A mathematical model is proposed to investigate the evolution of microstructures due to rapid solidification in laser materials processing. The instability of solid-liquid interface is analyzed by considering the diffusion process and perturbation method. The results of this model show that the neutral stability curve is largely dependent on solidification rate and partition coefficient. The decay, periodic oscillation and growth of the perturbations at the solid-liquid interface can be regarded as planar, cellular and dendritic microstructures respectively. Laser spot welding experiments were conducted for stainless steel AISI 304 to verify the theoretical predictions.
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