Two-phase Composites Research Articles

Average Eshelby tensor of an arbitrarily shaped inclusion from convexity to non-convexity: Effective elastic properties of composites

The effective mechanical properties of composites are strongly influenced by the morphology, volume fraction, and properties of the inclusion phase. Extensive theoretical models for the evaluation of effective properties are mainly based on the continuum micromechanics derived from the well-known Eshelby’s solution of an ellipsoidal inclusion problem, which are subjected to the limitations on the Eshelby tensor for a non-ellipsoidal inclusion. This work devises a three-step method to derive the average Eshelby tensor of an arbitrarily shaped inclusion from convexity to non-convexity in an elastic field. The proposed three-step method is user-friendly and avoids the singularity that arises from solving the complicated integrals for an arbitrarily shaped inclusion. The calculated average Eshelby tensors of inclusions with different morphologies, including Platonic solids, superballs, superellipsoids, doughnuts, helices, and non-convex particles, are thereafter compared against the existing data reported in the literature, in order to verify the reliability of the present method. Moreover, we also incorporate the proposed method into a micromechanical model to predict the effective elastic moduli of two-phase composites, in which congruent non-ellipsoidal inclusions of a specific volume fraction are randomly distributed in a homogeneous matrix. Comparisons with the direct finite element method (FEM) simulations indicate that the developed micromechanical model is a reliable means to evaluate the elastic properties of composites. The proposed average Eshelby tensor of an arbitrarily shaped inclusion can also be generalized to the theoretical predictions of the effective transport properties of composites with inclusions of diverse types and shapes, such as particles, rocks, granules, pores, fibers, and cracks.

Study on Key Mechanical Parameters of High-Strength Grouting Material

In order to better design and calculate in infrastructures, it is necessary to clarify the key mechanical parameters of structural materials, such as axial compressive strength, elastic modulus and Poisson’s ratio. High-strength grouting material (HSGM) have begun to be used as structural materials with the development of large and complex structures. A large number of test dates were used to analyze the relationship between the axial compressive strength and the cubic compressive strength of HSGM in the paper. ABAQUS software was used to model the specimens of axial compressive strength, and the strain cloud maps of concrete and HSGM were compared and analyzed. By considering HSGM as two-phase (sand and paste) composites, the relationship between elastic modulus of HSGM and mechanical parameters of component materials was derived, and the test results of the mechanical properties of HSGM with different ratios of sand to cement were used for verification. The test results show that the axial compressive strength of the HSGM is closer to the cubic strength than that of the concrete material, which accords with the finite element analysis results. The elastic modulus of high-strength grouting material conforms to the theoretical derivation of two-phase material. The material composition is one of the main factors affecting the elastic modulus. Poisson’s ratio range of high-strength grouting material is 0.25 ± 0.01 by statistical analysis.

Constitutive modeling of oriented and non-oriented magnetostrictive particulate composites

This study presents a mathematical framework for two-phase magnetostrictive composites composed of oriented or non-oriented magnetostrictive Terfenol-D particles embedded in passive polymer matrices. The phase constitutive behavior of the monolithic Terfenol-D with arbitrary crystal orientations is represented by a recently developed discrete energy averaged model. This unique Terfenol-D constitutive model results in close-form and linear algebraic equations accurately describing the nonlinear magnetostriction and magnetization in magnetostrictive composites subjected to a given loading or magnetic field increment. The effectiveness of this new mathematical framework in capturing magnetostrictive particle size orientation, phase volume fractions, mechanical loading conditions, and magnetic field excitations are validated using a series of experimental data available in literature. Compared to existing models that prevalently addressed particle orientation in composite constitutive level, the model framework in this study directly handles particle orientation in the phase constitutive level, and therefore achieves enhanced efficiency while maintaining comparable accuracy.

Laser ablation of RB-SiC composite by femtosecond laser irradiation

Reaction-bonded silicon carbide composites (RB-SiC), consisting of SiC grains and Si matrix, have a complex ablation mechanism as two-phase composites under femtosecond laser irradiation. The ablation threshold of RB-SiC was calculated, which decreases (from 1.01 J/cm2 to 0.56 J/cm2) with increasing pulse number N and finally stabilized. At low fluence (F/Fth ≤ 5) and a low number of pulses, photochemical ablation dominates. For a higher number of pulses and high fluence (5 <F/Fth ≤ 50), photothermal ablation dominates with photochemical ablation. The results show that structures such as pits, convex, and holes exist on the surface of Crater I, while Laser-induced Periodic Surface Structures (LIPSS), and condensation structures exist on the surface of Crater II. In both types of ablation craters, the SiC grain surface produces the Low Spatial Frequency LIPSS (LSFL) with a period of about 900 nm and the High Spatial Frequency LIPSS (HSFL) with a period of about 300 nm. Based on the surface morphology, microstructure, and physical phase analysis of the ablation craters, a preliminary model of the removal mechanism of the ablation craters by femtosecond laser irradiation was established. These findings are expected to provide theoretical and experimental support for the precision processing of RB-SiC by femtosecond laser.

Two-scale concurrent optimization of composites with elliptical inclusions under microstress constraints within the FE2 framework

In order to avoid the adverse effects of structural damage caused by stress concentration, the optimization problem considering stress constraints is very important in structural design. This paper aims at introducing microstress constraints within a multilevel finite element (FE2) analysis framework to perform the two-scale concurrent optimization and reduce the stress concentration while exhibiting better overall stiffness properties for composites with elliptical inclusions. In order to do that, at the macroscale, relying on the solid isotropic material with penalization (SIMP), a density-based optimization algorithm is raised for a maximum stiffness design and free material distribution optimization under a volume constraint, these displacement solutions and material distributions at the macroscopic structural scale provide kinematic constraints for microscale optimization. At the microscale, the parameterized composite microstructure (inclusion orientation and aspect ratio) is optimized under the principal strain direction constraints of the macroscale element’s Gauss integration point. The optimized microstructure in turn updates the macroscopic effective stress directly from the volume average of the microscopic stress field. The clustering strategy is used in order to improve the computation efficiency of the optimization. The novelty of the work lies in the use of microstress constraints to solve the concurrent optimization problems of two-phase composites within the FE2 framework. The effectiveness of the proposed concurrent optimization approach is validated through three numerical examples.

Pop-in phenomenon at nanoindentation and fracture toughness of two-phase ceramic composites

Material’s resistance to crack propagation corresponds to its fracture toughness. This characteristic can be calculated in laboratory tests, e.g. 3-point bending of notched bars or by indentation test. Spherical, conical, or pyramidal tips can be used during nanoindentation and micro indentation tests, e.g. Vickers, Berkovich, or Cube-Corner tip.The lower level of fracture toughness is a key parameter of ceramic materials and this attribute is not frequently investigated by nanoindentation. If the load force is quite small, an extra increase in penetration depth can occur, which can be described as the pop-in phenomenon.This paper shows the results of nanoindentation tests with the use of cube-corner tips and load levels of 2 mN and 5mN. Five types of ceramic composites Al2O3/ZrO2 with composition ratios of 20, 40, 60, and 80 wt% of Al2O3 content were tested. To estimate the fracture toughness by calculating the crack length force–displacement curves with visible pop-in phenomenon were selected for analysis.

Manipulation of the thermal conductivity for two-phase WC-Ni composites through a microstructure-based model along with key experiments

Thermal conductivity, one of critical properties for composite materials, constitutes an indispensable part of high-efficient materials design. However, a quantitative model to describe the thermal conductivity of two-phase composites has yet to be developed. In this work, we proposed an effective evaluation framework of a microstructure-based thermal conductivity model with key inputs from CALPHAD-type approach. Two-phase WC-Ni composites with Ni–W solid-solution matrix were used as the target system to validate this framework combined with key thermal conductivity measurements. Calculated thermal conductivities agree well with experimental results within the experimental error of 10%. Applying this well-established framework, thermal conductivities depending on wide ranges of temperature, WC grain size (dWC), and phase constitution are predicted, suggesting some unique features. The thermal conductivity becomes less dependent on dWC when dWC is >3 μm. Additionally, the thermal conductivity of nano-sized WC-Ni shows a quite different temperature-dependent variation tendency in contrast to that of micron-sized WC-Ni. These correlations are found and quantitatively described in the present work. Furthermore, the thermal conductivity for WC-Ni carbide rolls is predicted by the established framework, demonstrating a high accuracy. The present work is expected to guide the design of composite materials with desirable thermal properties efficiently.

A binary-medium-based constitutive model for geological materials based on the statistical meso-breakage concept and mean-field homogenization

This paper is devoted to determining the inelastic responses of geological materials by the binary-medium-based constitutive model. The geomaterials are conceptualized as two-phase composites that are composed of the bonded medium of elastic–brittle nature and the frictional medium of elastoplastic nature. The evolution of meso-structure upon loading is considered by the progressive transformation of the bonded medium into the frictional medium. By introducing the statistical meso-breakage concept, the breakage ratio indicating the degree of such transformation is determined by statistical approaches. The interactions among inclusions (the bonded medium) and matrix (the frictional medium) and the influence of the varying breakage ratio are considered with the help of the double-inclusion model within the framework of the mean-field homogenization scheme. An application is presented for the structured/bonding geomaterials based on the proposed model. The comparisons between computed results and experimental data of three kinds of structured soils show that the proposed model can reproduce the typical behaviors of cemented/structured geomaterials.

TG, DSC, XRD, and SEM studies of the substituted lithium ferrite formation from milled Sm2O3/Fe2O3/Li2CO3 precursors

Formation of substituted lithium ferrite Li0.5SmxFe2.5–xO4 (where x = 0.06 and 0.2) from Sm2O3/Fe2O3/Li2CO2 precursors was studied by X-ray diffraction analysis, thermogravimetry, differential scanning calorimetry, and scanning electron microscopy. The mixture of powders was subjected to preliminary mechanical activation in a planetary mill. We analyzed samples based on the precursors and synthesized at 900 °C for 4 h in a laboratory furnace. It was found that ball milling of the precursors mixture in a planetary mill increases the powder reactivity. In spite of this, no substituted lithium ferrites were formed. It was shown that a two-phase composite that consists of pure lithium ferrite Li0.5Fe2.5O4 and SmFeO3 is formed during synthesis. An increase in the Sm2O3 content in the initial mixture provides an increase in the amount of the formed SmFeO3 phase. The synthesis of Li0.5Fe2.5O4 ferrite was confirmed by XRD analysis data, the Curie temperature (627–630 °C) measured using TG analysis in a magnetic field, and by the presence of an endothermic peak on the DSC curve corresponding to the order–disorder transition in the Li0.5Fe2.5O4 phase.

An extended Hill’s lemma for non-Cauchy continua based on the modified couple stress and surface elasticity theories

An extended Hill’s lemma is provided for non-Cauchy continua satisfying the modified couple stress theory in the bulk and the surface elasticity theory in the surface layer. Based on the Hill–Mandel condition, four sets of boundary conditions (BCs) are identified. It is shown that each of these four sets of BCs satisfies the admissibility and average field requirements. In addition, the set of kinetic BCs meets the force and moment balance conditions, and the set of modified kinematic BCs satisfies the displacement and micro-rotation compatibility constraint. By applying the newly extended Hill’s lemma, a homogenization analysis of a two-phase composite is performed, in which the average strain energy of the composite is computed using a finite element model constructed using COMSOL. The effective elastic constants obtained in this analysis are found to satisfy the Voigt and Reuss bounds.

The effect of random field parameter uncertainty on the response variability of composite structures

The accurate quantification of the random spatial variation of material properties at different scales is crucial for the systematic propagation of uncertainties through engineering models. In a previous work, the spatial variability of the apparent material properties of two-phase composites has been quantified in a Bayesian framework. This framework enables a consistent modeling of the statistical uncertainty in the parameters of the respective mesoscale random fields and also allows selecting the most plausible correlation model among different models belonging to the Matérn family. In this work, the most plausible random field model is employed in the context of uncertainty propagation of composite structures. Sample functions of the mesoscale random fields are generated using a covariance decomposition approach and the response variability of various composite structures is computed through Monte Carlo simulation. Parametric investigations are conducted to highlight the effect of the identified parameter uncertainty on structural response variability.

Analysis of electrical conductivity of carbon nanotube-reinforced two-phase composites

This short paper presents a simple approach for calculating the effective electrical conductivity of carbon nanotubes-reinforced two-phase composite materials. The approach is developed by modifying the traditional effective medium approximation to include the effect of percolation threshold. The predicted electrical conductivity from the present approach is validated by using published experimental results. It is shown that the effective electrical conductivity of two-phase composites can be calculated by using the lower bound of the effective medium approximation if the inclusion volume fraction is below its percolation threshold, and the projection of the upper bound of the effective medium approximation if the inclusion volume fraction exceeds its percolation threshold.

Effective nonlinear responses of three-phase magnetoelectric composites

A computational method, dubbed simplified unit-cell micromechanics model, is generalized and applied to establish the effective nonlinear responses of three-phase magnetoelectric composites that are composed of two distinct magnetostrictive and piezoelectric phases embedded in elastic polymer matrices. The nature of nonlinear constitutive behavior of each constituent is expected to significantly influence the overall responses of the composites. To obtain the effective nonlinear responses, a mathematical linearization is first introduced to perform the constitutive linearization for the nonlinear materials, and the resulting constitutive equations are then unified and nested into the micromechanics model followed by iterations in order to minimize errors from the linearization process. For the purpose of comparison, we also reformulate the well-established Mori–Tanaka micromechanics model insofar as its mathematical structure is aligned with that of the simplified unit-cell model. Numerical results are first validated against limited experimental measurements available in literature. Parametric studies are then conducted in order to reveal the effect of phase constitutive laws, volume fractions, and geometries on the overall nonlinear responses of there-phase magnetoelectric composites. The contributions of this work complement those of earlier studies that prevalently devoted to two-phase magnetoelectric composites and linear magneto-electro-elastic coupled responses only.

Heterostructured Functional Materials through Molten Salt Synthesis for Solid Oxide Fuel Cells and Electrolysis Cells

La0.6Sr0.4Co0.2Fe0.8O3 (LSCF)−La0.8Sr0.2MnO3 (LSM) heterostructure crystalline materials have been synthesized in a simple, one-step via reaction-deposition process using a molten salt. Two-phase perovskite composites can be synthesized in times as short as 10 minutes in a molten salt solvent. X-ray diffraction and S/TEM energy dispersive X-ray spectroscopy have been utilized to confirm the formation of an LSM shell on LSCF cores in all samples when adjusting dwell time, core size, weight ratio between core and shell precursors, and weight ratio of powder to salt. Specifically, decreasing the LSCF core size increases core−shell yield. Smaller cores result in a greater density of facets on the crystal surface and provide more favorable sites for LSM heterogeneous nucleation. By decreasing the weight ratio of shell precursor to core decreases shell thickness, and reduces the number of homogeneously nucleated LSM nanoparticles, and thereby increases core−shell yield. Increasing the amount of molten salt solvent relative to precursors decreases supersaturation in the melt and results in less uniform, and isolated shell deposition on the cores. The synthesized heterostructred nanoparticles have been functionalized into electrodes for solid oxide fuel cells and electrolysis cells. Symmetrical cells fabricated from baseline LSCF electrodes are compared with symmetrical cells fabricated from the molten salt-synthesized heterostructred electrodes. The heterostructured electrodes are shown to have significantly lower polarization resistance compared to baseline LSCF electrodes, showing the promise of the molten salt process to achieve heterostructured electrodes with substantially reduced polarization resistance.

Thermal hydraulic design and evaluation of the solid microencapsulated fuel in light water reactors

Solid Microencapsulated Fuel (SMF) is a kind of solid fuel rod design that disperses TRISO coated fuel particles directly into a kind of matrix. Without cladding tube and associated failure mechanisms, this type of new fuel design is expected to provide improved performance under normal and even accident conditions. The purpose of this paper is to analyze the thermal hydraulic performance of SMF based on a single channel, compared to the traditional fuel in the 200 MW Nuclear Heating Reactor (NHR200-II). Two kinds of specific SMF by dispersing TRISO particles into Zirconium or SiC matrix were investigated. Thermal margin to DNB was assessed and confirmed by determining the heat transfer capacity under normal condition. Two-phase pressure drop was evaluated by using the homogeneous equilibrium boiling assumption. The centerline temperature of SMF rod was calculated by using effective thermal conductivity of two-phase composite. The analysis of flow instability and flow-induced vibration were also included and compared. This study showed that SMF has a better thermal transfer capacity, a higher margin from vortex shedding and fluid-elastic instability, and a lower fretting wear rate, while a higher sliding wear rate because of a higher Young’s modulus and fundamental frequency, which is compensated by a higher hardness for SiC matrix.

Study of Corrosion Mechanisms in Corrosive Media and Their Influence on the Absorption Capacity of Fe2O3/NdFeO3 Nanocomposites

This paper presents the results of a study of the change in the stability of Fe2O3/NdFeO3 nanocomposites when exposed to aggressive media over a long period of time. The main purpose of these studies is to investigate the mechanisms of degradation and corrosion processes occurring in Fe2O3/NdFeO3 nanocomposites, as well as the influence of the phase composition on the properties and degradation resistance. According to the X-ray phase analysis, it was found that the variation of the initial components leads to the formation of mixed composition nanocomposites with different Fe2O3/NdFeO3 phase ratios. During corrosion tests, it was found that the dominance of the NdFeO3 phase in the composition of nanocomposites leads to a decrease in the degradation and amorphization rate of nanostructures by a factor of 1.5–2 compared to structures in which the Fe2O3 phase dominates. Such a difference in the degradation processes indicates the high stability of two-phase composites. Moreover, in the case of an aqueous medium, nanocomposites dominated by the NdFeO3 phase are practically not subjected to corrosion and deterioration of properties. The results obtained helped to determine the resistance of Fe2O3/NdFeO3 nanocomposites to degradation processes caused by exposure to aggressive media, as well as to determine the mechanisms of property changes in the process of degradation. The results of the study of the absorption capacity of Fe2O3/NdFeO3 nanocomposites in the case of the purification of aqueous media from manganese and arsenic showed that a change in the phase ratio in nanocomposites leads to an increase in the absorption efficiency of pollutants from aqueous media.

A micromechanical model for the effective properties of two-phase magnetoelectric composites

A micromechanical model for the effective properties of two-phase magnetoelectric composites

Order to disorder in quasiperiodic composites

From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here.

Mechanical properties of samarium cobalt: A molecular dynamics study

Sm-Co permanent magnets are usually very brittle which makes them vulnerable to even mild impacts. Recently, it was reported by simulation and confirmed by experiment that SmCo5 can be plastically deformed via amorphous shear bands activated by external stress. Since most Sm-Co magnets mainly consist of the Sm2Co17 phase, it is necessary to study how the Sm2Co17 phase can be deformed compared with the SmCo5 phase (existing also in Sm-Co magnets). In addition, the mechanical properties of the two-phase composites with an interface should be investigated. In this paper, we show that the Sm2Co17 phase can also be plastically deformed under tensile loading due to the formation of amorphous shear bands. We find that the interfacial stress between SmCo5 and Sm2Co17 significantly affects the formation of amorphous shear bands. The formation energies of amorphous shear bands are lower than the energies needed for transgranular, intergranular and interphase cleavage. The two-phase samples notched at the interface are also deformed by tensile loading. When the amorphous shear band is initiated in the Sm2Co17 phase, the sample quickly necks toward failure. In contrast, when amorphous shear band is initiated in the SmCo5 phase, the sample can accommodate more strain. These results help us understand the intrinsic mechanical properties of Sm-Co magnets.

A micromechanical model for phase-change composites

Phase-change composites have a wide range of tunable mechanical properties caused by temperature-driven phase transition, and have been widely applied in many cutting-edge fields like soft robotics. Previous studies on the effective mechanical properties of phase-change composites mostly use experimental methods, and there have been few theoretical approaches. In this work, we develop a micromechanical framework capable of tracking the effective mechanical properties of phase-change composites throughout the entire phase transition. The phase-change materials embedded in the composites are modelled as inclusions, and the non-phase-change materials are modelled as the matrix. This allows us to determine the effective mechanical properties of phase-change composites via the energy equivalency approach. Moreover, since the new phase will be generated inside the phase-change inclusions in the form of sub-inclusions during the phase transition, the inclusions are modelled as two-phase composites, and their effective mechanical properties are then determined using the Mori–Tanaka method. Finally, by comparing theoretical predictions with experimental data, the accuracy and reliability of the present model are verified. We believe that the proposed model can serve as a powerful tool for evaluating the effective mechanical properties of phase-change composites and provide theoretical guidelines for the design of advanced devices with tunable mechanical performance.