|Title：||Distinctions of dendritic behavior influenced by constant pressure and periodic pressure|
|Author：||Shan Shang1, 2, Zhi-peng Guo3, Zhi-qiang Han4, *Xin-yu Zhang1, 2, **Yi-nuo Cheng5, Jun Li1, 2|
|Address：||1. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China; 2. School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China; 3. Beijing Supreium Co., Ltd., Beijing 100089, China; 4. School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China; 5. Beijing Jingwei Hirain Technologies Co., Inc., Beijing 100191, China|
|Key words：||periodic pressure; sidebranching; amplitude; tip velocity; undercooling; phase field method|
The distinctions of dendritic morphology and sidebranching behavior when solidified under atmosphere pressure, constant pressure which is higher than atmosphere pressure (hereinafter referred to as constant pressure) and periodic pressure were investigated using 3-D phase field method. When growing at atmosphere pressure, side branches (secondary dendritic arms) are irregular. When solidified under constant pressure with a relatively high value, side branches are much more luxuriant, with more developed high-order side branches. When applied with periodic pressure, resonant sidebranching happens, leading to many more regular side branches and the smallest secondary dendritic arm spacing (SDAS) in the three cases. The significant difference in dendritic morphology is associated with tip velocity modulated by total undercooling including pressure and temperature undercooling. In the case of constant pressure, tip velocity increases linearly with total undercooling, and it varies periodically in periodic pressure case. The different variation trend in tip velocity is the reason for the distinct dendrite growth behavior in different cases. Unlike the phenomenon in constant pressure case where the dendrite grows faster with higher pressure, the dendrite grows slower under periodic pressure with higher amplitude, resulting in less developed primary dendrite and side branches. This is influenced by tip remelting due to low undercooling or even negative undercooling. It is revealed that the accelerated velocity of tip remelting increases with the decline of undercooling. The greater the amplitude of periodic pressure, the faster the tip remelting velocity during one period. This is the reason why the average tip velocity decreases with the rise of amplitude of periodic pressure.