Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Effect of concentration dependent gradient energy coefficient on spinodal decomposition in the Fe-Cr system
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.ORCID iD: 0000-0003-3598-2465
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
2018 (English)In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 143, p. 446-453Article in journal (Refereed) Published
Abstract [en]

The Cahn–Hilliard equation is solved with thermodynamic and kinetic input, using the Thermo-Calc and DICTRA software packages rather than simpler models e.g. regular solution. A concentration dependent expression for the gradient energy coefficient is introduced and its effect on simulated decomposition is discussed. Simulations were carried out in 2D and 3D using the FiPy software package modified for non-linear problems.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 143, p. 446-453
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219887DOI: 10.1016/j.commatsci.2017.11.043ISI: 000424900000053Scopus ID: 2-s2.0-85036461179OAI: oai:DiVA.org:kth-219887DiVA, id: diva2:1166497
Funder
VINNOVA
Note

QC 20171215

Available from: 2017-12-15 Created: 2017-12-15 Last updated: 2018-09-25Bibliographically approved
In thesis
1. Modelling phase separation in Fe-Cr alloys: A continuum approach
Open this publication in new window or tab >>Modelling phase separation in Fe-Cr alloys: A continuum approach
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The formation of Cr-rich and Fe-rich domains upon ageing of an initially homogeneous Fe-Cr alloy at elevated temperatures (300-600 ºC) is commonly referred to as phase separation. The behaviour originates from a miscibility gap in the Fe-Cr phase diagram. The boundary of the miscibility gap is denoted the binodal, and the line where the second derivative of the molar Gibbs energy w.r.t. composition is zero, the spinodal. In the region between the binodal and spinodal lines, the phase separation is said to occur by means of nucleation and growth. Inside the spinodal line, no thermally activated nucleation event is needed, and the initially homogeneous alloy decomposes "spinodally" into Cr-rich and Fe-rich regions. This type of phase transformation can be viewed as a continuous build up of Cr-rich regions, that also are interconnected, forming a microstructure characteristic for alloys decomposed spinodally. Phase separation has been of great interest within the metallurgical community as well as industry, due to its embritteling effect. Phase separation in Cr-rich ferritic steels, and thus embrittlement, sets a practical upper service temperature of ~300 ºC for Cr-containing ferrites. It is desirable to develop understanding and modelling capability for decomposing alloy systems, since such knowledge could be used to relieve the limitation in service temperature. The current work has been focused around the development and use of computer simulations, using thermodynamic and kinetic input from databases, in order to progress towards alloy design where decomposition is minimized. Simulations in this work are based on solving the so called Cahn-Hilliard equation, where an important parameter is the gradient energy, since it influences both the morphology and rate of decomposition in the simulations. An attempt at formulating a general model for the gradient energy coefficients in multi-component systems has been made, but has yet to be properly tried against experimental data. Improvements, and insights, to the initial state used in simulations has also been achieved. The combination of above mentioned efforts is a step towards a predictive tool for decomposition of complex alloys. Such a tool could not only be an aid in future alloy design, but also be used as an aid as a diagnosis tool in life time assessment of critical components already in use and thereby difficult to assess on site by means of in-destructive testing, typically components in nuclear power facilities.

Abstract [sv]

Fasseparation i ferrit är uppdelningen av en, initialt homogen, Fe-Cr-legering i Cr-rika och Fe-rika domäner vid åldring vid förhöjd temperatur (300-600 ºC). Tendensen till fassepration tar sig termodynamiskt uttryck som en s.k. blandningslucka i det binära fasdiagrammet för Fe-Cr. Blandningsluckan, eller binodalen, och spinodalen - definierad som samlingen av punkter där andraderivatan av molära Gibbs energi är lika med noll, är centrala begrepp i teorin om fasseparation. I området mellan binodalen och spinodalen sker sönderfallet i form av termiskt aktiverad kärnbildning, tillväxt och förgrovning. Innanför spinodalen behövs ingen termisk aktivering och den initialt homogena legeringen sägs sönderfalla spinodalt, dvs. genom gradvis uppbyggnad av Cr-rika och Fe-rika områden. Fassepration genom spinodalt sönderfall ger upphov till en karaktäristisk mikrostruktur, bestående av kontinuerligt sammanhängande områden av Cr- och Fe-rika områden. Sönderfall av Fe-Cr-legeringar har rönt mycket intresse både inom akademien och industrin pga dess försprödande effekt, som därmed begränsar den maximala temperaturen vid vilken dessa material kan användas. Det är därför önskvärt att förbättra både förståelsen och möjligheterna att förutspå förekomsten av fassepration genom simulering, för att på så sätt utveckla material som är okänsliga för fassepration vid högre driftstemperaturer. Detta arbete fokuserar på utveckling och användning av simuleringar som utnyttjar termodynamiska och kinetiska databaser. Simuleringarna i detta arbete baseras på att lösa den s.k. Cahn-Hilliard ekvationen, kopplad till nämnda databaser. En viktig parameter i Cahn-Hilliard ekvationen är gradientenergikoefficienten, vilken påverkar såväl morfologi som sönderfallshastighet. I detta arbete har en generell formulering för gradientenergi i multikomponentsystem utvecklats, dock krävs mer arbete för att validera den framtagna modellen. Dessutom så har detta arbete lett fram till insikter vad gäller val av den initiala strukturen som används som startpunkt för simuleringarna. En sammanflätning av nämnda delförbättringar leder ett steg närmare ett funktionellt verktyg för förutsägelser om materials beteende gällande fasseparation vid åldring av komplexa legeringar. Ett sådant verktyg kan vara till hjälp vid framtida legeringsdesign, men även fungera som diagnosverktyg för komponenter som redan tagits i bruk och därmed är svåra att undersöka oförstörande på plats, t ex kritiska komponenter i kärnkraftverk.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. p. 56
Series
TRITA-ITM-AVL 2018:46
Keywords
Phase separation, spinodal decomposition, nucleation, diffusion, thermodynamics, kinetics, steel, ferritic
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-235394 (URN)978-91-7729-945-5 (ISBN)
Public defence
2018-10-19, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00
Opponent
Supervisors
Available from: 2018-09-25 Created: 2018-09-25 Last updated: 2018-09-25Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Barkar, ThomasHöglund, LarsOdqvist, JoakimÅgren, John

Search in DiVA

By author/editor
Barkar, ThomasHöglund, LarsOdqvist, JoakimÅgren, John
By organisation
Materials Science and Engineering
In the same journal
Computational materials science
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 45 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf