Aspect Ratio Of Inclusions Research Articles

First‐Principles Calculation and In Situ Observation on the Precipitation of Inclusions during Solidification of a High Sulfur Steel

The precipitation process of inclusions in the high sulfur steel with the cerium addition is observed using the high‐temperature confocal scanning laser microscope (CSLM). Rare earth (Re) inclusions formed in the molten steel, and MnS inclusions precipitate along grain boundaries or on oxide cores at the end of solidification. With the addition of cerium, the average aspect ratio of inclusions in the steel decreases from 6.5 to 5.0, and the addition of cerium effectively modifies the elongated MnS. Thermodynamic calculations show the inclusion transformation during solidification, yet it lacked the formation of Ce2O2S and Re sulfides. According to the first‐principles calculation, the priority of the inclusion formation was Ce2O3 > CeAlO3, Ce2O2S > CeS > Ce3S4 > MnS. The stability of MnS inclusions is much lower than that of cerium‐containing inclusions. It is in situ observed that the addition of cerium promotes the formation of cerium‐containing inclusions and reduces the precipitation of MnS in the high sulfur steel.

Effect of Different Calcium and Magnesium Treatments on the Evolution of Nonmetallic Inclusions in AH36 Ship Plate Steel

Comprehensive thermodynamic calculations and high‐temperature experiments are performed to systematically evaluate the effect of calcium and magnesium additions on the modification and control of inclusions in AH36 ship plate steel. The results show that Al2O3 or MgAl2O4 inclusions are formed under the casting temperature conditions. Calcium treatment modifies the inclusions into calcium aluminate, of which components partially fall into the liquidus region, and the aspect ratio and number density of inclusions became smaller, avoiding nozzle clogging, but the inclusions are easy to gather and grow up, which would affect the steel properties. Magnesium treatment modifies the inclusions into dispersed magnesium‐aluminum spinel with small size. However, the number density and aspect ratio of inclusions increase, as well as the melting points of inclusions are high, which would easily cause nozzle clogging. When calcium–magnesium synergistic treatment, with the increase of magnesium proportion, the inclusions types increased, and the liquidus area of inclusions became narrower until it disappeared. Synergistic treatment with more calcium and less magnesium (Ca2Mg1) is optimal since the inclusions were fine and diffuse, and the corresponding liquidus area of inclusions is wider than the calcium treatment.

Estimation of probable maximum aspect ratio of MnS inclusions in non-quenched and tempered steel after isothermal compression

Estimation of probable maximum aspect ratio of MnS inclusions in non-quenched and tempered steel after isothermal compression

Joint micromechanical model for determination of effective elastic and electromagnetic properties of porous materials

In this paper we propose an approach for calculating the effective physical properties of porous materials (for example, sedimentary rocks) which is based on the unified structure of the pore space. This approach is based on the Generalized Differential Effective Medium (GDEM) method. This method generalizes the classical differential scheme (DEM) for the case of many types of inclusions. The physical properties of a composite calculated using the GDEM depend on how the solution is constructed.A porous medium is represented by the elastic weakly conductive matrix with embedded inclusions of two types (spheroidal and cylindrical), saturated with a conductive liquid. The cylindrical inclusions appear in the system when the porosity value exceeds the void percolation. Parameters, that characterize the inclusions (the aspect ratio of spheroidal inclusions and the relative part of cylindrical inclusions), are determined in the inverse problem solving process for the experimental data approximation of the effective conductivity as a porosity function. These parameters, obtained by solving the inverse problem, were used to calculate the effective elastic moduli, electrical conductivity, and dielectric permittivity of porous media. The results obtained describe well the available experimental data for different effective physical properties.

The effect of property contrast in two-component piezoelectric composites

A Mori - Tanaka model of piezoelectric composites is used to study the effect of property contrast between the components of a two-component composite. The composite comprises a piezoelectric matrix and piezoelectric inclusions whose property values are scaled from those of the matrix. The scaling method allows a wide range of material combinations to be approximated without using explicit properties of specific materials. Additionally, the aspect ratio and volume fraction of inclusions is varied to seek optimum values of the piezoelectric coefficients in the composite. It was found that scaling the properties in the electroelastic moduli reveals significant results for the piezoelectric performance coefficients dhgh, κ33, g33 and kt. By varying the material scaling factors alongside the inclusion aspect ratio it is demonstrated that giant enhancements of the transducer figure of merit dhgh could potentially be achieved through composite design. This approach identifies some novel opportunities for optimised piezoelectric composites.

Study on Influence of Rare Earth Ce on Micro and Macro Properties of U75V Steel.

Non-metallic inclusions in steel have great influence on the continuity of the steel matrix and the mechanical properties of steel. The precipitation sequence of Ce inclusions in molten steel is predicted by thermodynamic calculations. The results show that Ce content will affect the precipitation sequence of rare earth inclusions in molten steel, and the formation of CeO2, Ce2O3 and CeAlO3 will be inhibited with the increase in Ce content. Our laboratory smelted the test steel without rare earth additive and the test steel with rare earth Ce additive (0.0008%, 0.0013%, 0.0032%, 0.0042%). It was found that the MnS inclusions and inclusions containing Al, Ca, Mg and Si oxides or sulfides in the steel after rare earth addition were modified into complex inclusions containing CeAlO3 and Ce2O2S. The size of inclusion in steel was reduced and the aspect ratio of inclusion was improved. The addition of Ce also improved the grain size of U75V steel and significantly refined the pearlite lamellar spacing. After mechanical property testing of the test steel, it was found that when Ce is increased within 0.0042%, the tensile and impact properties of U75V steel are also improved.

Initiation and evolution of butterflies in roller bearings due to rolling contact fatigue

This investigation entails analysis of 520 butterfly formations (BFs) and non-metallic inclusions without BFs in two RCF-tested roller bearings to elucidate the influence of inclusion characteristics and stress level they are subject to, on the initiation and growth of BFs. The results show duplex inclusions, though least frequent in the bearing steels, exhibit the highest butterfly formation rate comparing with pure sulphide/oxide inclusions. It is also found that larger inclusions and those with smaller aspect ratios are more prone to butterfly formation; BF wing length decreases with the increase of inclusion aspect ratio; BF orientation is significantly influenced by inclusion size and stress level; stress magnitude appears to either impede or facilitate BF wing growth depending on BF orientation.

An analysis of composites with two-dimensional decagonal quasicrystal matrix and spheroidal inclusions

Eshelby tensors in elasticity are obtained for two-dimensional (2D) decagonal quasicrystal containing an ellipsoidal inclusion. Based on the intrinsic strain formula and Mori–Tanaka theory, the effective elastic properties of 2D decagonal composites are obtained. The effects of inclusion volume fraction and inclusion aspect ratio on elastic properties of composites with 2D decagonal quasicrystal are discussed.

Introducing realistic distributions of gas bubble size and inclusion aspect ratio to model the coexistence of gas hydrate and free gas

The coexisting free gas within the hydrate stability zone is recognized by laboratory and field studies. The conventional resistivity method fails to obtain hydrate saturation in the sediment with gas hydrate and free gas because both of them are electrical insulators. Hydrate saturation can be obtained from a velocity log based on a certain rock physics model. However, few studies of rock physics have been conducted on gas and hydrate coexistence. In this study, a more realistic distribution of gas bubble size and inclusion aspect ratio was introduced into an effective medium model to elucidate how such coexistence affects velocity and attenuation at a broad-band frequency. The modeling results obtained indicate that such coexistence decreases P-wave velocity at low frequencies, while increases P- and S-wave velocities at high frequencies. The velocity decrease of P-wave at low frequencies is attributed to the overwhelming effect of gas bubble vibration, while it seems not to affect P-wave velocity at high frequencies significantly. Moreover, coexisting gas hydrate and free gas may strengthen P-wave attenuation at the broad-band frequency range. It is found that the damping of oscillating gas bubbles dominates P-wave attenuation at low frequencies, while squirt flow in the porous hydrate is more likely to contribute to P-wave attenuation at high frequencies. Hydrate morphology is also a significant factor affecting P-wave velocity and attenuation at high frequencies. This research reveals that rock physics modeling can provide insight into how to characterize the coexisting gas hydrate and free gas as referring to the acoustic velocity and attenuation at seismic, sonic, and ultrasonic frequencies.

The effect of non-metallic inclusion morphology on the hydrogen induced cracking (HIC) resistance of L80 steel

The hydrogen induced cracking (HIC) resistance of four (4) L80 casing steels, with different nominal compositions and processing conditions, was determined using the NACE TM0284 HIC test. Microstructural and inclusion characterization of each steel was undertaken using optical microscopy (OM), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). The morphology (equivalent diameter, aspect ratio and major length) of inclusions over identical analysis regions were measured for each steel. In total, >15,000 inclusions were characterized. Non-linear models correlating inclusion morphology with the measured values of CLR (crack length ratio) and CTR (crack thickness ratio) were developed. The models show that both CLR and CTR are complex functions of the diameter (equivalent) of oxide-based inclusions and the major length of the manganese sulfide (MnS) stringers. The models show that oxides <10 μm in diameter were found to have negligible effect on HIC resistance (CLR) while oxides >20 μm exhibited a significant and escalating negative impact on HIC resistance comparable to long (>50 μm) MnS stringers.

Effect of Magnesium Treatment and Cooling Method on Manganese Sulfide in U75V Heavy‐Rail Steel Deoxidized by Si–Mn

The effect of magnesium (Mg) on the morphology of sulfides in silicon–manganese deoxidized low‐sulfur and low‐aluminum steels is investigated by adding different amounts of nickel–magnesium (Ni–Mg) alloy to a heavy‐rail steel U75V melt and cooling the melt from 1600 °C to room temperature under different conditions. Herein, the effects of Mg content and cooling rate on MnS inclusions are investigated. It is indicated that with an increase in the Mg content in molten steel from 0 to 64 ppm, the main composition of inclusions changes following the path of CaO–SiO2–Al2O3 → MgO–Al2O3–MnS → MgO–MnS–MgS. Mg significantly inhibits the precipitation of long‐strip MnS and can decrease the average size and aspect ratio of the inclusions. Under furnace cooling, when Mg is 41 ppm, the minimum aspect ratio of the inclusions is 1.61. The higher the cooling rate, the smaller the inclusion size; however, compared to water and furnace coolings, with cooling rates of 126.3 and 0.12 °C s−1, respectively, the inclusion aspect ratio of the air‐cooling conditions with a cooling rate of 67.7 °C s−1 is low. Finally, thermal simulations verify the effect of Mg treatment on the suppression of MnS deformation during rolling.

Response surface optimization and finite element homogenization study of the effective elastic modulus and electrical conductivity of MXene‐polypyrrole hybrid nanocomposite as electrode material for electronic energy storage devices

AbstractElectrical energy storage devices are crucial for energy storage and distribution purposes. MXene (MX), a 2D material, and conductive organic polymers, such as polypyrrole (PPy), have been widely used as electrode material in electronic energy storage devices. This work calculated the elastic modulus and the electrical conductivity of a MX/PPy nanocomposite electrode using a finite element model. Response Surface Methodology (RSM) was used to optimize the electrical conductivity and elastic modulus response variables based on the finite element (FE) simulation findings. By assigning appropriate weights to these response factors in the optimization technique, the impacts of mass fraction and aspect ratio (AR) of MX inclusion on the electrical conductivity values and elastic modulus of the electrode were analyzed. When compared to the experimental findings, the results demonstrated that the suggested finite element model could provide a satisfactory estimate of the electrical conductivity and elastic modulus of the electrodes made of MX and PPy. However, these response variables might be optimized by using the response surface approach. Therefore, when RSM was employed, both electrical conductivity and Youngs modulus could be adjusted to close to their respective maximum optimal values, with a predicted electrical conductivity of 474.33 S/m and an elastic modulus of 3.24 GPa, at 50% mass fraction of the MX and the AR of 0.2. Based on these results, if a MX/PPy nanocomposite electrode could be built to achieve this modulus and electrical conductivity, such electrode would be a viable material for metal‐ion batteries.

Theoretical investigation of the nanoinclusions shape impact on the capacitance of a nanocomposite capacitor

A first-principles theoretical approach to the effective dielectric permittivity of a nanocomposite, which contains nanoinclusions dispersed in a host dielectric enclosed between two parallel metallic electrodes, is developed. The inclusions are modeled by spheroids, and their response to the external electric field is found using the point dipole approximation and Green’s function approach. As a result, besides the mutual interactions between the induced dipoles, the local field in the nanocomposite contains also a contribution from the dipole field reflected from the capacitor electrodes. It is shown that the nanocomposite dielectric permittivity is determined by an average inclusion polarizability density, and its dependence on the aspect ratio and orientations of inclusions is found analytically and investigated. The theoretical predictions derived in the paper are in excellent agreement with the available experimental data and can be used for a proper design of nanocomposite capacitors.

Revisiting analytic shear-lag models for predicting creep in composite materials

Analytic shear-lag models enjoy great popularity for assessing and interpreting microstructure dependent stationary creep in fibrous metal composites, especially the formulation of Kelly-Street (Kelly and Street, 1972 [2]). Beyond the original model's scope, i.e. large aspect ratios of inclusions, predictions are highly inaccurate, which was recently pointed out by Wicht et al. (Wicht et al., 2022 [10]), by comparing model predictions to micromechanical Fast-Fourier-Transform-based simulations. In this study we therefore modify basic Kelly-Street model assumptions, concerning effective creep rate, stress transfer and inclusion spacing to arrive at a modified model with an extended scope. To validate the modified model, we benchmark the model against Fast-Fourier-Transform-based micromechanical simulations. We show, that the proposed modifications are successful in extending the model's scope to inclusions with small aspect ratios ≤20. Thus, the reformulated model is a powerful tool to describe and interpret microstructure dependent creep.

Inclusion Engineering in Medium Mn Steels: Effect of Hot-Rolling Process on the Deformation Behaviors of Oxide and Sulfide Inclusions

Medium Mn steel (MMS) is a new category of the third-generation advanced high strength steel (3rd AHSS) which is developed in the recent 1-2 decades due to a unique trade-off of strength and ductility. Thus, this steel grade has a wide application potential in different fields of industry. The current work provides a fundamental study of the effect of hot-rolling on the inclusion deformation in MMS including a varied 7 to 9 mass pct Mn. Specifically, the deformation behavior of different types of inclusions (i.e., Mn(S,Se), liquid oxide (MnSiO3), MnAl2O4, and complex oxy-sulfide) was investigated. The results show that both MnSiO3 and Mn(S,Se) are soft inclusions which are able to be deformed during the hot-rolling process but MnAl2O4 does not. The aspect ratio of soft inclusions increases significantly from as-cast to hot-rolling conditions. When the maximum size of different inclusions is similar, Mn(S,Se) deforms more than MnSiO3 does. This is due to a joint influence of physical parameters including Young’s modulus, coefficient of thermal expansion (α), etc. However, when the maximum size of one type of inclusion (e.g., MnSiO3) is much larger than another one (e.g., Mn(S,Se)), this maximum size of soft inclusions plays a dominant role than other factors. In addition, the deformation behavior of dual-phase inclusion depends on the major phase, i.e., either oxide or sulfide. Last but not least, empirical correlations between the reduction ratio of the thickness of plate, grain size, and aspect ratio of oxide and sulfide inclusions after hot-rolling are provided quantitatively. This work aims to contribute to the ‘inclusion engineering’ concept in the manufacturing of new generation AHSS.

A shape-change model for isolated K-feldspar inclusions within a shear zone developed in the Teshima granite, Ryoke metamorphic belt, Japan: Estimation of the duration of deformation in a natural shear zone

A shear zone developed in the Teshima granite in the Ryoke metamorphic belt of Japan contains isolated K-feldspar inclusions showing various shapes within deformed host quartz grains. We present a shape-change model for isolated K-feldspar inclusions, which is a mathematical equation that considers stress, inclusion size, temperature, and the duration of deformation. To calculate the shape-change pattern (i.e., the aspect ratio and size of inclusions) with respect to deformation duration using the model, we used values for deformation temperature (~500–600 °C) and paleo-stress (90 ± 10 MPa) estimated from deformed quartz microstructures within the shear zone. Shape-change patterns were obtained by calculating the model at the estimated range of temperatures with an interval of 25 °C and at the estimated paleo-stress. Shape-change patterns were subsequently corrected by compensating for the effect of post-deformation annealing during exhumation of the shear zone. Deformation duration was estimated by identifying the shape-change pattern calculated by the model that most closely corresponded to the observed shape-change pattern for the shear zone and considering the cooling rate of the Ryoke belt. The resultant deformation duration of the shear zone is estimated as 16,500–8400 yr under conditions of T = 550 °C and σ = 90 ± 10 MPa. Shear strain in the shear zone is calculated as 50–260 by multiplying the shear strain rate by the deformation duration.

Raman Geobarometry of Quartz Inclusions in Kyanite: Application to Quartz Eclogite from the Gongen Area of the Sanbagawa Belt, Southwest Japan

ABSTRACT Residual pressure values of quartz inclusions in host kyanite were estimated using Raman spectroscopy and show that the quartz-inclusions-in-kyanite system can be used as a geobarometer for estimating peak metamorphic conditions. Samples of quartz eclogite, a pelitic high-pressure metamorphic rock composed mainly of garnet, omphacite, and quartz, with subordinate kyanite, were obtained for analysis from the Gongen area in the Sanbagawa metamorphic belt, southwest Japan. Residual pressure in the 236 analyzed quartz inclusions within kyanite grains varies from 0.12 to 0.76 GPa. Values are independent of inclusion size and inclusion aspect ratio, and the distribution of residual pressure within the inclusions is homogeneous, except at inclusion-host interfaces. Numerical calculations based on elastic modeling with the equations of state of quartz and kyanite were applied using the highest residual pressure value of 0.76 GPa, with the calculated isopleth being consistent with previous results obtained by conventional thermodynamic geothermobarometry. We conclude that the quartz-inclusions-in-kyanite system can be used as a reliable new Raman geobarometer.

Control of Inclusions in 49MnVS3 Non-Quenched and Tempered Steel by Mg Treatment

To explore the effect of different Mg contents on the morphology, composition, distribution, and deformation of sulfides in 49MnVS3 non-quenched and tem-pered steel, the inclusions were observed and counted by Zeiss metallographic microscope and scanning electron microscope, and the inclusions in the com-pressed samples were compared by Gleeble-3500 thermal simulation test ma-chine. Results showed that the size of sulfide in steel decreases and the distri-bution uniformity of sulfide are significantly improved with the increase of Mg content. The proportion of composite inclusions in steel increases obviously, and the proportion of individual MnS decreases. The composition of the included core is in accordance with the principle of Al2O3 → Al2O3 + MgO·Al2O3 → MgO·Al2O3 + MgO → MgO → MgO + MgS. After Gleeble compression, the aspect ratio of sulfide inclusions decreases, and the spindle ratio h increases significantly.

Modeling of geometric configuration and fiber interactions in short fiber reinforced composites via new modified Eshelby tensors and enhanced mean-field homogenization

Determination of the effective elastic properties of unidirectional short fiber reinforced composites (SFRCs) is a key fundamental requirement which is usually estimated by mean-field homogenization (MFH) methods. Available classical MFH methods only account for volume fraction and aspect ratio of the fibers and do not consider the physical cylindrical geometry of the fibers. Moreover, classical MFHs are not designed for predicting the effective properties of SFRCs with distinct packing configurations and order of fibers. In this work, new modified Eshelby tensors associated with an enhanced MFH are developed which resolve the mentioned limitations of the available MFH methods and preserve their computational efficiency. While classical Eshelby tensors used in MFHs depend only on the aspect ratio of the fictitious ellipsoidal inclusion and material properties of the matrix, the introduced modified Eshelby tensors additionally account for physical cylindrical geometry as well as interactions of the short fibers with different packing configurations. Moreover, non-uniform homogenizing eigenstrains required for accurate homogenization of the short fibers are also incorporated by the proposed analytical treatment. Predictions of the developed enhanced MFH for various packing configurations are compared with those obtained from Finite Element Method implementing periodic boundary conditions and very good agreements are observed. It is shown that packing configuration and geometrical specifications of short fibers can significantly affect the effective properties of the SFRC.

Rock physics templates for anisotropic and heterogeneous reservoir rocks considering mineralogy, texture and pore-filling fluid

Anisotropic Rock Physics Templates (RPTs) are efficient tools to interpret well logs. In this work, micromechanical modeling is used to calculate the effective properties of heterogeneous and anisotropic rocks due to the presence of fluid-filled aligned fractures or other minerals, e.g. clay, quartz and calcite. When the spheroidal inclusions are aligned, the transversely isotropic symmetry is described by Hill’s 5 elastic moduli, which are obtained after solving a system of nonlinear algebraic equations. New anisotropic Rock Physics Templates are based on these elastic moduli, in which it is easy to identify the presence of fluids in a reservoir. It has been observed that effective properties depend strongly on the aspect ratio of inclusions, pore fluid, and mineralogy. These new numerical results are similar to with others already published when the aspect ratio is set to 1. For aspect ratios δ of 0.25,0.5, and 0.75, these ternary plots give new elements of interpretation and analysis of results obtained either in a rock physics laboratory or in the field station. For instance, lower aspect ratios δ=0.5 until values nearly to δ=1 consider thick interbedded formations or fluid-filled pore under compaction. The latter will lead to a better characterization of the heterogeneous and anisotropic reservoir rocks, which are linked to producing commercial hydrocarbon areas. Herein, a shale gas reservoir is consistently identified by the proposed anisotropic RPTs.