考虑粒子分布特征的复合材料细观力学方法

研究了颗粒增强复合材料中颗粒增强体粒径分布对复合材料力学性能的影响,利用分形思想将增强粒子的概率分布特征考虑进来,对已有的复合材料细观力学等效夹杂方法进行修正,建立了一个考虑粒子统计分布的细观等效力方法.以混凝土为例,分析了颗粒增强体体积含量、夹杂与基体的模量比和分形结构的分辨率对复合材料力学性能的影响.结果表明,这种新方法能够适用于分析颗粒增强复合材料的细观结构对力学性能的影响.     

用多参数非均匀等效体研究圆柱正交异性复合材料的剪切有效模量

有效模量是复合材料力学细观解过渡到宏观解的桥梁。宏观非均匀复合材料的有效模量是一个尚未认真研究过的课题。本文提出用多参数非均匀等效体的新方法,来研究圆柱正交异性宏观非均匀复合材料的剪切有效模量,克服了最近Dhoopar B.L.和SinhaP.K提出的方法的一些不足之处。     

含微裂纹和椭球颗粒介质的强度及本构关系

针对含随机分布微裂纹及椭球颗粒的复合材料，通过考虑椭球颗粒内的本征应变及其与微裂纹的相互作用，利用等效夹杂方法研究了微裂纹损伤对材料有效模量和强度的影响，推导了复合材料的细观应力场及本构关系，并导出了材料破坏的临界条件．     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

多晶铁电材料的有效电弹性能预报

本文利用细观力学方法———Ｅｓｈｅｌｂｙ等效夹杂法和Ｍｏｒｉ Ｔａｎａｋａ的平均场理论,根据铁电材料的微结构特点,建立了一个细观统计模型对多晶铁电材料的有效电弹性能和模量进行分析预报．在本细观统计模型中,不仅考虑到单晶粒的形状影响,而且考虑铁电畴在外场作用下发生极化转动的影响．本文针对ＢａＴｉＯ３铁电陶瓷的有效电弹性能与系数的预报结果与实验观测结果相符     

近片层γ-TiAl基合金宏观屈服的微观表征

将近片层-γTiAl基合金视为以等轴γ颗粒为基体,PST颗粒为夹杂的两相复合材料,基于细观力学自洽理论,对合金的有效弹性模量及基体和夹杂中的应力和应变场进行了解析分析计算,并结合细观力学的宏细观关联方法,确定了近片层-γTiAl基合金的宏观屈服的微观表征.结果表明:夹杂颗粒中的应力和应变场与外载及夹杂的体积分数f和椭球长细比ρ有关,软取向PST夹杂颗粒的微变形屈服导致近片层-γTiAl基合金材料的整体宏观屈服.     

颗粒增强复合材料有效性能的三维数值分析

将细观力学和计算力学方法相结合用以确定复合材料中的局部和平均应力－应变场．对旋转体和非旋转体颗粒增强复合材料的有效模量进行了三维有限元数值计算，数值与实验结果对比表明，该方法是有效的、可靠的．分析了颗粒的排列分布、颗粒取向和颗粒的几何形状对有效模量的影响．数值结果表明，颗粒的排列对有效轴向弹性模量影响较大．颗粒的取向和颗粒的形状对有效性能的影响也是显著的     

复合材料动态粘弹性能的细观研究

利用细观力学的Eshelby等效夹杂方法研究了颗粒增强复合材料的动态粘弹性力学性能,分析了材料复模量随夹杂体积分数、载荷频率之间的变化规律,给出了许多有意义的结论,为复合材料结构的优化设计及应用提供了理论基础。     

弹塑性复合材料力学性能的细观研究

应用细观力学的Eshelby等效夹杂理论研究了复合材料的弹塑性问题。以铝基复合材料为例,建立了多轴载荷下复合材料弹塑性应力-应变关系,并且理论预报与实验结果符合较好,分析了夹杂形状、体积分数及加载路径对材料宏观性能的影响。同时,还研究了热塑性复合材料热膨胀系数与工艺温度之间的变化规律,分析了热残余应变对材料设计的影响。     

含有随机夹杂的统计非均匀弹性介质参数的分析

本文提出了随机点场理论用于研究含有随机夹杂的统计非均匀介质。本文不同于其它作者,一般均将随机理论建立在Eshelby的等效夹杂原理之上,而这里是建立在Kunin的微结构理论基础之上。作为理论的一个应用,本文对复合材料的有效模量及夹杂内部及周围微观场进行了计算。     

双周期圆柱形压电夹杂反平面问题的精确解及其应用

研究无限压电介质中双周期圆柱形压电夹杂的反平面问题.借鉴Eshelby等效夹杂原理,通过引入双周期非均匀本征应变和本征电场,构造了一个与原问题等价的均匀介质双周期本征应变和本征电场问题.利用双准周期Riemann边值问题理论,获得了夹杂内外严格的电弹性解.作为压电纤维复合材料的一个重要模型,预测了压电纤维复合材料的有效电弹性模量.     

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites. The project supported by the National Natural Science Foundation of China (No. 19704100) and the National Natural Science Foundation of Chinese Academy of Sciences (No. KJ951-1-201)     

Piezoelectric composites with periodic multi-coated inhomogeneities

A new, robust homogenization scheme for determination of the effective properties of a periodic piezoelectric composite with general multi-coated inhomogeneities is developed. In this scheme the coating does not have to be thin, the shape and orientation of the inclusion and coatings do not have to be identical, their centers do not have to coincide, their properties do not have to remain uniform, and the microstructure can be with the 2D elliptic or the 3D ellipsoidal inclusions. The development starts from the local electromechanical equivalent inclusion principle through the introduction of the position-dependent equivalent eigenstrain and electric field. Then with a Fourier series expansion and a superposition procedure, the volume-averaged equivalent eigenstrain and electric field for each phase are obtained. The results in turn are used in an energy equivalent criterion to determine the effective properties of the composite. In this model the interphase interactions in each multi-coated particle and the long-range interactions between the periodically distributed particles are fully accounted for. To demonstrate its wide range of applicability, we applied it to examine the properties of several periodic composites: (i) piezoelectric PZT spherical particles in a polymer matrix, (ii) continuous glassy fibers with thin PZT coating in an epoxy matrix, (iii) spherical PZT particles coated by thick or functionally graded piezoelectric layer, (iv) spheroidal voids coated with a thick non-piezoelectric layer in a PZT matrix, and (v) spherical piezoelectric inhomogeneities with eccentric, non-uniform thickness coating. The calculated results reflect the complex nature of interplay between the properties of core, matrix, and coating, as well as whether the coating is uniform, functionally graded, or eccentric. The accuracy of this new scheme is checked against the double-inclusion and other micromechanics models, and good agreement is observed.     

The averaged mechanical properties of prismatic lattice formed by ellipsoidal inclusions

Summary The objective of this paper is to evaluate the averaged elastic properties of 3-D grained composites in which identical inclusions form a prismatic network interacting with the matrix material. The inclusions are of ellipsoidal shape with transverse circular sections located at the nodes of a doubly-periodic lattice with an orthogonal elementary cell. When the arrays of inclusions are set at equal spacings in normal directions through the thickness of the matrix, the material formed is an anisotropic composite with tetragonal symmetry at planes transverse to the fiber axis. The longitudinal and transverse elastic and shear moduli as well as the longitudinal Poisson's ratios of such composites are evaluated in this paper. The averaged properties are studied in terms of the aspect ratio and volume fraction of the inclusions as well as the relative rigidity of the constituent phases. Employing the Eshelby's theory for the stress field around a single ellipsoidal inhomogeneity, which is surrounded by the effective anisotropic material, and considering the Mori-Tanaka's concept for the mutual interaction of the neighboring inclusions, we may evaluate the averaged elastic properties of grained composites with aligned ellipsoidal inclusions at finite concentrations. The results provided in a closed-form solution concern the stiffness of 3-D grained composites with parallely dispersed ellipsoidal inclusions forming a prismatic network inside the principal material. It is shown that the stiffness is affected by both the geometry of the inclusions and their concentration. The use of different composite models in the analysis shows that intense variations of stiffness occur mainly in hard composites weakened by soft ellipsoidal inclusions. These findings come in full verification with experimental or theoretical results from the literature. Received 10 February 1998; accepted for publication 27 November 1998     

Effective mechanical properties of unidirectional composites in the presence of imperfect interface

In this paper, the equivalent inclusion method is implemented to estimate the effective mechanical properties of unidirectional composites in the presence of an imperfect interface. For this purpose, a representative volume element containing three constituents, a matrix, and interface layer, and a fiber component, is considered. A periodic eigenstrain defined in terms of Fourier series is then employed to homogenize non-dilute multi-phase composites. In order to take into account the interphase imperfection effects on mechanical properties of composites, a stiffness parameter in terms of a matrix and interphase elastic modulus is introduced. Consistency conditions are also modified accordingly in such a way that only the part of the fiber lateral stiffness is to be effective in estimating the equivalent composite mechanical properties. Employing the modified consistency equations together with the energy equivalence relation leads to a set of linear equations that are consequently used to estimate the average values of eigenstrain in non-homogeneous phases. It is shown that for composites with both soft and hard reinforcements, largest stiffness parameter that indicates complete fiber–matrix interfacial debonding causes the same equivalent lateral properties.     

Eshelby's problem of non-elliptical inclusions

The Eshelby problem consists in determining the strain field of an infinite linearly elastic homogeneous medium due to a uniform eigenstrain prescribed over a subdomain, called inclusion, of the medium. The salient feature of Eshelby's solution for an ellipsoidal inclusion is that the strain tensor field inside the latter is uniform. This uniformity has the important consequence that the solution to the fundamental problem of determination of the strain field in an infinite linearly elastic homogeneous medium containing an embedded ellipsoidal inhomogeneity and subjected to remote uniform loading can be readily deduced from Eshelby's solution for an ellipsoidal inclusion upon imposing appropriate uniform eigenstrains. Based on this result, most of the existing micromechanics schemes dedicated to estimating the effective properties of inhomogeneous materials have been nevertheless applied to a number of materials of practical interest where inhomogeneities are in reality non-ellipsoidal. Aiming to examine the validity of the ellipsoidal approximation of inhomogeneities underlying various micromechanics schemes, we first derive a new boundary integral expression for calculating Eshelby's tensor field (ETF) in the context of two-dimensional isotropic elasticity. The simple and compact structure of the new boundary integral expression leads us to obtain the explicit expressions of ETF and its average for a wide variety of non-elliptical inclusions including arbitrary polygonal ones and those characterized by the finite Laurent series. In light of these new analytical results, we show that: (i) the elliptical approximation to the average of ETF is valid for a convex non-elliptical inclusion but becomes inacceptable for a non-convex non-elliptical inclusion; (ii) in general, the Eshelby tensor field inside a non-elliptical inclusion is quite non-uniform and cannot be replaced by its average; (iii) the substitution of the generalized Eshelby tensor involved in various micromechanics schemes by the average Eshelby tensor for non-elliptical inhomogeneities is in general inadmissible.     

Bounds on the overall properties of composites with ellipsoidal inclusions

A new model is put forward to bound the effective elastic moduli of composites with ellipsoidal inclusions. In the present paper, transition layer for each ellipsoidal inclusion is introduced to make the trial displacement field for the upper bound and the trial stress 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 upper and lower bounds on the effective elastic moduli 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 elastic moduli are analyzed in details. The present upper and lower bounds are still finite when the bulk and shear moduli of ellipsoidal inclusions tend to infinity and zero, respectively. It should be mentioned that the present method is simple and needs not calculate the complex integrals of multi-point correlation functions. Meanwhile, the present paper provides an entirely different way to bound the effective elastic moduli of composites with ellipsoidal inclusions, which can be developed to obtain a series of bounds by taking different trial displacement and stress fields.     

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.     

The effective properties of piezocomposites, part II: The effective electroelastic moduli

Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroelastic Eshelby's tensors obtained in the part I of this paper and the generalized Budiansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and experimental results shows that the theoretical values in this paper agree quite well with the experimental results. These expression can be readily utilized in analysis and design of piezocomposites. The project supported by the National Natural Science Foundation of China     

A continuum micromechanical theory of overall plasticity for particulate composites including particle size effect

Classical continuum micromechanics cannot predict the particle size dependence of the overall plasticity for composite materials, a simple analytical micromechanical method is proposed in this paper to investigate this size dependence. The matrix material is idealized as a micropolar continuum, an average equivalent inclusion method is advanced and the Mori–Tanaka's method is extended to a micropolar medium to evaluate the effective elastic modulus tensor. The overall plasticity of composites is predicted by a new secant moduli method based on the second order moment of strain and torsion of the matrix in a framework of micropolar theory. The computed results show that the size dependence is more pronounced when the particle's size approaches to the matrix characteristic length, and for large particle sizes, the prediction coincides with that predicted by classical micromechanical models. The method is analytical in nature, and it can capture the particle size dependence on the overall plastic behavior for particulate composites, and the prediction agrees well with the experimental results presented in literature. The proposed model can be considered as a natural extension of the widely used secant moduli method from a heterogeneous Cauchy medium to a micropolar composite.