Prediction of thermal conductivity of air voided-fiber-reinforced composite laminates part II: 3D simulation

Applying the fundamental definition of thermal conductivity to a unit cell of unidirectional fiber reinforced composite with air voids, one can deduce simple empirical formula to predict the thermal conductivity of the composite material with estimated air void volume percent. The inherent 3-D problem is modeled using finite element analysis. The model is tested at different fiber to resin volume ratios and various fibers to resin thermal conductivity ratios for three different air void volume percent. The air voids are modeled as cylindrical shapes with different lengths aligned with fiber direction. Two prediction schemes have been developed through the present work. One is to predict the longitudinal thermal conductivity and the other is to predict the transverse thermal conductivity of the fibers. Also, the model can be used to estimate the voids volume percent if the fiber thermal conductivity has been provided. Such expression can, also, serve as useful guides for quality and perfect bonding for material development.     

Prediction of the thermal conductivity of the constituents of fiber reinforced composite laminates

Three empirical formulas are developed to predict the thermal conductivities of fiber-reinforced composite laminates (FRCL) and its constituents. The inherent two or three-dimensional problem that is common in composites is simplified to a one-dimensional problem. The validity of the models is verified through finite element analysis. This method utilizes the parallel and series thermal models of composite walls. The models are tested at different fiber-to-resin volume ratios (30:70–75:25) and various fiber-to-resin thermal conductivity ratios (0.2–5). The predicted thermal conductivity of the fiber can be accurately predicted throughout the spectrum via two models. The first model is a first-order formula (R ² = 0.94) while the second model is a second-order formula (R ² = 0.976). These two models can be used to predict the fiber thermal conductivity based on the easily measured resin and laminate values. A third model to predict the overall laminate thermal conductivity is introduced. The thermal conductivity of the composite panel is predicted with very high accuracy (R ² = 0.995). The thermal conductivity predicted via the use of these models has an excellent agreement with the experimental measurements. Another use of these models is to determine the fiber-to-resin volume ratio (if all thermal conductivities of fiber, resin and laminate are known).     

含大量随机分布细小纤维的单向纤维增强复合材料横向弹性性能参数计算的内嵌区域模型法

利用有限元方法求取单向纤维增强复合材料的横向弹性性能参数的计算模型包括三维模型、两维平面应变模型、单胞模型等等.由于单胞模型仅仅适用于纤维规则排列情况.在纤维随机分布且纤维大小亦为随机时,单向纤维增强复合材料横向弹性性能参数必须通过对于复合材料块体的计算才能获得.同时在随机分布纤维的数量增大时,三维模型和二维平面应变模型的计算量急剧增加,模型的处理能力不强.该文提出一种利用内嵌区域模型来计算含大量随机大小、随机分布细小纤维的单向纤维增强复合材料块体的横向弹性性能参数的方法,有效降低了计算量.在较低的计算费用下,能够快速获得单向纤维增强复合材料的横向弹性性能参数.     

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins with temperature-dependent thermal conductivity.     

纤维增强复合材料热隐身斗篷设计

基于变换热动力学原理可获得具有热隐身性能的隐身结构(隐身斗篷)所需要的材料性质的空间分布。但这种材料性质的复杂分布形式以及局部热传导性能无限大等极值性质需求,使得隐身斗篷设计的实现非常困难,需要研究基于常规材料的隐身斗篷设计。本文基于常规材料的热隐身结构实现问题,提出了基于纤维增强复合材料圆环结构的实现热隐身的结构形式。首先,基于变换热动力学原理获得热隐身所需的热传导系数沿半径方向的变化规律;进而,通过设计复合材料不同位置的纤维铺设方式(含量和铺设方向)实现热隐身对材料性能的需求。选择金属银作为纤维,空气作为基体,设计出了具有热隐身性能的复合材料圆环结构纤维含量和铺设方向沿径向的分布方案。对该设计方案进行数值仿真,结果显示所设计的隐身结构具有良好的热隐身性能。由于设计方案基于常规材料,因此具有容易实现的优点。     

含空心纤维热电复合材料的能量转换效率及力学性能

空心纤维常用于热电复合材料的结构设计。纤维附近产生的不均匀温度场会引起局部热应力集中,威胁材料的可靠性并可能导致结构失效。本文采用圆环夹杂模型,研究了含空心纤维热电复合材料在均匀远场电流和能流作用下的力学响应。基于非线性全耦合的热电本构方程,利用复变函数中的级数法得到了纤维和基体中热电场和应力场的解析解。通过数值算例,分析了空心纤维的传导能力和几何尺寸对温度场、应力场和局部热电转换效率的影响。结果表明：随着空心纤维内径和界面热阻的增大,界面周围的应力场增大,但并不改变应力场的分布趋势。此外,我们发现：温度分布和应力场对几何参数比对界面热阻更为敏感。     

Prediction of overall tension behavior of short fiber-reinforced composites

The bridging stress of fibers along the crack surface plays an important role in analyzing the tension behavior of short or long fiber-reinforced composites. This paper uses the inclusion theory to obtain the expression of bridging stress for short fiber reinforced composite (SFRC) . A simplified model with periodically distributed fibers is proposed to estimate the average fiber spacings. The total fracture resistance is calculated as an energy summation including interface debonding energy dissipation, frictional sliding work between fibers and matrix, strain energy increment of fibers and matrix. The bend over point (BOP) stress is calculated by this fracture resistance. The necessary conditions of the fibers and matrix for the multiple cracking in SFRCs are discussed and the expression of ultimate external stress is derived. The critical fiber volume fraction for the strain hardening response is determined by an iteration method. In the meanwhile, the average spacing between two short fibers is proposed by a periodical distribution assumption. The theoretical prediction is compared with experimental data.     

On the effect of fiber creep-compliance in the high-temperature deformation of continuous fiber-reinforced ceramic matrix composites

Creep models for unidirectional ceramic matrix composites reinforced by long creeping fibers with weak interfaces are presented. These models extend the work of Du and McMeeking (1995) [Du, Z., McMeeking, R. 1995. Creep models for metal matrix composites with long brittle fibers. J. Mech. Phys. Solids 43, 701–726] to include the effect of fiber primary creep present in the required operational temperatures for ceramic matrix composites (CMCs). The effects of fiber breaks and the consequential stress relaxation around the breaks are incorporated in the models under the assumption of global load sharing and time-independent stochastics for fiber failure. From the set of problems analyzed, it is found that the high-temperature deformation of CMCs is sensitive to the creep-compliance of the fibers. High fiber creep-compliance drives the composite to creep faster, leading however to greater lifetimes and greater overall strains at rupture. This behavior is attributed to the fact that the greater the creep-compliance of the fibers, the higher the creep rate but the slower the matrix stress relaxation – since the matrix must deform with a rate compatible with the more creep-resistant fibers – and therefore the less the load carried by the main load-bearing phase, the fibers. As a result, fewer fibers fail and less damage is accumulated in the system. Moreover, the greater the creep-compliance of the fibers, the slower the matrix shear stress relaxation – and thus the lower the levels of applied stress for which this effect becomes important. The slower the shear stress relaxes, the slower the “slip” length increases. Due to the Weibull nature of the fibers, the fiber strengths at the smaller gauge length of the slip length are stronger; therefore fewer fibers undergo damage. Hence, high fiber creep-compliance is desirable (in the absence of any explicit creep-damage mechanism) in terms of composite lifetime but not in terms of overall strain. These results are considered of importance for composite design and optimization.     

碳纤维长度与取向对纸基摩擦材料热负荷及摩擦学性能影响

采用湿法成型工艺制备了碳纤维长度为0.1~12 mm的5种碳纤维增强纸基摩擦材料.采用梯度能量试验方法测试了所制备材料承载热负荷的能力以及在各级能量负荷条件下的摩擦磨损性能.借助扫描电镜及热导率测试仪,研究了材料承载热负荷的机理.结果表明:碳纤维长度与取向对材料的热负荷及摩擦学性能有显著影响;当碳纤维长度为6 mm时,材料承载热负荷的能力最高;长度为3~12 mm的碳纤维能够在摩擦面形成稳固的框架结构,使材料在不同能量负荷条件下保持稳定的摩擦磨损性能;纤维长度对碳纤维在材料中的排列取向有直接影响,垂直于摩擦面排列的碳纤维能够显著提高材料的热导率并降低材料所承受的最大功率密度.     

Modeling of fiber-reinforced cement composites: Discrete representation of fiber pullout

The discrete modeling of individual fibers in cement-based materials provides several advantages, including the ability to simulate the effects of fiber dispersion on pre- and post-cracking composite performance. Recent efforts in this direction have sought a balance between accurate representation of fiber behavior and computational expense. This paper describes a computationally efficient approach to representing individual fibers, and their composite behavior, within lattice models of cement-based materials. Distinguishing features of this semi-discrete approach include: (1) fibers can be positioned freely in the computational domain, irrespective of the background lattice representing the matrix phase; (2) the pre- and post-cracking actions of the fibers are simulated with little computational expense, since the number of system degrees of freedom is independent of fiber count. Simulated pullouts of single fibers are compared with theory and test results for the cases of perfectly-plastic and slip-hardening behavior of the fiber–matrix interface. To achieve objective results with respect to discretization of the matrix, pullout forces are distributed along the embedded lengths of fibers that bridge a developing crack. This is in contrast to models that lump the pullout force at the crack surfaces, which can lead to spurious break-off of matrix particles as the discretization of the matrix is refined. With respect to fracture in multi-fiber composites, the proposed model matches theoretical predictions of post-cracking strength and pullout displacement corresponding to the load-free condition. The work presented herein is a significant step toward the modeling of strain-hardening composites that exhibit multiple cracking.     

Meshless method for nonlinear heat conduction analysis of nano-composites

Carbon nanotubes (CNTs) may become ideal reinforcing materials for high-performance nano-composites due their exceptional properties. Still, much work is needed to be done before the potentials of CNT based composites can be fully realized. The evaluation of effective material properties of nano-composites is one of many difficult tasks. Simulations using continuum mechanics approach can play a significant role in the analysis of these composites. In the present work, nonlinear heat conduction analysis of CNT based composites has been carried out using continuum mechanics approach. Element free Galerkin method has been applied as a numerical tool. Thermal conductivities of nanotube and polymer matrix are assumed to vary quadratically with temperature. Picard and quasi-linearization schemes have been utilized to obtain the solution of a system of nonlinear equations. Cylindrical representative volume element has been used to evaluate the thermal properties of nano-composites. Present simulations show that the temperature dependent matrix thermal conductivity has a significant effect on the equivalent thermal conductivity of the composite, whereas temperature dependent nanotube thermal conductivity has a small effect on the equivalent thermal conductivity of the composite. The results obtained by Picard method have been found almost similar with those obtained by quasi-linearization approach.     

Softening in random networks of non-identical beams

Random fiber networks are assemblies of elastic elements connected in random configurations. They are used as models for a broad range of fibrous materials including biopolymer gels and synthetic nonwovens. Although the mechanics of networks made from the same type of fibers has been studied extensively, the behavior of composite systems of fibers with different properties has received less attention. In this work we numerically and theoretically study random networks of beams and springs of different mechanical properties. We observe that the overall network stiffness decreases on average as the variability of fiber stiffness increases, at constant mean fiber stiffness. Numerical results and analytical arguments show that for small variabilities in fiber stiffness the amount of network softening scales linearly with the variance of the fiber stiffness distribution. This result holds for any beam structure and is expected to apply to a broad range of materials including cellular solids.     

An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites

The present work deals with the modeling of 1–3 periodic composites made of piezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especially focus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fiber composites using representative volume element method (unit cell method). In this paper the focus is on square arrangements of cylindrical fibers in the composite. Two ways for calculating the effective coefficients are presented, an analytical and a numerical approach. The analytical solution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. Special attention is given on definition of appropriate boundary conditions for the unit cell to ensure periodicity. With the two introduced methods the effective coefficients were calculated for different fiber volume fractions. Finally the results are compared and discussed.     

End-shaped copper fibers in an epoxy matrix—predicted versus actual fracture toughening

End-shaped copper fibers are placed in a brittle thermoset epoxy matrix at 10 vol% and tested in four-point bending to determine the fracture toughness of the composite. Results from four-point bend tests agree well with the theoretical predictions of the fracture toughness increment ‘ΔG’ of a metal fiber/brittle thermoset matrix composite based on single fiber pullout (SFP) tests. This close agreement demonstrates that SFP testing, along with the theoretical model, can be used as an effective end-shape screening tool for ductile fibers before full scale composite testing. The model predicts that the composite’s fracture toughness will be 46% higher with flat end-impacted fibers and 4% lower with rippled fibers compared to straight fibers at a 0° orientation. Four-point bend results show the actual composite’s fracture toughness is 49% higher with flat end-impacted fibers and 5% lower with rippled fibers compared to straight fibers. Further, four-point bend results show that end-shaped copper fibers improve both the flexural strength and modulus of the composite, demonstrating that end-shaped ductile fibers provide a good stress transfer to the fibers by anchoring the fibers into the matrix. Lastly, experimental validation of the model also indicates that at low fiber volume fractions, fiber–fiber interaction has only a minor influence on the fracture toughness for the tested ductile fiber/brittle matrix composite.     

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.     

氧化铝纤维含量对Al2O3f＋Cf／ZL109混杂复合材料耐磨性能的影响

利用挤压铸造法制备了Al2O3f Cf/ZL09短纤维混杂金属基复合材料，并探讨了炭纤维体积分数为4％时，Al2O3纤维含量变化对该复合材料耐磨性能的影响。结果表明：随着Al2O3体积分数增加，复合材料的摩擦系数逐渐增大，复合材料从轻微磨损到急剧磨损的临界转变载荷大幅度提高，并随Al2O3含量的增加而逐渐增大；在临界载荷以下，影响复合材料磨损率的Al2O3含量临界值为12％，当Al2O3含量低于临界值时复合材料磨损表面无明显剥落，而当Al2O3含量超过临界值后，复合材料磨损表面存在大量的剥落坑，磨损率增大。     

Micromechanical prediction of the two-way shape memory effect in shape memory alloy composites

The two-way shape memory effect in monolithic shape memory alloys has been widely investigated both theoretically and experimentally. In the present study, this effect is analyzed for shape memory alloy composites by employing a micromechanical model. To this end, the responses of polymeric matrix and metal matrix unidirectional composites with embedded shape memory alloy fibers are determined. For the polymeric matrix composite, the effect of axial, transverse and shear loadings as well as the fiber volume fraction on the resulting two-way shape memory behavior are studied. The local distributions of stresses among the shape memory alloy fiber and epoxy matrix in the low- and high-temperature shapes of the composite are also investigated. Two training procedures that generate the two-way shape memory effect in the metal matrix composite are offered. The present analysis shows that the two-way shape memory effect in the chosen type of metal matrix composite is not as useful as in the polymeric matrix one. Finally, for a polymeric matrix composite that is subjected to a transverse normal loading, the effect of imperfect bonding between the shape memory alloy fibers and the neighboring matrix is investigated.     

Macroscopic response of particle-reinforced elastomers subjected to prescribed torques or rotations on the particles

Particle-reinforced rubbers are composite materials consisting of randomly distributed, stiff fibers/particles in a soft elastomeric material. Since the particles are stiff compared to the embedding rubber, their deformation can be ignored for all practical purposes. However, due to the softness of the rubber, they can undergo rigid body translations and rotations. Constitutive models accounting for the effect of such particle motions on the macroscopic response under prescribed deformations on the boundary have been developed recently. But, in some applications (e.g., magneto-active elastomers), the particles may experience additional torques as a consequence of an externally applied (magnetic) field, which, in turn, can affect the overall rotation of the particles in the rubber, and therefore also the macroscopic response of the composite. This paper is concerned with the development of constitutive models for particle-reinforced elastomers, which are designed to account for externally applied torques on the internally distributed particles, in addition to the externally applied deformation on the boundary of the composite. For this purpose, we propose a new variational framework involving suitably prescribed eigenstresses on the particles. For simplicity, the framework is applied to an elastomer reinforced by aligned, rigid, cylindrical fibers of elliptical cross section, which can undergo finite rotations in the context of a finite-deformation, plane strain problem for the composite. In particular, expressions are derived for the average in-plane rotation of the fibers as a function of the torques that are applied on them, both under vanishing and prescribed strain on the boundary. The results of this work will make possible the development of improved constitutive models for magneto-active elastomers, and other types of smart composite materials that are susceptible to externally applied torques.     

Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method

When the stresses of the functionally graded materials (FGMs) are discussed under thermal and/or mechanical loading conditions, the different thermomechanical effective properties are needed. For the steady state thermal analyses, these properties include the Young’s modulus, Poisson’s ratio, thermal expansion coefficient and thermal conductivity. For the transient analyses of the heat conduction problem, on the other hand, the density and heat capacity should be added to the aforementioned properties. The homogenization method (HM) based on the finite element method (FEM) is used as it has advantages, such as it is appropriate for estimating the effective properties of composites with a given periodic fiber distribution and complicated geometries. For a periodic composite structure, it is not necessary to study the whole structure but only a representative volume element (RVE) or a unit cell (UC). As the overall behavior of composites depends on the arrangement of the reinforcements, the corresponding UCs of two different arrangements of the fibers are analyzed; namely the square and hexagonal arrangements. It is found that the square arrangement predicts higher values of the Young’s modulus than the hexagonal one but with small difference. In order to verify the computed values of the properties, the results are compared with previous experimental measurements and results of analytical and numerical methods, and good agreement is achieved.     

Uncertainties of unidirectional composite strength under tensile loading and variation of environmental condition

A probabilistic strength model is developed for unidirectional composites with fibers in hexagonal arrays. The model assumes that, a central core of broken fibers surrounded by unbroken fibers which are subjected to unidirectional tensile loading. The proposed approach consists in using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. The main feature in the model lies in incorporating the variation of composite properties due to temperature and moisture, in order to predict degradation of fibers and matrix characteristics. The strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks, leading to stress concentrations in intact neighboring fibers. As fiber breaks are intrinsically random, the variability of input data allows us to describe the probabilistic model by using the Monte-Carlo method. The sensitivities of the mechanical response are evaluated regarding the uncertainties in design variables such as Young’s modulus of fibers and matrix, fiber reference strength, shear yield stress, fiber volume fraction and shear parameter defining the shear stress in the inelastic region.