Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects

A new technique is presented for evaluating the effective properties of linearly elastic, multi-phase unidirectional composites. Various effects on the fiber/matrix interfaces (perfect bond, homogeneously imperfect interfaces, uniform interphase layers) are allowed. The analysis of nano-composite materials based on the Gurtin and Murdoch model of material surface is also included. The basic idea of the approach is to construct a circular inhomogeneity in an infinite plane whose effects on the displacements and stresses at distant points are the same as those of a finite cluster of inhomogeneities (fibers of circular cross-section) arranged in a pattern representative of the composite material in question. The elastic properties of the equivalent inhomogeneity then define the effective elastic properties of the material. The volume ratio of the composite material is found after the size of the equivalent circular inhomogeneity is defined in the course of the solution procedure. This procedure is based on a semi-analytical solution of a problem of an infinite plane containing a cluster of non-overlapping circular inhomogeneities subjected to loading at infinity. The method works equally well for periodic and random composites and – importantly – eliminates the necessity for averaging either stresses or strains. New results for nano-composite materials are presented.     

Thin interphase/imperfect interface in elasticity with application to coated fiber composites

The imperfect interface conditions which are equivalent to the effect of a thin elastic interphase are derived by a Taylor expansion method in terms of interface displacement and traction jumps. Plane and cylindrical interfaces are analyzed as special cases. The effective elastic moduli of a unidirectional coated fiber composite are obtained on the basis of the derived imperfect interface conditions. High accuracy of the method is demonstrated by comparison of solutions of several problems in terms of the imperfect interface conditions or explicit presence of interphase as a third phase. The problems considered are transverse shear of a coated infinite fiber in infinite matrix and effective transverse bulk and shear moduli and effective axial shear modulus of a coated fiber composite. Unlike previous elastic imperfect interface conditions in the literature, the present ones are valid for the entire range of interphase stiffness, from very small to very large.     

Effective magnetoelastic properties of laminated composites

Effective physical parameters of a fine-layered medium whose layers exhibit linearized magnetostriction as ferrites are determined. Ferromagnetic materials of cubic system with ferromagnetic resonance are considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 36–43, August 2006.     

Effective elastic moduli of triply periodic particulate matrix composites with imperfect unit cells

In many problems the material may possess a periodic microstructure formed by the spatial repetition of small microstructures, or unit cells. Such a perfectly regular distribution, of course, does not exist in actual cases, although the periodic modeling can be quite useful, since it provides rigorous estimations with a priori prescribed accuracy for various material properties. Triply periodic particulate matrix composites with imperfect unit cells are analyzed in this paper. The multiparticle effective field method (MEFM) is used for the analysis of the perfect and imperfect periodic structure composites. The MEFM is originally based on the homogeneity hypothesis (H1) (see for details [Buryachenko, V.A., 2001. Multiparticle effective field and related methods in micromechanics of composite materials. Appl. Mech. Rev. 54, 1–47]) of effective field acting on the inclusions. In this way the pair interaction of different inclusions is taken directly into account by the use of analytical approximate solution. For perfect periodic structures the hypothesis (H1) is enough for estimation of effective properties. Imperfection of packing necessitates exploring some additional assumption called a closing hypothesis. The next imperfections are analyzed. (A) The probability of location of an inclusion in the center of a unit cell below one (missing inclusion). (B) Some hard inclusions are randomly replaced by the porous (modeling the complete debonding) with some probability. At first, one obtains general explicit integral representations of the effective elastic moduli and strain concentrator factors depending on three numerical solutions: for the perfect periodic structure, for the infinite periodic structure with one imperfection, and for the infinite periodic structure with two arbitrary located imperfections. The method proposed is general; it is not limited by concrete numerical scheme. No restrictions were assumed on both the concrete microstructure and inhomogeneity of stress fields in the inclusions. The inclusions of one kind are assumed to be aligned. The problem (A) is solved at the level of numerical results obtained in the framework of the hypothesis (H1). For the problem (B) the numerical results are obtained if the elastic inclusions (for example hard inclusions) are randomly replaced by another inclusion (for example by the voids modeling the complete debonding). The mentioned problems are solved by three methods. The first one is a Monte Carlo simulation exploring an analytical approximate solution for the binary interacting inclusions obtained in the framework of the hypothesis (H1). The second one is a generalization of the version of the MEFM proposed for the analysis of the perfect periodic particulate composites and based on the choice of a comparison medium coinciding with the matrix. The third method uses a decomposition of the desired solution on the solution for the perfect periodic structure and on the perturbation produced by the imperfections in the perfect periodic structure. All three methods lead to close results in the considered examples; however, the CPU times expended for the solution estimation by Monte Carlo simulation differ by a factor of 1000.     

Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal–mechanical connections

This work examines the overall thermoelastic behavior of solids containing spherical inclusions with surface effects. Elastic response is evaluated as a superposition of separate solutions for isotropic and deviatoric overall loads. Using a variational approach, we construct the Euler–Lagrange equation together with the natural transition (jump) conditions at the interface. The overall bulk modulus is derived in a simple form, based on the construction of neutral composite sphere. The transverse shear modulus estimate is derived using the generalized self-consistent method. Further, we show that there exists an exact connection between effective thermal expansion and bulk modulus. This connection is valid not only for a composite sphere, but also for a matrix-based composite reinforced by many randomly distributed spheres of the same size, and can be viewed as an analog of Levin’s formula for composites with surface effects.     

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

Applied Mathematics and Mechanics - The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The...     

Effective dynamic properties and transverse waves in disperse composites

Transverse waves in a dispersive composite formed by a viscoelastic matrix and rigid inclusions are considered. They are described in the long-wave approximation on the basis of complex dynamic properties of the composite, i.e., the dynamic density and shear-rotational elasticity, which takes into account the interaction between the matrix and the rigid inclusions in their translational, deformation, and rotational vibrations. The dependencies describing the effective dynamic properties of the composite and determining the resonance dispersion of transverse waves are obtained.     

An elastoplastic damage model for metal matrix composites considering progressive imperfect interface under transverse loading

An elastoplastic damage model considering progressive imperfect interface is proposed to predict the effective elastoplastic behavior and multi-level damage progression in fiber-reinforced metal matrix composites (FRMMCs) under transverse loading. The modified Eshelby’s tensor for a cylindrical inclusion with slightly weakened interface is adopted to model fibers having mild or severe imperfect interfaces [Lee, H.K., Pyo, S.H., 2009. A 3D-damage model for fiber-reinforced brittle composites with microcracks and imperfect interfaces. J. Eng. Mech. ASCE. doi:10.1061/(ASCE)EM.1943-7889.0000039]. An elastoplastic model is derived micromechanically on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. A multi-level damage model [Lee, H.K., Pyo, S.H., 2008a. Multi-level modeling of effective elastic behavior and progressive weakened interface in particulate composites. Compos. Sci. Technol. 68, 387–397] in accordance with the Weibull’s probabilistic function is then incorporated into the elastoplastic multi-level damage model to describe the sequential, progressive imperfect interface in the composites. Numerical examples corresponding to uniaxial and biaxial transverse tensile loadings are solved to illustrate the potential of the proposed micromechanical framework. A series of parametric analysis are carried out to investigate the influence of model parameters on the progression of imperfect interface in the composites. Furthermore, a comparison between the present prediction and experimental data in the literature is made to assess the capability of the proposed micromechanical framework.     

Effective thermoelastic properties of composites with periodicity in cylindrical coordinates

The aim of this work is to study composites that present cylindrical periodicity in the microstructure. The effective thermomechanical properties of these composites are identified using a modified version of the asymptotic expansion homogenization method, which accounts for unit cells with shell shape. The microscale response is also shown. Several numerical examples demonstrate the use of the proposed approach, which is validated by other micromechanics methods.     

Fundamental solutions of the theory of unidirectional composites

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 120–127, May–June, 1992.     

Influence of imperfect elastic contact condition on the antiplane effective properties of piezoelectric fibrous composites

A fiber-reinforced periodic piezoelectric composite, where the constituents exhibit transverse isotropic properties, is considered. The fiber cross-section is circular and the periodicity is the same in two orthogonal directions. Imperfect mechanic contact conditions at the interphase between the matrix and fibers are represented in parametric form. In order to analyze the influence of the imperfect interface effect over the behavior of the composite, the effective axial piezoelectric moduli are obtained by means of the Asymptotic Homogenization Method. Some numerical examples are given.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

A model of imperfect interface with damage

In this paper two models of damaged materials are presented. The first one describes a structure composed by two adherents and an adhesive which is micro-cracked and subject to two different regimes, one in traction and one in compression. The second model is a model of interface derived from the first one through an asymptotic analysis, and it can be interpreted as a model for contact with adhesion and unilateral constraint. Simple numerical examples are presented.     

Microstructure and mechanical properties of three-dimensional five-directional braided composites

Three-dimensional (3D) five-directional braided composites are significant structural materials in the fields of astronauts and aeronautics. On the basis of the 3D five-directional braiding process, three types of microstructural unit cell models are established with respect to the interior, surface and corner regions. The mathematical relationships among the structural parameters, such as fiber orientation, fiber volume fraction, the yarn packing factor, are derived. By using these three unit cell models, a micromechanical prediction procedure is described to simulate the stiffness and strength properties of 3D five-directional braided composites. Only the in situ constituent fiber and matrix properties of the composites and the fiber volume proportion are required in the simulation. The stress states generated in the constituent fiber and matrix materials are explicitly correlated with the overall applied load on the composites. The predictive stiffness and strength are in good agreement with available experimental data, which demonstrates the applicability of the present analytical model.     

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoin- homogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.