Three Phase Composite Cylinder Assemblage Model for Analyzing the Elastic Behavior of MWCNT-Reinforced Polymers

Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube (CNT) reinforced polymer composites recently. This paper presents the composite cylinder assemblage (CCA) approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes (MWCNTs). A three-phase cylindrical representative volume element (RVE) model is employed based on CCA technique to elucidate the effects of inter layers, chirality, interspacing, volume fraction of MWCNT, interphase properties and temperature conditions on the elastic modulus of the composite. The interface region between CNT and polymer matrix is modeled as the third phase with varying material properties. The constitutive relations for each material system have been derived based on solid mechanics and proper interfacial traction continuity conditions are imposed. The predicted results from the CCA approach are in well agreement with RVE-based finite element model. The outcomes reveal that temperature softening effect becomes more pronounced at higher volume fractions of CNTs.     

Effect of straight and wavy carbon nanotube on the reinforcement modulus in nonlinear elastic matrix nanocomposites

Elastomers, particularly rubbers, are viscoelastic polymers with low Young’s modulus. In this research, carbon nanotubes were used in the rubber and a rubber–carbon nanotube composite was modeled by ABAQUS™ software. Due to hyperelastic behavior of the rubber, strain function energy was used for the modeling. A sample of rubber was tested and uniaxial, biaxial, as well as planar test data obtained in these tests were used to get an energy function. Polynomial and reduced polynomial form are two common methods to achieve strain energy function. In this paper, elasticity modulus and Poisson ratio were measured for a representative volume element (RVE) of composite. Rubber was also considered as an elastic material and its composite properties in this state compared by hyperelastic rubber matrix assumption. ABAQUS was used to create a three dimensional finite element model of a single long wavy nanotube with diameter of D which perfectly bonded to matrix material. Nanotube waviness was modeled by sinusoidal carbon nanotube shape. Results showed that mechanical properties of the rubber will extremely change by adding carbon nanotube. Furthermore, several volume fractions of carbon nanotube in rubber were modeled and it was shown that stiffness of nanocomposite increases by more volume fraction of carbon nanotubes.     

Effects of particulate reinforcement and strain‐rates on deformation and fracture behavior of Aluminum 6061‐T6 under high velocity impact

Aluminum matrix composites (AMC) exhibit an attractive combination of mechanical and physical properties such as high stiffness and low density, which favors their utilization in many structural applications. Thus, increasing the structural applications of AMC is the driving force for the need to adequately understand their deformation and failure mechanisms under various types of loading conditions. In this study, plastic deformation of alumina particle reinforced Aluminum 6061‐T6 matrix composite is investigated and compared to that of an un‐reinforced Aluminum 6061‐T6 alloy at high strain‐rates under compressive loading. Dynamic stress‐strain curves are obtained using direct impact Split Hopkinson Pressure Bar (SHPB). Particulate reinforcement increases the deformation resistance of the aluminum alloy at high strain‐rates. Strain localization along narrow adiabatic shear bands is observed in both the reinforced and un‐reinforced alloy. Whereas the microstructure of shear bands in un‐reinforced alloy showed finer grain size compared to that of the bulk material, the shear bands observed in the AMCs are darker than the bulk material and the reinforcing particles are observed to be more closely spaced along the shear bands.     

Buckling of Carbon/Glass Composite Tubes Under Uniform External Hydrostatic Pressure

Abstract: This paper describes an experimental and an analytical investigation into the collapse of 44 circular cylindrical composite tubes under external hydrostatic pressure. The results for 22 of these tubes were from a previous investigation and the results for a further 22 models are reported for the first time in this paper. The investigations concentrated on fibre‐reinforced plastic tube specimens made from a mixture of three carbon and two E‐glass fibre layers. The lay‐up was 0°/90°/0°/90°/0; the carbon fibres were laid lengthwise (0°) and the E‐glass fibres circumferentially (90°). The theoretical investigations were carried out using a simple solution for isotropic materials, namely a well‐known formula by ‘von Mises’. The previous investigation also used a numerical solution based on ANSYS, but this was found to be rather disappointing. The experimental investigations showed that the composite specimens behaved similarly to isotropic materials previously tested, in that the short vessels collapsed through axisymmetric deformation while the longer tubes collapsed through non‐symmetric bifurcation buckling. Furthermore, it was discovered that the specimens failed at changes of the composite lay‐up due to the manufacturing process of these specimens. These changes seem to be the weak points of the specimens. For the theoretical investigations, two different types of material properties were used to analyse the composite. These were calculated properties derived from the properties of the single layers given by the manufacturer and also the experimentally obtained properties. Two different approaches were chosen for the investigation of the theoretical buckling pressures, of the previously analysed models, namely a program called ‘MisesNP’, based on a well‐known formula by von Mises for single‐layer isotropic materials, and two finite element analyses using the famous computer package called ‘ANSYS’. These latter analyses simulated the composite with a single‐layer orthotrophic element (Shell93) and also with a multi‐layer element (Shell99). The results from Shell93 and Shell99 agreed with each other but, in general, their predictions were higher than the analytical solution by von Mises. The von Mises solution agreed better than the finite element solutions for the longer vessels, which collapsed by elastic instability, particularly when the experimentally obtained material properties were used. Thus, it was concluded that the results obtained from the finite element analyses predicted ‘questionable’ buckling pressures. The report provides design charts by all approaches and material types, which allow the possibility of obtaining a ‘plastic knockdown factor’ for these vessels. The theoretical buckling pressures obtained using the computer programs MisesNP or ANSYS can then be divided by the plastic knockdown factor obtained from the design charts, to give the predicted buckling pressures. It is not known whether or not this method can be used for the design of very large vessels.     

Ballistic-performance optimization of a hybrid carbon-nanotube/E-glass reinforced poly-vinyl-ester-epoxy-matrix composite armor

The material model for a multi-walled carbon nanotube (MWCNT) reinforced poly-vinyl-ester-epoxy matrix composite material (carbon nanotube reinforced composite mats, in the following) developed in our recent work (M. Grujicic et al. submitted), has been used in the present work within a transient non-linear dynamics analysis to carry out design optimization of a hybrid polymer-matrix composite armor for the ballistic performance with respect to the impact by a fragment simulating projectile (FSP). The armor is constructed from E-glass continuous-fiber poly-vinyl-ester-epoxy matrix composite laminas interlaced with the carbon nanotube reinforced composite mats. Different designs of the hybrid armor are obtained by varying the location and the thickness of the carbon nanotube reinforced composite mats. The results obtained indicate that at a fixed thickness of the armor, both the position and the thickness of the carbon nanotube reinforced composite mats affect the ballistic performance of the armor. Specifically, it is found that the best performance of the armor is obtained when thicker carbon nanotube reinforced composite mats are placed near the front armor face, the face which is struck by the projectile. The results obtained are rationalized using an analysis of the elastic wave reflection and transmission behavior at the lamina/met and laminate/air interfaces.     

Investigating the mechanical properties of single walled carbon nanotube reinforced epoxy composite through finite element modelling

Varying experimental results on the mechanical properties of carbon nanotube reinforced polymer composites (CNTRPs) have been reported due to the complexities associated with the characterization of material properties in nano-scale. Insight into the issues associated with CNTRPs may be brought through computational techniques time- and cost-effectively. In this study, finite element models are generated in which single walled carbon nanotube models are embedded into the epoxy resin. For modelling interface regions, two approaches named as non-bonded interactions and perfect bonding model are utilized and compared against each other. Representative volume finite element (RVE) models are built for a range of CNTRPs and employed for the evaluation of effects of diameter and chirality on the Young’s modulus and Poisson’s ratio of CNTRPs, for which there is a paucity in the literature. The outcomes of this study are in good agreement with those reported available in the literature earlier. The proposed modelling approach presents a valuable tool for determining other material properties of CNTRPs.     

On a numerical strategy to simulate nanotube‐reinforced composite materials

The application of carbon nanotubes as the reinforcing phase in composite materials is considered. A literature review in regards to the simulation approaches that have been done in order to study the behavior of nanotube‐reinforced composites from several aspects is provided. After that, a new approach for investigating the mechanical properties of the composites reinforced with randomly oriented fibers using the finite element method is proposed. The main idea is to create regular shaped islands around the distributed fibers and to connect these islands to each other and to the representative volume element. Two application examples show the flexibility and the reliability of the proposed method. It has been shown that this approach can handle both aligned and arbitrary distributions of the nanotubes.     

A semi-continuum finite element approach to evaluate the Young’s modulus of single-walled carbon nanotube reinforced composites

This paper describes a micromechanical finite element approach for the estimation of the effective Young’s modulus of single-walled carbon nanotube reinforced composites. These composite materials consist of aligned carbon nanotubes that are uniformly distributed within the matrix. Based on micromechanical theory, the Young’s modulus of the nanocomposite is estimated by considering a representative cylindrical volume element. Within the representative volume element, the reinforcement is modeled according to its atomistic microstructure while the matrix is modeled as a continuum medium. Spring-based finite elements are employed to simulate the discrete geometric structure and behavior of each single-walled carbon nanotube. The load transfer conditions between the carbon nanotubes and the matrix are modeled using joint elements of changeable stiffness that connect the two materials, simulating the interfacial region. The proposed model has been tested numerically and yields reasonable results for variable stiffness values of the joint elements. The effect of the interface on the performance of the composite is investigated for various volume fractions. The numerical results are compared with experimental and analytical predictions.     

Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis

Bending behaviour of one-dimensional structures is an important consideration in the design of structural components. In the present study a multiscale analysis of the deflection and stress behaviour of carbon nanotube (CNT) reinforced polymer composite beams is presented. The micromechanics models used in the study include straight CNTs aligned in one direction, randomly oriented CNTs and a two parameter model of agglomeration. The effects of volume fraction of CNTs and the nanotube diameter are investigated on the beam deflection and comparisons are made with carbon fibre reinforced composites. The main purpose of the study is to observe the stiffening effect of CNTs when used in structural applications such as beams.     

Generalized B‐bar: unlocking multiple compliance modes of finite elements with stiff‐fiber anisotropy

Element locking is often seen in homogenized models of elastic fiber‐reinforced materials, and splitting the material compliance into two separate terms isolates troublesome strain modes. Once isolated, the locking modes can be addressed with tailored integration schemes or the opportune introduction of field variables. The canonical application of this approach is seen in the dilatational‐deviatoric split used to treat so‐called ‘volumetric locking’. In the present work, we invoke the spectral decomposition of the material compliance to provide a generalized split. Doing so naturally parses the response into six independent strain modes, with varying propensity for locking. This split can be used to generalize fundamental techniques, such as selective reduced integration and the B‐bar method. This broadened approach works to remedy locking suffered by lower order finite elements used to discretize troublesome materials. Applying these generalized methods to achieve the dilational‐deviatoric split is trivial. However, the compliance spectrum's ability to naturally isolate stiff material response modes makes it a uniquely valuable tool for use on homogenized anisotropic materials. Applying the split, defined by only the first compliance mode, has given rise to the generalized methods, which have proven effective in unlocking finite element models of anisotropic materials. In the present work, the generalization is broadened to treat more than one constrained mode. While treating six modes is equivalent to simple reduced integration techniques, up to five compliance modes are now separated for advantageous treatment. However, some attention must be paid to the stability of the resulting finite element stiffness matrices. We focus here on the treatment of two principal compliance modes. These ‘two‐mode’ applications of the generalized B‐bar method are shown to be a more robust default treatment of linear hexahedral elements than is provided by classical selective reduced integration. This is achieved with a negligible computational overhead. A framework for assessing element stability is delineated, and commonly arising instabilities are analyzed. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling carbon nanotube reinforced composite materials with the cylindrical method of cells

Micromechanics modeling, utilizing a cylindrical method of cells (CMOC) model, is employed to obtain the effective mechanical properties of an elastic transversely isotropic, isothermal material system consisting of a hollow carbon nanotube (CNT) embedded in an isotropic polymeric material matrix. It is shown that weak interfacial bonding between the CNT and polymeric matrix, which is characteristic of this type of material system, can be modeled with the CMOC. Numerical solutions of the effective independent material constants are obtained, based upon appropriate values of the properties of the carbon nanotube and epoxy matrix. The numerical results are presented graphically and compared with corresponding classical closed‐form solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Processing,structure and flexural strength of CNT and carbon fibre reinforced,epoxy-matrix hybrid composite

Advanced materials such as continuous fibre-reinforced polymer matrix composites offer significant enhancements in variety of properties, as compared to their bulk, monolithic counterparts. These properties include primarily the tensile stress, flexural stress and fracture parameters. However, till date, there are hardly any scientific studies reported on carbon fibre (C_f) and carbon nanotube (CNT) reinforced hybrid epoxy matrix composites (unidirectional). The present work is an attempt to bring out the flexural strength properties along with a detailed investigation in the synthesis of reinforced hybrid composite. In this present study, the importance of alignment of fibre is comprehensively evaluated and reported. The results obtained are discussed in terms of material characteristics, microstructure and mode of failure under flexural (3-point bend) loading. The study reveals the material exhibiting exceptionally high strength values and declaring itself as a material with high strength to weight ratio when compared to other competing polymer matrix composites (PMCs); as a novel structural material for aeronautical and aerospace applications.     

Self‐sensing damage in CNT infused epoxy panels with and without glass‐fibre reinforcement

The objective of the study is to utilise a material's inherent electrical conductivity as means of damage quantification and damage location detection. After determining the percolation threshold for a carbon nanotube (CNT)‐epoxy mixture, an optimum concentration was chosen to infuse it into glass‐fabric reinforced panels to make them electrically conductive. Two different multiwalled CNT‐epoxy composites were manufactured for this study: CNT enhanced epoxy resin and glass‐fabric reinforced CNT epoxy resin. Epoxy resin‐based glass‐fabric reinforced composite panels enhanced with carbon nanotubes were manufactured with embedded electrodes and then subjected to damages. Rectangular panels of various proportions were studied. Disks made out of copper foil were affixed to surfaces of CNT epoxy panel, whereas in glass‐fabric CNT epoxy specimen, total of 64 electrodes (grid of 8 × 8) were embedded inside the composite panel under the top layer of the 10‐ply fabric. The disks acted as electrodes, enabling voltage measurements using in‐line 4‐probe technique, which minimises contact resistance between the electrodes and the material. Two different configurations of electrode network were employed to scan voltage change in the entire composite panel. The networks included evenly spaced (3 in. for inner ones) electrodes that spanned the surface of the panel. To further investigate influence of electrodes distribution, finite element simulations were used to solve the electrical potential distribution in the panel for various damage sizes and location. Predamage and postdamage voltage field was used as gauge in sensing the damage and its extent for quantification. The finite element method simulation results matched the experimental data closely. The results indicate that there is a consistent behaviour that can be correlated to the size and location of the damage. As spacing between electrodes is increased, they become less responsive to smaller damages. Forty‐eight electrodes (out of 64) were actively used and were enough to confirm that the method can be used as an alternative to electrical tomography method where fewer (boundary) electrodes per area are employed but at a higher cost of computational cost. One important aspect of this study with embedded and distributed electrodes is the fact that the method can be applied to larger panels increasing its utility in practical applications.     

Micromechanics modeling of fatigue failure mechanisms in a hybrid polymer matrix composite

Initiation of fatigue damage for a hybrid polymer matrix composite material was studied via 3-Dimensional viscoelastic representative volume element modeling in order to gain further understanding. It was found that carbon fiber reinforced composites perform better in fatigue loading, in comparison to glass fiber reinforced composites, due to the fact that the state of stress within the matrix material was considerably lower for carbon fiber reinforced composites eliminating (or at least prolonging) fatigue damage initiation. The effect of polymer aging was also evaluated through thermal aging of neat resin specimens. Short-term viscoelastic material properties of unaged and aged neat resin specimens were measured using Dynamic Mechanical Analysis. With increasing aging time a corresponding increase in storage modulus was found. Increases in the storage modulus of the epoxy matrix subsequently resulted in a higher state of predicted stress within the matrix material from representative volume element analyses. Various parameters common to unidirectional composites were numerically investigated and found to have varying levels of impact on the prediction of the initiation of fatigue damage.     

Finite element modelling of fibre reinforced polymer sandwich panels exposed to heat

A finite element model that predicts temperature distribution in a composite panel exposed to a heat source, such as fire, is described. The panel is assumed to be composed of skins consisting of polymer matrix reinforced with fibres and a lightweight core (the paper concentrates on the crucial aspect of the problem, i.e. the behaviour of the ‘hot’ skin of the panel. The core is assumed not to decompose, and the ‘cold’ skin is treated exactly as the ‘hot’ skin.) It is assumed that the polymer matrix undergoes chemical decomposition. Such a model results in a set of coupled non‐linear transient partial differential equations. A Galerkin finite element framework is formulated to yield a fully implicit time stepping scheme. The crucial input parameters for the model are carefully identified for subsequent experimental determination. Copyright © 2004 John Wiley & Sons, Ltd.     

A strategy for improving mechanical properties of a fiber reinforced epoxy composite using functionalized carbon nanotubes

Carbon fiber reinforced epoxy composite laminates are studied for improvements in quasi static strength and stiffness and tension-tension fatigue cycling at stress-ratio (R-ratio) = +0.1 through strategically incorporating amine functionalized single wall carbon nanotubes (a-SWCNTs) at the fiber/fabric-matrix interfaces over the laminate cross-section. In a comparison to composite laminate material without carbon nanotube reinforcements there are modest improvements in the mechanical properties of strength and stiffness; but, a potentially significant increase is demonstrated for the long-term fatigue life of these functionalized nanotube reinforced composite materials. These results are compared with previous research on the cyclic life of this carbon fiber epoxy composite laminate system reinforced similarly with side wall fluorine functionalized industrial grade carbon nanotubes. Optical and scanning electron microscopy and Raman spectrometry are used to confirm the effectiveness of this strategy for the improvements in strength, stiffness and fatigue life of composite laminate materials using functionalized carbon nanotubes.     

Meso-scale modeling of hypervelocity impact damage in composite laminates

ObjectivesThis paper presents an approach to numerical modeling of hypervelocity impact on carbon fiber reinforced plastics (CFRP).MethodsThe approach is based on the detailed meso-scale representation of a composite laminate. Material models suitable for explicit modeling of laminate structure, including fiber-reinforced layers and resin-rich regions, are described. Two numerical impact tests with significantly different impact energies were conducted on thermoplastic AS4/PEEK materials with quasi-isotropic layups. Simulations employed both SPH and Finite element methods.ResultsResults of simulations are verified against experimental data available from the literature and demonstrate good correlation with the experiments.ConclusionsDeveloped modeling approach can be used in simulations where post-impact damage progression in composite material is of the main focus.     

Solution strategies for the delamination analysis based on a combination of local‐control arc‐length and line searches

The paper describes a local‐control arc‐length method which can be combined with various forms of line‐search procedure. In particular, a new ‘double‐line‐search’ method is developed, which significantly improves the solution procedure and turns out to be efficient and robust. Although the potential range of applications is wide, the method is here limited to the finite element analysis of delamination in a laminated composite using a cohesive‐zone model combined with interface elements. Three problems have been analysed and comparisons have been made with experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

Effective Moduli Evaluation of Carbon Nanotube Reinforced Polymers Using Micromechanics

A multistep homogenization method is adopted to compute the effective moduli of carbon nanotube reinforced composites. The composite is assumed to be reinforced with isolated individual fibers and clustered fibers. A uniform agglomeration model is introduced assuming constant carbon nanotube cluster size throughout the matrix. Agglomeration volume fraction—a critical parameter in the simulation—is considered to be an explicit function of inter-particle distance and quality of dispersion of fibers. The micromechanics model also incorporates random fiber orientation using a statistical approach. It is seen that these parameters reduce the stiffening effect of carbon nanotubes significantly in the composite.     

Shear Characterisation of Woven Carbon/Epoxy Composite Under Various Adverse Environments

Abstract: In this article, an investigation into the shear properties of bi‐directional carbon fibre reinforced composite has been carried out by ‘rail‐shear’ test method (D4255). The specimens were tested under various adverse environmental conditions after subjecting them to different durations of exposure. A comparison between time‐dependent degradation of the shear properties of the material with respect to virgin shear properties is made, and the results have been analysed with emphasis on material weight gain or loss under those adverse environments.