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In situ crack growth observation and fracture behavior of short carbon fiber reinforced geopolymer matrix composites
Materials Science and Engineering A 527 (2010) 2404–2407
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
In situ crack growth observation and fracture behavior of short carbon fiber reinforced geopolymer matrix composites Tiesong Lin, Dechang Jia ∗ , Peigang He, Meirong Wang Institute for Advanced Ceramics, Harbin Institute of Technology, Harbin, 150001, China
a r t i c l e
i n f o
Article history: Received 6 August 2009 Received in revised form 2 December 2009 Accepted 2 December 2009
Keywords: In situ observation Geopolymer Short carbon fiber Crack propagation Fracture behavior
a b s t r a c t The crack initiation and propagation of short carbon fiber reinforced geopolymer matrix composites (Cf /geopolymer composites) during bending test were observed in situ by environmental scanning electron microscope (ESEM). Lots of micro cracks initiate, and then propagate on the side of the beam sample with the increase of the bending load. A nearly elastic response of load–displacement curve and significant deformation of the composites are observed at the initial stages. The propagation of the micro cracks ceases, and these cracks tend to close to some extent while the main crack forms. The fiber bridging effect in the micro and main cracks effectively keeps the composites integrity and makes the composites exhibit a non-catastrophic fracture behavior. A simple mode for the damage behavior of the composites during the bending test is discussed. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
Short fiber reinforced composites are an important category of materials for engineering applications because of their adaptability to conventional manufacturing techniques and low cost of fabrication [1,2]. The increasing applications of short fiber reinforced composites show the great importance of the fracture mechanisms investigation [3,4]. Over the past years, many researches on the failure mechanisms of short fiber reinforced composites have been conducted [5–12]. These research results have demonstrated that the cracks play an important role in the mechanical properties and fracture behavior of the composites. In addition, some macroscopic and theoretical relations between the cracks and the fracture mechanism of the composites have been proposed [7–10]. However, the details of failure mechanism, especially for the effects of micro cracks propagation and distribution on fracture behavior of the composites, are unspecified up to now. In the present study, the bending test of short fiber reinforced composites was firstly employed on an environmental scanning electron microscope (ESEM) to determine the crack growth and the fracture behavior with increasing displacement of the crosshead. Relations between the crack growth and the fracture behavior of the composites were discussed.
Short carbon fibers with an average length of 7 mm are used in this study. The short carbon fibers are distributed in the composites uniformly. The volume fraction of short carbon fibers in the asprepared composites is 3.5 vol.%. The preparation process of the composites was described in the previous study [13]. Mechanical testing and in situ observation are conducted on the specimens (4 × 2 × 36 mm3 ) using a three-point bend flexure inside a Quanta 200 ESEM with a span length of 30 mm at a crosshead speed of 0.5 mm/min. All flexural bars are machined with the tensile surface perpendicular to the direction of lamination. Images of the crack initiation and propagation on the surface of lamination direction are in situ taken and the load/displacement curves are recorded simultaneously.
∗ Corresponding author. Tel.: +86 451 86418792; fax: +86 451 86414291. E-mail addresses: [email protected], [email protected] (D. Jia). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.12.004
3. Results and discussion The typical load/displacement curve for the Cf /geopolymer composites is given in Fig. 1 Fig. 2. The composites exhibit a significant deformation and an obvious non-catastrophic fracture behavior during the bending test, which is regard as a great toughening effect for the short carbon fiber with such a low volume percentage (3.5 vol.%). The composites exhibit a nearly elastic response in the initial stages (stages I and II) though a change appears at a load of about 6 N, which is similar to that of unidirectional continuous fiber reinforced composites [14]. Beyond the elastic limit, the applied load produces plastic deformation until the maximum load is reached. Then the load gradually
T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
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Fig. 1. Load/displacement curve for the Cf /geopolymer composites.
decreases with the increasing displacement, and forms a long tail (stage III). shows a series of ESEM images of crack initiation and propagation process on the side of the beam sample of the composites, which corresponds to the test points in the load/displacement curve in Fig. 1. At the first elastic stage (stage I), no crack is found on the beam sample as shown in Fig. 2(a). However, at the beginning of the second elastic stage (stage II), a lot of micro cracks (Fig. 2(b)) appear on the side of the beam sample. To encourage a crack growth, the increasing energy is required. When the bending stress is higher than the strength of the geopolymer matrix, a micro crack will initiates firstly in the geopolymer matrix of on sample beam surface. With higher load applied, the micro crack will propagate and meet with the reinforced fibers inevitably. Due to their high mechanical strength, the reinforced fibers will try to keep the composite integrity instead of being broken. Hence, the micro crack growth will be greatly slow down and an internal stress will be cumulated between the matrix and the reinforced fibers. When the increasing cumulation internal stress in the matrix is high enough (the mechanical strength of the reinforced fiber is much higher than that of the matrix), other new micro cracks will occur on the beam surface, as shown in Fig. 2(b). This interesting phenomenon indicates that the stress distribution in the matrix has been well changed due to the enhancement effect of the reinforced fibers. The study on this phenomenon will be carried out in the future. Though the formation of these micro cracks reduces the matrix elastic modulus, as indicated by the load/displacement curve slopes in Fig. 1, the sample still keep a nearly elastic deformation behavior companying with the propagation of the micro cracks (Fig. 2(c)). Under the increasing bending load, the micro cracks are grown up with similar rates. This unconventional fracture behavior is sup-
Fig. 2. Series of ESEM images (a)–(e) of crack initiation and propagation process on the side of a beam sample of the Cf /geopolymer composites corresponding to the position a–e of the load/displacement curve in Fig. 1 separately.
posed to be attributed to the following reasons. The short carbon fibers used in this study have a length of 7 mm and the gap lengths are 300–500 m, as shown in Fig. 2(c). Hence, the fibers are long enough to bridge several micro cracks together. As discussed above, the fibers have a far higher mechanical strength than that of the matrix. Thus, the bridging fibers in the micro cracks are difficult to be fractured, which is helpful to keep the composites integrity and to retard the formation of a main crack. The significant deformation of the composites can be attributed to the large number of the micro cracks during the bending test. A schematic drawing of the fiber bridging cracks is shown in Fig. 3. Assuming the fiber is rigid and its elastic deformation during the bending test can be neglected. The fibers which bridge more than two micro cracks are under the effects of the tension
Fig. 3. Analytical models of a fiber bridging cracks and the forces appearing in the fiber: (a) a fiber bridging a crack; (b) a fiber bridging two cracks.
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T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
Fig. 4. Schematic figures of the elastic deformation as well as their stress pattern of usual rigid materials (a), (b) and the Cf /geopolymer composites (c), (d) under the three-point bending test.
Fig. 5. The evolution of the stress on the tensile surface of the composite beam sample under bending load: (a) after the initiation of the micro cracks; (b) during the extension of the micro cracks; (c) after the formation of the main crack.
force, Ft , and the holding forces, FHS , which are from the matrix blocks. For point A, with the increasing bending load, the fiber is undergoing an increasing Ft and FH2 which is from Block 2. It will not be pulled out from the matrix if Ft < FH2 . When Ft > FH2 , FH1 , which is supplied by Block 1, starts to affect on the same fiber. As FH2 < Ft < FH1 + FH2 , the fiber will still be arrested in the matrix. Only when Ft > FH1 + FH2 (assuming only two matrix blocks in the left side of point A), the fiber will be pulled out from the matrix. If there are lots of matrix blocks (the number is N) in the left side of point A, the fiber will be broken instead of being pulled out when Fb < Ft < FH1 + FH2 + · · · + FHN . (Fb is the ultimate breaking load of the fiber.) As the Fb is very high, the bridging fibers show significant “arrest effects” on the micro cracks and prevent them from further opening and propagation.
It is supposed that the “arrest effects” from the reinforced fibers have changed the stress distribution in the sample beam during the three-point bending test. For usual rigid materials, their stress distribution on the tension side of the beam samples is trianglelike, as shown in Fig. 4(b). Normally only one main crack will form at the central area, as shown in Fig. 4(a). However, there are lots of similar micro cracks nearly homogeneous distribute on the surface of the Cf /geopolymer composites, as shown in Fig. 2(c). It is indicated that the stress distribution in this deformation stage is different from that in Fig. 4(b). As they have been effectively transferred from the central area to the edge area by the bridging fibers, the stress in the edge area will be a little bit lower, as illustrated in Fig. 4(d). The maximum stress is still in the center point. The increasing deformation amount of the beam sample is attributed
Fig. 6. The side of a bar specimen of the Cf /geopolymer composites after a three-point flexural test (a) and series of images of fiber pulling-out (b), fiber bridging (c), crack deflection (d) and crack branching (e) corresponding to the zones 1–4 in the image (a) separately.
T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
to the homogeneous growth of the cracks during stage II. The beam sample has presented a pseudoelastic deformation behavior until a main crack is formed, as shown in Fig. 1. With the increase of the bending load, the stress level distributed in the tension surface will be improved accordingly. The cracks will continue to grow up until the stress in the central point reach their critical value. The fibers will be pulled out from the matrix or be broken when the Ft is high enough. As a result, the bridging effect from the pulled out or broken fibers will disappear and the stress in the tensile surface will be redistributed. At this time, the deformation steps into stage III. Most of the loading stress will gather in the crack front in the central area. The stress in other areas will be decreased gradually. Hence, a main crack is formed in the central area and the growth of the micro cracks in other areas slow down till arrested or closed to some degree as shown in Fig. 2(d). With more gathering stress, more fibers are pulled out or broken. The main crack is gradually broadened, and the pulled out and broken fibers are easily found in the main crack as shown in Fig. 2(e). The left fibers still show the bridging effect, which prevents the beam sample from a catastrophic fracture. The evolution of the stress on the tensile surface of the beam sample can be described by Fig. 5. It can be seen from Fig. 6(a), the micro cracks are generated nearly on the whole span side surface of the beam sample. The gaps between two neighbor micro cracks are 300–500 m. The gaps become broader as they are far away from the main crack, which means that the stress will be less as the stress locations are far from the crosshead. It is also found that the fracture path is un-straight, as shown in Fig. 6(b) and (c). A lot of crack deflection (Fig. 6(d)) and the crack branching (Fig. 6(e)) are found, which undoubtedly lead to the increase of the fracture toughness. 4. Conclusions In situ crack growth observation during the three-point flexural test shows that lots of micro cracks form on the whole surface of
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the beam sample. With the increase of the bending load, the beam sample keeps a nearly elastic deformation behavior at initial stages and exhibits an obvious displacement. The beam sample produces pseudoplastic deformation as the maximum load is reached. The propagation of the micro cracks ceases, and they tend to close to some extent while the main crack forms because the stress in the micro crack area is somewhat relaxed and the stress in the main crack area greatly increased. The fiber bridging effect in the micro and main cracks effectively keeps the composites integrity and bears the load during the bending test, which makes the composites exhibit a non-catastrophic fracture behavior. Acknowledgements This work was supported by Program of Excellent Team in Harbin Institute of Technology and the Science Fund for Distinguished Young Scholars of Heilongjiang Province. References [1] I.M. Robinson, J.M. Robinson, J. Mater. Sci. 29 (1994) 4663–4677. [2] X. Wang, R.Y. Luo, Y.F. Ni, R.Q. Zhang, S.B. Wang, Mater. Lett. 63 (2009) 25– 27. [3] N. Sato, T. Kurauchi, O. Kamigaito, J. Mater. Sci. Lett. 4 (1985) 1095–1098. [4] C. Atkinson, R.V. Craster, Prog. Aerospace Sci. 31 (1995) 1–83. [5] A. Carpinteri, A. Spagnoli, S. Vantadori, Int. J. Solids Struct. 43 (2006) 4917– 4936. [6] Y.L. Zhang, Y.M. Zhang, J.C. Han, Y.Y. Han, W. Yao, Mater. Lett. 62 (2008) 2810–2813. [7] J. Li, R.Y. Luo, Y.H. Bi, Q. Xiang, C. Lin, Y.F. Zhang, N. An, Carbon 46 (2008) 1957–1965. [8] S. Sirivedin, D.N. Fenner, R.B. Nath, C. Galiotis, Compos. Sci. Technol. 60 (2000) 2835–2847. [9] H. Huang, R. Talreja, Compos. Sci. Technol. 66 (2006) 2743–2757. [10] J. Tsai, A.K. Patra, R. Wetherhold, Composites Part A 34 (2003) 1255–1264. [11] S. Kumaria, S. Kumar, R.N. Singh, Acta Mater. 45 (1997) 5177–5185. [12] J.M.L. Reis, A.J.M. Ferreira, Construct. Build. Mater. 18 (2004) 523–528. [13] T. Lin, D. Jia, P. He, M. Wang, D. Liang, Mater. Sci. Eng. A 497 (2008) 181–185. [14] G.H. Zhou, S.W. Wang, X.X. Huang, J.K. Guo, Ceram. Int. 33 (2007) 1395–1398.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
In situ crack growth observation and fracture behavior of short carbon fiber reinforced geopolymer matrix composites Tiesong Lin, Dechang Jia ∗ , Peigang He, Meirong Wang Institute for Advanced Ceramics, Harbin Institute of Technology, Harbin, 150001, China
a r t i c l e
i n f o
Article history: Received 6 August 2009 Received in revised form 2 December 2009 Accepted 2 December 2009
Keywords: In situ observation Geopolymer Short carbon fiber Crack propagation Fracture behavior
a b s t r a c t The crack initiation and propagation of short carbon fiber reinforced geopolymer matrix composites (Cf /geopolymer composites) during bending test were observed in situ by environmental scanning electron microscope (ESEM). Lots of micro cracks initiate, and then propagate on the side of the beam sample with the increase of the bending load. A nearly elastic response of load–displacement curve and significant deformation of the composites are observed at the initial stages. The propagation of the micro cracks ceases, and these cracks tend to close to some extent while the main crack forms. The fiber bridging effect in the micro and main cracks effectively keeps the composites integrity and makes the composites exhibit a non-catastrophic fracture behavior. A simple mode for the damage behavior of the composites during the bending test is discussed. © 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
Short fiber reinforced composites are an important category of materials for engineering applications because of their adaptability to conventional manufacturing techniques and low cost of fabrication [1,2]. The increasing applications of short fiber reinforced composites show the great importance of the fracture mechanisms investigation [3,4]. Over the past years, many researches on the failure mechanisms of short fiber reinforced composites have been conducted [5–12]. These research results have demonstrated that the cracks play an important role in the mechanical properties and fracture behavior of the composites. In addition, some macroscopic and theoretical relations between the cracks and the fracture mechanism of the composites have been proposed [7–10]. However, the details of failure mechanism, especially for the effects of micro cracks propagation and distribution on fracture behavior of the composites, are unspecified up to now. In the present study, the bending test of short fiber reinforced composites was firstly employed on an environmental scanning electron microscope (ESEM) to determine the crack growth and the fracture behavior with increasing displacement of the crosshead. Relations between the crack growth and the fracture behavior of the composites were discussed.
Short carbon fibers with an average length of 7 mm are used in this study. The short carbon fibers are distributed in the composites uniformly. The volume fraction of short carbon fibers in the asprepared composites is 3.5 vol.%. The preparation process of the composites was described in the previous study [13]. Mechanical testing and in situ observation are conducted on the specimens (4 × 2 × 36 mm3 ) using a three-point bend flexure inside a Quanta 200 ESEM with a span length of 30 mm at a crosshead speed of 0.5 mm/min. All flexural bars are machined with the tensile surface perpendicular to the direction of lamination. Images of the crack initiation and propagation on the surface of lamination direction are in situ taken and the load/displacement curves are recorded simultaneously.
∗ Corresponding author. Tel.: +86 451 86418792; fax: +86 451 86414291. E-mail addresses: [email protected], [email protected] (D. Jia). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.12.004
3. Results and discussion The typical load/displacement curve for the Cf /geopolymer composites is given in Fig. 1 Fig. 2. The composites exhibit a significant deformation and an obvious non-catastrophic fracture behavior during the bending test, which is regard as a great toughening effect for the short carbon fiber with such a low volume percentage (3.5 vol.%). The composites exhibit a nearly elastic response in the initial stages (stages I and II) though a change appears at a load of about 6 N, which is similar to that of unidirectional continuous fiber reinforced composites [14]. Beyond the elastic limit, the applied load produces plastic deformation until the maximum load is reached. Then the load gradually
T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
2405
Fig. 1. Load/displacement curve for the Cf /geopolymer composites.
decreases with the increasing displacement, and forms a long tail (stage III). shows a series of ESEM images of crack initiation and propagation process on the side of the beam sample of the composites, which corresponds to the test points in the load/displacement curve in Fig. 1. At the first elastic stage (stage I), no crack is found on the beam sample as shown in Fig. 2(a). However, at the beginning of the second elastic stage (stage II), a lot of micro cracks (Fig. 2(b)) appear on the side of the beam sample. To encourage a crack growth, the increasing energy is required. When the bending stress is higher than the strength of the geopolymer matrix, a micro crack will initiates firstly in the geopolymer matrix of on sample beam surface. With higher load applied, the micro crack will propagate and meet with the reinforced fibers inevitably. Due to their high mechanical strength, the reinforced fibers will try to keep the composite integrity instead of being broken. Hence, the micro crack growth will be greatly slow down and an internal stress will be cumulated between the matrix and the reinforced fibers. When the increasing cumulation internal stress in the matrix is high enough (the mechanical strength of the reinforced fiber is much higher than that of the matrix), other new micro cracks will occur on the beam surface, as shown in Fig. 2(b). This interesting phenomenon indicates that the stress distribution in the matrix has been well changed due to the enhancement effect of the reinforced fibers. The study on this phenomenon will be carried out in the future. Though the formation of these micro cracks reduces the matrix elastic modulus, as indicated by the load/displacement curve slopes in Fig. 1, the sample still keep a nearly elastic deformation behavior companying with the propagation of the micro cracks (Fig. 2(c)). Under the increasing bending load, the micro cracks are grown up with similar rates. This unconventional fracture behavior is sup-
Fig. 2. Series of ESEM images (a)–(e) of crack initiation and propagation process on the side of a beam sample of the Cf /geopolymer composites corresponding to the position a–e of the load/displacement curve in Fig. 1 separately.
posed to be attributed to the following reasons. The short carbon fibers used in this study have a length of 7 mm and the gap lengths are 300–500 m, as shown in Fig. 2(c). Hence, the fibers are long enough to bridge several micro cracks together. As discussed above, the fibers have a far higher mechanical strength than that of the matrix. Thus, the bridging fibers in the micro cracks are difficult to be fractured, which is helpful to keep the composites integrity and to retard the formation of a main crack. The significant deformation of the composites can be attributed to the large number of the micro cracks during the bending test. A schematic drawing of the fiber bridging cracks is shown in Fig. 3. Assuming the fiber is rigid and its elastic deformation during the bending test can be neglected. The fibers which bridge more than two micro cracks are under the effects of the tension
Fig. 3. Analytical models of a fiber bridging cracks and the forces appearing in the fiber: (a) a fiber bridging a crack; (b) a fiber bridging two cracks.
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T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
Fig. 4. Schematic figures of the elastic deformation as well as their stress pattern of usual rigid materials (a), (b) and the Cf /geopolymer composites (c), (d) under the three-point bending test.
Fig. 5. The evolution of the stress on the tensile surface of the composite beam sample under bending load: (a) after the initiation of the micro cracks; (b) during the extension of the micro cracks; (c) after the formation of the main crack.
force, Ft , and the holding forces, FHS , which are from the matrix blocks. For point A, with the increasing bending load, the fiber is undergoing an increasing Ft and FH2 which is from Block 2. It will not be pulled out from the matrix if Ft < FH2 . When Ft > FH2 , FH1 , which is supplied by Block 1, starts to affect on the same fiber. As FH2 < Ft < FH1 + FH2 , the fiber will still be arrested in the matrix. Only when Ft > FH1 + FH2 (assuming only two matrix blocks in the left side of point A), the fiber will be pulled out from the matrix. If there are lots of matrix blocks (the number is N) in the left side of point A, the fiber will be broken instead of being pulled out when Fb < Ft < FH1 + FH2 + · · · + FHN . (Fb is the ultimate breaking load of the fiber.) As the Fb is very high, the bridging fibers show significant “arrest effects” on the micro cracks and prevent them from further opening and propagation.
It is supposed that the “arrest effects” from the reinforced fibers have changed the stress distribution in the sample beam during the three-point bending test. For usual rigid materials, their stress distribution on the tension side of the beam samples is trianglelike, as shown in Fig. 4(b). Normally only one main crack will form at the central area, as shown in Fig. 4(a). However, there are lots of similar micro cracks nearly homogeneous distribute on the surface of the Cf /geopolymer composites, as shown in Fig. 2(c). It is indicated that the stress distribution in this deformation stage is different from that in Fig. 4(b). As they have been effectively transferred from the central area to the edge area by the bridging fibers, the stress in the edge area will be a little bit lower, as illustrated in Fig. 4(d). The maximum stress is still in the center point. The increasing deformation amount of the beam sample is attributed
Fig. 6. The side of a bar specimen of the Cf /geopolymer composites after a three-point flexural test (a) and series of images of fiber pulling-out (b), fiber bridging (c), crack deflection (d) and crack branching (e) corresponding to the zones 1–4 in the image (a) separately.
T. Lin et al. / Materials Science and Engineering A 527 (2010) 2404–2407
to the homogeneous growth of the cracks during stage II. The beam sample has presented a pseudoelastic deformation behavior until a main crack is formed, as shown in Fig. 1. With the increase of the bending load, the stress level distributed in the tension surface will be improved accordingly. The cracks will continue to grow up until the stress in the central point reach their critical value. The fibers will be pulled out from the matrix or be broken when the Ft is high enough. As a result, the bridging effect from the pulled out or broken fibers will disappear and the stress in the tensile surface will be redistributed. At this time, the deformation steps into stage III. Most of the loading stress will gather in the crack front in the central area. The stress in other areas will be decreased gradually. Hence, a main crack is formed in the central area and the growth of the micro cracks in other areas slow down till arrested or closed to some degree as shown in Fig. 2(d). With more gathering stress, more fibers are pulled out or broken. The main crack is gradually broadened, and the pulled out and broken fibers are easily found in the main crack as shown in Fig. 2(e). The left fibers still show the bridging effect, which prevents the beam sample from a catastrophic fracture. The evolution of the stress on the tensile surface of the beam sample can be described by Fig. 5. It can be seen from Fig. 6(a), the micro cracks are generated nearly on the whole span side surface of the beam sample. The gaps between two neighbor micro cracks are 300–500 m. The gaps become broader as they are far away from the main crack, which means that the stress will be less as the stress locations are far from the crosshead. It is also found that the fracture path is un-straight, as shown in Fig. 6(b) and (c). A lot of crack deflection (Fig. 6(d)) and the crack branching (Fig. 6(e)) are found, which undoubtedly lead to the increase of the fracture toughness. 4. Conclusions In situ crack growth observation during the three-point flexural test shows that lots of micro cracks form on the whole surface of
2407
the beam sample. With the increase of the bending load, the beam sample keeps a nearly elastic deformation behavior at initial stages and exhibits an obvious displacement. The beam sample produces pseudoplastic deformation as the maximum load is reached. The propagation of the micro cracks ceases, and they tend to close to some extent while the main crack forms because the stress in the micro crack area is somewhat relaxed and the stress in the main crack area greatly increased. The fiber bridging effect in the micro and main cracks effectively keeps the composites integrity and bears the load during the bending test, which makes the composites exhibit a non-catastrophic fracture behavior. Acknowledgements This work was supported by Program of Excellent Team in Harbin Institute of Technology and the Science Fund for Distinguished Young Scholars of Heilongjiang Province. References [1] I.M. Robinson, J.M. Robinson, J. Mater. Sci. 29 (1994) 4663–4677. [2] X. Wang, R.Y. Luo, Y.F. Ni, R.Q. Zhang, S.B. Wang, Mater. Lett. 63 (2009) 25– 27. [3] N. Sato, T. Kurauchi, O. Kamigaito, J. Mater. Sci. Lett. 4 (1985) 1095–1098. [4] C. Atkinson, R.V. Craster, Prog. Aerospace Sci. 31 (1995) 1–83. [5] A. Carpinteri, A. Spagnoli, S. Vantadori, Int. J. Solids Struct. 43 (2006) 4917– 4936. [6] Y.L. Zhang, Y.M. Zhang, J.C. Han, Y.Y. Han, W. Yao, Mater. Lett. 62 (2008) 2810–2813. [7] J. Li, R.Y. Luo, Y.H. Bi, Q. Xiang, C. Lin, Y.F. Zhang, N. An, Carbon 46 (2008) 1957–1965. [8] S. Sirivedin, D.N. Fenner, R.B. Nath, C. Galiotis, Compos. Sci. Technol. 60 (2000) 2835–2847. [9] H. Huang, R. Talreja, Compos. Sci. Technol. 66 (2006) 2743–2757. [10] J. Tsai, A.K. Patra, R. Wetherhold, Composites Part A 34 (2003) 1255–1264. [11] S. Kumaria, S. Kumar, R.N. Singh, Acta Mater. 45 (1997) 5177–5185. [12] J.M.L. Reis, A.J.M. Ferreira, Construct. Build. Mater. 18 (2004) 523–528. [13] T. Lin, D. Jia, P. He, M. Wang, D. Liang, Mater. Sci. Eng. A 497 (2008) 181–185. [14] G.H. Zhou, S.W. Wang, X.X. Huang, J.K. Guo, Ceram. Int. 33 (2007) 1395–1398.