Three-phase Composites Research Articles

A coated inclusion-based homogenization scheme for viscoelastic composites with interphases

A coated inclusion-based homogenization scheme is developed for three-phase viscoelastic composites in the Laplace–Carson domain. The interphase between inclusion and matrix is considered as a coating in a composite-like inclusion and shows altered viscoelastic behavior compared to the matrix. The strain concentration equations between the viscoelastic inclusion and the viscoelastic coating are derived with two different models: the double inclusion (denoted DI) model, and the reconsidered double inclusion (RDI) model. Then, the homogenization scheme is based on a modified Mori–Tanaka scheme for three-phase viscoelastic composites, which is validated with the exact analytical formulation in the case of spherical composite inclusions and isotropic behaviors for all constituents. The comparison of the proposed coated inclusion-based homogenization scheme based on the RDI model with the exact analytical solution shows a significant improvement compared to the one based on the DI model in the prediction of effective properties for composites with interphases. Finally, considering experimental dynamic mechanical analyses (DMA) in the frequency domain for a carbon-black filled styrene butadiene rubber from the literature, the effective viscoelastic behavior is estimated with a good accuracy in terms of the storage and loss moduli for different volume fractions of composite inclusions.

Development of designing lightweight composites and structures for tailorable thermal expansion

Thermal expansion coefficient is an important parameter of thermal physical properties. Materials with zero thermal expansion (ZTE) are urgently needed in engineering applications, particularly in aerospace, precision instruments, and civil engineering, where the control of thermally induced expansion and stress over a wide range of temperatures is of significance. On the other hand, thermal expansion compensation requires materials to possess negative thermal expansion (NTE) and even a desirable positive thermal expansion (PTE). For example, thermal expansion modulation can be achieved via composites with an appropriate ratio of NTE inclusions and PTE substrates. In general, engineering applications have a serious need for materials and structures with tailorable CTEs. Hence, development of material with tailorable thermal expansion is of important scientific significance and engineering applications. At present, the available range of CTE in engineering materials is quite narrow. To obtain wide range of CTE, most of current researches are mainly concentrated on bulk materials and composites. Specifically, few bulk materials with low and negative CTEs have been reported. FeNi-based Invar alloysexhibit low CTEs because of the magneto-volume effect which, however, only exists under the Curie temperature (about 100°C). A family of ceramics with isotropic NTE and metal oxides with anisotropic NTEs, has been widely studied. Unfortunately, the inherent brittleness and low fracture toughness of the NTE ceramics restrict their usage in load-bearing applications. Fiber-reinforced composites are capable of providing tailorable CTEs because some fibers, such as carbon and graphite fibers, possess negative axial CTEs. However, largely different CTEs between the fiber and the matrix always result in matrix cracking under large temperature variation. Besides, through topology optimization of the three-phase composites, ZTE and the maximum uniaxial/biaxial stiffness characteristics can be obtained. However, the optimized geometries are still too complex for practical manufacture and engineering applications. It is important to integrate tailorable CTE with lightweight and robust mechanical properties for the materials. Lightweight composites attract intensive studies by virtue of their low density, excellent mechanical properties as well as tailorable thermal expansion coefficient. This paper firstly summarizes the significant engineering applications of thermal expansion controlling as well as the bulk materials with low and negative thermal expansion. Moreover, research achievements of the laminate, particle reinforced and topologically optimal composites with tailorable thermal expansion are detailly introduced. Finally, we present the latest research progress including geometry design methods, mechanisms, fabrication process and experimental characterization of tailorable thermal expansion for lightweight lattice composites. The design of lattice materials which are assembled through dual-material members, and honeycomb-like hybrid lattices which are composed of inner triangle and outside honeycomb initiates the macro scale lightweight lattice composites for tailorable CTE. However, the lattice composites with bending-dominated members display less stiffness compared with stretch-dominated lattices. Moreover, the complicated geometrical connections of the members lead to manufacture complexity. Triangle lattice composite exhibits tailorable CTE and are used as the basic unit to construct other lattice configurations such as the near zero thermal expansion lattice structures. Thus, numerous studies find the planar lattices and structures design based on this unit. With the development of advanced manufacturing technology, the study of the lightweight lattice composites will be promoted more deeply.

Efficient Removal Phenol Red over Ternary Heterostructured Ag-Bi2MoO6/BiPO4 Composite Photocatalyst

The fabrication of multicomponent composite systems may provide benefits in terms of charge separation and the retardation of charge pair recombination. In this work, a ternary heterostructured Ag-Bi2MoO6/BiPO4 composite was fabricated through a low-temperature solution-phase route for the first time. The XRD, SEM, EDX and XPS results indicated the prepared sample is a three-phase composite of BiPO4, Bi2MoO6, and Ag. Ag nanoparticles were photodeposited on the surface of Bi2MoO6/BiPO4 nanosheets, which not only increase visible-light absorption via the surface plasmon resonance, but also serve as good electron acceptor for facilitating quick photoexcited electron transfer. The interface between Bi2MoO6 and BiPO4 facilitates the migration of photoinduced electrons from Bi2MoO6 to BiPO4, which is also conductive to reduce the recombination of electron-holes. Thus, the ternary heterostructured Ag-Bi2MoO6/BiPO4 composite showed significant photocatalytic activity, higher than pure Bi2MoO6, BiPO4, and Bi2MoO6/BiPO4. Moreover, the possible photocatalytic mechanism of the Ag-Bi2MoO6/BiPO4 heterostructure related to the band positions of the semiconductors was also discussed. In addition, the quenching effects of different scavengers revealed that the reactive ·OH and O2·− play a major role in the phenol red decolorization.

Multiphase Differential Scheme for Effective Properties of Magnetoelectroelastic Composite Materials

The differential scheme is extended to predict the effective properties of multiphase magnetoelectroelastic composite materials. The prediction of effective properties is done gradually by adding a series of incremental additions of a small volume of particulate phase materials to an initial material (matrix phase). The construction process is compatible with high volume concentration of inclusion. A system of coupled differential equations is formulated and its numerical solution leads to effective properties of reinforced magnetoelectroelastic composites. For the numerical results, two-phase and three-phase magnetoelectroelastic composites are considered. The effective properties are presented as function of volume fractions and shapes of inclusions and compared with predictions based on the Mori–Tanaka and incremental self-consistent models.

The influence of two-point statistics on the Hashin–Shtrikman bounds for three phase composites

In this work we analyse the influence of the spatial distribution function, introduced by Ponte Castañeda and Willis (1995), on the Hashin–Shtrikman bounds on the effective transport properties of a transversely isotropic (TI) three-phase particulate composite, i.e. when two distinct materials are embedded in a matrix medium. We provide a straightforward mechanism to construct associated bounds, independently accounting for the shape, size and spatial distribution of the respective phases, and assuming ellipsoidal symmetry.The main novelty in the present scheme resides in the consideration of more than a single inclusion phase type. Indeed, unlike the two-phase case, a two-point correlation function is necessary to characterize the spatial distribution of the inclusion phases in order to avoid overlap between different phase types. Moreover, once the interaction between two different phases is described, the scheme developed can straightforwardly be extended to multiphase composites.The uniform expression for the associated Hill tensors and the use of a proper tensor basis set, leads to an explicit set of equations for the bounds. This permits its application to a wide variety of phenomena governed by Laplace’s operator. Some numerical implementations are provided to validate the effectiveness of the scheme by comparing the predictions with available experimental data and other theoretical results.

Ag-NBCTO-PVDF composites with enhanced dielectric properties

Three-phase composites with enhanced dielectric permittivity and low dielectric loss were prepared by incorporating the giant dielectric permittivity material Na0.5Bi0.5Cu3Ti4O12 (NBCTO) and conductive Ag nanoparticles in Poly(vinylidene fluoride) (PVDF) polymer matrix by melt mixing and hot pressing process, in which the filler content (volume fraction) of Ag nanoparticles and NBCTO powders was set at 50vol% and PVDF was set at 50vol%. The structure and thermal stability of the composites were characterized using X-ray diffraction (XRD) and thermo-gravimetric analysis (TGA). Studies on the dielectric properties of composites in the frequency range from 10 to 106Hz showed that the Ag-NBCTO-PVDF composite exhibited high dielectric permittivity of 222.4 and low loss tangent of 0.32 at 1kHz when the content of Ag was 5vol%. A percolation threshold of fAg=5.9vol% was calculated through the percolation theory.

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.

Interphase effects on the thermo-mechanical properties of three-phase composites

A three-dimensional micromechanics-based analytical model is developed to investigate the influence of interphase on the thermo-mechanical properties of three-phase composites. The representative volume element (RVE) of composites is extended to c × r × h cells in three dimensions and the RVE consists of three phases including filler, matrix and interphase. The arrangement state of filler within the matrix materials is assumed to be random with uniform distribution. Fillers are surrounded by the interphase in the whole composite. The effects of interphase such as its thickness and stiffness on the thermo-mechanical properties of composite with various aspect ratios of filler are studied. The results illustrate that while the effects of interphase is significant for composites with randomly distributed spherical particles, it turns to be less effective as the aspect ratio of filler of composite increases. Moreover, the results demonstrate that the effect of interphase on the thermo-mechanical properties of fibrous composites in the transverse direction is more significant than that of fiber composites in the longitudinal direction.

Deformation behaviors of peat with influence of organic matter.

Peat is a kind of special material rich in organic matter. Because of the high content of organic matter, it shows different deformation behaviors from conventional geotechnical materials. Peat grain has a non-negligible compressibility due to the presence of organic matter. Biogas can generate from peat and can be trapped in form of gas bubbles. Considering the natural properties of peat, a special three-phase composition of peat is described which indicates the existence of organic matter and gas bubbles in peat. A stress–strain–time model is proposed for the compression of organic matter, and the surface tension effect is considered in the compression model of gas bubbles. Finally, a mathematical model has been developed to simulate the deformation behavior of peat considering the compressibility of organic matter and entrapped gas bubbles. The deformation process is the coupling of volume variation of organic matter, gas bubbles and water drainage. The proposed model is used to simulate a series of peat laboratory oedometer tests, and the model can well capture the test results with reasonable model parameters. Effects of model parameters on deformation of peat are also analyzed.

Magneto-electro-elastic properties of multiferroic composites containing periodic distribution of general multi-coated inhomogeneities

In this paper, a homogenization scheme with several desirable features is developed to determine the overall magneto-electro-elastic behavior of multiferroic composite materials containing periodic distribution of multi-inhomogeneities. The configuration of a typical inhomogeneity system is taken to be composed of an inner ellipsoidal particle surrounded by many coating layers of ellipsoidal shape. As such, the morphology of composite is sufficiently general, and then the developed methodology can be quite robust to handle a wide range of problems. Through the present analysis, we first adopt the equivalent inclusion principle in conjunction with a superposition procedure to decompose the multi-inhomogeneity system into a series of single-inclusion problems with position-dependent eigenstrain–electric–magnetic fields. The periodic microstructure will be accounted for through the Fourier series expansion of field quantities. The local form of consistency equations are then called upon, and integrated to give the expression for the average eigenfields. Finally, considering the relation between far-field loads and the local microscopic fields in the constituent phases the overall effective moduli of composite are obtained in terms of derived average eigenfields. The accuracy and generality of proposed theory is verified through consideration of several three-phase multiferroic composites with complex microstructures. In this process, the strong dependence of overall behavior of fibrous and particulate multiferroics on the microstructure parameters, such as the interface condition, thickness, eccentricity and material properties of core inhomogeneities and their coating layers is well demonstrated.

Analytical effective elastic properties of particulate composites with soft interfaces around anisotropic particles

Understanding the effects of interfacial properties on effective elastic properties is of great importance in materials science and engineering. In this work, we propose a theoretical framework to predict the effective moduli of three-phase heterogeneous particulate composites containing spheroidal particles, soft interfaces, and a homogeneous matrix. We first derive the effective moduli of two-phase representative volume elements (RVEs) with matrix and spheroidal inclusions using the variational principle. Subsequently, an analytical model considering the volume fraction of soft interfaces around spheroidal particles is presented. The effective moduli of such three-phase particulate composites are eventually derived by the generalized self-consistent scheme. These theoretical schemes are compared with experimental studies, numerical simulations, and theoretical approximations reported in the literature to verify their validity. We further investigate the dependence of the effective elastic modulus on the interfacial properties and the geometric characteristics of anisotropic particles based on the proposed theoretical framework. Results show that the interfacial volume fraction and the effective elastic modulus of particulate composites are strongly dependent on the aspect ratio, geometric size factor, volume fraction, and particle size distribution of ellipsoidal particles.

An interphase model for effective elastic properties of concrete composites

In this work, the Eshelby tensor of a finite spherical domain is employed to construct an interphase model to evaluate elastic properties of concrete composites. Explicit formulations of the interphase model via multi-inclusion method for a class of concrete composites are derived. The theoretical estimate based on an improved Hashin–Shtrikman bounds for the Young’s modulus of two-phase concrete composite material are used as a comparison result in the analysis, and the influence of the interfacial transition zone (ITZ) on elastic properties of three-phase concrete composite is studied. Moreover, the homogenization results predicted by the proposed interphase model are compared with the published experimental data. Results obtained in this work show that the proposed interphase model can provide a very accurate estimate of the effective elastic properties of complex concrete composite materials.

Transient liquid phase spark plasma sintering of B4C-based ceramics using Ti-Al intermetallics as sintering aid

Fully-dense B4C-based ceramics were fabricated using Ti-Al intermetallics as sintering aid by Spark Plasma Sintering at a low temperature of 1700°C whilst applying 32MPa uniaxial pressure. The influence of the intermetallic additions on the phase composition, morphology and mechanical properties of the ceramics were investigated. The intermetallics flowed and react with B4C to form a three-phase composite containing B4C, TiB2 and Al4C3 during the transient liquid phase sintering process. The TiB2 and Al4C3 particles were located on the boundaries between B4C grains and effectively inhibited the growth of B4C, which improved the mechanical properties. Good bonding between B4C and the phases formed was confirmed by TEM analysis. The specimens with 5wt.% Ti-Al provide an attractive combination of homogeneous morphology and excellent mechanical properties, including a Vickers hardness of 33.5±0.4GPa, a flexural strength of 506±16MPa and a fracture toughness of 5.5±0.1MPam0.5.

Orientation relationships, interface structures, and mechanical properties of directionally solidified MoSi2/Mo5Si3/Mo5Si3C composites

The microstructures, orientation relationships, and high-temperature deformation behavior of directionally solidified (DS) ingots of MoSi2/Mo5Si3/Mo5Si3C three-phase eutectic composites were investigated. The DS three-phase composites exhibit a fine and homogeneous script lamellar microstructure. Mo5Si3 and Mo5Si3C individually form interconnected networks that extend in the growth direction (GD) of the MoSi2 matrix and maintain [11¯0]MoSi2, [001]Mo5Si3, and [0001]Mo5Si3C approximately parallel to the GD. High-temperature strength is higher in the DS three-phase composite than in the binary two-phase counterpart, especially below 1200 °C. This is mainly because of MoSi2 matrix refinement and the presence of the strengthening phase Mo5Si3C. The observed orientation relationship between component phases is discussed in relation to lattice misfits.

Radial fracture in a three-phase composite: Application to wellbore cement liners at early ages

Little understanding exists between the early-age stress developments in a wellbore cement sheath and its risk of impairment. During hydration, the cement morphology and pore-pressure changes induce eigenstresses in the solid and pore volumes. Utilizing these stresses as the driving mechanism of fracture, this paper formalizes the inspection of a radial crack in an elastic cement sheath constrained by an inner steel casing and an outer rock formation. The solution is constructed in the framework of analytic function theory and seeks the Green’s function for an edge dislocation in the intermediate cement phase. A dislocation pile-up along the line of fracture constructs a singular integral equation for the crack opening displacement derivative, from which the energy release rate is readily deduced.Under the uniform development of eigenstresses, the stiffness ratios of steel-to-cement and rock-to-cement generally predict the crack to initiate along the steel-cement interface. Here, the impacts of (i) a rigid bond and (ii) a sliding interface with no shear are assessed. This leads to the primary result of the paper: the potential for radial fracture is substantially mitigated by ensuring the shear connection between the steel casing and the cement sheath.

颗粒/纳米复合材料细观损伤及本构关系分析

本文得到了带有弱化表面的颗粒增强复合材料的本构模型，其可以描述颗粒的脱黏破坏以及基体的塑性和颗粒对复合材料损伤的影响。此损伤模型是基于Eshelby等效夹杂方法和自洽方法，假设基体、完整颗粒和带有弱化表面的颗粒都属于复合材料的夹杂体，根据Eshelby细观力学的方法，通过数值计算估算出三相颗粒增强复合材料的有效弹性模量。得出在复合材料损伤过程中，颗粒体积分数变化对颗粒复合材料有效刚度的影响，并且通过分析计算说明颗粒的体积分数与尺寸对复合材料应力–应变关系的影响。 This paper deals with a constitutive model of particulate-reinforced composites (PRCs) with weakened interfaces, which can describe the evolution of debonding damage, matrix plasticity and particle effects on deformation and damage. This damage model is based on the Eshelby’s equivalent inclusion method and self-consistent method. It is assumed that the intact particle, the particle with a weakened interface and matrix are all inclusions of composites. According to the Eshelby’s micromechanics method, the effective elastic modulus of three-phase composites is estimated through a numerical calculation. The influence of particle volume fraction change on the effective stiffness of particle composites can be predicted during the material damage process. This article also illustrates the influences of particle volume fraction and size on the stress-strain relation of composites.

Solutions of a crack interacting with a three-phase composite in plane elasticity

The interaction between a crack and a circularly cylindrical layered media under a remote uniform load for plane elasticity is investigated. Based on the method of analytical continuation associated with the alternation technique, the solutions to the crack problem for a three-phase composite are derived. A rapidly convergent series solution for the stress field, expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The solution procedures for solving this problem consist of two parts. In the first part, the complex potential functions of dislocation interacting with a three-phase composite are obtained. In the second part, the derivation of logarithmic singular integral equations by introducing the complex potential functions of dislocation along the crack border is made. The stress intensity factors (SIFs) are then obtained numerically in terms of the dislocation density functions of the logarithmic singular integral equations. The stress intensity factors (SIFs) as a function of the dimensionless crack length for various material properties and geometric parameters are shown in graphic form. The obtained results may provide some guidance for material and geometry selections by minimizing the SIF.

Analysis of fibrous elastic composites with nonuniform imperfect adhesion

In most composites, the fiber–matrix adhesion is imperfect; the continuity conditions for stresses and displacements are not satisfied. In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method (AHM), for three-phase fibrous composites (matrix/mesophase/fiber) with parallelogram periodic cell. Interaction between fiber and matrix is considered, and this is called the mesophase model where the nonuniform mesophase is studied. Besides, there is another type of matrix–fiber contact which is called nonuniform spring imperfect contact. In this case, the contrast or jump of the displacements in the boundary of each phase is proportional to the corresponding component of the tension in the interface in terms of a parameter given by a certain function that depends on the position. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The three-phase model is validated by the Finite Element Method and the AHM both approaches applied to two-phase composites with nonuniform spring imperfect contact. Comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of composites with presence of nonuniform imperfect interface and parallelogram cell. The effect of the nonuniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.

Micromechanics of stress transfer through the interphase in fiber-reinforced composites

A micromechanical model to predict the interphasial/interfacial stress transfer in a three-phase fiber-reinforced composite is presented. The axisymmetric system consists of a fiber embedded in a compliant matrix having an interphase between them. Each constituent of the composite is regarded as a linear elastic continuum. The matrix is treated as an isotropic material while the fiber and interphase are considered as a transversely isotropic material. Traction-free boundary conditions are strictly enforced. It is assumed that the interfaces are perfect and strong. A pair of uncoupled governing partial differential equations is obtained in terms of unknown displacements. Furthermore, assuming that the Eigenvalues exist for this system of equations, Eigenfunction expansion method is employed to derive an exact solution in terms of the Bessel functions. Analytical solutions are obtained for free boundary conditions at the external surface of the matrix cylinder to model a single fiber pull-out problem, and for fixed boundary conditions to approximately model a hexagonal array of fibers in the matrix material. This formulation provides an analytical framework for the analysis of interphasial and interfacial stresses as well as displacements in the entire 3D axisymmetric system. Finite element (FE) analysis was also performed to simulate stress transfer from the fiber to the matrix through the interphase. Analytically obtained stress fields are verified with FE results. Shear and radial interphasial stresses provide insight into the design of engineered interfaces/interphases.

Interphase Model for Effective Moduli of Nanoparticle-Reinforced Composites

AbstractA novel interphase model is constructed based on the double-inclusion theory and the Eshelby tensor in a finite domain, which can be used to calculate the effective material properties of three-phase composites. The refinement of the double-inclusion theory takes into account the effect of a finite matrix and that of a finite interphase. In the model proposed, the multiphase composites are reinforced by different material fillers, which are embedded in a matrix with finite size. The general formulations are derived following the method of Eshelby’s equivalent inclusion. The Dirichlet and Neumann Eshelby tensors for a spherical inclusion in a finite spherical domain are applied to the homogenization of composite materials. By the explicit inversions of the fourth-order tensors involved, the relationships between the elastic moduli of transversely isotropic and orthotropic materials are derived, which are then validated through numerical results from the homogenization of several Al2O3/mullite/Al co...