Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion

TL;DR

This paper combines analytical calculations and phase-field simulations to study how diffusion in all phases affects lamellar eutectoid growth in steel, revealing differences in growth rates and morphology.

Contribution

It extends Jackson-Hunt analysis to eutectoid transformation by including diffusion in all phases and validates findings with phase-field simulations.

Findings

Growth rates differ when diffusion occurs in all phases.

Diffusion in austenite and ferrite increases transformation kinetics.

Tapered cementite forms due to diffusion effects.

Abstract

We investigate the lamellar growth of pearlite at the expense of austenite during the eutectoid transformation in steel. To begin with, we extend the Jackson-Hunt-type calculation (previously used to analyze eutectic transformation) to eutectoid transformation by accounting for diffusion in all the phases. Our principal finding is that the growth rates in presence of diffusion in all the phases is different as compared to the case when diffusion in growing phases is absent. The difference in the dynamics is described by a factor '{\rho}' which comprises of the ratio of the diffusivities of the bulk and the growing phases, along with the ratios of the slopes of the phase co-existence lines. Thereafter, we perform phase-field simulations, the results of which are in agreement with analytical predictions. The phase-field simulations also reveal that diffusion in austenite as well as ferrite leads to the formation of tapered cementite along with an overall increase in the transformation kinetics as compared to diffusion in austenite (only). Finally, it is worth noting that the aim of present work is not to consider the pearlitic transformation in totality, rather it is to isolate and thereby investigate the influence of diffusivity in the growing phases on the front velocity.