A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.     

Moment Mechanics of Composites

Based on the gradient (multimoment) theory of composites, the stress-strain state in structural elements is analyzed. Approximate formulas for the moduli and stresses of fibrous composites in longitudinal shear and other stress states are found. The effect of scale parameters on the state of supercomposites is revealed.     

含随机分布缺陷的多晶铁电材料的有效电弹性能

针对铁电材料含有随机分布缺陷以及微结构在外场作用下发生变化的特点,建立起一个细观统计力学模型,考虑到缺陷和酶极化转动之间的相互影响,利用细观力学方法－Eshelby等效夹杂法和Mori-Tanaka的平均理论,具体分析了所含缺陷以及外场对铁电材料有效电弹性能和模量的影响。针对BaTiO3铁电陶瓷的有效电弹性能与常数的预报结果表明了缺陷的存在将增强材料的压电性能。     

双材料中带均匀本征应变椭球夹杂的弹性场

探讨了在两理想结合半无限大体中一带均匀本征应变椭球形夹杂引起的弹性场。通过体积元素积分得到的调和势函数通过椭圆积分及其导数表示。在椭球夹杂边界上的法向力、切向力和椭球夹杂内部主轴上的主应力都得到准确的计算。对于夹杂形状、距界面距离、材料的弹性常数等参数的影响也进行了分析。     

基于细观力学均匀化等效材料参数的复合泡沫热致应力预测方法

环氧复合泡沫采用空心玻璃微珠改性环氧树脂，对于降低电子封装材料的热致应力非常有效．为提高环氧复合泡沫的设计效率，本文提出了一种宏细观结合的环氧复合泡沫热致应力分析方法．首先通过细观力学建立不同微珠粒径、壁厚、微珠体积分数等微观结构参数下环氧复合泡沫的等效性能预测模型，然后结合宏观线弹性热应力分析模型，进行环氧复合泡沫电子封装的热致应力分析，最终获得了一种电子封装热致应力与环氧复合泡沫微观结构之间的关联模型．基于模型探讨了微珠壁厚、微珠体积分数、微珠配比等微观结构参数对封装热致应力的影响规律，并基于两种典型封装结构证明了方法的可行性，研究成果对于开发低应力封装技术、提高电子封装的可靠性及环境适应性具有重要的意义．     

Fracture strength testing of a self-passivating tungsten alloy at the micrometre scale

The brittle fracture strength of a self-passivating W-Cr10-Ti2 alloy (in wt.%) was measured through un-notched cantilever bending at the microscopic scale. The material behaved purely elastic and fractured catastrophically in an unstable fashion. An average nominal strength of 5.9 GPa was measured. The scatter in strength was shown to be significantly higher than the sum of all random errors indicating an inherent variability of the material’s strength. The measurements from 28 tests followed a Weibull distribution with a modulus of m = 12. Results from a size effect study at the microscopic scale were successfully predicted through Weibull scaling. Extrapolation into the macroscopic range overestimated the measured three-point bend strength, which is likely due to the presence of large-scale heterogeneities. The test technique sampled a material thickness of only several micrometres and is hence suitable for future ion irradiation studies.     

A micromechanical analysis of the nonlinear elastic and viscoelastic constitutive relation of a polymer filled with rigid particles

Micromechanical theory is applied to study the nonlinear elastic and viscoelastic constitutive relations of polymeric matrix filled with high rigidity solid particles. It is shown that Eshelby's method can be extended to the case of nonlinear matrix and Eshelby's tensor still exists provided that Poisson's ratio of the nonlinear matrix assumes constant value in deforming process and the rigidity of elastic filling particles is much higher than that of the matrix. A new method for averaging process is proposed to overcome the difficulty that occured in applying the ordinary equivalent inclusion method or the self-consistant method to nonlinear matrices. A rather simple constitutive equation is obtained finally and the strengthening effect of solid particles to composites is investigated. The work supported by the LNM, Institute of Mechanics, Chinese Academy of Sciences and by the National Natural Science Foundation of China     

On the Size of RVE in Finite Elasticity of Random Composites

This paper presents a quantitative study of the size of representative volume element (RVE) of random matrix-inclusion composites based on a scale-dependent homogenization method. In particular, mesoscale bounds defined under essential or natural boundary conditions are computed for several nonlinear elastic, planar composites, in which the matrix and inclusions differ not only in their material parameters but also in their strain energy function representations. Various combinations of matrix and inclusion phases described by either neo-Hookean or Ogden function are examined, and these are compared to those of linear elastic types.     

Micromechanics of particle-reinforced elasto-viscoplastic composites: Finite element simulations versus affine homogenization

The micromechanics of elasto-viscoplastic composites made up of a random and homogeneous dispersion of spherical inclusions in a continuous matrix was studied with two methods. The first one is an affine homogenization approach, which transforms the local constitutive laws into fictitious linear thermo-elastic relations in the Laplace–Carson domain so that corresponding homogenization schemes can apply, and the temporal response is computed after a numerical inversion of Laplace transform. The second method is the direct numerical simulation by finite elements of a three-dimensional representative volume element of the composite microstructure. The numerical simulations carried out over different realizations of the composite microstructure showed very little scatter and thus provided – for the first time – “exact” results in the elasto-viscoplastic regime that can be used as benchmarks to check the accuracy of other models. Overall, the predictions of the affine homogenization model were excellent, regardless of the volume fraction of spheres, of the loading paths (shear, uniaxial tension and biaxial tension as well as monotonic and cyclic deformation), particularly at low strain rates. It was found, however, that the accuracy decreased systematically as the strain rate increased. The detailed information of the stress and strain microfields given by the finite element simulations was used to analyze the source of this difference, so that better homogenization methods can be developed.     

纤维复合材料损伤过程的数值模拟

利用界面断裂力学和有限元法数值模拟纤维增强复合材料的细观损伤过程，研究各种主要破坏模式之间的相互转变和影响，指出以断裂能和混合度表示的界面性能是控制复合材料损伤过程的主要细观参数。分析了界面韧度对破坏性能的影响，探讨了基于破坏模式控制的复合材料韧度设计的新途径。