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Modeling C-Curves for the Growth Rate of Widmanstatten and Bainitic Ferrite in Fe-C Alloys
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: 0000-0002-7656-9733
2016 (English)In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 47A, no 1, p. 19-25Article in journal (Refereed) Published
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Text
Abstract [en]

When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstatten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstatten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 47A, no 1, p. 19-25
National Category
Metallurgy and Metallic Materials
Identifiers
URN: urn:nbn:se:kth:diva-180978DOI: 10.1007/s11661-015-3241-5ISI: 000367468100004Scopus ID: 2-s2.0-84947917227OAI: oai:DiVA.org:kth-180978DiVA, id: diva2:898549
Note

QC 20160128

Available from: 2016-01-28 Created: 2016-01-26 Last updated: 2018-05-14Bibliographically approved
In thesis
1. Modeling Bainite Formation in Steels
Open this publication in new window or tab >>Modeling Bainite Formation in Steels
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This study examines the fundamental aspects of bainite formation in a guided effort to lay a foundation for development of a model capable of predicting bainite formation. In the first part of this study, the tenets of an existing model for growth, developed by Zener and later modified by Hillert are examined. A number of interacting and adjustable parameters are identified namely, diffusivity, driving force, radius of the ferrite plate tip, interfacial carbon content, and thermodynamic barriers. Amongst which, there are a number of assumptions which are no longer justifiable because of the availability of software and databases from which more accurate calculations can be obtained. The approximation of the driving force is one such example. Another is the carbon content in ferrite, which was assumed negligible. The capillarity effect of the curved ferrite interface had initially been assigned by Zener as having a fixed, optimal value at the maximum growth rate. Although this principle was kept it led to quite different results when the earlier approximations were removed. It is shown that the shape of the C-curves is largely dependent on the diffusivity.

The second focus of this thesis is aimed towards developing a model for the start temperatures of bainite, WBs and is achieved twofold. The first procedure was to develop an empirical model. Experimental information on which it is based refers to the start conditions for both bainite and Widmanstätten ferrite. A systematic approach is adapted by which Fe-C is the basis and the effect of alloying elements are evaluated separately from ternary alloys. Regression analysis of data on five ternary systems with Mn, Ni, Si, Cr and Mo gives separate coefficients. A linear empirical equation for the WBs is defined from their sum which was possible because their effects were independent. Carbon had by far the largest effect and Ni the smallest. The equation has good agreement with data but further improvement can be achieved with more reliable experimental data. The second procedure is directed towards a thermodynamic description of the start condition. The critical driving forces corresponding to the critical conditions depicted in the empirical equation are calculated. The results are presented with a dependence on temperature and the same could be translated to a carbon dependence. The critical driving force increases substantially with decreasing temperature and increasing carbon content and the effect of alloying elements is varied.

In the final section, the growth model is further developed. A more generalized expression for the barrier is formulated and together with the capillarity effect, consists of the energy requirement to move the growth interface. This is balanced with the available driving force and is solved with an optimization procedure. The predicted C-curves are compared with experimental results and reasonably good agreement is found.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2018. p. 51
Series
TRITA-ITM-AVL ; 2018:16TSC-MT
National Category
Metallurgy and Metallic Materials
Identifiers
urn:nbn:se:kth:diva-227863 (URN)978-91-7729-779-6 (ISBN)
Public defence
2018-06-15, B3, Brinellvägen 23, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2018-05-15 Created: 2018-05-14 Last updated: 2018-05-18Bibliographically approved

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