Two-phase Composite Material Research Articles

パレート解集合の非凸性及び多峰性を考慮した多目的最適化法による非均質材料の波動分散特性評価

The aim of this work is to estimate upper bounds of the Burnett coefficients in the high order homogenized wave equation, along with optimal microgeometries using a non-convex and mutimodal optimization method. We assumed that the two-dimensional unit cell is consist of a two-phase composite material with an 8-fold symmetry assumption. Under this geometrical assumption in the unit cell, the Burnett tensor is characterized by two scalar parameters. In order to estimate the upper bounds of the wave dispersion, we numerically compute Pareto fronts in the plane of the two scalar parameters under two equality constraints for the the phase proportions and for the homogenized tensor. The optimization problem is formulated considering a non-concave bound and solved using a shape optimization method.

Magnetic Properties of Two-Phase Composite Magnetic Material and Its Application to Electrical Equipment

A detailed research on the magnetic properties, preparation, and application of two-phase composite magnetic material was conducted in this paper. Firstly, in order to obtain the characteristics of high remanence and low coercivity, a micro field mathematical model of hysteresis was established and the magnetization model of this material was determined on the basis of micro magnetic theory. Secondly, the relationship between remanence and coercivity was analyzed and the preparation technology of the material was proposed from the perspective of the elemental composition, the heat treatment, and the other steps. Finally, after mastering the magnetization characteristic, conversion and control mechanism of the material, a new power transformer with function of DC bias compensation based on the two-phase composite magnetic material was proposed. The simulation and experimental results showed that the transformer could achieve a good compensation for the DC bias problem by using material remanence, which provides intelligent and energy-saving electrical equipment for the electric network safe operation. DOI: http://dx.doi.org/10.5755/j01.ms.21.4.9707

Analytical solution for Young's modulus of concrete with aggregate aspect ratio effect

This paper presents an analytical solution for Young's modulus of concrete with the aggregate aspect ratio effect. By taking the interfacial transition zone (ITZ)-coated aggregate as an ‘equivalent aggregate', the three-phase concrete is reduced to a two-phase composite material. The interaction direct derivative estimate is then adopted to derive an analytical solution for Young's modulus of concrete. After the validity of the analytical solution is verified with three sets of experimental results, the effects of various key factors on Young's modulus of concrete are evaluated quantitatively. The numerical results indicate that Young's modulus of concrete increases with an increase in maximum aggregate size, aggregate aspect ratio and Young's modulus of the aggregate, but decreases with increasing ITZ thickness. It is also found that the aggregate gradation has a certain influence on Young's modulus of concrete.

Analysis of Residual Stress Distribution in Anisotropic Thermo-Elastic Bimorph Systems

We present an analysis of residual stresses in longitudinal and transversal direction of a bimorph element induced by a change in external temperature field due to mismatch in thermal and elastic characteristics in dissimilar two-phase composite material with laminated structure. Representative Volume Element of the system is defined as a heterogeneous two-phase layered element bonded at an interface in a sense of coherent bi-layer, where each phase possesses distinct anisotropic material characteristics. We use a homogenization procedure with particular form of strain field, which satisfies compatibility equations in the bulk and at an interface. Special rule of mixtures derived from a spatial averaging principle yields explicit dependence of through-thickness residual stress on a compositional parameter defined as a volumetric fraction of one phase of the system.

OS1411-440 周期的な微視構造を有する弾性材料の寸法に依存した強度評価手法に関する研究

To estimate the strain energy caused by the macroscopic strain gradient, the relationship between strain gradient and its work conjugate higher order stress is formulated. Strain energy required for the macroscopic strain gradient of two-phase composite material was estimated by the Taylor, homogenization, extended Taylor and extended homogenization models. Extended models estimate the strain energy depend on the size of periodical microstructure.

Hashin–Shtrikman bounds on the effective thermal conductivity of a transversely isotropic two-phase composite material

This paper is concerned with the estimation of the effective thermal conductivity of a transversely isotropic two phase composite. We describe the general construction of the Hashin–Shtrikman bounds from first principles in the conductivity setting. Of specific interest in composite design is the fact that the shape of the inclusions and their distribution can be specified independently. This case covers a multitude of composites used in applications by taking various limits of the spheroid aspect ratio, including both layered media and unidirectional composites. Furthermore the expressions derived are equally valid for a number of other effective properties due to the fact that Laplace’s equation governs a significant range of applications, e.g. electrical conductivity and permittivity, magnetic permeability and many more. We illustrate the implementation of the scheme with several examples.

The simulation of inelastic matrix strains in cementitious materials using micromechanical solutions

A new approach is described for simulating inelastic behaviour in the matrix component of a two-phase composite material. Quasi-isotropic distributed micro-cracking, accompanying volumetric matrix changes, is combined with anisotropic micro-cracking arising from directional loading. An exterior point Eshelby solution is used to obtain stress concentrations adjacent to inclusions. The accuracy of these solutions is assessed using a series of three dimensional finite element analyses. A set of stress/strain paths are considered to illustrate the model’s characteristics. The model is then applied to the problem of autogenous shrinkage in a cementitious composite, giving results that compare favourably with experimental data.

Synthesis and Dielectric Behavior of a New Two-Phase Percolative BaTiO<sub>3</sub>-Cu/Polyimide Composite

The chemical reduction method was used to deposit copper nanoparticles (about 20nm) on the surface of the barium titanate (BT, r=50nm). Then the dielectric properties and the mechanism of BaTiO3-Cu/polyimide composite were studied. The results showed that the effective dielectric permittivity of the composite with 60 wt% of BT-Cu (less than 13.00 wt% of copper) fillers was greater than 120, and the dielectric loss of which was lower than 0.025. Due to very low dielectric loss, so this composite was a two-phase composite material, different from the three-phase composite (metal-ceramics-poly). It was concluded that copper nanoparticles were deposited on the surface of the BT nanoparticles by chemical bond. Owing to good dielectric properties of as-prepared composite, such new two-phase composites had a potential to become the most important ferroelectric material.

Study of extracellular matrix in vocal fold biomechanics using a two-phase model.

The extracellular matrix (ECM) of the vocal fold tissue consists primarily of fibrous and interstitial proteins. The purpose of this study was to investigate the effects of selective enzymatic digestion of two ECM proteins, namely elastin and versican, on the elasticity of rabbit vocal fold tissue. Quasi-static, sinusoidal, uniaxial tensile tests were performed. The data were analyzed within the framework of a model of the ECM as a two-phase composite material consisting of collagen fibrils as the reinforcing fibers and noncollagenous ECM proteins as the matrix. To validate the two-phase model, the regression parameters for the fibers' volume fraction and shear modulus in a different animal model were compared with corresponding published data. The proposed model was then used to analyze rabbit vocal fold tissues. The mean value and the standard deviation of the fiber volume fraction were found to be 8.49 ± 3.75 % for the control samples (n = 4), 0.59 ± 1.13 % after elastin removal (n = 4), and 8.22 ± 1.06 % after versican removal (n = 4). The results suggest that elastin removal may lead to a reduction in tissue stiffness, through counteracting the reinforcement of collagen fibrils.

Fan-beam geometry based inversion algorithm in computed tomography (CT) for imaging of composite materials

The investigation is concerned first with reconstruction of the density function of an object from computed tomography data. The projection (Fourier Slice) theorem is discussed for fan-beam geometry. A rebinning algorithm, based on the slant stacking approach, is introduced in order to transform fan-beam geometry data into its parallel-beam counterpart. The density function is reconstructed using a filtered back-projection algorithm. The sampling criteria for fan beam computed tomography are also derived. The MATLAB package has been utilized to implement these algorithms for the simulation of Shepp–Logan head phantom and implementation of the discrete normal Radon transform based on fan-beam geometry. The reconstruction of transverse cross-sectional micro-structures of fiber reinforced composite material test specimens has also been discussed. In addition, the MATLAB package has been utilized to demonstrate the image reconstruction of the cross-section of a two-phase composite material using parallel beam geometry (Radon transform).

Effective medium method for predicting the chloride diffusivity in concrete with ITZ percolation effect

In predicting the chloride diffusivity in concrete as a three-phase material, composed of aggregates, interfacial transition zone (ITZ), and bulk cement paste, not only the volume fractions, physical properties, and interactions of the three phase constituents but also the ITZ percolation effect should be taken into account. This paper attempts to develop an effective medium method to achieve this. Based on the stereological analysis of the aggregate size distribution and the statistical geometry of composites, the ITZ volume fraction is formulated analytically for the general aggregate gradation. By taking the ITZ-coated aggregate as an “equivalent aggregate”, the three-phase concrete is reduced to a two-phase composite material. An analytical solution is then derived for the chloride diffusivity in concrete applying the general effective medium theory. The primary advantage of the derived analytical solution is that the ITZ percolation effect and the Hashin–Shtrikman bounds are taken into account. Finally, the validity of the derived analytical solution is verified with two sets of experimental data and the effects of the ITZ thickness of and the chloride diffusivity in ITZ on the chloride diffusivity in concrete are evaluated through sensitivity analysis. The paper concludes that the presented analytical solution can predict the chloride diffusivity in concrete with an average relative error of 6%.

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin-Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations, and a new finite element model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.

Synthesis by spark plasma sintering of a novel protonic/electronic conductor composite: BaCe0.2Zr0.7Y0.1O3−δ /Sr0.95Ti0.9Nb0.1O3−δ (BCZY27/STN95)

A novel two-phase ceramic composite (cercer) material consisting of a solid solution of barium cerate and -zirconate doped with yttrium (BaCe0.2Zr0.7Y0.1O3−δ: BCZY27), together with niobium-doped strontium titanate (Sr0.95Ti0.9Nb0.1O3−δ: STN95), has been synthesized by solid-state reaction and sintered conventionally (CS) at 1350–1500 °C, as well as by spark plasma sintering (SPS) at 1300–1350 °C. CS samples were porous and exhibited high degrees of inter-phase reaction. Nickel oxide sintering aids did not improve CS sample density. In contrast, samples made by SPS were significantly denser (>95 %) and showed less reaction between phases. A pseudo-optimum SPS profile was developed, accounting for the effects of thermal expansion mismatch between BCZY27 and STN95. X-ray diffraction indicated secondary phases exist, but there was no indication of their presence at grain boundaries based on thorough study of these regions with high-resolution transmission electron microscopy and selective area electron diffraction. We thus suggest that these phases are present as independent grains in the bulk. It is believed these secondary phases inhibit electronic conductivity in the composite.

Near-room-temperature refrigeration through voltage-controlled entropy change in multiferroics

Composite materials with large magnetoelectric effect are proposed for application in advanced near-room-temperature refrigeration. The key innovation rests on utilizing the magnetocaloric effect in zero applied magnetic fields. This approach promises sizable isothermal entropy change and virtually temperature-independent refrigerant capacity through pure voltage-control. It is in sharp contrast with the conventional method of exploiting the magnetocaloric effect through applied magnetic fields. We outline the thermodynamics and estimate an isothermal entropy change specifically for the La0.7Sr0.3MnO3/Pb(Mg1/3Nb2/3)O3-PbTiO3(001) two-phase composite material. Finally, we propose structural variations of two-phase composites, which help in overcoming the challenging task of producing nanostructured material in macroscopic quantities.

Numerical analysis of the effect of coarse aggregate distribution on concrete carbonation

This paper presents the results of a mesoscopic numerical simulation of the influence of the distribution of coarse aggregate on concrete carbonation. In the study, concrete was considered as a two-phase composite material that consisted of cement mortar and coarse aggregate. The numerical simulation results indicate that the concrete carbonation depth decreased and its variation increased with the increased use of coarse aggregates or the increased fraction of relatively small aggregates. It was also found that, for the same coarse aggregate distribution, the variation of the concrete carbonation depth in the core area of the concrete increased with increased penetration depth of carbon dioxide (CO2). On the other hand, such variation in the boundary layers became less significant, since the coarse aggregate distribution density increased with the distance from the perimeter of the concrete.

INFLUENCE OF DIFFERENT FEED PHOSPHATE ON MECHANICAL PROPERTIES OF SWINE BONE TISSUE

The function of the highly complex structure such as the human skeletal system is possible by the appropriate construction and properties of bone tissue. Bone tissue, due to its design, is a material that continuously adapts its mechanical properties and structural response to the smallest change in load condition. Bone should be viewed as a twophase composite material, consisting of a collagen matrix with low elasticity and HA crystals with high elasticity modulus. The main mineral components of these crystals are Ca and P. The degree of digestibility of P compounds is affected by many factors, which include, type of feed, breed and species of animals, amount of vitamins and probiotics, and the ratio of Ca vs. P. The primary feed used in swine feeding is grain, which is also the main source of P that has in the form of phytate. This form of phosphorus is very difficult absorb as molecules of phytic. Consequently, in neutral pH phytate forms sparingly soluble complexes with amino acids, sugars and divalent metal cations, thus reducing its absorption. Amount of P supplied with the feed, even when supplemented by microbial phytase, does not cover the requirements of extensively growing pigs. The most frequently commercial products which are intended to supplement deficiencies are 1, 2 and 3-calcium, calcium-sodium, sodium-calcium-magnesium. Studies in literature (Jongbloed, 2000) present that the best results in swine nutrition is obtained when one or disodium phosphate is used. The main goal of this study was to determine the mechanical properties and elemental content of bone tissue derived from pigs fed with forage with different amounts of Ca and P. In addition, the study was to determine the fodder value of the new dicalcium phosphate feed (n-DCP) produced by the Gda sk Phosphate Fertilizer Plants' Fosfory Ltd. according to patent No. P-369805, when compared to monocalcium phosphate, calcium and sodium.

EVALUATION OF GENERALIZED CONTINUUM SUBSTITUTION MODELS FOR HETEROGENEOUS MATERIALS

Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.

Anisotropic constitutive model of plasticity capable of accounting for details of meso-structure of two-phase composite material

In this work, we discuss a novel anisotropic constitutive model of plasticity, which can be used to replace the classical phenomenological models for composite materials, like concrete, with marked difference of behavior in tension and compression. The model is constructed from fine scales by making use of the corresponding meso-scale representation of concrete distinguishing aggregate from cement paste. The elastic response and failure mechanisms at this scale are represented by the corresponding unstructured mesh of truss elements, which is shown to be capable of representing a number of fine features of inelastic response, such as the statistical isotropy of elastic response placed in-between the stringent Hashin–Shtrikman bounds, the pronounced difference of behavior in tension and compression, the sensitivity of bi-axial compression strength to the volume fraction of aggregate and the bi-axial fracture energy corresponding to each particular mode of failure. The results of this kind obtained with meso-model are then packed within a new meso-scale model with these enhanced features, which can be used to successfully replace the standard phenomenological models of concrete in ultimate state computations of complex structures providing increased predictive capabilities.

Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women

At the mesoscale (i.e. over a few millimeters), cortical bone can be described as two-phase composite material consisting of pores and a dense mineralized matrix. The cortical porosity is known to influence the mesoscopic elasticity. Our objective was to determine whether the variations of porosity are sufficient to predict the variations of bone mesoscopic anisotropic elasticity or if change in bone matrix elasticity is an important factor to consider. We measured 21 cortical bone specimens prepared from the mid-diaphysis of 10 women donors (aged from 66 to 98 years). A 50-MHz scanning acoustic microscope (SAM) was used to evaluate the bone matrix elasticity (reflected in impedance values) and porosity. Porosity evaluation with SAM was validated against Synchrotron Radiation μCT measurements. A standard contact ultrasonic method was applied to determine the mesoscopic elastic coefficients. Only matrix impedance in the direction of the bone axis correlated to mesoscale elasticity (adjusted R(2)=[0.16-0.25], p<0.05). The mesoscopic elasticity was found to be highly correlated to the cortical porosity (adj-R(2)=[0.72-0.84], p<10(-5)). Multivariate analysis including both matrix impedance and porosity did not provide a better statistical model of mesoscopic elasticity variations. Our results indicate that, for the elderly population, the elastic properties of the mineralized matrix do not undergo large variations among different samples, as reflected in the low coefficients of variation of matrix impedance (less than 6%). This work suggests that change in the intracortical porosity accounts for most of the variations of mesoscopic elasticity, at least when the analyzed porosity range is large (3-27% in this study). The trend in the variation of mesoscale elasticity with porosity is consistent with the predictions of a micromechanical model consisting of an anisotropic matrix pervaded by cylindrical pores.

Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities

This paper discusses a stochastic homogenization problem for evaluation of stochastic characteristics of a homogenized elastic property of a particle reinforced composite material especially in case of considering a non-uniform distribution of a material property or geometry of a component material and its random variation. In practice, some microscopic random variations in composites may not be uniform. In this case, a non-uniformly distributed random variation of a microscopic material or geometrical property should be taken into account. For this problem, this paper proposes a hierarchical stochastic homogenization method. This method assumes that a two-phase composite material can be separated into three-scales, and propagation of the randomness through the different scales can be evaluated with the perturbation-based technique. As an example, stochastic characteristics of homogenized elastic properties of a glass-particle reinforced plastic are estimated using the proposed approach. With the numerical results, importance of the problem and validity of the proposed method are discussed.