A generalized mechanical blocking criterion for the columnar-to-equiaxed transition during additive manufacturing

We present a fully general model for the columnar-to-equiaxed transition (CET) that extends the classical mechanical blocking models to completely arbitrary nucleation-undercooling distributions and dendrite growth laws. The general approach is compared to the classical models for a recently reported die steel developed for additive manufacturing (AM). Notably, the models employ a completely pre-characterized and physically motivated set of material parameters, i.e., the kinetic coefficients and nucleation parameters. A method of calculating the nucleation parameters using CALPHAD (CALculation of PHAse Diagrams) software is also demonstrated and discussed. The general model can directly utilize this full distribution of nucleation parameters, as well as the full dendrite growth law obtained from a CALPHAD-coupled model that incorporates non-equilibrium kinetic effects in multicomponent alloys. Finally, a morphology selection map is constructed for the printable die steel to predict regions of equiaxed dendritic, columnar dendritic, and plane-front solidification, showing that the general model of the CET provides higher fidelity in predicting regions of columnar and equiaxed solidification, and that tailoring the inoculant particle-size distribution is a viable method of controlling the CET under AM processing conditions. • CET model generalized to arbitrary dendrite growth laws and undercooling distribution. • CALPHAD model is calibrated to estimate nucleation parameters for in-situ inoculation. • CET calculations using as-measured parameters agree qualitatively with experiment.