基于多尺度数值模型的复合材料各向异性热膨胀系数预测

依据复合材料内部纤维在基体内的排布规律及层合板铺层特性,基于多尺度方法,建立单层板和层合板代表性体积单元(RVE)模型,施加相应的边界条件,预测单层板的热膨胀系数和工程常数,进而预测复合材料层合板各向异性的等效热膨胀系数。通过与实验数据对比发现,基于正六边形单层板RVE模型预测的热膨胀系数,相比理论预测值,整体更接近实验值,其中预测的单向T300/5208碳纤维增强环氧树脂基复合材料、P75/934碳纤维增强环氧树脂基复合材料和C6000/Pi碳纤维增强环氧树脂基复合材料的横向热膨胀系数与实验结果的误差分别只有3%、1%和2%;采用单层板RVE预测的单向ECR/Derakane 510C玻璃纤维增强乙烯基酯树脂基复合材料的工程常数与实验值最大相差7.5%;层合板RVE模型预测的正交AS4/8552碳纤维增强环氧树脂基复合材料厚度方向的热膨胀系数与实验结果误差可以忽略,只有0.08%。最后以大型复合结构常用的正交铺层结构为研究对象,基于给出的单层板和层合板RVE模型预测了不同铺层复合材料烟道层合板的等效热膨胀系数,环向铺层比例对厚度方向的热膨胀系数影响较小。      

A New Model for the Transverse Modulus of Unidirectional Fiber Composites

In this paper a new micromechanical model for predicting the transverse modulus of unidirectional continuous and discontinuous fiber composites is proposed. This model is based on modeling a composite with a regular array of volume elements and constructing a stress pattern based on simple averaging procedures in the direction transverse to the fiber axis for a representative volume element. The effects of fiber aspect ratio, interfiber spacing and fiber end gap on the transverse modulus of discontinuous fiber composites are discussed in detail. The predictions of the model are compared with existing experimental results for various fiber/matrix systems and very good agreement is found. The present model has advantages over other existing models not only because the effects of fiber aspect ratio, interfiber spacing and fiber end gap are taken into account and the expression for the transverse modulus of composites is simple in form but also because the present model gives precise predictions of the transverse composite modulus.     

Aspect ratio requirements for nanotube-reinforced, polymer–matrix composites

A fiber’s efficiency in a short-fiber composite can be accurately solved by shear-lag methods, which can account for fiber geometry, an imperfect interface (or interphase), and extend to low volume fractions. Such an analysis was used to evaluate the aspect ratio requirements for single-walled nanotubes (SWNT) in a polymeric composite and contrast it to conventional fibers. The aspect ratio requirements are indistinguishable among all stiff fibers, except at low volume fractions where stiffer fibers require higher aspect ratios. The required aspect ratio decreases significantly at higher volume fractions. A scaling effect in the interphase term implies the interphase is more important for nano-fibers than for larger fibers. If the interface between nano-fibers and the matrix is not excellent, those fibers will not provide effective reinforcement. The most promising SWNT composites should use higher volume fractions and focus on systems where the fiber can stiffen the matrix in the interphase region.     

The effects of volume percent and aspect ratio of carbon fiber on fracture toughness of reinforced aluminum matrix composites

Carbon fiber reinforced aluminum matrix composites are used as advanced materials in aerospace and electronic industries. In order to investigate role of aspect ratio of carbon fiber on fracture toughness of aluminum matrix composite, the composite was produced using stir casting. Al–8.5%Si–5%Mg selected as a matrix. The samples were prepared with three volume fractions (1, 2 and 3) and three aspect ratios (300, 500 and 800). Three-point bending test was performed on the specimens to evaluate the fracture toughness of the materials. The results showed that the fracture toughness of composites depends on both fiber volume fraction and aspect ratio. Scanning electron microscopy (SEM) was employed to elucidate the fracture behavior and crack deflection of composites. The study also, showed that the toughening mechanism depends strongly on fiber volume fraction, aspect ratio and the degree of wetting between fiber and matrix.     

A comprehensive validation of analytical homogenization models: The case of ellipsoidal particles reinforced composites

This paper presents a rigorous and exhaustive evaluation of the analytical homogenization models accuracy for the case of randomly distributed and oriented ellipsoidal fibers reinforced composites. Artificial random microstructures were generated using a molecular dynamics (MD) algorithm. Numerical effective properties were computed using a Fast Fourier Transforms (FFT) based technique. The numerical predictions were compared to those of the analytical models for a wide range of phases mechanical properties, fibers volume fractions and aspect ratios. The validation campaign involved a rigorous Representative Volume Element (RVE) determination process and approximately, 66,000 simulations were performed. The results show that the analytical models accuracy is more sensitive to the mechanical properties contrasts than to the fibers volume fraction and aspect ratio. Among all the studied models, Lielens’ model remains the most accurate, especially for high contrasts and volume fractions. For high aspect ratio fibers, Lielens’s model and Beveniste’s interpretation of the Mori–Tanaka model provide similar estimates, especially when predicting the effective shear modulus. In this case, the latter could be an alternative to Lielens’ model, especially for composites where the fibers are not completely stiffer than the matrix. All conclusions of this study apply to both prolate and oblate ellipsoidal fibers.     

Tensile properties and thermal expansion behaviors of continuous molybdenum fiber reinforced aluminum matrix composites

The tensile properties and thermal expansion behaviors of continuous molybdenum fiber reinforced aluminum matrix composites (Mo_f/Al) have been studied. The Mo_f/Al composites containing different volume percents of Mo fibers were processed by diffusion bonding. The strengths of unidirectional Mo_f/Al composites were close to the rule-of-mixtures. The strengths of 0°/90° dual-directional composites increased with fiber content, while those of 45°/135° composites remained relatively low. The coefficients of thermal expansion (CTEs) of the composites decreased as the fiber content increased, close to the values of Mo fibers. With increasing temperature, the CTEs of unidirectional composites increased, while those of dual-directional composites decreased due to large accumulated thermal stresses. The CTEs of 45°/135° composites were lower than those of 0°/90° composites because of contraction effect. At temperatures above 250 °C, the CTEs of the dual-directional composites gradually increased due to matrix yielding and interfacial decohesion.     

The effect of non-symmetric distribution of fiber orientation and aspect ratio on elastic properties of composites

A composite’s microstructure significantly influences its overall properties. Orientation and aspect ratio of the fiber are two key parameters that describe the microstructures of a composite with straight short fibers. This paper discusses the effects of fiber orientation and aspect ratio distribution on the overall elastic properties of composites using the Mori–Tanaka’s method in this paper. The results show that using an average aspect ratio of the fibers to estimate overall elastic properties is not appropriate under some conditions. When the aspect ratio of the fibers does not follow a symmetric distribution, the overall elastic properties obtained by the average aspect ratio of the fibers may differ by more than 30% from those obtained by the method considering the aspect ratio distribution. This paper presents a model used to predict the properties of nanotube-reinforced composites. The results obtained by the model were compared with experimental results.     

Simulation of the percolation behavior of quasi- and transversely isotropic short-fiber composites with a continuum model

This study uses a continuum model to predict the percolation threshold of composites consisting of electrically conducting fibers in an insulating matrix. The influence of preferred orientations (resulting from differences in processing conditions) on the threshold volume fractions is discussed. The model consists of an impenetrable cylindrical core surrounded by a fully penetrable soft shell. The hard core represents a physical fiber whereas the soft shell represents an effective range for electrical conduction in the otherwise insulating matrix. The simulation procedure consists of the addition of fibers to a control volume to probe the formation of a 3-D interconnected network. Finite size scaling (FSS) theory is used to predict the threshold volume fractions for infinite systems. The correlation length exponent was found to be 0·89, in agreement with values reported in our earlier study for particulate composites as well as in other literature studies. For transversely isotropic composites, the threshold values were found to be anisotropic for finite systems. However, the anisotropy vanishes as the system size becomes infinitely large. The correlation length exponent for these transversely isotropic composites was also found to be 0·89. The effect of shell thickness on the threshold volume fractions is investigated. The influence of fiber aspect ratio on percolation behavior is discussed, and the simulation results are compared with experimental results reported in the literature.     

Experimental and modeling study of the thermal conductivity of SiC<Subscript>p</Subscript>/Al composites with bimodal size distribution

The thermal conductivity of SiC_p/Al composites with high volume fractions of 46 to 68% has been investigated. The composites were fabricated by pressureless infiltrating liquid aluminum into SiC preforms with monomodal and bimodal size distributions. The density measurement indicates that a small amount of pores is presented for the composites approaching their maximum volume fractions. An analytical model with an explicit expression is proposed for describing the thermal conductive behavior of the composites with multimodal-reinforced mixtures in terms of an effective medium approach taking into account the porosity effect. Predictions of the developed effective medium expression reveal good correspondence with the experimental results, and explore how each of the considered factors (i.e., particle size ratio, volume fraction ratio, and porosity) can have a significant effect on the thermal conductivity of the composites with bimodal mixtures.     

Effects of particle size on the thermal expansion behavior of SiCp/Al composites

The coefficients of thermal expansion (CTEs) of 20 vol% SiCp/Al composites fabricated by powder metallurgy process were measured and examined from room temperature to 450 °C. The SiC particles are in three nominal sizes 5, 20 and 56μm. The CTEs of the SiCp/Al composites were shown to be apparently dependent on the particle size. That the larger particle size, the higher CTEs of the composites, is thought to be due to the difference in original thermal residual stresses and matrix plasticity during thermal loading. At low temperature, the experimental CTEs show substantial deviation from the prediction of the elastic analysis derived by Kerner and rule of mixture (ROM), while the Kerner’s model agrees relatively well at high temperatures for the composite with the larger particle size.     

Apparent coefficient of thermal expansion and residual stresses in multilayer capacitors

The thermal expansion behavior and residual stresses in multilayer capacitor (MLC) systems are analyzed in the present study. An MLC consists of a laminate of multiple alternating electrode layers and dielectric layers sandwiched between two ceramic cover layers. An analytical model is developed to derive simple closed-form solutions for the apparent coefficients of thermal expansion (CTEs) of the laminate. Plasticity of electrodes is included in the analysis. The predicted apparent CTEs are compared with measurements of some laminated ceramic composites. The effects of plasticity on apparent CTEs and residual stresses in MLC systems are discussed.     

Generalized Bruggeman Formula for the Effective Thermal Conductivity of Particulate Composites with an Interface Layer

Combining the well-known Bruggeman theory and Nan et al. results, formulas for predicting the effective thermal conductivity of anisotropic particulate composites with an interface layer are derived. These formulas are valid for a composite material containing arbitrarily oriented ellipsoidal particles with any aspect ratio, and they can be expected to be suitable mainly for large volume fractions, when the thermal interaction between neighboring particles needs to be considered. Results of the present approach are reduced to simpler formulas for some limiting cases in the particle shape. Theoretical analysis of the effective thermal conductivity as a function of volume fraction and shape of the particles is performed. Comparison of the obtained formulas with previously reported experimental data for the effective thermal conductivity is also presented.     

Analyses of thermal expansion behavior of intergranular two-phase composites

Both analytical modeling and numerical simulations were performed to analyze residual thermal stresses and coefficients of thermal expansion (CTEs) of intergranular two-phase composites in a two-dimensional sense. A composite-circle model was adopted for analytical modeling. Model microstructures consisting of square-array, hexagon-array, and brick wall-array of grains with an intergranular phase as well as an actual microstructure of random-array grains with an intergranular phase were adopted for numerical simulations. The results showed that in predicting CTEs, the simple analytical model represents the two-dimensional composite well except that with brick wall-array grains, which induced significant anisotropic CTEs in the composite. The residual thermal stresses in composites were also discussed.     

Elastic properties of an orthotropic binary fiber-reinforced composite with auxetic and conventional constituents

Closed-form expressions for the nine effective elastic constants of a binary fiber-reinforced composite with transversely isotropic constituents with positive (conventional) and negative (auxetic) Poisson’s ratio are considered. Such formulae were obtained by means of the asymptotic homogenization method and were verified numerically with an independent finite element model. The overall properties display explicit dependence on (i) the properties of the constituents, (ii) the volume fraction or radius of inclusion and (iii) the array periodicity. They are finally obtained by solving a normal infinite symmetric linear system of algebraic equations by truncation to a relatively small order term. This allows a fast solution and low computation cost. The overall orthotropy of the elastic properties is obtained by varying the distance between the fibers in two of the principal directions leading to different spacial aspect ratio for fiber distribution. In addition to this, an analytical relation between the effective properties based on the symmetry of the stiffness tensor is introduced. With the previous elements, we present reliable predictions for auxetic and conventional composites of this kind wherein a significant enhancement in Young’s modulus is found in a composite with an auxetic matrix reinforced by conventional fibres. Finally, we compute auxeticity windows (i.e., intervals of volume fraction where the composite is auxetic) when the fibres are auxetic. It is reported that spacial fiber aspect ratio plays a key role in the composite auxetic behavior.     

二维编织C/SiC复合材料的热膨胀系数预测

根据二维编织 C/ SiC复合材料的细观结构及其制备工艺特点 , 提出了一种预测该材料面内热膨胀系数的单胞模型。模型充分考虑了编织结构复合材料中的纤维束弯曲和 CVI工艺制备陶瓷基复合材料产生的孔洞对热膨胀系数的影响。利用单胞模型预测了二维编织 C/ SiC的结构参数、 纤维体积含量、 孔洞含量对复合材料热膨胀系数的影响规律 , 结果表明 : 随着纤维束扭结处产生间隙与纱线宽度比值的增大 , 热膨胀系数增大 ; 当其它参数不变时 , 随着纤维体积含量的增大 , 热膨胀系数反而下降; 随着孔洞含量的增加 , 热膨胀系数也出现了下降的趋势。利用 DIL402C热膨胀仪测试了二维编织 C/ SiC复合材料纵向热膨胀系数 , 试验结果与模型预测结果吻合较好。     

Numerical Investigation of Thermal and Thermo-mechanical Effective Properties for Short Fibre Reinforced Composite

This study aims to investigate the thermal conductivity and the linear coefficient of thermal expansion for short fibre reinforced composites. The study combines numerical and statistical analyses in order to primarily examine the representative size and the effective properties of the volume element. Effects of various micromechanical parameters, such as fibre’s aspect ratio and fibre’s orientation, on the minimum representative size are discussed. The numerically acquired effective properties, obtained for the representative size, are presented and compared with analytical models.     

Modeling and analyses of thermo-elastic properties of radially grown carbon nanotubes-based woven fabric hybrid composite materials

Carbon nanotubes (CNTs) may be useful due to their sound thermo-mechanical properties. The present work deals with the evaluation and analysis of elastic properties and coefficient of thermal expansions (CTEs) of a CNTs-based 2D plane woven fabric composite material system where the CNTs are radially grown on the surface of the carbon fiber. Detailed constructional features of the proposed trans-scale composite material system is explained in detail. The mathematical modeling for the material properties of each constituent or building block of the hybrid composite is developed. The mathematical model for the thermo-elastic properties of yarns is also formulated based on strength of material method whereas the thermo-elastic properties of representative unit cell is based on the unit cell method. Various numerical results have been obtained by varying the CNTs content, carbon fiber contents, and temperatures. Effects of different geometrical parameters (such as yarn thickness, yarn width, and the ratio of gap length to yarn width of the yarn) on the elastic properties as well as the CTEs are also investigated.     

不同界面SiC纤维束复合材料的拉伸力学行为

利用国产三代SiC纤维通过化学气相渗透工艺(CVI)制备不同界面厚度和基体体积分数的SiC纤维束复合材料,并对其拉伸力学行为进行研究;同时,通过有限元方法研究界面厚度和基体体积分数对SiC纤维束复合材料热残余应力的影响。有限元分析结果表明:该纤维束复合材料的界面存在较为明显的径向和环向热残余应力,而且这两种应力均随着界面厚度增加而减小,随着基体体积分数的增加而增加。拉伸实验结果表明:随着界面厚度增加SiC纤维束复合材料的拉伸强度有增大趋势,且纤维拔出长度也相应增加;但在界面厚度相同的情况下,过高的基体体积分数将导致复合材料拉伸强度和韧性下降。     

Effect of filler geometry on coefficient of thermal expansion in carbon nanofiber reinforced epoxy composites

This study involves the investigation of the geometry effect of nano-fillers on thermally induced dimensional stability of epoxy composites by experimentally evaluating the linear coefficient of thermal expansion (CTE). Carbon nanofibers (CNF) were chosen as the filler in epoxy matrix to investigate the effect of an aspect ratio on the CTE of the nanocomposites at three different volume fractions of 0.5, 1, and 2% of the nano-filler. The composites were fabricated using a mechanical mixing method. The CTE values were evaluated by measuring thermal strains of the composites and also compared with a micromechanics model. It was observed that the composites with short CNF (average L/d = 10) show better thermal stability than one of the composites with long CNF (average L/d = 70), and the thermal stability of the composites was proportional to the volume fraction of the filler in each composite. In addition, the CTE of mutliwalled carbon nanotubes (MWNT) reinforced epoxy composites was evaluated and compared with the CTE of the CNF reinforced composites. Interestingly, the MWNT reinforced composites show the greatest thermal stability with an 11.5% reduction in the CTE over the pure epoxy. The experimental data was compared with micromechanics model.     

Thermoelastic Characterization and Evaluation of Residual Stresses in Bi-Directional Fibrous Composites

The thermoelastic behavior of bi-directional fibrous composites will be studied through the use of a finite element-based micromechanical model. The model is used to study the effect of the crossing angle of the fibers on the composite’s coefficient of thermal expansion (CTE) and the residual thermal stresses that develop after a temperature change. The effect of the fiber volume fraction (V _f ) on the same results is also studied. For anisotropic materials, one can see that in addition to normal strains, shear strains will also be developed due to temperature change. This method will lend itself to evaluate the coefficients of thermal expansions not only due to normal expansion, but also due to shear expansion for composites with no principal directions. In this micromechanical model, parallelepiped unit cells incorporating the fibers at different cross angles are created to represent the periodic microstructure of the angular bi-directional composite. The volume averaged stresses per unit temperature of the individual constituents are used to study the residual thermal stresses that develop. Two different sets of materials are used to test this model. Results show that when the fiber’s cross angle is not 0^o or 90^o, shear strains are created. Also, residual stresses in the unit cell are functions of the cross angle between the fibers.