Influence of the Crystal Orientation of Epitaxial Solidification on the Linear Instability Dynamic during the Solidification of Welding Pool

To study the influence of the crystal orientation of epitaxial solidification on the linear instability dynamic, coupled equations are conducted to present the transient conditions of crystal growth near the fusion line of the welding pool. A quantitative phase field model is used to simulate the epitaxial solidification with different crystal orientations. Moreover, a linear instability dynamic analytical model is presented to describe the variation of the onset of the initial planar instability with surface tension anisotropy. The initial average wavelengths obtained by the phase field model and the analytical model are in good agreement with that in experiment result. The epitaxial solidification results show that the greater the angle between the crystal orientation and the temperature gradient, the better the stability of the interface, and the larger the critical time of onset of initial planar instability. Due to the transient of the growth conditions in welding pool and the randomness of the amplification mechanism, it could not show up the law that the greater the crystal orientation angle, the larger the initial average wavelength. Thus, the initial average wavelength of planar instability is seemly independent of the crystal orientation of epitaxial solidification.