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Critical driving forces for formation of bainite
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
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(English)Manuscript (preprint) (Other academic)
Abstract [en]

An empirical equation for predicting bainite start temperatures of steels was recently derived by starting from binary Fe-C alloys and continuing with ternary Fe-C-M alloys. That result is now illustrated with a family of Bs lines in a T,C diagram for a series of constant Mn contents. The critical driving force for the formation of ferrite is calculated for a diffusionless or diffusional process and these quantities are used as dependent variables with carbon content or temperature as independent variables. Negative critical driving forces are predicted for a diffusionless process in binary Fe-C alloys, showing that this process cannot apply to the formation of bainite. The critical driving force for a diffusional process increases strongly with decreasing temperature and increasing carbon content. Mn and Ni, contrary to Cr, Mo and Si, have remarkably small effects on this critical driving force. The results are discussed by imagining that the magnitude of the critical driving force is governed by the height of an energy barrier that must be surmounted during growth. It is modelled as completely determined by the alloy composition. It is represented with an equation evaluated by fitting to the recent empirical equation and describing the carbon dependence of the barrier.

Keyword [en]
Diffusion, Phase transformation, Bainite, Modeling, Thermodynamics
National Category
Metallurgy and Metallic Materials
Identifiers
URN: urn:nbn:se:kth:diva-227695OAI: oai:DiVA.org:kth-227695DiVA, id: diva2:1205208
Note

QC 20180525

Available from: 2018-05-11 Created: 2018-05-11 Last updated: 2018-05-25Bibliographically 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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Leach, Lindsay

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