Analysis Of Microsegregation Research Articles

Time evolution of interface shape distribution of equiaxed dendrite: A phase-field study

An understanding of the morphology of growing dendrites in alloys is needed for an analysis of microsegregation, as well as an estimation of the permeability for macroscopic fluid dynamics. Quantitative phase-field simulations were used to study the growth process of three-dimensional (3D) equiaxed dendrites in an Al-1.0 mass%Cu alloy during continuous cooling. The dendrites were analysed using an interface shape distribution (ISD) map, which provides the probability of the local interface having a morphology with a given curvedness (C) and shape factor (S). Morphological changes in the microstructure can be measured sensitively from the change in the average value of the curvedness 〈C〉 relative to the solid volume fraction. The ISD map continued to change over time during continuous cooling, implying that it was not time-invariant. Furthermore, when microstructural changes occurred, similarities between the ISD maps were observed, independent of the cooling rates and system sizes.

Analysis of Micro-Segregation of Solute Elements on the Central Cracking of Continuously Cast Bloom

On the basis of the Brody–Flemings model and modified Voller–Beckermann model, an analytical model of micro-segregation is established by considering the actual solidification cooling conditions of bloom. According to the developed model, the interdendritic solute distribution at the origin of the cracking gap is obtained. It is found that both phosphorus and sulfur have quite severe segregation, but both carbon and manganese have slight segregation; these results agree well with the semiquantitative analysis results of the scanning electron microscope (SEM). At the same time, the interdendritic segregation leads to an enhanced increase in the temperature range of crack formation; correspondingly, the possibility of cracking significantly increases and, thus, element segregation is the internal cause of crack formation. On the other hand, taking into account heat transfer, phase transformation, and metallurgical pressure, the strain of the solid shell is revealed through finite element software. When the solid shell thickness is equal to the distance of 90 mm between the opening point of the crack and the inner arc side, the tensile strain of the solid front is much bigger than the critical strain, which meets the external cause of crack formation; therefore, reasons for the cracking of blooms are successfully found.

A permanent cordon sanitaire: intra-village spatial segregation and social distance in India

ABSTRACT ‘Social distance,’ and ‘social distancing’ have become the linguae francae of our world ravaged by COVID-19. Pandemic related social distancing prescriptions, however, do not operate in a vacuum. How do social distancing strategies for containing the pandemic intersect with extant social divisions? Using a unique census-scale micro-dataset from rural Karnataka (an Indian state as large as France), we meditate on this question by drawing on theoretical insights from multiple disciplines including the intellectual genealogy of ‘social distance’ as a measure of social divisions. Our rich dataset contains independent India’s first census-scale enumeration (n ≈ 36.5 million) and coding of elementary caste categories (≈700 jatis). Our dataset is also the first to combine self-reported jati and religion information. To the best of our knowledge, we present the first systematic large-n portrait of intra-village residential segregation in rural India. Our micro-segregation analysis along jati and religion axes provides evidence for a ‘permanent cordon sanitaire.’ Our analysis also sheds light on how the pandemic intersects with internal migration trajectories in India.

Floating Grain Characterization and Its Effects on Centerline Segregation of Direct-Chill Cast Al–Mg–Si Alloy Billets

Microstructure and microsegregation analysis were performed on a direct-chill (DC) cast Al–Mg–Si alloy billet, aiming to quantitatively investigate the microscopic features of floating grain and its contribution to the negative centerline segregation. Microstructure results show some irregular grains, whose grain size and secondary dendrite arm spacing (DAS) are two times larger than that of the regular fine grains, appear only in the billet central region. The duplex grain structure, a mixture of internal coarse and peripheral finer dendrites within one grain, was clearly shown by the EPMA results, exhibiting special microsegregation features. The coarse dendrites are more solute-depleted than the nearby finer-DAS structure, in which the average concentration of solute Mg nearly equals to the nominal content. Based on the microscale features and solidification information of the alloy, the irregular grains exhibiting duplex dendrite feature are confirmed to be floating grain, which internal coarse dendrites are believed to mainly contribute to the negative centerline segregation. And the resulting segregation degree is quantitatively evaluated to be ∼0.041 for solute Mg considering the floating grains in the billet center as against with the assumed 100% fine-DAS microstructure.

Analysis of Microsegregation in Al-Si-Cu Ternary Alloys: Interdependence of Solute Composition at the Solubility Limit during Non-Equilibrium Solidification

Abstract Virtually all metals used industrially undergo a solidification process during their production. Depending on the material and its manufacturing process, its physical/mechanical properties are affected to a greater or lesser extent by the microstructure and microsegregation obtained during the phase change. Aluminum casting alloys are good examples of products where this microstructure is vital for obtaining the desired properties. A sequence of experiments to analyze the upward vertical unidirectional solidification with transient heat transfer conditions in Al-Si-Cu ternary alloys was developed in the present work. The experimental results obtained were compared with classical microsegregation models. Discrepancies related to their use for ternary alloys were raised. Since the calculated results by these models do not take into account the influence of one alloying element on the solubility of the other element, disparities were founded between experimental and numerical results. A microsegregation model was proposed based on the solubility limits of the Si in the alloy as a function of the Cu concentration present in the liquid. The model, combined with the concepts of classical microsegregation theory, allows a realistic description of the microsegregation phenomenon. The model showed an excellent agreement between microsegregation profiles of solute experimentally measured and calculated.

Uncertainty analysis of microsegregation during laser powder bed fusion

Quality control in additive manufacturing can be achieved through variation control of the quantity of interest (QoI). We choose in this work the microstructural microsegregation to be our QoI. Microsegregation results from the spatial redistribution of a solute element across the solid–liquid interface that forms during solidification of an alloy melt pool during the laser powder bed fusion process. Since the process as well as the alloy parameters contribute to the statistical variation in microstructural features, uncertainty analysis of the QoI is essential. High-throughput phase-field simulations estimate the solid–liquid interfaces that grow for the melt pool solidification conditions that were estimated from finite element simulations. Microsegregation was determined from the simulated interfaces for different process and alloy parameters. Correlation, regression, and surrogate model analyses were used to quantify the contribution of different sources of uncertainty to the QoI variability. We found negligible contributions of thermal gradient and Gibbs–Thomson coefficient and considerable contributions of solidification velocity, liquid diffusivity, and segregation coefficient on the QoI. Cumulative distribution functions and probability density functions were used to analyze the distribution of the QoI during solidification. Our approach, for the first time, identifies the uncertainty sources and frequency densities of the QoI in the solidification regime relevant to additive manufacturing.

Problems in Solidification Model for Microsegregation Analysis of Fe–Cr–Ni–Mo–Cu Alloys

Microsegregation of a Fe–Cr–Ni–Mo–Cu alloy was studied with the calculation model on the basis of two-dimensional concept considering diffusion of solutes during and after solidification. The calculated results were compared with the previous experimental results of the microsegregation profiles obtained by random sampling method. At first, a calculation model was created by applying two database sets of diffusion coefficients reported on Fe(γ)-X binary and Fe–Cr–Ni systems. The results using the database of the Fe–Cr–Ni systems fitted the experimental data better than those using the Fe(γ)-X systems in the region of lower solid fraction (fs). Meanwhile, in the higher fs region, the calculated lines passed below the arranged experimental data plots particularly for Cr and Mo. This inconsistency could be attributed to the following problems:

Derivation of Property Distribution Images from Microstructural Analyses of X2CrNi18-9 with Regard to Hydrogen Embrittlement

Abstract The scope of this research project covers the examination of the microstructure of different austenitic steels with regard to H embrittlement. It is known from the literature that the alloy X2CrNi18-9 is susceptible to H embrittlement, whereas steel X2CrNiMo18-14-3 is highly resistant to the embrittlement process. Austenitic steels with a low γ stability are susceptible to form α‘ martensite during plastic deformation. The γ stability can be estimated using empirical formulas, while one drawback of this approach is that only a limited amount of alloying elements is considered by those equations. A thermodynamic approach has proven effective for the estimation of the γ stability of multicomponent alloys. Hence, results from the microsegregation analysis for alloy X2CrNi18–9 using energy dispersive X-ray spectroscopy are presented and their influence on the local γ stability is discussed based on property distribution images.

Microsegregation in multicomponent alloy analysed by quantitative phase-field model

Microsegregation behaviour in a ternary alloy system has been analysed by means of quantitative phase-field (Q-PF) simulations with a particular attention directed at an influence of tie-line shift stemming from different liquid diffusivities of the solute elements. The Q-PF model developed for non-isothermal solidification in multicomponent alloys with non-zero solid diffusivities was applied to analysis of microsegregation in a ternary alloy consisting of fast and slow diffusing solute elements. The accuracy of the Q-PF simulation was first verified by performing the convergence test of segregation ratio with respect to the interface thickness. From one-dimensional analysis, it was found that the microsegregation of slow diffusing element is reduced due to the tie-line shift. In two-dimensional simulations, the refinement of microstructure, viz., the decrease of secondary arms spacing occurs at low cooling rates due to the formation of diffusion layer of slow diffusing element. It yields the reductions of degrees of microsegregation for both the fast and slow diffusing elements. Importantly, in a wide range of cooling rates, the degree of microsegregation of the slow diffusing element is always lower than that of the fast diffusing element, which is entirely ascribable to the influence of tie-line shift.

A study of shell growth irregularities in continuously cast 310S stainless steel

Growth irregularities in continuous casting are believed to be associated with crack formation and breakouts. Differential thermal analysis on 310S stainless steel samples indicated primary precipitations of both austenite and ferrite during solidification. In tensile tests on solidifying samples, abrupt shrinkages in volume were detected in the peritectic range of temperatures. Micrographic and microsegregation analysis on samples extracted from a breakout shell revealed high ratios of primary-precipitated austenite in the thick sections of the shell, and high ratios of primary-precipitated ferrite in the thin sections. Alternating precipitations of austenite and ferrite are proposed to occur during solidification. Regions of the shell with high ratios of primary austenite remain in contact with the mould and exhibit high growth rates, whereas regions with high ratios of primary ferrite shrink in volume due to the ferrite to austenite transformation, which results in the formation of air gaps between the shell and the mould and reductions in growth rate.

Solidification of high Nb containing TiAl based alloys

Casting of titanium aluminides is an attractive processing route for production of near net shape components: turbocharger wheels, valves and aero-engine components are presently at the heart of casting developments. Among the casting alloys under consideration are a number of niobium rich TiAl based alloys that contain low boron additions for grain refinement and minor additions of other elements to enhance creep resistance. An essential condition that must be met to achieve grain refinement is a solidification pathway competed via β-(Ti), e.g. a pathway that avoids peritectic growth of α-Ti. In this contribution we describe the microsegregation analysis of a unidirectionally solidified sample from the ternary alloy Ti–45Al–8Nb. The corresponding solidification path is discussed on the basis of thermodynamic calculations and is shown to closely follow Scheil predictions with some amount of back-diffusion for aluminium. The analysis indicates that the nucleation undercooling for peritectic α (Ti) in the deep mushy zone is significant.

Weld metal cracking in laser beam welded single crystal nickel base superalloys

The weldability of two single crystal nickel base superalloys CMSX-4 and CMSX-486 were investigated by autogenous bead-on-plate laser beam welding. The analysis of microsegregation that occurred during solidification in the fusion zone indicated that while W and Re segregated into the γ dendrites, γ′ forming elements Ti, Ta, and Al as well as Hf were rejected into the interdendritic liquid. Fusion zone cracking was observed in both the materials and was observed to have initiated and propagated along the high angle stray grain boundaries in the weld metal of the two alloys. Increased formation of stray grains and increased extent of fusion zone cracking were, however, observed in the CMSX-486 alloy. Extension of solidification temperature range mainly by microsegregation of grain boundary strengthening elements B, Hf, and Zr in CMSX-486 was suggested to be responsible for the increased susceptibility of the alloy to stray grain formation and weld metal cracking compared to CMSX-4 superalloy.

Heat affected zone liquation cracking in electron beam welded third generation nickel base superalloys

The weldability of directionally solidified nickel base superalloy TMS-75 and TMS-75+C was investigated by autogenous bead-on-plate electron beam welding. The analysis of microsegregation that occurred during solidification of the as-cast alloys indicated that while W and Re segregated into the γ dendrites of both the alloys, Ta, Hf and C were rejected into the interdendritic liquid in the TMS-75+C. Heat affected zone intergranular liquation cracking was observed in both the materials and was observed to be closely associated with liquated γ–γ′ eutectic microconstituent. The TMS-75+C alloy, however, exhibited a reduced extent of HAZ cracking compared to TMS-75. Suppression of terminal solidification reaction involving non-invariant γ–γ′ eutectic transformation due to modification of primary solidification path by carbon addition is suggested to be an important factor contributing to reduced susceptibility of TMS-75+C alloy to HAZ liquation cracking relative to the TMS-75 superalloy.

Analysis of microsegregation in RF-heated float zone growth of silicon—comparison to the radiation-heated process

Float zone growth of silicon was performed using a ring-shaped radio-frequency (RF) inductor of 600 kHz. The grown crystals were analyzed with respect to interface curvature and microsegregation, i.e. the width, the frequency, and the intensity of convectively induced dopant inhomogeneities. The results were compared to crystals grown in a radiation-heated growth facility. The influence of a rotating magnetic field (RMF) with B max=7 mT and f max=300 Hz on the growth was investigated. The axial temperature profile was determined by a pyrometer (spot size: 0.7 mm, working distance: 140 mm). The temperature gradient at the solid–liquid interface amounts to 275 K/cm, which is about a factor of 3 larger than for the radiation-heated process. Convective temperature fluctuations, measured at the free melt surface, reached fluctuation amplitudes of 5 K (radiation-heated case: 1 K), with a pronounced frequency distribution between 2 and 4 Hz and around 8 Hz, respectively (radiation-heated zones: ⩽0.4 Hz). The spacing of the dopant striations agrees well with the main part of the temperature fluctuations and reveals a maximum between 2 and 4 Hz. Applying an RMF, the dopant striations can be suppressed considerably, similar to the results obtained in radiation-heated crystals. The required RMF intensity is higher in the RF-case. The interface deflection is reduced due to the rotating field. The azimuthal flow velocity generated by the rotating magnetic field, was measured by tracer observation, the flow increases linearly with the Taylor number and reaches a velocity of 12 cm/s under a field strength of B=7 mT/ f B =300 Hz.

A new criterion for internal crack formation in continuously cast steels

To estimate the cracking condition in continuously cast steels, a new model for critical fracture stress given from the measured critical strain has been proposed, which can take into account the brittle temperature range and strain rate. The effects of brittle temperature range and strain rate on critical strain for internal crack formation were analyzed. When the brittle temperature range and strain rate were increased, the possibility of internal crack formation increased due to the decreasing critical strain. To describe the thermomechanical property model of the mushy zone between zero strength temperature (ZST) and zero ductility temperature (ZDT), the yield criterion for porous metals, which can take into account δ/γ transformation, was used. Using the fitting equation for the measured critical strain and the microsegregation analysis, the thermomechanical behavior of the mushy zone could be successfully described by the proposed model, which incorporates the effects of microsegregation of solute elements and δ/γ transformation on hot tear during solidification at the given range of steel compositions and strain rates. A cracking criterion based on the difference of deformation energy in the brittle temperature range is proposed to explain the cracking phenomenon of whole carbon range.

Phase-field Model for Solidification of Ternary Alloys.

The phase-field model for dilute ternary alloys is proposed and the relationships between phase-field parameters and material properties are derived at a thin interface limit. One-dimensional and two-dimensional numerical simulations show that the model reproduces the equilibrium conditions including Gibbs–Thomson effect. We apply the model for ternary alloys to micro-segregation analysis in Fe–C–P alloy and the results are compared with analytical models. The results show good agreement with those of Clyne–Kurz equation. For two-dimensional computations, isothermal dendritic growth is simulated for Fe–C and Fe–C–P alloys. The change in phosphorous concentration affects significantly the interface velocity and the dendrite shape even when the phosphorous concentration is much lower than that of carbon because of the small diffusivity of phosphorous.

Approximate models of microsegregation with coarsening

Microsegregation refers to the processes of solute rejection and redistribution at the scale of the dendrite arm spaces in the mushy region of a solidifying alloy. A representative geometry for a microsegregation analysis is the half-arm spacing in a platelike morphology. Models of microsegregation are based on a solute balance within this domain. A recent review by Kraft and Chen covers the range of available models. Common assumptions used in modeling include a binary eutectic alloy; a fixed average composition, C{sub 0}; equilibrium at the solid-liquid interface; a constant partition coefficient k {lt} 1; and a straight liquidus line in the phase diagram. The two features of the solute balance that need to be included in a comprehensive model are the following. (1) The mass diffusion of the solute. Typically, the solute diffusion in the liquid is rapid, and, at each instant in time, a uniform distribution of solute, C{sub {ell}}(t), can be assumed. In the solid, however, diffusion is much slower and the solute balance needs to account for the so-called back-diffusion of solute into the solid. (2) Changes in morphology. As solidification proceeds, the arm spacing will coarsen. If the overall solute balance is maintained in the half-armmore » domain, this feature will dilute the solute in the liquid.« less

Effect of Cooling Rate on ZST, LIT and ZDT of Carbon Steels Near Melting Point.

The effect of cooling rate on the characteristic temperatures such as liquidus temperature (TL), zero strength temperature (ZST), liquid impenetrable temperature (LIT) and zero ductility temperature (ZDT) has been investigated by calculating the non-equilibrium pseudo binary Fe–C phase diagram. The effect of cooling rate on TL was not significant. The effect of cooling rate on ZST, LIT and ZDT was significant due to segregation of solute elements at the final stage of solidification. Using the microsegregation analysis proposed by Ueshima, the calculated temperatures at the solid fractions of 0.75 and 0.99 corresponded to the experimentally measured ZST and ZDT, respectively. Prediction equation on ZST, LIT and ZDT, which can take into account cooling rate and steel composition, was proposed. At given steel compositions and cooling rates, the suggested prediction equation on ZST, LIT and ZDT could successfully describe the experimentally measured data and the calculated data from microsegregation analysis.

Laves phase in superalloy 718 weld metals

The important consequence of the solidification in cast or welded superalloy 718 is the segregation of Nb and the formation of laves phase. Laves phase is a brittle intermetallic topologically close-packed phase with hexagonal structure, known for its detrimental effect on mechanical properties at room temperature [1]. Although data available with regard to wrought materials is somewhat elaborate it is not true for welds in general and for electron beam welds in particular. In this letter the formation of laves phase in high heat input gas tungsten arc (GTA) and low heat input electron beam (EB) welds of 2 mm thick superalloy 718 in as-welded and post-weld heat treated (PWHT) conditions is evaluated. The results have a bearing on the tensile ductility and other properties of welds. Sheets of superalloy 718 of thickness 2 mm in solution treated condition (chemical composition in Table I) were autogenously welded by automatic GTA and EB welding processes, resulting in full penetration using the weld process parameters listed in Table II. The as-welded samples were subjected to two PWHT schedules: direct duplex ageing and solution treatment followed by ageing. Solution treatment was carried out at 980 °C for 20 rain with air cooling and the duplex ageing was carried out at 720 °C for 8 h with furnace cooling to 620 °C for 8 h with air cooling. The as-welded and heat treated samples were then subjected to scanning electron microscopic (SEM) examination and quantitative electron probe micro-analysis (EPMA) for the analysis of microsegregation of elements and determination of the formation of laves phase. Figs 1 and 2 show SEM micrographs of the aswelded microstructures of EB and GTA weld metals, respectively. Essentially, the solidified structure is of dendritic type. EB weld metal showed relatively finer

Determination of free charge carrier distribution and micro-segregation of dopants in n-type GaAs

An experimental approach to the rapid determination of the micro-distribution of free charge carriers in n-type GaAs is reported. Computer based video processing techniques are used to determine the IR absorption characteristics of wafers with a spatial resolution of less than 10 μm and to convert this data after calibration into charge carrier density. The application of this technique to microsegregation analysis of Te-doped GaAs is demonstrated.