Analysis of hollow inclusion–matrix debonding in particulate composites

This work aims at understanding the effect of particle–matrix interfacial debonding on the tensile response of syntactic foams. The problem of a single hollow inclusion with spherical-cap cracks embedded in a dissimilar matrix material is studied. Degradation of elastic modulus, cavity formation in the proximity of debonded regions, stress localization phenomena in the inclusion, debonding energetics, and crack kinking are studied for a broad range of inclusion wall thickness and debonding extent. A series solution based on the Galerkin method is proposed and validated through comparison with findings from boundary element and finite element methods. Results are specialized to glass particle-vinyl ester matrix systems widely used in marine structural applications. The insight gained into the role of particle–matrix debonding extent and inclusion wall thickness is useful in understanding the possible failure mechanisms of syntactic foams under tensile and flexural loading conditions and in tailoring their parameters for specific applications.     

A combined viscoelastic–viscoplastic behavior of particle reinforced composites

This study formulates a micromechanical model for predicting effective viscoelastic–viscoplastic responses of composites. The studied composites consist of solid spherical particle reinforcements dispersed in a homogeneous matrix. The particle constituent is assumed linear elastic, while the matrix exhibits combined viscoelastic–viscoplastic responses. The Schapery integral model is used for the 3D isotropic non-linear viscoelastic responses. Two viscoplastic models are considered: the Perzyna model, having a rate-independent yield surface and an overstress function, and the Valanis endochronic model based on an irreversible thermodynamics without a yield surface. The Valanis model is suitable for materials when viscoplastic responses occur at early loadings (small stress levels). A unit-cell model with four particle and polymer sub-cells is generated to obtain homogenized responses of the particle-reinforced composites. Available micromechanical models and experimental data in the literature are used to verify the proposed micromechanical model in predicting effective time-dependent and inelastic responses of composites. Field variables in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having detailed particle geometries, are modeled using finite element (FE) method.     

A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading

A fracture mechanics based failure criterion for unidirectional composites under combined loading has been developed. The predictions from this criterion have been compared with experimental data obtained from combined compression–torsion loading of glass and carbon fiber reinforced polymer composites of 50% fiber volume fraction. The specimens were loaded under rotation control and displacement control in a proportional manner. Comparison of the Budiansky–Fleck kinking model, specialized to a solid circular cylinder, and the new failure model against experimental data suggests that the Budiansky–Fleck model predictions do not capture the variation of compressive strength as a function of shear stress for glass fiber composites. This is because these composites fail predominantly by compressive splitting. The Budiansky–Fleck model predictions are appropriate for composites that fail by compressive kinking. The new model predictions capture the experimental results for glass composites where the compression strength is initially unaffected by shear stress but undergoes a drastic reduction when a critical value of shear stress is reached.     

Modeling of particle–resin suspension impregnation in compression resin transfer molding of particle-filled,continuous fiber reinforced composites

A particle–resin suspension impregnation model is used for analyzing the mold filling process in compression resin transfer molding (CRTM) of particle-filled, continuous fiber composites. The model is based on Darcy flow coupled with particle filtration and is applicable to two-dimensional impregnation through isotropic/anisotropic fiber preforms. Comparisons with simple analytical solutions and experimental results from the literature were made to validate the numerical solution. Simulations showed that CRTM was advantageous over resin transfer molding (RTM) for smaller non-homogeneity in composite microstructure, when particle filtration was high. Limits on certain process parameters were observed beyond which molding pressures in CRTM became comparable with those in RTM. The preform anisotropy was effective in the particle distribution profile. The choice of inlet gate configuration in CRTM was found influential in the particle distribution homogeneity and molding pressures. The developed modeling tool can be extended to analyze any composite liquid molding process involving particle fillers.     

Electromechanical response of (3–0, 3–1) particulate,fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method

An analytical framework based on the homogenization method has been developed to predict the effective electromechanical properties of periodic, particulate and porous, piezoelectric composites with anisotropic constituents. Expressions are provided for the effective moduli tensors of n-phase composites based on the respective strain and electric field concentration tensors. By taking into account the shape and distribution of the inclusion and by invoking a simple numerical procedure, solutions for the electromechanical properties of a general anisotropic inclusion in an anisotropic matrix are obtained. While analytical forms are provided for predicting the electroelastic moduli of composites with spherical and cylindrical inclusions, numerical evaluation of integrals over the composite microstructure is required in order to obtain the corresponding expressions for a general ellipsoidal particle in a piezoelectric matrix. The electroelastic moduli of piezoelectric composites predicted by the analytical model developed in the present study demonstrate excellent agreement with results obtained from three-dimensional finite-element models for several piezoelectric systems that exhibit varying degrees of elastic anisotropy.     

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr–Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading.In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.     

The effect of microstructural morphology on the elastic,inelastic, and degradation behaviors of aluminum–alumina composites

Micromechanical models with idealized and simplified shapes of inhomogeneities have been widely used to obtain the average (macroscopic) mechanical response of different composite materials. The main purpose of this study is to examine whether the composites with irregular shapes of inhomogeneities, such as in the aluminum–alumina (Al–Al₂O₃) composites, can be approximated by considering idealized and simplified shapes of inhomogeneities in determining their overall macroscopic mechanical responses. We study the effects of microstructural characteristics, on mechanical behavior (elastic, inelastic, and degradation) of the constituents, and shapes and distributions of the pores and inclusions (inhomogeneities), and thermal stresses on the overall mechanical properties and response of the Al–Al₂O₃ composites. Microstructures of a composite with 20% alumina volume content are constructed from the microstructural images of the composite obtained by scanning electron microscopy (SEM). The SEM images of the composite are converted to finite element (FE) meshes, which are used to determine the overall mechanical response of the Al–Al₂O₃ composite. We also construct micromechanics model by considering circular shapes of the inhomogeneities, while maintaining the same volume contents and locations of the inhomogeneities as the ones in the micromechanics model with actual shapes of inhomogeneities. The macroscopic elastic and inelastic responses and stress fields in the constituents from the micromechanics models with actual and circular shapes of inhomogeneities are compared and discussed.     

Special issue on conveying and handling of particulate solids–Challenges of discrete element simulation,application and calibration

<正>A series of international Conveying and Handling of Particulate Solids(CHoPS)conferences was initiated in Herzliya,Israel in 1995and has since proceeded with six successive conferences held in Jerusalem(1997),the Dead Sea(2000),Budapest(2003),Sorrento(2006),Brisbane(2009)and Friedrichshafen(2012).The conference series covers processes involving particulate solids,for example     

Preparation of ternary Cr2O3–SiC–TiO2 composites for the photocatalytic production of hydrogen

Novel ternary Cr₂O₃–SiC–TiO₂ composites were synthesized by implanting Cr³⁺ into SiC–TiO₂ via sol–gel and impregnation approaches. The results from X-ray diffraction, scanning electron microscopy and transmission electron microscopy show that the Cr³⁺ species were doped onto the surface of the SiC–TiO₂ carrier. The diffuse reflectance ultraviolet–visible absorption spectra revealed that the absorption edges of the ternary Cr₂O₃–SiC–TiO₂ composites were gradually shifted red with increasing chromium content. The luminescence intensities of the composites decreased with increasing doped Cr³⁺ content due to the reduction in the number of recombination sites of electron–hole pairs. The ternary Cr₂O₃–SiC–TiO₂ composites showed high hydrogen-producing activities, which probably results from the formation of donor levels of the Cr³⁺ species in the forbidden band of the SiC semiconductor.     

An experimental investigation of a superplastic constitutive equation in Al–Mg–Si alloy composites reinforced with Si3N4 whiskers

Superplastic properties at 818 K were investigated by tensile tests for Al–Mg–Si alloy composites reinforced with Si₃N₄ whiskers whose volume fractions were 0–30%. The 20 and 30 vol.% composites exhibited large elongation of 615 and 285% at a high strain rate of 2×10⁻¹ s⁻¹, respectively. High strain rate superplasticity of the composites is attributed to the very small grain size of less than 3 μm. The stress–strain rate relation for the composites was almost the same as that of the alloy, taking into consideration the influences of threshold stress and grain size, and the relation was independent of the volume fraction of whisker. This is probably because grain boundary sliding was not hampered by the whiskers due to the presence of liquid phase for the composites.     

Computational analysis on Hopf bifurcation and stability for a consumer–resource model with nonlinear functional response

We consider a consumer–resource model with nonlinear functional response and reaction–diffusion terms. By taking the growth rate of the resource as the parameter, we give a computational and theoretical analysis on Hopf bifurcation emitting from the positive equilibrium for the model and discuss the conditions for determining the bifurcation direction and the stability of the bifurcating periodic solutions by space decomposition and vector operation techniques. It is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Some numerical examples are presented to support and illustrate our theoretical analysis.     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses

This paper presents the application of a new constitutive damage model for an epoxy matrix on micromechanical analyses of polymer composite materials. Different representative volume elements (RVEs) are developed with a random distribution of fibres. Upon application of periodic boundary conditions (PBCs) on the RVEs, different loading scenarios are applied and the mechanical response of the composite studied. Focus is given to the influence of the interface between fibre and matrix, as well as to the influence of the epoxy matrix, on the strength properties of the composite, damage initiation and propagation under different loading conditions.     

The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer–matrix composites

The interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (non-linear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.     

Experimental and Numerical Investigation on Strain Rate-Dependent Tensile Behavior of ZrB2–SiC Ceramic Composite

In this study,the strain rate-dependent dynamic tensile behavior of ZrB2-20%SiC ceramic composite was investigated using experimental and numerical approaches.The split Hopkinson pressure bar apparatus was used to measure the dynamic splitting tensile response at strain rates of 17-67 s^?1.The experiment results demonstrate a significant strain rate dependence of the dynamic tensile behavior of the ZrB2-SiC ceramic composite.The dynamic tensile strength increased linearly with the strain rate,from 288 MPa at 17 s^?1to 654 MPa at 67 s^?1.Moreover,a strain rate-dependent tensile strength was introduced into a modified JH-2 model to describe the dynamic tensile behavior and fracture process of ZrB2-SiC ceramics.The numerical results of dynamic tensile strength agree well with the experimental result.Moreover,the fracture process of ZrB2-SiC ceramics under dynamic tension was further studied by combining high-speed images and numerical results.The effect of strain rate on the fracture process and failure patterns of the ZrB2-SiC ceramic composite could be verified by the modified JH-2 model.     

Transport of airborne particulate matters originating from Mentougou, Beijing, China

In this study, a coupled regional air quality modeling system is applied to investigate the time spatial variations in airborne particulate matters （PM10）, originating from Mentougou to Beijing municipal area in the period of April 1-7, 2004, and the influences of complex terrain and meteorological conditions upon boundary layer structure and PM10 concentration distributions. An intercomparison of the performance with CALPUFF against the observed data is presented and an examination of scatter plots is provided. The statistics show that the correlation coefficient and STD between the modeled and observed data are 0.86 and 0.03, respectively. Analysis of model results illustrates that the pollutants emitted from Mentougou can be transported to Beijing municipal area along certain transport pathways, and PM10 concentration distributions show heterogeneity characteristics. Contributions of the Mentougou sources to the PM10 concentrations in Beijing municipal area are up to 0.1-15 μg/m^3.     

Determination of the effective elastic–plastic response of metal–ceramic composites

The mechanical response of metal–ceramic composites is analysed through a homogenization model accounting for the mechanical behaviour of the constituent materials. In order to achieve this purpose a nonlinear homogenization method based on the phase field approach has been suitably implemented into a numerical code. A prescribed homogenized strain state is applied to a unit volume element of a metal–ceramic composite with proportional loading in which all components of the strain tensor are proportional to one scalar parameter. The mechanical response of the material has been modeled by considering a von Mises plasticity model for the metal phase and a Drucker–Prager associative elastic–plastic material model for the ceramic phase. A two stages plasticity has been obtained in which inelastic strain develops in the metal phase followed by a fully plastic response. A comparison with a finite element model of the stress–strain response of an axisymmetric unit cell has been carried out with the purpose to validate the homogenization based modeling presented in the paper. Plastic parameters of a Drucker–Prager yield surface for the homogenized composite have been calculated at different materials compositions. Associative Drucker–Prager plasticity has been found to be accurate for high ceramic content.     

A unified model for polystyrene–nanorod and polystyrene–nanoplatelet melt composites

We present a unified constitutive model capable of predicting the steady shear rheology of polystyrene (PS)–nanoparticle melt composites, where particles can be rods, platelets, or any geometry in between, as validated against experimental measurements. The composite model incorporates the rheological properties of the polymer matrix, the aspect ratio and characteristic length scale of the nanoparticles, the orientation of the nanoparticles, hydrodynamic particle–particle interactions, the interaction between the nanoparticles and the polymer, and flow conditions of melt processing. We demonstrate that our constitutive model predicts both the steady rheology of PS–carbon nanofiber composites and the steady rheology of PS–nanoclay composites. Along with presenting the model and validating it against experimental measurements, we evaluate three different closure approximations, an important constitutive assumption in a kinetic theory model, for both polymer–nanoparticle systems. Both composite systems are most accurately modeled with a quadratic closure approximation.     

Theoretical and numerical studies on the flow multiplicity phenomenon for gas–solids two-phase flows in CFB risers

The dependence of the fully-developed flow profiles on the inlet flow conditions for gas–solids two-phase flows, i.e. the flow multiplicity phenomenon, in circulating fluidized bed (CFB) risers was proposed and discussed in this article. The flow multiplicity phenomenon for gas–solids two-phase flows was first proved mathematically based on the conservation equations of mass and momentum. Then the CFD model using Eulerian–Eulerian approach with k–ε turbulence model for each phase was further adopted to analyze the details of this flow multiplicity phenomenon. It is theoretically and numerically revealed that for gas–solids two-phase flows, the flow profiles in the fully-developed region are always dominated by the flow profiles at the inlet. The solids concentration profile is closely coupled with the velocity profile, and the inlet solids concentration and velocity profiles can largely influence the fully-developed concentration and velocity profiles.