Numerical characterization of CNT-based polymer composites considering interface effects

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. Load transfer in nanocomposite materials is achieved through the CNT/matrix interface. Thus, to determine nanocomposite mechanical properties, the interface behavior must be determined. In this investigation, finite element method is used to investigate the effects of interface strength on effective CNT-based composite mechanical properties. Nanocomposite mechanical properties are evaluated using a 3D nanoscale representative volume element (RVE). A single nanotube and the surrounding polymer matrix are modeled. Two cases of perfect bonding and an elastic interface are considered. For the perfect bonding interface, the no slip conditions are applied. To better investigate the elastic interface behavior, two models are proposed for this type of interface. The first elastic interface model consists of a thin layer of an elastic material surrounding the CNT. In the second elastic interface model, a series of spring elements are used as the nanotube/matrix interface. The results of numerical models indicate the importance of adequate interface bonding for a more effective strengthening of polymer matrix by CNT’s.     

The role of thermal residual stress on the yielding behavior of carbon nanotube–aluminum nanocomposites

The initial yield envelopes of aluminum (Al) nanocomposites reinforced with carbon nanotubes (CNTs) subjected to biaxial loading are predicted in the presence of thermal residual stress (TRS) arising from the manufacturing process. Micromechanical model based on the unit cell method is presented to generate the yielding surfaces. The formation of the interphase caused by the interfacial reaction between the CNT and Al matrix is taken into account in the analysis. The effects of several important parameters, i.e. the change of temperature, CNT volume fraction, interphase thickness and Al material properties on the yielding onset of the CNT/Al nanocomposite are explored extensively. The results clearly reveal that the initial yield surfaces of nanocomposite are dependent on the TRS. Also, the interphase has a significant influence on the yielding behavior of Al nanocomposite in the presence of TRS. The results demonstrate that the size of initial yield surfaces become minimum with considering the coupled effects of TRS and interphase. With increasing the temperature variation, interphase thickness, elastic modulus and coefficient of thermal expansion of Al matrix, the size of initial yield surfaces reduces. The present study is consequential for understanding the key role of TRS on the initial damage of CNT/Al nanocomposites.     

Influence of post-buckling behaviour of composite stiffened panels on the damage criticality

In stiffened panels with defects, such as skin delaminations or stringer debonding, buckling may occur prior to the designed critical buckling load. Depending on the damage parameters, such defects may also affect the post-buckling behaviour and consequently the structural performance. An automated finite element (FE) modelling tool has been developed to predict the post-buckling behaviour of panels. It was coupled with a linear elastic fracture mechanics approach to determine damage criticality, based on the “no-growth” principle. The structural behaviour in the post-buckling range and its interaction with the damage parameters were analysed. Local buckling occurred as a result of localised stiffness reduction in the damage region. Global buckling occurred when sufficient in-plane strain was reached. The onset of local buckling was an important factor on stringer debonding criticality as the local buckling mode had an effect on the corresponding global buckling. In comparison, the onset of local buckling for the skin delamination was lower due to the thin sub-laminate separation. However, it was less influential on the damage criticality because the local buckling slowly dissipated in the far post-buckling range. It was found that the initiation of local buckling, and the interaction between the local and global buckling mode, would determine the damage criticality.     

Nonlinear analysis of bimodular composite plates under compression

The present work deals with the buckling and post-buckling behaviour of bimodular laminated composite plates. The fiber-governed bimodular constitutive model is adopted for the analysis and the geometrical nonlinearities are accounted for by using the consistent small strain and moderate rotation theory for a shear deformable Mindlin plate. Governing equations of the problem are developed and the finite element formulation is given using lagrangian C°-elements. Some numerical examples are developed to analyze the buckling and post-buckling behaviour of laminated bimodular plates.     

Load transfer of graphene/carbon nanotube/polyethylene hybrid nanocomposite by molecular dynamics simulation

Load transfer of the graphene/carbon nanotube (CNT)/polyethylene hybrid nanocomposite is studied here from molecular dynamics (MD) simulations. Simulations of this composite material under uniaxial tension were conducted by varying CNT’s position and diameter in the polymer matrix. The obtained results show that: (1) The peak strength of stress and strain evolution in the polymer matrix is lower than the peak strength of the graphene/graphene and graphene/polymer interfaces. Hence, the damage zone is always located in the polymer matrix. (2) Agglomerated two-layer graphenes do not possess an increased value in the peak strength compared with single-layer graphene-reinforced polymer nanocomposite (PNC), while two separate layers of graphene show slightly higher peak strength. (3) The largest peak strength is observed before CNT moves to the center of the polymer matrix. The damage location moves from the upper to the lower part of CNT when the CNT is located at the centre of polymer matrix. (4) The influence of the CNT diameter on the peak strength is not obvious, while the damage location and shape in the polymer matrix changes with respect to varying CNT diameters. In addition, the damage zone always falls outside the interphase zone.     

Post-buckling of elastic annular plates at multiple eigenvalues

The buckling and post-buckling problem of elastic annular plates is treated at multiple eigenvalues making strong use of symmetry properties of the problem in deriving bifurcation equations (amplitude equations of the critical modes) from the von Karman plate equations by means of the Ljapunov-Schmidt method. Further, a restricted generic unfolding of the bifurcation equations is made and some practically interesting results concerning the post-buckling behaviour are presented.     

A molecular dynamics study on the thickness and post-critical strength of carbon nanotubes

This paper presents a molecular dynamics (MDs) study on the linear, buckling and post-buckling behaviour of carbon nanotubes (CNTs) under pure shortening and pure twisting. Its objectives are (i) to clarify the issue about the most correct thickness value to adopt in the simulation of CNTs using shell models and (ii) to evaluate their post-critical strength. Three CNTs with similar length-to-diameter ratio but different atomic structures (zig-zag, armchair and chiral) are selected for this study. Then, MD simulations are performed to investigate the pre-critical, critical buckling and post-critical behaviour of CNTs under pure shortening and pure twisting. Using available analytical formulae derived from shell models, the influence of CNT thickness on their critical strain and critical angle of twist is investigated. Some conclusions are drawn regarding (i) the most appropriate choice of the thickness value to use in shell models and (ii) the effectiveness of post-critical stiffness and strength of CNTs.     

Post-buckling of elastic annular plates at multiple eigenvalues

The buckling and post-buckling problem of elastic annular plates is treated at multiple eigenvalues making strong use of symmetry properties of the problem in deriving bifurcation equations (amplitude equations of the critical modes) from the von Karman plate equations by means of the Ljapunov-Schmidt method. Further, a restricted generic unfolding of the bifurcation equations is made and some practically interesting results concerning the post-buckling behaviour are presented.     

Interface tailoring to enhance mechanical properties of carbon nanotube reinforced magnesium composites

This study highlights the use of a metallic coating of nanoscale thickness on carbon nanotube to enhance the interfacial characteristics in carbon nanotube reinforced magnesium (Mg) composites. Comparisons between two reinforcements were targeted: (a) pristine carbon nanotubes (CNTs) and (b) nickel-coated carbon nanotubes (Ni–CNTs). It is demonstrated that clustering adversely affects the bonding of pristine CNTs with Mg particles. However, the presence of nickel coating on the CNT results in the formation of Mg₂Ni intermetallics at the interface which improved the adhesion between Mg/Ni–CNT particulates. The presence of grain size refinement and improved dispersion of the Ni–CNT reinforcements in the Mg matrix were also observed. These result in simultaneous enhancements of the micro-hardness, ultimate tensile strength and 0.2% yield strength by 41%, 39% and 64% respectively for the Mg/Ni–CNT composites in comparison with that of the monolithic Mg.     

弹性地基上加热弹性圆板的热过屈曲及临界屈曲模态跃迁

基于von Kármán薄板理论建立了Winkler弹性基础上弹性圆板在均匀升温下的轴对称热过屈曲控制方程。这是一组以中面位移为基本未知量的非线性常微分方程,其中包含了温度载荷和弹性地基刚度两个参数。采用打靶法数值求解相应的非线性两点边值问题,获得了周边不可移简支圆板的热屈曲及热过屈曲响应。绘出了前三阶屈曲模态对应的临界温度载荷随地基参数连续变化的特性曲线,获得了反映临界热屈曲模态跃迁特性的地基参数值。给出了弹性圆板按一阶模态失稳后的热过屈曲平衡路径和平衡构形,分析了地基刚度参数对临界屈曲温度载荷以及过屈曲平衡构形的影响。     

Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments

In the present article, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed. In this regard, the governing equations are derived based on higher-order shear deformation plate theory and von Kármán geometrical nonlinearity. Three types of distributions of the temperature field and moisture concentrations, namely, uniformly, linearly, or nonlinearly through the thickness direction of the plates are considered. The effective material properties of the multiphase nanocomposite are calculated using fiber micromechanics and Halpin–Tsai equations in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the matrix. The contact force between the impactor and the plate is obtained with the aid of the modified nonlinear Hertzian contact law models. After examining the validity of the present work, the effects of the weight percentage of CNT, moisture concentration, temperature variations, distribution of temperature and moisture concentration, elastic foundation, and the eccentricity on the contact force, indentation, and central deflection of polymer-CNT-fiber multiscale nanocomposite plate are studied in details.     

Effects of interface characteristics on mechanical properties of carbon nanotube reinforced polymer composites

Abstract

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. To take full advantage of their exceptional properties, load sharing mechanisms needs to be understood in the composite materials. Load transfer in composites is achieved through the fibre/matrix interface. In the present paper, finite element method is used to investigate the effects of interface behaviour on carbon nanotube based composite mechanical properties. The effective nanocomposite mechanical properties are evaluated using a three-dimensional nanoscale representative volume element (RVE). In this RVE approach, a single nanotube and the surrounding polymer matrix are modelled. Two cases of perfect bonding and an elastic interface are considered. In addition, the rule of mixtures relations is used to validate the results of numerical models. The results indicate that mechanical properties of nanocomposite materials are significantly influenced by the interface strength.     

Tensile properties of carbon nanotube reinforced aluminum nanocomposite fabricated by plasma spray forming

Uniaxial tensile tests were performed on plasma spray formed (PSF) Al–Si alloy reinforced with multiwalled carbon nanotubes (MWCNTs). The addition of CNTs leads to 78% increase in the elastic modulus of the composite. There was a marginal increase in the tensile strength of CNT reinforced composite with degradation in strain to failure by 46%. The computed critical pullout length of CNTs ranges from 2.1 to 19.7 μm which is higher than the experimental length of CNT, leading to relatively poor load transfer and low tensile strength of PSF nanocomposites. Fracture surface validates that tensile fracture is governed strongly by the constitutive hierarchical microstructure of the plasma sprayed Al–CNT nanocomposite. The fracture path in Al–CNT nanocomposite occurs in Al–Si matrix adjacent to SiC layer on CNT surface.     

A simple approach to prepare Al/CNT composite: Spread–Dispersion (SD) method

In carbon nanotube (CNT) reinforced metal matrix composites (MMCs), the good dispersion of CNTs in the matrix as well as the processing problems are the major challenges inhibiting the development of these composites. In this study, well-dispersed CNTs reinforced aluminum (Al) matrix nanocomposite was fabricated by a novel Spread–Dispersion (SD) method. Specimens with ultra-fine grain size down to 20 nm were obtained. The tensile strength of the CNT nanocomposite was 66% greater than the base matrix with a minor decrease in ductility. Such enhancement was analyzed on the basis of segregation and uniform distribution of clustered CNTs, disappearance of the CNT-free zones, eliminated porosity, stronger Al/CNT bonding and the retention of CNT graphitic structure.     

Algorithms for non-linear contact constraints with application to stability problems of rods and shells

In this paper a class of non-linear problems is discussed where stability as well as post-buckling behaviour is coupled with contact constraints. The contact conditions are introduced via a perturbed Lagrangian formulation. From this formulation the penalty and Lagrangian multiplier method are derived. Both algorithms are investigated together with an algorithm based on an augmented Lagrangian method. The resulting finite element formulation is applied to structural problems of beams and shells undergoing finite elastic deflections and rotations. For the examination of the post-buckling behaviour the arc-length method is used. The performance of the element formulation and a comparison of the different contact algorithms are demonstrated by numerical examples.     

Effects of substrate compliance on circular buckle delamination of thin films

The present work analyzes circular delamination buckling in a film/substrate system based on the Von Karman nonlinear plate theory with the consideration of elastic deformation of the substrate. Due to the axisymmetry of circular buckling, the substrate deformation is modeled by coupled springs and the spring compliances are determined from the dimension analysis and finite element calculations. The numerical shooting method is used to solve the nonlinear post-buckling problem. The stress intensity factors, the energy release rate, and the phase angle are given here for a variety of the elastic mismatch between the film and the substrate. The results show that in some cases, the energy release rate can be several times larger than that derived from the widely used clamped edge condition.     

Elastic large deflection analysis of plates subjected to uniaxial thrust using meshfree Mindlin-Reissner formulation

A meshfree approach for plate buckling/post-buckling problems in the case of uniaxial thrust is presented. A geometrical nonlinear formulation is employed using reproducing kernel approximation and stabilized conforming nodal integration. The bending components are represented by Mindlin–Reissner plate theory. The formulation has a locking-free property in imposing the Kirchhoff mode reproducing condition. In addition, in-plane deformation components are approximated by reproducing kernels. The deformation components are coupled to solve the general plate bending problem with geometrical non-linearity. In buckling/post-buckling analysis of plates, the in-plane displacement of the edges in their perpendicular directions is assumed to be uniform by considering the continuity of plating, and periodic boundary conditions are considered in assuming the periodicity of structures. In such boundary condition enforcements, some node displacements/rotations should be synchronized with others. However, the enforcements introduce difficulties in the meshfree approach because the reproducing kernel function does not have the so-called Kronecker delta property. In this paper, the multiple point constraint technique is introduced to treat such boundary conditions as well as the essential boundary conditions. Numerical studies are performed to examine the accuracy of the multiple point constraint enforcements. As numerical examples, buckling/post-buckling analyses of a rectangular plate and stiffened plate structure are presented to validate the proposed approach.     

Effect of interphase on fibre-bridging toughness of a unidirectional FRP composite thin plate

A parametric analysis of the toughening mechanisms in a uniaxially fibre reinforced polymer (FRP) thin plate with a power-law hardening shear interphase is presented. An interfacial shear-lag model is used to analyse the relationship between the crack surface traction exerted by the intact fibres and the crack opening displacement (COD). Numerical solutions of the equations governing bridge-toughening are given. Two special kinds of interphase, i.e. linearly elastic and perfect plastic, are discussed. The results demonstrate that the toughening ratio of the composite thin plate is sensitive to several parameters, e.g. the thickness of the interphase between fibre and matrix, the hardening parameter of the interphase, the interfacial shear properties (stiffness and strength), the fibre radius and the far-field load. The results of this investigation will be beneficial to the selection of constitutive materials, the improvement of mechanical behaviour and the fabrication process of FRP composites.     

Numerical analysis and experimental correlation of composite shell buckling and post-buckling

This paper deals with the buckling and post-buckling behaviour of carbon fibre reinforced plastic cylindrical shells under axial compression. The finite element analysis is used to investigate this problem and three different types of analysis are compared: eigenvalue analysis, non-linear Riks method and dynamic analysis. The effect of geometric imperfection shape and amplitude on critical loads is discussed. A numerical–experimental correlation is performed, using the results of experimental buckling tests. The geometric imperfections measured on the real specimens are accounted for in the finite element model. The results show the reliability of the method to follow the evolution of the cylinder shape from the buckling to the post-buckling field and good accuracy in reproducing the experimental post-buckling behaviour.     

Micromechanical analysis of nanocomposites using 3D voxel based material model

A computational study on the effect of nanocomposite structures on the elastic properties is carried out with the use of the 3D voxel based model of materials and the combined Voigt–Reuss method. A hierarchical voxel based model of a material reinforced by an array of exfoliated and intercalated nanoclay platelets surrounded by interphase layers is developed. With this model, the elastic properties of the interphase layer are estimated using the inverse analysis. The effects of aspect ratio, intercalation and orientation of nanoparticles on the elastic properties of the nanocomposites are analyzed. For modeling the damage in nanocomposites with intercalated structures, “four phase” model is suggested, in which the strength of “intrastack interphase” is lower than that of “outer” interphase around the nanoplatelets. Analyzing the effect of nanoreinforcement in the matrix on the failure probability of glass fibers in hybrid (hierarchical) composites, using the micromechanical voxel-based model of nanocomposites, it was observed that the nanoreinforcement in the matrix leads to slightly lower fiber failure probability.