Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility...

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Main Authors:	Tohid Naseri, Daniel Larouche, Rémi Martinez, Francis Breton, Denis Massinon
Format:	Article
Language:	English
Published:	MDPI AG 2019-08-01
Series:	Metals
Subjects:	growth dissolution interfacial mobility mixed-mode reversed-growth Al–Cu DICTRA
Online Access:	https://www.mdpi.com/2075-4701/9/8/889

id	doaj-31c6fc1f16244b50b6cde10339dbe55e
record_format	Article
spelling	doaj-31c6fc1f16244b50b6cde10339dbe55e2020-11-24T22:12:52ZengMDPI AGMetals2075-47012019-08-019888910.3390/met9080889met9080889Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite SystemTohid Naseri0Daniel Larouche1Rémi Martinez2Francis Breton3Denis Massinon4Department of Mining, Metallurgy and Materials Engineering, Aluminum Research Center–REGAL, Laval University, 1065, ave de la Médecine, Québec, QC G1V 0A6, CanadaDepartment of Mining, Metallurgy and Materials Engineering, Aluminum Research Center–REGAL, Laval University, 1065, ave de la Médecine, Québec, QC G1V 0A6, CanadaLinamar Corporation—The Center, 700 Woodlawn Road West, Guelph, ON N1K 1G4, CanadaRio Tinto, Arvida Research and Development Centre, 1955, Mellon Blvd, Saguenay, QC G7S 4K8, CanadaLinamar Montupet Light Metal Division, 3, rue de Nogent, 60290 Laigneville, FranceIn this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical <i>θ</i>-Al<sub>2</sub>Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.https://www.mdpi.com/2075-4701/9/8/889growthdissolutioninterfacial mobilitymixed-modereversed-growthAl–CuDICTRA
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tohid Naseri Daniel Larouche Rémi Martinez Francis Breton Denis Massinon
spellingShingle	Tohid Naseri Daniel Larouche Rémi Martinez Francis Breton Denis Massinon Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System Metals growth dissolution interfacial mobility mixed-mode reversed-growth Al–Cu DICTRA
author_facet	Tohid Naseri Daniel Larouche Rémi Martinez Francis Breton Denis Massinon
author_sort	Tohid Naseri
title	Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System
title_short	Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System
title_full	Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System
title_fullStr	Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System
title_full_unstemmed	Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System
title_sort	analytical modeling of the mixed-mode growth and dissolution of precipitates in a finite system
publisher	MDPI AG
series	Metals
issn	2075-4701
publishDate	2019-08-01
description	In this paper, a novel analytical modeling of the growth and dissolution of precipitates in substitutional alloys is presented. This model uses an existing solution for the shape-preserved growth of ellipsoidal precipitates in the mixed-mode regime, which takes into account the interfacial mobility of the precipitate. The dissolution model is developed by neglecting the transient term in the mass conservation equation, keeping the convective term. It is shown that such an approach yields the so-called reversed-growth approximation. A time discretization procedure is proposed to take into account the evolution of the solute concentration in the matrix as the phase transformation progresses. The model is applied to calculate the evolution of the radius of spherical <i>θ</i>-Al<sub>2</sub>Cu precipitates in an Al rich matrix at two different temperatures, for which growth or dissolution occurs. A comparison of the model is made, with the results obtained using the numerical solver DICTRA. The very good agreement obtained for cases where the interfacial mobility is very high indicates that the time discretization procedure is accurate.
topic	growth dissolution interfacial mobility mixed-mode reversed-growth Al–Cu DICTRA
url	https://www.mdpi.com/2075-4701/9/8/889
work_keys_str_mv	AT tohidnaseri analyticalmodelingofthemixedmodegrowthanddissolutionofprecipitatesinafinitesystem AT daniellarouche analyticalmodelingofthemixedmodegrowthanddissolutionofprecipitatesinafinitesystem AT remimartinez analyticalmodelingofthemixedmodegrowthanddissolutionofprecipitatesinafinitesystem AT francisbreton analyticalmodelingofthemixedmodegrowthanddissolutionofprecipitatesinafinitesystem AT denismassinon analyticalmodelingofthemixedmodegrowthanddissolutionofprecipitatesinafinitesystem
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Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

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