Buckling analysis of functionally graded plates subjected to uniaxial loading

Elastic bifurcational buckling of functionally graded plates under in-plane compressive loading is studied. It is supposed that the gradients of material properties throughout the structure are produced by a spatial distribution of the local reinforcement volume fraction v_f = v_f(x, y, z). To analyze the problem, a method based on a combination of micromechanical and structural approaches is employed. This establishes the effective constitutive behavior at every point of a nonhomogeneous composite plate and provides a buckling criterion. The derived criterion enables one to calculate the critical buckling load R_x^cr for a given distribution v(x, y, z).

Furthermore, with the aim to improve the buckling resistance of the functionally graded plate, the functional R_x^cr(v_f) is maximized. This yields an optimal spatial distribution v_f(x, y, z) of the reinforcement phase.

Results are presented for both short- and long-fiber SiC/Al plates in which the fibers are nonuniformly distributed in the x-, y-, or z-directions. The effects of length-to-width ratio of the plate, and of different types of boundary conditions are studied. Buckling load improvements of up to 100%, as compared to the corresponding uniformly reinforced structure, are shown.     

Ag glasses based on Zn-phosphate

The partial substitution of Zn²⁺ for Ag⁺ in Ag₄P₂O₇ leads to the formation of a wide glassy domain of composition [Ag₄P₂O₇] _(1−y) [Zn₂P₂O₇] _(y) with 0.20y0.87. The introduction of AgI in these materials results in a new series of glasses of formula [(Ag₄P₂O₇)_(1−y) (Zn₂P₂O₇)_(y)] _(1−X) [AgI] _(x), which domain for the composition y = 0.25 corresponds to 0x 0.64. The structure as well as the thermal and electrical properties of these materials are compared with those of the [AgPO₃] _(1−X) [AgI] _(x) and [Ag₄P₂O₇] _(1−x) [AgI] _(x) glasses.     

三向正交预制体织造参数对C/C复合材料性能的影响

以Z向间距不同的三向正交结构预制体为研究对象,采用化学气相渗透和浸渍树脂相结合的工艺制备碳/碳(C/C)复合材料,研究织造参数对C/C复合材料微观结构和弯曲性能的影响。以三向正交预制体最小的重复结构为单元建立计算模型,获得三向正交预制体纤维含量与织造参数的关系式并进行验证,结果表明：Z向纤维间距及X,Y向纤维层间距越小,预制体纤维含量越高;Z向纤维间距越大,纤维交织处扭曲变形大,预制体孔隙结构发生变化;相同致密化工艺下,孔隙结构的变化影响C/C复合材料中基体碳的组成和分布,对基体碳形貌无影响;X,Y向纤维含量越高,Z向纤维间距越小,致密后的C/C复合材料弯曲强度越高。     

Incremental constitutive equation for large strain elasto plasticity

Starting from the standard theory with intermediate configuration for finite deformations of an isotropic elasto-plastic material with isotropic hardening, rate type constitutive equations are obtained. The small elastic strain approximation is then discussed and it is shown that, in this approximation, these equations reduce to Hill's formalism of large strain elasto-plasticity obtained from the classical Prandtl-Reuss relations of infinitesimal plasticity by substituting for the infinitesimal strain rate, stress and stress rate respectively the rate of deformation tensor, the Cauchy stress tensor and the Jaumann stress rate tensor. The limiting case of perfect plasticity is also investigated.     

Some concepts concerning twinning and cellular growth of bulk barium metaborate (BBO) crystals

Bulk single β-BaB₂O₄ (BBO) crystals have been grown by the TSSG method in Czochralski variant, using Na₂O and NaF as the solvents. It was found that formation of twins (electric type) or cellular substructures of different scales is their specific growth feature. We believe that their formation is governed by changes in the composition and structure of the double-electric layer (DEL) at the interface of crystal growth. In Z-axis crystals only microtwins structures were revealed whose number and localization are determined by the composition of used solvent. The cellular growth of these crystals at a particular stage is a result of the impossibility of frontal formation of an antipolar structure (macrotwin) under the conditions of increasing charge density in the DEL. In the Y(X-)-axis crystals the conditions for formation of one or three (five, etc.) macrotwin boundaries and, hence, noncellular growth are always realized. Model concepts, characterizing seeding and growth of Y(X-)- and Z-axis BBO crystals are discussed.     

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

This paper presents alternative forms of hyperelastic–plastic constitutive equations and their integration algorithms for isotropic‐hardening materials at large strain, which are established in two‐point tensor field, namely between the first Piola–Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non‐symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two‐point hyperelastic stress–strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return‐mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non‐symmetric tensor functions is applied to derive the two‐point closed‐form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations. Copyright © 2008 John Wiley & Sons, Ltd.     

空间环境模拟设备穿透式隔振系统性能仿真分析

某些航天器产品,特别是光学载荷在进行空间环境试验时对试验环境的振动指标通常有严格的要求,需要采用隔振系统。而空间环境模拟设备内部特殊的真空、低温环境,对隔振系统的设计提出了特殊的要求。本文给出了一种穿透式隔振系统的总体设计方案,并采用整体模态分析、系统振幅分析方法对隔振系统的性能进行了分析计算。结果表明,隔振系统能够满足在1~2 Hz频段内,3个方向的振动位移幅值均≤0.4μm,具有良好的低频隔振性能,能够满足航天器产品空间环境模拟试验时对振动的隔离需求。     

Design and study on a 1–3 anisotropy piezocomposite sensor

A design method is presented for 1–3 anisotropy piezocomposite so as to differentiate each strain component when it is used as the sensor in smart materials and structures. The 1–3 piezocomposite has been tailored to anisotropy by matching the scales of the piezoelectric phase and the non-piezoelectric phase. The composite samples have been fabricated by an aligning–casting–slicing process and the piezoelectric properties of the composites in the x and y directions have been measured and analyzed physically. It is shown that the difference of the piezoelectric properties of the composite between the x and y directions is up to approximately 40%.     

复合固体推进剂黏弹性微裂纹损伤本构模型

为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量。在Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式。该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载。其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程。该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致。数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力。     

Optical transitions near the band edge in bulk CuInxGa1−xSe2 from ellipsometric measurements

From the analysis of the variation of optical absorption coefficient with incident photon energy between 0.8 and 2.6 eV, obtained from ellipsometric data, the energy E_G of the fundamental absorption edge and E_G′ of the forbidden direct transition for CuIn_xGa_1−xSe₂ alloys are estimated. The change in E_G and the spin-orbit splitting Δ_SO=E_G′−E_G with the composition x can be represented by parabolic expression of the form E_G(x)=E_G(0)+ax+bx² and Δ_SO(x)=Δ_SO(0)+a′x+b′x², respectively. b and b′ are called “bowing parameters”. Theoretical fit gives a=0.875 eV, b=0.198 eV, a′=0.341 eV and b′=−0.431 eV. The positive sign of b and negative sign of b′ are in agreement with the theoretical prediction of Wei and Zunger [Phys. Rev. B 39 (1989) 6279].     

Limitations of the constitutive equation of a simple elastic solid

Summary The constitutive equation of a simple, isotropic elastic solid can be arranged in such a form as to give rise to a fundamental identity between Lode's stress parameter and a corresponding deformation parameter. Using the concept of a stress intensity function, it is shown that at initial yield the constitutive equation of a simple, isotropic elastic solid satisfies only the von Mises yield criterion. A general form for the deformation response coefficients is obtained by way of the concept of a deformation intensity function. In general, there are two broad classes of deformation intensity function, defined in terms of whether the deformation intensity function is continuously differentiable or whether it is piece-wise linear and continuous. Use of the fundamental identity between Lode's stress parameter and the corresponding deformation parameter leads to the conclusion that the constitutive equation of the simple, isotropic elastic solid is incompatible with any form of piece-wise linear deformation intensity function. The stretching tensor has been expressed in terms of the co-rotational and convected time derivatives of the left Cauchy-Green deformation tensor and its inverse. This form of the stretching tensor is entered into a particular form of constitutive equation of the rate-type for a simple, isotropic elastic solid. By considering infinitesimal deformations from an arbitrary configuration, the constitutive equation of the rate-type is reduced to a constitutive equation of the incremental-type. In a similar way, an incremental-type constitutive equation is obtained from the constitutive equation of a simple, isotropic elastic solid. Comparison of these two incremental-type constitutive equations leads to the identification of a particular form for the material response coefficients associated with the constitutive equation of a simple elastic solid. Further limitations of the constitutive equation of a simple, isotropic elastic solid are considered in the context of two simple modes of deformation.     

Structural characterization of ion-beam-induced epitaxially crystallized thin layers of III–V and IV–IV semiconductors

Structural properties of ion-beam-induced epitaxial crystallization (IBIEC) for amorphous layers of GaAs on GaAs(100), BP on BP(100) and Si_1−xGe_x and Si_1−x−yGe_xC_y on Si(100) have been investigated. Crystallization was induced by ion bombardment with 400 keV Ne, Ar or Kr at 150 °C for GaAs and at 350 °C for BP. Epitaxial crystallization up to the surface was observed both in GaAs and BP at temperatures much below those required for the solid phase epitaxial growth (SPEG). The growth rate per nuclear energy deposition density has shown a larger dependence on ion dose rate in cases of heavier ion bombardments both for GaAs and BP. Crystallization of a-GaAs with ions whose projected ranges are within the amorphous layer thickness was also observed at 150 °C. Epitaxial crystallization of Si_1−xGe_x and Si_1−x−yGe_xC_y layers (x = 0.13 and y = 0.014 at peak concentration) on Si(100) formed by high-dose implantation of 80 keV Ge and 17 keV C ions has been observed in the IBIEC process with 400 keV Ar ion bombardments at 300–400 °C. Crystalline growth by IBIEC has shown a larger growth rate in Si_1−x−yGe_xC_y/Si} than in Si_1−xGe_x/Si} with the same Ge concentration for all bombardments under investigation. X-ray rocking-curve measurements have shown a strain-compensated growth in Si_1−x−yGe_xC_y/Si}, whereas Si_1−xGe_x/Si} samples have shown a growth with strain accommodation.     

Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy

In this paper some results of the tensor function theory are applied to the formulation of constitutive equations of isotropic and anisotropic materials in the secondary and tertiary creep stage. The creep process, in its tertiary phase, is characterized by a damage tensor. Because of its microscopic nature, damage has, in general, an anisotropic character even in cases where the material was originally isotropic, i.e. isotropic in its virgin state. Fissure orientation and length cause anisotropic macroscopic behaviour. In the first part of the paper some possible ways of representing constitutive equations involving (initial) anisotropy of the material (e.g. from rolling) and involving anisotropic creep-damage are dealt with. The formulations of such equations are based upon theorems concerning tensor-valued functions. Furthermore, some simplified constitutive equations for more practical use are discussed. The main problem of this part is: to find an irreducible set of tensor generators. Besides the problem of finding such tensor generators it is very important to determine the scalar coefficients in constitutive equations as functions of the invariants and experimental data. The second part of the paper is concerned with the determination of the scalar functions. This can be done by using tensorial interpolation methods as pointed out in detail.     

Isotropic linear constitutive relations for nonsimple fluids

We investigate the general constitutive relation of an isotropic linear fluid when the stress tensor can depend on higher-order spatial gradients of the velocity. We apply the results to the case of second-grade and third-grade fluids, be they compressible or not. However, the expression of the general isotropic tensor can be a matter of interest also for other classes of nonsimple material.     

On asymptotic behavior of oscillatory solutions of operator differential equations perturbed by a fast Markov process

We study the asymptotic behavior of the distributions of the solution of the differential equation of the form

in a separable Hilbert space H where y(t) is an ergodic homogenous Markov process in a measurable space (Y, C) satisfying some mixing conditions and A(y), y Y is a family of commuting closed linear operators with the same dense domain. Using the spectral representation of the solution we construct an H-valued process û_ε(t) which is expressed in terms of the solution of the averaged equation

where = ƒ A(y)(dy) and is the ergodic distribution of Y(t), and some Gaussian random fields with independent increments. We show that the distributions of u_ε(t/ε) and û_ε(t) asymptotically coincide.     

The flexure and torsion of bones viewed as anisotropic poroelastic bodies

Two-phase poroelastic material is taken as a model of the bone, in the sense that the osseous tissue is considered as a perfectly elastic solid and the fluid substances filling the cavities as a viscous compressible fluid. Biot's theory of consolidation is adopted, assuming interconnections between the cavities. For a transversely isotropic body the theory leads to seven linear constitutive equations, connecting seven stress components with seven deformation components, by means of eight material coefficients. The theory is applied to beam-like structural elements by using the procedure of Michell, consisting of representation of stress and deformation components as rational integral functions of the axial coordinate z.

General equations are derived for two particular cases; (a) when the stress and strain components do not depend on z, (b) when the latter are linear functions of z. The first case corresponds to the action of terminal couples (both flexural and torsional); the second case is associated with the action of terminal forces.

Illustrative examples are solved, involving (a) cylindrical bending of poroelastic plates by terminal couples, (b) pure bending of poroelastic beams of arbitrary cross section having one axis of symmetry, (c) pure torsion of poroelastic beams of arbitrary cross section.

The explicit solution of the case (b) shows that the behavior of the poroelastic material is analogous to that of a three-element visco-elastic model. This agrees qualitatively with the experimental findings of Sedlin for bones.     

风力发电机叶片用玻璃纤维织物的渗透率

通过改变纤维层数来改变纤维织物的孔隙率, 采用一维饱和流动方法测量了风力发电叶片用玻璃纤维织物(Windstrand^TM)三个方向(x、y和z)的饱和渗透率大小。考察了孔隙率、模具尺寸以及纤维方向(平行于和垂直于2%的纤维束两个方向)对其饱和渗透率的影响。结果表明: 渗透率随孔隙率的降低而迅速降低; 当孔隙率为34.6%~54.7%时, 模具尺寸对y向饱和渗透率影响不大; 改变2%的纤维束方向(由平行到垂直), 当孔隙率为34.6%~54.7%时, 对饱和渗透率有一定影响。当孔隙率为45%~55%时, 玻璃纤维织物x和y方向的饱和渗透率约为z方向饱和渗透率的3~7倍。