Spatial Distribution Of Inclusions Research Articles

Effects of the orientation distribution of thin soft inclusions on the effective elastic moduli of microheterogeneous material

Many natural composite materials such as carbonate rocks contain systems of oriented or partially oriented thin inclusions (microcracks) filled with a soft elastic cement. In this paper we have studied the influence of the inclusion orientation, shape, and elastic properties on the effective elastic properties of micro-inhomogeneous materials. We have calculated the components of the compliance tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with elastic compliance much larger than the elastic compliance of the matrix. To calculate the effective compliance tensor, we have used the “non-interaction approximation” (NIA). The application of the NIA allows us to evaluate the influence of peculiarities in the spatial distribution of inclusions on the effective properties of the medium. To simplify the calculations, we have used the special tensorial basis (T-basis). We have obtained the explicit expressions for the effective elastic compliance tensor of inhomogeneous materials. To verify the analytical expressions, we have compared our results for elastic moduli to the results obtained by numerical modeling of a material containing crack-like inclusions. The results obtained by using the two methods are in very good agreement, thus indicating that our analytic method can be applied even at sufficiently large values of crack density.

High‐fidelity random fiber distribution algorithm based on fiber spreading process

AbstractThe performance of fiber‐reinforced composites is not only determined by their constituents, but also by the spatial distribution of inclusions. The traditional random distribution algorithm only considers the randomness of its relative position, and every newly generated fiber has to be checked with all the existing fibers, which requires a large amount of calculation. In this paper, inspired by the spreading process that the fibers are not arranged randomly, but the forces acting on the upper and lower rows of fibers. A random fiber distribution algorithm based on partition randomness is proposed, and a microscopic model of in‐plane fibers with random distribution is established. The maximum volume fraction of fibers generated by the algorithm is 75%, and the generation time is less than 20s. Statistical characterization and finite element analysis of the structure generated by the algorithm are compared with the experimental data to verify the randomness and effectiveness of fibers. The algorithm overcomes the jamming limit of the traditional hard‐core method, and can efficiently generate random microstructure models with different volume fractions, which can be a promising alternative for modeling and analysis of unidirectional fiber‐reinforced composites.

Characterization and analysis of alumina clusters in steel by X-ray Micro-CT

The properties of steel are affected by the non-metallic inclusions. It is critical to control the morphology of inclusions for producing the high-quality steel. However, due to the morphology of inclusions is complex and diverse, it is difficult to reveal the real morphology of inclusions by using the traditional two-dimensional (2D) observation method, and making it hard to quantitatively analyze the size and morphology of inclusions. In this study, the three-dimensional (3D) morphology of the alumina clusters in steel samples was observed by using the X-ray Micro-CT in the beamline of BL16U2 at Shanghai Synchrotron Radiation Facility (SSRF). Avizo software was used to reconstruct the 3D morphology of the alumina clusters, which intuitively shows the actual morphology of alumina clusters. The accuracy of 2D and 3D observation methods is discussed based on the stereological analysis of individual alumina cluster. A series of parameters were defined to characterize the morphological characteristics of the alumina clusters based the 3D observation. The fractal theory was introduced to quantitatively describe the morphological of alumina clusters. In the current study, the 2D fractal dimension of alumina clusters was determined as 1.64. The complexity of 3D morphology of alumina clusters was analyzed by 3D fractal dimension and shape factor. The current work provides an effective method for quantitative description of the morphology and spatial distribution of inclusions, which provides an important reference for effective control of alumina inclusions.

Mechanical characterization of highly heterogeneous brittle materials by optical techniques

Fragmentation processes like crushing and grinding are complex and extensively energy-consuming activities in the mining and mineral processing industry. By studying the processes and the typically brittle material involved in a virtual environment, i.e. numerical simulations, knowledge will be gained to support improvement of the efficiency and thereby meet established environmental goals. Although, a challenge is the lack of experimental data both for calibration and validation hampering the development of constitutive models. As a case of study, a mechanical characterization of MnSiFe-slag was performed. X-ray Computed Tomography was used for 3D imaging and quantitative characterization of the material texture, with focus on the shape, size and spatial distribution of inclusions. Diametral and axial compressive tests under quasi-static conditions were used to load the mineral material and obtain a strain field (ε) during increasing and cyclic loading until failure accounting for progressive damage. The evolution of the strain captured by digital image correlation (DIC) techniques exposed a mechanical behavior of composite-like material where random failure of the components caused high variability of the elastic parameters. These were found to be load dependent and they are strongly related to the ability of the material to internal re-arrangement during loading. Irreversible damage affects the structure of the material and it is perceived as non-linearities in the load–strain curves. It was found a degradation of the material under repetitive loading. A decrease of the elastic modulus exposes a weakening of the matrix and dominant behavior of the inclusions on the mechanical response of the material.

Effect of the orientation distribution of thin highly conductive inhomogeneities on the overall electrical conductivity of heterogeneous material

Many natural composite materials contain systems of partially oriented thin low-resistivity inclusions (for example, water-saturated microcracks in a double porosity sedimentary formation). We have calculated the components of the electrical conductivity tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with conductivity (electrical or thermal) much larger than the matrix conductivity. To calculate the effective conductivity, we have used the effective field method (EFM). We have obtained the explicit expressions for the effective parameters of inhomogeneous materials. The application of the EFM allows one to describe the influence of the peculiarities in the spatial distribution of inclusions on the effective properties of the medium. General explicit expressions, obtained in this work, are illustrated by calculation examples for inclusions, homogeneously distributed in the sector [-Beta, Beta], where Beta is the disorientation angle, and some continuous angle distribution functions. The calculations have shown that the spatial distribution of the crack-like inclusions strongly affects the conductive properties of the effective medium and the symmetry of their tensor.

Prediction on the three-dimensional spatial distribution of the number density of inclusions on the entire cross section of a steel continuous casting slab

In the current study, the LES turbulent model, heat transfer, solidification, species transport model, and discrete phase model (DPM) were coupled to investigate the three-dimensional transient flow, temperature, solidification, segregation, and inclusion transport during the slab continuous casting (CC) process. The number, size, and spatial distribution of inclusions on the entire cross section of the CC slab were successfully predicted using the coupled full solidification model, DPM, and capture criteria at the solidification front. The improved capture criteria that considering the primary dendrite arm spacing (PDAS), different forces acting on inclusions, and the critical capture speed, successfully eliminated the banded distribution characteristics of inclusions under the simple capture criterion. The prediction results were in good agreement with the detection results. Four accumulation zones of inclusions along the thickness of the CC slab were predicted, including the 1/4 thickness and 3/4 thickness from the loose side, and the layer beneath the surface of the CC slab. Two accumulation zones near the layer beneath the surface of the CC slab were issued from the double roll flow pattern in the CC strand. The probability of inclusions contacting the solidification front in the upper recirculation zone increased, increasing the entrapment rate. The accumulation zones near the 1/4 thickness and 3/4 thickness from the loose side were corresponded to the peak value of the Marangoni force on inclusions at the 1/4 thickness and 3/4 thickness from the loose side. The Marangoni force increased the probability of inclusions being pushed to the solidification front. In addition, the accumulation near the 1/4 thickness from the loose side became more severe as the diameter of the inclusions increased due to the buoyancy.

Non-metallic inclusions in a superalloy during refining through cold crucible levitation melting process

Oxide and nitride inclusions in a Ni-based superalloy during the cold crucible levitation melting (CCLM) process were investigated towards a better understanding for the removal of inclusions from the metal. The number, morphology, size distribution and spatial distribution of inclusions were characterized using an automated scanning electron microscopy with energy-dispersive X-ray spectroscopy. Inclusions in the alloy were efficiently agglomerated and removed by floating during CCLM process. Inclusion clusters as big as 30-400 ?m were observed. Oxide clusters were efficiently floated during pouring process. The removal ratios of oxides were about 21% without pouring and 62% with pouring, respectively. Additionally, CCLM promotes the separation of oxides from nitrides. The effect of CCLM on the removal of nitride inclusions is not such evident compared with oxides. The mechanism of inclusion removal during CCLM was clarified.

Damage Evolution of Coal with Inclusions Under Triaxial Compression

Along with the advance of the working face, coal experiences different loading stages. Laboratory tests and numerical simulations of fracture and damage evolution aim to better understand the structural stability of coal layers. Three-dimensional lab tests are performed and coal samples are reconstructed using X-ray computer tomography (CT) technique to get detailed information about damage and deformation state. Three-dimensional discrete element method (DEM)-based numerical models are generated. All models are calibrated against the results obtained from uniaxial compressive strength (UCS) tests and triaxial compression (TRX) tests performed in the laboratory. A new approach to simulate triaxial compression tests is established in this work with significant improved handling of the confinement to get realistic simulation results. Triaxial tests are simulated in 3D with the particle-based code PFC3D using a newly developed flexible wall (FW) approach. This new numerical simulation approach is validated by comparison with laboratory tests on coal samples. This approach involves an updating of the applied force on each wall element based on the flexible nature of a rubber sleeve. With the new FW approach, the influence of the composition (matrix and inclusions) of the samples on the peak strength is verified. Force chain development and crack distributions are also affected by the spatial distribution of inclusions inside the sample. Fractures propagate through the samples easily at low confining pressures. On the contrary, at high confining pressure, only a few main fractures are generated with orientation towards the side surfaces. The evolution of the internal fracture network is investigated. The development of microcracks is quantified by considering loading, confinement, and structural character of the rock samples. The majority of fractures are initiated at the boundary between matrix and inclusions, and propagate along their boundaries. The internal structure, especially the distribution of inclusions has significant influence on strength, deformation, and damage pattern.

Effect of powder characteristics and oxygen content on modifications to the microstructural topology during hot isostatic pressing of an austenitic steel

The effect of powder size distribution and oxygen content on the extent of multiple twinning and spatial distribution of oxide inclusions in hot isostatic pressed (HIPed) 316L steels was investigated using powders with different characteristics. Modifications to, and differences in their microstructural topology, were tracked quantitatively by evaluating the metrics related to twin related domains (TRDs) on specimens produced by interrupting the HIPing process at various points in time. Results revealed that powder size distribution has a strong effect on the extent of multiple twinning in the fully HIPed microstructure, with specimens produced using narrow distribution showing better statistics (i.e., homogeneously recrystallized) than the ones produced using broad size distribution. The oxide inclusion density in fully HIPed microstructures increased with the amount of oxygen content in the powders while prior particle boundaries (PPBs) were only observed in the specimens that were HIPed using broad powder distribution. More importantly, results clearly revealed that the spatial distribution of the inclusions was strongly affected by the homogeneity of recrystallization. Implications of the results are further discussed in a broader context, emphasizing the importance of utilizing the occurrence of solid state phase transformations during HIPing for controlling the microstructure evolution.

Effect of Powder Characteristics and Oxygen Content on Modifications to the Microstructural Topology During Hot Isostatic Pressing of an Austenitic Steel

The effect of powder size distribution and oxygen content on the extent of multiple twinning and spatial distribution of oxide inclusions in hot isostatic pressed (HIPed) 316L steels was investigated using powders with different characteristics. Modifications to, and differences in their microstructural topology, were tracked quantitatively by evaluating the metrics related to twin related domains (TRDs) on specimens produced by interrupting the HIPing process at various points in time. Results revealed that powder size distribution has a strong effect on the extent of multiple twinning in the fully HIPed microstructure, with specimens produced using narrow distribution showing better statistics (i.e., homogeneously recrystallized) than the onesproduced using broad size distribution. The oxide inclusion density in fully HIPed microstructures increased with the amount of oxygen content in the powders while prior particle boundaries (PPBs) were only observed in the specimens that were HIPed using broad powder distribution. More importantly, results clearly revealed that the spatial distribution of the inclusions was strongly affected by the homogeneity of recrystallization. Implications of the results are further discussed in a broader context, emphasizing the importance of utilizing the occurrenceof solid state phase transformations during HIPing for controlling the microstructure evolution.

Detection of Non-metallic Inclusions in Centrifugal Continuous Casting Steel Billets

In the current study, automated particle analysis was employed to detect non-metallic inclusions in steel during a centrifugal continuous casting process of a high-strength low alloy steel. The morphology, composition, size, area fraction, amount, and spatial distribution of inclusions in steel were obtained. Etching experiment was performed to reveal the dendrite structure of the billet and to discuss the effect of centrifugal force on the distribution of oxide inclusions in the final solidified steel by comparing the solidification velocity with the critical velocity reported in literature. It was found that the amount of inclusions was highest in samples from the tundish (~250 per mm2), followed by samples from the mold (~200 per mm2), and lowest in billet samples (~86 per mm2). In all samples, over 90 pct of the inclusions were smaller than 2μm. In steel billets, the content of oxides, dual-phase oxide–sulfides, and sulfides in inclusions were found to be 10, 30, and 60 pct, respectively. The dual-phase inclusions were oxides with sulfides precipitated on the outer surface. Oxide inclusions consisted of high Al2O3 and high MnO which were solid at the molten steel temperature, implying that the calcium treatment was insufficient. Small oxide inclusions very uniformly distributed on the cross section of the billet, while there were more sulfide inclusions showing a banded structure at the outside 25 mm layer of the billet. The calculated solidification velocity was higher than the upper limit at which inclusions were entrapped by the solidifying front, revealing that for oxide inclusions smaller than 8μm in this study, the centrifugal force had little influence on its final distribution in billets. Instead, oxide inclusions were rapidly entrapped by solidifying front.

Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: a size effect study

Size effect in concrete under tension is studied by Monte Carlo simulations of mesoscale finite element models containing random inclusions (aggregates and pores) with prescribed volume fractions, shapes and size distributions (called meso-structure controls). For a given size and a set of controls, a number of realisations with different spatial distribution of inclusions are simulated to produce statistical data for macroscopic load/stress–strain curves. The complex meso-crack initiation and propagation is captured by pre-inserted cohesive interface elements. The effects of specimen size and meso-structure controls on macroscopic strength and toughness are analysed, and empirical size-effect laws for their dependences are proposed by data regression. It is also shown that the mesoscale porosity affects both strength and toughness and should not be ignored in size effect studies of concrete.

Intrinsic electromagnetic parameters of particulate inclusions

A scheme is proposed for predicting the intrinsic electromagnetic parameters of particulate inclusions which taking into account the aspect ratio, orientation, shape and the spatial distribution of inclusions. The predicted intrinsic complex dielectric constant and complex permeability of flaky carbonyl-iron particles from carbonyl-iron–paraffin composites with different volume concentrations which considering the directional distribution of flaky particles are very close to each other, and the predicted effective dielectric constant of carbonyl-iron–paraffin composite based on the numerical results agree well with the experimental data.

Dispersion quantification of inclusions in composites

Distribution of constituents within a composite material dictates important constitutive properties and is therefore of interest for all multiphase materials including nano-, micro-, and macro-composites. In the first part of this paper, previously proposed methods for quantifying dispersion are reviewed and their applications and possible shortcomings are discussed. In the second part, we propose a novel definition for dispersion based on the thermodynamic concept of work; dispersion is measured based on the amount of work required to translate inclusions so they form the state of maximum uniformity. The method quantifies dispersion with a single parameter. Although multiple parameter methods can provide more information about the spatial distribution of inclusions, the proposed method is particularly useful when comparing overall dispersion quality of different domains. As an example, the dispersion of carbon nanotubes in an Al coating is quantified to demonstrate the robustness and practicality of the novel dispersion quantification method.

Propagation of low-frequency elastic waves in double-porositymedia containing viscoelastic component in the pores

A self-consistent scheme named the effective field method (EFM) is applied for the calculation of the velocities and quality factors of elastic waves propagating in double-porosity media. A double-porosity medium is considered to be a heterogeneous material composed of a matrix with primary pores and inclusions that are represent by flat (crack-like) secondary pores. The prediction of the effective viscoelastic moduli consists of two steps. First, we calculate the effective viscoelastic properties of the matrix with the primary small-scale pores (matrix homogenization). Then, the porous matrix is treated as a homogeneous isotropic host where the large-scale secondary pores are embedded. Spatial distribution of inclusions in the medium is taken into account via a special two-point correlation function. The results of the calculation of the viscoelastic properties of double-porosity media containing isotropic fields of crack-like inclusions and double-porosity media with some non-isotropic spatial distributions of crack-like inclusions are presented.

X-ray computer tomography of natural fibrous diamonds and ballas

The results of investigation of natural fibrous diamonds by laboratory X-ray computer tomography using monochromatic radiation are presented. The existence of numerous heterophase microinclusions in fibrous crystals is established. Spatial distribution of inclusions can be connected both with morphological features of crystals, and with growth conditions. It is established that the ballas practically does not contain inclusions of extraneous phases.

Thermal conductivity of composite material with coated inclusions: Applications to tetragonal array of spheroids

The aim of this article is to determine the effective thermal conductivity of a composite material made of ellipsoidal coated inclusions bonded to a homogeneous isotropic matrix. The distribution of inclusions is considered to be periodic, nevertheless complex pattern can be investigated. An analytical approximate method, which takes into account interactions between inclusions at finite concentration, is proposed to solve steady state heat conduction problems. This method is an extension of the cluster scheme proposed, for elastic materials, by A. Molinari and M. E. Mouden Int. J. Solids Struct., 33, 3131 (1996). The morphological and spatial distribution of inclusions is accounted for in the present approach. Through different examples, results are compared to existing analytical or numerical solutions.

A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions

In this paper, a generalized self-consistent method is proposed to predict the effective moduli of a material containing single-phase and randomly oriented spheroidal inclusions, with same aspect ratios. This is achieved by using an energy equivalence framework, associated with a generalization of the classical three phase model to spheroidal inclusions. The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix. Finally, the determination of the effective moduli is equivalent to solving a system of nonlinear equations. Effective moduli are presented for various types of inclusions, and comparisons are made with the estimations obtained from the self-consistent and Mori-Tanaka methods. Moreover, the effects of inclusion geometry and spatial distribution of inclusions on the effective moduli are investigated and compared to each other.

Molecular Theory of Lipid-Protein Interaction and the Lα- HII Transition

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer ( L α ) to the inverse-hexagonal ( H II) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., “cylinder-like,” “barrel-like,” or “vase-like.” We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the H II lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the L α → H II transition. At the transition, a peptide-poor L α phase coexists with a peptide-rich H II phase.

Numerical Simulation of Inclusion Size Distribution Responsible for Fatigue Crack Initiation.

Numerlcal simulations considering spatial and size distributions of nonmetallic inclusions in the material have been carried out for the purpose of initiating a discussion concerning the critical size of the inclusion responsible for the fatigue failure of high-strength steel. Results show that the geometrically largest inclusion within a critical volume of the specimen is not necessarily responsible for the fatigue failure of such material, and that the most dangerous inclusion for fatigue failure is that of the near surface having the largest relative inclusion size calculated from the spatial distribution of inclusions within the critical volume of the specimen.