Ng, F.S.L. orcid.org/0000-0001-6352-0351 (2016) Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model. Acta Materialia, 120. pp. 453-462. ISSN 1359-6454
Abstract
We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE’s solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain-size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Geography (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Aug 2016 08:50 |
Last Modified: | 25 Oct 2018 13:35 |
Published Version: | https://dx.doi.org/10.1016/j.actamat.2016.08.033 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.actamat.2016.08.033 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103862 |