Influence of periodic pressure on dendritic morphology and sidebranching

The influence of periodic pressure with low and high frequencies on microstructure and dendritic sidebranching was studied by using 3-D phase field method. In both low and high frequency cases, the variation trend of SDAS (secondary dendritic arm spacing) with increasing pressure frequency is opposite to that of sidebranching frequency, while the variation trend of the average length of secondary arms is consistent with that of sidebranching frequency. The high sidebranching frequency indicates that more secondary arms share the whole driving force of dendrite growth, resulting in lower driving force for each one and leading to less developed secondary arms. The smallest SDAS is obtained when perturbed by the periodic pressure with the frequency of 0.157/τ₀ (τ₀ is the physical unit of time in the dimensionless phase field model) and 2.200/τ₀ in low and high frequency cases, respectively. Comparisons of dendritic morphology and secondary arms are made between the low and high frequency cases. Firstly, in the low frequency case, secondary arms are luxuriant especially when pressure frequency is low, with many high-order side branches stretching out. Secondly, the average length of secondary arms in primary dendrite is longer in the low frequency case than that without pressure, and much longer than that in the high frequency case. Thirdly, the dendrite tip without side branches in the high frequency case is much longer than that in the low frequency case. All of the differences in dendritic morphology and sidebranching in the two cases can be attributed to the different modulation mechanism. In the low frequency case, periodic pressure determines tip velocity and then modulates sidebranching directly. While in the high frequency case, periodic pressure cannot determine sidebranching directly, but via modulating tiny protuberances in dendrite tip, part of which evolves into side branch. In this case, the tiny protuberances take part of the whole driving force, leading to less developed secondary arms.