Numerical calculation of microsegregation in coarsened dendritic microstructures

Roósz, András; Halder, E.; Exner, Hans Eckart

doi:10.1179/mst.1986.2.11.1149

Cited by 72 publications

(17 citation statements)

References 7 publications

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“…There is also an influence on the solidification path and potentially on the type of secondary phases that crystallise toward the end of solidification. 129 Various work is concerned with these aspects of coarsening in binary 130 and multicomponent alloys. 131,132 Both melting of secondary dendrite arms at the root and mechanical breakdown have been discussed as cause for dendrite fragmentation and thus for the columnarto-equiaxed transition in castings and for microstructural defects like freckles or stray crystals.…”

Section: Melting and Simultaneous Solidification Dendrite Arm Coarsen...mentioning

confidence: 99%

Melting and remelting phenomena

Rettenmayr¹

2009

International Materials Reviews

131

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Melting processes influence the microstructure evolution in metal alloys during casting and heat treatments. Melting is often treated as 'inverse solidification', which is only appropriate in a limited number of cases. In the present article, asymmetry between solidification and melting is reviewed in detail. The current state of the thermodynamic description of melting under diffusion control is outlined. Kinetic aspects that break the symmetry between solidifi-cation and melting that are discussed are solute partitioning, solute concentration gradients and solute transport in the involved phases. The view on nucleation of liquid and pre-melting phenomena, mostly of pure materials, based on experimental and theoretical work, is given. Emphasis is laid on aspects of melting with technical relevance, i.e. melting of alloys. Particu-larities of thermally and solutally controlled melting are introduced. Mechanisms that involve both melting and solidification simultaneously are capillary driven coarsening, temperature gradient zone melting and liquid film migration. The impact of these processes on microstructural evolution is discussed. Open questions concerning modelling and simulation of melting, namely, the interaction of different melting mechanisms and the role of the solid/liquid inter-face, are identified.

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Section: Melting and Simultaneous Solidification Dendrite Arm Coarsen...mentioning

confidence: 99%

Melting and remelting phenomena

Rettenmayr¹

2009

International Materials Reviews

131

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“…• Owing to the coarsening process, the size of the microsegregation domain X(t) increases with time (the model proposed by Roosz et al [12] will be used in this work).…”

Section: Micro-scale Assumptionsmentioning

confidence: 99%

“…and using the Landau transformation (25) the problem can be reduced to a single equation in a fixed domain 0 ≤ ξ ≥ 1, viz., The application of this last boundary condition requires the specification of a mixture solute density history [ρC] and a coarsening history X(t); in addition, calculation of other model parameters requires a cooling history for the domain T(t). A successful model for the coarsening is that of Roosz et al [12], (32)…”

Section: The Micro-scale Equationsmentioning

confidence: 99%

Computational issues in using a dual‐scale model of the segregation process in a binary alloy

Sundarraj

Voller

1997

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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IntroductionDuring the solidification of a metal, on the scale of the process (~meters), three distinct regions can be identified: a solid region, a mushy region and a liquid region. Usually the mushy region consists of a dendritic crystal morphology with a length scale, defined by the secondary arm spacing, on the order or microns (see Figure 1). Key solidification phenomena occur within the mushy region. Many of these phenomena are associated with both the macro-scale of the process and the micro-scale of the dendrite arm spaces. An important example is segregation of the alloy components. Consider the solidification of a dilute binary alloy with a partition ratio k o < 1. When the solid forms in the mushy region, the solute phase is rejected into the liquid. At the micro-scale (i.e. the dendrite arm spaces), this solute is redistributed in the solid and liquid phase by diffusion, a process referred to as microsegregation. At the macroscopic scale of the casting, the solute phase is redistributed by fluid flow (driven by thermal and solutal natural convection), a process referred to as macrosegregation. If segregation processes are to be modelled numerically, owing to the complex interaction of the phenomena across a wide range of length scales, innovative computational approaches are required.In this paper, the computational issues involved in modelling segregation phenomena are examined, with particular emphasis placed on methodologies which can capture the disparate length scales of the problem. Towards this end, a test problem involving the unidirectional solidification, from below, of an aluminum copper alloy is investigated. Modelling this system involves the coupling of a macroscopic model, describing the heat and mass transfer in the This work was supported by a resource and a travel grant from the Minnesota Supercomputer Institute, University of Minnesota.

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“…The numerical model of microsegregation is based on the models of Roósz et al [21,22], Roósz and Exner [25,27] and Sasikumar and Exner [26]. The phase equilibria were calculated with thermodynamically formulated phase diagrams as described by Rettenmayr [24].…”

Section: Numerical Modelmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) such as the limitation to binary alloys, unrealistic phase diagram approximations in the case of multicomponent alloys or omissions of undercooling or coarsening effects. Over many years the authors and other coworkers have developed numerical procedures to simulate microsegregation phenomena [21][22][23][24][25][26][27][28][29]. During the past decade various restrictions have been released stepwise improving the model to a state where it covers a large range of applications in technical problems and starts to gain commercial interest.…”

Section: Introductionmentioning

confidence: 99%

An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys

Kraft

Rettenmayr

Exner

1996

Modelling Simul. Mater. Sci. Eng.

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A numerical model for the prediction of microstructure and microsegregation in multicomponent alloys during dendritic solidification using a finite difference scheme is presented. The main kinetic and thermodynamic effects that can influence microsegregation (solid state back diffusion, secondary dendrite arm coarsening, primary tip and eutectic undercooling and the thermodynamic correction of the interface concentrations) are accounted for. The liquid/solid phase equilibria in the thermodynamically stable and metastable range are calculated with thermodynamically formulated phase diagrams. For the calculation at high cooling rates non-equilibrium phase diagrams for multi-component alloys are assessed. The consideration of undercooling effects extends the applicability of the model to very low and very high cooling rates. The model thus covers the whole range of cooling conditions where dendritic solidification occurs. As compared with other models in the literature, the number of adjustable parameters is reduced to a minimum.

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Numerical calculation of microsegregation in coarsened dendritic microstructures

Cited by 72 publications

References 7 publications

Melting and remelting phenomena

Melting and remelting phenomena

Computational issues in using a dual‐scale model of the segregation process in a binary alloy

An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys

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