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.

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.

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 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.

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.

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.

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.

THE VALIDITY OF THE MODIFIED MORI-TANAKA METHOD FOR COMPOSITES WITH SLIGHTLY WEAKENED INTERFACE

This paper presents a direct Mori-Tanaka approach to calculate the effective moduli of particle-reinforced composites and fiber-reinforced composites with spring-like imperfect interfaces. By a comparison between these results and those obtained from the approximate Mori-Tanaka method developed by Qu for composites with slightly weakened interface, the validity of the Qu's method is revealed.

TORSION OF COMPOSITE LAMINATED BARS WITH A LARGE NUMBER OF LAYERS

In view of rite effective elastic moduli theory([1]), analyzing the thick composite laminated bars subjected to an externally applied torque are presented by three-dimensional finite element (3-D FEM) and global-local method in this paper. Numerical results involving the distribution of shearing stresses olt cross-section and the torsional deformation and the interlaminar stresses near to free edges are given. If necessary elements discretization may be densely carried out only in the high stress gradient, region. Obviously, it requires less computer memory and computational time so that it offers an effective way for evaluating strength of laminated bars torsion with a greet number of layers.

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 properties of coated fibrous piezoelectric composites with spring-type interfaces under anti-plane mechanical and in-plane electrical loads

In this paper,we investigate the effective properties of three-phase(matrix/coating/fiber)cylindrical piezoelectric composites with imperfect interfaces under anti-plane mechanical and in-plane electrical loads.By using the electromechanically coupling spring-type interface model and the generalized self-consistent method(GSM),we analytically derived the effective electroelastic moduli.The present solutions include as special cases the three-phase cylindrical piezoelectric composites with perfect interfaces as well as the two-phase(matrix/fiber)case with imperfect or perfect interfaces.Selected calculations are graphically shown to demonstrate dependence of the effective moduli on the interfacial properties.The particular size-dependent characteristic due to the interfacial imperfection is also discussed.