A simple model for dendrite arm coarsening during solidification

Kirkwood, David H.

doi:10.1016/0025-5416(85)90319-2

Cited by 152 publications

(98 citation statements)

References 4 publications

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“…The subsidiary side-branches are indicated with arrows for clarity. Although it is well established that secondary arm coarsening proceeds by the dissolution of unfavourable branches from the tip back towards the trunk [28,29], this appears not to be the case here, as the branches never fully develop. Instead, these appear to be remnants indicative of a period doubling instability as described by [13].…”

Section: Figurementioning

confidence: 62%

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Mullis

2015

Journal of Applied Physics

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The accepted view on dendritic side-branching is that side-branches grow as the result of selective amplification of thermal noise and that in the absence of such noise dendrites would grow without the development of side-arms. However, recently there has been renewed speculation about dendrites displaying deterministic side-branching [see e.g. ME Glicksman, Metall. Mater. Trans A 43 (2012) 391]. Generally, numerical models of dendritic growth, such as phase-field simulation, have tended to display behaviour which is commensurate with the former view, in that simulated dendrites do not develop side-branches unless noise is introduced into the simulation. However, here we present simulations that show that under certain conditions deterministic side-branching may occur. We use a model formulated in the thin interface limit and a range of advanced numerical techniques to minimise the numerical noise introduced into the solution, including a multigrid solver. Spontaneous side-branching seems to be favoured by high undercoolings and by intermediate values of the capillary anisotropy, with the most branched structures being obtained for an anisotropy strength of 0.03. From an analysis of the tangential thermal gradients on the solid-liquid interface, the mechanism for side-branching appears to have some similarities with the deterministic model proposed by Glicksman.

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Section: Figurementioning

confidence: 62%

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Mullis

2015

Journal of Applied Physics

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“…Secondary-arm spacings, unlike primary spacings, are known to change moving through the mushy zone due to coarsening (GibbsThomson effect), with kinetics that are likely to vary with 7,[187][188][189][193][194][195][197][198][199][200][201][202][203] Accounting for this coarsening is very important in both microsegregation and permeability models, which can be implemented at any location within the mushy zone. Theoretical secondary-arm relations which account for coarsening have been developed, 7,200,201) but they are often more complicated and require many more input parameters (hence, they can deliver very different results to the expressions in Table 1). There are a number of microsegregation models which have accounted for secondary-arm coarsening directly, see Voller and Beckermann 148) for example, but the affect on permeability has not been dealt with in great detail, and studies usually work with an approximate secondary spacing that is kept constant.…”

Section: Dendrite-arm Spacingsmentioning

confidence: 99%

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Pickering

2013

ISIJ Int.

146

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The macro-scale segregation of alloying elements during the casting continues to afflict the manufacturers of steel ingots, despite many decades of research into its prediction and elimination. Defects such as A-segregates are still commonplace, and components are regularly scrapped due to their presence, leading to increased economic and environmental costs. With the growth of the nuclear power industry, and the increased demands placed on new pressure vessels, it is now more important than ever that today's steel ingots are as chemically homogeneous as possible.This article briefly reviews the development of our current understanding of macrosegregation phenomena during the 20 th century, before going on to assess the latest developments in the field of macrosegregation modelling. The aim of the text is to highlight the shortcomings of applying contemporary macromodels to steel-ingot casting, and to suggest practical alternatives. In addition, the experimental characterisation of macrosegregation is explored, and a review of the various techniques currently available is presented.

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“…Theoretically, the process is well understood, with thinner secondary arms melting back from their tips and eventually disappearing due to their higher curvature, thereby increasing the spacing between adjacent arms [11,12]. Experimentally, this gives rise to an expression for the SDAS, λ, which is given by [13] as,…”

Section: Introductionmentioning

confidence: 99%

Estimation of Cooling Rates During Close-Coupled Gas Atomization Using Secondary Dendrite Arm Spacing Measurement

Farrell

Mullis

Adkins

2013

Metall Mater Trans B

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Al-4 wt.%Cu alloy has been gas atomized using a commercial close-coupled gas atomization system. The resulting metal powders have been sieved into six size fractions and the secondary dendrite arm spacing has been determined using electron microscopy. Cooling rates for the powders have been estimated using a range of published conversion factors for Al-Cu alloy, with reasonable agreement being found between sources. We find that cooling rates are very low compared to those often quoted for gas atomized powders, of the order of 10 4 K s -1 for sub-38 μm powders. We believe that a number of numerical studies of gas atomization have overestimated the cooling rate during solidification, probably as a consequence of overestimating the differential velocity between the gas and the particles. From the cooling rates measure here we estimate that such velocities are unlikely to exceed 20 m s -1 .

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A simple model for dendrite arm coarsening during solidification

Cited by 152 publications

References 4 publications

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Spontaneous deterministic side-branching behavior in phase-field simulations of equiaxed dendritic growth

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Estimation of Cooling Rates During Close-Coupled Gas Atomization Using Secondary Dendrite Arm Spacing Measurement

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