Phase-field simulation of tilted growth of dendritic arrays during directional solidification

The tilted growth of dendritic arrays during directional solidification of non-axially oriented crystals has been simulated in two-dimensional system by using a quantitative phase-field model. A convergence study with respect to the diffuse interface width has been carried out, showing that the results are reasonably independent of the diffuse interface width for W0/d0⩽11.3. A parametric study is performed to investigate the effects of the primary spacing, the misorientation angle and the pulling velocity on the tip undercooling, the upper limit of primary spacing, and the tilted angle. Results show that the tip undercooling decreases when increasing the primary spacing or decreasing the misorientation angle. It has been found that the upper limit, resulting from tertiary branching, depends on both the solidification condition (the pulling velocity and the thermal gradient) and the preferred crystalline orientation (the misorientation angle) for the tilted growth of dendritic arrays. Previous rotation law, describing the relation between the tilted angle and the Péclet number, is evaluated according to phase-field simulation results. Moreover, the effect of the development of sidebranches on the growth direction selection was discussed. Further studies on the microstructure evolution from the onset of planar instability during directional solidification show that the selection of the steady-state primary spacing is sensitive to the misorientation angle.