Numerical modeling of solidification and subsequent transformation of Fe-Cr-Ni alloys

A computational method for the analysis of phase transformation involving solidification was developed with the assumption of thermodynamic equilibria at interfaces. The region of interest was divided into finite segments, and solute diffusion across the segments was computed by the use of the direct finite difference method (FDM). Simultaneously, thermodynamic equilibrium at each interface was updated at every step of the diffusion analysis to determine the location of the interfaces. The temperature decrease and the increment of fraction solid were calculated based on thermal balance, including a heat extraction condition. Solid state transformation from δ to γ phase within each FDM segment was modeled by the use of a Clyne-Kurz (C-K) type analysis with assumptions of complete mixing of solutes in theδ phase and limited back diffusion in theγ phase. The calculation results were compared with welding solidification experiments in the iron-chromium-nickel ternary system. Good agreement was obtained with respect to solute distribution and residual fraction ofδ phase over different compositions and solidification modes of the alloys used.