Showing papers on "Directional solidification published in 1993"

Prediction of dendritic spacings in a directional-solidification experiment.

Abstract: We present a theoretical analysis of the formation of a dendritic array in a directional-solidification experiment. Our calculation contains three sequential ingredients: acceleration of an initially flat interface and the concomitant buildup of a solutal boundary layer in front of it; onset of a morphological instability, triggered by thermal fluctuations, producing a relatively finely spaced array of dendritic tips; coarsening of this array and final selection of a steady-state primary spacing. For sufficiently large growth speeds, where the resulting dendrites interact with each other weakly, we find--with no adjustable parameters--good agreement with the experiments of Trivedi and Somboonsuk [Acta Metall. 33, 1061 (1985)] and Somboonsuk, Mason, and Trivedi [Metall. Trans A 15A, 967 (1984)].

Nonlinear analysis of buoyant convection in binary solidification with application to channel formation

Abstract: We consider the problem of nonlinear thermal-solutal convection in the mushy zone accompanying unstable directional solidification of binary systems. Attention is focused on possible nonlinear mechanisms of chimney formation leading to the occurrence of freckles in solid castings, and in particular the coupling between the convection and the resulting porosity of the mush. We make analytical progress by considering the case of small growth Peclet number, δ, small departures from the eutectic point, and infinite Lewis number. Our linear stability results indicate a small O(δ) shift in the critical Darcy-Rayleigh number, in accord with previous analyses. We find that nonlinear two-dimensional rolls may be either sub- or supercritical, depending upon a single parameter combining the magnitude of the dependence of mush permeability on solids fraction and the variations in solids fraction owing to melting or freezing. A critical value of this combined parameter is given for the transition from supercritical to subcritical rolls. Three-dimensional hexagons are found to be transcritical, with branches corresponding to upflow and lower porosity in either the centres or boundaries of the cells. These general results are discussed in relation to experimental observations and are found to be in general qualitative agreement with them.

Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

Abstract: A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.

Mechanisms of porosity formation during solidification: A theoretical analysis

Abstract: The formation of porosity during solidification is of great commercial importance and scientific interest. This is particularly so for the question of the “feeding length” of a riser. In this work, a number of theoretical models are derived and their predictions are compared to experimental observations. The comparisons show that in directional solidification, a “thermodynamic” model is useful in predicting when porosity may form. The amount of porosity predicted is too high, however, since it ignores the nucleation of the pore and growth by diffusion of dissolved gas to growing pores. A surprising conclusion of this study is that Darcy’s law does not appear to be a controlling factor in porosity distribution or formation. In particular, Darcy’s law cannot explain feeding length measurements made in steel castings. A simple “geometrical” criterion is presented instead to describe when shrinkage porosity will occur. This new model suggests a number of interesting experiments, which are proposed in discussion.

Secondary and tertiary dendrite arm spacing relationships in directionally solidified Al-Si alloys

Abstract: Secondary, λ2, and tertiary, λ3, dendrite arm spacings have been measured from Al-Si alloys which were directionally solidified as functions of growth velocity,V, temperature gradient,G, and composition,C o. Both λ2 and λ3 decreased as the imposed growth velocity and silicon concentrations were increased, and for each function a systematic variance in the rate was seen. Complications with measuring secondary arm spacings are shown and it was found that the tertiary arm data agree much better with coarsening theory, the implication being that λ3, when measurable, is a more representative and reliable measure of the solidification history than λ2.

Modelling of microsegregation

Abstract: After a brief review of existing models of microsegregation in the dendritic arm spaces of binary alloys, a numerical microsegregation model based on conservative variables (to account for the solidification phase change) and a coordinate transformation (to account for coarsening) is outlined. In the context of this model appropriate conditions and parameters required for a comprehensive description of microsegregation are discussed and summarised. The role of submodels describing density changes and undercooling phenomena is investigated, and predictions from the model are compared with the results of recent directional solidification experiments.MST/1752

Interface dynamics and banding in rapid solidification

Abstract: Rapid-solidification experiments on metallic alloys in the last decade have provided widespread observations of a novel banded structure.'' We report the results of numerical and analytical studies of the interface dynamics underlying the formation of this structure in a model of directional solidification which includes both solute and heat diffusion and nonequilibrium effects. The thrust of these studies is on the unsteady dynamics of the planar interface and thermal effects. The main conclusion is that the origin of banding can be related to relaxation oscillations of the solidification front, characterized by large variations of the interface velocity, which are dramatically affected by latent-heat diffusion. Without the latter, the oscillations are found to be reasonably well approximated by the phenomenological model of Carrard [ital et] [ital al]. [Acta Metall. 40, 983 (1992)], and the band spacing is inversely proportional to the temperature gradient. In contrast, with latent-heat diffusion the band spacing is insensitive to the temperature gradient, but is controlled instead by the interplay of solute and heat diffusion. The smallness of the solutal diffusivity to thermal diffusivity ratio is exploited to explain analytically this effect and to derive considerably simpler equations of interface motion that provide an efficient numerical meansmore » to study the nonplanar interface dynamics expected to cause dark bands. A reasonable agreement with experiment is found for the spacing of banded structures dominated by light-band microsegregation-free regions in Al-Fe alloys.« less

Flow and Morphological Conditions Associated With Unidirectional Solidification of Aqueous Ammonium Chloride

Abstract: Using a 27 percent aqueous ammonium chloride solution as a transparent analog, shadowgraph and dye injection techniques have been employed to observe flow and morphological conditions associated with unidirectional solidification (UDS) from below. Dendritic crystals, which initially form at the cold surface, reject lighter, solute deficient fluid, and the attendant instability is manifested by finger-type double-diffusive convection phenomena. As a two-phase (solid/liquid), or mushy, region grows from the bottom surface, vertical channels develop in the muschy region, and solutal plumes that emanate from the channels are characterized primarily by an ascending, oscillatory motion and secondarily by wisps of fluid, which detach and descend from bends in the plumes

Three-Dimensional Considerations of Unidirectional Solidification in a Binary Liquid

Abstract: Unidirectional solidification of an aqueous NH4Cl solution has been simulated using a fully three-dimensional model for the strongly coupled transport of momentum, energy, and species in the mushy and melt regions of the solution. The predictions reveal the nucleation and development of pencil-like vertical channels in the mushy region and the complex, three-dimensional flow and thermosolutal conditions associated with channel formation. The number of channels is at a maximum shortly after nucleation and thereafter decreases with increasing time, as solidification progresses. Favorable agreement is obtained between three- and two-dimensional predictions of global parameters such as heat rate and mass fraction of solid formation.

Interfacial shear strength of cast and directionally solidified NiAl-sapphire fiber composites

Abstract: The feasibility of fabricating intermetallic NiAl-sapphire fiber composites by casting and zone directional solidification has been examined. The fiber-matrix interfacial shear strengths measured using a fiber push-out technique in both cast and directionally solidified composites are greater than the strengths reported for composites fabricated by powder cloth process using organic binders. Microscopic examination of fibers extracted from cast, directionally solidified (DS), and thermally cycled composites, and the high values of interfacial shear strengths suggest that the fiber-matrix interface does not degrade due to casting and directional solidification. Sapphire fibers do not pin grain boundaries during directional solidification, suggesting that this technique can be used to fabricate sapphire fiber reinforced NiAl composites with single crystal matrices.

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

Abstract: 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.

Directional solidification in two and three dimensions.

Abstract: A symmetric phase-field model is used to study directional solidification in two and three dimensions. Numerical evidence of tip-splitting, breathing modes, solitary modes, and other non-steady-state behavior is seen in 2D. A simple model for the breathing modes is proposed. Finally, 3D simulations indicate a hexagonal ordering of cells.

Dendritic sidebranching with periodic localized perturbations : directional solidification of pivalic acid-coumarin 152 mixtures

Abstract: We have studied the response of the sidebranches of pivalic acid dendrites, growing by directional solidification, to localized periodic thermal perturbations. The perturbations were generated by a laser beam focused near the tip of a single dendrite growing in a glass capillary, with the pulse duration, repetition rate, and intensity controlled separately. The perturbation dramatically altered the sidebranch structure, producing ordered sidebranches of well-defined wavelength, synchronous with the perturbation, which were strongly correlated on the two sides of the dendrite

Array of doublets: A branch of cellular solutions in directional solidification.

Abstract: In directional solidification of alloys, the interface pattern assumes a cellular structure, with a periodic array of cells, when the velocity is increased beyond the threshold of planar interface instability. A detailed experimental study in the succinonitrile-acetone system has revealed a branch of cellular structure in which the interface pattern consists of a periodic array of coupled cells or doublets. This doublet interface evolves with two characteristic length scales at the advancing front: a small intraspacing between the cells in a doublet, whose selection is sharp, and a larger interspacing corresponding to the distance between cells in adjoining doublets, whose selection is weak. The dynamics of the time-dependent evolution of a doublet interface is investigated by statistical analysis of tip spacings, by using a Fourier transform of the interface shape and through the study of the variation of shape parameters with time. These dynamical studies have confirmed the selection of doublet interface as a stable solution of the cellular pattern formation. A range of stable regime for an array with doublets is determined and the key factor that controls the formation of regular cells or doublets in an array is discussed. When doublets are unstable, time dependency may follow duemore » to a source mechanism at grain boundaries, which induces strong spatiotemporal chaos.« less

Experimental investigation of the development of microsegregation during solidification of an AlCuMgSi aluminium alloy

Abstract: Chemical heterogeneities which build up during dendritic solidification of metallic alloys are of great importance to their service properties. In nominally single-phase alloys, off-equilibrium eutectic often appears which is associated with large compositional changes in the primary phase at the scale of the solidification microstructure. In order to obtain a precise description of solute heterogeneities, it has become common practice to draw distribution curves obtained from numerous microprobe point counts. The experimental distribution curves show differences with respect to the usual predictions, these differences being related to the sign of curvature at low solid fraction and to the amount of highly segregated material at high solid fraction. The present study is an attempt to investigate experimentally microsegregation build-up during solidification, and was carried out on an aluminium alloy quenched during directional solidification.

Method and apparatus for directional solidification of a metal melt

Abstract: The invention relates to a casting device which inside a heating chamber (6) has a casting mould (5) which can be displaced from the heating chamber to a bath of cooled molten metal (10) situated below said heating chamber. As heat insulation between the heating chamber (6) and the bath of cooled molten metal (10) the invention provides for a heat insulating layer (13) floating on said bath of cooled molten metal (10) through which the casting mould (5) dips into the cooled molten metal (10). To prevent the formation of clumps within the heat insulating layer (13) the invention provides for a rake or stirrer (19) which is moved by a shaking device (17) and agitates or mixes the heat insulating layer.

Dendritic sidebranching with periodic localized perturbations: Directional solidification of pivalic acid-coumarin 152 mixtures

Abstract: We have studied the response of the sidebranches of pivalic acid dendrites, growing by directional solidification, to localized periodic thermal perturbations. The perturbations were generated by a laser beam focused near the tip of a single dendrite growing in a glass capillary, with the pulse duration, repetition rate, and intensity controlled separately. The perturbation dramatically altered the sidebranch structure, producing ordered sidebranches of well-defined wavelength, synchronous with the perturbation, which were strongly correlated on the two sides of the dendrite. The dependencies of the sidebranch amplitude on the frequency of the perturbation and on the distance from the dendrite tip were compared to the predictions of Barber, Barbieri, and Langer [Phys. Rev. A 36, 3340 (1987)] and found to be in qualitative agreement. The value of the selection parameter \ensuremath{\sigma} found from these fits to the theory is compared to a value obtained from material parameters also determined in this experiment, and to a value deduced from the initial Mullins-Sekerka instability of the planar crystal-melt interface.

Experimental study of the planar-to-cellular transition during thin-film directional solidification : observations of the long-time-scale dynamics of microstructure formation

Abstract: The morphological evolution of the crystal-melt interface formed during the thin-film directional solidification of the succinonitrile-acetone alloy is studied using an experimental system that permits extremely-long-time-scale experiments under conditions close to those for the onset of cellular growth from the planar interface. Long exposure times of the alloy to high temperatures result in thermal decomposition of the succinonitrile, which increases the total concentration of solute or impurity in the sample. This effect alone may be responsible for the apparent hysteresis observed by others in the measurement of the critical solidification rate ${\mathit{V}}_{\mathit{c}}$ for the onset of cellular growth and may explain the differences between those experiments and numerical calculations. We show that the evolution of the planar interface into cellular structures occurs first in packets of more rapidly growing undulations separated by regions of slower growing cells. These cellular structures propagate over the entire interface and at very long times the interface exhibits shallow cells without a selected wavelength. The interface dynamics appears to be spatiotemporally chaotic. The wavelength distribution is dispersed about a mean that is almost a factor of 4 below the critical value expected from linear stability theory. Deeper cells exhibit stronger wavelength selection behavior and are observed at solidification rates only slightly above ${\mathit{V}}_{\mathit{c}}$; the mean wavelength increases with increasing V for deep cells.

Void initiation and growth in unidirectional freezing: the influence of natural convection

Abstract: Experiments were conducted to observe the solidification sequence and final shrinkage void distribution more precisely than was previously possible for liquids frozen from above in a rigid, constant-volume container. Physical models have been developed to give quantitative predictions about the different regimes of void initiation and why voids ultimately cease to grow downward with the freezing front. In both models, natural convection is of paramount importance for understanding the heat flows within the solidification chamber. Agreement of the results with experimental data is encouraging. We feel that these results will eventually lead to better void management in phase-change materials for storing thermal energy.