W. Kurz

Rapid dendrite growth in undercooled alloys

The theory of dendritic growth into undercooled alloy melts is extended to the case of large undercoolings, i.e. to high growth rates. This is done by applying the results of the complete stability analysis of a plane interface to the tip of an Ivantsov dendrite. For small Peclet numbers this model corresponds to a model published previously. For large Peclet numbers i.e. large undercoolings, however, the stability parameters become functions of Peclet numbers and cause drastic changes in the growth behaviour of the dendrite. Furthermore the limit of absolute stability is predicted when the undercooling is equal to the sum of the thermal unit undercooling and the equilibrium freezing range of the alloy.

Solidification Microstructures: Recent Developments, Future Directions

The status of solidification science is critically evaluated and future directions of research in this technologically important area are proposed. The most important advances in solidification science and technology of the last decade are discussed: interface dynamics, phase selection, microstructure selection, peritectic growth, convection effects, multicomponent alloys, and numerical techniques. It is shown how the advent of new mathematical techniques (especially phase-field and cellular automata models) coupled with powerful computers now allows the following: modeling of complicated interface morphologies, taking into account not only steady state but also non-steady state phenomena; considering real alloys consisting of many elements through on-line use of large thermodynamic data banks; and taking into account natural and forced convection effects. A series of open questions and future prospects are also given. It is hoped that the reader is encouraged to explore this important and highly interesting field and to add her/his contributions to an ever better understanding and modeling of microstructure development.

Solute redistribution during solidification with rapid solid state diffusion

Unidimensional solute redistribution during freezing is modelled for the important case of complete diffusion in the liquid and incomplete back-diffusion in the solid by the Brody and Flemings analysis. The treatment, however, does not conserve solute and leads to predictions which are incorrect unless solid state diffusion is very limited. This paper outlines the origin of this effect and presents a modification to the model in which the predicted behavior is quantitatively correct in the important limits. Application of the modified analysis is shown to be simple and to lead to realistic descriptions of the solidification behavior in mushy freezing alloys. As an example, the model is applied to two steels solidifying over a range of cooling rates and the results indicate that such systems will in many cases be quite close to thermodynamic equilibrium with respect to carbon redistribution.

Dendritic growth into undercooled alloy metals

Free dendrites growing in a liquid alloy reject both heat and (for k0 < 1) solute. A growth equation has been developed both by coupling their diffusion fields for a parabolic tip and by applying a stability criterion. This relationship indicates that (1) the dendrite tip radius passes through a minimum with increasing solute concentration and (2) at a given undercooling the growth velocity should increase with increasing solute concentration and then decrease as higher solute levels are reached. These findings are shown to correspond to experimental results obtained using succinonitrile-acetone alloys.

SINGLE-CRYSTAL LASER DEPOSITION OF SUPERALLOYS: PROCESSING-MICROSTRUCTURE MAPS

Abstract In order to extend the life cycle of modern single-crystal (SX) high-pressure high-temperature gas turbine blades, repair of cracked or worn parts is of great interest. The success of the repair technique depends critically on a close process control in order to ensure SX repair. Based on solidification theory a process called epitaxial laser metal forming (E-LMF) has been developed. This paper presents the important concepts necessary for any process control for SX repair based on processing maps which relate the expected solidification microstructures and growth morphologies to the processing conditions. These maps are obtained in two steps. Firstly, the relationships between local solidification conditions and the resulting solidification microstructures, i.e. columnar or equiaxed, are formulated. Secondly, the local solidification conditions as a function of the laser processing parameters are calculated with an analytical heat flux model. By a combination of both approaches, processing–microstructure maps are obtained which define processing windows for SX generation and repair by laser deposition.

Theory of eutectic growth under rapid solidification conditions

Abstract The Jackson-Hunt model of eutectic growth at small undercoolings is extended to large undercooling values which are commonly encountered under rapid solidification conditions. The parameters, λ2V and λΔT, are found to deviate from constant values at high velocities, and these deviations depend upon the nature of the metastable phase diagram below the eutectic temperature. A limiting velocity is predicted for the formation of a regular, coupled eutectic structure, and the reason for this limiting velocity is shown to be either the temperature dependent diffusion coefficient or the limit of undercooling.

Epitaxial laser metal forming: analysis of microstructure formation

Epitaxial laser metal forming (E-LMF) is presented as a new cladding technique which combines the advantage of near-net-shape manufacturing with a close control of the solidification microstructure. E-LMF is a process where metal powder is injected into a molten pool formed by controlled laser heating. Laser surface treatment has the advantage that heat input is very localised, thus leading to large temperature gradients. This is used, in unison with closely controlled solidification velocities, to stabilise the columnar dendritic growth, thereby avoiding nucleation and growth of equiaxed grains in the laser clad. It is possible with this technique to deposit a single crystal clad by epitaxial growth onto a single crystal substrate. In this paper, the microstructure obtained by E-LMF is analysed by scanning electron microscopy (SEM), optical microscopy (OM) and indexing electron backscattered diffraction (EBSD) patterns. In particular, the grain structure formation in the deposit during the process and the influence of a subsequent heat treatment on precipitation and recrystallisation is characterised.

Effect of growth rate dependent partition coefficient on the dendritic growth in undercooled melts

The theory of alloy dendritic growth at large undercoolings is extended to include the effect of growth rate dependent partition coefficient on the growth rate, tip radius and composition of dendrites. Three distinct behaviors are observed depending on the value of the dimensionless rate v. For small values of v, k ≅ k0. For the intermediate range, when v is between 0.01 and 100, a significant effect of the velocity dependent partition coefficient is found. When v > 100, k → 1 and the dendrite behavior in an alloy is found to approach that for the pure material. In undercooled alloy melts segregation free zones could then be obtained by dendrite growth.

Phase selection during solidification of peritectic alloys

Abstract Formation of stable and metastable phases under directional solidification conditions in materials showing peritectic phase equilibria is discussed. Based on interface response functions for single phase growth morphologies (dendrites and plane front) and on competitive growth arguments, a kinetic stabilisation of metastable peritectic phases with respect to stable ones is predicted for various growth conditions. This method is applied to two industrially important classes of materials such as steels and NdFeB permanent magnets, the properties of which depend closely on the phases formed.

Nucleation ahead of the advancing interface in directional solidification

During directional solidification of an alloy, it is possible to nucleate the growing phase or a new phase at or ahead of the interface. This is critical in the phase selection, in the columnar to equiaxed transition under casting, welding or rapid solidification conditions and the formation of bands in peritectic systems. Following Hunt, an appropriate theoretical model is developed to determine the conditions under which nucleation can occur in the liquid close to a moving solid-liquid interface for both, low and high interface velocities. At high growth rates, non-equilibrium effects are shown to play an important role in predicting such transitions.