Cuboidal Inclusions Research Articles

Experimental observations of nucleation and crack growth paths of hydrogen-induced cracking in pipeline steel

The microstructural features that favor hydrogen-induced cracking (HIC) in internal, middle, and external layers of pipeline steels were investigated. The electrochemical cathodic charging was used to induce HIC, and straight beam ultrasonic inspection was identified in which steel layers HIC nucleate and grow. The cracked plates were examined by optical microscope and scanning electron microscope (SEM). The hydrogen microprint technique (HMT) was used to visualize the site of high hydrogen concentrations. Electron backscatter diffraction (EBSD) was used to analyze the role of crystallographic texture in HIC pathways. The results revealed that HIC nucleation and growth are influenced by the segregation degree and inclusion contents, which are higher in the internal surface layer of our studied steels but not consistently so in the middle thickness layer. Further, HIC nucleated in cuboidal and spinal inclusions and propagated along ferrite/pearlite bands with high misorientations. The HMT results showed that hydrogen is present in pearlite colonies, grain boundaries, and non-metallic inclusions. The results indicated that HIC is not solely controlled by the crack geometry.

The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions

The article offers a general formulation for the multipolar field expansion of an inclusion. The multipolar moments of arbitrary order for the ellipsoidal inclusion are derived, showing known features of their elastic fields in both the far and near field. Using integer point enumeration theory, the same formulation is extended to all polytopal inclusions, which serve to model faceted inclusions found in, e.g. igneous and metamorphic rocks, particle reinforced composite materials, or as intermetallic precipitates in alloys. A general algorithm for the calculation of the multipolar moments of polytopes of any number of vertices is derived. A number of examples for tetrahedral, cuboidal and dodecahedral inclusions are given. It is shown that the parity of the axial moment function of a polytopal inclusion mirrors the symmetry of the inclusion. This represents the main properties of their elastic fields, including the long- and near-field decay. If the inclusion is symmetric with respect to a given axes, the fields will decay with 1 / r 2 in the far field and 1 / r 4 in the near field. If symmetry along that direction is lost, as is expected in most real inclusions, the decay rate progresses with 1 / r 2 but the near field with 1 / r 3 .

Distribution behavior of inclusions in compact-strip-produced martensitic steel and its influence on mechanical properties

The distribution behavior of inclusions in martensitic steel produced by compact strip production process (CSP-MS) and its influence on mechanical properties were systematically investigated. The inclusions in the CSP-MS specimen are mainly composed of spherical Al2O3-CaO-CaS, MnS with high aspect ratio and small-sized TiN, whereas many coarse cuboidal TiN inclusions do exist in conventional martensitic steel (Con-MS). The high inclusion density of the CSP-MS specimen resulted in lower total elongation and impact toughness, and the MnS inclusions with high aspect ratio led to significantly stronger mechanical anisotropy than that for Con-MS specimen. The in-situ tensile results indicated that when the fracture direction is parallel to MnS direction, the microcracks induced by MnS inclusions tend to propagate into the matrix, leading to the formation of valley-like features, which significantly deteriorate the properties such as the total elongation and impact toughness. The microcracks caused by TiN inclusions are sharper than those caused by spherical Al2O3-CaO-CaS inclusions, and are easy to propagate into the matrix. This work is expected to guide the optimization of the mechanical properties of martensitic steels produced by CSP process and provide a theoretical basis for the CSP process design.

Larvicidal toxicity and parasporal inclusion of native Bacillus thuringiensis BK5.2 against Aedes aegypti.

Native Bacillus thuringiensis BK5.2, isolated from soil of Baluran National Park, East Java, Indonesia, has been shown to be toxic against Aedes aegypti larvae. This study aims to determine the strength and the speed of the toxicity of B.thuringiensis BK5.2 against A.aegypti larvae in lethal concentration (LC) and lethal time (LT), as well as detection of toxin structure and parasporal inclusion. LC values were determined by the mortality of A.aegypti third instar larvae after 24 and 48h exposure to five various concentrations of B.thuringiensis BK5.2, while LT values were determined based on the mortality of A.aegypti third instar larvae due to exposure to LC90 concentration at 0; 0.5; 1; 2; 4; 8; 10; 20; 24; and 48h. Larvicidal toxicity was determined based on value of LC50 and LC90 (CFU/mL), as well as LT50 and LT90 (hours) analysed ​​with Probit analysis. Parasporal inclusion was detected using transmission electron microscope (TEM) and scanning electron microscope (SEM). Based on bioassay, LC50 and LC90 values ​​were 11.6×106 and 22.7×106CFU/mL, respectively, at 24h exposure, as well as 8.3×106 and 15.4×106CFU/mL, respectively, at 48h exposure, while the value of LT50 and LT90 were 19.0 and 26.6h, respectively. Morphological observation of the dead larvae showed there was damage on abdomen and thorax region. Detection by TEM and SEM showed there was cuboidal parasporal inclusion. Native B.thuringiensis BK5.2 has high toxicity against A.aegypti larvae and detected flatcuboidal toxin in parasporal inclusion.

An efficient method for the elastic field in a transversely isotropic full space due to arbitrary inclusions

The present study is on the analytical solution for the elastic field due to a cuboidal inclusion of uniform eigenstrain within a transversely isotropic full-space material, and a numerical method to model inclusions of any arbitrary shapes and with any eigenstrain distributions as the integration of a set of such cuboidal inclusions. The fast Fourier transform (FFT) is applied for efficient computation. The developed method and results are implemented to analyze the elastic field in a transversely isotropic full-space material containing inclusions of different shapes, different eigenstrain distributions, and multiple cuboids of different densities. Furthermore, the effect of material anisotropy on the stress field subjected to a spherical inclusion with pure dilatant eigenstrains is explored by comparing the behavior of a transversely isotropic material with that of a corresponding isotropic one. The numerical results show that the induced stresses are drastically influenced by the Young’s moduli of transversely isotropic materials, and that material constant C33 has a large influence on normal stress σ33.

A coupled damage model and a semi-analytical contact solver to simulate butterfly wing formation around nonmetallic inclusions

This paper presents a damage modeling approach to simulate the formation of butterfly wings in rolling contact fatigue coupled with a fast method for solving 3D contact problems with the presence of a spherical heterogeneity. The damage model is implemented in a semi-analytical model using the Eshelby’ s equivalent inclusion method in the contact solver. The proposed technique can easily include the effects of heterogeneous inclusions to the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to the use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space are superimposed to represent the microstructural alterations during butterfly wings formation.

Inversion of displacement fields to quantify the magnetic particle distribution in homogeneous elastic media from magnetomotive ultrasound

Magnetomotive ultrasound (MMUS) contrasts superparamagnetic iron-oxide nanoparticles (SPIOs) that undergo submicrometer-scale displacements in response to a magnetic gradient force applied to an imaging sample. Typically, MMUS signals are defined in a way that is proportional to the medium displacement, rendering an indirect measure of the density distribution of SPIOs embedded within. Displacement-based MMUS, however, suffers from ‘halo effects’ that extend into regions without SPIOs due to their inherent mechanical coupling with the medium. To reduce such effects and to provide a more accurate representation of the SPIO density distribution, we propose a model-based inversion of MMUS displacement fields by reconstructing the body force distribution. Displacement fields are modelled using the static Navier-Cauchy equation for linear, homogeneous, and isotropic media, and the body force fields are, in turn, reconstructed by minimizing a regularized least-squares error functional between the modelled and the measured displacement fields. This reconstruction, when performed on displacement fields of two tissue-mimicking phantoms with cuboidal SPIO-laden inclusions, improved the range of errors in measured heights and widths of the inclusions from 54%–282% pre-inversion to-15%–20%. Likewise, the post-inversion contrast to noise ratios (CNRs) of the images were significantly larger than displacement-derived CNRs alone (p = 0.0078, Wilcoxon signed rank test). Qualitatively, it was found that inversion ameliorates halo effects and increases overall detectability of the inclusion. These findings highlight the utility of model-based inversion as a tool for both signal processing and accurate characterization of the number density distribution of SPIOs in magnetomotive imaging.

Semi-analytical solution for steady state heat conduction in a heterogeneous half space with embedded cuboidal inhomogeneity

A three dimensional model for solving steady state heat conduction in a semi-infinite domain containing an elementary cuboidal inhomogeneity is established in this paper. A set of analytical formulas for steady state heat conduction in a full space with an embedded cuboidal inclusion is derived. The temperature field of a half space distributed with arbitrarily shaped inhomogeneities is then obtained via the application of numerical discretization and the method of images. Benchmark comparisons involving a cuboidal/ellipsoidal inhomogeneity and double-inhomogeneity particle with the results produced by the finite element method (FEM) are conducted. Good agreements between the results of the two methods demonstrate the effectiveness and capability of the proposed model. Further, a case of heterogeneous material containing arrayed inhomogeneities is studied to explore the disturbance and interaction of the temperature field due to distributed inhomogeneities.

A damage model for fretting contact between a sphere and a half space using semi-analytical method

This paper presents a fast method of solving 3D contact problems when one of the mating bodies has an elastic-damageable behavior. The damage model is implemented in a semi-analytical model using Eshelby’ s equivalent inclusion method in the contact solver. The proposed technique can be seen as an enrichment technique for which the effect of heterogeneous inclusions is surimposed on the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to a massive use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space and with the same elastic properties are surimposed. The damage model affects the elastic properties of the cuboidal inclusions. The emphasis is put on the effects of the fretting regimes on the contact pressure and damage evolution.

Elastic fields caused by eigenstrains in two joined half-spaces with an interface of coupled imperfections: Dislocation-like and force-like conditions

This paper presents the derivation of a set of the novel closed-form solutions for the eigenstrain-induced elastic fields in two joined half-space solids with an interface of coupled dislocation-like and force-like imperfects. A model is proposed to characterize the interfacial discontinuity properties concerning displacements and stresses, which permits quantitative jumps of either the displacements or the stresses from one medium to the other. Basic Galerkin vectors in these two imperfectly joined half-spaces are derived based on the boundary conditions, and thus the elastic responses are obtained in explicit expressions. Taking advantage of the three-dimensional fast Fourier Transform algorithms for the convolution and correlation, the elastic fields subjected to one arbitrarily shaped inclusion or more can be efficiently and accurately evaluated. The influences of several types of interfaces, such as the perfectly bonded interface, the dislocation-like interface, and the force-like interface, on the stress and displacement transmissions are discussed. Cases for the elastic fields due to a cuboidal, a spherical, and an array of multiple cuboidal inclusions, are investigated.

On the elastic field of Al/SiC nanocomposite

This study aims to analyze the linear elastic behavior of an aluminum matrixnanocomposite reinforced with SiC nanoparticles. Once, a representative volume element was consideredfor the nanocomposite with a cuboidal inclusion. The elastic moduli of the matrix and the inclusion werethe same, but it contained eigenstrain. The stress and the strain fields were obtained for the inclusionand the aluminum by Galerkin vector method. The stress and the strain fields in the inclusion problemwere in a good agreement with the results in the literature. A similar representative volume element wasconsidered for the nanocomposite with a cuboidal inhomogeneity. The elastic moduli of the matrix andthe inhomogeneity were different, but it did not have any eigenstrain. For the calculation of the Eshelbytensor and the elastic fields for the inhomogeneity problem, the equivalent inclusion method (EIM) wasapplied. In the EIM, the uniform and equivalent eigenstrain were considered. The stress and the strainfields within the inhomogeneity and the matrix were obtained. Results showed that the stress and thestrain in the cuboidal inclusion were less than the cuboidal inhomogeneity due to the difference betweenthe matrix and the reinforcement materials.

Additively manufactured artificial materials with metallic meta‐atoms

The paper presents the analysis and fabrication of artificial materials with metallic cuboid inclusions (termed here as meta-atoms) in a dielectric host material. These synthetic materials or metamaterials have been additively manufactured with a fused deposition modelling (FDM) 3D-printer. The effective permittivity and permeability have been numerically analyzed using the Maxwell-Garnett and Lewin’s approximation. Simulations and measurements have shown good agreement with analytical calculations. The anisotropy of the heterogeneous mixture due to the orientation of the meta-atoms has been demonstrated. The effective permittivity has been increased by the presence of the meta-atoms, which has the potential of producing 3D-printing metamaterials with tailored electromagnetic properties.

Viscoelastic properties of heterogeneous materials: The case of periodic media containing cuboidal inclusions

This paper presents analytical solutions for the effective viscoelastic properties of composite materials based on a homogenization approach. The cases of spherical inclusions and cracks were recently developed. The objective of this paper is to use the same technique to deal with the case of periodic media containing cuboidal inhomogeneities. The viscoelastic behavior of both the matrix and the homogeneous equivalent medium is modeled by the Zener rheological model while inclusions are assumed to be linearly elastic. The viscoelastic Hill tensor required for the calculation of the effective viscoelastic tensors is obtained explicitly in the Laplace-Carson space in terms of Fourier series. The final expressions show that overall behavior depends on the viscoelastic properties of the matrix, the 3D dimensions of the inclusions and the thickness of the matrix layer between two nearby inclusions. Applications to masonry structures are presented to illustrate the theoretical results.

Analytical solutions for the elastic fields caused by eigenstrains in two frictionlessly joined half-spaces

Analytical solutions to the elastic fields induced by eigenstrains, such as plastic strains, in materials subjected to different types of joints are important for developing numerical simulations of advanced materials. This paper reports the derivation of a set of explicit integral kernels for the eigenstrain-induced elastic fields in two frictionlessly joined half-space solids or bi-materials. The elastic responses caused by arbitrary inclusions inside one of the two joined half-spaces are solved for the cases of known Galerkin vectors for the inclusion in the half-space solid. By discretizing the arbitrarily shaped single or multiple inclusions into a number of small elementary cuboids, the entire elastic response to the inclusions can be obtained through summation of the contributions from all elements with the assistance of the fast Fourier transform algorithms for convolution or correlation involved in the solutions. Cases for the elastic fields which subjected to a cuboidal, and a spherical, as well as multiple cuboidal inclusions are analyzed; and key results compared with the corresponding results for perfectly bonded half spaces. The phenomenon of probable interface separation associated with frictionless interfacial condition is further discussed.

Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems

This paper reports the derivation of the explicit integral kernels for the elastic fields due to eigenstrains in two joined and perfectly bonded half-space solids or bimaterials. The domain integrations of these kernels result in the analytical solutions to displacements and stresses. When the eigenstrains are all in solid I, the kernel for the elastic fields has four groups in this solid and two groups in the other joined solid. Explicit closed-form solutions for a cuboidal inclusion with uniform eigenstrains are derived as the basic solutions, i.e., the influence coefficients. When the computational domain is meshed into cuboidal elements of the same sizes, the total elastic fields can be quickly obtained by implementing three-dimensional fast Fourier transform-based algorithms. The results for the fields due to a cuboidal, a spherical, and a cylindrical inclusion, as well as multiple cuboidal inclusions are presented and discussed. Residual stresses in an elasto-plastic contact involved a coated substrate is further analyzed with the new solution approach.

Microstrip Patch Antennas With Anisotropic and Diamagnetic Synthetic Heterogeneous Substrates

This communication examines the performance of a rectangular patch antenna on heterogeneous substrates composed of metallic cuboid inclusions compared with homogenous substrates via simulations and measurements. The communication examines how the orientation of the inclusions affects the performance of the patch antenna. Anisotropy and diamagnetism of the heterogeneous substrate with metallic cuboid inclusions have been analyzed. As the resonant frequency of the patch is dependent on the electromagnetic (EM) parameters of its substrate(s), fixing the size of the patch and altering its substrates allows the EM properties of the substrates to be estimated and compared with predictions from theory and simulations.

Studies of permittivity and permeability of dielectric matrix with cuboid metallic inclusions in different orientations

In this paper, we investigate the possibility of using the heterogeneous materials, with cuboid metallic inclusions inside a dielectric substrate (host) to control the effective permittivity. We find that in the gigahertz range, such a material demonstrates a significantly larger permittivity compared to the pure dielectric substrate. Three principal orientations of microscale cuboid inclusions have been taken into account in this study. The highest permittivity is observed when the orientation provides the largest polarization (electric dipole moment). The detrimental side effect of the metallic inclusion, which leads to the decrease of the effective magnetic permeability, can be suppressed by the proper choice of shape and orientation of the inclusions. This choice can in fact reduce the induced current and hence maximize the permeability. The dissipative losses are shown to be negligible in the relevant range of frequencies and cuboid dimensions.

High Resolution Diffraction of a Superalloy during HT Processing and Mechanical Testing: Experiments and Modeling

We present a computer inexpensive method to calculate the profile of the high resolution diffraction pattern of a single crystal superalloy. The displacement field is taken as the sum of the individual fields of cuboidal inclusions with uniform eigenstrains. Early simulations are compared to experimental data.

An Efficient Numerical Method With a Parallel Computational Strategy for Solving Arbitrarily Shaped Inclusions in Elastoplastic Contact Problems

Abstract The plastic zone developed during elastoplastic contact may be effectively modeled as an inclusion in an isotropic half space. This paper proposes a simple but efficient computational method to analyze the stresses caused by near surface inclusions of arbitrary shape. The solution starts by solving a corresponding full space inclusion problem and proceeds to annul the stresses acting normal and tangential to the surface, where the numerical computations are processed by taking advantage of the fast Fourier transform techniques with a parallel computing strategy. The extreme case of a cuboidal inclusion with one facet on the surface of the half space is chosen to validate the method. When the surface truncation domain is extended sufficiently and the grids are dense enough, the results based on the new approach are in good agreement with the exact solutions. When solving a typical elastoplastic contact problem, the present analysis is roughly two times faster than the image inclusion approach and six times faster than the direct method. In addition, the present work demonstrates that a significant enhancement in the computational efficiency can be achieved through the introduction of parallel computation.

On the polarizability and capacitance of the cube

An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually every permittivity ratio for which it exists. For example, polarizabilities accurate to between five and ten digits are obtained (as complex limits) for negative permittivity ratios in minutes on a standard workstation. In passing, the capacitance of the unit cube is determined with unprecedented accuracy. With full rigor, we develop a natural mathematical framework suited for the study of the polarizability of Lipschitz domains. Several aspects of polarizabilities and their representing measures are clarified, including limiting behavior both when approaching the support of the measure and when deforming smooth domains into a non-smooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials.