Spherical Inclusions Research Articles

Indenting a thick gel with a solid spherical inclusion

A spherical inclusion is embedded in a soft gel block. A vertical force is applied on the gel surface by means of a spherical indenter. The loading axis is not aligned with the inclusion but placed at a horizontal offset displacement from the inclusion. The measurement of indentation force and inclusion trajectory are compared to the computational results from two-dimensional (2D) Finite Element Analysis (FEA) simulations. A discernible instability emerges when the indentation reaches a critical depth, in accordance with the Southwell instability theory. The three-dimensional (3D) trajectory shows distinct features that were previously not captured by the 2D FEA simulations.

A chloride diffusion model for cementitious material with pore-solution viscosity enhancement

A promising approach to retard chloride attack has been proposed by increasing the pore solution viscosity in contrast to the traditional methods, but the dependence of chloride diffusion coefficient on viscosity has not been included in the current transport models. This paper presents a model for the diffusion of chloride in cementitious materials based on the viscosity-enhancing behavior of pore solution using viscosity modifying admixtures (VMAs). The parameters affecting the diffusion of chloride in the viscosity-enhancing solution are proposed to be the VMA molecular shape factor and VMA volume fraction based on the Maxwell approximation of spherical inclusions in the effective medium approximation theory. VMA shape factor is modeled with VMA molecular mass as a key variable. VMA volume fraction is calculated as a function of water-cement ratio, hydration age, initial VMA volume fraction, and VMA leaching residual fraction. This chloride diffusion model is developed and validated, which is based on the modification of Fick's second law and takes into account the pore solution viscosity-enhancing behavior and VMA-induced pore coarsening. This model differs from traditional models based on ion transport paths and provides a new reference for concrete durability design in terms of the intrinsic properties of the pore solution.

The all‐polymer composites and blends made of ethylene–octene copolymer and partially disentangled polypropylene using a new processing approach

AbstractAll‐polymer composites and blends of ethylene–octene copolymer (EOC) and polypropylene (PP) were produced in the extrusion process. They had the same composition (96:4 wt.%), but five different entanglement densities of PP macromolecules. Depending on the processing temperature, below or above the melting point of PP, fibers or spherical inclusions were formed inside the EOC matrix. The production of PP fibers directly during mixing was possible by reducing the entanglement of macromolecules in this polymer. During fiber formation by solid‐state plastic deformation, the crystallinity of PP decreased, especially for the less entangled polymers. The presence of fibers influenced the mechanical properties of the composites, which were different from those of the blends. Both in blends and composites, the matrix was reinforced, but in the composites the effect was stronger and the measured stresses increased with the lower degree of PP entanglement. SAXS and microscopic observations showed that cavitation occurred in the deformed composites. All‐polymer composites, in which the reinforcement was created as a result of polymer deformation with limited entanglements, have properties that are advantageously different from traditional ones, which opens the prospect of their application.

Influence of powder surface chemistry on the defect formation in AlSi10Mg alloy processed via laser powder bed fusion additive manufacturing

In laser powder bed fusion(LPBF) additive manufacturing(AM) of Al alloys, surface chemistry and dissolved gas composition(oxygen/oxides/hydroxides, hydrogen and moisture) of AM powders is a major influencing factor for porosity formation. Therefore, in the present investigation, this aspect is addressed using two sets of virgin AM AlSi10Mg powders, namely, Hi-Ox (2770 ppm oxygen) and Lo-Ox (660 ppm oxygen), to assess the printability under various processing parameters and defect formation in printed parts. Comprehensive and in-depth metallurgical analysis of both powders utilizing multiple characterisation techniques established the presence of various types of oxides/hydroxides with different complex chemistries on the powders’ surface. Enhanced spherical gas porosity and oxide inclusions were witnessed in Hi-Ox print coupons in contrast to the least defects in Lo-Ox coupons rationalized due to surface chemistry difference between the virgin powders. Consequently, the mechanical properties of the Hi-Ox print coupons, even with minimum defect density, are significantly inferior to Lo-Ox specimens. These observations suggest a competing influence of surface chemistry/dissolved gas composition and laser parameters for the processing of both powders. Overall, by correlating the microstructures with processing conditions and oxide concentration, defects morphology, the probable melt pool formation mechanism in LPBF of AlSi10Mg alloy (for high and low oxygen concentration) is elucidated.

The method of determining optimal control of the thermoelastic state of piece-homogeneous body using a stationary temperature field

This paper proposes a new highly effective method for determining the optimal control of the stress-strain state of spatially multi-connected composite bodies using a stationary temperature field. The proposed method is considered based on the example of a stationary axisymmetric thermoelastic problem for a space with a spherical inclusion and cavity. The proposed method is based on the generalized Fourier method and reduces the original problem to an equivalent problem of optimal control, in which the state of the object is determined by an infinite system of linear algebraic equations, the right-hand side of which parametrically depends on the control. At the same time, the functional of the cost of the initial problem is transformed into a quadratic functional, which depends on the state of the equivalent system and parametrically on the control. The limitation on the temperature distribution is replaced by the value of the control norm in the space of square summable sequences. In fact, this paper considers for the first time the problem of optimal control of an infinite system of linear algebraic equations and develops a method for its solution. The proposed method is based on presenting the solutions of infinite systems in a parametric form, which makes it possible to reduce equivalent problem to the problem of conditional extremum of a quadratic functional, which explicitly depends on the control. A further solution to this problem A further solution to this problem is found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. found by the Lagrange method using the spectral decomposition of the quadratic functional matrix. The method developed in this paper is strictly justified. For all infinite systems, the Fredholm property of their operators is proved. As an important result necessary for substantiation, for the first time, an estimate from below of the module of the multi-parameter determinant of the resolving system of the boundary value problem of conjugation – space with a spherical inclusion – was obtained when solving it using the Fourier method. The theorem that establishes the conditions for the existence and uniqueness of the solution of equivalent problem or optimal control problem without restrictions in the space of square summable sequences is proved. The numerical algorithm is based on a reduction method for infinite systems of linear algebraic equations. Estimates of the practical accuracy of the numerical algorithm demonstrated the stability of the method and sufficiently high accuracy even with close location of the boundary surfaces. Graphs showing the optimal temperature distribution for various geometric parameters of the problem and their analysis are provided. The proposed method extends to boundary value problems with different geometries.

Effect of Silicon–Manganese Deoxidation on Oxygen Content and Inclusions in Molten Steel

In order to improve the cleanliness of steel, non-aluminum deoxidation processes have begun to replace aluminum deoxidation processes. Although the aluminum deoxidation process can reduce the oxygen content in steel to <10 × 10−6, this deoxidation method causes fatigue failure resulting from the formation of large-grained spherical (Ds-type) inclusions composed of calcium–aluminate. It also tends to lead to nozzle blockage during casting. Given the above problems, this study conducted an in-depth investigation of silicon–manganese deoxidation. Thermal experiments and thermodynamic calculations were used to assess the impact of different Mn–Si ratios on the oxygen content and inclusion characteristics during the deoxidation process of molten steel with different initial oxygen contents. The experimental samples were analyzed using an oxygen–nitrogen–hydrogen analyzer, a direct reading spectrometer, and an automatic scanning electron microscope. After that, the samples were electrolyzed to observe the 2D morphology and 3D morphology of the inclusions using scanning electron microscopy. Finally, thermodynamic calculations were carried out using FactSage to verify the experimental results. The results indicated that, regardless of the initial oxygen content, silicon–manganese deoxidation maintained the total oxygen content at 35 × 10−6. It effectively managed the plasticization of inclusions in molten steel, predominantly yielding spherical silicates while minimizing Al-containing inclusions. Nevertheless, as the initial content of [O] increased, the size and density of the silicate inclusions in the steel also increased. An optimal point in the number and size of inclusions was observed with an increased Mn–Si ratio. Moreover, the combined utilization of silicon–manganese deoxidation, diffusion deoxidation, and vacuum deoxidation enabled ultra-low oxygen content control of molten steel.

Enhanced Thermoelectric Performance of PbTe Nanocomposites with Sb Nanoinclusions.

In the present work, the thermoelectric properties of PbTe embedded with spherical Sb nanoscale inclusions were calculated in detail, following the idea that energy-selective carrier scattering can effectively increase the Seebeck coefficient. The quantitative relationships between such nanostructures in PbTe and thermoelectric properties indicated that interface potential barrier induced by Sb nanoinclusions results in a significant enhancement of the Seebeck coefficient, especially when around room temperature. Furthermore, the optimal parameters for boosting the thermoelectric performance of PbTe were found to be 4 nm-radius Sb nanoinclusions with high concentration.

Multiscale modelling of particulate composites with spherical inclusions

AbstractThis paper presents a novel and effective strategy for modelling three-dimensional periodic representative volume elements (RVE) of particulate composites. The proposed method aims to generate an RVE that can represent the microstructure of particulate composites with hollow spherical inclusions for homogenization (e.g., deriving the full-field effective elastic properties). The RVE features periodic and randomised geometry suitable for the application of periodic boundary conditions in finite element analysis. A robust algorithm is introduced following the combined theories of Monte Carlo and collision driven molecular dynamics to pack spherical particles in random spatial positions within the RVE. This novel technique can achieve a high particle-matrix volume ratio of up to 50% while still maintaining geometric periodicity across the domain and random distribution of inclusions within the RVE. Another algorithm is established to apply periodic boundary conditions (PBC) to precisely generate full field elastic properties of such microstructures. Furthermore, a user-friendly automatic ABAQUS CAE plug-in tool ‘Gen_PRVE’ is developed to generate three-dimensional RVE of any spherical particulate composite or porous material. Gen_PRVE provides users with a great deal of flexibility to generate Representative Volume Elements (RVEs) with varying side dimensions, sphere sizes, and periodic mesh resolutions. In addition, this tool can be effectively utilized to conduct a rapid mesh convergence study, an RVE size sensitivity study, and investigate the impact of inclusion/matrix volume fraction on the solution. Lastly, examples of these applications are presented.

The use of antigens derived from Bacillus thuringiensis bacteria for further differentiation

This study is devoted to studying Bacillus thuringiensis antigens and their insecticide activity as critical features in bacterial differentiation. Indeed, 190 samples were examined for flagellar antigenicity as well as the insecticidal activity exhibited. From a serological perspective, 122 isolates (64.2 %) were attributed to 8 H-serogroups, including 3 non-typeable and 65 unverified. The dominant serotype was H3abc (82 % frequency); H6 was less frequent (8.5 %). The other 6 serotypes accounted for a low frequency of occurrence (up to 1.5 %). Of the 190 isolates tested, 125 (65.8 %) formed bipyramidal, and 63 (33.2 %) represented spherical inclusions. All H3abc isolates contained bipyramidal inclusions. The same applied to H8ab and H7 isolates. Insecticide activity was noted in 70.1 % of the population. In general, 128 samples were toxic to both species (Bombyx mori, Aedes sp.). Another 3 samples were toxic only to B. mori, and 2 for Aedes sp. Among the samples exhibiting toxicity to both species, 97.6 % belonged to bipyramidal paraspore inclusions (H3abc). All H7 samples were toxic to two insect species. Monotoxic B. thuringiensis against Aedes sp. were found only among organisms producing spherical parasporal inclusions in the cell. Examples of such microorganisms include an isolate of the H4ab/43 serotype.

Metallization characteristics and gold ore controlling factors in the south region of Tra Nu - Phuoc Thanh, Quang Nam Province

The gold mineralization in the southern region of Tra Nu-Phuoc Thanh was initially discovered and assessed by the Central Geological Division. However, mineralization characteristics and ore-controlling factors in the Tra Nu-Phuoc Thanh area remain inadequately understood. To assess the gold mineralization potential in this research area, this study conducts a comprehensive synthesis of prior research findings, complemented by the analysis of an additional 50 thin sections, 100 thick sections, SEM scanning electron microscopy, and 10 ICP-MS samples. The research results reveal the presence of gold deposits within the study area, including native gold and electrum. The identified gold-bearing minerals in the deposits encompass quartz, pyrite, galena, sphalerite, pyrrhotite, and goethite. The ore formations predominantly exhibit disseminated, vein, and breccia structures, along with granular, semi-granular, spherical, and solid inclusions. It has been ascertained that the gold ore in the study area belongs to the gold-quartz-sulfur formation and can be categorized into two types: gold-quartz-pyrite ore and polymetallic gold-quartz-sulfur ore. The ore is primarily situated within ancient metamorphic sedimentary rocks of the Kham Duc formation and young granitoid rocks of the Ba Na complex. Typically, the gold ore body occurs in a single-vessel form, with less common branched, vascular zone, and infiltrative vascular forms. All gold ore bodies are aligned along the fault systems, primarily oriented in the northeast-southwest direction. These sub-meridian fault systems serve as conduits for hydrothermal solutions carrying gold ore in the study area.

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources.

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to the macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense medium of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here, we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron, and so forth. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI measurements of an ex vivo mouse brain at ultra-high field.

Nonlinear electro-elastic finite element analysis with neural network constitutive models

In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets describing the constitutive response of dielectric elastomers. These include an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.

A differential scheme for the effective conductivity of microinhomogeneous materials with the Hall effect

A differential scheme is proposed for the calculation of the components of the effective electrical conductivity tensor of a microinhomogeneous material taking into account the Hall effect. The presence of the Hall effect results in an appearance of asymmetry of the components of the conductivity tensor and a dependence of these components on the magnitude of the magnetic field applied to the material. In this case, the differential scheme leads to a system of matrix differential equations that were solved numerically in the current work. This solution was obtained for materials containing spherical or cylindrical inclusions. In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes parallel or orthogonal to the magnetic field. A comparison of the results obtained by the proposed methodology to the low concentration approximation was carried out.

Effect of rare-earth Ce on the texture of non-oriented silicon steels

Abstract Macroscopic and microscopic textures of non-oriented silicon steel hot rolled sheets with different rare-earth Ce contents were investigated using X-Ray Diffraction, Electron Back Scatter Diffraction, and field emission scanning electron microscopy, and the magnetic properties of the cold-rolled annealed sheets were examined using a silicon steel sheet testing system. The results show that the addition of rare-earth Ce reduces the proportion of unfavorable γ texture intensity and texture {111} and enhances the proportion of favorable η texture intensity and texture {100} and {110} in the steel. Magnetic property tests show that rare-earth Ce favors the reduction in test steel loss and the increase in magnetic susceptibility. The main reason is that rare-earth Ce combines with O and S in steel to form large-size inclusions, which preferentially precipitate in the liquid steel and inhibit the precipitation of fine AlN and MnS inclusions, while denaturing the inclusions to spherical composite inclusions such as Ce2O2S-MnS, CeS-AlN, and CeAlO3, thus exerting a good effect of purifying the liquid steel and denaturing the inclusions.

Energy variation and stress fields of spherical inclusions with eigenstrain in three-dimensional anisotropic bi-materials

In this study, expressions for the interior stress fields of a spherical inclusion with uniform eigenstrain embedded in an anisotropic bi-material featuring a planar interface are derived. These expressions involve surface integrals of the imaginary term of the first derivative of the Green tensor in an anisotropic bi-material which are well-suited for standard numerical integrations. Specific formulations are provided for cases where the inclusion belongs to either the same material or both materials. Additionally, expressions are presented for the equivalent Eshelby tensor. The interior stress fields and variations in elastic strain energy are computed using cubic elastic constants of Cu. Various inclusion positions relative to the interface, eigenstrain forms, and crystallographic orientations are considered. For instances involving dilatational eigenstrain, the elastic strain energy variation with the inclusion’s position may exhibit multiple extrema. The global minimum and maximum consistently occur when the inclusion spans both materials. In the context of symmetrical tilt boundaries, energy variations are perfectly symmetric, with a global minimum on the interface that decreases with the tilt angle. The significance of the observed energy variations for defects segregation is quantitatively assessed by comparing them with the interaction energy between an eigenstrain and a grain boundary stress field.

Organosilicon elastomers of MWCNTs and nano-sized metals for heating purposes

Silicone elastomers are continuously gaining importance in a variety of industrial applications, including strain gauges, electrical heaters, electromagnetic interference, and electrostatic discharge protection coatings. But these materials have certain drawbacks such as high cost, poor resistance to solvents, low tear strength, limited high-temperature resistance, difficulty in bonding and limited abrasion resistance. Therefore, unique nanocomposites of organosilicon elastomers with metals have been prepared using MWCNTs. The prepared nanocomposites demonstrated nano-diameter structures (15–60 nm) with micron-sized fibrous structures (12–60 μm). Aluminum elongated inclusions (60 µm in size) and bronze spherical inclusions (12–30 µm) were observed in the nanocomposites. The composites containing MWCNTs, Co-Mo/Al2O3-MgO catalyst and bronze (3 wt. %) had the maximum thermal and electrical conductivity. The prepared nanocomposites were used to make the heaters. The heating of the heaters was carried out by applying a voltage of 12–24 V. The Highest temperature achieved was more than 50 °C in all the heaters. By supplying 12–24 V electricity to the heaters in the ventilation and heat recirculation system, the interior of a minibus or living space can be heated. The developed electric heater has another important economic application in temperature-controlled materials.

Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine.

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.

Finite element modelling of complex 3D image data with quantification and analysis

Abstract The purpose of this study was to examine how to model aggregated material microstructure and its meshing volumic generation that is provided by any data from 3D tomographic image data. The accurate reconstruction of 3D geometry structures from tomographic images is a powerful method in various application areas of materials science. The resulting mesh can be voxelized or conforming based on volumetric tetrahedral meshing. We investigate this creation depending on improving multiple materials marching cubes algorithm (M3C) with smoothing and remeshing algorithms. Then, a strategy for generating good-quality meshing and its robustness is presented, and this is performed with numerical tests. The novelty of this study is to generate a conforming mesh from complicated topology structures, particularly, when the interfaces of bi-materials are connected. This leads to a reduction in the node count in the generated mesh. The influence of some parameters involved in this algorithm is explored during different levels of meshing. In this work, the numerical homogenization approach from various spherical inclusions in the two-phase system using the algorithm M3C is considered to estimate the effective elastic properties. We created the framework with all the associated information, such as inputs in the format .inp files, to make it possible to run it over the Abaqus solver. Then, the Abaqus model based on the finite element method (FEM) was executed in this case for various material microstructures such as polycrystalline, composite, and fiber. We show the main workflow for providing desired results by visualizing the FEM analysis. We also demonstrate the capabilities of meshing methodology in the solver for these material models. The validation of the local mechanical environment from FEM with loading scenarios is achieved to predict displacements and deformations. Mechanical compression tests are performed to investigate the compressive behavior. Finally, stress-strain curves provided a comparison between simulations and experimental data for materials, and a good agreement is obtained.

Mean field homogenization schemes using averages of stress, strain and strain energy density and applications

The average of stress (AS) and average of strain (AN) were often used in the development of conventional mean-field homogenization (MFH) schemes, but their correlation with the average of strain energy density (AE) has rarely been discussed. In this work, we examined the correlations of AE with AS and AN, and found that AE can be reduced to the product of AS or AN under uniform boundary stress or linear surface displacement associated with a uniform strain field. By introducing a reference matrix and using any two among AE, AS and AN, three MFH schemes were developed: NS (using AN and AS); NE (using AN and AE); and SE (using AS and AE). Following the concept of the Mori-Tanaka's (MT) method, three MFH schemes obtained above were reduced to MT-NS, MT-NE and MT-SE, respectively. Effective elastic properties of composites consisting of isotropic elastic matrices and spherical isotropic elastic inclusions were predicted using these schemes and compared with experimental results. The comparison revealed that MT-SE and MT-NS can reasonably replicate the experimental results in the case of moderate particle volume fractions and ratios between the Young's moduli of matrix and the reinforcement particles, demonstrating the validity of the MFH schemes. This work is significant because it not only clarifies the correlation of AE with AN and AS, but also provides more options for the development of MFH schemes, which can enrich the theory and methods for the analysis of the effective properties of composites.

Фазовый состав и морфология поверхности бронзы БрО10С10 после ее электроискровой обработки анодным материалом аналогичного состава

The coating on the surface of BrO10C10 bronze was studied by scanning electron microscopy and X-ray diffractometry. It was obtained by electrospark processing with an anode material with a composition similar to that of the substrate. X-ray studies of the phase composition revealed the presence of phases of the “copper – tin” system (Cu, α-(Cu; Sn), Cu3Sn, ε-Cu3Sn and Cu5.6Sn) and lead. The incorporation of atmospheric elements and initial bronze components into lead leads to the formation of regions with a distorted crystal lattice. An increase in the energy of a single pulse of an electric spark discharge is accompanied by a decrease in the α-(Cu; Sn) phase and an increase in the content of ε-Cu3Sn and Cu5.6Sn. The ratio of intensities indicates the absence of a predominant orientation of growth (texture) in the electrospark coating. Scanning electron microscopy data indicate the presence of melted areas, pores, spherical and oval inclusions, irregularly shaped particles, cracks, rounded pits, etc. in the surface layer. The main reason for the presence of melted areas is high temperatures in the interelectrode region during an electric spark discharge. The appearance of surface cracks is primarily associated with the occurrence of high thermal stresses and interelectrode mechanical contact. The presence of spherical/oval particles is a consequence of the interaction of liquid droplets with the surface of the cathode substrate. Irregularly shaped particles appear as a result of explosive emission from the edges of the erosion crater of the anode material.