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

doi:10.3901/JME.2018.02.062

Abstract

Abstract: 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.

Key words: crystal orientation, epitaxial solidification, linear instability, phase field, solidification of welding pool

CLC Number:

TG156

ZHENG Wenjian, HE Yanming, YANG Jianguo, DONG Zhibo. Influence of the Crystal Orientation of Epitaxial Solidification on the Linear Instability Dynamic during the Solidification of Welding Pool[J]. Journal of Mechanical Engineering, 2018, 54(2): 62-69.

References

[1] CHEN S,GUILLEMOT G,GANDIN C-A. Three-dimensional cellular automaton-finite element modeling of solidification grain structures for arc-welding processes[J]. Acta Materialia,2016,115:448-467.
[2] 陈飞,崔振山,董定乾. 微观组织演变元胞自动机模拟研究进展[J]. 机械工程学报,2015,51(4):30-39. CHEN Fei,CUI Zhenshan,DONG Dingqian. Research progress in cellular automaton simulation of microstructure evolution[J]. Journal of Mechanical Engineering,2015,51(4):30-39.
[3] WEI H L,ELMER J W,DEBROY T. Origin of grain orientation during solidification of an aluminum alloy[J]. Acta Materialia,2016,115:123-131.
[4] ZHENG W J,DONG Z B,WEI Y H,et al. Phase field investigation of dendrite growth in the welding pool of aluminum alloy 2A14 under transient conditions[J]. Computational Materials Science,2014,82:525-530.
[5] TAN W,BAILEY N S,SHIN Y C. Numerical modeling of transport phenomena and dendritic growth in laser spot conduction welding of 304 stainless steel[J]. Journal of Manufacturing Science and Engineering,2012,134(4):041010.
[6] WEI H L,ELMER J W,DEBROY T. Origin of grain orientation during solidification of an aluminum alloy[J]. Acta Materialia,2016,115:123-31.
[7] WEI H L,ELMER J W,DEBROY T. Three-dimensional modeling of grain structure evolution during welding of an aluminum alloy[J]. Acta Materialia,2017,126:413-425.
[8] HAN R,LI Y,LU S. Macro-micro modeling and simulation for the morphological evolution of the solidification structures in the entire weld[J]. International Journal of Heat and Mass Transfer,2017,106:1345-1355.
[9] FARZADI A,DO-QUANG M,SERAJZADEH S,et al. Phase-field simulation of weld solidification microstructure in an Al-Cu alloy[J]. Modelling and Simulation in Materials Science and Engineering,2008,16(6):065005.
[10] FALLAH V,AMOOREZAEI M,PROVATAS N,et al. Phase-field simulation of solidification morphology in laser powder deposition of Ti-Nb alloys[J]. Acta Materialia,2012,60(4):1633-1646.
[11] WANG D,KADOI K,SHINOZAKI K. Prediction of residual liquid distribution of austenitic stainless steel during laser beam welding using multi-phase field modeling[J]. ISIJ International,2017,57(1):139-147.
[12] ZHENG W,DONG Z,WEI Y,et al. Onset of the initial instability during the solidification of welding pool of aluminum alloy under transient conditions[J]. Journal of Crystal Growth,2014,402:203-209.
[13] MULLINS W W,SEKERKA R F. Stability of a planar interface during solidification of a dilute binary alloy[J]. Journal of Applied Physics,1964,35(2):444-451.
[14] 黄卫东,周尧和. 定向凝固的界面形态转变[J]. 金属学报,1991,27(2):86-91. HUANG Weidong,ZHOU Yaohe. Interface morphology transitions during directional solidification in a transparent model alloy[J]. Acta Metallurgica Sinica,1991,27(2):86-91.
[15] WARREN J,LANGER J. Prediction of dendritic spacings in a directional-solidification experiment[J]. Physical Review E,1993,47(4):2702-2712.
[16] LOSERT W,SHI B Q,CUMMINS H Z. Evolution of dendritic patterns during alloy solidification:Onset of the initial instability[J]. Proceedings of the National Academy of Sciences of the United States of America,1998,95(2):431-438.
[17] 林鑫,李涛,王琳琳,等. 单相合金凝固过程时间相关的界面稳定性(I)[J]. 物理学报,2004,11(53):3971-3977. LIN Xin,LI Tao,WANG Linlin,et al. Time-dependent interface stability during directional solidification of a single phase alloy(I)[J]. Acta Metallurgica Sinica,2004,11(53):3971-3977.
[18] WANG Z,WANG J,YANG G. Fourier synthesis predicting onset of the initial instability during directional solidification[J]. Applied Physics Letters,2009,94(6):061920.
[19] CHEN Y,BOGNO A A,XIAO N M,et al. Quantitatively comparing phase-field modeling with direct real time observation by synchrotron X-ray radiography of the initial transient during directional solidification of an Al-Cu alloy[J]. Acta Materialia,2012,60(1):199-207.
[20] DONG Z,ZHENG W,WEI Y,et al. Dynamic evolution of initial instability during non-steady-state growth[J]. Physical Review E,2014,89:062403.
[21] WANG L,WEI Y,ZHAN X,et al. Simulation of dendrite growth in the laser welding pool of aluminum alloy 2024 under transient conditions[J]. Journal of Materials Processing Technology,2017,246:22-29.
[22] WANG Z J,WANG J C,YANG G C. Onset of initial planar instability with surface-tension anisotropy during directional solidification[J]. Physical Review E,2009,80:052603
[23] FORNARO O,PALACIO H A. Planar front instabilities during directional solidification of hcp:Zn-Cd dilute alloys[J]. Scripta Materialia,2006,54:2149-2153.
[24] 王理林,王贤斌,王红艳,等. 晶体取向对定向凝固平界面失稳行为的影响[J]. 物理学报,2012,61(14):148104. WANG Lilin,WANG Xianbin,WANG Hongyan,et al. Effect of crystallographic orientation on instability behavior of planar interface in directional solidification[J]. Acta Metallurgica Sinica,2012,61(14):148104.
[25] 刘会杰. 焊接冶金与焊接性[M]. 北京:机械工业出版社,2002. LIU Huijie. Welding metallurgy and weldability[M]. Beijing:China Machine Press,2002.
[26] KARMA A. Phase-field formulation for quantitative modeling of alloy solidification[J]. Physical Review Letters,2001,87(11):115701.
[27] ECHEBARRIA B,KARMA A,PLAPP M. Quantitative phase-field model of alloy solidification[J]. Physical Review E,2004,70(6):061604.
[28] WANG Z,LI J,WANG J,et al. Phase field modeling the selection mechanism of primary dendritic spacing in directional solidification[J]. Acta Materialia,2012,60(5):1957-1964.
[29] 陈轩,卢庆华,张静,等. 高频微振条件下激光焊接组织研究[J]. 机械工程学报,2016,52(20):60-65. CHEN Xuan,LU Qinghua,ZHANG Jing,et al. Microstructure characteristic of laser welded joint under high frequency micro-vibration condition[J]. Journal of Mechanical Engineering,2016,52(20):60-65.
[30] 彭必荣,卢庆华,何晓峰,等. 机械振动对激光焊接接头组织的影响[J]. 机械工程学报,2015,51(20):94-100. PENG Birong,LU Qinghua,HE Xiaofeng,et al. Effects of mechanical vibration on microstructure of laser welded joint[J]. Journal of Mechanical Engineering,2015,51(20):94-100.