Modeling of damage sensing in fiber composites using carbon nanotube networks

Composites Science and Technology 68 (2008) 3373–3379

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Modeling of damage sensing in fiber composites using carbon nanotube networks Chunyu Li *, Tsu-Wei Chou 1 Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

a r t i c l e

i n f o

Article history: Received 30 April 2008 Received in revised form 1 September 2008 Accepted 9 September 2008 Available online 25 September 2008 Keywords: A. Carbon nanotube A. Composites B. Electrical conductivity C. Damage sensing C. Modeling

a b s t r a c t This paper presents the modeling of damage sensing in [0°/90°]s cross-ply glass fiber composites using embedded carbon nanotube network. The wavy nanotubes are distributed in the polymer matrix between fibers and their contact resistances are modeled considering the electrical tunneling effect. The effective electrical resistance of the percolating nanotube network is calculated by considering nanotube matrix resistors and employing the finite element method for electrical circuits. The entire deformation process of the composite, from initial loading to final failure, is simulated by using the finite element method for two-dimensional stress analyses. The deformation and damage induced resistance change is identified in each loading step. The results demonstrate that the current simulation model captures the essential parameters affecting the electrical resistance of nanotube networks, which can serve as an efficient tool for structural health monitoring of fiber composites. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction The failure of a fiber composite is usually a complex process which may involve an accumulation of microscopic damage, including fiber fracture, fiber matrix interfacial debonding, matrix cracking and delamination. The concept of damage sensing in composites based upon the carbon fiber reinforcements was pioneered by Schulte and co-workers (see Refs. [1–4]). The basic idea of this approach is in the use of conductive carbon fibers as the electric current carrier and the measurement of resistivity change in the fiber direction due to fiber breakages or in the transverse direction due to the separation of fiber contacts [5]. However, the technique is not applicable to composites with non-conductive fibers such as glass and ceramic fibers. Even in carbon fiber composites, some matrix-dominated damage may not be detected by the fiber network. Thus, more versatile technique is needed for in situ damage sensing of fiber-reinforced composites, and carbon nanotubes (CNTs) turn out to have great potential for such applications [6,7]. CNTs possess exceptionally high stiffness and strength [8,9] as well as high electrical and thermal conductivities [10,11]. The unique mechanical and physical properties of CNTs combined with their high aspect ratio (length/diameter) and low density have brought about extensive research in creating composite material systems to exploit these properties [7,8]. Besides the effort in utilizing nanotubes as passive reinforcement to tailor toughness, impact resistance, vibration damping, electrical conductivity and

* Corresponding author. Tel.: +1 302 831 6541. E-mail addresses: [email protected] (C. Li), [email protected] (T.-W. Chou). 1 Tel.: +1 302 831 1550; fax: +1 302 831 3619. 0266-3538/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2008.09.025

thermal conductivity, much attention has also been devoted to developing sensors and actuators using CNTs [12,13]. An interesting recent development in nanocomposites is the use of CNTs as multi-functional reinforcements where they serve as strain or damage sensors. Wood et al. [14] and Zhao et al. [15,16] examined the Raman spectral shifts of carbon nanotubes embedded in a polymer matrix due to the elastic strain in the nanotubes, and proposed the use of nanotubes as microscale strain sensors for measuring the strain fields around defects or fibers. Dharap et al. [17] investigated resistance-based CNT strain sensors by using thin films of randomly oriented CNTs. Zhang and co-workers [18] reported that multi-walled CNT reinforced composites can be utilized as strain sensors and suggested that the instantaneous change in resistance with strain can be utilized for self-diagnostics and real-time health monitoring. Kang et al. [19,20] utilized singlewalled CNT/polymer composite films for strain sensing and suggested that a sensor network attached to the surface of a structural component could enable structural health monitoring. Some researchers [21–23] have also proposed using CNT composites as chemical sensors based on their changes in electrical resistivity. The principle behind these examples of CNT-based composite sensors is the sensing of the change in volume resulted from chemical, thermal or mechanical loading. Fiedler and co-workers [5] were the first to propose the concept of conductive modification with nanotubes for both strain and damage sensing. Because CNTs possess higher electrical conductivity than carbon fibers, it is expected that the sensitivity of changes in electrical resistance resulted from strain or damage could be enhanced. Thostenson and Chou [6] concluded that the change in the size of reinforcements, from conventional micron-sized fiber reinforcement to carbon nanotubes with nanometer-level diameters, enables

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unique opportunity for the creation of multi-functional in situ sensing capability. They demonstrated that the percolating networks of CNTs are remarkably sensitive to the onset of matrix-dominated failure and can detect the progression of damage. More recently, Park et al. [24] evaluated the inherent sensing of CNT/epoxy composites using an electro-mechanical testing technique and concluded that uniform dispersion and interfacial adhesion are key factors for improving sensing performance. Although some modeling work has been carried out on the electrical resistance-based damage detection in carbon fiber composites [25,26], there has been no report on the modeling of nanotube network for damage sensing of fiber composites. Given the potential applications of multi-functional nanocomposites, an in-depth understanding of the key factors controlling the effectiveness of carbon nanotube network for damage sensing is indispensable. This paper reports our studies on the computational modeling of a carbon nanotube network embedded in a glass fiber composite with a particular focus on the variation of electrical resistance with damage evolution. 2. Nanotube network in fiber-reinforced composites In the recent experimental work of Thostenson and Chou [6], they activated some of the typical fiber composite failure modes and correlated them to the electrical resistance measurements from distributed carbon nanotube sensor networks. Among the patterns of damage evolution in unidirectional and cross-ply composites, the matrix cracking in the 90° layer of the [0°/90°]s laminate exhibited a progressive accumulation of damage and is particularly interesting from both the experimental and analytical modeling point of view. Thus the cross-ply configuration is chosen as the model system for our simulation research. In the following study, we assume that the CNTs form a percolation network in the [0°/90°/90°/0°] laminate of glass fiber-reinforced epoxy composite. The focus of the simulation is on the demonstration of the interaction between the CNT network and transverse cracks in the 90° plies. For simplicity of the simulation, we adopt a two-dimensional model as shown in Fig. 1. This two-dimensional model may inevitably increase the contact between nanotubes comparing with an actual nanocomposite, in which the conductivity

network is three-dimensional in nature and nanotubes are not limited to a planar distribution. But this undesirable effect is somewhat reduced in our simulations by assuming the gaps of internanotube contacts are statistically distributed in a rather large range. The middle section shows two layers of 90° fibers, while the two sections on the sides represent the 0° fiber layers. The fiber diameter is assumed to be 3.15 lm in order to keep the total fiber volume fraction of 55%, which is a in the range commonly used for structural composites. The multi-walled carbon nanotubes in the simulation have a diameter of 15  25 nm and a length in the range of 1.0  1.5 lm. The carbon nanotubes are allowed to penetrate into the inter-fiber matrix region in the 90° layers. To avoid the complexity in dealing with overlapping nanotubes and fibers, the two 0° layers are replaced by their effective medium and consequently the 0° fibers are not shown in Fig. 1. The CNTs naturally assume a three-dimensional network. But for simplicity of simulation, we only consider a small two-dimensional model with limited size of 30  30 lm. Here, the assumed nanotube size is reasonable. But the fiber size is smaller than that of typical E-glass fibers, which have diameters in the range of 8  15 lm. We initially attempted to simulate the problem with 10 lm E-glass fibers inside a 100  100 lm specimen. But the task in FEM meshing turned out to be rather daunting because of the huge number of nanotubes distributed in the composite. The purpose of the simulation is just to demonstrate the effect of the essential factors contributing to the nanocomposite electro-mechanical behavior in damage sensing. The current model size is adequate in demonstrating the general characteristics of electrical resistance in the carbon nanotube network. Waviness is a prevailing feature of CNTs in a composite. In a CNT/ fiber hybrid composite, where the fibers occupy a significant portion of the volume, the nanotubes are infused into the gaps between neighboring fibers and may assume a larger degree of waviness. Wavy CNTs dispersed in a matrix also tend to have more contact points than straight nanotubes, which could have a considerable effect on the electric conductivity due to the dominant role of contact resistance [27]. Thus, the nanotube waviness needs to be considered in order to simulate the composites in a more realistic manner. The method for generating wavy nanotubes is based on a versatile approach proposed by the authors for composites containing multiple fillers of arbitrary shapes [28], which are approximated by polygons. The wavy nanotubes so generated are then placed in random locations in the designated area. The orientation of a nanotube in the 90° ply may need to be adjusted for avoiding overlapping with the fiber cross-section. If a nanotube cannot fit into a designated position after a certain number of adjustments, it is abandoned and a new nanotube is selected for a new position. The process continues until the designated volume fraction of nanotubes is reached. The contact points between two neighboring nanotubes are determined by following the method described in Ref. [27]. Based on the knowledge of contact points, the nanotube clusters can be identified. The next step is to check the existence of spanning cluster. In some cases, there is no spanning cluster, while in others more than one spanning cluster has formed. The percolation probability at a specific nanotube volume fraction can be determined by the percentage of the number of times that at least one spanning cluster has occurred out of the total number of Monte Carlo simulations. Here, we only need to select one percolation nanotube network for studying the effect of damage on electrical conductivity of the network. Fig. 2 gives the percolating nanotube network in the composite shown in Fig. 1.

3. Electrical resistance of nanotube network

Fig. 1. Nanotube network in the [0°/90°/90°/0°] composite laminate.

The electrical resistance of a percolating nanotube network comes from two sources, i.e., the intrinsic resistance of nanotubes

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10 9

Probability (%)

8 7 6 5 4 3 2 1 0

0

2

4

6

8

10

12

14

16

18

20

Log[Rc (ohms)] Fig. 3. The distribution of contact resistance Rc.

Fig. 2. A percolating nanotube network in the fiber composite.

and the contact resistance at nanotube junctions. Thus the electrical conductivity of the nanotube network strongly depends on the morphology of nanotube network and the number of contact points. The electric conductivity of individual carbon nanotubes is in the order of 104  107 S/m. But the contact resistance is rather complicated and depends on nanotube diameter, tunneling gap at contact points and matrix material filling the tunneling gap. A recent study of the authors indicated that the contact resistance plays a dominant role in the electric conductivity of nanotubebased composites [26]. It was concluded that the thickness of insulating film that fills the tunneling gap at a contact point needs to be less than 1.8 nm in order for the electric tunneling to take place. Depending on a number of contributing factors, the contact resistance between carbon nanotubes in composites could vary in a wide range, from 102 kX to 1016kX. Here, different approaches are adopted for dealing with the two possible nanotube contact configurations. One configuration is the overlapping contact. In this case, it is often difficult to determine the thickness of an insulating film and, hence, the precise value of the contact resistance. Here, we assume that the thicknesses of insulating films follow a normal distribution in the range of 0  1.8 nm, and the corresponding distribution of contact resistances is calculated using the method introduced in Ref. [26]. The distribution of contact resistance resulted from the normal distribution of insulating films is shown in Fig. 3, which is similar to the contact resistance distribution adopted in Ref. [29]. The lower bound of contact resistance is taken as 100 kX; which is the lowest contact resistance between nanotubes assuming no insulating film. The other nanotube contact configuration is the in-plane contact, where two neighboring nanotubes are not overlapping but are situated close enough to permit electrical tunneling. In this case, based on the tunneling gap size, the contact resistance at a specific contact point is approximately calculated using the formula given in Ref. [26]. The calculation of the electrical current flowing through the percolating nanotube network can be carried out by using the finite element method [30]. We assume that the nanotube segment between any two contact points is represented by a resistor. The resistance of this resistor is calculated based on the Ohms law. The electrical conductivity rcnt of CNTs is taken as 106 S/m. The resistance at a contact point, which is assumed to follow the distribution

in Fig. 3, is also represented by a resistor. Thus the nanotube network is replaced by a resistor network. Although the nanotube network of the model composite is two-dimensional, the resistor network is actually located in a three-dimensional space (see Fig. 4). Fortunately, only one unknown, i.e. electrical potential, needs to determined at each node. Assuming that the two opposite sides of the model composite are connected to superconducting electrodes, a voltage is applied to the superconducting electrodes by assigning the electric potential at one side to be zero and at the opposite side to be unity. The electric potential distribution at each node of the resistor network can be obtained by solving a system of algebraic equations [31]. For a typical resistor element i–j, the elemental matrix representing the relation between the current (I) entering the element at the ends and the end voltage (V) is

8 e9 >      = < Ii > Vi Vi 1 1 1 e ¼ e : Iej ¼ ½K ij  > R 1 1 Vj Vj ; : >

ð1Þ

According to the Kirchhoff’s current law, a system of algebraic equations can be assembled for the entire network:

I ¼ KV;

ð2Þ T

where V ¼ fV 1 ; V 2 ; :::; V n g stands for the nodal voltages, I ¼ fI1 ; I2 ; :::; In gT is the vector of external input current at the nodes. The global coefficient matrix is obtained from

Fig. 4. A schematic diagram of resistor network (Yellow: nanotube resistance; Brown: Contact resistance; the inset showing the pseudo 3D model of contact resistance [26]). (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

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K¼

C. Li, T.-W. Chou / Composites Science and Technology 68 (2008) 3373–3379 m X ½K eij ;

ð3Þ

e¼1

where m is the number of resistors in the network. After applying the boundary conditions to Eq. (2), the electrical potential at each node can be obtained. The current flowing through each resistor element is then determined by

Ie ¼ ðV i  V j Þ=Re ;

ð4Þ

and the total current passing through the network can be obtained by summing up the currents in the resistors directly connected to one side of boundaries. The effective resistance of the entire percolating network is then obtained from

Reff ¼ ðV top  V bottom Þ=Itotal :

ð5Þ

4. Damage evolution in composites As indicated in the introduction of the model composite of Fig. 1, the 0° plies are replaced by their effective media, of which the elastic modulus and tensile strength are computed from the rule-of-mixtures. The total number of nanotubes placed in the model composites is about 750. The elastic and strength properties as well as volume fractions of the constituents are given in Table 1. The damage evolution of the model composite is simulated by fixing the lower boundary while applying a uniform displacement on the upper end. This configuration of deformation is equivalent to an isostrain axial loading condition of a specimen with a length of twice of that of Fig. 1. It is well known in the short fiber composite literature, for instance, the presence of stiff, discontinuous fillers tends to induce high concentration of strains in the matrix material with lower modulus at the ends of the discontinuous reinforcements [32,33]. In the fiber/nanotube/polymer hybrid composite, the degrees of deformation of the matrix, nanotube and fiber are very different. Relatively larger deformation developed in the polymeric matrix due to its lower modulus. Furthermore, the CNTs in this hybrid composite, in spite of their low volume fraction, can also significantly affect the local stress and strain distributions at the tubeends because of their high modulus. Thus, it is for the same reason as in short fiber composites that high strain concentration occurs both at nanotube tips as well as in the inter-fiber matrix region where a unidirectional continuous fiber composite is subjected to transverse loading. To simulate the damage evolution of fiber-reinforced composites with randomly distributed CNTs, we employ the commercial finite element method software ANSYS [34]. The coordinates of wavy nanotubes, glass fibers and matrix are generated by in-house software and then exported into ANSYS. The nanotubes with overlapping contacts are assumed to be directly connected because of the two-dimensional nature of the model. The meshing is conducted by first manually assigning the material numbers to the four types of constituents and then automatically performed by the ANSYS software with mixed triangular and quadrilateral elements. The final mesh (shown in Fig. 5) is composed of about 357,000 elements and 360,000 nodes.

Fig. 5. Finite element mesh of the carbon nanotube/fiber cross-ply composite.

The criterion for damage initiation is set by the use of principal tensile stress. For identifying the location of potential damage, the maximum principal stress in each element is traced in every load step in the simulation process. If the maximum principal stress of an element is equal to or larger than the tensile strength of the corresponding material of that element, the critical element is identified and assigned as a death element and deactivated in the next load step. In most cases, there could be a few up to many elements becoming death elements at one load step. The death elements give rise to stress redistribution, which may result in significant stress concentrations. These stress concentrations contribute to the deterioration of the load-carrying capacity as well as the damage progression of the composite. The strain concentrations at nanotube ends are depicted in Fig. 6, which shows some close-up views of damage evolution. Here, at point A, two adjacent nanotubes are in contact with each other. As the applied strain increases, the two nanotube ends move apart, resulting in high strain concentration in the matrix and eventually leading to microcracks along the nanotube/matrix interface. Also, at point B, the matrix strain concentration at the nanotube end initiates nanoscopic crack at e0 ¼ 0:500%, which evolves into a microscopic matrix crack at e0 ¼ 1:167%. At this level of applied strain, another site of damage initiation is noticed at point C. Fig. 7 displays the overall view of damage evolution in the composite with increasing applied strain. Multiple damage spots are visible at the strain level of about 0.433%. These damage spots are located in the inter-fiber matrix region where the strain concentration is high, as shown by the strain contours in Fig. 7(a).

Table 1 Material properties of composite constituents

0° composite ply Epoxy Matrix[35] E-glass fiber[34] Carbon nanotube[7,8]

Young’s modulus (GPa)

Tensile strength (GPa)

Poisson’s ratio (GPa)

Volume fraction (%)

39 3.7 73 800

1.08 0.09 3.45 30.0

0.28 0.35 0.23 0.20

43.15 54.80 2.05

The nanotube volume fraction refers to the entire composite specimen.

C. Li, T.-W. Chou / Composites Science and Technology 68 (2008) 3373–3379

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Fig. 6. A close-up view of damage evolution in the vicinity of nanotube ends.

With increasing tensile strain, the number of damage spots also increases and the size of damage spots expands, as shown in Fig. 7(b). When the applied strain reaches 1.167% (Fig. 7(c)), it can be seen that the damage spots merge to form microscopic cracks, which extend through the entire width of 90° plies. These cracks could further propagate into the 0° plies, eventually resulting in the failure of the cross-ply composite. 5. Damage sensing by electrical resistance method The effective resistance of a composite can be changed when it is deformed under applied loading. Several factors may contribute to the electrical resistance change. First, when a fiber/nanotube/ polymer hybrid composite is deformed, the nanotube length and diameter will alter, resulting in the change of nanotube intrinsic resistance, and hence, the effective resistance of the nanotube network. However, this resistance change is expected to be negligible because of the extremely small elastic deformation in nanotubes. The second and more important factor contributing to the resistance change of the composite is the contact resistance. Under applied load, the thickness of the insulating matrix film between adjacent nanotubes may be changed considerably. The contact resistance increases dramatically with the increase in insulating film thickness [26]. The matrix damage also contributes to the change of contact resistance. It has been shown in Fig. 6 that the matrix damage first appears at low applied strain at the nanotube contact points where there are high strain concentrations. Fig. 8 illustrates the effect of damage evolution on the change of contact resistance. The damage spot assumes the form of a nanoscopic void and its formation give rise to the increase of the opening gap at the

contact area where electrical tunneling takes place and thus increases the contact resistance. With the evolution of damage, the electrical tunneling at a damage area can be eventually cut off, resulting in significant change of the effective resistance of the entire composite. The real effect of the damage is in changing the contact resistance. Fig. 9 displays the load–strain relationship of the cross-ply composite. A ‘‘knee” is visible in the curve at about 0.433% strain which is an indication of significant damage accumulation in the composite. This is evident from the multiple damage spots in the 90° plies of Fig. 7(a). The ultimate load level of the composite occurs at about 1.2% applied tensile strain, when multiple microcracks have formed in the 90° plies and also extended into the 0° plies. The load-carrying capacity of the composite drops rapidly after 1.2% applied strain and eventually the composite fails at about 1.5% applied strain when microcracks propagate through the 0° plies. Fig. 9 also shows the change of electrical resistance with applied tensile strain. It can be seen that the resistance change is very small in the beginning. But significant change occurs around 0.4% strain, which roughly corresponds to the knee point in the load-strain curve. A careful browsing of the image of strain distribution at this stage (Fig. 7(a)) reveals that some damage spots are located right in the percolation path and two of the conducting branches have been cut off. The resistance change reflects the cutoff of current path due to matrix cracking. It should be noted that several small damage areas actually appeared earlier when the loading level was lower, but the resulting resistance change is insignificant because the locations of these damages are not on the percolation path. It can also be seen in Fig. 9 that after the first significant stepincrease, the resistance curve exhibits a period of relatively small

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Fig. 8. An illustration of electrical tunneling affected by the damage evolution.

8

2.4

Tensile load (x1000nN)

Resistance 6

2.3

5

2.2

4

2.1

3 2.0 2 1.9

1 Fig. 7. Damage evolution in the composite under different imposed strains (a) e0 = 0.433%, (b) e0 = 0.500%, (c) e0 = 1.167% (Contours showing the first principal strain).

0 0.0

0.3

0.6

0.9

1.2

Electrical resistance (GΩ)

7

2.5 Load

1.8 1.5

Tensile strain (%) Fig. 9. Variations of tensile load and electric resistance with applied tensile strain.

changes. The nearly flat resistance curve indicates no further cutoff of the percolation path. With the increase of loading level, the existing damages are continuously expanded and new damages initiate. When these damage areas cut off one or more percolation branches, the resistance again changes significantly. The final sharp increase in resistance occurs when the load level of the

composite just passes its maximum. A closer examination of Fig. 7(c) indicates that all the percolation branches but one have been cut off at this stage. The last current carrying path (the leftmost path in Fig. 2) is cut off at 1.2% strain when the composite is close to complete failure.

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6. Conclusion and discussion The methodology developed in this study is capable of capturing the key contributing factors to composite electrical percolation and effective resistance: nanotube waviness, electrical contact resistance, nanotube spanning cluster and conductive backbone. A detailed analysis of the local strain/stress concentrations at the inter-fiber as well as inter-nanotube matrix regions is also performed. Then, a combination of the knowledge in load–strain and resistance–strain relations enables the modeling of sensing of the initiation and evolution of damage in fiber composites. The capability so developed parallel to the relevant experimental work on nanotube-based damage sensing further enhances the potential of its use for structural health monitoring of composites. The modeling work of nanotube-based damage sensing indicates that the technique is capable of detecting the onset of damage, which is vital for any tool of structural health monitoring. However, it should be noted that the electric percolation behavior is statistical in nature and the sensitivity of the nanotube network strongly depends on the nanotube distribution and the structure of percolation clusters. If the damage at the early stage happens to cut the percolation path, the resistance change would be noticed early. If the damage at the early stage does not cut a percolation path, the resistance still changes but it may not be clearly noticeable. Based on the analysis of percolating network, the fraction of nanotubes in the percolation clusters could be just a small percentage of total nanotubes in a composite, depending on the volume fraction of nanotubes. Thus it is likely that the resistance change does not reflect the damage occurrence in a timely manner. Such deficiency in damage sensing can be minimized by enhancing the uniform dispersion of nanotubes and, hence, forming more percolation paths. Finally, further comments are needed regarding the implication on the modulus and strength of the fiber composite due to the addition of carbon nanotubes for the purpose of damage sensing. Existing experimental work has demonstrated that the addition of a small amount of carbon nanotube to a polymeric matrix material can result in enhancements in its elastic modulus and strength. The presence of nanotubes in a matrix of lower modulus inevitably induces local stress concentration and thus, higher probability of initiation of flaws. However, it is well known that the ultimate failure of laminated composites is controlled by the fibers. The presence of nanotubes in a fiber composite may have influence on the initiation of microcracks and the onset of nonlinear behavior but will not significantly degrade its strength. In the present simulation, for the purpose of convenience in numerical work the assumed nanotube volume fraction of 2.05% is much higher than the 0.1  0.5% wt.% used by the authors in their experimental work [7]. Furthermore, the local stress concentration at nanotube ends is expected to be much higher in a 2D model comparing to that in a 3D model with the same amount of fillers [32]. Lastly, the assumed carbon nanotube Young’s modulus of 800 GPa ignores the large scattering in experimentally measured modulus values. Acknowledgments This work has been supported by the Air Force Office of Scientific Research (AFOSR), Grant No. FA9550-06-1-0489 (Dr. Byung-Lip Lee, Program Director), and the Office of Naval Research (ONR), Grant No. N00014-07-1-0345 (Dr. Yapa Rajapakse, Program Director). References [1] Schulte K, Baron C. Load and failure analyses of CFRP laminates by means of electrical-resistivity measurements. Compos Sci Technol 1989;36:63–76.

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[2] Schulte K. Sensing with carbon fibres in polymer composites. MSR Int 2002;8(2):43–52. [3] Kupke M, Schulte K, Schuler R. Non-destructive testing of FRP by DC and AC electrical methods. Compos Sci Technol 2001;61:837–47. [4] Schueler R, Joshi SP, Schulte K. Damage detection in CFRP by electrical conductivity mapping. Compos Sci Technol 2001;61:921–30. [5] Todoroki A, Tanaka Y. Delamination identification of cross-ply graphite/epoxy composite beams using electric resistance change method. Compos Sci Technol 2002;62:629–39. [6] Fiedler B, Gojny FH, Wichmann MHG, Bauhofer W, Schulte K. Can carbon nanotubes be used to sense damage in composites? Ann Chim-Sci Mat 2004;29:81–94. [7] Thostenson ET, Chou TW. Carbon nanotube networks: sensing of distributed strain and damage for life prediction and self healing. Adv Mater 2006;18:2837–41. [8] Thostenson ET, Ren ZF, Chou TW. Advances in the science and technology of carbon nanotubes and their composites: a review. Compos Sci Technol 2001;61:1899–912. [9] Thostenson ET, Li CY, Chou TW. Nanocomposites in context. Compos Sci Technol 2005;65:491–516. [10] Kim P, Shi L, Majumdar A, McEuen PL. Thermal transport measurements of individual multiwalled nanotubes. Phys Rev Lett 2001;87:215502. [11] Ebbesen TW, Lezec HJ, Hiura H, Bennett JW, Ghaemi HF, Thio T. Electrical conductivity of individual carbon nanotubes. Nature 1996;382(6586):54–6. [12] Li CY, Chou TW. Atomistic modeling of carbon nanotube-based mechanical sensors. J Intel Mater Sys Struct 2006;17:247–54. [13] Li CY, Thostenson ET, Chou TW. Sensors and actuators based on carbon nanotubes and their composites: a review. Compos Sci Technol 2008;68:1227–49. [14] Wood JR, Zhao Q, Frogley MD, Meurs ER, Prins AD, Peijs T, et al. Carbon nanotubes: from molecular to macroscopic sensors. Phys Rev B 2000;62: 7571. [15] Zhao Q, Wood JR, Wagner HD. Stress fields around defects and fibers in a polymer using carbon nanotubes as sensors. Appl Phys Lett 2001;78: 1748. [16] Zhao Q, Frogley MD, Wagner HD. Direction-sensitive strain-mapping with carbon nanotube sensors. Compos Sci Technol 2002;62:147–50. [17] Dharap P, Li ZL, Nagarajaiah S, Barrera EV. Nanotube film based on single-wall carbon nanotubes for strain sensing. Nanotechnology 2004;15: 379–82. [18] Zhang W, Suhr J, Koratkar N. Carbon nanotube/polycarbonate composites as multifunctional strain sensors. J Nanosci Nanotechnol 2006;6:960–4. [19] Kang IP, Schulz MJ, Kim JH, Shanov V, Shi DL. A carbon nanotube strain sensor for structural health monitoring. Smart Mater Struct 2006;15: 737–48. [20] Kang I, Lee JW, Choi GR, Jung JY, Hwang SH, Choi YS, et al. Structural health monitoring based on electrical impedance of a carbon nanotube neuron. Key Eng Mat Adv Nondestruct Eval 2006;321–323:140–5. [21] Yoon H, Xie JN, Abraham JK, Varadan VK, Ruffin PB. Passive wireless sensors using electrical transition of carbon nanotube junctions in polymer matrix. Smart Mater Struct 2006;15:S14–20. [22] Zhang B, Fu RW, Zhang MQ, et al. Preparation and characterization of gassensitive composites from multi-walled carbon nanotubes/polystyrene. Sensor Actuat B-Chem 2005;109:323–8. [23] Wei C, Dai LM, Roy A, Tolle TB. Multifunctional chemical vapor sensors of aligned carbon nanotube and polymer composites. J Am Chem Soc 2006;128:1412–3. [24] Park JM, Kim DS, Kim SJ, Kim PG, Yoon DJ, DeVries KL. Inherent sensing and interfacial evaluation of carbon nanofiber and nanotube/epoxy composites using electrical resistance measurement and micromechanical technique. Composites B 2007;38:847–61. [25] Curtin WA. Stochastic damage evolution and failure in fiber-reinforced composites. Adv Appl Mech 1999;36:163–253. [26] Xia ZH, Curtin WA. Modeling of mechanical damage detection in CFRPs via electrical resistance. Compos Sci Technol 2007;67:1518–29. [27] Li CY, Chou TW. Dorminant role of contact resistance in the electrical conductivity of carbon nanotube reinforced composites. Appl Phys Lett 2007;91:223114. [28] Li CY, Chou TW. Continuum percolation of nanocomposites with fillers of arbitrary shapes. Appl Phys Lett 2007;90:174108. [29] Li CY, Thostenson ET, Chou TW. Effect of nanotube waviness on the electrical conductivity of carbon nanotube-based composites. Compos Sci Technol 2008;68:1445–52. [30] Zienkiewicz OC. The finite element method. 3rd ed. London, UK: Mcgraw-Hill Book Company Ltd; 1974. 12–13. [31] Li CY, Chou TW. Direct electrifying algorithm for backbone identification. J Phys A: Math Theor 2007;40:14679–86. [32] Chou TW. Microstrucutral design of fiber composites. Cambridge, UK: Cambridge University Press; 1992. [33] Chou TW, McCullough RL, Pipes RB. Compos Sci Am 1986;255:92–100. [34] Moaveni S. Finite element analysis: theory and applications with ANSYS. 2nd ed. New Jersey: Prentice Hall; 2003. [35] Daniel IM, Ishai O. Engineering mechanics of composites materials. 2nd ed. Oxford University Press; 2006.