Rapid melting and solidification of surface due to stationary heat flux

A general two-dimensional computer heat flow model is developed in an oblate spheroidal coordinate system for rapid melting and subsequent solidification of the surface of a semiinfinite solid subjected to a high intensity heat flux over a circular region on its bounding surface. Generalized numerical solutions are presented for an aluminum substrate subjected to both uniform and Gaussian heat flux distributions. Temperature distributions, melt depth and geometry, and melting and solidification interface velocities are calculated as a function of applied heat flux, radius of the circular region, and time. It is shown that the important melting and solidification parameters are a function of the product of the absorbed heat flux, q, and the radius of the circular region, a. General trends established show that melt depth perpendicular to the surface is inversely proportional to the absorbed heat flux for a given temperature at the center of the circular region. Dimensionless temperature distributions and the ratio of liquid-solid interface velocity to absorbed heat flux,R/q, as a function of dimensionless melt depth remain the same if the productqa is kept constant, whileq anda are varied. For a given total power absorbed melting and solidification parameters are compared for uniform and Gaussian heat flux distributions. For a given temperature at the center of the circular region both melt depth and width are smaller for the Gaussian distribution while temperature gradients and interface velocities are larger. Formerly Graduate Research Assistant, Department of Mechanical and Industrial Engineering, University of Illinois. Formerly Research Associate, Department of Metallurgy and Mining Engineering,University of Illinois. Formerly Professor at the University of Illinois, Urban, IL.     

Liquid- solid interface migration at grain boundary regions during transient liquid phase brazing

A two-dimensional (2-D) finite difference model has been used to analyze the effect of grain boundary regions on the migration of the liquid-solid interface during transient liquid phase (TLP) brazing of Ni with Ni-11 wt pct P filler metal. This work has been carried out to explain the differences observed between actual and calculated completion times for isothermal solid- ification during TLP brazing and the faster isothermal solidification rates when brazing fine- grained nickel-base material. Modeling considers the situation where the grain boundary intersects the liquid-solid interface at right angles. Four factors are considered in addition to solute diffusion in solid and liquid phases,viz., (1) high diffusivity at the grain boundary region, (2) the balance between the grain boundary energy and the liquid-solid interfacial energy, (3) the interfacial energy due to the curvature of the liquid-solid interface, and (4) diffusional flow along the liquid-solid interface (produced by the gradient of solute chemical potential resulting from factors (2) and (3)). Increased solute diffusivity at the grain boundary region has a neg- ligible effect on migration of the liquid-solid interface in the bulk region and shifts the interface at the grain boundary region in a direction opposite that observed in actual brazed samples. On the other hand, when factors (2) through (4) above are taken into account, the liquid-solid interface in the region of the grain boundary is displaced in the same direction as in the ex- perimental results and liquid penetration comparable with the experimental results occurs at the grain boundary region. Factors (2) through (4) accelerate the isothermal solidification process in the bulk region in accordance with actual experimental test results. Formerly Visiting Scientists Formerly Visiting Scientists     

Macrosegregation caused by thermosolutal convection during directional solidification of Pb-Sb alloys

Pb-2.2 and 5.8 wt pct Sb alloys were directionally solidified with a positive thermal gradient of 140 K cm⁻¹ at growth speeds ranging from 0.8 to 30 μm s⁻¹, and then quenched to retain the mushyzone morphology. Chemical analysis along the length of the directionally solidified portion and in the quenched melt ahead of the dendritic array showed extensive longitudinal macrosegregation. Cellular morphologies growing at smaller growth speeds are associated with larger amounts of macrosegregation as compared with the dendrities growing at higher growth speeds. Convection is caused, mainly, by the density inversion in the overlying melt ahead of the cellular/dendritic array because of the antimony enrichment at the array tip. Mixing of the interdendritic and bulk melt during directional solidification is responsible for the observed longitudinal macrosegregation.     

Evolution of interaction domain microstructure during spray deposition

An interaction domain, defined in the present article as the region where semisolid, atomized droplets impinge and are collected during spray atomization and deposition, was systematically investigated on the basis of a semisolid metal-forming mechanism. Accordingly, microstructural evolution in the interaction domain was rationalized by quantitative analyses of (1) the solid fraction of semisolid metal, (2) the extent of deformation and deformation strain rate, and (3) the solidification cooling rate. The results demonstrate that the fraction of solid in the interaction domain ranges from 0.5 to 0.8 for the materials studied here: Ni₃Al, Al-6 wt pct Si, and Al-6 wt pct Fe. Moreover, the results show that the semisolid material in the interaction domain experiences a severe deformation during deposition with an associated strain rate of up to 10⁶ s^-1. As a result of this deformation; the solidification structure is modified, and, in particular, any dendritic structure that is present will undergo extensive fragmentation. The severe deformation that is experienced by the interaction domain and the presence of a solidification cooling rate that is on the order of 10 to 10₅ Ks^-1 were proposed to be critical factors that promote the formation of a spheroidal grain morphology during spray atomization and deposition. Experimental support to this suggestion was provided by microstructural observations on Ni₃Al, Al-6Si, and Al-6Fe. In particular, the morphological modification of the primary Si phase that is observed in spray-atomized and spray-deposited Al-6Si was rationalized on the basis of these factors.     

Effect of crucible diameter reduction on the convection, macrosegregation, and dendritic morphology during directional solidification of Pb-2.2 wt pct Sb alloy

The Pb-2.2 wt pct Sb alloy has been directionally solidified in 1-, 2-, 3-, and 7-mm-diameter crucibles with planar and dendritic liquid-solid interface morphology. For plane front solidification, the experimentally observed macrosegregation along the solidified length follows the relationship proposed by Favier.^[17,18] Application of a 0.4 T transverse magnetic field has no effect on the extent of convection. Reducing the ampoule diameter appears to decrease the extent of convection. However, extensive convection is still present even in the 1-mm-diameter crucible. An extrapolation of the observed behavior indicates that nearly diffusive transport conditions require ampoules that are about 40 μm in diameter. Reduction of the crucible diameter does not appear to have any significant effect on the primary dendrite spacing. However, it results in considerable distortion of the dendrite morphology and ordering. This is especially true for the 1-mm-diameter samples.     

Analysis of heat flow and microstructure evolution during spray deposition of Fe-3C-1.5Mn alloy

A theoretical model for the concomitant solidification of droplets and preform during spray deposition has been proposed, based on heat-flow analysis. It has been unambiguously demonstrated that cooling rates approaching those in the rapid solidification (RS) regime can only be achieved when the droplets are still in free flight during the deposition process. The cooling rates in the droplets range from 10⁴–10⁶ Ks^?1 depending upon their size for the experimental conditions employed in the present studies. In contrast, the model predicted cooling rates for the deposits in the region of 10³–10⁴ Ks^?1. A hypoeutectic Fe-3C-1.5Mn-0.3Si has been chosen as an experimental alloy for studies relating to microstructural characterization. The microstructure of powder developed fully during solidification of droplets in free flight revealed dendritic morphology of the metastable austenitic phase, whereas the spray-deposited alloy exhibited characteristic homogeneous and refined substructure. The evolution of microstructure during spray deposition as also during atomization has been compared and discussed by invoking the proposed model.     

Heat flow model for surface melting and solidification of an alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The eq11Ations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer eq11Ation is written in terM_s of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region,a, and time. General trends established show that for a given product ofqa all isotherM_s are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

Influence of low-gravity solidification on heterogeneous nucleation in stable iron-carbon alloys

The processes of nucleation and growth of alloys during solidification are linked to the level of gravitational force. In a low-gravity environment, buoyancy-induced convection becomes negligible, resulting in lower convection as compared to normal or high gravity. In this paper, heterogeneous nucleation and grain multiplication during solidification of gray cast iron, and the effect of gravitational level on them, have been studied by means of directional solidification on ground and under low-gravity (low-g) and high-gravity (high-g) conditions obtained by aircraft parabolic flights. It has been assumed that the final number of eutectic grains results from the contribution of heterogeneous nucleation,N _h , heterogeneous nucleation induced by inoculation,N _i , and heterogeneous nucleation induced by convection,N _c . In turn,N _c has two components, a grain multiplication component,N _c ^m , and a kinetics of chemical reactions component,N _c ^k . In all cases, it was found that a higher number of grains are obtained when solidifying in highg as compared with lowg. This was attributed to higher convection in highg. It was demonstrated that grain multiplication due to convection can contribute 20 to 23 pct from the total number of grains resulting from heterogeneous nucleation of uninoculated samples. For the case of inoculated samples, it was shown that the contribution to the convection-induced nucleation of the kinetics of chemical reactions can be as high as 30 pct but can be zero at very low or very high grain numbers. A possible mechanism and an explanation have been given to those findings. The silicon distribution, graphite morphology, and the influence of soak time on experimental results have also been discussed.     

High-speed temperature measurements during rapid solidification of iron-silicon ribbons,produced by planar flow casting

In order to investigate the melt undercooling and the non-equilibrium solidification of crystalline Fe 5 wt.% Si melt spun ribbons, produced by planar flow casting (PFC), high speed temperature measurements and appropriate process simulations have been performed. Using a rotating fibre optical system with a fast response double pyrometer, the temperature radiation of the solidifying ribbon during the casting process has been recorded with a measuring frequency of 50 kHz. The obtained cooling curves have been interpreted by computer simulations. It is shown that with increasing wheel temperature the overall cooling becomes more efficient. This is caused by an improved wetting behaviour of the melt-wheel system and an increase in the heat transfer coefficient at the interface of the solidifying ribbon and the wheel from 6 · 10⁴ to about 2 · 10⁵ W/(m²K). The solidification of 100 to 200 μm thick ribbons takes place in a time interval of 2 to 5 ms. The average growth rate varies between 10 and 60 mm/s. The high cooling rate results in a fine dendritic solidification morphology with diminishing microsegregations.     

Heat Flow Model for Surface Melting and Solidification of an Alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The equations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer equation is written in terms of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region, a, and time. General trends established show that for a given product ofqa all isotherms are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

Rapid solidification effects in martensitic Cu-Zn-AI Alloys

The effects of rapid solidification on martensitic transformations were studied in Cu-Zn-AI samples prepared by the method of melt-spinning, with an estimated cooling rate of about 10⁶ K per second near the freezing point. A diffusionless solidification reaction L → β occurs, and a very fine-grained β structure is obtained, with highly structured grain boundaries. The average β grain diameter (∼5 μm) is about two orders of magnitude smaller than that obtained by conventional solid state solution and quench treatment. The β:β grain boundaries contain extraordinary features such as large steps, and the matrix dislocation density is abnormally high. The M^s temperature is depressed significantly in as-melt-spun ribbon material, but as the martensitic transformation is cycled, it shifts upward in temperature and obtains a more narrow hysteresis loop. The martensite has the usual 9R structure (ABCBCACAB stacking) found in bulk alloys, and while the morphology is similar to that in bulk alloys, it is finer in scale. It is suggested that the β → 9R transformation is affected through the combined influence of rapid solidification on parent β grain size, disorder, β:β grain boundary structure, internal stresses, and dislocation substructure. Shape memory behavior is qualitatively similar in the rapidly solidified alloys.     

Microstructural development during solidification of stainless steel alloys

The microstructures that develop during the solidification of stainless steel alloys are related to the solidification conditions and the specific alloy composition. The solidification conditions are determined by the processing method,i.e., casting, welding, or rapid solidification, and by parametric variations within each of these techniques. One variable that has been used to characterize the effects of different processing conditions is the cooling rate. This factor and the chemical composition of the alloy both influence (1) the primary mode of solidification, (2) solute redistribution and second-phase formation during solidification, and (3) the nucleation and growth behavior of the ferrite-to-austenite phase transformation during cooling. Consequently, the residual ferrite content and the microstructural morphology depend on the cooling rate and are governed by the solidification process. This paper investigates the influence of cooling rate on the microstructure of stainless steel alloys and describes the conditions that lead to the many microstructural morphologies that develop during solidification. Experiments were performed on a series of seven high-purity Fe-Ni-Cr alloys that spanned the line of twofold saturation along the 59 wt pct Fe isopleth of the ternary alloy system. High-speed electron-beam surface-glazing was used to melt and resolidify these alloys at scan speeds up to 5 m/s. The resulting cooling rates were shown to vary from 7°C/s to 7.5×10⁶°C/s, and the resolidified melts were analyzed by optical metallographic methods. Five primary modes of solidification and 12 microstructural morphologies were characterized in the resolidified alloys, and these features appear to be a complete “set” of the possible microstructures for 300-series stainless steel alloys. The results of this study were used to create electron-beam scan speedvs composition diagrams, which can be used to predict the primary mode of solidification and the microstructural morphology for different processing conditions. Furthermore, changes in the primary solidification mode were observed in alloys that lie on the chromium-rich side of the line of twofold saturation when they are cooled at high rates. These changes were explained by the presence of metastable austenite, which grows epitaxially and can dominate the solidification microstructure throughout the resolidified zone at high cooling rates. J. W. ELMER, formerly Graduate Student at the Massachusetts Institute of Technology     

Mechanisms of the Origin of Fine and Non-Dendritic Grains at the Sonotrode–Liquid Metal Interface During Ultrasonic Solidification of Metals

Proposed grain refinement mechanisms during ultrasonic solidification have been explained in terms of refinement between cavitation enhanced nucleation and fragmentation of dendrites according to the casting conditions. Solidification studies also describe the activation of nucleation under pressure pulses after bubble implosion as an additional supporting mechanism for grain refinement. This study clarifies some overlooked concepts and proposes a plausible grain refinement mechanism explaining the role of cavitation in pure Zn and a Mg–6 wt pct Zn alloy. Equivalent grain size and grain density have been obtained in pure Zn and the Mg–6 wt pct Zn alloy (grain size distribution ranging from 40 to 200 µm) when UST was applied after the onset of solidification. These fine, non-dendritic grains originate from the cavitation zone beneath the sonotrode. Significant thermal undercooling surrounding the low superheat sonotrode in contact with the melt is responsible for the formation of a solidified layer (typically the thickness is equivalent to the average grain diameter) at the sonotrode–melt interface. High-frequency vibrations with or without cavitation at this interface assist the separation of these fine grains, which are then carried into the melt by acoustic streaming. A possible mechanism for the separation of fine grains produced from the cavitation zone is explained with the help of established concepts reported for the ultrasonic atomization process.

     

An integrated model for dendritic and planar interface growth and morphological transition in rapid solidification

Rapid solidification can be achieved by quenching a thin layer of molten metal on a cold substrate, such as in melt spinning and thermal spray deposition. An integrated model is developed to predict microstructure formation in rapidly solidified materials through melt substrate quenching. The model solves heat and mass diffusion equations together with a moving interface that may either be a real solid/liquid interface or an artificial dendrite tip/melt interface. For the latter case, a dendrite growth theory is introduced at the interface. The model can also predict the transition of solidification morphology, e.g., from dendritic to planar growth. Microstructure development of Al-Cu alloy splats quenched on a copper substrate is investigated using the model. Oscillatory planar solidification is predicted under a critical range of interfacial heat-transfer coefficient between the splat and the substrate. Such oscillatory planar solidification leads to a banded solute structure, which agrees with the linear stability analysis. Finally, a microstructure selection map is proposed for the melt quenching process based on the melt undercooling and thermal contact conditions between the splat and the substrate.     

Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling

Equiaxed dendritic solidification in the presence of melt convection and solid-phase transport is investigated in a series of three articles. In part I, a multiphase model is developed to predict com-position and structure evolution in an alloy solidifying with an equiaxed morphology. The model accounts for the transport phenomena occurring on the macroscopic (system) scale, as well as the grain nucleation and growth mechanisms taking place over various microscopic length scales. The present model generalizes a previous multiscale/multiphase model by including liquid melt convec-tion and solid-phase transport. The macroscopic transport equations for the solid and the interdendritic and extradendritic liquid phases are derived using the volume averaging technique and closed by supplementary relations to describe the interfacial transfer terms. In part II, a numerical application of the model to equiaxed dendritic solidification of an Al-Cu alloy in a rectangular cavity is dem-onstrated. Limited experimental validation of the model using a NH₄C1-H₂O transparent model alloy is provided in part III.     

Liquid separation effects in Fe−Cu alloys solidified under different cooling rates

The effect of cooling rates on the microstructure of Fe−Cu alloys was investigated. A variety of solidification techniques was employed, in order to obtain a wide range of cooling rates. At high cooling rates (about 10⁴ K/sec), and in the composition range 30 to 80 wt pct Cu, the microstructures showed clear evidence of metastable liquid separation. This indicates a melt supercooling of about 50 to 100 K. Liquid separation coupled with high interfacial velocities resulted in solute trapping, and in a spherical morphology for one of the solids. At cooling rates lower than 10⁴ K/sec no liquid separation was observed, and the alloys solidified in a conventional manner,i.e., with a polycrystalline or a dendritic microstructure, depending on the Cu content. The type of the γ-Fe to α-Fe solid state transformation, taking place during cooling after solidification, depends on the cooling rates as well as on the Cu content in the γ-Fe phase. At medium cooling rates the transformation is martensitic, while at low or high cooling rates a polycrystalline transformed structure is obtained. A. MUNITZ, formerly Visiting Research Associate at the University of Florida at Gainesville, FL 32611     

Al-TiC composites In Situ-processed by ingot metallurgy and rapid solidification technology: Part I. Microstructural evolution

The present work was undertaken to highlight a novel in situ process in which traditional ingot metallurgy plus rapid solidification techniques were used to produce Al-TiC composites with refined microstructures and enhanced dispersion hardening of the reinforcing phases. Microstructures of the experimental materials were comprehensively characterized by optical microscopy, electron microscopy, and X-ray diffraction. The results show that the in situ-synthesized TiC particles possess a face-centered cubic crystal structure with an atomic composition of TiC_0.8 and a lattice parameter of 0.431 nm. The typical ingot metallurgy microstructures exhibit aggregates of TiC particles segregated generally at the α-Al subgrain or grain boundaries and consisting of fine particles of 0.2 to 1.0 μm in size. The rapidly solidified microstructures formed under certain thermal history conditions contained a uniform, fine-scale dispersion of TiC phase particles with a size range of 40 to 80 nm in an α-Al supersaturated matrix of 0.30 to 0.85 μm in grain size. These dispersed TiC particles generally have a semicoherent relationship with the α-Al matrix. Based on the experimental results, a comprehensive kinetic mechanism of in situ TiC synthesis, which includes a solid-liquid interface reaction between the carbon particles and the Al melt and multiple nucleation and growth of TiC from the Al melt, was proposed. Then, the evolution of the aggregate TiC particles in a superheated melt before rapid solidification, i.e., dissolution, nucleation, and growth of the regenerated TiC dispersed particles, was analyzed. Furthermore, the behavior of rapid solidification kinetics, the nucleation of α-Al on TiC-dispersed particles, and the interaction between TiC particles and the solidification front were documented experimentally and theoretically. These studies provided the theoretical criteria and an experimental basis for the optimum design of this kind of composite.     

Heterogeneous nucleation during rapid solidification by laser surface melting

Crystal nucleation during rapid solidification generally occurs rather slowly except at active heterogeneities or unless very large undercoolings are achieved. Many typical microstructures are then essentially of columnar morphology, for example from the bottom surface of a melt-spun ribbon or from a heterigeneity on the surface of a powder particle. In such cases the microstructure may be considerably refined by the presence of many active nucleants for heterogeneous nucleation distributed throughout the melt. Such microstructural refinement is analysed here during rapid solidification of a laser-melted surface containing fine TiB₂ particles. Simulation of the cooling and solidification conditions confirms these particles to be highly effective nucleating substrates, capable of greatly increasing nucleating rates. As a result it is possible to obtain materials possessing greatly refined grain sizes.     

Computer simulation of the crystal morphology and growth rate during ultrarapid cooling of an Fe-B Melt

The solidification of a binary Fe-B melt is studied by computer simulation with regard for the temperature dependence of the diffusion coefficient and the possibility of nonequilibrium alloying-component entrapment (i.e., the dependence of the distribution coefficient on the ratio of the solidification rate V to the diffusion rate V _D). The effect of high cooling rates of the melt on the dendritic morphology is analyzed. The dependence of the dendrite-tip growth rate on the melt supercooling is obtained. At large supercoolings, a morphological transition is shown to occur; it is related to the change from a diffusion to a diffusionless dendrite growth mode.     

Further discussions on the solute redistribution during dendritic solidification of binary alloys

After a review over former works about the solute redistribution during dendritic solidification, a new“local solute redistribution equation ”is deduced based on Flemings's model, where lim-ited diffusion in solid during solidification is carefully treated. Because a form parameter is also included, the equation can be used for the solidification processes with different shapes of den-drites. By solving the equation at the condition of directional solidification, more completef _s -C, functions for both needlelike and platelike dendritic solidifications with both linear and parabolic solidification rates are obtained. As examples, the volume fractions of nonequilibrium phase in Al-4.5 pct Cu alloy is evaluated with differentf _s -C _l functions. On the thinking that the dendrites in actual solidification process is usually between needlelike and platelike ones, the volume fraction of the nonequilibrium phase is suggested to be in the region between the one calculated by the model for platelike dendrites and that for needlelike dendrites. The relationship between the region and local solidification time is also presented by figures, which are compared with the data of former researchers.