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NASA NTRS1984

Macrosegregation in aluminum alloy ingot cast by the semicontinuous direct chill method

A theoretical model of the semicontinuous DC casting method is developed to predict the positive segregation observed at the subsurface and the negative segregation commonly found at the center of large commercial-size aluminum alloy ingot. Qualitative analysis of commercial-size aluminum alloy semicontinuous cast direct chill (DC) ingot is carried out. In the analysis, both positive segregation in the ingot subsurface and negative segregation at the center of the ingot are examined. Ingot subsurface macrosegregation is investigated by considering steady state casting of a circular cross-section binary alloy ingot. Nonequilibrium solidification is assumed with no solid diffusion, constant equilibrium partition ratio, and constant solid density.

Yu, H.↗

NASA NTRS1985

Double-diffusive convection with sidewalls

Stommel et al. (1956) have first described an instability, known as thermosolutal convection, thermohaline convection, or double-diffusive convection. This instability may occur in the case of a fluid in a gravitational field with two diffusing components present. The present study is concerned with the effect of sidewalls on flow in the fingering regime in the absence of applied horizontal gradients. The work was motivated by numerical results obtained on the basis of a simulation of thermosolutal convection occurring during the unidirectional solidification of a binary alloy. In this case, the unperturbed solute field in the liquid ahead of the solidifying planar interface has an exponential vertical profile because of the rejection or preferential incorporation of solute by the solid phase.

Mcfadden, G. B.↗

NASA NTRS1985

Convection During Unidirectional Solidification

The fluid flow and solute segregation which occur during directional solidification, including effects of gravity and microgravity were studied. The nature of the fluid flow, its effects on the shape of the crystal-metal interface and the resulting distribution of solutes are examined. During solidification of a binary alloy at constant velocity vertically upwards, thermosolutal convection occurs if the solute rejection or preferential incorporation at the crystal-melt interface decreases the density of the melt. Numerical calculations of the solute, temperature, and flow fields are carried out by using previously developed algorithms for Schmidt numbers Sc = 1, 10, 81. The time periodic flow, which occurs over a narrow range of parameters, is investigated.

Coriell, S. R.↗

NASA NTRS1987

Thermosolutal convection during directional solidification. II - Flow transitions

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Mcfadden, G. B.↗

NASA NTRS1993

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

NASA NTRS1990

Influence of convection on microstructure

In eutectic growth, as the solid phases grow they reject atoms to the liquid. This results in a variation of melt composition along the solid/liquid interface. In the past, mass transfer in eutectic solidification, in the absence of convection, was considered to be governed only by the diffusion induced by compositional gradients. However, mass transfer can also be generated by a temperature gradient. This is called thermotransport, thermomigration, thermal diffusion or the Soret effect. A theoretical model of the influence of the Soret effect on the growth of eutectic alloys is presented. A differential equation describing the compositional field near the interface during unidirectional solidification of a binary eutectic alloy was formulated by including the contributions of both compositional and thermal gradients in the liquid. A steady-state solution of the differential equation was obtained by applying appropriate boundary conditions and accounting for heat flow in the melt. Following that, the average interfacial composition was converted to a variation of undercooling at the interface, and consequently to microstructural parameters. The results obtained show that thermotransport can, under certain circumstances, be a parameter of paramount importance.

Wilcox, William R.↗

NASA NTRS1990

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy. III - Weakly nonlinear theory

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.

Wheeler, A. A.↗

NASA NTRS1993

Approximate formula for recalescence in binary eutectic alloys

Supercooling of a liquid prior to the nucleation of a solid and the subsequent rapid growth are necessary conditions for producing novel microstructures including metastable phases which are not formed by conventional solidification processes. Since containerless techniques, such as levitation and free fall of a sample, are capable of achieving a significant supercooling level of liquids, they are under consideration as possible techniques for material processing on earth and in space.

ALLOY STRUCTURE FORMATION↗

NASA NTRS1984

Analysis and calculation of macrosegregation in a casting ingot, exhibits C and E

A computer model which describes the solidification of a binary metal alloy in an insulated rectangular mold with a temperature gradient is presented. A numerical technique, applicable to a broad class of moving boundary problems, was implemented therein. The solidification model described is used to calculate the macrosegregation within the solidified casting by coupling the equations for liquid flow in the solid/liquid or mushy zone with the energy equation for heat flow throughout the ingot and thermal convection in the bulk liquid portion. The rate of development of the solid can be automatically calculated by the model. Numerical analysis of such solidification parameters as enthalpy and boundary layer flow is displayed. On-line user interface and software documentation are presented.

Poirier, D. R.↗

NASA NTRS1984

Separation processes during binary monotectic alloy production

Observation of microgravity solidification processes indicates that outside of sedimentation, at least two other important effects can separate the phases: critical-point wetting and spreading; and thermal migration of second-phase droplets due to interfacial tension gradients. It is difficult to study these surface tension effects while in a unit gravity field. In order to investigate the processes occurring over a temperature range, i.e., between a consolute point and the monotectic temperature, it is necessary to use a low-gravity environment. The MSFC drop tube (and tower), the ballistic trajectory KC-135 airplane, and the Space Shuttle are ideal facilities to aid formation and testing of hypotheses. Much of the early work in this area focuses on transparent materials so that process dynamics may be studied by optical techniques such as photography for viewing macro-processes; holography for studying diffusional growth; spinodal decomposition and coalescence; ellipsometry for surface wetting and spreading effects; and interferometry and spectroscopy for small-scale spatial resolution of concentration profiles.

Frazier, D. O.↗

NASA NTRS1988

Directional solidification with heat losses

The upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered. Heat losses from the sidewalls produce curved isotherms, interface deformations, and melt convection. An asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions are obtained for the resulting melt convection, interface deflection, and the distribution of heat and solute. The model is compared to the numerical results of Chang and Brown (1983) which exclude the effects of solute buoyancy and thermodynamic equilibrium at the interface. The radial segregation at the interface (consistent with both interface shapes and temperature fields) is computed, and it is found that the radial segregation is independent of interfacial shapes; the radial segregation cannot be calculated from only a knowledge of the interface shape.

Brattkus, K.↗

NASA NTRS2000

Effects of Space Environment on Flow and Concentration During Directional Solidification

A study of directional solidification of a weak binary alloy (specifically, Bi - 1 at% Sn) based on the fixed grid single domain approach is being undertaken. The enthalpy method is used to solve for the temperature field over the computational domain including both the solid and liquid phases; latent heat evolution is treated with the aid of an effective specific heat coefficient. A source term accounting for the release of solute into the liquid during solidification has been incorporated into the solute transport equation. The vorticity-stream function formulation is used to describe thermosolutal convection in the liquid region. In this paper we numerically investigate the effects of g-jitter on directional solidification. A background gravity of 1 micro-g has been assumed, and new results for the effects of periodic disturbances over a range of amplitudes and frequencies on solute field and segregation have been presented.

Benjapiyaporn, C.↗

NASA NTRS1986

An exact solution for the solidification of a liquid slab of binary mixture

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

Antar, B. N.↗

NASA NTRS1992

Cellular instability in rapid directional solidification - Bifurcation theory

Merchant and Davis performed a linear stability analysis on a model for the directional solidification of a dilute binary alloy valid for all speeds. The analysis revealed that nonequilibrium segregation effects modify the Mullins and Sekerka cellular mode, whereas attachment kinetics has no effect on these cells. In this paper, the nonlinear stability of the steady cellular mode is analyzed. A Landau equation is obtained that determines the amplitude of the cells. The Landau coefficient here depends on both nonequilibrium segregation effects and attachment kinetics. This equation gives the ranges of parameters for subcritical bifurcation (jump transition) or supercritical bifurcation (smooth transition) to cells.

Braun, R. J.↗

NASA NTRS1992

Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis

In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.

Merchant, G. J.↗

NASA NTRS1994

Shear stabilization of solidification fronts

A linear-stability analysis is performed on the interface formed during the directional solidification of a dilute binary alloy in the presence of a time-periodic flow. In general, the flow is generated by the elliptical motion of the crystal parallel to the interface. The presence of the flow can either stabilize or destabilize the system relative to the case without flow with the result depending on the frequency and amplitude of the oscillations as well as the properties of the material. In the particular, we find that the morphological instability present in the absence of flow can be entirely suppressed with respect to disturbances of the same frequency as the oscillation.

Davis, Stephen H.↗

NASA NTRS1988

Gravitational macrosegregation in unidirectionally solidified lead-tin alloy

Nine small samples of binary lead-tin alloys were solidifed unidirectionally upward, with both cooling rate and thermal gradient being closely controlled. Results presented include thermal measurements, chemical composition measurements, and microstructural characterization. In the six Pb-15 wt pct Sn ingots, normal macrosegregation was observed, with Sn content being highest at the top of the ingot. No significant macrosegretation was noted in the three ingots of nominal composition Sn-15 wt pct Sn.

Wang, L.↗

NASA NTRS1990

Directional solidification of a planar interface in the presence of a time-dependent electric current

Directional solidification of pure materials and binary alloys with a planar crystal-metal interface in the presence of a time-dependent electric current is considered. For a variety of time-dependent currents, the temperature fields and the interface velocity as functions of time are presented for indium antimonide and bismuth and for the binary alloys germanium-gallium and tin-bismuth. For the alloys, the solid composition is calculated as a function of position. Quantitative predictions are made of the effect of an electrical pulse on the solute distribution in the solidified material.

Brush, L. N.↗