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Since discovered in 1991 by lijima , carbon nanotubes have attracted a lot of interests because of their superior properties, including their excellent mechanical performance, high electrical conductivity and thermal conductivity, which indicate their wide application prospect.
1.1 Structure of CNTs
Carbon nanotubes, in general, are classified as two broad categories, single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs). SWNTs can be imaged as seamless rolls made by graphene. A three-dimension finite element model is constructed to describe SWNTs quantificationally. In this model, the way of grapheme wrapping is denoted by a chiral vector C, which is consisted of two integers, n and m. C can be indicated by (na1+ma2), where a1 and a2 are the unit cell vectors . The structure of SWNTs is defined as three patterns according to different values of n and m, including zigzag, armchair and chiral, showed in Figure .
Figure 1:Three patterns of SWCNTs (from left to right: armchair, zigzag, chiral)
On the basic of SWNTs structure, two models of MWNTs were proposed: Russian Dolls model and Parchment model . For Russian Dolls model, sheets of graphene are rolled up, forming a lot of concentric cylinders. As for the parchment model, one sheet of graphene is rolled, like a scroll of parchment.
1.2 Mechanical properties of CNTs
Carbon nanotubes possess high specific tensile strength, high stiffness and resilience. It was reported that the modulus of CNTS is up to 1.25TPa, which is larger in order of magnitude to metal. The remarkable tension strength, reaching up to 53 GPa as the maximum, makes it a good candidate for the application as the reinforcement of structural materials. Epoxy/single-wall carbon nanotube was prepared in L. Sun and his colleges` experiment. The corresponding mechanical properties, including Young`s modulus, tensile strength, elongation and mode I critical stress intensity factor (KIC) were measured, showed in Table 1.. It can be seen thatâ€¦..(description of the improvement first, then..due toâ€¦)
Table 1 Mechanical property of different experimental groups
1.3 Applications of CNTs
Because of their superior properties, many potential applications are proposed for carbon nanotubes, such as high conductivity components, high strength composites and energy storage and energy conversion devices, etc .
Firstly, CNTs can be used to make good conducting composites because of their high aspect ratio and high conductivity. As shown in Fig. 2, a remarkable improvement is obtained by using MWNTs instead of carbon black.
Fig. 2 Three different carbon/epoxy composites showing their different percolation threshold 
Another typical application of CNTs is to manufacture low density structural materials. Because carbon nanotubes possess a high Young`s modulus, about 1TPa, CNTs are the ideal candidate to reinforce composites. However, the ideal performance has not been obtained since the dispersion of nanotubes is not controlled well . A similar difficulty occurs in almost every application field for CNTs.
Besides the two applications mentioned above, several other applications, like field emission, hydrogen storage and electrochemical devices are all potential areas.
1.4 Functionalisation of CNTs
In order to achieve better dispersion in the polymer matrix, an effective surface fuctionalisation is essential, which means introducing some special chemical functional groups to the bulk materials. According to former research, two different methods are used commonly: covalent functionalization, providing the hydroxyl group (OH-CNTs) by acid treatment, and non-covalent functionalization .
2. Fabrication of Carbon/Epoxy Composites Embedded with CNT Nano-laminates
2.1 Processing techniques of CNTs introduction into composite hosts
Several methods are utilised to introduce carbon nanotubes into composites hosts. One common way is to make CNTs as dopant. According to the report of T. Yokozeki et al , three typical steps were employed. As the first step, epoxy and CSCNTs (cup-stack carbon nanotubes) are combined using the planetary mixer at 70â„ƒ. Then, CSCNTs are dispersed under the help of wet mill with zirconia beads at 70â„ƒ for 45 min. After that, the epoxy system with CSCNTs was diluted by itself.
According to the previous description, it is obvious that the quality of products cannot be controlled easily. One main reason is that the procedure is not quantificational. The second disadvantage of this method is time consuming in materials preparation. On the other hand, this method requires simple equipment and easy operations.
The second method is to make carbon nanotubes grow in situ on the fibres surface. As described in relative reports, the synthesis method involves a modified chemical vapour deposition (CVD) process . Firstly, an alumina cloth was soaked in a Fe (NO3)3Â·H2O solution for 5 min, then dried in ambient atmosphere. Next, the cloth covered the fibre surface before it was heated. In the heating process, catalyst nanoparticles could produce on the surface of the fibre. After that, hydrogen was introduced to reduce the catalyst. Finally, ethylene was introduced to make the CNTs start to grow.
In the "growing in situ" way, the length of carbon nanotubes can be better controlled by varying the ethylene flow compared with the former method. In addition, the materials used in the experiment are available, like alumina, which is inexpensive. If the interlaminar shear strength is sensitive to the length of CNTs, this method is more suitable.
Another approach to introduce carbon nanotubes into composite hosts is to use ultrasonic agitation. It was utilised to improve the interlaminar shear property of modified glass fibre-reinforced polymer with different MWNTs according to L. Sun and his co-workers`s report . As their results, the interlaminar shear strength (ILSS) was increased 8.16% via filling one type of MWNTs. A similar method was conducted by Y. Zhou et al . In their experiment, a high-intensity ultrasonic processor was the main equipment to mix their components, including the epon 862 epoxy resin, MWNTs and W curing agent .
The ultrasonic agitation is one of the most convenient and effective methods to dispersing CNTs. There is the equipment in our laboratory, so it is the best practicable means for us. To ensure CNTs disperse well, controlling the pulse frequency and operation time must be the main means.
2.2 Manufacturing methods of composite hosts
Autoclave and Vacuum Assisted Resin Transfer Moulding (VARTM), shown in Fig.3 are the main methods to fabricate laminates.
Fig. 3 Processing steps of VARTM 
For laminates, there is no marked difference in the degree of cure between these two methods. The selection criterion for the two processes is the determinant for the desired properties. For autoclave, it is utilised to get a high performance dominated by fibre. The matrix dominated properties can be higher manufactured by RTM . Some basic characteristics of RTM and autoclaving are illustrated in Table 2.
Table 2 Main characteristics of RTM and autoclaving 
According to the table above, it is evident that the autoclaving processing is suitable when the high quality is required, while RTM method has its advantages in low cost and high production output.
In the researching of matrix cracking behaviours, T. Yokozeki and his co-workers utilised the autoclaving method. Considerable improvements were found on the matrix cracking behaviour in cross-ply laminates. In addition, a 40% increase of the fracture toughness was indicated in the report as well . In the case, unidirectional laminates (UD) and cross-ply (CP) laminates were both involved, and the improvement of mechanical properties basically reached the expected levels.
As another example, E. J. Garcia et al did their experiment by using the same method to assemble laminates . In the short beam shear test, the laminates presented a significant enhancement of 69% compared with the unreinforced laminates. Although three-point bend was applied in their test, which is different from our project, an effective improvement of interlaminar shear strength is still prospective.
3. Interlaminar Shear Strength (ILSS)
3.1 Testing methods
Generally, there are five methods are commonly used to measured interlaminar shear strength: short beam shear (SBS), compression shear test (CST), iosipescu shear test, inclined double notch shear test and five-point bending test. In this review, it focuses on the analyses of the short beam shear (SBS) and the five-point bending test.
3.1.1 Short beam shear test (SBS)
SBS is an indirect method to measure ILSS, which is showed in Fig. 4 schematically. The main advantage of the SBS test is its simplicity and economy in term of materials and equipment. However, the shortcomings of this method are numerous: it is affected by the geometry of specimens, and it is precise only if pure interlaminar shear failure takes place .
Fig. 4 Short beam shear test 
According to the variation of the geometric configurations of the supports, six methods are classified: knife-edge supports, large radius supports, medium radius supports, large diameter rotating roller supports, rotating rollers on swinging links and small diameter roller supports , shown in Fig.5 in sequence.
Fig.5 Schematic of six configurations for three-point bending test
3.1.2 Five-point bending test
Five-point bending is a widely applied method. There is a degree of resemblance between five-point bending and three-point bending. The mechanical configuration is illustrated in Fig. 6.
Fig. 5 Schematic of five-point bending test 
Compared with three-point bending, five-point bending provides a smaller stress concentration in the middle zone. Additionally, in the particular middle section of the beam, there is pure shear stress with negligible bending stress and almost zero contact stress . The normalized applied force distribution drawing of five-point bending is showed in Fig. 6.
Fig. 6 Normalized applied force distribution for the five-point bending 
In the same report, the shear stress distribution across the middle plane is illustrated in Fig. 7. In this figure, it is evident that the maximum value of the shear stress is present at the section of 0.25 in, where is the position with pure shear stress according to analysing. The stress distribution at 0.25 in across the height is showed in Fig. 8.
Because of the high shear stress and the small bending stress at the sensitive section provided by five-point bending testing, the test method is the most popular one to measure the interlaminar shear strength.
Fig. 7 Shear stress distributions along the middle plane for five-point bending 
Fig. 8 Stress distributions at 0.25 in 
3.1.3 Other testing methods
CST is one of the most reliable methods to characterize ILSS seen from its principle. As shown in Fig. 9, the shear stress on the specimen is generated from two clamps directly. The advantage of CST is that this method can create pure interlaminar shear stress excluding the influence of other factors .
Fig. 9 Compression shear test .
As another important way, iosipescu shear test has its feature for its specimen configuration (see Fig. 10). The most significant advantage of this method is to average the shear properties over an area .
Fig. 10 Schematic of loading fixture for Iosipescu shear test .
3.2 Factors affect ILSS
In the sample design, several correlative factors influencing the final interlaminar shear strength should be taken into account, such as the patterns of lay-up, the dimensions of samples and the contents of CNTs in samples.
Traditionally, there are three main patterns of lay-up, namely unidirectional (UD), cross-ply (CP) and quasi-isotropic (QI). This literature review focuses on the last pattern. For the quasi-isotropic pattern, one typical stack sequence is (-45o/0o/45o/90o) 4s. According to the research taken by P. Feraboli and K. Tedward shows that the ILS of quasi-isotropic lay-up samples is slightly smaller than the other two patterns . The experimental results are shown in Table 3. Although the difference between them is not significant, in the view of the isotropy of other mechanical properties, the stack sequence of quasi-isotropic is the most adopted pattern.
Table 3 Experimental data about shear stress of specimens in different lay-ups 
For the samples with different dimensions, the shear stress distributions are different. The value of width/thickness (b/h) must be considered carefully in the short beam shear testing. As reported, for one particular composite, such as carbon fibre reinforced plastic, or glass fibre reinforced plastic, the shear stress distributions across the beam width are varying, showed in Fig. 11.
Fig. 11 Shear stress distributions across beam width for unidirectional laminate with different width/thickness ratio 
In addition to width/thickness ratio, the span-to-depth ratio has a significant effect on the shear fracturing experiments as well, because the ratio determinates the fracture mechanism of the samples. When the span-to-depth ratio (L/d) is less than 5, an interlaminar shear fracture starts first, while the value is larger than 16, a tensile fracture plays a dominate role, and a mixed mechanism occurs when 5< L/d <16 . Recommended by many relative reports, to measure the ILSS accurately, the span-to-depth ratio is about 4. Due to the embedment of carbon nanotubes in specimens, the content of CNTs is another influence factor for ILSS. CNTs is the reinforcement in the composite system, however, its enhancement to the mechanical properties is not proportional to the concentration of CNTs. As reported, the maximum of enhancement is obtained with 0.3 wt% CNT loading, shown in Table 4.
Table 4 Mechanical properties of CNTs/epoxy composite 
In the table above, the interlaminar shear strength is not included, but it is evident that the concentration of CNTs is not the more the better, because CNTs maybe agglomerate in the epoxy matrix. Fig. 12 shows a SEM picture including both individual CNTs and agglomerated CNTs in the 0.3 wt% system. The relationship between the concentration of CNTs and ILSS is illustrated in Fig. 13. According to this diagram, it is obvious that the modest concentration is 0.5 wt% around. Additionally, compared to the system without dispersant, the composite with dispersant behaves a higher ILS strength.
Fig. 12 Individual CNTs and agglomerated CNTs in 0.3 wt% CNTs system 
Fig. 13 ILSS of CNTs/epoxy composite with different concentrations of CNTs 
3.3 Mode â… and Mode â…¡ fracture toughness
There are three modes of fracture, each having their cracking mechanism, illustrated in Fig. 14.
Fig. 14 Three fracture modes 
In the laminate fracture, mode â… and mode â…¡ are the two modes involved. For mode â… the applied force is perpendicular to the fracture plane. Nowadays, the double cantilever beam (DCB) test is the most widely used method to measure the mode â… interlaminar critical strain energy release rate, showed in Fig. 15.
Fig. 15 The schematic of the double cantilever beam 
For mode â…¡, the fracture occurs in the direction of the shear stress. So far, the test method for mode â…¡ is not standardised. There are several candidates to measure the mode â…¡ energy release rate, Gâ…¡, including end-notch flexure (ENF), and the four-point end-notched flexure (4ENF). The schematic plots of the two methods are illustrated in Fig. 16.
According to relative report, the disadvantage of the three-point bend end-notched flexure is that the crack growth is not stable and there is only one data point can be obtained in per sample . Compared to ENF, the four-point bend end-notched flexure test has a significant improvement in these two aspects. As a result, 4ENF is the more reliable option to measure the interlaminar fracture toughness for mode â…¡.
Fig. 16 Schematic plots of ENF (a), 4ENF (b) [28, 29]
4. Investigating the Load Transfer Efficiency in Carbon Nanotubes Reinforced Nanocomposites
The load transfer from matrix to the CNTs is an important influencing factor for reinforcing effects. The load transfer efficiency in CNTs/epoxy system is dependent on the CNT aspect ratios (l/d), CNT volume fractions (vf) and the matrix properties.
A research about axial stress and interfacial shear stress transfer in SWNTs/epoxy system was undertaken by A. Haque and A. Ramasetty . In their report, a series of analyses on the influence factors mentioned above are presented. The distribution of normalized axial stress along the CNTs length is illustrated in Fig. 17. It is obvious that the axial stress increases from the ends of CNTs and climbs up to the top at the centre of CNTs. Another piece of important information observed from Fig. 16 is that the axial stress increasing rate becomes higher and the saturation plateau becomes longer with the increased aspect ratios. This phenomenon implies us that the CNT aspect ratio should be equivalent to 1000. As for the interfacial shear stress, a contrary trend is presented in the same report, showed in Fig. 18. According to the results, there is almost no shear stress along CNTs when the aspect ratios reach 1000 around.
Fig. 17 Axial stress distribution vs. CNT length for different aspect ratios 
Fig. 18 Interfacial shear stress distribution vs. CNT length for different aspect ratios 
The variation trend of the shear stress with the increased CNT volume fraction is similar to that with aspect ratios, illustrated in Fig. 19. However, as stated previously, CNTs tend to agglomerate when the content is too high (above 1 wt %). According to research, the matrix mechanical properties, like modulus, have little effect on the load transfer.
Fig. 19 Interfacial shear stress vs. CNT length for different volume fraction of CNTs 
To quantify the load transfer efficiency of CNTs/epoxy system, the concept of effective length (Leff) of CNTs is defined as follows:
Where is the axial stress in the SWNTs, and is the saturated stress 
The ratio of Leff/L indicates the efficiency of the load transfer. The more close to one the ratio is, the more efficient the transfer is. The ratio increases with the aspect ratio of CNTs, and the trend chart is illustrated in Fig. 20.
Fig. 20 Load transfer efficiency vs. aspect ratios