Bollada, PC, Jimack, PK and Mullis, AM (2012) A new approach to multi-phase field for the solidification of alloys. In: IOP Conference Series: Materials Science and Engineering. MCWASP XIII: International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, 17-22 Jun 2012, Schladming, Austria. IOP Publishing Ltd
Abstract
We show that the standard approach to the modeling of multi-phase field dynamics for the solidification of alloys has three major defects and offer an alternative more successful formulation. The model contains an action made up of a free energy functional of the temperature, concentration and the phase variables. In addition there is a penalty functional for the gradients of the phase variables, which keeps all field variables continuous-the phase field method. A variation of this action is related to time derivatives of the variables in the field. At any physical point there exists up to N phases, φi, each of which represent the proportion of each phase at that point, thus implying the constraint, ΣNi=1 φi 1. The standard Lagrange multiplier treatment for imposing this constraint has three major defects: non-reduction to standard single phase formulation; a dependence on the value of N; generation of unphysical additional phases. We demonstrate a multi-phase formulation that avoids these two defects and, partly as a consequence, does not generate spurious additional phases. Moreover, this aim is achieved without losing the active part that three non-zero phases should play if present at any point.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2012, IOP Publishing Ltd. This is an author produced version of a paper published in IOP Conference Series: Materials Science and Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Multi-phase; phase field; lagrange multiplier; solidification; crystal growth; eutectic; peritectic; Gibbs free energy |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Chemical & Process Engineering (Leeds) > Institute for Materials Research (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Feb 2015 16:41 |
Last Modified: | 19 Dec 2022 13:30 |
Published Version: | http://dx.doi.org/10.1088/1757-899X/33/1/012099 |
Status: | Published |
Publisher: | IOP Publishing Ltd |
Identification Number: | 10.1088/1757-899X/33/1/012099 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82969 |