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 electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky'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 exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.

Effective Moduli of Two-Layered Spherical Inclusions Reinforced Composites

A model is proposed to evaluate the,effective modufi of a composite reinforced by two-layered spherical inclusions.This model is based on the localisation problem of a two- layered spherical inclusion embedded in an infinite matrix.The interations of the reinforced phases are taken into account by using the average matrix stress concept.When the external layer vanishes,the proposed model reduces to the classical Mori-Tanaka's model for spherical inclusions.Theoretical results for the composite of polyester matrix filled by hollow glass spheres and voids show excellent agreement with experimental results.

DETERMINATION OF EFFECTIVE MODULI FOR FOAM PLASTICS BASED ON THREE PHASE SPHEROIDAL MODEL

The relations of bulk modulus, shear modulus, Young's modulus and the Poisson's ratio with porosity of foam plastics are determined by a three phase spheroidal model commonly used in Composite Mechanics. The results are compared with those using differential scheme. It is shown that the material properties derived from the present model normally are larger than those obtained by differential scheme for foam plastics with identical porosity. The differences in shear moduli and Young's moduli obtained by the two methods are small but they are larger for bulk moduli of incompressible matrix and Poisson's ratios. The Young's moduli of high density foam plastics derived by the present model agree better with experimental ones.

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.

EFFECTIVE ELASTIC MODULI OF AN INHOMOGENEOUS MEDIUM WITH CRACKS

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material.

Effective elastic moduli of in-situ A356/TiB_2 composites

The effective elastic moduli （EEM） of A356/TiB2 composites formed by gravity casting and adjusted pressure casting （APC） were measured and compared. The results show that the EEM of A356/TiB2 composites are improved obviously by TiB2 particles and affected by forming methods. The EEM of the specimens formed by APC are higher than those in the gravity casting case. For 9.5%A356/TiB2（volume fraction）, the EEM of the specimens formed by APC reaches 93GPa, which is 9GPa higher than those in the gravity casting case. An analytic model is established to explain the mechanics of the EEM of composites reinforced with TiB2 particles.

AN EXPLICIT EXPRESSION OF THE EFFECTIVE MODULI FOR COMPOSITE MATERIALS FILLED WITH COATED INCLUSIONS

The obvious shortcoming of the generalized self-consistent method (GSCM) is that the effective shear modulus of composite materials estimated by the method can not be expressed in an explicit form. This is inconvenient in engineering applications. In order to overcome that shortcoming of GSCM, a reformation of GSCM is made and a new micromechanical scheme is suggested in this paper. By means of this new scheme, both the effective bulk and shear moduli of an inclusion-matrix composite material can be obtained and be expressed in simple explicit forms. A comparison with the existing models and the rigorous Hashin-Shtrikman bounds demonstrates that the present scheme is accurate. By a two-step homogenization technique from the present new scheme, the effective moduli of the composite materials with coated spherical inclusions are obtained and can also be expressed in an explicit form. The comparison with the existing theoretical and experimental results shows that the present solutions are satisfactory. Moreover, a quantitative comparison of GSCM and the Mori-Tanaka method (MTM) is made based on a unified scheme.

A GENERALIZED SELF-CONSISTENT MORI-TANAKA MODEL FOR PREDICTING THE EFFECTIVE MODULI OF THE COATED INCLUSION BASED COMPOSITE MATERIALS

The weak point of the generalized self-consistent method (GSCM) isthat its solution for the effective shear moduli involves determiningthe complicated displacement and strain fields in con- stituents.Furthermore, the effective moduli estimated by GSCM cannot beexpressed in an explicit form. Instead of following the procedure ofGSCM, in this paper a generalized self-consistent Mori- Tanaka method(GSCMTM) is developed by means of Hill's interface condition and theassumption that the strain in the inclusion is uniform. A comparisonwith the existing theoretical and experimental results shows that thepresent GSCMTM is sufficiently accurate to predict the effectivemoduli of the coated inclusion-based composite materials.

THE EFFECTIVE PROPERTIES OF PIEZOELECTRIC COMPOSITE MATERIALS WITH TRANSVERSELY ISOTROPIC SPHERICAL INCLUSIONS

The effective properties of piezoelectric composite materials are very important in engineering. In this paper, the closed_form solutions of the constraint_strain and the constraint_electric_field of a transversely isotropic spherical inclusion in an infinite non_piezoelectric matrix are obtained. The dilute solutions of piezoelectric composite materials with transversely isotropic spherical inclusions are also given. The solutions in the paper can be readily utilized in analysis and design of piezoelectric composite materials or smart materials and smart structures.

PREDICTION OF THE OVERALL MODULI OF A CYLINDRICAL SHORT-FIBER REINFORCED COMPOSITE

With respect to obtaining the effective elastic moduli of the composite, the present theory dif- fers from both Eshelby's equivalent inclusion method and Hill's self-consistent one, both of which only consid- er the mechanical properties of the matrix and inclusions(fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes, sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others. Finally, numerical re- sults are given.

Study on the squeezing effect of open-ended pipe piles

During the installation of a pipe pile,the soil around the pile will be squeezed out. This paper deals with this squeezing effect of open-ended pipe piles using the cylindrical cavity expansion theory. The characteristics of soil with different tension and compression moduli and dilation are involved by applying the elastic theory with different moduli and logarithmic strain. The closed-form solutions of the radius of the plastic region,the displacement of the boundary between the plastic region and the elastic region and the expansion pressure on the external surface of the pipe piles are obtained. When obtaining these solutions,the soil plug in the open-ended pipe pile is considered by employing an incremental filling ratio to quantify the degree of soil plugging. Moreover,the effects of the ratio of tension and compression moduli,angle of dilation and incremental filling ratio on the radius of the plastic region and the expansion pressure on the external surface of the pipe pile are investigated. The parametric analyses show that it is necessary and important to consider the difference between the tension modulus and compression modulus,dilation angle and incremental filling ratio for studying the squeezing effect of open-ended pipe pile installation. It is concluded that the analytical solutions presented in this paper are suitable for studying the squeezing effect of open-ended pipe piles.

Elastic Moduli in Cadmium Selenide Doped with Chromium

Temperature dependence of elastic moduli , , and the latter for the piezo-active and non-piezo-active versions, have been measured in the interval of 4 - 180 K at 28 - 262 MHz in a CdSe: Cr2+ crystal. Anomalies below 40 K have been found for all the moduli, except . The interpretation of the results has been carried out involving the Jahn-Teller effect and relaxation between the equivalent distortions of the tetrahedral CrSe4 centers.

基于致密砂岩岩石物理模型的静态模量预测方法

岩石静态模量是油气勘探开发过程中重要的力学性质参数,直接实验测量的成本较高,而且数量有限。以前的通过经验公式实现动静态模量转换的方法,物理意义不明确、精度不高,不能满足工程需要。为此,提出了一种基于岩石物理模型的静态模量预测方法,即先利用测井数据构建孔隙裂缝型岩石物理模型来计算动态模量,在动态模量的基础上考虑频散效应和排水效应获得岩石低频干燥的模量,最后考虑动静态模量之间应变振幅的差异,模拟岩石发生静态形变的过程,实现从动态到静态模量的预测。该方法考虑了动静态模量转换的微观因素,理论上更严谨。对川西实际工区实验数据进行了静态模量预测,预测结果与实验数据吻合较好,其中动态杨氏模量的误差为4%,静态杨氏模量的误差为8%,证明了方法的适用性。

Analytical modeling of effect of interlayer on effective moduli of layered graphene-polymer nanocomposites

Nanocomposites enhanced with two-dimensional, layered graphene fillers are a new class of engineering materials that exhibit superior properties and characteristics to composites with conventional fillers.However, the roles of ＂interlayers＂ in layered graphene fillers have yet to be fully explored. This paper examines the effect of interlayers on mechanical properties of layered graphene polymer composites.As an effective filler, the fundamental properties（in-plane Young＇s modulus E（L1）, out-of-plane Young＇s modulus E（L2）; shear modulus G（L12）, major Poisson＇s ratio V（L12）） of the layered graphene were computed by using the Arridge＇s lamellar model. The effects of interlayers on effective moduli of layered graphene epoxy composites were examined through the Tandon-Weng model. The properties of the interlayer show noticeable impact on elastic properties of the composites, particular the out-of-plane properties（Young＇s modulus E2 and shear modulus G（12））. The interlayer spacing is seen to have much great influence on properties of the composites. As the interlayer spacing increases from 0.34 nm to 2 nm, all elastic properties of the composites have been greatly decreased.

Effective elastic moduli of polymer-layered silicate nanocomposites

Polymer-layered silicate (PLS) nanocomposites exhibit some mechanical properties that are much better than conventional polymer filled composites. A relatively low content of layered silicate yields a significant enhancement of material performance. After the volume fraction of clay reaches a relatively low 'critical value'; however, further increasing does not show a greater stiffening effect. This phenomenon is contrary to previous micromechanical predictions and is not understood well. Based on the analysis on the microstructures of PLS nanocomposites, the present note provides an insight into the physical micromechanisms of the above unexpected phenomenon. The Mori-Tanaka scheme and a numerical method are employed to estimate the effective elastic moduli of such a composite.

An anisotropic micromechamcal model for calculation of effective elastic moduli of Ni-based single crystal superalloys

An anisotropic micromechanical model based on Mori-Tanaka method is developed to calculate the effective elastic moduli of

Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interac ti ons between different microcracks is used for analyzing the elastic problem of m ultiple cracks solids. The effective elastic moduli for randomly oriented crack s and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with thos e from various micromechanics models and experimental data. These results show t hat the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks.

高温后花岗岩力学性能的试验研究

对经历不同高温后花岗岩的力学性能进行了试验研究,分析了花岗岩应力-应变曲线、峰值应力、峰值应变、弹性模量和泊松比等的变化情况。研究结果表明,经历400℃以内的高温后,温度对花岗岩的力学性能的影响不明显。但经历的温度超过400℃后,随受热温度升高花岗岩力学性能迅速劣化,花岗岩峰值应力(或强度)和弹性模量急剧降低,而峰值应变迅速增长。高温后花岗岩泊松比随经历高温的增加而呈减少趋势。

纤维沥青混凝土等效模量的探讨

目的根据复合材料细观力学理论探讨了低温条件下纤维沥青混凝土等效劲度模量的分析方法.方法采用Zhao Y.H和Weng G.J.在Eshelby-Mori-Tanaka理论基础上提出的纤维增强复合材料的等效模量公式,计算了具有不同纤维质量分数的纤维沥青混凝土在不同温度状态下的等效劲度模量,对计算结果与劈裂试验结果进行了比较和误差分析.从温度、纤维掺量和纤维性状三个方面分析误差产生的原因.结果温度为主要影响因素,同时随着纤维质量分数的增大误差也逐渐增大,而纤维本身的性能对结果误差基本没有影响.结论在一定条件下,理论计算结果与试验结果相对误差较小,由于温度的影响需要对等效模量公式进行温度修正.

煤层顶板砂岩高温状态下力学特征试验研究

对44块鹤壁六矿煤层顶板砂岩试件在高温下和高温后的力学性质进行试验研究,揭示砂岩的强度和变形特征随温度的变化规律。试验结果表明:随温度升高,高温下和高温后的砂岩的弹性参数(峰值强度、弹性模量、变形模量)均逐渐降低,但总体变化趋势相似,个别试件的弹性参数在400℃前高于常温状态;两者相比,高温后砂岩的峰值强度、弹性模量和变形模量有所提高,两者受温度影响均以脆性破坏为主。这为研究煤炭地下气化时热作用下燃空区的围岩稳定及应力场和位移场的变化规律提供试验依据。