Multi-scale modeling of carbon nanotube reinforced polymers using irregular tessellation technique

A multi-scale modeling approach to extract mechanical properties of CNTRP emphasizing on the effective parameters associated with meso- and micro-scale is developed. Investigated material region at macro scale is regularly tessellated into constitutive blocks. Assigning random CNT volume fractions to each block, non-uniform dispersion of CNT is modeled. Irregular tessellation technique based on Voronoi method and Bayes algorithm is employed to partition the RVE at meso scale into constitutive polygons containing one single aggregated CNTs. Mechanical properties of the tessellated regions are extracted by a modified micromechanics rules addressing local positions of aggregates in the material region. A bounding technique accounting for non-straight shape of CNT is utilized to consider any arbitrary shapes of wavy CNT. The obtained results of modeling are compared with experimental observations. A novel formulation is developed taking into account all inconsistencies attributed to CNTRPs.     

Stochastic multi-scale modeling of CNT/polymer composites

A full stochastic multi-scale modeling technique is developed to estimate mechanical properties of carbon nanotube reinforced polymers. Developing a full-range multi-scale technique to consider effective parameters of all nano, micro, meso and macro-scales and full stochastic implementation of integrated modeling procedures are the novelties of the present research. The length, orientation, agglomeration, curvature and dispersion of carbon nanotubes are taken into account as random parameters. It is proven that random distribution of carbon nanotube length and volume fraction can be replaced with corresponding mean values. The results of predictions are in a very good agreement with published experimental observations.     

弹道防护用超高分子量聚乙烯纤维增强热塑性树脂基复合材料的拉伸力学行为

以弹道防护用超高分子量聚乙烯(Ultra-high molecular weight polyethylene,UHMWPE)纤维增强热塑性树脂基复合材料作为研究对象,通过热压工艺制备单向正交结构的复合材料层压板。基于自主设计的拉伸试验装置,开展UHMWPE纤维增强热塑性树脂基复合材料在宏观尺度和准细观尺度上的面内拉伸试验,研究其面内拉伸力学性能及失效模式。研究结果显示：弹道防护用UHMWPE纤维增强热塑性树脂基复合材料在准细观尺度上的面内拉伸力学性能是其本征性能;随着偏轴角度的增加,拉伸断裂强度呈现指数型下降,这是由于失效模式由纤维的拉伸断裂破坏转变为纤维-树脂基体的界面破坏;此外,其在宏观尺度上的拉伸破坏强度比在准细观尺度上的拉伸断裂强度降低了50.52%,这是由于宏观尺度上的面内拉伸力学响应是其面内拉伸变形和层间分层破坏的耦合结果,即层压板的叠层效应。     

Mechanical properties of carbon nanotube reinforced polymer nanocomposites: A coarse-grained model

In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced polymer matrix composites is developed. A distinguishing feature of the CG model is the ability to capture interactions between polymer chains and nanotubes. The CG potentials for nanotubes and polymer chains are calibrated using the strain energy conservation between CG models and full atomistic systems. The applicability and efficiency of the CG model in predicting the elastic properties of CNT/polymer composites are evaluated through verification processes with molecular simulations. The simulation results reveal that the CG model is able to estimate the mechanical properties of the nanocomposites with high accuracy and low computational cost. The effect of the volume fraction of CNT reinforcements on the Young's modulus of the nanocomposites is investigated. The application of the method in the modeling of large unit cells with randomly distributed CNT reinforcements is examined. The established CG model will enable the simulation of reinforced polymer matrix composites across a wide range of length scales from nano to mesoscale.     

Modeling the tensile stress–strain response of carbon nanotube/polypropylene nanocomposites using nonlinear representative volume element

This paper presents a finite element model for predicting the mechanical behavior of polypropylene (PP) composites reinforced with carbon nanotubes (CNTs) at large deformation scale. Existing numerical models cannot predict composite behavior at large strains due to using simplified material properties and inefficient interfaces between CNT and polymer. In this work, nonlinear representative volume elements (RVE) of composite are prepared. These RVEs consist of CNT, PP matrix and non-bonded interface. The nonlinear material properties for CNT and polymer are adopted to solid elements. For the first time, the interface between CNT and matrix is simulated using contact elements. This interfacial model is capable enough to simulate wide range of interactions between CNT and polymer in large strains. The influence of adding CNT with different aspect ratio into PP is studied. The mechanical behavior of composites with different interfacial shear strength (ISS) is discussed. The success of this new model was verified by comparing the simulation results for RVEs with conducted experimental results. The results shows that the length of CNT and ISS values significantly affect the reinforcement phenomenon.     

Hybrid carbon fiber composite lattice truss structures

Carbon fiber reinforced polymer (CFRP) composite sandwich panels with hybrid foam filled CFRP pyramidal lattice cores have been assembled from linear carbon fiber braids and Divinycell H250 polymer foam trapezoids. These have been stitched to 3D woven carbon fiber face sheets and infused with an epoxy resin using a vacuum assisted resin transfer molding process. Sandwich panels with carbon fiber composite truss volumes of 1.5–17.5% of the core volume have been fabricated, and the through-thickness compressive strength and modulus measured, and compared with micromechanical models that establish the relationships between the mechanical properties of the core, its topology and the mechanical properties of the truss and foam. The through thickness modulus and strength of the hybrid cores is found to increase with increasing truss core volume fraction. However, the lattice strength saturates at high CFRP truss volume fraction as the proportion of the truss material contained in the nodes increases. The use of linear carbon fiber braids is shown to facilitate the simpler fabrication of hybrid CFRP structures compared to previously described approaches. Their specific strength, moduli and energy absorption is found to be comparable to those made by alternative approaches.     

Elastic response of a carbon nanotube fiber reinforced polymeric composite: A numerical and experimental study

Premature failure due to low mechanical properties in the transverse direction to the fiber constitutes a fundamental weakness of fiber reinforced polymeric composites. A solution to this problem is being addressed through the creation of nanoreinforced laminated composites where carbon nanotubes are grown on the surface of fiber filaments to improve the matrix-dominated composite properties. The carbon nanotubes increase the effective diameter of the fiber and provide a larger interface area for the polymeric matrix to wet the fiber. A study was conducted to numerically predict the elastic properties of the nanoreinforced composites. A multiscale modeling approach and the Finite Element Method were used to evaluate the effective mechanical properties of the nanoreinforced laminated composite. The cohesive zone approach was used to model the interface between the nanotubes and the polymer matrix. The elastic properties of the nanoreinforced laminated composites including the elastic moduli, the shear modulus, and the Poisson’s ratios were predicted and correlated with iso-strain and iso-stress models. An experimental program was also conducted to determine the elastic moduli of the nanoreinforced laminated composite and correlate them with the numerical values.     

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.     

Structural health monitoring of glass fiber reinforced composites using embedded carbon nanotube (CNT) fibers

In the present work, carbon nanotube (CNT) fibers had been embedded to glass fiber reinforced polymers (GFRP) for the structural health monitoring of the composite material. The addition of the conductive CNT fiber to the non-conductive GFRP material aims to enhance its multi-function ability; the test specimen’s response to mechanical load and the insitu CNT fiber’s electrical resistance measurements were correlated for sensing and damage monitoring purposes. It is the first time this fiber is used in composite materials for sensing purposes; CNT fiber is easy to be embedded and does not downgrade the material’s mechanical properties. Various incremental loading–unloading steps had been applied to the manufactured specimens in tension as well as in three-point bending tests. The CNT fiber worked as a sensor in both, tensile and compression loadings. A direct correlation between the mechanical loading and the electrical resistance change had been established for the investigated specimens. For high stress (or strain) level loadings, residual resistance measurements of the CNT fiber were observed after unloading. Accumulating damage to the composite material had been calculated and was correlated to the electrical resistance readings. The established correlation between these parameters changed according to the material’s loading history.     

Compressive response and failure of fiber reinforced unidirectional composites

The compressive response of polymer matrix fiber reinforced unidirectional composites (PMC's) is investigated via a combination of experiment and analysis. The study accounts for the nonlinear constitutive response of the polymer matrix material and examines the effect of fiber geometric imperfections, fiber mechanical properties and fiber volume fraction on the measured compressive strength and compressive failure mechanism.Glass and carbon fiber reinforced unidirectional composite specimens are manufactured in-house with fiber volume fractions ranging over 1060 percent. Compression test results with these specimens show that carbon fiber composites have lower compressive strengths than glass fiber composites. Glass fiber composites demonstrate a splitting failure mode for a range of low fiber volume fractions and a simultaneous splitting/kink banding failure mode for high fiber volume fractions. Carbon fiber composites show kink banding throughout the range of fiber volume fractions examined. Nonlinear material properties of the matrix, orthotropic material properties of the carbon fiber, initial geometric fiber imperfections and nonuniform fiber volume fraction are all included in an appropriate finite element analysis to explain some of the observed experimental results. A new analytical model predictionof the splitting failure mode shows that this failure mode is favorable for glass fiber composites, which is in agreement with test results. Furthermore, this modelis able to show the influence of fiber mechanical properties, fiber volume fraction and fiber geometry on the splitting failure mode.     

On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region

The longitudinal behavior of a carbon nanotube in a polymeric matrix is studied using a non-linear analysis on a full 3D multi-scale finite element model consisting of carbon nanotube, non-bonded interphase region and surrounding polymer. The bonding between carbon nanotube and its surrounding polymer is treated as van der Waals interactions. The results of simulation of carbon nanotube reinforced polymer implies on a non-linear stress–strain behavior. A comparison between finite element analysis results and the rule of mixture for conventional composites shows that the rule of mixture overestimates the result and cannot capture the scale difference between micro- and nano-scale. An equivalent fiber is developed to overcome this difficulty and corresponding longitudinal, transverse and shear moduli are calculated. The results reveal that the length of CNT affects the efficiency of reinforcement phenomenon.     

Hybrid carbon nanotube–carbon fiber composites with improved in-plane mechanical properties

In this study carbon nanotubes (CNTs) were grown on carbon fibers to enhance the in-plane and out-of-plane properties of fiber reinforced polymer composites (FRPs). A relatively low temperature synthesis technique was utilized to directly grow CNTs over the carbon fibers. Several composites based on carbon fibers with different surface treatments (e.g. growing CNTs with different lengths and distribution patterns and coating the fibers with a thermal barrier coating (TBC) layer) were fabricated and characterized via on- and off-axis tensile tests. The on-axis tensile strength and ductility of the hybrid FRPs were improved by 11% and 35%, respectively, due to the presence of the TBC and the surface grown CNTs. This configuration also exhibited 16% improvement on the off-axis stiffness. Results suggest that certain CNT growth patterns and lengths are more pertinent than the other surface treatments to achieve superior mechanical properties.     

A Modeling Approach Across Length Scales for Progressive Failure Analysis of Woven Composites

This paper presents a multiscale modeling approach for the progressive failure analysis of carbon-fiber-reinforced woven composite materials. Hierarchical models of woven composites at three different length scales (micro, meso, and macro) were developed according to their unique geometrical and material characteristics. A novel strategy of two-way information transfer is developed for the multiscale analysis of woven composites. In this strategy, the macroscopic effective material properties are obtained from property homogenizations at micro and meso scales and the stresses at three length scales are computed with stress amplification method from macroscale to microscale. By means of the two-way information transfer, the micro, meso and macro structural characterizations of composites are carried out so that the micromechanisms of damage and their interactions are successfully investigated in a single macro model. In addition, both the nucleation and growth of damages are tracked during the progressive failure analysis. A continuum damage mechanics (CDM) method is used for post-failure modeling. The material stiffness, tensile strength and damage patterns of an open-hole woven composite laminate are predicted with the proposed multiscale method. The predictions are in good agreement with the experimental results.     

Effects of nanotube helical angle on mechanical properties of carbon nanotube reinforced polymer composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. The CNTs, however, form complicated shapes and do not usually appear as straight reinforcements when introduced in polymer matrices. This results in a decrease in nanotube effectiveness in enhancing the matrix mechanical properties. In this paper, theory of elasticity of anisotropic materials and finite element method (FEM) are used to investigate the effects of CNT helical angle on effective mechanical properties of nanocomposites. Helical nanotubes with different helical angles are modeled to investigate the effects of nanotube helical angle on nanocomposite effective mechanical properties. In addition, the results of models consisting of helical nanotubes are compared with the effective mechanical properties of nanocomposites reinforced with straight nanotubes. Ultimately, the effects of helical CNT volume fraction on nanocomposite longitudinal modulus are investigated.     

Propagation of material and surface profile uncertainties on MEMS micro‐resonators using a stochastic second‐order computational multi‐scale approach

This paper aims at accounting for the uncertainties because of material structure and surface topology of micro‐beams in a stochastic multi‐scale model. For micro‐resonators made of anisotropic polycrystalline materials, micro‐scale uncertainties exist because of the grain size, grain orientation, and the surface profile. First, micro‐scale realizations of stochastic volume elements are obtained based on experimental measurements. To account for the surface roughness, the stochastic volume elements are defined as a volume element having the same thickness as the microelectromechanical system (MEMS), with a view to the use of a plate model at the structural scale. The uncertainties are then propagated up to an intermediate scale, the meso‐scale, through a second‐order homogenization procedure. From the meso‐scale plate‐resultant material property realizations, a spatially correlated random field of the in‐plane, out‐of‐plane, and cross‐resultant material tensors can be characterized. Owing to this characterized random field, realizations of MEMS‐scale problems can be defined on a plate finite element model. Samples of the macro‐scale quantity of interest can then be computed by relying on a Monte Carlo simulation procedure. As a case study, the resonance frequency of MEMS micro‐beams is investigated for different uncertainty cases, such as grain‐preferred orientations and surface roughness effects. Copyright © 2016 John Wiley & Sons, Ltd.     

碳纤维弹性常数的微观复合法

提出了碳纤维为复合结构的观点。根据复合材料力学性能的细观力学分析理论及连续纤维增强的单层板理论, 结合碳纤维的微观结构特点, 研究了碳纤维实际弹性常数与结晶度、 微纤维取向、 孔隙状态等的关系, 得到了分析方法和计算方法, 找出了影响弹性常数的主要因素, 给出了理论分析方法和确定的计算公式。理论计算值与实验结果具有良好的一致性。揭示出孔隙密度、 微纤维尺寸、 微纤维取向、 结晶度等对碳纤维弹性常数的决定关系, 为碳纤维生产工艺的改进提供了理论依据。      

碳纳米管增强PA6纤维的性能

将碳纳米管(CNT)在分散剂或分散剂和聚合物(PA6)载体中处理后制备出两种母粒,将其作为增强材料分别和PA6切片熔融共混纺丝,制备出碳纳米管的增强PA6纤维,研究其结构和力学性能.CNT含量低于0.5%(质量分数)时,使用两种母粒制备出的纤维强度和模量都提高,NT含量为0.03%时增强的效果最好.由碳纳米管和分散剂组成的母粒增强效果更好,NT的含量为0.03%时就能使PA6纤维的强度和模量分别提高23%和76%.这种增强纤维是一种微纤增强纤维,纳米CNT在纤维中均匀分散且沿着纤维轴的方向取向.这种结构能有效地转移载荷,具有增强作用,且取向性越好,增强效果越好.     

Effects of the carbon nanotube distribution on the macroscopic stiffness of composite materials

Having extremely high stiffness and low specific weight, carbon nanotubes (CNTs) have been known recently as perfect reinforcing fibers in nanotechnology. They can improve the stiffness and strength of nanocomposites by being used as reinforcing elements for example in polymer matrices. The corresponding properties of the fibers and matrix, such as volume fraction and aspect ratio are some of the significant factors in the characterization of mechanical properties of CNT reinforced composites. In recent years, the way in which fibers are distributed inside the matrix, in terms of randomness, has introduced another important factor in characterizing the mechanical properties of such composites. Based on this factor, composites can be classified into two types namely, aligned and randomly distributed. This research has studied the effect of random distribution of fibers in the matrix on the elastic modulus and initial yield stress of the nanocomposite. Therefore, several models of composites, with different distribution of fibers, were considered while holding the volume fractions and aspect ratio constant. As a result, the effect of randomness on the effective modulus of CNT reinforced composites was estimated. The finite element method (FEM), using the MSC.Marc software, was employed to predict the effective modulus of CNT reinforced composites and the results were successfully validated by comparison with the analytical Halpin-Tsai method.     

Hierarchical composites of carbon nanotubes on carbon fiber: Influence of growth condition on fiber tensile properties

Growing carbon nanotubes (CNT) on the surface of high performance carbon fibers (CF) provides a means to tailor the thermal, electrical and mechanical properties of the fiber–resin interface of a composite. However, many CNT growth processes require pretreatment of the fiber, deposition of an intermediate layer, or harsh growth conditions which can degrade tensile properties and limit the conduction between the fiber and the nanotubes. In this study, high density multi-wall carbon nanotubes were grown directly on two different polyacrylonitrile (PAN)-based carbon fibers (T650 and IM-7) using thermal Chemical Vapor Deposition (CVD). The influence of CVD growth conditions on the single-fiber tensile properties and CNT morphology was investigated. The mechanical properties of the resultant hybrid fibers were shown to depend on the carbon fiber used, the presence of a sizing (coating), the CNT growth temperature, growth time, and atmospheric conditions within the CVD chamber. The CNT density and alignment morphology was varied with growth temperature and precursor flow rate. Overall, it was concluded that a hybrid fiber with a well-adhered array of dense MWCNTs could be grown on the unsized T650 fiber with no significant degradation in tensile properties.     

三维五向炭纤维/酚醛编织复合材料的压缩性能及破坏机制

针对不同编织角、 不同纤维体积分数的三维五向炭纤维/酚醛编织复合材料在不同温度下进行了纵向(编织方向)压缩和横向压缩试验 , 获得了其主要压缩力学性能 , 分析了编织参数、 温度对材料压缩力学性能的影响。对试件断口进行了宏观及扫描电镜观察 , 从宏、 细观角度研究了材料的变形及其破坏机制。结果表明 , 三维五向炭纤维/酚醛编织复合材料的压缩应力2应变曲线呈现明显的非线性特征 , 且温度效应明显; 编织角和纤维体积分数是影响材料压缩性能的主要参数。三维五向炭纤维/酚醛编织复合材料的纵向压缩与横向压缩具有完全不同的破坏机制。