Concurrent γ-Phase Nucleation as a Possible Mechanism of δ-γ Massive-like Phase Transformation in Carbon Steel: Numerical Analysis Based on Effective Interface Energy

Effective interface energies of various homo- and hetero-interfaces of iron were calculated with an aid of phase-field modeling, taking into account geometric constraints by competition among grains or interfaces. Calculated effective interface energies for delta/gamma, delta/delta and gamma/gamma interfaces are 0.56, 0.44 and 0.37 J/m(2), respectively. Using two simple geometric models for nucleation on or off an interface in the matrix, the optimal shape of a nucleus at a given radius and undercooling, a critical radius and an energy barrier for nucleation for each possible circumstance were numerically calculated. It is found that, although the energy barrier for gamma-phase nucleation in homogeneous delta-phase matrix is more than three orders of magnitude greater than that for homogeneous solidification of delta-phase, the gamma nucleation on a delta/delta grain boundary in the solidifying matrix suppresses the energy barrier, increasing a nucleation rate. Furthermore, it is found that the gamma-phase nucleation on an existing gamma nucleus halves undercooling needed with smaller critical radius. This suggests that, once gamma nucleation is initiated, then following gamma nucleation is promoted by doubled driving force, enabling multiple gamma nucleation as in chain reaction. These findings are sufficient to explain experimentally observed phenomena during the delta-gamma massive-like phase transformation even if other factors such as solute re-distribution or transformation is neglected.