Carbon solute drag effect on the growth of carbon supersaturated bainitic ferrite: Modeling and experimental validations

Zongbiao Dai*, Hao Chen, Junjie Sun, Sybrand van der Zwaag, Jun Sun

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


The carbon partitioning and lengthening rate of bainitic ferrite (αb) are excellent experimental parameters to estimate our level of understanding of the mechanism of bainitic transformation from a continuum perspective and our ability to capture it in analytical expressions. For Fe-C alloys and relatively simple steels the classical Zener-Hillert theory captures the bainitic transformation rather well but mispredicts the level of carbon in solution in the bainite and overestimates the lengthening rates for transformations at lower temperatures. To address this issue, this paper presents a new thermo-kinetic model based on the Zener-Hillert theory and the Gibbs energy balance concept to simulate the lengthening behavior of αb in the Fe-C and low alloyed steels. The model incorporates the effect of the temperature dependent carbon diffusion within the migrating interface via a temperature dependent ferrite/austenite interfacial energy and a temperature dependent diffusion coefficient but does not impose local equilibrium across the interface. The good agreement between the model predictions and nine sets of published experiments indicates that both the carbon supersaturation in αb and the slower lengthening rate are caused by carbon diffusion within the migrating interface. It is found that the degree of carbon supersaturation in αb increases significantly with decreasing temperature. Consequently, the enhanced carbon solute drag effect, resulting from carbon diffusion within the interface, strongly retards the lengthening rates of αb at lower temperatures. Transformation strain is shown to have a modest effect on the lengthening rates but to lower the degree of carbon supersaturation.

Original languageEnglish
Article number119791
JournalActa Materialia
Publication statusPublished - 2024

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  • Bainite formation
  • Carbon diffusion
  • Carbon supersaturation
  • Energy dissipation
  • Lengthening kinetics


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