Effective Properties Of Composites Research Articles

Effective properties of particulate composites with surface-varying interphases

Abstract A concept of equivalent inhomogeneity is adopted to facilitate analysis of effective properties of particulate composites with surface-varying interphases. The basic idea is to replace the inhomogeneity and its interphase by a single equivalent inhomogeneity, combining properties of both. It is illustrated considering spherical inhomogeneity with spring layer model of interphases. Due to surface-varying properties of the interphase the resulting equivalent inhomogeneity is anisotropic. Thus, the Method of Conditional Moment – developed for composites with anisotropic constituents – is applied in analysis of the effective properties of the composite. For particular case of homogeneous interphase, the results obtained here are compared with those available in the literature.

Implementation of multiphase piezoelectric composites energy harvester on aircraft wingbox structure with fuel saving evaluation

The multiphase composite with active structural fiber (ASF) has proven able to provide better optimization between actuating and load bearing capability compared to a pure piezoelectric material. In this paper, the multiphase composite application is further extended for energy harvesting purpose. The Double-Inclusion model combined with Mori-Tanaka method is implemented in a computational code to estimate the effective electro-elastic properties of the multiphase composite. The effective composite properties obtained via the present code are in good agreement with the analytical, experimental and finite element results. The multiphase composite with different composition is applied to a typical jet aircraft wingbox with 14.5 m halfspan. The energy harvesting evaluation by means of hybrid FEM/analytical piezoelectric energy harvester model is presented. A new procedure to investigate the trade-off between the aircraft weight, the fuel saving and the energy harvested is developed. The results pointed out that the equivalent fuel saved from the power generated by the wingbox is more than enough for 1 h Auxiliary Power Unit (APU) operation.

Micromechanical Constitutive Equations for the Effective Thermoelastic Properties of Carbon Nanotube-Reinforced Composites

Predicting thermomechanical properties of composites containing carbon nanotubes (CNTs) is significantly depending on the assumed microstructural parameters (MSPs) of CNTs and CNT/matrix morphology. These MSPs include geometry, dispersion and orientation. On the other hand, CNT/matrix morphology refers to two microstructural observations. The first is whether or not an interphase exists between CNTs and matrix, whereas the second is whether or not voids exist due to, for example, debonding of CNTs. In this work, the aim is to propose micromechanical constitutive equations, which are based on the micromechanics principles of Eshelby and Mori-Tanaka models, for considering all of these MSPs altogether in addition to the other well-known MSPs. Accordingly, these equations can be used for modeling realistic nanocomposites to predict their effective thermomechanical properties in different directions. The obtained computational results are compared with other results of both experimental and theoretical investigations found in the literature, and good agreement is obtained.

An asymptotic generalized self-consistent scheme for the effective rheological properties of viscoelastic composites

ABSTRACTThis study provides an asymptotic generalized self-consistent scheme for viscoelastic composites. The effective rheological properties are derived without using the inverse Laplace–Carson transform. It is shown that a viscoelastic composite made of a viscoelastic matrix and elastic inclusions can be perfectly represented by the same rheology of the matrix of which the effective rheological properties are functions of the viscoelastic properties of the matrix and the volume fraction as well as the elastic moduli of the inclusions. The solutions obtained herein can be also employed to study viscoelastic composites containing multi-coated inclusions or inclusions with imperfect interfaces.

Influence of stochastic variations in manufacturing defects on the mechanical performance of textile composites

This paper presents a methodology to evaluate the effects of microscopic manufacturing defects, namely fibre misalignment, waviness and volume fraction, on the mechanical performance. Influences of these defects on the effective elastic properties of composites are quantified by a dual homogenization method. For estimating stochastic characteristics of the properties induced by the variations in these defects, a probabilistic extension of the dual homogenization method is developed and numerically implemented through a perturbation-based stochastic finite element method. It is further incorporated in a multiscale finite element based reliability method to measure the influences of these manufacturing defects on structural performance in terms of reliability. The effectiveness of the proposed method in capturing defects is illustrated initially by investigating the effective elastic properties of a unidirectional fibre composite based yarn and then a plain woven textile composite. The capability of the proposed method in quantifying the variations in these defects is further demonstrated through statistical analysis of the effective elastic properties and a woven textile composite and structural reliability analysis of a textile composite laminate. This paper represents a significant advancement in the probabilistic prediction of the behaviour of woven and non-woven composites.

Effect of piezoelectric interphase on the effective magneto-electro-elastic properties of three-phase smart composites: A micromechanical study

ABSTRACTA unit cell-based micromechanical model is presented to investigate the effect of PZT-7A piezoelectric interphase on the effective magneto-electro-elastic properties of CoFe2O4 piezomagnetic matrix composites reinforced with piezoelectric fibers. The carbon fiber is coated with the PZT-7A piezoelectric material. The model is used to determine effective stresses, electric and magnetic field properties of the smart composite. By applying loads over the RVE of unit cell model in electric and magnetic fields, the in-plane strains, corresponding piezoelectric constants and corresponding piezomagnetic constants are obtained. The influences of interphase thickness on effective magneto-electro-elastic properties are investigated at different piezoelectric fiber volume fractions.

Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method

In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.

Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites

A stress-gradient material model was recently proposed by Forest and Sab (Mech. Res. Comm.40, 16–25, 2012) as an alternative to the well-known strain-gradient model introduced in the mid 60s. We propose a theoretical framework for the homogenization of stress-gradient materials. We derive suitable boundary conditions ensuring that Hill–Mandel’s lemma holds. As a first result, we show that stress-gradient materials exhibit a softening size-effect (to be defined more precisely in this paper), while strain-gradient materials exhibit a stiffening size-effect. This demonstrates that the stress-gradient and strain-gradient models are not equivalent as intuition would have it, but rather complementary. Using the solution to Eshelby’s spherical inhomogeneity problem that we derive in this paper, we propose Mori–Tanaka estimates of the effective properties of stress-gradient composites with spherical inclusions, thus opening the way to more advanced multi-scale analyses of stress-gradient materials.

N-Phase micromechanical framework for the conductivity and elastic modulus of particulate composites: Design to microencapsulated phase change materials (MPCMs)-cementitious composites

The smart design of microencapsulated phase change materials (MPCMs) in cementitious composites requires an explicit understanding of effects of soft microcapsule particles, stiff aggregates and their surrounding weak interfaces on the physico-mechanical properties of particulate composites. This paper devises a n-phase micromechanical framework to predict the effective thermal conductivity and elastic modulus of multicomponent particulate composites that consist in stiff and soft anisotropic-shaped inclusions, their surrounding weak interfaces and matrix. In this micromechanical model, the volume fraction of weak interfaces treated as the interphase model is quantified and incorporated into the n-phase differential effective medium model. It is found that the structural configuration of interfaces has a significant effect on the effective physico-mechanical properties of particulate composites. The micromechanical model leads to predictions of the effective conductivity and elastic modulus of multicomponent particulate composites to a good accuracy by comparing with available experimental data for regular concrete, quartz mortar and MPCMs-cementitious composites. By utilizing the micromechanical model, the authors further develop a theoretical design rule for the robust overall performance of MPCMs-cementitious composites with the better thermal resistance and elastic modulus. These results can also be used to design other multiphase particulate composites and porous media with the cherry-pit structure.

Effective thermoelectric conversion properties of thermoelectric composites containing a crack/hole

Despite the wide applications in engineering of thermoelectric materials, effective thermoelectric conversion behavior of cracked thermoelectric composites has never been investigated so far. To establish the effective properties of a thermoelectric composite, we revisit the general model of a bi-layered thermoelectric composite system with an interfacial crack and study the effect of interfacial cracking on the thermoelectric properties. Through an equivalent principle, the effective thermoelectric properties are given and the influence of applied temperature, crack boundary, crack size, and crack shape are discussed in detail. Generally, a higher effective figure of merit (thermoelectric conversion efficiency) can be obtained in a cracked thermoelectric composite. A significant increase of the effective figure of merit can be observed as the crack size getting larger. In practical engineering, the results in this paper will have a good approximation for cracked thermoelectric composites and can be directly used for design and optimization of thermoelectric devices.

Computation of effective electrical conductivity of composite materials: A novel approach based on analysis of graphs

In this work we continue the investigation of different approaches to conception and modelling of composite materials. The global method we focus on, is called ‘stochastic homogenization’. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic part is due to averaging over some series of samples, and the fact that these samples fit into the concept of RVE (Representative Volume Element) in order to reduce the variance effect.In this article, we present a novel method for computation of effective electric properties of composites – it is based on the analysis of the connectivity graph (and the respective adjacency matrix) for each sample of a composite material. We describe how this matrix is constructed in order to take into account complex microscopic geometry. We also explain what we mean by homogenization procedure for electrical conductivity, and how the constructed matrix is related to the problem. The developed method is applied to a test study of the influence of micromorphology of composites materials on their conductivity.

Design of Particulate-Reinforced Composite Materials.

A microstructure-based model is developed to study the effective anisotropic properties (magnetic, dielectric or thermal) of two-phase particle-filled composites. The Green’s function technique and the effective field method are used to theoretically derive the homogenized (averaged) properties for a representative volume element containing isolated inclusion and infinite, chain-structured particles. Those results are compared with the finite element approximations conducted for the assumed representative volume element. In addition, the Maxwell–Garnett model is retrieved as a special case when particle interactions are not considered. We also give some information on the optimal design of the effective anisotropic properties taking into account the shape of magnetic particles.

A study on the performance of piezoelectric composite materials for designing embedded transducers for concrete assessment

Ultrasonic measurements of concrete can provide crucial information about its state of health. The most common practice in the construction industry consists in using external probes which strongly limits the use of the method since large parts of the in-service structures are difficult to access. It is also possible to assess in real time the setting process of the concrete using ultrasonic measurements. In practice, the field measurement of the concrete hardening is limited by the formworks. As an alternative, some research teams have studied the possibility to directly embed the transducers into the concrete structures. The current embedded ultrasonic transducers are of two categories: bulk piezoelectric elements surrounded by several coating and matching layers and composites piezoelectric elements. Both technologies aim at optimizing the wave energy transmitted to the tested medium. The performances of the transducers of the first kind have been studied in a previous study. A fair amount of recent research has been focused on the development of novel cement-based piezoelectric composites. In this study, we first compare the effective properties of such cement-based materials with more widespread composites made with matrices of epoxy resins or polyurethane. The study only concerns the 1–3 fiber arrangement composites. The effective properties are computed using both an analytical mixing rule method and a finite element based homogenization method using representative volume elements (RVEs) which allows for considering more realistic fiber arrangements, leading yet to very similar results. The effective piezoelectric properties of cement-based composites appear to be very low compared to composites made of epoxy or polyurethane. This result is underlined by looking at the acoustic response and the electric input impedance of different piezoelectric disks where we compare performances of such transducers with a low-cost bulk piezoelectric disc element. The first radial mode of the latter is responsible for an acoustic response of the same order of magnitude as those for the piezo-composites. This result confirms that the design of efficient low-cost embedded ultrasonic transducers can be done with such piezoceramic disks.

Effective elastic properties of layered composites considering non-uniform imperfect adhesion

• Analytical expressions for elastic interlayer properties of layered composites. • Two-layer model considered with non-uniform imperfect adhesion. • The three-layer model provides an excellent approximation of the two-layer model. • Effective properties for layered composites by numerical/analytical models. In this study, the effective elastic properties of layered composites are predicted by considering the influence of non-uniform imperfect adhesion. In practical terms, the influence of non-uniform imperfection on the effective properties of layers is evaluated when debonding or delamination occurs between adjacent layers. Thus, the effective properties of two- and three-layer composites with imperfect and perfect interfaces are calculated using the finite element method and an analytical technique based on the two-scale asymptotic homogenization method, respectively. In the analyses, it was used a two-layer model with imperfect interface conditions and a three-layer model with perfect conditions to derive analytical expressions of the interlayer properties, which are equivalent to the effect of the imperfection (e.g., debonding). Our numerical results demonstrate that the three-layer model provides an excellent approximation of the two-layer one and it illustrates how the effective properties of the layered composites made from titanium Ti6Al4V and ceramic AD-96 are affected by non-uniform imperfect adhesion.

A Combined Self-Consistent Method to Estimate the Effective Properties of Polypropylene/Calcium Carbonate Composites.

In this work, trying to avoid difficulty of application due to the irregular filler shapes in experiments, self-consistent and differential self-consistent methods were combined to obtain a decoupled equation. The combined method suggests a tenor γ independent of filler-contents being an important connection between high and low filler-contents. On one hand, the constant parameter can be calculated by Eshelby’s inclusion theory or the Mori–Tanaka method to predict effective properties of composites coinciding with its hypothesis. On the other hand, the parameter can be calculated with several experimental results to estimate the effective properties of prepared composites of other different contents. In addition, an evaluation index of the interactional strength between matrix and fillers is proposed based on experiments. In experiments, a hyper-dispersant was synthesized to prepare polypropylene/calcium carbonate (PP/CaCO3) composites up to 70 wt % of filler-content with dispersion, whose dosage was only 5 wt % of the CaCO3 contents. Based on several verifications, it is hoped that the combined self-consistent method is valid for other two-phase composites in experiments with the same application progress as in this work.

Thermomechanical nonlinear analysis of axially compressed carbon nanotube-reinforced composite cylindrical panels resting on elastic foundations with tangentially restrained edges

ABSTRACTBuckling, postbuckling, and nonlinear responses of composite cylindrical panels reinforced by single-walled carbon nanotubes (CNTs), supported by an elastic foundation, exposed to elevated temperature and axially compressed by uniform load are investigated in this article. Distribution of CNTs is uniform or graded in the thickness direction and the effective properties of CNT-reinforced composite are assumed to be temperature dependent, and are estimated by extended rule of mixture through a micromechanical model. Governing equations are established based on thin shell theory taking von Kármán–Donnell nonlinearity, initial geometrical imperfection, Pasternak-type elastic foundation and tangential elastic constraints of boundary edges into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to derive explicit expressions of load–deflection relation from which critical buckling loads can be obtained. Unlike works in the literature, the present study accounts for elasticity of tangential restraint of two unloaded straight edges in model of cylindrical panel. The study also gives conditions for which bifurcation type buckling response can occur and novel findings in numerical examples.

Modeling the effective mechanical properties of “fuzzy fiber” composites across scales length

Abstract We employ a variant of generalized Eshelby's homogenization method to deduce effective properties of multilayered nanostructured fiber composites where one layer is highly heterogeneous with respect to its mechanical response strain gradients. We focus on carbon (C) fibers coated by carbon nanotubes (CNT) embedded in polymeric matrix with the aid of CNT “blistered” interphase layer developed between the coating and the matrix during processing and/or use. Each of the three phases is treated for simplicity by classical elasticity, while the interphase layer around the coated fibers (“fuzzy fibers”) to provide adhesion, and is treated by the simple gradient elasticity (GradELa) model. The novelty of the work lies on the fact of treating the CNT “fuzzy” layer by the GradEla model, that consequently allows to consider the extra gradient coefficient or internal length (characterizing this model) in relation to other constitutive and geometric parameters of the composite to optimize its overall mechanical properties and functionality. The method is general and can apply to treat other types of “fuzzy fiber” composites.

Aeroelastic assessment of cracked composite plate by means of fully coupled finite element and Doublet Lattice Method

This paper presents an investigation on flutter speed of cracked composite plates. This work is divided into two sections: (a) variation of crack length at a fixed location on the plate, and (b) variation of crack location on the plate with a fixed crack length, modelled as a unidirectional composite for 00,900 and 1350 orientations. Mori-Tanaka homogenization model is applied to obtain the effective composite constitutive properties as the function of fiber and matrix volume fraction. Doublet Lattice Method (DLM) is used to calculate the unsteady aerodynamic forces, i.e., lift distributions. It is found that the existence of small crack ratio on the composite plate (less than 0.4) has triggered an increment of the flutter speed. To support this statement, flutter response modes for each crack ratio are plotted, where the structure appears to be more stiffened than the undamaged plate. However, the crack results in the reduction of flutter speed when the crack ratio reaches 0.5. For the crack location assessment, the flutter speed increases as the crack location moves from the root to the tip due to the reduction of flutter frequency. The results show a good agreement with the validation using Strip Theory considering unsteady aerodynamics.

Computational Thermal Model of Unidirectional Composites with Random Fiber Array

The purpose of this work was to study the influence of microstructure on effective transverse thermal behavior of unidirectional fiber reinforced composites. Three types of microstructures are taken into account, including square periodic, hexagonal periodic and random arrangements of circular fibers. Unlike classical results at low fiber volume fractions and low thermal conductivity contrast between fibers and matrices, results provided by finite elements simulations for copper matrix composite reinforced with Carbon T-300 fibers have shown that random microstructures strongly affect the effective thermal properties of unidirectional composites for both high volume fractions and thermal conductivity contrast and can give closer predictions to the experimental results than the regular microstructures and the theoretical model.

横观各向同性基体复合材料的等效弹性常数

One of the main objectives of micromechanics is to predict the effective elastic properties of composites. Most existent explicit micromechanics models are based on an assumption of isotropic matrices and on that only 2-phase constituent materials are involved. In reality, a composite may possess a 3rd interphase between the fiber and the matrix, which is generally transversely isotropic. Accordingly, the prediction of the elastic properties of a 3-phase composite can be achieved through the combination of 2 kinds of 2-phase composites, to which a micromechanics model with transversely isotropic matrix should be applicable. The explicit bridging tensor elements to correlate the internal stresses of a transversely isotropic matrix with those of a reinforcing fiber in a concentric cylinder assemblage (CCA) model were derived firstly. Then this obtained bridging tensor was used to deduce analytical formulae for all the 5 effective elastic moduli of the composite made with the transversely isotropic matrix. An extension of the bridging model applicable to fiber reinforced transversely isotropic matrix composites was achieved as well. With properly chosen bridging parameters, the predicted elastic moduli of the composite with the 2 models are quite close to each other.