Numerical prediction of the secondary dendrite arm spacing using a phase-field model

Abstract

The secondary arm spacing in Fe-C, Fe-P, Fe-C-P and Al-Cu alloys are numerically predicted using a phase-field model. The calculated arm spacing and the exponent of the local solidification time are compared with the experimental data. Each calculated exponent differs depending on Fe-base or Al-base alloys. The change in the arm spacing and the exponent depending on alloy is systematically examined by the imposing artificial sets of physical properties. Interface energy and solute diffusivity in liquid change the arm spacing but not the exponent. On the other hand, liquidus slope and partition coefficient change both the arm spacing and the exponent. The change of the exponent is discussed by examining the process of deriving the value of 1/3 in the analytical model by Kattamis et al. and the expression for the estimation of the exponent is proposed.