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Buckling Response of Carbon Nanotube
Polycarbonate Composites Columns
Wei Zhang* and Nikhil Koratkar**
Department of Mechanical, Aerospace and Nuclear Engineering
Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
ABSTRACT An experimental study on the buckling behavior of single-walled carbon nanotube and polycarbonate nanocomposite beam structures is presented. Significant increase (29-51%) in critical buckling load is observed with the addition of relatively small weight fraction (1-2%) of oxidized nanotubes into the polycarbonate matrix. Such nano-composite systems with high buckling stability show potential as lightweight and buckling resistant structural elements in aeronautical and space applications.
INTRODUCTION Carbon nanotubes with their unusual blend of mechanical, thermal and electrical properties [1] have been the focus of intense research in a variety of disciplines. Carbon nanotubes can be formed by roll-up of graphene sheets into a seamless cylindrical shape. There are two main types of carbon nanotubes: single-wall carbon nanotubes (SWNT) and multi-wall carbon nanotubes (MWNT). The MWNT are comprised of concentric SWNT which are held together by weak Van der Waal forces. The Young’s modulus and strength of individual SWNT was found to be in the range of ~1 TPa and ~50 GPa respectively [2-3]; which is significantly better than current state-of-the-art engineering material such as the carbon fiber composites. This has generated great interest [4-6] in the use of nanotubes as reinforcement fibers in composite materials. While --------------------------------------------------- * Graduate Research Assistant ** Associate Professor, Member AIAA, AHS Copyright 2007 by W. Zhang and N. Koratkar. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission
most of the work to date has focused on quantifying the tensile strength and Young’s modulus of nano-composites, the buckling stability of nano-composite structures has yet to be investigated in detail. In this paper, we perform carefully designed compression tests to quantify the buckling behavior of nanocomposite systems. Buckling is a structural instability failure mode and is a major concern for structural design. Buckling is related to both the geometry and the material properties of the structure. For a slender column under compression, buckling usually occurs well before the allowable normal stress of the material is reached. For a column under an axial compressive load, the smallest critical load which defines the onset of structural instability is given by Euler’s equation [7]:
2
2
ebuckling L
EIP
π= (1)
Where: is the critical buckling load, E is the Elastic Modulus of the column, is the effective length of the column and I is the moment of inertia of the cross-section. The effective length depends on the column boundary conditions. For fixed-fixed boundary condition, the effective length is half of the gage length of the column. The specimens used in this study have slenderness ratio greater than the critical slenderness ratio which means that the column can be consider as long and the Euler’s equation can be utilized. The slenderness ratio and the critical slenderness ratio are computed [8] using the following equations.
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br> 15th23 - 26 April 2007, Honolulu, Hawaii
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AI
LL gagee
/
2/=
ρ (2)
plc
ESRσπ 2
= (3)
Where: is the gage length, I is the least moment of inertia of the cross section, A is the cross section area and is the proportional limit of the material. For the polycarbonate specimens used in this study, the proportional limit ( plσ ) obtained from the stress-strain curve is approximately 20 MPa (~ 1/3 of the yield strength of the material). From the classical Euler equation, it is clear that addition of nanotube reinforcement fibers into the matrix material will increase the elastic modulus (E) of the sample, causing a corresponding increase in the critical buckling load. Therefore the buckling stability enhancement is expected to be proportional to the stiffening (i.e. elastic modulus enhancement) of the composite structure. To investigate this we tested SWNT-polycarbonate composite beams with different weight fractions of SWNT fillers. Subsequent sections will describe the protocols that were used to fabricate the nano-composites, the test procedure and key results from the study. The mechanical properties of nano-composites are strongly related to the dispersion [9-10] of carbon nanotubes within the polymer matrix. However it is very challenging to prevent the agglomeration of SWNT. The interfacial adhesion between SWNT and polycarbonate, which is caused by weak Van der Waals interaction, is generally not strong enough to achieve good quality dispersion of SWNT. To help alleviate this effect, we oxidized as-received SWNT by sonication in nitric acid. The resulting carboxylic groups on the SWNT help to exfoliate the nanotube bundles and also the intermolecular forces caused by dipole-dipole interaction between polar groups (i.e. carboxylic acid groups on the sidewall of nanotubes and the polar carbonate groups along polycarbonate chains), lead to better quality [10] of dispersion. The procedure used to oxidize the SWNT is described in the experimental section. The protocol (figure 1A) used for dispersing the oxidized SWNT (OSWNT) in the polycarbonate system is also described in detail in the experimental section. The dimensions of the baseline polycarbonate and the nano-composite samples were ~ 89.45 mm in clamped length (measured after mounting the samples into the grips of the MTS-858 system), ~ 6.35 mm in width and ~
2.98 mm in thickness. To determine dispersion quality of SWNT, Scanning Electron Microscopy (SEM) images (figure 1B) are taken of the fracture surface of the samples. As seen in the SEM images, OSWNT fibers are reasonably well-dispersed in the polymer matrix and are pulling out of the fracture surface. Note that although the dispersion quality is good, dispersion down to the single-tube level is not possible for singlewalled nanotubes; each nanotube fiber is a small bundle of nanotubes (~ 35 nm in diameter) and appears to be coated with a polymer layer.
TEST RESULTS
In this study we tested three categories of samples: (1) baseline or pure polycarbonate (with no nanotube fillers), (2) nanocomposite with 1 wt% of OSWNT and (3) nanocomposite with 2 wt% of OSWNT. We did not test beyond 2 wt% because it was difficult to maintain dispersion quality for higher nanotube loading fractions. Tensile elastic modulus of each of the test specimens was measured prior to the buckling tests. An extensometer was attached to the specimen to measure the strain during the tests. The slope of the stress-strain curves gives the measured tensile elastic modulus figure 2 of the specimens. The measured elastic modulus of the pure polycarbonate is ~2.175 GPa, which is close to the manufacturer quoted value. With addition of nanotube fillers we expect a stiffening of the polycarbonate matrix material. Figure 2 indicates that with the addition of 1wt% and 2wt% of OSWNT, the elastic modulus of the OSWNT-polycarbonate nanocomposite increases by ~5% and ~17% respectively over the baseline polycarbonate. Having measured the elastic modulus of the samples, the samples were then buckled by applying a monotonically increasing compressive displacement to the specimen (at 0.1 mm/min). The resulting load-displacement response is used to determine the buckling load. At the point of buckling the system is unstable with the displacement continuing to increase without further increase in load (i.e. the load response levels off as shown in figure 3). The measured buckling load from figure 3 was scaled appropriately (using equation 4):
II
LLPP ref
refBucklingscaledBuckling 2
2
, = (4)
Where: scaledBucklingP , is the scaled buckling load used for comparison, is the buckling load obtained from
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the experiment, L is the clamped length of the nano-composite samples, I is the moment of inertia of the nano-composite samples, is the clamped length of the reference (pure polycarbonate) sample, and is the moment of inertia of the reference (pure polycarbonate) sample. The scaling of the buckling load (equation 4) with the polycarbonate beam dimensions taken as a reference allows us to directly compare the buckling loads of the specimens. This is necessary to account for slight variations in the clamped length, thickness and width of the samples. For the baseline (pure) polycarbonate specimen, the scaled buckling load (figure 3) is ~136 N and is in reasonable agreement (~143 N) with the theoretical result for classical Euler buckling (equation 1). Note that when computing the theoretical buckling load, the measured tensile modulus was used. We also measured the compressive modulus of each test specimen on initial compressive loading (up to -0.15% strain) and the measured compressive modulus was very close to the tensile modulus values (maximum difference of only ±1.75%). We did not measure compressive modulus at the higher compressive strains since the bowing of the specimen resulted in inaccurate strain measurement from the extensometer. Figure 3 indicates that with the addition of 1wt% OSWNT in the polycarbonate matrix, the scaled buckling load was increased by 29.2% to 175.7 N. For the 2wt% OSWNT-PC sample, the buckling load was increased by 51.2% to 205.6 N. According to the classical Euler buckling equation, the buckling load is only a function of geometry and the elastic modulus of the specimen. Since the critical buckling load is corrected for geometry variation by proper scaling (equation 4), the increase in buckling load should be fully accounted for by the increase in the elastic modulus of the PC-OSWNT composite. Therefore we expect the buckling loads with 1wt% and 2wt% of OSWNT to increase by 5% and 17% (based on the elastic modulus increase- figure 2), however the test data indicates a 29% and 51% increase in the critical buckling load. This suggests that the elastic modulus of the nanocomposite under large compressive loading (more specifically at the onset of buckling) is significantly enhanced. There is some prior evidence for this in the literature. For example- Schadler and co-workers [4, 11] studied the elastic modulus of nanotube polymer composites under compressive forcing by analyzing shifts in the Raman peak spectra. When the composite was subjected to a large compressive load, a larger shift in Raman peak position was observed as compared to the tension case, which indicated that load transfer in the nanotube bundles improved under large compressive stress. When the specimen is subjected
to a tensile load, possibly only the peripheral surface of the nanotubes bundles that are bonded to the polycarbonate matrix are effective for load transfer, and the weak inter-tube bonding contributes little to the load transfer. In contrast, when the specimen is subjected to a compressive load, high compressive stress might force the polymer to infiltrate the nanotubes bundles to create more interaction zone between the polymer and the nanotube bundles and thus improve the polymer-nanotube load transfer. Another important consideration is that when the nanotube diameter is small, individual tubes can be easily buckled or bent as shown by Wagner and co-workers[12-13] and Chou and co-workers[14]. For our samples, the nanotube bundles (Figure 1D) are comprised of singlewalled nanotubes with very small diameter and therefore individual tubes within these bundles are expected to buckle and bend. Under severe bending, distortions [13-17] start to form on the compressive side of the nanotubes and the cross-section of the nanotube starts to deform from circular to elliptical. The radial distortion of the nanotube cross-section and the bowing (or bending) of the nanotubes can increase the frictional interlocking between the nanotubes and thus provide better tube-tube load transfer within the nanotube bundle. As a consequence, the classical Euler buckling formula (equation 1) is not adequate to predict the critical buckling loads for nanotube-polymer composite systems. Improved polymer-nanotube and tube-tube load transfer under large compressive forcing implies that Euler buckling calculations tend to severely under-predict the critical buckling loads as shown in figure 3.
DETAILS REGARDING SAMPLE FABRICATION
Protocol for the oxidation of nanotubes: Purified HiPCO SWNT was purchased from Carbon Nanotechnology Inc., with an average diameter and length of ~1.4 and ~1 respectively. First, 250 mL of nitric acid is added to the SWNT (60 mg) in a round flask. Then, this mixture is sonicated using a bath sonicator (Branson 2510) for three hours at room temperature. Next, the acid-SWNT mixture is filtered to remove the SWNT. To ensure that the nitric acid is completely removed from the oxidized SWNT, large amount of distilled water is used to neutralize the oxidized SWNT. Finally, the filtered oxidized SWNT (OSWNT) is dried out inside a vacuum oven overnight at 80 deg C to remove any remaining water vapor and nitric acid.
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Protocol used to disperse the oxidized nanotubes in the polymer matrix: First, proper amount of OSWNT and polycarbonate for desired weight fraction is measured and then the polycarbonate is dissolved in Tetrahydrofuran (THF) by sonication for approximately 90 minutes. Separately, THF is added to the OSWNT and the THF-OSWNT mixture is sonicated for approximately 60 minutes. Next, the polycarbonate-THF solution and THF-OSWNT solution are mixed together and sonicated for 15 minutes. Finally, methanol which is an anti-solvent for polycarbonate is poured very slowly into the solution to precipitate the polycarbonate-OSWNT composite material. The precipitate is filtered out of the mixture and dried overnight at a temperature of 60�C inside a vacuum oven to remove the remaining THF and Methanol. Next, the dried polycarbonate-OSWNT in powder form is poured into a compressive mold (preheated to 205 deg C) and loaded under a hydraulic press. Finally, the test specimen is removed from the compressive mold and the surface is polished to form the final test specimen.
SUMMARY AND CONCLUSIONS The addition of oxidized singlewalled carbon nanotubes into a polycarbonate matrix was shown to dramatically improve structural stability. With addition of 1% and 2% wt of oxidized carbon nanotubes, the critical buckling load is projected to increase by 5% and 17% based on the nanotube induced stiffening of the composite. The test data indicates 29% and 51% increase in the buckling load. This suggests a significant enhancement in load transfer effectiveness between the polymer and the nanotube bundles when subjected to a compressive load. Carbon nanotube reinforced composites show potential to provide significant enhancement in buckling stability which is an important consideration for the design of ultra lightweight and highly optimized structural elements used in aeronautical and space applications.
ACKNOWLEDGEMENTS We thank the National Science Foundation for sponsoring this research under the Faculty Early Career Development (CAREER) program, with Dr Yip-Wah Chung serving as the technical monitor.
REFERENCES
[1] P. M. Ajayan, Chem. Rev. 1999, 99, 1787. [2] M. M. J. Treacy, T. W. Ebbesen, J. M. Gibson, Nature 1996, 381, 678. [3] M. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelley, R. S. Ruoff, Science 2000, 287, 637. [4] P. M. Ajayan, L. S. Shadler, C. Giannaris & A. Rubio, Adv. Mater. 2000, 12, 750. [5] H. D. Wagner, O. Lourie, Y. Feldman & R. Tenne, Appl. Phys. Lett. 1998, 72, 188. [6] E. T. Thostenson & Chou, T.-W, J. Phys. D: Appl. Phys. 2002, 35, 77. [7] J. Singer, J. Arbocz, T. Weller, Buckling experiments: experimental methods in buckling of thin-wall structures, Vol.1, John Wiley & Sons, 1998. [8] F. Cheng, Applied Strength of Materials, Macmillan Publishing Company, 1986. [9] O. Breuer, U. Sundararaj, Polym. Compos. 2004, 25, 630. [10] N. Koratkar, J. Suhr, A. Joshi, R. Kane, L. S. Schadler, P. Ajayan, S. Bartolucci, Appl. Phys. Lett. 2005, 87, 063102. [11] L. S. Schadler, S. C. Giannaris, P. M. Ajayan, Appl. Phys. Lett. 1998, 98, 252. [12] H. D. Wagner, R. A. Vaia, Mater. Today 2004, 38. [13] O. Lourie, D. M. Cox, H. D. Wagner, Phys. Rev. Lett. 1998, 81, 1638. [14] E. T. Thostenson, T-W Chou, Carbon 2004, 42, 3003. [15] A. H. Barber, S. R. Cohen, H. D. Wagner, Appl. Phys. Lett. 2003, 82, 4140. [16] M. R. Falvo, G. J. Clary, R. M. Taylor II, V. Chi, F. P. Brooks Jr, S. Washburn, R. Superfine, Nature 1997, 389, 582. [17] D. Qian, W. K. Liu, S. Subramoney, R. S. Ruoff, J. Nanosci. Nanotechnol. 2003, 3, 185.
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FIGURES
OSWNTPOLYCARBONATE
THF
SONICATION MIXING
THF-OSWNT THF-PC
OSWNT-PC-THF
PRECIPITATION
METHANOL
PC+OSWNT
FILTERATION
DRY-OUT
PC+OSWNT
PRESS MOLDING
PCOSWNT-PC Composite
OSWNTPOLYCARBONATE
THF
SONICATION MIXING
THF-OSWNT THF-PC
OSWNT-PC-THF
PRECIPITATION
METHANOL
PC+OSWNT
FILTERATION
DRY-OUT
PC+OSWNT
PRESS MOLDING
PCOSWNT-PC Composite
A
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Figure 1 (A) Schematic of the protocol used to disperse oxidized singlewalled carbon nanotubes in polycarbonate matrices. (B) SEM image of the fracture surface of the 1wt % oxidized singlewalled nanotube polycarbonate specimen. The uniform distribution of nanotube fibers on the fracture surface indicates good dispersion quality.
B
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1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
PC 1w t% OSWNT 2w t% OSWNT
Tens
ile E
last
ic M
odul
us (G
Pa)
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
PC 1w t% OSWNT 2w t% OSWNT
% In
crea
se in
E
1.9
2
2.1
2.2
2.3
2.4
2.5
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PC 1w t% OSWNT 2w t% OSWNT
Tens
ile E
last
ic M
odul
us (G
Pa)
0%
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8%
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PC 1w t% OSWNT 2w t% OSWNT
% In
crea
se in
E
Figure 2 Percent increase in elastic modulus of the polycarbonate with addition of oxidized singlewalled nanotube fillers.
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100
120
140
160
180
200
220
PC 1wt% OSWNT 2wt% OSWNT
Criti
cal B
uckl
ing
Load
(N)
Projected P_crActual P_cr
Figure 3 Predicted Euler’s critical buckling load based on the increase in elastic modulus vs. the actual buckling load measured in the experiment. The under-prediction of Euler’s column buckling formula indicates a significant enhancement in load transfer effectiveness between the polymer and the nanotube bundles when subjected to a compressive load.
