A quantitative phase field model is developed to simulate dendrite morphology and solute distributions of the Al–4 wt-% Cu alloy in Gas Tungsten Arc Welding (GTAW) welding molten pool under transient conditions. The functions of temperature gradient and travel velocity are used to obtain transient conditions of the welding molten pool. Time evolutions of the dendrite morphology, solute distributions of different positions and interfaces are obtained. The dendrite growth process can be divided into four stages, namely linear growth, non-linear growth, competitive growth and short-term steady growth. The solute concentration near the primary dendrite tip region is the smallest, while solute concentration is larger in the front of plane crystals growth interface and the solute concentration in the liquid region among the primary dendrites is obviously the largest, where the solute segregation forms readily. For the given welding parameters, the dendrite morphology and the initial instability of solid/liquid interface agree well with the experimental result.
DavidS. A., BabuS. S. and VitekJ. M.: ‘Welding solidification and microstructure’, JOM-US, 2003, 55, 14–20. doi: 10.1007/s11837-003-0134-7
2.
ZhanX. H., DongZ. B., WeiY. H. and MaR. J.: ‘Simulation of grain morphologies and competitive growth in weld pool of Ni–Cr alloy’, J. Cryst. Growth, 2009, 311, 4778–4783. doi: 10.1016/j.jcrysgro.2009.09.008
3.
SongK. J., WeiY. H., DongZ. B., ZhanX. H., ZhengW. J. and FangK.: ‘Numerical simulation of β to α phase transformation in heat affected zone during welding of TA15 alloy’, Comp. Mater. Sci., 2013, 72, 93–100. doi: 10.1016/j.commatsci.2013.01.006
4.
KosekiT., InoueH., FukudaY. and NogamiA.: ‘Numerical simulation of equiaxed grain formation in weld solidification’, Sci. Technol. Adv. Mater., 2003, 4, 183–195. doi: 10.1016/S1468-6996(03)00026-3
5.
RibicB., RaiR. and DebRoyT.: ‘Numerical simulation of heat transfer and fluid flow in GTA/Laser hybrid welding’, Sci. Technol. Weld. Join., 2008, 13, 683–693. doi: 10.1179/136217108X356782
6.
KimC., KangM. and KangN.: ‘Solidification crack and morphology for laser weave welding of Al 5J32 alloy’, Sci. Technol. Weld. Join., 2013, 18, 57–61. doi: 10.1179/1362171812Y.0000000073
7.
KobayashiR.: ‘Modeling and numerical simulations of dendritic crystal growth’, Physica D, 1993, 63, 410–423. doi: 10.1016/0167-2789(93)90120-P
8.
KarmaA. and RappelW.: ‘Quantitative phase-field modeling of dendritic growth in two and three dimensions’, Phys. Rev. E, 1998, 57, 4323–4349. doi: 10.1103/PhysRevE.57.4323
9.
BoettingerW. J., WarrenJ. A., BeckermannC. and KarmaA.: ‘Phase-filed simulation of solidification 1’, Annu. Rev. Mater. Res., 2002, 32, 163–194. doi: 10.1146/annurev.matsci.32.101901.155803
10.
KimS. G., KimW. T. and SuzukiT.: ‘Phase-field model for binary alloys’, Phys. Rev. E, 1999, 60, 7186–7197. doi: 10.1103/PhysRevE.60.7186
11.
FukumotoS., OikawaY., TsugeS. and NomotoS.: ‘Prediction of s phase formation in Fe – Cr – Ni – Mo – N alloys’, ISIJ Int., 2010, 50, 445–449. doi: 10.2355/isijinternational.50.445
12.
PlanasG. and BoldriniJ. L.: ‘A bidimensional phase-field model with convection for change phase of an alloy’, J. Math. Anal. Appl., 2005, 303, 669–687. doi: 10.1016/j.jmaa.2004.08.068
13.
DongZ. B., ZhengW. J., WeiY. H. and SongK. J.: ‘Dynamic evolution of initial instability during non-steady-state growth’, Phys. Rev. E, 2014, 89, 062403-1–062403-8. doi: 10.1103/PhysRevE.89.062403
14.
FarzadiA., Do-QuangM., SerajzadehS., KokabiA. H. and AmbergG.: ‘Phase-field simulation of weld solidification microstructure in an Al–Cu alloy’, Model. Simul. Mater. Sci., 2008, 16, 1932–1936. doi: 10.1088/0965-0393/16/6/065005
15.
ZhengW. J., DongZ. B., WeiY. H. and SongK. J.: ‘Onset of the initial instability during the solidification of welding pool of aluminum alloy under transient conditions’, J. Cryst. Growth, 2014, 402, 203–209. doi: 10.1016/j.jcrysgro.2014.05.025
16.
WeiY. H., ZhanX. H., DongZ. B. and YuL.: ‘Numerical simulation of columnar dendritic grain growth during weld solidification process’, Sci. Technol. Weld. Join., 2007, 12, 138–146. doi: 10.1179/174329307X164427
17.
XieY., DongH., LiuJ., DavidchackR., DantzigJ., DugganG., TongdM. and BrowneD.: ‘A multi-scale approach to simulate solidification structure evolution and solute segregation in a weld pool’, J. Algorithm Comput. Technol., 2013, 7, 489–508. doi: 10.1260/1748-3018.7.4.489
18.
EchebarriaB., FolchR., KarmaA. and PlappM.: ‘Quantitative phase-field model of alloy solidification’, Phys. Rev. E, 2004, 70, 691–738. doi: 10.1103/PhysRevE.70.061604
19.
ZhengW. J., DongZ. B., WeiY. H., SongK. J., GuoJ. L. and WangY.: ‘Phase field investigation of dendrite growth in the welding pool of aluminum alloy 2A14 under transient conditions’, Comp. Mater. Sci., 2014, 82, 525–530. doi: 10.1016/j.commatsci.2013.08.022
20.
AmoorezaeiM., GurevichS. and ProvatasN.: ‘Spacing characterization in Al–Cu alloys directionally solidified under transient growth conditions’, Acta Mater., 2010, 58, 6115–6124. doi: 10.1016/j.actamat.2010.07.029
21.
WangZ. J., LiJ. J., WangJ. C. and ZhouY. H.: ‘Phase field modeling the selection mechanism of primary dendritic spacing in directional solidification’, Acta Mater., 2012, 60, 1957–1964. doi: 10.1016/j.actamat.2011.12.029
22.
LosertW., ShiB. Q., CumminsH. Z. and WarrenJ. A.: ‘Spatial period-doubling instability of dendritic arrays in directional solidification’, Phys. Rev. Lett., 1996, 77, 889–891. doi: 10.1103/PhysRevLett.77.889
