Overall elastoplastic property for micropolar composites with randomly oriented ellipsoidal inclusions

Overall linear and non-linear properties for micropolar composites containing 3D and in-plane randomly oriented inclusions are examined with an analytical micromechanical method. This method is based on Eshelby solution for a general ellipsoidal inclusion in a micropolar media and secant moduli method. The influence of inclusion’s shape, size and orientation on the classical effective moduli, yielding surface and non-linear stress and strain relation are examined. The results show that the effective moduli and non-linear stress–strain curves are always higher for micropolar composites than the corresponding classical composites. When the inclusion’s size is sufficiently large, the classical results can be recovered.     

Rigorous bounds on the effective thermal conductivity of composites with ellipsoidal inclusions

A new method is developed to derive the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions. The transition layer for each ellipsoidal inclusion is introduced to make the trial temperature field for the upper bound and the trial heat flux field for the lower bound satisfy the continuous interface conditions which are absolutely necessary for the application of variational principles. According to the principles of minimum potential energy and minimum complementary energy, the bounds of the effective thermal conductivity of composites with ellipsoidal inclusions are rigorously derived. The effects of the distribution and geometric parameters of ellipsoidal inclusions on the bounds of the effective thermal conductivity of composites are analyzed. It should be shown that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present method provides a powerful way to bound the effective thermal conductivity of composites, which can be developed to obtain a series of bounds by taking different trial temperature and heat flux fields. In addition, the present upper and lower bounds still are finite when the thermal conductivity of ellipsoidal inclusions tends to ∞ and 0, respectively.     

Micromechanics modeling of viscoelastic properties of hybrid composites with shunted and arbitrarily oriented piezoelectric inclusions

A comprehensive micromechanics model is developed to estimate the effective viscoelastic properties of hybrid composites containing polymer matrix, conductive inclusions and shunted piezoelectric inclusions. The model is derived using the viscoelastic correspondence principle in conjunction with the Mori-Tanaka approach and the orientation averaging scheme. Three dimensional complex moduli are explicitly presented for hybrid composites with any orientation distribution. The model is first validated by comparison with available experimental results. Then, the loss factors are examined for hybrid composites with inclusions of various volume fractions and of shapes ranging from thin disks to long fibers. It is seen that hybrid composites with randomly oriented inclusions exhibit shear loss factors which are not possible with monolithic piezoelectric plate. Furthermore, the numerical results indicate that composites with long spheroid inclusions provide the best damping performance. The results recommend that aligned inclusion composites are good for alleviating longitudinal oscillations. If oscillation energy needs to be dissipated in all directions and for all modes, three dimensional random composites should be used. It is also observed that spherical inclusion composites cannot improve shear damping irrespective of the orientation and the volume fraction. In general, to achieve a pronounced damping piezoelectric inclusions that lie in aspect ratio range 0.1?α?2 should be avoided.     

Bounds on effective magnetic permeability of three-phase composites with coated spherical inclusions

An effective model is developed to bound the effective magnetic permeability of three-phase composites with coated spherical inclusions. In the present model, the trial magnetic potential for the upper bound and the trial magnetic induction field for the lower bound are constructed to satisfy continuity interface conditions. According to the variational principle, the upper and lower bounds on the effective magnetic permeability of three-phase composites with coated spherical inclusions are derived. In this paper, trial magnetic potentials with different function forms are taken and the optimal upper bound is obtained for the trail magnetic potential corresponding to the third-order function. When the three-phase model degenerates into the composite spheres assemblage model [1], it is interesting that the optimal upper and lower bounds are the same. The effects of the volume fraction of coated spherical inclusions and the thickness and magnetic permeability of coated layers between the matrix and spherical inclusions on the effective magnetic permeability of composites are analyzed. The upper and lower bounds are finite non-zero values when the magnetic permeability of spherical inclusions tends to ∞$\infty$ and 0, respectively.     

Transient creep behavior of a metal matrix composite with a dilute concentration of randomly oriented spheroidal inclusions

The transient creep behavior of a metal matrix composite containing a dilute concentration of randomly oriented spheroidal inclusions is derived explicitly from the constitutive equation of the matrix. This theory can account for the influence of inclusion shape, elastic inhomogeneity between both phases, and the volume fraction of inclusions. The micro-macro transition is carried out by considering the mechanics of incremental creep, which discloses the nature of stress relaxation in the ductile matrix and the connection between the micro and macro creep strains. The transient creep curves of the composite are displayed with several inclusion shapes. Consistent with the known elastic behavior, spherical inclusions are found to provide the weakest reinforcing effect, whereas thin, circular discs possess the most effective strengthening shape. According to this theory and in line with the experimental data, the creep resistance of cobalt at 500°C can improve by more than 80% after adding a mere 5% of rutile particles into it.     

多相周期压电纤维复合材料反平面变形问题的解析解

研究了具有周期微结构的多相压电纤维复合材料在反平面变形下的电弹性场。通过在各非均匀相内引入非均匀的广义本征应变,将原问题等价为带有周期广义本征应变的均匀介质问题,建立了两者间的等价条件。利用等价问题各区域交界处的广义应力连续条件和广义位移协调条件,并结合双准周期Riemann边值问题理论和等价条件,获得了各相材料电弹性场的解析解,进而由平均场理论预测了材料的有效压电系数。比较了相同压电材料体积分数下中空压电纤维、碳芯压电结构纤维和实心压电纤维复合材料有效压电系数的差异,讨论了压电结构纤维中非压电芯刚度及压电结构纤维与基体间涂层的刚度对有效压电系数的影响。研究结果可为高灵敏度压电复合材料的设计提供有价值的参考。     

Micro-structure of composites with randomly distributed particles on the impact of the effective thermal conductivity parameters

结合建立的颗粒随机分布复合材料的微结构模型和基于均匀化理论统计的双尺度计算方法,针对氮化硼颗粒增强高密度聚乙烯（BN/HDPE）复合材料,研究了颗粒形状、体积分数和空间分布参数等微结构特征对复合材料有效热传导系数的影响。结果表明：颗粒体积分数的增加将导致有效热传导系数升高;球形颗粒的位置参数、长椭球颗粒的取向程度都对有效热传导系数有重要影响。数值试验表明,材料的微结构特征对复合材料的有效热传导系数具有极大影响。     

A nanostructural design to produce high ductility of high volume fraction SiCp/Al composites with enhanced strength

High ductility and increased strength of SiC_p/Al composites are highly desirable for their applications in complicated components. However, high ductility and high strength are mutually exclusive in high volume fraction SiC_p/Al composites. Here, we report a novel nanostructuring strategy that achieves SiC_p/Al–Sc–Zr composites with superior maximum tensile strain and enhanced tensile strength. The new strategy is based on combination of grain refinement down to ultra-fine scale with nanometric particles inside the grain through adding distinctive elements (Sc, Zr) and refining nucleation centers to nanoscale under the action of high volume fraction reinforcement during the fabrication process. The nanostructured SiC_p/Al–Sc–Zr composites had an increase of ∼300% in maximum tensile strain and a 21% increase in tensile strength. This thought provides a new sight into enhancement of both strength and ductility of particle reinforcement metal matrix composites.     

Numerical studies on the effective shear modulus of particle reinforced composites with an inhomogeneous inter-phase

Numerical studies on the effective shear modulus of particle reinforced composites with an inhomogeneous inter-phase are performed. The influences of many parameters to the equivalent shear modulus of composites are carefully analyzed, including the inter-phase thickness, variation of interfacial properties, boundary conditions and volume fraction of particles, etc. Numerical results show that the Poisson ratio can be assumed as a constant across the whole inter-phase zone in the computation. The form of property variation across the inter-phase also greatly affects the effective shear modulus of composite. Numerical results predicted by the rigid boundary conditions are remarkably higher than those by the free boundary conditions and the exact solutions. The reasonability and exactness of the available models for predicting the effective shear modulus of composites are accessed by the numerical results in the present work.     

An analytical model to study the effective stiffness of the composites with periodically distributed sphere particles

In order to analytically study the overall elastic stiffness of the composite containing periodically dispersed sphere particles, a new micro-mechanics model is developed in this paper. Three kinds of typical particle packing arrangements in the form of simple cubic lattice, body-centered cubic lattice and face-centered cubic lattice are considered and compared. The special characteristics of regular distribution are fully considered by incorporating the necessary geometrical symmetry conditions into strain Green’s function. It is found that particle arrangement obviously affects the macroscopic elastic response of such the kind of composite. Moreover, most of the predictions by the present model are in good agreement with the FEM computations. The effective Young’s modulus of BCC composite the effective shear modulus of SC composite are not in the range of the Hashin–Shtrikman bounds. The present model is also useful to verify some other numerical results mainly obtained by the unit-cell model, for instance, damage variables, matrix plasticity, etc.     

On the effective elastic properties of matrix composites: Combining the effective field method and numerical solutions for cell elements with multiple inhomogeneities

The work is devoted to calculation of effective elastic constants of homogeneous materials containing random or regular sets of isolated inclusions. Our approach combines the self-consistent effective field method with the numerical solution of the elasticity problem for a typical cell. The method also allows analysis of detailed elastic fields in the composites. By the numerical solution of the elasticity problem for a cell, integral equations for the stress field are used. Discretization of these equations is carried out by Gaussian approximating functions. For such functions, elements of the matrix of the discretized problem are calculated in explicit analytical forms. If the lattice of approximating nodes is regular, the matrix of the discretized problem proves to have the Toeplitz structure. The matrix-vector products with such matrices may be carried out by the Fast Fourier Transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. Results are given for 2D-media with regular and random sets of circular inclusions, and compared with existing exact solutions.     

FeSiCrB amorphous soft magnetic composites filled with Co2Z hexaferrites for enhanced effective permeability

Z-type Sr₃Co₂Fe₂₄O₄₁ hexaferrites (Co₂Z hexaferrites) were synthesized with sol–gel method and were mechanically mixed with spherical Fe₈₈Si₇Cr_2.5B_2.5 (FeSiCrB) amorphous powders, and then compacted to form toroidal Co₂Z hexaferrites/FeSiCrB amorphous soft magnetic composites (Co₂Z/FeSiCrB SMCs). The compositions, morphology and soft magnetic performance were characterized through SEM, XRD, VSM, EDS, B-H analyzer and impedance analyzer. All results reveal that Co₂Z hexaferrites in Co₂Z/FeSiCrB SMCs should mainly exist in air gaps between spherical FeSiCrB amorphous powders, leading to the increasing density. Saturation magnetization decreases a little for magnetic dilution and coercivity increases for the stronger magnetic interaction of Co₂Z/FeSiCrB SMCs. The introduction of Co₂Z hexaferrites in air gaps increases the conduction area of magnetic circuits and decreases the demagnetization effect, leading to the higher effective permeability of 27.4 for Co₂Z/FeSiCrB SMCs, much higher than 25.0 for FeSiCrB SMCs. Furthermore, Co₂Z/FeSiCrB SMCs present the smaller core loss and more stable DC bias characteristics owing to the insulating Co₂Z hexaferrites.     

Cross-property connections for fiber reinforced piezoelectric materials with anisotropic constituents

The paper addresses the problem of the connection between effective elastic stiffnesses, piezoelectric coefficients and dielectric permeabilities of a fiber reinforced piezoelectric composite with both phases (the matrix and the fibers) being transversely-isotropic. These connections allow one to predict the entire set of macroscopic elastic stiffnesses through one or two measurements of dielectric permeability. The solutions for square and hexagonal arrays of fibers and for randomly located parallel fibers are constructed and compared. The analytical results show very good agreement with available experimental data. As a side result, it is shown that the mutual positions of inhomogeneities produce only a minor effect and that applicability of the non-interaction approximation is much wider than expected.     

Statistical continuum theory for the effective conductivity of fiber filled polymer composites: Effect of orientation distribution and aspect ratio

Effective conductivity of polymer composites, filled with conducting fibers such as carbon nanotubes, is studied using statistical continuum theory. The fiber orientation distribution in the matrix plays a very important role on their effective properties. To take into account their orientation, shape and distribution, two-point and three-point probability distribution functions are used. The effect of fibers orientation is illustrated by comparing the effective conductivity of microstructures with oriented and non-oriented fibers. The randomly oriented fibers result in an isotropic effective conductivity. The increased fiber orientation distribution can lead to higher anisotropy in conductivity. The effect of fiber’s aspect ratio on the effective conductivity is studied by comparing microstructures with varying degrees of fiber orientation distribution. Results show that the increase in anisotropy leads to higher conductivity in the maximum fiber orientation distribution direction and lower conductivity in the transverse direction. These results are in agreement with various models from the literature that show the increase of the aspect ratio of fibers improves the electrical and thermal conductivity.     

A polarization‐based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast

It is recognized that the convergence of FFT‐based iterative schemes used for computing the effective properties of elastic composite materials drastically depends on the contrast between the phases. Particularly, the rate of convergence of the strain‐based iterative scheme strongly decreases when the composites contain very stiff inclusions and the method diverges in the case of rigid inclusions. Reversely, the stress‐based iterative scheme converges rapidly in the case of composites with very stiff or rigid inclusions but leads to low convergence rates when soft inclusions are considered and to divergence for composites containing voids. It follows that the computation of effective properties is costly when the heterogeneous medium contains simultaneously soft and stiff phases. Particularly, the problem of composites containing voids and rigid inclusions cannot be solved by the strain or the stress‐based approaches. In this paper, we propose a new polarization‐based iterative scheme for computing the macroscopic properties of elastic composites with an arbitrary contrast which is nearly as simple as the basic schemes (strain and stress‐based) but which has the ability to compute the overall properties of multiphase composites with arbitrary elastic moduli, as illustrated through several examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Graphene sheets segregated by barium titanate for polyvinylidene fluoride composites with high dielectric constant and ultralow loss tangent

In this paper, we report a unique method to develop polyvinylidene fluoride (PVDF) composites with high dielectric constant and low loss tangent by loading relatively low content of graphene-encapsulated barium titanate (BT) hybrid fillers. BT particles encapsulated with graphene oxide (BT-GO) were prepared via electrostatic self-assembly and subsequent chemical reduction resulted in BT-RGO particles. SEM morphology revealed that RGO sheets were segregated by BT particles. The hybrid fillers have two advantages for tuning dielectric properties: loading extremely low content of RGO can be exactly controlled and individual RGO sheets segregated by BT particles would prevent leakage current. As a result, PVDF composites filled with BT-RGO displayed improved dielectric properties before percolative behavior occurred. Composites filled with 30 vol% BT-RGO have a dielectric constant and loss tangent (tan δ) value of 67.5 and 0.060 (1 kHz), respectively. By contrast, dielectric constant and tan δ of composites filled with 30 vol% BT-GO and BT were 57.7 and 38.3, 0.076 and 0.042 (1 kHz), respectively. The improvement of dielectric constant is attributable to the formation of microcapacitors by highly conductive RGO sheets segregated by BT particles. Meanwhile, the distance between adjacent RGO sheets is large enough to prevent leakage current from tunneling conductance, by which tan δ is remarkably constrained. The composites could achieve excellent dielectric properties by loading relatively low amount of ceramic fillers, which indicates that this method can be used as guideline for reduce the usage amount of ceramic fillers.     

Fabrication and characterization of aluminum nitride polymer matrix composites with high thermal conductivity and low dielectric constant for electronic packaging

Polymethyl methacrylate (PMMA) composites filled with Aluminum Nitride (AlN) were prepared by powder processing technique. The microstructures of the composites were investigated by scanning electron microscopy techniques. The effect of AlN filler content (0.1–0.7 volume fraction (vf)) on the thermal conductivity, relative permittivity, and dielectric loss were investigated. As the vf of AlN filler increased, the thermal conductivity of the specimens increased. The thermal conductivity and relative permittivity of AlN/PMMA composites with 0.7 vf AlN filler were improved to 1.87 W/(m K) and 4.4 (at 1 MHz), respectively. The experimental thermal conductivity and relative permittivity were compared with that from simulation model.     

Combining self-consistent and numerical methods for the calculation of elastic fields and effective properties of 3D-matrix composites with periodic and random microstructures

The work is devoted to the calculation of static elastic fields in 3D-composite materials consisting of a homogeneous host medium (matrix) and an array of isolated heterogeneous inclusions. A self-consistent effective field method allows reducing this problem to the problem for a typical cell of the composite that contains a finite number of the inclusions. The volume integral equations for strain and stress fields in a heterogeneous medium are used. Discretization of these equations is performed by the radial Gaussian functions centered at a system of approximating nodes. Such functions allow calculating the elements of the matrix of the discretized problem in explicit analytical form. For a regular grid of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and matrix-vector products with such matrices may be calculated by the fast fourier transform technique. The latter accelerates significantly the iterative procedure. First, the method is applied to the calculation of elastic fields in a homogeneous medium with a spherical heterogeneous inclusion and then, to composites with periodic and random sets of spherical inclusions. Simple cubic and FCC lattices of the inclusions which material is stiffer or softer than the material of the matrix are considered. The calculations are performed for cells that contain various numbers of the inclusions, and the predicted effective constants of the composites are compared with the numerical solutions of other authors. Finally, a composite material with a random set of spherical inclusions is considered. It is shown that the consideration of a composite cell that contains a dozen of randomly distributed inclusions allows predicting the composite effective elastic constants with sufficient accuracy.     

含非均匀界面相纤维增强复合材料热传导性能预测的递推公式

研究了含非均匀界面相纤维增强复合材料的宏观等效传热性能。将热导率沿径向连续变化的界面相离散为多个热导率均匀的同心圆柱层,采用广义自洽法和复变函数理论,推导了复合材料宏观等效热导率的解析递推公式,并由递推公式给出了均匀界面相和理想零厚度界面的封闭公式。理想零厚度界面复合材料的热导率与已有理论结果一致。理想零厚度界面和非均匀界面相模型的计算结果与实验数据比较表明,当纤维体积分数较小时,2种模型的预测结果与实验数据吻合均较好,当体积分数较大时,与实验数据相比,非均匀界面相模型的精度大大高于理想零厚度界面模型的精度。本文中给出的递推公式亦可用于计算多涂层纤维增强复合材料的热导率。