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.     

Effect of soy spent flakes and carbon black co-filler in rubber composites

The rubber composites that are reinforced by a mixture of soy spent flakes (SSF) and carbon black (CB) are investigated in terms of their viscoelastic properties. Soy spent flakes is a plentiful renewable material from the waste stream of commercial soy protein extraction. SSF contains mostly soy carbohydrate and dry SSF increases rubber modulus significantly. The aqueous dispersions of SSF and CB were first mixed and then blended with styrene–butadiene latex to form rubber composites by freeze-drying and compression molding method. The mixtures of SSF and CB at three different ratios are investigated as co-fillers. A 30% co-filler reinforced composite exhibits about 100 times increase in the shear elastic modulus compared with unfilled SB rubber, showing a significant reinforcement effect by the co-filler. Compared with the SSF composites, the recovery behaviors of the co-filler composites after the eight consecutive deformation cycles of dynamic strain are improved and are similar to that of the CB composites. The comparison of viscoelastic properties of the composites prepared by freeze-drying and casting methods indicates the composites prepared by freeze-drying method have a lower elastic modulus, but have a better recovery behavior due to its polymer mediated filler network structure. The co-filler composites with 50–75% substitution of CB by SSF have a greater elastic modulus than the CB reinforced composites.     

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.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

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.     

基于周期性边界条件的炭黑填充橡胶复合材料力学行为的预测

在分析炭黑填充橡胶复合材料的宏观与细观特征之间联系的基础上,提出了具有随机分布形态的代表性体积单元,推导并应用了周期性细观结构的边界约束条件,建立了三维多颗粒夹杂代表性体积单元的数值模型,对炭黑填充橡胶复合材料的宏观力学行为进行了模拟仿真。研究表明,该模型通过周期性边界条件的约束保证了宏观结构变形场和应力场的协调性;计算得到的炭黑填充橡胶复合材料的弹性模量明显高于未填充橡胶材料,并随着炭黑颗粒所占体积分数的增加而增大;该模型对复合材料有效弹性模量的预测结果与实验结果吻合较好,而且比Bergstrom三维模型的预测结果更好,证实了该模型能够用于炭黑颗粒增强橡胶基复合材料有效性能的模拟分析。     

Modeling the elastic properties of carbon nanotube array/polymer composites

In this work, the elastic properties of single-walled carbon nanotube (SWNT) arrays and their composites are investigated. The properties of twisted SWNT nano-arrays or ropes of circular cross-section are predicted through a finite element analysis by applying proper boundary conditions to the model and using the strain energy method. The nano-array properties are then used to describe the properties of twisted SWNT nano-array/polymer composites. The effect of volume fraction and aspect ratio of the nano-array as reinforcement for dilute polymer composite systems are examined for aligned and random reinforcement distribution using conventional micromechanics. Finally, elastic properties of the twisted SWNT nano-array/polymer composites are compared to the results from constitutive model of individual nanotube-reinforced polymer composites.     

Thermal conductivity of wood-derived graphite and copper–graphite composites produced via electrodeposition

The thermal conductivity of wood-derived graphite and graphite/copper composites was studied both experimentally and using finite element analysis. The unique, naturally-derived, anisotropic porosity inherent to wood-derived carbon makes standard porosity-based approximations for thermal conductivity poor estimators. For this reason, a finite element technique which uses sample microstructure as model input was utilized to determine the conductivity of the carbon phase independent of porosity. Similar modeling techniques were also applied to carbon/copper composite microstructures and predicted conductivities compared well to those determined via experiment.     

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.     

A micromechanical model for non-linear viscoelastic behavior of particle-reinforced rubber with distributed damage

A model based on micromechanics for predicting effective viscoelastic stress-strain equations and microcrack growth in particle-reinforced rubber (or other relatively soft viscoelastic matrix) is described. Geometric idealization of the microstructure follows that of the composite spheres assemblage and generalized self-consistent scheme originally used for linear elastic composites without damage. The approach combines a perturbation analysis of the matrix, which becomes more accurate as the particle volume fraction is increased, with the Rayleigh-Ritz energy method for predicting mechanical response of the composite. Results for linear elastic behavior with crack growth are first obtained, and then extensions to linear and non-linear viscoelastic behavior are discussed. It is shown that the elasticity theory may be easily extended to predict mechanical response of a viscoelastic composite, and that an approximate equation governing microcrack growth is analogous to one for an aging elastic material. Finally, a limited assessment of the theory is made through comparison with some existing theoretical effective modulus results and experimental data on a particle-filled rubber.     

不同维数填料对橡胶Payne效应的影响

在变外力作用下,填充橡胶的动态模量会随着应变的增加而急剧下降的现象称为Payne效应。研究填充橡胶的Payne效应可以保证橡胶制品在使用过程中的安全性和可靠性,同时获得具有良好力学性能的橡胶制品。文中通过胶乳-双辊连用法制备了炭黑/天然橡胶复合材料(RCB)、碳纳米管/天然橡胶复合材料(RCNT)和石墨烯/天然橡胶复合材料(RGE)。扫描电镜和透射电镜图像显示,该方法可以将填料均匀分散在橡胶基体中。Mooney-Rivlin曲线和动态力学性能测试显示RGE复合材料的Payne效应最强,RCB复合材料的Payne效应最弱。     

A constitutive model for self-reinforced ductile polymer composites

Self-reinforced polymer composites are gaining increasing interest due to their higher ductility compared to traditional glass and carbon fibre composites. Here we consider a class of PET composites comprising woven PET fibres in a PET matrix. While there is a significant literature on the development of these materials and their mechanical properties, little progress has been reported on constitutive models for these composites. Here we report the development of an anisotropic visco-plastic constitutive model for PET composites that captures the measured anisotropy, tension/compression asymmetry and ductility. This model is implemented in a commercial finite element package and shown to capture the measured response of PET composite plates and beams in different orientations to a high degree of accuracy.     

Modelling creep behaviour of orthotropic composites by the coincident element method

In this paper, the coincident method proposed previously is applied to model the four-point-bending creep experiments conducted at the Cooperative Research Centre for Advanced Composite Structures (CRC-ACS) on carbon-epoxy composite laminates. A parameter identification methodology is first developed to determine the elastic and viscoelastic material models to be used for a coincident element. Simulations are then conducted to model the flexural creep response of the composite laminates under different loading and temperature conditions. The predicted results are in reasonably good agreement with those obtained by experiments. It is demonstrated that the coincident element method is a relatively simple and useful tool for modelling orthotropic and viscoelastic response of laminated composites by using a finite element package that only supports isotropic viscoelastic material models.     

Multi-Inclusion modeling of multiphase piezoelectric composites

Recent work on multifunctional materials has shown that a functionally graded interface between the fiber and matrix of a composite material can lead to improved strength and stiffness while simultaneously affording piezoelectric properties to the composite. However the modeling of this functional gradient is difficult through micromechanics models without discretizing the gradient into numerous layers of varying properties. In order to facilitate the design of these multiphase piezoelectric composites, accurate models are required. In this work, Multi-Inclusion models are extended to predict the effective electroelastic properties of multiphase piezoelectric composites. To evaluate the micromechanics modeling results, a three dimensional finite element model of a four-phase piezoelectric composite was created in the commercial finite element software ABAQUS with different volume fractions and aspect ratios. The simulations showed excellent agreement for multiphase piezoelectric composites, and thus the modeling approach has been applied to study the overall electroelastic properties of a composite with zinc oxide nanowires grown on carbon fibers embedded in the polymer. The results of this case study demonstrate the importance of the approach and show the system cannot be accurately modeled with a homogenized interphase.     

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.     

Epoxy based photoresist/carbon nanoparticle composites

We have fabricated composites of SU-8 polymer and three different types of carbon nanoparticles (NPs) using ultrasonic mixing. Structures of composite thin films have been patterned on a characterization chip with standard UV photolithography. Using a four-point bending probe, a well defined stress is applied to the composite thin film and we have demonstrated that the composites are piezoresistive. Stable gauge factors of 5–9 have been measured, but we have also observed piezoresistive responses with gauge factors as high as 50. As SU-8 is much softer than silicon and the gauge factor of the composite material is relatively high, carbon nanoparticle doped SU-8 is a valid candidate for the piezoresistive readout in polymer based cantilever sensors, with potentially higher sensitivity than silicon based cantilevers.     

A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite

Textile composites are well known for their excellent through thickness properties and impact resistance. In this study, a representative unit cell model of a triaxial braided composite is developed based on the composite fiber volume ratio, specimen thickness and microscopic image analysis. A meso-scale finite element (FE) mesh is generated based on the detailed unit cell dimensions and fiber bundle geometry parameters. The fiber bundles are modeled as unidirectional fiber reinforced composites. A micromechanical finite element model was developed to predict the elastic and strength material properties of each unidirectional composite by imposing correct boundary conditions that can simulate the actual deformation within the braided composite. These details are then applied in the meso-mechanical finite element model for a 0°/+60°/−60° triaxially braided T700s/E862 carbon/epoxy composite. Model correlations are conducted by comparing numerical predicted and experimental measured axial tension and transverse tension response of a straight-sided, single-layer (one ply thick) coupon. By applying a periodic boundary condition in the loading direction, the meso model captures the local damage initiation and global failure behavior, as well as the periodic free-edge warping effect. The failure mechanisms are studied using the field damage initiation contours and local stress history. The influence of free-edge effect on the failure behaviors is investigated. The numerical study results reveal that this meso model is capable of predicting free-edge effect and allows identification of its impact on the composite response.     

Mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air voids

In random-chopped fiber-reinforced polymer (FRP) composites used as a retrofit material, a high volume fraction of voids is inevitable due to the manufacturing characteristics. In this paper, the mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air porosity are investigated through experiments and numerical analysis. Coupon-shaped specimens with various material compositions were manufactured to examine the uniaxial tensile performance, and the air voids in the composites were measured by a microscope camera. In order to predict the overall performance of the composites, a micromechanical formulation that accounts for porosity was newly developed. The derived model was incorporated into a finite element (FE) code, and the model parameters were estimated by comparing uniaxial tensile test results for various systems of random-chopped FRP composites. In addition, concrete beams strengthened with the composites were produced to evaluate their load-carrying capacity. The FE predictions of the composite structures were then compared with experimental data to verify the predictive capability of the proposed numerical framework.     

Free-volume correlation with mechanical and dielectric properties of natural rubber/multi walled carbon nanotubes composites

The microstructure, mechanical strength, dielectric properties, Doppler broadening measurements and positron life time studies of the composites containing multi walled carbon nanotubes (MWCNTs) and natural rubber (NR) are investigated. The uniform distribution of MWCNTs in the elastomer medium is studied by Raman spectroscopy and the electron microscopy images show the composite’s internal microstructure. Free volume sizes and interstitial mesopore sizes of the nanocomposites are determined by positron annihilation lifetime spectroscopy (PALS). PALS investigates the influence of the nanotubes in regulating the interphase nanoscale character. Strong interfacial interaction causes an apparent reduction of the free-volume fraction of NR probably by depressing the formation of free-volume holes in the interfacial region. The mechanical percolation and percolation observed from the dielectric measurements are correlated with the life time values. It is established that the sub-nano level free volumes and nano level structure of the composites have significant roles in regulating the mechanical properties.     

Simulation of interphase percolation and gradients in polymer nanocomposites

Experimental data suggests that well dispersed nanoparticles within a polymer matrix induce a significant interphase zone of altered polymer mobility surrounding each nanoparticle, which can lead to a percolating interphase network inside of the composite. To investigate this concept and the nature of the interphase, a two-dimensional finite element model is developed to study the impact of interphase zones on the overall properties of the composite. Thirty non-overlapping identical circular inclusions are randomly distributed in the matrix with layers of interphase surrounding the inclusions. The simulation results clearly show that the loss moduli of composites are either broadened or shifted corresponding to the absence or presence of a geometrically percolating interphase network. Our numerical study correlates well with experimental data showing broadening of loss peaks for unfunctionalized composites and a large shift of the loss modulus for functionalized nanotube polymer composites. Further, our results indicate the existence of a gradient in properties of the interphase layer and that incorporating this gradient into modeling is critical to reflect the behavior of polymer nanocomposites.