Diffusion-Controlled Lengthening Rates of Bainitic Ferrite a Part of the Steel Genome
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THE materials genome is the combination of models and databases that supports efficient materials design,[1] the aim being to decrease the development time and costs for materials and processes. The CALPHAD type of models and databases for thermochemical and diffusional data may be seen as role models for materials genomic databases. The purpose of the present work is to provide a practical formalism based on the CALPHAD methodology and databases for predicting the lengthening rate of bainitic ferrite, an important part of the bainite transformation. The approach is inspired by the remarkable success of CALPHAD in materials science and engineering. The bainite transformation in steels is now considered because it has received a lot of attention over the last decade. Such steels hold promises of excellent engineering properties, e.g., high hardness and strength, good wear resistance and toughness, to mention a few. In order to optimize product and performance, models are increasingly being used to facilitate tailoring of material properties. In this paper we shall not discuss the mechanism of the bainite transformation as such discussions can be found elsewhere, e.g., in References 2 and 3. We will
LINDSAY LEACH, JOHN A˚GREN, LARS HO¨GLUND, and ANNIKA BORGENSTAM are with the Unit of Structures, Department of Materials Science and Engineering, KTH Royal Institute of Technology, Brinellvgen 23, 10044, Stockholm, Sweden. Contact e-mail: [email protected] Manuscript submitted on May 07, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
rather base our approach on the hypothesis that the primary ferritic component in bainite grows by the same diffusional mechanism as Widmansta¨tten ferrite over the whole temperature range,[4] i.e., the transformation rate is mainly controlled by carbon diffusion in austenite. The approach is developed through a combined thermodynamic and phenomenological model and the parameters in the model will be evaluated from experimental data on starting temperatures and growth rates.
II.
GROWTH OF ACICULAR FERRITE
A. Modified Zener–Hillert Model The present work stems from the classical Zener–Hillert model[5,6] which was recently improved by Leach et al.[7] A key quantity in the improved model is the thermodynamic barrier for growth, suggested already by Hillert in 1960[8] and in the later work by Hillert et al. in 2004.[9] We will simply refer to it as ‘‘the barrier for growth’’, denoted as Bm and expressed per mole of metal of formed ferrite, a. All molar quantities in the present work are expressed per mole of metal atom, i.e. they are calculated from the normal molar quantities by dividing with ð1 xC Þ and will be denoted with the subscript m. The barrier will be discussed in later sections. The Zener–Hillert equation was based on two major mathematical approximations which were removed in the improved model. The first one is that the capillarity effect was accounted for by the Gibbs-Thomson equation. The second one is the equation for the driving force. Both these equations are direct consequences
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