Failure of carbon nanotube/polymer composites and the effect of nanotube waviness

This paper studies the failure of CNT/polymer composites by combining micromechanics model and finite element simulation. A computational model of composite of adequate size is employed so the interactions between nanotubes embedded in the matrix can be taken into account. The effects of nanotube waviness and random nanotube distribution relative to aligned straight nanotubes are investigated. The computational results indicate that the nanotube waviness tend to reduce the elastic modulus but increase the ultimate strain of a composite. The randomness of nanotube distribution tends to reduce both the composite elastic modulus and tensile strength. The damage initiation and evolution in composites with random wavy nanotubes have also been analyzed.     

Mechanical property enhancement of aligned multi-walled carbon nanotube sheets and composites through press-drawing process

A solid-state drawing and winding process was done to create thin aligned carbon nanotube (CNT) sheets from CNT arrays. However, waviness and poor packing of CNTs in the sheets are two main weaknesses restricting their reinforcing efficiency in composites. This report proposes a simple press-drawing technique to reduce wavy CNTs and to enhance dense packing of CNTs in the sheets. Non-pressed and pressed CNT/epoxy composites were developed using prepreg processing with a vacuum-assisted system. Effects of pressing on the mechanical properties of the aligned CNT sheets and CNT/epoxy composites were examined. Pressing with distributed loads of 147, 221, and 294 N/m showed a substantial increase in the tensile strength and the elastic modulus of the aligned CNT sheets and their composites. The CNT sheets under a press load of 221 N/m exhibited the best mechanical properties found in this study. With a press load of 221 N/m, the pressed CNT sheet and its composite, respectively, enhanced the tensile strength by 139.1 and 141.9%, and the elastic modulus by 489 and 77.6% when compared with non-pressed ones. The pressed CNT/epoxy composites achieved high tensile strength (526.2 MPa) and elastic modulus (100.2 GPa). Results show that press-drawing is an important step to produce superior CNT sheets for development of high-performance CNT composites.     

On the contribution of carbon nanotube deformation to piezoresistivity of carbon nanotube/polymer composites

The change in electrical resistance due to mechanical deformation of carbon nanotube (CNT)/polymer composites can be rationalized in terms of two effects: (i) changes in the composite electrical resistivity due to changes in the CNT network configuration and (ii) deformation of the CNTs themselves. The contribution of CNT dimensional changes (ii) to the piezoresistivity of CNT/polymer composites is investigated here. An analytical model based exclusively on dimensional changes which describes the CNT change of electrical resistance in terms of its mechanical deformation is proposed. A micromechanics approach and finite element analysis are performed to correlate the macroscale composite strain to the individual CNT strain. The CNT change of electrical resistance is quantified for different matrix elastic moduli and CNT weight fractions. The CNT/polymer composite is also modeled as an effective continuum material in terms of both its electrical and mechanical responses so that the effect of dimensional changes on the global piezoresistivity can be investigated. Based on the modeling predictions and previous experimental results, it is estimated that the CNT change of resistance due to the macroscale composite strain is marginal (∼5%) compared to the total composite change of resistance commonly measured in the laboratory, suggesting that the dominant effect in the piezoresistivity of CNT/polymer composites is the change in the CNT network configuration.     

Effect of carbon nanotube waviness on the effective thermoelastic properties of a novel continuous fuzzy fiber reinforced composite

This paper deals with the investigation of the effect of carbon nanotube (CNT) waviness on the effective coefficient of thermal expansion (CTE) of a novel continuous fuzzy fiber reinforced composite (FFRC). This novel FFRC is composed of carbon fibers, sinusoidally wavy CNTs and epoxy matrix. The sinusoidally wavy CNTs are radially grown on the circumferential surfaces of the carbon fibers. Analytical micromechanics model based on the method of cells (MOC) approach is derived to investigate the influence of the waviness of CNTs on the effective CTEs of the FFRC. The present study reveals that if the amplitudes of the radially grown sinusoidally wavy CNTs are parallel to the axis of the carbon fiber then the thermoelastic properties of the FFRC are significantly improved over those of the FFRC being composed of straight CNTs.     

Tensile modulus of carbon nanotube/polypropylene composites – A computational study based on experimental characterization

Micromechanical and computational models significantly over-predict the tensile modulus of composites, as they ignore many experimentally observed factors. Computational models that capture the effect of polymer-filler contact, the presence of carbon nanotube (CNT) agglomerates and the alignment of CNTs with respect to the applied load on the tensile modulus of CNT-reinforced polypropylene (PP) are proposed and discussed in detail in this study. The CNT/PP composites are made by melt mixing and injection molding. The CNT/PP contact area is characterized in terms of width and modulus using Atomic Force Microscope (AFM). The presence, including the size and distribution of CNT agglomerates, is characterized using Scanning Electron Microscope (SEM). The tensile modulus of CNT/PP composites, measured as a function of CNT content according to ASTM D638, is compared to predictions made using numerical methods based on Finite Element Analysis (FEA) within the composite’s elastic regime. The model over-predicts the modulus of the CNT/PP composites by 85% for 5 wt.% CNT/PP composites assuming perfect filler–polymer interfacial contact. When imperfect CNT/PP contact, CNT agglomerates and alignment are accounted for in the model the effective composite modulus predicted is in good agreement with the experimental data. The computational design tools proposed in this study by systematically incorporating experimentally observed characteristics, in combination with the manufacturing method used to make the CNT/PP composites, can lead to composites with engineered properties made by a scalable and cost effective method.     

A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics

A study on the mechanical properties of polyethylene and carbon nanotube (CNT) based composites is presented using molecular mechanics simulations. The systems being investigated consist of amorphous as well as crystalline polyethylene (PE) composites with embedded single-walled CNTs. All the systems are subjected to quasi-static tensile loading, with the assumption that no cross-link chemical bonds exist between the CNT and polyethylene matrix in the case of nanocomposites. Based on the numerical simulations, we report Young’s moduli (C₃₃) of 212–215 GPa for crystalline PE, which closely match the experimental measurement. Furthermore, elastic stiffness of 3.19–3.69 GPa and tensile strength of 0.21–0.25 GPa are obtained for amorphous PE. The tensile responses are found to be highly isotropic. In the case of crystalline PE reinforced by long through CNTs, moderate improvements in the tensile strength and elastic stiffness are observed. However, the results differ from the predictions using the rule of mixtures. On the other hand, although significant increase in the overall tensile properties is observed when amorphous PE is reinforced by long through CNTs, the load transfer at the nanotube/polymer interface has negligible effect. Finally, degradations in both tensile strength and elastic stiffness are reported when amorphous PE is reinforced by embedded CNTs. The study presented indicates the importance of specific CNT and polymer configurations on the overall properties of the nanocomposite.     

A comprehensive study on thermal conductivities of wavy carbon nanotube-reinforced cementitious nanocomposites

The thermal conductivities of cementitious nanocomposites reinforced by wavy carbon nanotubes (CNTs) are determined by the effective medium (EM) micromechanics-based method. The nanocomposite is composed of sinusoidally wavy CNTs as reinforcement and cement paste as matrix. The interfacial region between the CNTs and cementitious material is considered in the analysis. The effects of volume fraction and waviness parameters of CNTs, interfacial thermal resistance, type of CNTs placement within the matrix including aligned or randomly oriented CNTs, cement paste properties on the thermal conductivity coefficients of the nanocomposite are studied. The estimated values of the model are in very good agreement with available experimental data. Two parameters of CNT waviness and interfacial region contributions should be included in the modeling to predict realistic results for both aligned and randomly oriented CNT-reinforced nanocomposites. The results reveal that thermal conductivities K₂₂ (transverse in-plane thermal conductivity) and K₃₃ (longitudinal in-plane thermal conductivity) of the nanocomposites are remarkably dependent on the CNT waviness. Also, it is found that the CNT waviness moderately affects the thermal conductivity of a cementitious nanocomposite containing randomly oriented CNTs. However, the non-straight shape of CNTs does not influence the value of thermal conductivity K₁₁ (transverse out of plane thermal conductivity). The achieved results can be useful to guide the design of cementitious nanocomposites with optimal thermal conductivity properties.     

Effective moduli and failure considerations for composites with periodic fiber waviness

A finite element micromechanical model for fibrous materials introduced in a previous work [J. Compos. Mater. 38 (4) (2004) 273] is used to further study the effects of periodic and localized fiber waviness. A periodic unit cell based on hexagonal fiber packing and sinusoidal fiber waviness was assumed as a representative volume element. Equivalent to this wavy-shaped unit cell, a straight unit cell but with wavy material-orientation is introduced. This type of homogenized continuum modeling simplifies the analysis since the wavy geometry with details of constituent materials is avoided. Thus, stiffness parameters associated with individual lamina with waviness are estimated when subject to the constraining effects of neighboring isotropic or straight fiber material layers. It is shown that the shear constraint of the added layers increases the effective moduli of the wavy layer by inhibiting the fiber straightening deformation mechanism. The local stress distribution is also examined and the potential for material failure is investigated. The methodology provides a platform to study the behavior of wavy fiber composites in a systematic manner.     

Homogenization of structures with generalized periodicity

In this paper, the analytical and computational homogenization of composites with generalized microstructural periodicity is presented. The role of non-linear periodicity function is established in the analytical expressions of the effective properties and clarified through the waviness effect in wavy stratified composites and through the cylindrical periodicity in fiber composites. A numerical example is presented, that validates the two-step analytical homogenization in wavy multilayered materials. Moreover, an approximate computational technique, based on locally periodic homogenization, is proposed, followed by a numerical example.     

Interphase effect on the macroscopic elastic properties of non-bonded single-walled carbon nanotube composites

Compared to the small diameter of a carbon nanotube (CNT), the thickness of the CNT–matrix interphase in a CNT–composite is considerable. Hence, the interphase property can significantly influence the macroscopic properties of the composite. This paper applies an effective multi-scale method to explore such an interphase effect on the properties of nano-composites reinforced by single-walled CNTs. The method integrates the van der Waals (vdW) gap interphase, the dense interphase, and the randomly distributed wavy CNTs in a matrix to realize an accurate prediction of macroscopic properties with a nanoscopic resolution, by using a conventional finite element code commercially available. The study concluded that with the same volume fraction, increasing CNT waviness and diameter reduces the composite Young's modulus, and that ignoring either the vdW gap interphase or the dense interphase can lead to an erroneous characterization, and that both interphases can be ignored in some circumstances.     

A comparative study of the load transfer mechanisms of the carbon nanotube reinforced polymer composites with interfacial crystallization

With the help of shear-lag theory, load transfer analysis is performed on the carbon nanotube reinforced polymer composites with interfacial crystallization of different morphologies, including transcrystallinity layer (TCL) and nanohybrid shish-kebab (NHSK) structures. By comparison, we find that the TCL structures can ease the burden of the CNT while the NHSK structures can lead to a fluctuating distribution of the axial stress in the CNT. Both structures can improve the effective elastic modulus of the composites, though the effect of the TCL structures is more pronounced. Besides, the enhancement of the load transfer efficiency of the composites is also observed, the study of the interfacial stress on different kinds of interfaces shows that the reinforcing effect of the TCL structures is sensitive to both the CNT/crystalline polymer interface and crystalline polymer/amorphous polymer interface, while the major decisive factor for the NHSK structures is confined to be the CNT/crystalline polymer interface because of the interlocking effect. Based on these features, some suggestions are given for tailoring the high-performance carbon nanotube reinforced polymer composites.     

The effective properties and local aggregation effect of CNT/SMP composites

A micromechanics model of the thermomechanical constitutive behavior and micro-structural inhomogeneity of carbon nanotubes (CNTs)/shape memory polymer (SMP) composites is presented. It is assumed that the CNTs are elastic and the SMP obeys a thermomechanical constitutive law. The effective properties of CNT/SMP composites are examined using a micro-mechanics method. The effect of CNT aggregation in the composite, frequently encountered in real engineering situations, is studied. The degree of aggregation is described by an aggregation coefficient, and the effective properties of SMP composites with aggregated CNTs are calculated using a stepping scheme. It is shown that the degree of CNT aggregation dramatically influences the effective properties of the CNT/SMP composites. A homogeneous microstructure leads to maximum levels of effective composite properties.     

Effect of carbon nanotube orientation on the mechanical properties of nanocomposites

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young’s modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.     

Modulus–density negative correlation for CNT-reinforced polymer nanocomposites: Modeling and experiments

Mechanical and weight properties of polymer nanocomposites (PNCs) are measured and modeled at the interlaminar region, predicting the density and elastic modulus of individual carbon nanotubes (CNTs). A simple model of the CNTs density and elastic modulus within the PNC, accounting for fundamental material properties, geometry, and interactions, is developed, capable of predicting CNT contributions in the PNCs. Furthermore, the model is validated with experimental results that demonstrate enhancement of the elastic modulus, while reducing density in the presence of aligned CNTs. By establishing an inverse relation of density and elastic modulus (negative correlation), it is demonstrated the potential of increasing mechanical properties while reducing weight. Therefore, by introducing controlled nanoporosity through suitable CNT distributions within the interlayer of multi-lamina structures, it is possible to simultaneously control effective weight reduction and enhanced modulus, toward bio-inspired carbon fiber reinforced polymer composites.     

Compressive failure of finite size unidirectional composite laminates with a region of fibre waviness

The compressive behaviour of finite unidirectional composites with a region of misaligned reinforcement is investigated via finite element analyses. Models with and without fibre bending stiffness are compared, confirming that compressive strength is accurately predicted without modelling fibre bending stiffness for real composite components which typically have waviness defects of several millimetres wavelength. Various defect parameters are investigated. Results confirm the well-known sensitivity of compressive strength to misalignment angle, and also show that compressive strength falls rapidly with the proportion of laminate width covered by the wavy region. A simple empirical equation is proposed to model the effect of a single patch of waviness in finite specimens. Other parameters such as length and position of the wavy region are found to have a smaller effect on compressive strength. The modelling approach is finally adapted to model distributed waviness and thus determine the compressive strength of composites with realistic waviness defects.     

Mechanical and electrical property improvement in CNT/Nylon composites through drawing and stretching

The excellent mechanical properties of carbon nanotubes (CNTs) make them the ideal reinforcements for high performance composites. The misalignment and waviness of CNTs within composites are two major issues that limit the reinforcing efficiency. We report an effective method to increase the strength and stiffness of high volume fraction, aligned CNT composites by reducing CNT waviness using a drawing and stretching approach. Stretching the composites after fabrication improved the ultimate strength by 50%, 150%, and 190% corresponding to stretch ratios of 2%, 4% and 7%, respectively. Improvement of the electrical conductivities exhibited a similar trend. These results demonstrate the importance of straightening and aligning CNTs in improving the composite strength and electrical conductivity.     

Analysis of elastic properties of carbon nanotube reinforced nanocomposites with pinhole defects

Due to their unique molecular structure, carbon nanotubes exhibit outstanding properties. They are regarded as ideal reinforcements of composites. In this paper, the effects of pinhole defects on mechanical properties are investigated for wavy carbon nanotubes based nanocomposites using 3-D Representative Volume Element with long carbon nanotubes. The carbon nanotubes are modeled as continuum hollow cylindrical shape elastic material with pinholes, having some curvature in its shape. These defects are considered on the single walled carbon nanotubes. The mechanical properties like Young’s modulus of elasticity are evaluated for various values of waviness index, as well as type and number of pinhole defects. The effects of interactions between both defects as well as their influence on the nanocomposites are studied under an axial loading condition. Numerical equations are used to extract the effective material properties for the different geometries of Representative Volume Elements with non-defective carbon nanotubes. The finite element method results obtained for non-defective carbon nanotubes are consistent with analytical results for cylindrical Representative Volume Elements, which validate the proposed model. It is observed that the presence of pinhole defects as well as waviness, can significantly reduces the effective reinforcement, when compared with nanotubes without pinhole defects and this reinforcement decreases with the increase of the number of pinhole defects.     

Fracture behaviour of cracked carbon nanotube‐based polymer composites: Experiments and finite element simulations

This paper studies the fracture behaviour of cracked carbon nanotube (CNT)‐based polymer composites by a combined numerical–experimental approach. Tensile tests were conducted on single‐edge cracked plate specimens of CNT/polycarbonate composites at room temperature and liquid nitrogen temperature (77 K), and the critical loads for fracture instabilities were determined. Elastic–plastic finite element simulations of the tests were then performed to evaluate the J‐integrals corresponding to the experimentally determined critical loads. Scanning electron microscopy examinations were also made on the specimen fracture surfaces, and the fracture mechanisms of the CNT‐based composites were discussed.     

Influence of the concentration of carbon nanotubes on electrical conductivity of magnetically aligned MWCNT–polypyrrole composites

The goal of this work is to study the effect of high magnetic pulses on electrical property of carbon nanotube–polypyrrole (CNT–PPy) composites with different CNT concentrations. CNT–PPy composites are produced in fractions of 1, 5 and 9 wt%. During the polymerization process, the CNTs are homogeneously dispersed throughout the polymer matrix in an ultrasonic bath. Nanocomposite rods are prepared. After exposure to 30 magnetic pulses, the resistivity of the rods is measured. The surface conductivity of thin tablets of composites is studied by 4-probe technique. The magnitude of the pulsed magnetic field is 10 Tesla with time duration of 1.5 ms. The results show that after applying 30 magnetic pulses, the electrical resistivity of the composites decreases depending on the concentration of CNTs in the composites. The orientation of CNTs is probed by atomic force microscopy (AFM) technique. AFM images approved alignment of CNT–polymer fibres in the magnetic field. We found that the enhancement in the electrical properties of CNT–PPy composites is due to rearrangement and alignment of CNTs in a high magnetic field. The stability of nano-composites is studied by Fourier transform infrared spectroscopy.     

Investigation of the Embedded Element Technique for ModellingWavy CNT Composites

This paper presents a comparison of different finite element approaches to modelling polymers reinforced with wavy, hollow fibres with the aim of predicting the effective elastic stiffness tensors of the composites. The waviness of the tubes is described by sinusoidal models with different amplitude-to-wavelength parameters. These volume elements are discretized by structured volume meshes onto which fibres in the form of independently meshed beam, shell or volume elements are superimposed. An embedded element technique is used to link the two sets of meshes. Reference solutions are obtained from conventional three-dimensional volume models of the same phase arrangements. Periodicity boundary conditions are applied in all cases and fibre volume fractions of up to a few percent are considered. The results indicate that embedded element techniques using shell elements for discretizing the fibres may provide an attractive combination of accuracy, computational cost and flexibility for modelling composites reinforced by arbitrarily, three-dimensionally curved nanotubes.