The Master SN curve approach – A hybrid multi-scale fatigue simulation of short fiber reinforced composites

Typical short fiber reinforced composites (SFRCs) components have a different statistical distribution of orientation of fibers at different points leading to different static and fatigue behavior at different locations across the component. To link component-scale calculations with this variability of fiber orientations, each element in the FE model is modeled as a Representative Volume Element (RVE); the static and fatigue properties must be calculated for each of these elements. While there are established methods to estimate the static properties, there are none for the fatigue properties. A hybrid (combination of micromechanics and tests) and multi-scale (damage in micro-scale linked to macroscale fatigue properties) method of predicting the SN curve for every point in a short fiber composite has been developed. This proposed method is based not only on tests but on a combination of manufacturing simulation, tests and multi-scale mechanics. An extensive test program was undertaken to study the fatigue behavior of short fiber composites and validate the concept of the Master SN curve (MSNC) approach. The MSNC approach is compared with two prevalent approaches – strength based scaling and test based interpolation. The MSNC approach was found to be in a good agreement with the experimental results and was confirmed to be more accurate than the prevalent methods.     

Predictions of elastic property on 2.5D C/SiC composites based on numerical modeling and semi-analytical method

In this paper, the predictions of elastic constants of 2.5D (three-dimension angle-interlock woven) continue carbon fiber reinforced silicon carbide (C/SiC) composites are studied by means of theoretical model and numerical simulation. A semi-analytical method expressing elastic constants in terms of microstructure geometrical parameters and constitute properties has been proposed. First, both the geometrical model of the 2.5D composite and the representative volume element (RVE) in both micro- and meso-scale are proposed. Second, the effective elastic properties of the RVE in 2.5D C/SiC composites are obtained using finite element method (FEM) simulation based on energy equivalent principle. Finally, the remedied spatial stiffness average (RSSA) method is proposed to obtain more accurate elastic constants using nine correction factor functions determined by FEM simulations, also the effects of geometrical variables on mechanical properties in 2.5D C/SiC composites are analyzed. These results will play an important role in designing advanced C/SiC composites.     

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.     

Prediction on viscoelastic properties of three-dimensionally braided composites by multi-scale model

Three-dimensional viscoelastic properties of four-step three-dimensionally (3D) braided composites are studied in this paper. Based on the three-cell division scheme, a multi-scale model for 3D braided composites is proposed. A periodic boundary condition is applied to characterize the periodic structure of 3D braided composites and yarns. Given the viscoelastic parameters of resin matrix and the elastic constants of fibers, the viscoelastic properties of yarns are obtained by the finite element method and Prony Series fitting. The three-dimensional viscoelastic constitutive relationship of interior cells is derived based upon the viscoelastic properties of yarns and resin matrix. Moreover, the viscoelasticity of 3D braided composites is studied by creep experiment. The viscoelastic deformation obtained from the multi-scale method agrees well with the experimental results. The influence of the two independent micro-structural parameters, braiding angles, and fiber volume fractions, on the viscoelastic properties of 3D braided composites is investigated in detail.     

Eigenstrain and Fourier series for evaluation of elastic local fields and effective properties of periodic composites

The elastic stress and strain fields and effective elasticity of periodic composite materials are determined by imposing a periodic eigenstrain on a homogeneous solid, which is constrained to be equivalent to the heterogeneous composite material through the imposition of a consistency condition. To this end, the variables of the problem are represented by Fourier series and the consistency condition is written in the Fourier space providing the system of equations to solve. The proposed method can be considered versatile as it allows determining stress and strain fields in micro-scale and overall properties of composites with different kinds of inclusions and defects. In the present work, the method is applied to multi-phase composites containing long fibers with circular transverse section. Numerical solutions provided by the proposed method are compared with finite element results for both unit cell containing a single fiber and unit cell with multiple fibers of different sizes.     

Microstructure effects on transverse cracking in composite laminae by DEM

A particle discrete element method (DEM) was employed to simulate transverse cracking in laminated fiber reinforced composites. The microstructure of the laminates was modeled by a DEM model using different mechanical constitutive laws and materials parameters for different constituents, i.e. fiber, matrix and fiber/matrix interface. Rectangular, hexagonal and random fiber distributions were simulated to study the effect of fiber distribution on the transverse cracking. The initiation and dynamic propagation of transverse cracking and interfacial debonding were all captured by the DEM simulation, which showed similar patterns to those observed from experiments. The effect of fiber volume fraction was also studied for laminae with randomly distributed fibers. It was found that the distribution and volume fraction of fibers affected not only the transverse cracking path, but also the behavior of matrix plastic deformation and fiber/matrix interface yielding in the material.     

Deformation,yield and fracture of unidirectional composites in transverse loading: 2. Influence of fibre–matrix adhesion

The influence of the adhesion between fibre and matrix on the transverse properties of unidirectional composites was studied using a combination of experimental and numerical analyses. The interface is modelled on a nano(metre)-scale and the aim is to investigate its local influence on the ultimate macroscopic transverse properties. Fibre-to-matrix stress transfer (i.e. fibre-to-matrix surface interaction) is simulated by introducing elastic interface springs. Since these elastic springs represent the chemical (covalent) bonds formed at the interface as a result of oxidative chemical surface treatment, the micromechanical model can be directly related to the effects of this treatment. For the verification of the numerical analyses, the influence of the interface is determined experimentally by transverse testing of carbon fibre reinforced composites, using fibres that were subjected to different levels of surface treatment. A direct relation between the oxygen concentration on the surface of the fibres, the interfacial bond strength and the resulting transverse strength was found. The interface strength required to obtain perfect bonding was found to be dependent on the fibre volume fraction and at increased fibre volume fractions a higher level of adhesion is required.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

An evaluation of the elastic properties and thermal expansion coefficients of medium and high modulus graphite fibers

In this work, the elastic properties and coefficients of thermal expansion of T650-35, M40J and M60J graphite fibers were determined from the macroscopic properties of either unidirectional and/or woven composites of these fibers embedded in polyimide resins. The T650-35 fibers were embedded in a PMR-15 matrix, whereas the M40J and M60J fibers were embedded in a PMR-II-50 polyimide. The three-component oscillator resonance method was employed to determine the elastic properties of the unidirectional and woven composites and their neat resins. The macroscopic coefficients of thermal expansion of the composites and the neat resins were measured by length dilatometry. Subsequently, the fiber properties were calculated from the unidirectional composite macro-data using the Eshelby/Mori-Tanaka approach. For the woven composites, a finite element approach based on the concept of a representative volume element was employed to determine the elastic and thermal properties of the fibers. In the case of the T650-35 fibers, both the longitudinal and transverse elastic and thermal properties of the fibers determined from the unidirectional and woven composites agreed very well with each other. However, for the M40J fibers, noticeable differences were observed between the fiber properties determined from the unidirectional and woven system, which was attributed to the lack of transverse isotropy of the unidirectional system. Since the properties of the M60J fibers were evaluated only from the woven system no direct comparison could be made between the properties obtained from the unidirectional and woven composite architectures. Overall, the methodology was shown to be highly applicable for the accurate determination of fiber properties from both unidirectional and woven systems.     

Analysis of effective elastic modulus for multiphased hybrid composites

Short fiber reinforced composites inherently have fiber length distribution (FLD) and fiber orientation distribution (FOD), which are important factors in determining mechanical properties of the composites. Since the internal structure has a direct effect on the mechanical properties of the composites, a Micro-CT was used to observe the three dimensional structure of fibers in the composites and to acquire FLD and FOD. It was successful to investigate FLD, FOD, and fiber orientation states and to predict the elastic modulus of the hybrid system. Since hybrid composites used in this study consist of three phases of particles, glass fibers, and matrix, theoretical hybrid modeling is required to consider reinforcing effects of both particles and glass fibers. Interaction between the particles and matrix was considered by using a perturbed stress–strain theory, the Tandon–Weng model. In addition, the laminating analogy approach (LAA) was used to predict the overall elastic modulus of the composite. Theoretical prediction of hybrid moduli indicated that there was a possibility of poor adhesion between glass fibers and matrix. The poor interfacial adhesion was confirmed by morphological experiments. This theoretical and experimental platform is expected to provide more insightful understanding on any kinds of multiphased hybrid composites.     

Enhancing damping features of advanced polymer composites by micromechanical hybridization

A hybrid configuration at the micromechanical level is presented and described as a suitable approach to enhance the damping features of advanced polymer composites. A micro-level hybridization was achieved on dry preform reinforcements by embedding visco-elastic fibres within standard carbon tows. Unidirectional composites with two viscoelastic volume fractions (2.5% and 5% vol/vol) were manufactured by a vacuum infusion process and later tested by dynamic mechanical analysis along the principal directions. Final results reveal a significant enhancement (+80% and +56%) of the damping properties, respectively, for the longitudinal and the transverse directions in the case of the highest viscoelastic fibre content.In turn, the elastic properties of the final composite were greatly reduced (−37% and −35%) with respect to the standard composite. Final results support further work in the direction of micromechanical hybridization looking at the potential exploitation of standard textile configurations with different viscoelastic fibre content to enhance damping properties.     

Effects of interphase properties in unidirectional fiber reinforced composite materials

A micromechanical study has been performed to investigate the mechanical properties of unidirectional fiber reinforced composite materials under transverse tensile loading. In particular, the effects of different properties of interphase within the representative volume element (RVE) on both the transverse effective properties and damage behavior of the composites have been studied. In order to evaluate the effects of interphase properties on the mechanical behaviors of unidirectional fiber reinforced composites considering random distribution of fibers, the interphase is represented by pre-inserted cohesive element layer between matrix and fiber with tension and shear softening constitutive laws. Results indicate a strong dependence of the RVE transverse effective properties on the interphase properties. Furthermore, both the damage initiation and its evolution are also clearly influenced by the interphase properties.     

Tensile,impact and dielectric properties of three dimensional orthogonal aramid/glass fiber hybrid composites

Aramid/glass hybrid composites with three different stacking sequences and their corresponding single fiber type composites have been fabricated and their tensile, impact and dielectric properties were investigated. The trend of tensile strength and modulus of the composites followed the rule of mixture (ROM) closely and a small but positive hybrid effect for tensile strength of the hybrid composites was observed. The hybrid composites in general had a higher impact resistance than the single fiber type composites and the hybrid composite in which fiber volume fractions for glass and aramid fiber were the most balanced showed the highest impact ductility. The aramid fiber composite showed a lower dielectric constant and a higher dielectric loss than the glass fiber composites. However, the dielectric constant of the hybrid composites decreased first and then increased as the volume fraction of aramid fiber increased, which did not follow the mixing rule for dielectric constants of compounds. The dielectric loss of the composites increased monotonically as the volume fraction of aramid fiber increased which agreed well with the mixing rule.     

三维四步编织复合材料刚度和强度的数值模拟

为了研究三维四步法编织复合材料的力学性能,利用ANSYS有限元软件对材料的细观体胞模型进行数值模拟,计算三维编织复合材料的宏观弹性常数,讨论了纤维编织角和体积比对弹性常数的影响。采用不同的强度准则分别对纤维束和基体材料进行强度校核,从而得到材料发生破坏时失效单元的体积百分比。根据失效单元的分布情况分析材料的破坏机理,进而预报材料的拉伸强度。模拟计算结果与实验值吻合较好。     

Effective transverse elastic moduli of three-phase hybrid fiber-reinforced composites with randomly located and interacting aligned circular fibers of distinct elastic properties and sizes

A higher-order multi-scale structure for three-phase hybrid fiber-reinforced composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. Two non-equivalent formulations are considered in detail to derive effective transverse elastic moduli of three-phase composites leading to new higher-order bounds. Numerical examples and comparisons among our theoretical predictions and other analytical predictions are rendered to illustrate the potential capability of the present method.     

三维全五向编织复合材料弹性性能及热物理性能的有限元分析

在三维全五向(Q5D)编织复合材料细观结构模型的基础上, 建立了其单胞参数化有限元模型。通过施加合理的边界条件, 计算得到了Q5D编织复合材料的弹性常数、 热传导系数和热膨胀系数, 所得结果与现有的实验数据吻合较好。在此基础上, 深入研究了纤维体积分数、 编织角等工艺参数对材料弹性性能和热物理性能的影响规律, 并将计算结果与三维四向(4D)和三维五向(5D)编织复合材料的相应结果进行了对比。结果表明, Q5D编织复合材料具有较好的力学性能和纵向导热性能, 其零膨胀结构的可设计性更强, 为进一步研究此种结构材料的强度问题和热力耦合问题奠定了基础。     

基于三维流场模型的含孔隙复合材料弹性常数有限元预测模型

为预测含孔隙复合材料单向层合板的有效弹性常数, 基于孔隙周边纤维分布和形态与三维Rankine椭圆体绕流流场的相似性, 提出了一种基于三维Rankine椭圆体绕流流场比拟的含孔隙复合材料弹性常数计算模型与方法。建立了含孔隙复合材料的有限元单胞计算模型, 用流场的速度变化比拟单胞内纤维体积分数的变化, 用流线形状比拟孔隙周边纤维的形态。通过对单胞施加周期性边界条件, 结合孔隙形态的概率分布模型和刚度平均法, 计算了含孔隙复合材料单向层合板的弹性常数。计算结果与实验数据有较好的一致性, 数值计算可以有效反映孔隙对复合材料单向层合板弹性常数的影响。      

Mechanical properties and damping capacity of SiCp/TiNif/Al composite with different volume fraction of SiC particle

SiC_p/TiNi_f/Al composite with 20 Vol.% TiNi fibers were fabricated by pressure infiltration method. The effect of volume fraction of SiC particle on the mechanical properties and damping capacity of the composite were studied. Four different volume fractions of SiC particle in the composite were 0%, 5%, 20% and 35% respectively. The microstructure and damping capacity of the composites was studied by SEM and DMA respectively. As the gliding of dislocation in the Al matrix was hindered by SiC particle, the yield strength and elastic modulus of the composites increased, while the elongation decreased with the increase in volume fraction of SiC particle. Furthermore, the damping capacity of the composites at room temperature was decreased when the mount of strain was more than 1 × 10⁻⁴. In the heating process, the damping peak at the temperature of 135 °C was attributed to the reverse martensitic transformation from B19′ to B2 in the TiNi fibers.     

Hybrid effects on tensile properties of hybrid short-glass-fiber-and short-carbon-fiber-reinforced polypropylene composites

Hybrid composites of polypropylene reinforced with short glass fibers and short carbon fibers were prepared using extrusion compounding and injection molding techniques. The tensile properties of these composites were investigated taking into account the effect of the hybridization by these two types of short fibers. It was noted that the tensile strength and modulus of the hybrid composites increase while the failure strain of the hybrid composites decreases with increasing the relative carbon fiber volume fraction in the mixture. The hybrid effects for the tensile strength and modulus were studied by the rule of hybrid mixtures (RoHM) using the tensile strength and modulus of single-fiber composites, respectively. It was observed that the strength shows a positive deviation from that predicted by the RoHM and hence exhibits a positive hybrid effect. However, the values of the tensile modulus are close to those predicted by the RoHM and thus the modulus shows no existence of a hybrid effect. Moreover, the failure strains of the hybrid composites were found to be higher than the failure strain of the single carbon fiber-reinforced composite, indicating that a positive hybrid effect exists. Explanations for the hybrid effects on the tensile strength and failure strain were finally presented.     

New higher-order bounds on effective transverse elastic moduli of three-phase fiber-reinforced composites with randomly located and interacting aligned circular fibers

A higher-order structure for three-phase composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. In the special event, two-phase composites with same elastic properties and sizes of fibers are studied. Two non-equivalent formulations are considered in detail to derive effective transverse elastic moduli of two-phase composites leading to new higher-order bounds. Furthermore, the effective transverse elastic moduli for an incompressible matrix containing randomly located and identical circular rigid fibers and voids are derived. It is demonstrated that significant improvements in the singular problems and accuracy are achieved by the proposed methodology. Numerical examples and comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered to illustrate the potential of the present method.