Nonlinear Multi-Scale Finite Element Method to Predict Tensile Behavior of Carbon Nanotube-Reinforced Polymer Composites (original) (raw)
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Materials & Design, 2014
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.
International Journal of Modeling and Optimization, 2011
Multi-scale material modeling was used to investigate the role of nanotubes specifications on the nonlinear tensile behavior of nanocomposites. Particularly, the effect of diameter, chirality and volume fraction of nonlinearly modeled SWCNTs is studied on their composites. Multi-scale modeling is applied to assemble various RVEs composed of different SWCNTs embedded in polymer. Nanotubes are modeled in continuum mechanics based on their atomic structures in the case of space frame structures. Elements in this structure are defined in such a way to resemble carbon bonds characteristics in molecular mechanics. Polymer portion of RVE is modeled as a linear elastic continuum material, regarding the modeling convenience. Attained stress-strain curves of modeled nanocomposites revealed that using Armchair SWCNTs in RVEs rather than Zigzags makes nanocomposites tougher in tensile loading. Also diameter of CNT has an inverse effect on the stress-strain curves level. Using CNTs with lower diameter in RVEs, regardless of the chirality and CNTs type, make nanocomposites more strengthen in tension. Furthermore, the effect of diameter is more obvious in higher volume fraction of CNTs.
Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites
Theoretical and Applied Fracture Mechanics, 2008
A multi-scale representative volume element (RVE) for modeling the tensile behavior of carbon nanotube-reinforced composites is proposed. The RVE integrates nanomechanics and continuum mechanics, thus bridging the length scales from the nano-through the mesoscale. A progressive fracture model based on the modified Morse interatomic potential is used for simulating the behavior of the isolated carbon nanotubes and the FE method for modeling the matrix and building the RVE. Between the nanotube and the matrix a perfect bonding is assumed until the interfacial shear stress exceeds the corresponding strength. Then, nanotube/matrix debonding is simulated by prohibiting load transfer in the debonded region. Using the RVE, a unidirectional nanotube/polymer composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. A significant enhancement in the stiffness of the polymer owing to the adding of the nanotubes is predicted. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. Stiffness is found to be unaffected while tensile strength to significantly decrease with decreasing the interfacial shear strength.
Composite Structures, 2011
Multiscale modeling was presented for the nonlinear properties of polymer/single wall carbon nanotube (SWNT) nanocomposite under tensile, bending and torsional loading conditions. To predict the mechanical properties of both armchair and zigzag SWNTs, a finite element (FE) model based on the theory of molecular mechanics was used. For reducing the computational efforts, an equivalent cylindrical beam element was proposed, which has the unique advantage of describing the mechanical properties of SWNTs considering the nonlinearity of SWNT behavior. For a direct evaluation of the rigidities of the proposed equivalent beam, the data obtained through atomistic FE analyses of SWNT were fitted to six different equations, covering the three types of loading for both armchair and zigzag configurations. The proposed equivalent beam element was then used to build a cylindrical representative volume element (RVE) using which the effects of the interphase between SWNT and the polymer on the mechanical properties of RVE could be studied. It was found that while the interphase has a small effect on the nanocomposite stiffness, the ratio of (SWNT length)/(RVE length) dramatically affects the nanocomposite stiffness.
Constitutive modeling of nanotube–reinforced polymer composites
Composites Science and Technology, 2003
In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalentcontinuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube shapes, sizes, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/LaRC-SI (with a PmPV interface) composite systems, one with aligned SWNTs and the other with three-dimensionally randomly oriented SWNTs. The Young's modulus and shear modulus have been calculated for the two systems for various nanotube lengths and volume fractions.
Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems
2001
In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalentcontinuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.
2011
Carbon nanotubes (CNTs) demonstrate unusually high stiffness, strength and resilience, and may become an ideal reinforcing material for new composites. This paper describes a finite element formulation that is appropriate forthe numerical prediction of the mechanical behavior ofpolypropylenematrix nanocomposite.In current work it is assumed that the deformed cross sectional area of CNT is ellipse.Non-linear spring-based line elements are employed to simulate the vander Waals bonds.Elastic moduli of nanocomposites are evaluated using a representative volume element (RVE) based on the continuum mechanics and FEM.A significant enhancement in the stiffness of the polymer owing to the adding of the ECNTsis found. Addition of ECNTs in a matrix at a determined volume fraction can increase the stiffness of the composite.
Composite Structures, 2010
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.
In this study concept of experimental design is successfully applied for the determination of optimum condition to produce PP/SWCNT (Polypropylene/Single wall carbon nanotube) nanocomposite. Central composite design as one of experimental design techniques is employed for the optimization and statistical determination of the significant factors influencing on the tensile modulus and yield stress as mechanical properties of this nanocomposite. The significant factors are SWCNT weight fraction and acid treatment time for functionalizing the nanoparticles. Optimum conditions are in 0.7 % of SWCNT weight fraction and 210 min as acid treatment time for 1112.75 ± 28 MPa as maximum tensile modulus and in 216 min and 0.65 % as acid treatment time and SWCNT weight fraction respectively for 40.26 ± 0.3 MPa as maximum yield stress. Also after setting new experiments for test these optimum conditions, found excelent agreement with predicted values.
Tensile behaviour of carbon nanotube/ polypropylene composite material
The tensile behaviour of the polypropylene (PP) material reinforced by multiwalled carbon nanotubes (MWCNTs) was characterised by mechanical testing. Two different MWCNT weight ratios, namely 2 and 5%, were considered. The strains were measured using strain gauges and a digital image correlation system. The results from mechanical tests were evaluated using scanning electron microscopy (SEM). An increase in the average Young's modulus of 20?29 and 25?19% and in average maximum stress of 26?13 and 33?31% was obtained for the 2 and 5 wt-% MWCNT/PP specimens respectively. The Young's modulus and maximum stress of the MWCTN/ PP specimens show a considerable scatter, which is attributed to the varying dispersion and agglomeration size. For specimens with mechanical properties lower than the average values, SEM interpretation revealed poor dispersion and formation of large agglomerations.