Simulating the effects of carbon nanotube continuity and interfacial bonding on composite strength and stiffness

Abstract

Molecular dynamics simulations of carbon nanotube (CNT) composites, in which the CNTs are continuous across the periodic boundary, overestimate the experimentally measured mechanical properties of CNT composites along the fiber direction. Since the CNTs in these composites are much shorter than the composite dimensions, load must be transferred either directly between CNTs or through the matrix, a mechanism that is absent in simulations of effectively continuous CNTs. In this study, the elastic and fracture properties of high volume fraction discontinuous carbon nanotube/amorphous carbon composite systems were compared to those of otherwise equivalent continuous CNT composites using ReaxFF reactive molecular dynamics simulations. These simulations were used to show how the number of nanotube-matrix interfacial covalent bonds affect composite mechanical properties. Furthermore, the mechanical impact of interfacial bonding was decomposed to reveal its effect on the properties of the CNTs, the interfacial layer of matrix, and the bulk matrix. For the composites with continuous reinforcement, it was found that any degree of interfacial bonding has a negative impact on axial tensile strength and stiffness. This is due to disruption of the structure of the CNTs and interfacial matrix layer by the interfacial bonds. For the discontinuous composites, the modulus was maximized between 4%–7% interfacial bonding and the strength continues to increase up to the highest levels of interfacial bonding studied. Areas of low stress and voids were observed in the simulated discontinuous composites at the ends of the tubes, from which fracture was observed to initiate. Experimental carbon nanotube yarn composites were fabricated and tested. The results were used to illustrate knockdown factors relative to the mechanical performance of the tubes themselves.

1.0. INTRODUCTION

From improving the efficiency of atmospheric flight to enabling more affordable and capable deep space mission designs, ongoing advances in lightweight, high performance structural materials are critical to progress in aerospace vehicle development. Decades of focused research and development have produced a range of highly optimized conventional carbon fiber composites with mechanical properties that are beginning to plateau. As a result, attention has turned to materials that have the potential to eventually surpass the properties of state of the art carbon fiber composites [1]. Carbon nanotubes (CNTs), for example, have been shown by modeling and nano/micro-scale measurements to have much higher specific strength and stiffness than carbon fibers [2–4]. In recent years, rapid advances in manufacturing and processing have led to the availability of large quantities of high quality CNTs in practically useful material formats, such as large sheets and kilometer-length yams [5–7]. As a result, it is now possible to fabricate high volume fraction CNT composites with specific strength and stiffness values that approach those of current aerospace carbon fiber composites [6–9]. These properties are achieved in samples with notably non-optimal microstructures: they exhibit large voids, both within and between the reinforcing yarns [6]. Optimization of the composites will require ongoing improvements in both modeling and experimental methods to address their hierarchical nature: CNTs have important features on length scales ranging from 1 nm (their typical diameter) to 1 mm (their length), to even larger scales (bundles, fibers, and composites) [10–12].

This work used molecular dynamics simulations to predict the mechanical properties of composites composed of CNTs in an amorphous carbon matrix. The newly predicted elastic and fracture behaviors of discontinuous CNT/amorphous carbon composites were compared with continuous CNT analogs reported previously [13]. As in the previous work, amorphous carbon was selected as the matrix material to both reduce the complexity of constructing and equilibrating the model structure, relative to the use of a polymer matrix, and because it permitted the use of a well-validated reactive force field in the molecular dynamics simulations. Additionally, amorphous carbon is relevant to the experimental material as it is often found in CNT sheets and yarns as a byproduct of the synthesis process [14]. Since amorphous carbon is stiffer and stronger than polymer matrices, these results represent an upper bound on several properties typical of CNT-polymer matrix composites.

While the length of the discontinuous tubes used in these simulations, 22.1 nm, is much smaller than in the experimental material, they are quite long compared to those in previous simulation work. Our new studies have also added CNT-matrix linking, and used a method capable of modeling material failure [15,16]. Simulations of direct linking between CNTs improved the mechanical properties relative to systems without bonds [17–23]. Other work using the ReaxFF reactive force field, which is capable of modeling covalent bond breaking [24,25], has examined the mechanical properties of allotropie carbon systems [26,27] and continuous CNT/amorphous carbon composites [13]. The present paper goes beyond this previous work by simulating the mechanical deformation to failure of reasonably long but discontinuous CNTs chemically linked to an amorphous carbon matrix.

2.0. COMPUTATIONAL DETAILS

The molecular dynamics simulations were performed using the reactive force field ReaxFF [24,28], as implemented in the LAMMPS molecular dynamics package [29,30]. The ReaxFF_c-2013 parameters, originally developed to investigate fullerene formation, were used in this work [25]. The ReaxFF_c-2013 parameters have previously been used to study single-and multi-walled nanotube composites [13], nanoparticle impacts on graphene [31], CNT vacancies [32], and they have been incorporated into expanded parameter sets [33–36]. The reliability of the ReaxFF_c-2013 parameterization for predicting the elastic and fracture properties of diamond, graphene, amorphous carbon, and carbon nanotubes has been validated previously by comparison with experimental measurements and density functional theory results [26]. Molecular structure images were rendered using the Ovito visualization software package [37].

Molecular models of the continuous and discontinuous CNT/amorphous carbon matrix composites are shown in Fig. 1. Here, Fig. 1a depicts the continuous system in which the CNTs continue through the periodic boundaries of the 10.2 nm long simulation cell. The discontinuous system, shown in Fig. 1b, is composed of 22.1 nm long CNTs terminated with hemispherical end-caps. A longer box length was used in the discontinuous systems to increase the CNT aspect ratio. The discontinuous CNTs were offset to maximize the distance between adjacent CNT ends. The axial length of the simulation cell was 24.0 nm resulting in ~2 nm of matrix between the endcaps of each CNT. All systems had a CNT mass fraction of 37%. All CNTs had a chirality of (20,0) and a diameter of ~1.56 nm. The atoms in each system were grouped into four constituent groups for analysis purposes, as indicated by coloring in Fig. 1.

Fig. 1.

Equilibrated systems composed of (a) continuous CNTs and (b) discontinuous CNTs. Atoms are colored according to their structure.

For both continuous and discontinuous systems, five models were created with CNT-matrix interfacial bonding fractions of approximately <1%, 5%, 10%, 15%, and 20%. These correspond to number densities of approximately 0.0, 1.9, 3.8, 5.7, and 7.6 bonds/nm², respectively. Additional description of the systems is provided in the supplemental information. To assess the dependence of the predicted properties on initial configurations, two independent systems were created at each interfacial bonding fraction, resulting in a total of 20 independent simulated systems. Each system was created using an equilibration procedure that lasted for 607 ps, as described in [13].

All mechanical properties in this work are reported in specific units of GPa/(g/cm³), which is volume independent and can be reduced to N/(g/km) or N/tex, which is the unit commonly used in the fiber community. Specific stiffness tensors (C) were computed from

$${\overline{\sigma }}_c=\mathit{C}{\epsilon }_g$$ (1)

where ${\overline{\sigma }}_c$ is the average specific stress in the constituent and ε_g is the global strain. Engineering constants are then computed from the stiffness tensor in the standard manner [38]. This tensor, referred to as the effective intermediate modulus tensor in the literature, is a good approximation of the local stiffness when the strains in the system are homogenous [39,40]. For the continuous CNT models, the strains of the bulk matrix, matrix interface, and continuous CNTs are directly coupled to the global strains, being continuously connected across the periodic boundaries. It is reasonable to expect that the strains in these constituents can be approximated as the global strains. This is not the case for the discontinuous CNTs, as the deformation of the CNTs fails to track the overall deformation of the composite due to the formation of voids at the tube ends. The treatment of this void space in the calculation of the constituent moduli in the discontinuous systems is somewhat ambiguous, and various approaches have appeared in the literature (see supplementary information). The results presented in this paper used the actual change in discontinuous CNT length during the tensile simulation in calculating the CNT constituent axial strain. The elastic modulus was taken to be the slope of the best fit line, up to 1% strain, of a plot of CNT specific stress against CNT strain, using this strain definition.

3.0. RESULTS

3.1. INTERFACE STRUCTURING

As mentioned in Section 2, the matrix atoms were subdivided into an interfacial group and a bulk matrix group. Removal of portions of the CNTs from the visualization, as shown in Fig. 2a and Fig. 2b, reveals the structuring that was induced in the interfacial region by the CNTs during the heating and equilibration phases of the structure building process. This interfacial surface was composed of a mixture of connected fused ring systems of varying sizes and resembles a highly defective CNT.

Fig. 2.

Matrix interface surface of the <1% bonded (a) continuous and (b) discontinuous systems. A portion of the CNT atoms have been hidden to expose the interfacial matrix layer. (c) cylindrical distribution functions comparing <1% bonded discontinuous and continuous systems, and (d) continuous systems with different amounts of interfacial bonding. Atoms in (a) and (b) are colored according to their structure as in Fig. 1.

Cylindrical distribution functions were computed, as described in the supplemental information, to permit a quantitative description of interfacial structuring. Fig. 2c compares the structure of the matrix at the lowest extent of interfacial bonding for continuous and discontinuous systems. Both systems were found to have large peaks at ~0.34 nm, corresponding to the first structured interface layer, followed by a second, smaller peak at approximately 0.68 nm. Beyond the second peak, the cylindrical distribution function plateaued to the bulk matrix value. The less pronounced peaks found in the discontinuous system reflect the less structured interface seen in Fig. 2b. Here, Fig. 2d shows the cylindrical distribution function for the continuous systems at different interfacial bonding fractions. The magnitude of the peak was greatest in the <1% system, and steadily decreased until essentially all interfacial structure is lost at 18% interfacial bonding. The peak was also observed to shift to shorter distances as interfacial bonding increased. The impact of this ordered interfacial layer on composite mechanical properties is discussed in more detail below.

3.2. ELASTIC PROPERTIES

The dependence of the axial elastic moduli of the continuous and discontinuous CNT composites on the degree of interfacial bonding is shown in Fig. 3a. The modulus of the continuous system was highest in the model with <1% bonding, and steadily decreased as the degree of bonding increased. While the interfacial bonds effectively acted as defects in the CNTs, there exists an optimal degree of bonding in the discontinuous composites that maximizes load transfer while minimizing damage to the CNTs, and disruption of the structured matrix interface. Rather than being a linearly decreasing function of the degree of interfacial bonding, as was the case for the continuous composite, the moduli of the discontinuous composites were highest between 4% and 7% bonding, where the moduli were 131 and 133 GPa/(g/cm³).

Fig. 3.

Axial moduli of (a) composites, (b) CNT constituents, and (c) matrix constituents as a function of degree of interfacial bonding. The colors of the constituents in (b) and (c) match the structures in Fig. 1. Trendlines are a guide to the eye.

The specific axial moduli of the central and outer CNT constituents are compared in Fig. 3b. The stiffness of the continuous outer CNTs, to which all interfacial bonds were formed, fall by 28% for increasing degrees of bonding. The continuous central CNTs, which were shielded from interfacial bonding, were unaffected by matrix bonding to the outer CNTs. At <1% interfacial bonding, the discontinuous outer CNTs were not sufficiently bonded to the matrix to be strained during the tensile deformation, which prevents reliable calculation of a modulus. With 4% or more interfacial bonding, the discontinuous outer CNTs become sufficiently mechanically connected to the composite to achieve measurable strains. These discontinuous CNTs behaved similarly to the continuous outer CNTs: their moduli decreased due to disruption of the CNT structure by the interfacial bonds. The central CNTs of the discontinuous system are not shown in Fig. 3b because they were unconnected to the matrix, and were not strained by the overall deformation of the composite.

The trends in the moduli of the interfacial matrix constituents, shown in Fig. 3c, followed trends very similar to those of the outer CNTs. For both the continuous and discontinuous systems, the highest moduli were found for the least bonded systems, and they decreased when interfacial bonds were introduced. This was because of the trend in structural ordering that is quantified with the cylindrical distribution function in Fig. 2d. At the highest degrees of interfacial bonding, both the structural ordering and the elastic moduli approached the values for the bulk matrix. The magnitude of the moduli for the discontinuous systems were lower at each degree of interfacial bonding, which was a reflection of the lower average degree of order shown in Fig. 2c. For both the continuous and discontinuous systems the moduli of the bulk matrices were essentially the same regardless of the extent of interfacial bonding. This is not surprising as the bulk matrix was defined previously from the density distribution function to exclude the structured interface. These results indicate that the elastic modulus can be maximized by keeping interfacial bonding to a minimum for composites reinforced with very high aspect ratio CNTs. Composites reinforced with shorter tubes, however, will benefit from a moderate degree of interfacial bonding. The remaining elastic constants, shear moduli, and Poisson’s ratios, are included in supplemental information.

3.3. FRACTURE PROPERTIES

The axial stress-strain responses of the composites and constituents (shown in columns) at different degrees of interfacial bonding (shown in rows) are plotted in Fig. 4, in which maximum stresses are marked with ‘X’ symbols. As shown in these figures, the maximum stress experienced by a constituent does not always coincide with that of the other constituents in the same system, or the overall composite. For example, in the 18% bonded continuous system (center column of the bottom row), the central CNT, which was not bonded to the matrix, broke at a much higher strain and stress than either the matrix, or the outer CNTs. Because the central CNT is a minor component of the overall composite (~5% by mass), the composite properties, shown in the green line in the first column of the bottom row, were dominated by the ultimate properties of the matrix and outer CNTs.

Fig. 4.

Axial stress-strain responses of continuous and discontinuous composites and their constituents at a range of interfacial bonding. Maximum stresses are indicated with ‘X’ symbols. The central CNTs in the discontinuous systems are not shown as their stresses are near zero.

For the <1% bonded systems shown in the top row of Fig. 4, the maximum strain of the continuous composite was determined by the CNTs, while the matrix appeared to limit the maximum stress. For the discontinuous composite, the CNTs that were essentially disconnected from the composite, have an overall negative impact on composite properties. This can be seen by comparing the top left and top right panels, which show that the discontinuous composite had a lower strength than its matrix constituents, due to the mass of CNTs that did not contribute to structural reinforcement.

At the intermediate levels of interfacial bonding shown in the middle row of Fig. 4, the strengths of the continuous and discontinuous composites have begun to converge, as shown in the left panel. The middle panel shows that the unbonded central CNTs in the continuous system retained their pristine properties, while interfacial bonding reduced the strength of both the outer CNTs and the matrix interface. In the discontinuous system, shown in the right panel, interfacial bonding led to an increase in the stress in the outer CNTs, a decrease in the matrix interface stress, and had no effect on stress in the central CNT.

Finally, at the maximum level of interfacial bonding shown in the bottom row of Fig. 4, the composite properties of the two systems were nearly equal. This was a result of the continued weakening of the outer CNTs and matrix interface in the continuous system, shown in the middle panel, and the increasing load transfer to the outer CNTs in the discontinuous system, shown in the right plot. Similar plots for axial deformation at the other degrees of interfacial bonding, as well as plots of the results for tensile deformation simulations conducted in the transverse directions, are provided in the supplemental information.

The composite and constituent maximum axial stresses for all interfacial bonding fractions are summarized in Fig. 5. As illustrated in Fig. 5a, increasing the degree of interfacial bonding had very different effects on the continuous and discontinuous systems. While increasing interfacial bonding resulted in a 16% decrease in the strength of the continuous composite, the discontinuous composite strength increased by 85%. Focusing on the contributions of the central and outer CNTs, Fig. 5b shows that the strength of the central tubes, which were not bonded to the matrix, was unaffected by the interfacial bonding of the outer tubes. The outer tubes, on the other hand, reflect the changes seen in the overall composite properties. Specifically, the strengths of the outer tubes in the continuous composite decreased by 32%, while those in the discontinuous composite increased from essentially 0 to 28 GPa/(g/cm³). As in the case of the elastic properties, the interfacial matrix constituents behaved similarly in the two composites, although the more highly structured interface in the continuous system is reflected in its 16% higher strength at <1% interfacial bonding and its slower convergence to bulk properties with increasing interfacial bonding. The strength of the bulk matrix was rather insensitive to the extent of interfacial bonding, having a specific maximum stress approximately 18 GPa/(g/cm³) in both the continuous and discontinuous systems.

Fig. 5.

Comparison of continuous and discontinuous CNT maximum axial specific stresses for the (a) composite, (b) CNT constituents, and (c) matrix constituents. Trendlines are a guide to the eye.

For the continuous composite, the trends in maximum tensile stress were very similar to those found for the specific tensile modulus: the largest values were found for the <1% interfacial bonding system, and steadily decreased with increasing degree of interfacial linking. The strength of the discontinuous composite continued to increase until it plateaued at around 14% interfacial bonding. The specific modulus reached a peak value at around 5%, followed by a steady decrease with additional interfacial bonding. This indicates that the extent of interfacial bonding may be used to tailor a composite to maximize strength or stiffness, although tight control over the process is required. In experimental composites where the bundle sizes are larger, the mass fraction of central CNTs is higher, and therefore their mechanical response will have a larger influence on the overall composite response.

3.4. STRESS DISTRIBUTION IMAGES

The distribution of stresses within the composite structures are shown in Figs. 6 and 7, with atoms colored according to the axial component of their specific stress tensors. Since the results in this paper are given in specific units, the stresses shown are properties of the atoms, and do not require the specification of physically ambiguous atomic volumes, as is the case when using non-specific stress. Diversity of local atomic bonding configurations and thermodynamic fluctuations produced substantial variability in the atomic specific stress values. To improve interpretability, the values depicted in Figs. 6 and 7 were averaged over several consecutive time steps, and over neighboring atoms within 0.19 nm.

Fig. 6.

Stress distributions in continuous and discontinuous systems at 18% strain.

Fig. 7.

Void formation and fracture initiation in a 20% bonded discontinuous system.

The stress distributions for the composites with the minimum, median, and maximum interfacial bonding are shown at 18% strain in Fig. 6. The highest stresses in the continuous CNT composites were found in the <1% bonded continuous system, and show a decreasing trend with the extent of interfacial bonding. The distribution of stresses along the continuous CNTs was reasonably homogenous, as expected for a random distribution of interfacial bond sites, although some larger stress concentrations were found in the most bonded system, due to the agglomeration of neighboring bonds that act as a larger defect. In the discontinuous systems, the <1% bonded CNTs exhibited essentially no stress buildup, which was consistent with the negligible stress noted for this system in Fig. 4 and Fig. 5. The stress began to build in the outer CNTs at an interfacial bonding fraction of 7%, eventually resembling that of the continuous systems, for the 20% bonded composite. In contrast to the continuous system, the stress distribution along the length of the CNTs varied, with the center of the CNTs having a much higher stress than the ends. This is due to the load transfer through the individual interfacial bonds, with each bond resulting in an increase in axial CNT stress from the ends of the CNT towards the center. A similar stress distribution is predicted by micromechanics models of discontinuous fibers wherein load is transferred to the fibers through a continuous interface [38]. This effect was particularly pronounced in the 7% bonded system, although it was also observed near the ends of the CNTs in the 20% bonded system. As was found in the continuous composites, the most bonded discontinuous CNTs had clear local stress concentrations.

In both the continuous and discontinuous systems, the stresses in the matrix were much less uniform than in the CNTs. This was likely due to the existence of a wide variety of bonding geometries in the amorphous matrix, as opposed to the more highly oriented, crystalline bonds of the CNTs. The matrix stresses were relatively homogenous in the continuous composites. In the discontinuous systems, it was clear that the stresses in the matrix between CNT endcaps were lower, and the regions between adjacent bundles were similar in appearance to the continuous composites.

Five snapshots from the simulation at times immediately preceding the initiation of fracture in the 20% bonded discontinuous system are shown in Fig. 7. The first frame shows that the lowest atomic specific stresses in the pre-fracture state were found at the CNT ends, which separated from the matrix slightly. This small void between the endcap and matrix, marked with a red arrow in left-most panel of Fig. 7, served as a fracture nucleation point. As the composite strain increases, a void grew from the lower bundle towards the upper bundle, eventually bridging completely between the two endcap voids as the system severs completely. This endcap void nucleation mechanism contributes to the lower fracture strength of the discontinuous systems, although to a lesser degree than the CNT-matrix interfacial strength, which dominates the fracture strength of the composites.

3.5. COMPARISON WITH EXPERIMENT

To facilitate comparison of the simulated systems with experimental materials, a carbon nanotube yam composite was fabricated and tested. The CNT yarn composite was fabricated by infiltrating a nanotube yarn (Nanocomp Technologies, Inc.) with a bismaleimide (BMI) polymer matrix (RM-3010, Renegade Materials Corp.) to yield a composite that is 18 wt.% polymer. Additional composite fabrication and mechanical testing data are published elsewhere [41,42], and in the supplemental information. The axial specific moduli and maximum specific stresses of the discontinuous and continuous composites, and of the CNT constituents reported in the previous sections are plotted together in Fig. 8a. Each symbol represents an average of the five interfacial bonding fractions. Experimental values for an individual multiwall carbon nanotube (MWCNT) [2], a single wall carbon nanotube (SWNT) bundle [3], a short CNT yarn [43], and the CNT yam composite from this work are shown in Fig. 8b. The CNT yarn composite had a specific strength and stiffness of 1.461±0.185 and 75.4±10.1 GPa/(g/cm³), respectively, which are 97% and 84% lower than the experimentally measured properties (45 and 468 GPa/(g/cm³)) for single MWCNT strength and stiffness, respectively. Note that the individual MWCNT values are plotted in specific units in Fig. 8, but correspond closely to the commonly cited maximum non-specific strength and stiffness values of 100 GPa and 1 TPa, respectively. Details of the conversion to specific values are provided in the supplemental information.

Fig. 8.

(a) Trends of the averaged simulated composite and constituent CNT specific strength and modulus. (b) Trends of specific strength and modulus of experimental CNTs at various length scales. Individual MWCNT properties are from ref. [2], SWCNT bundle from ref [3], short CNT yarn from ref [43], and CNT yarn composite from this work.

The data plotted in Fig. 8b shows the property knockdowns that are commonly encountered when scaling materials from nano-scale testing to larger and more complex material forms. These experimental samples are helpful in evaluating the relative importance of the simulated mechanical property knockdown mechanisms, and illustrate the challenges involved in translating individual CNT properties to a macroscale CNT yarn composite. The experimental knockdown from the individual CNT to the CNT bundle was a 75% reduction in specific strength, but only a 4% reduction in specific modulus. The simulations showed a similar trend for the knockdown on going from pristine to bonded CNTs, with reductions of 32% in specific strength and 11% in specific modulus. The greater strength knockdown in the experimental results may indicate a larger extent of damage to these CNTs than what was caused by the interfacial bonding in the simulations. Overall simulated continuous composite strength and modulus are 35% and 41% lower than the corresponding properties of just the bonded CNT constituents. Finally, the lowest simulated properties were for the discontinuous composite, which was 61% lower in both specific strength and stiffness than the bonded CNTs, and 74% and 65% lower than the pristine CNT values, respectively.

Practical limitations on the volume of material that can be simulated at the atomistic level prevent the inclusion of microscale features such as entanglements, voids, and large-scale bundles that were observed in the experimental material [44,45]. As a result, the present simulations cannot address their relative contributions to the substantial reductions in specific strength and modulus that are found in the experimental materials, going from the CNT bundle to the short yarn and yam composite samples. There were many additional differences between the simulated material and the experimental yarn composite, including matrix material, CNT volume fraction, CNT length and diameter, CNT misalignment, strain rate, and system size. The experimental yarns also contain impurities such as iron catalyst particles, graphitic cages, oxygen, and various functional groups not present in the simulation [14]. As a result, quantitative agreement cannot yet be expected when making comparisons of the simulated and experimental composites.

4.0. CONCLUSIONS

Molecular dynamics simulations were performed on high volume fraction, continuous and discontinuous CNT/amorphous carbon composite systems with CNT-matrix covalent linking fractions ranging from 0–20% of the outer tube atoms. This work led to several interesting insights.

First, a mechanically significant structuring of the amorphous carbon matrix at the CNT interface was observed and characterized. This layer was found to have 48–68% higher axial specific stiffness and 35–50% higher maximum stress than the bulk matrix in the <1% bonded systems. At higher degrees of interfacial bonding, the mechanical properties of the interface layer decreased, until they become equal to those of the bulk matrix at 15% interfacial bonding.

Second, the highest composite axial elastic modulus in the continuous CNT systems was found in the <1% bonded system and it was steadily decreased by increasing interfacial bonding. The maximum modulus for the discontinuous systems was found for an intermediate degree of interfacial bonding of 4%–7%.

Third, the maximum axial tensile stress found for the continuous CNT composites occurred in the <1% bonded system, and stresses were lowest in the 18% bonded system. The discontinuous composites were found to have their lowest strength at <1% interfacial bonding and their strengths increased continuously with interfacial bonding, reaching a maximum quite close to that of the similarly bonded continuous system.

Finally, areas of low stress were observed at the ends of the discontinuous tubes, and in the matrix between them. Interfacial bonding decreased the extent of these areas and localized them at the ends of the tubes. Under loading, voids invariably formed in these low stress regions, creating initiation sites for material failure.

While morphological and other differences in the present simulations prevent quantitative comparison with experimental fibers, qualitative comparisons offer some insight into the relative importance of the various simulated property reduction mechanisms. Comparing the nano-scale experimental knockdown from individual CNTs to a bundle, to the simulated CNT interfacial bonding knockdown, both decreased in strength much more than modulus. The experimental knockdown in strength was also much larger than the simulated crosslinking knockdown indicating that the damage was more severe in the experimental sample. The remaining experimental knockdown to macoscale composites gives an indication of the importance of features beyond the nanoscale such as entanglements and voids.