Multi-scale simulation of directional dendrites growth in superalloys

The directional dendrite growth behavior and morphology were simulated based on the cellular automaton-finite difference (CA-FD) considering macro directional solidification (DS) parameters such as withdrawal rate and pouring temperature. Two types of directional dendrite growth models were proposed to realize the multi-scale simulation. A 3D dendrite growth model based on heat transfer and solute diffusion was built to simulate the dendrite growth during a real DS process, which is proved useful for the detail dendrite growth and morphology prediction at a micro 3D scale. A modified shaped function model was proposed to predict the evolution behavior of a large number of dendrites in the entire section of a DS cast sample at a macro scale, based on which the evolution behavior of thousands of dendrites was predicted in the 2D section during the DS process. In these models, the temperature interpolation algorithm and the dendrite orientation mathematical projection were used to transfer information between macro DS process calculation and micro dendrite growth simulation. The corresponding DS experiment was performed to verify the numerical models, and they agreed well. The DS dendritic evolution behavior and detail morphology, especially thousands of dendrites distribution at a large scale, were successfully simulated based on the two models proposed on the condition of a real DS process.