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A new structure for multi-walled carbon nanotubes reinforced alumina nanocomposite with high strength and toughness
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Materials Letters 62 (2008) 641 – 644 www.elsevier.com/locate/matlet
A new structure for multi-walled carbon nanotubes reinforced alumina nanocomposite with high strength and toughness Tong Wei a,b , Zhuangjun Fan a,b,⁎, Guohua Luo a , Fei Wei a,⁎ a
b
Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China School of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin, Heilongjiang, 150001, China Received 16 December 2006; accepted 8 June 2007 Available online 15 June 2007
Abstract Multi-walled carbon nanotubes (MWCNTs)/Al2O3 massive composites with a new carbon nanotubes (CNTs) dispersion structure have been prepared by hot-pressing. Microstructure observations of the nanocomposite show that some CNTs site along alumina grains boundary and others embed into the alumina grains to knit neighboring alumina grains together just like “pin” structure, which would contribute to toughness increase and bending strength increase respectively. The reinforcement mechanism is mainly CNT pullout and crack bridging being observed by scanning electron microscope (SEM) and transmission electron microscope (TEM). For 3 vol.% CNTs/Al2O3 composite, a fracture toughness increase of 79% and bending strength increase of 13%, comparing with that of pure nanocrystalline alumina, can be achieved. © 2007 Elsevier B.V. All rights reserved. Keywords: Nanocomposites; Mechanical properties; Microstructure
1. Introduction Since the discovery of carbon nanotubes (CNTs), they have been considered as the most promising reinforcements for composite materials due to high aspect ratios and exceptional mechanical characteristics [1–13]. Until now, however, most results for toughening have been disappointing, only very little or no improvements of toughening were reported in carbon nanotube reinforced ceramic. For instance, 10 vol.% MWCNT/ SiC composite showed only a 10% increase in bending strength and toughness over monolithic SiC [3]. Siegel et al. [9] reported that 10 vol.% MWCNT/Al2O3 nanocomposites showed a 24% increase of fracture toughness over pure alumina. Although Peigney [6–8] used an in situ vapour method to prepare CNTs/ Fe/Al2O3 composites with CNTs uniformly dispersion in the matrix, mechanical properties showed no obvious improvement due to its low CNTs purity and damage during sintering. Zhan et al., reported significant fracture toughness improvements, three times higher than an unreinforced matrix, based on indentation measurements [1]. However, Sheldon et al. [14] pointed out that the toughness of the nanocomposite may be severely ⁎ Corresponding authors. Tel.: +86 10 6279 6110; fax: +86 10 6277 2051. E-mail addresses: [email protected] (Z. Fan), [email protected] (F. Wei). 0167-577X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2007.06.025
overestimated when measured by indentation method. At the same time, Wang et al., fabricated CNT-alumina materials using the method of Zhan et al., and performed the far more reliable single edge V-notched beam test, which showed no enhanced toughening and thus refuted the claims of high toughness by Zhan et al.[2]. It is considered crack deflection and crack-bridging mechanisms are ineffective in matrix due to small toughening-zone sizes resulting from the fine length of SWNTs comparing with size of alumina powders [15–17]. New work by Xia et al.[5] has prepared a thin (20–90 μm thickness) alumina composites reinforced with a highly ordered and aligned MWCNTs. It has been directly observed collapse of the MWCNTs, crack deflection, crack bridging, and MWCNTs pullout induced by nanoindentation. In this study, the massive CNT-Al2O3 composites with a new CNTs dispersion structure were prepared by hot-pressing. The toughening mechanisms were directly observed by scanning electron microscope (SEM) and transmission electron microscope (TEM), and the relationships between CNTs microstructure and mechanical properties of the composites were also discussed. 2. Experimental Alumina powder with particle sizes of 70 nm was obtained from Jiangsu nanotech Corporation (China). MWCNTs samples
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T. Wei et al. / Materials Letters 62 (2008) 641–644
used in this work were prepared by the catalytic decomposition of propylene on Fe/Al2O3 catalyst [18,19]. To disperse nanotubes homogeneously in the alumina, three steps were used. First, CNTs were treated by a mixed acid (98% sulfuric and 68% nitric acids, 3:1) in ultrasonic bath in order to remove impurity and open some agglomerates of CNTs. The resulting CNTs and sodium dodecyl sulfate (SDS) were put into water to get a stable suspension by ultrasonication method. Then, alumina was added into CNTs suspension and sand-milled (7000 rpm) for 24 h using zirconia ball media. Finally, the mixture powders were hot pressed in a graphite die with a diameter of 60 mm at 1600 °C (at 20 MPa under N2 for 1 h). The microstructures of the samples were observed by means of SEM (JSM 7401F, JEOL) and TEM (2010) operated at 100 keV. Measurements of the fracture toughness were made using a single edge nicked beam (SENB) specimen containing precracks, which was about 3 mm in depth and 0.2 mm in width. Four bar samples were tested for each material. 3. Results and discussion Fig. 1 shows the configuration of the as-grown CNTs. It can be observed that the CNTs are made up of many agglomerates (8–20 μm) due to preparation in a Nano-Agglomerate Fluidized-Bed Reactor
Fig. 1. Morphology of MWCNTs (a, SEM image and b, bright-field TEM image).
Fig. 2. Variation of the fracture toughness as a function of nanotube content (A comparison of our results with previously reported carbon nanotube toughening in alumina matrix nanocomposites [4,8,9,20]).
(NAFBR) [18,19], as shown in Fig. 1a. The eventual structures of CNTs by TEM observation (Fig. 1b) show that agglomerates (100– 200 nm) are randomly entangled and cross-linked, and the length of CNT is 1–2 μm. The densities of 3 vol.% CNTs/Al2O3 (3.90 g cm− 3) is almost the same as that of pure alumina (3.91 g cm− 3), suggesting that addition of 3 vol.% CNTs to the alumina matrix has no effect on the sintering process. This result is in accordance with Zhan's report [1]. The addition of 3 vol.% CNTs into alumina matrix improves the flexure strength from 363 MPa to 410 MPa. When 6 vol.% CNTs is added into alumina matrix, however, the density of composite(3.85 g cm− 3 ) is sharply down due to inhibition of some diffusion processes [6], and the flexure strength is only 330 MPa. Fig. 2 shows variation of the fracture toughness as a function of nanotube content, and the previous reports are also given for comparison. It is considered that there is no reinforcing effect for in situ CNTs–Fe– Al2O3 nanocomposites due to the inhibition of some diffusion processes and damage of carbon nanotubes during hot pressing [6–8]. However, our results show that the toughness of 3 vol.% CNT/Al2O3 composite is 5.01 ± 0.2 MPa m0.5, which is 79% increase in toughness over pure alumina (2.80 ± 0.3 MPa m0.5). Fig. 3 shows micrographs of 3 vol.% CNTs/Al2O3 composites. It can be seen that CNTs not only are homogeneously dispersed in the matrix as shown in Fig. 3a and Fig. 3b, but also form a pin-like network in the matrix, some CNTs bundles siting along the Al2O3 grains (marked by arrow in Fig. 3c) and others embedding into the grains (marked by an arrow in Fig. 3a and marked by a circle in Fig. 3d), which is different from the previous reports that most of the CNTs locate at grain boundaries of alumina matrix [3–8]. The reasons maybe as follows: CNTs agglomerates are opened and formed one or more sub-agglomerates (see Fig. 1b) during mixing by strong mechanical tear force and mixed homogeneously with pristine Al2O3 powder. Some CNTs of sub-agglomerates are embedded into the alumina grains when they grow during sintering process to knit neighboring alumina grains together just like “pin” structure. The XRD spectrum (Fig. 4) shows that the peak of the alumina shifts to higher angle when 3 vol.% CNTs is added into the matrix, possibly due to residual stresses imposed by the CNTs embedding into ceramic matrix [2]. On the other hand, CNTs bundles siting along the alumina grain boundaries also inhibit the growth and congregation of alumina grains during sintering process, resulting in the refinement of grain size, which is consistent with previous observations [2].
T. Wei et al. / Materials Letters 62 (2008) 641–644
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Fig. 3. Micrographs of 3 vol.% CNT /Al2O3 composite (a, SEM images of CNT/Al2O3 composite, the circle and arrows indicate CNTs at the grain boundaries and in the grains, respectively, CNTs pullout can be seen; b, SEM image of polished specimen by dimpling and ion-milling procedures, white dots are CNTs; c and d, TEM images of polished specimen by dimpling and ion-milling procedures).
It is well known that the refinement of grain size results in the improvement of strength of ceramic [1,2]. Besides, CNT pull out from the matrix also contributes to the reinforcement. The tensile strength
increase mainly comes from short pullout lengths of CNTs in the grains due to high interfacial friction, as shown in Fig. 3a (Marked by white arrows), and single CNT pull out could dissipate more fracture energy than those of nanotube bundles due to high cohesion between the carbon nanotube and the matrix [20]. For toughness increase, it mainly comes from the pullout of CNTs bundles from the grain boundaries due to poor interfacial friction (the residual hole was marked by a circle in Fig. 3a) and crack bridging at the CNTs/matrix interface (see Fig. 3d). Therefore, to obtain better toughening effect, the interfacial bond strength between CNTs and matrix must be kept in some weak level to ensure pullout of CNTs and crack bridging. These results suggest that the dispersion structure of CNTs might be an important factor to increase both strength and toughness.
4. Conclusions
Fig. 4. XRD result of pure alumina and 3 vol.% CNT/alumina composite.
MWCNTs/Al2O3 composites with a new CNTs dispersion structure have been prepared by hot-pressing. A fracture toughness
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T. Wei et al. / Materials Letters 62 (2008) 641–644
increase of 79% and strength increase of 13%, comparing with that of pure nanocrystalline alumina, can be achieved. It is suggested that CNTs form a pin-like network in the matrix, some CNTs bundles siting along the Al2O3 grains and others embedding into the grains, which contribute to toughness increase and strength increase respectively. Multi-wall carbon nanotubes are attractive materials for reinforcement (strength and toughness) of ceramics, and both strong and weak bonding of CNTs with matrix play an important role for reinforcement. Future work is planned to optimize the process in order to disperse CNTs uniformly in the matrix with reasonable structure, and to control alumina grains size as possible as small during sintering. Acknowledgements This research was partially supported by the Foundation of National Nature Science (20236020), Harbin Foundation of Innovation Plan for Young Scientists, China (2006RFQXG030) and the Science Foundation for Post Doctorate Research from Hei Longjiang Province, China. References [1] G.D. Zhan, J.D. Kuntz, J. Wan, A.K. Mukherjee, Nat. Matters 2 (2003) 38.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
X.T. Wang, N. Padture, H. Tanaka, Nat. Matters 3 (2004) 539. R.Z. Ma, J. Wu, B.Q. Wei, J. Liang, D.H. Wu, J. Mater. Sci. 33 (1998) 5243. E. Flahaut, et al., Acta Mater. 48 (2000) 3803. Z. Xia, et al., Acta Mater. 52 (2004) 931. A. Peigney, C.H. Laurent, O. Dumortier, A. Rousset, J. Eur. Ceram. Soc. 18 (1998) 1995. A. Peigney, C.H. Laurent, E. Flahaut, A. Rousset, Ceram. Int. 26 (2000) 677. A. Peigney, C.H. Laurent, F. Dobigeon, A. Rousset, J. Mater. Res. 12 (1997) 613. R.W. Siegel, et al., Scr. Mater. 44 (2001) 2061. M.F. Yu, O. Lourie, M.J. Dyer, K. Molor, T.F. Kelly, R.S. Ruoff, Science 287 (2000) 637. H.D. Wagner, O. Lourie, Y. Feldman, R. Tenne, Appl. Phys. Lett. 72 (1998) 188. B.I. Yakobson, P. Avouris, Top. Appl. Phys. 80 (2001) 287. M.B. Nardelli, B.I. Yakobson, J. Bernholc, Phys. Rev. Lett. 81 (1998) 4656. B.W. Sheldon, W.A. Curtin, Nat. Matters 3 (2004) 505. B.R. Lawn, Fracture of Brittle Solids, 2nd edn., Cambridge Univ. Press, Cambridge, UK, 1993. A.G. Evans, J. Am. Ceram. Soc. 73 (1990) 187. N.P. Padture, J. Am. Ceram. Soc. 77 (1994) 519. Y. Wang, F. Wei, G.H. Luo, Chem. Phys. Lett. 364 (5) (2002) 568. H. Yu, Q.F. Zhang, F. Wei, W.Z. Qian, G.H. Luo, Carbon 41 (2003) 2855. S.I. Cha, K.T. Kim, Scr. Mater. 53 (2005) 793.
Materials Letters 62 (2008) 641 – 644 www.elsevier.com/locate/matlet
A new structure for multi-walled carbon nanotubes reinforced alumina nanocomposite with high strength and toughness Tong Wei a,b , Zhuangjun Fan a,b,⁎, Guohua Luo a , Fei Wei a,⁎ a
b
Department of Chemical Engineering, Tsinghua University, Beijing, 100084, China School of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin, Heilongjiang, 150001, China Received 16 December 2006; accepted 8 June 2007 Available online 15 June 2007
Abstract Multi-walled carbon nanotubes (MWCNTs)/Al2O3 massive composites with a new carbon nanotubes (CNTs) dispersion structure have been prepared by hot-pressing. Microstructure observations of the nanocomposite show that some CNTs site along alumina grains boundary and others embed into the alumina grains to knit neighboring alumina grains together just like “pin” structure, which would contribute to toughness increase and bending strength increase respectively. The reinforcement mechanism is mainly CNT pullout and crack bridging being observed by scanning electron microscope (SEM) and transmission electron microscope (TEM). For 3 vol.% CNTs/Al2O3 composite, a fracture toughness increase of 79% and bending strength increase of 13%, comparing with that of pure nanocrystalline alumina, can be achieved. © 2007 Elsevier B.V. All rights reserved. Keywords: Nanocomposites; Mechanical properties; Microstructure
1. Introduction Since the discovery of carbon nanotubes (CNTs), they have been considered as the most promising reinforcements for composite materials due to high aspect ratios and exceptional mechanical characteristics [1–13]. Until now, however, most results for toughening have been disappointing, only very little or no improvements of toughening were reported in carbon nanotube reinforced ceramic. For instance, 10 vol.% MWCNT/ SiC composite showed only a 10% increase in bending strength and toughness over monolithic SiC [3]. Siegel et al. [9] reported that 10 vol.% MWCNT/Al2O3 nanocomposites showed a 24% increase of fracture toughness over pure alumina. Although Peigney [6–8] used an in situ vapour method to prepare CNTs/ Fe/Al2O3 composites with CNTs uniformly dispersion in the matrix, mechanical properties showed no obvious improvement due to its low CNTs purity and damage during sintering. Zhan et al., reported significant fracture toughness improvements, three times higher than an unreinforced matrix, based on indentation measurements [1]. However, Sheldon et al. [14] pointed out that the toughness of the nanocomposite may be severely ⁎ Corresponding authors. Tel.: +86 10 6279 6110; fax: +86 10 6277 2051. E-mail addresses: [email protected] (Z. Fan), [email protected] (F. Wei). 0167-577X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2007.06.025
overestimated when measured by indentation method. At the same time, Wang et al., fabricated CNT-alumina materials using the method of Zhan et al., and performed the far more reliable single edge V-notched beam test, which showed no enhanced toughening and thus refuted the claims of high toughness by Zhan et al.[2]. It is considered crack deflection and crack-bridging mechanisms are ineffective in matrix due to small toughening-zone sizes resulting from the fine length of SWNTs comparing with size of alumina powders [15–17]. New work by Xia et al.[5] has prepared a thin (20–90 μm thickness) alumina composites reinforced with a highly ordered and aligned MWCNTs. It has been directly observed collapse of the MWCNTs, crack deflection, crack bridging, and MWCNTs pullout induced by nanoindentation. In this study, the massive CNT-Al2O3 composites with a new CNTs dispersion structure were prepared by hot-pressing. The toughening mechanisms were directly observed by scanning electron microscope (SEM) and transmission electron microscope (TEM), and the relationships between CNTs microstructure and mechanical properties of the composites were also discussed. 2. Experimental Alumina powder with particle sizes of 70 nm was obtained from Jiangsu nanotech Corporation (China). MWCNTs samples
642
T. Wei et al. / Materials Letters 62 (2008) 641–644
used in this work were prepared by the catalytic decomposition of propylene on Fe/Al2O3 catalyst [18,19]. To disperse nanotubes homogeneously in the alumina, three steps were used. First, CNTs were treated by a mixed acid (98% sulfuric and 68% nitric acids, 3:1) in ultrasonic bath in order to remove impurity and open some agglomerates of CNTs. The resulting CNTs and sodium dodecyl sulfate (SDS) were put into water to get a stable suspension by ultrasonication method. Then, alumina was added into CNTs suspension and sand-milled (7000 rpm) for 24 h using zirconia ball media. Finally, the mixture powders were hot pressed in a graphite die with a diameter of 60 mm at 1600 °C (at 20 MPa under N2 for 1 h). The microstructures of the samples were observed by means of SEM (JSM 7401F, JEOL) and TEM (2010) operated at 100 keV. Measurements of the fracture toughness were made using a single edge nicked beam (SENB) specimen containing precracks, which was about 3 mm in depth and 0.2 mm in width. Four bar samples were tested for each material. 3. Results and discussion Fig. 1 shows the configuration of the as-grown CNTs. It can be observed that the CNTs are made up of many agglomerates (8–20 μm) due to preparation in a Nano-Agglomerate Fluidized-Bed Reactor
Fig. 1. Morphology of MWCNTs (a, SEM image and b, bright-field TEM image).
Fig. 2. Variation of the fracture toughness as a function of nanotube content (A comparison of our results with previously reported carbon nanotube toughening in alumina matrix nanocomposites [4,8,9,20]).
(NAFBR) [18,19], as shown in Fig. 1a. The eventual structures of CNTs by TEM observation (Fig. 1b) show that agglomerates (100– 200 nm) are randomly entangled and cross-linked, and the length of CNT is 1–2 μm. The densities of 3 vol.% CNTs/Al2O3 (3.90 g cm− 3) is almost the same as that of pure alumina (3.91 g cm− 3), suggesting that addition of 3 vol.% CNTs to the alumina matrix has no effect on the sintering process. This result is in accordance with Zhan's report [1]. The addition of 3 vol.% CNTs into alumina matrix improves the flexure strength from 363 MPa to 410 MPa. When 6 vol.% CNTs is added into alumina matrix, however, the density of composite(3.85 g cm− 3 ) is sharply down due to inhibition of some diffusion processes [6], and the flexure strength is only 330 MPa. Fig. 2 shows variation of the fracture toughness as a function of nanotube content, and the previous reports are also given for comparison. It is considered that there is no reinforcing effect for in situ CNTs–Fe– Al2O3 nanocomposites due to the inhibition of some diffusion processes and damage of carbon nanotubes during hot pressing [6–8]. However, our results show that the toughness of 3 vol.% CNT/Al2O3 composite is 5.01 ± 0.2 MPa m0.5, which is 79% increase in toughness over pure alumina (2.80 ± 0.3 MPa m0.5). Fig. 3 shows micrographs of 3 vol.% CNTs/Al2O3 composites. It can be seen that CNTs not only are homogeneously dispersed in the matrix as shown in Fig. 3a and Fig. 3b, but also form a pin-like network in the matrix, some CNTs bundles siting along the Al2O3 grains (marked by arrow in Fig. 3c) and others embedding into the grains (marked by an arrow in Fig. 3a and marked by a circle in Fig. 3d), which is different from the previous reports that most of the CNTs locate at grain boundaries of alumina matrix [3–8]. The reasons maybe as follows: CNTs agglomerates are opened and formed one or more sub-agglomerates (see Fig. 1b) during mixing by strong mechanical tear force and mixed homogeneously with pristine Al2O3 powder. Some CNTs of sub-agglomerates are embedded into the alumina grains when they grow during sintering process to knit neighboring alumina grains together just like “pin” structure. The XRD spectrum (Fig. 4) shows that the peak of the alumina shifts to higher angle when 3 vol.% CNTs is added into the matrix, possibly due to residual stresses imposed by the CNTs embedding into ceramic matrix [2]. On the other hand, CNTs bundles siting along the alumina grain boundaries also inhibit the growth and congregation of alumina grains during sintering process, resulting in the refinement of grain size, which is consistent with previous observations [2].
T. Wei et al. / Materials Letters 62 (2008) 641–644
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Fig. 3. Micrographs of 3 vol.% CNT /Al2O3 composite (a, SEM images of CNT/Al2O3 composite, the circle and arrows indicate CNTs at the grain boundaries and in the grains, respectively, CNTs pullout can be seen; b, SEM image of polished specimen by dimpling and ion-milling procedures, white dots are CNTs; c and d, TEM images of polished specimen by dimpling and ion-milling procedures).
It is well known that the refinement of grain size results in the improvement of strength of ceramic [1,2]. Besides, CNT pull out from the matrix also contributes to the reinforcement. The tensile strength
increase mainly comes from short pullout lengths of CNTs in the grains due to high interfacial friction, as shown in Fig. 3a (Marked by white arrows), and single CNT pull out could dissipate more fracture energy than those of nanotube bundles due to high cohesion between the carbon nanotube and the matrix [20]. For toughness increase, it mainly comes from the pullout of CNTs bundles from the grain boundaries due to poor interfacial friction (the residual hole was marked by a circle in Fig. 3a) and crack bridging at the CNTs/matrix interface (see Fig. 3d). Therefore, to obtain better toughening effect, the interfacial bond strength between CNTs and matrix must be kept in some weak level to ensure pullout of CNTs and crack bridging. These results suggest that the dispersion structure of CNTs might be an important factor to increase both strength and toughness.
4. Conclusions
Fig. 4. XRD result of pure alumina and 3 vol.% CNT/alumina composite.
MWCNTs/Al2O3 composites with a new CNTs dispersion structure have been prepared by hot-pressing. A fracture toughness
644
T. Wei et al. / Materials Letters 62 (2008) 641–644
increase of 79% and strength increase of 13%, comparing with that of pure nanocrystalline alumina, can be achieved. It is suggested that CNTs form a pin-like network in the matrix, some CNTs bundles siting along the Al2O3 grains and others embedding into the grains, which contribute to toughness increase and strength increase respectively. Multi-wall carbon nanotubes are attractive materials for reinforcement (strength and toughness) of ceramics, and both strong and weak bonding of CNTs with matrix play an important role for reinforcement. Future work is planned to optimize the process in order to disperse CNTs uniformly in the matrix with reasonable structure, and to control alumina grains size as possible as small during sintering. Acknowledgements This research was partially supported by the Foundation of National Nature Science (20236020), Harbin Foundation of Innovation Plan for Young Scientists, China (2006RFQXG030) and the Science Foundation for Post Doctorate Research from Hei Longjiang Province, China. References [1] G.D. Zhan, J.D. Kuntz, J. Wan, A.K. Mukherjee, Nat. Matters 2 (2003) 38.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
X.T. Wang, N. Padture, H. Tanaka, Nat. Matters 3 (2004) 539. R.Z. Ma, J. Wu, B.Q. Wei, J. Liang, D.H. Wu, J. Mater. Sci. 33 (1998) 5243. E. Flahaut, et al., Acta Mater. 48 (2000) 3803. Z. Xia, et al., Acta Mater. 52 (2004) 931. A. Peigney, C.H. Laurent, O. Dumortier, A. Rousset, J. Eur. Ceram. Soc. 18 (1998) 1995. A. Peigney, C.H. Laurent, E. Flahaut, A. Rousset, Ceram. Int. 26 (2000) 677. A. Peigney, C.H. Laurent, F. Dobigeon, A. Rousset, J. Mater. Res. 12 (1997) 613. R.W. Siegel, et al., Scr. Mater. 44 (2001) 2061. M.F. Yu, O. Lourie, M.J. Dyer, K. Molor, T.F. Kelly, R.S. Ruoff, Science 287 (2000) 637. H.D. Wagner, O. Lourie, Y. Feldman, R. Tenne, Appl. Phys. Lett. 72 (1998) 188. B.I. Yakobson, P. Avouris, Top. Appl. Phys. 80 (2001) 287. M.B. Nardelli, B.I. Yakobson, J. Bernholc, Phys. Rev. Lett. 81 (1998) 4656. B.W. Sheldon, W.A. Curtin, Nat. Matters 3 (2004) 505. B.R. Lawn, Fracture of Brittle Solids, 2nd edn., Cambridge Univ. Press, Cambridge, UK, 1993. A.G. Evans, J. Am. Ceram. Soc. 73 (1990) 187. N.P. Padture, J. Am. Ceram. Soc. 77 (1994) 519. Y. Wang, F. Wei, G.H. Luo, Chem. Phys. Lett. 364 (5) (2002) 568. H. Yu, Q.F. Zhang, F. Wei, W.Z. Qian, G.H. Luo, Carbon 41 (2003) 2855. S.I. Cha, K.T. Kim, Scr. Mater. 53 (2005) 793.