Vibration damping of interleaved carbon fiber-epoxy composite beams. J Compos Mater 1994;28(18):1840–54. [5] Moser K, Lumassegger M. Increasing the damping of flexural vibration of laminated FPC structures by incorporation of soft intermediate plies with minimum reduction of stiffness. Compos Struct 1988;10:321–33. [6] Koratkar NA, Wei BQ, Ajayan PM. Multifunctional structural reinforcement featuring carbon nanotube films. Compos Sci Technol 2003;63(11):1525–31. [7] Koratkar NA, Wei BQ, Ajayan PM. Carbon nanotube films for damping applications. Adv Mater 2002;14(13–14):997–1000.
[8] Koratkar NA, Suhr J, Joshi A, Kane RS, Schadler LS, Ajayan PM, et al. Appl Phys Lett 2005;87:063102. [9] Zhou X, Shin E, Wang KW, Bakis CE. Interfacial damping characteristics of carbon nanotube composites. Compos Sci Technol 2004;64:2425–37. [10] Rajoria H, Jalili N. Passive vibration damping enhancement using carbon nanotube-epoxy reinforced composites. Compos Sci Technol 2005;65:2079–93. [11] Sham ML, Kim JK. Surface functionalities of multi-wall carbon nanotubes after UV/ozone and TETA treatments. Carbon 2006;44:768–77. [12] Ma PC, Kim JK, Tang BZ. Effects of silane functionalization on the properties of carbon nanotube/epoxy nanocomposites. Compos Sci Technol 2007;67:2965–72. [13] Buldum A, Lu JP. Atomic scale sliding and rolling of carbon nanotubes. Phys Rev Lett 1999;83:5050–3. [14] Sham ML, Li J, Ma PC, Kim JK. Cleaning and functionalizaton of polymer surfaces and nanoscale carbon fillers by UV/ozone treatment: a review. J Compos Mater 2009;43:1537–64. [15] Ma PC, Siddiqui NA, Marom G, Kim JK. Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: a review. Composites: Part A 2010;41:1345–67. [16] Geng Y, Liu MY, Li J, Shi XM, Kim JK. Effects of surfactant treatment on mechanical and electrical properties of CNT/epoxy nanocomposites. Composites: Part A 2008;39:1876–83. [17] Mahi AE, Assarar M, Sefrani Y, Berthelot JM. Damping analysis of orthotropic composites materials and laminates. Composites: Part B 2008;39:1069–76. [18] Berthelot JM, Sefrani Y. Damping analysis of unidirectional glass and kevlar fibre composites. Compos Sci Technol 2004;64:1261–78. [19] Yam LH, Wei Z, Cheng L. Non destructive detection of internal delamination by vibration-based method for composite plates. J Compos Mater 2004;38:2183. [20] Liang JZ, Li RKY, Tjong SC. Effects of glass bead size and content on the viscoelasticity of filled polypropylene composites. Polym Test 2000;19:213–20. [21] Ma M, Wang X. Preparation, microstructure and properties of epoxy-based composites containing carbon nanotubes and PMN-PZT piezoceramics as rigid piezo-damping materials. Mater Chem Phys 2009. [22] Gu J, Wu G, Zhang Q. Effect of porosity on the damping properties of modified epoxy composites filled with fly ash. Scripta Mater 2007;57:529–32. [23] Tsantzalis S, Karapappas P, Vavouliotis A, Tsotra P, Paipetis A, Kostopoulos V. Enhancement of the mechanical performance of an epoxy resin and fiber reinforced epoxy resin composites by the introduction of CNF and PZT particles at the microscale. Composites: Part A 2007;38:1076–81. [24] Suhr J, Koratkar N, Keblinski P, Ajayan PM. Viscoelasticity in carbon nanotubes composites. Nat Mater 2005;4:134–7.