Temperature filed numerical simulation of Laser Welding for TA15 Titanium Alloy by coupling thermal and phase transformation

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1 1 8 th Internatonal Conference on Physcal and Numercal Smulaton of Materals Processng, ICPNS 16 Seattle Marrott Waterfront, Seattle, Washngton, USA, October 14-17, 2016 Temperature fled numercal smulaton of Laser Weldng for TA15 Ttanum Alloy by couplng thermal and phase transformaton Wenmn. Ou 1, Yanhong. We 1, Gaoyang. M 2 and Xaohong. Zhan 1 1 College of Materal Scence and Technology Nanjng Unversty of Aeronautcs and Astronautcs, Nanjng , Chna 2 State Key Laboratory of Materals Processng and Mould & Des Technology, Huazhong Unversty of Scence and Technology, Wuhan , Chna ( 1 E-mal:yhwe@nuaa.edu.cn 2 E-mal:hustmgaoyang@163.com) ABSTRACT The phase volume fracton and temperature thermal cycle are nfluencng factors for the mechncal propertes of welded jonts. A Fnte Elementary model and the correspondng solver s developed to smulate the temperature feld consderng the effect of coupled temperature and phase transformaton for TA15 laser weldng. The phase transformaton model s mproved on the bass of JMAK equaton. Furthermore the lnear nterpolaton method s employed to study the materal propertes n dfferent temperature. It s found that the peak temperature of the weld thermal cycle s about 2200 whle t reduced to about 2000 when usng coupled temperature and phase transformaton model for the weldng process. Keywords: Numercal smulaton, Temperature fled, phase transformaton, TA15 Ttanum, Laser Weldng 1. INTRODUCTION T-6Al-2Zr-1Mo-1V ttanum alloy (TA15) s wdely used n aerospace ndustry, and heat transfer phenomenon s major focused for ts weldng technology researches. The reason may be that heat transfer s specal n weldng because of the nteracton between materal and heat source, resultng n that temperature feld s dffcult to predct precsely. The relatonshp of ntegrated weldng modelng methodology proposed by Krkaldy (Krkaldy, 1991) s shown n Fg.1. For the lmt knowledge of us, ths model s dealsm. However some parts of the model can be developed and combned by the effort of many academc researches. In temperature feld modelng, famous Fourer heat transfer law s wdely appled (Deng & Murakawa, 2006, 2008). The nterestng work manly s how to consder the weldng heat source, snce the character of weldng s such dfferent. The poneerng work from D Rosonthal (Rosenthal, 1941) who put forward the analytc movement pont heat source model. Then V. Pavelc (Pavelc, 1969) proposed famous gauss heat source model wth Gaussan flux dstrbuton. It was a surface heat source and was dffculty employed n molten pool. The famous body heat source, double ellpsod heat source model, s proposed by Goldak (JOHN GOLDAK, 1984). The model s wdely appled n arc weldng now. For laser weldng, whch has a nal heads morphology, t was not as applcable. In order to smulate the character of laser weldng, Lankalapall (Lankalapall, 1996) developed a cone heat source model and Wu S (Wu, 2004) proposed a Rotatng gauss body heat source model. These models were further mproved for the complex physcal phenomena n laser weldng and then the combned heat source models were often used. Xu G.X and Wu C.S et al. (Xu, 2008a, 2008b, 2009) proposed four combned heat source models ncludng gauss and cone combned heat source model. Meanwhle, the transformaton knetcs n the weldng thermal cycles were contnuously studed. Phase volume fracton s functon of coordnate and tme. The poneerng research may be the Johnson-Mehl- Avram-Kolmogorov (JMAK) equaton (Avram, 1939, 1940, 1941) whch was obtaned n sothermal

2 2 condton. Based on JMAK equaton, TC4 ttanum phase transformaton knetcs of the weldng process was studed by Elmer and Palmer et al (Elmer, 2004). The phase transformaton dffuson actvaton energy was determned by growth - control mechansm and the Avrn ndex was determned by the dffuson - control mechansm. Malnov et al. (Malnov, 2003; S. Malnov, Novoselova, & Sha, 2004; S. Malnov, 2001) conducted systematcally researches for phase transformaton smulatons of many ttanum such as T-6Al-4V, T-8Al-1Mo-1V and T-10V-2Fe-3Al durng sothermal phase change process. The β to α phase transformaton model was developed and verfed by resstvty and dfferental scannng calormeter (DSC) experments. TC4 ttanum phase transformaton model n TIG weldng was proposed by GaoyangM (M, We, Zhan, Gu, & Yu, 2014), whch ft the nonsothermal process well. In ths paper the coupled thermal-phase transformaton FE model s further mproved to quanttatvely nvestgate the nfluence of phase transformaton on temperature felds durng laser weldng of TA15. The dfference temperature felds and phase transformaton s analyzed. Fgure 1 Overvew of ntegrated weldng modelng methodology proposed by Krkald. 2. Model theory 2.1 Geometry Model The plate n the model s 10cmⅹ5cmⅹ0.6cm, and the mesh s shown n Fg.2. The unt element s 0.25 ⅹ 0.25 ⅹ 0.2, the fnal node number s 3444 and element number s Fgure 2 Geometry model wth mesh result 2.2 Materal Model TA15 ttanum alloy s approxmate α ttanum, whch s chosen as base metal. Temperature feld smulaton s related to materal physcal propertes whch are thermal conductvty, specfc and densty lst n table 1. Table 1 Materal physcal propertes of TA15 ttanum. Temperature ( ) Thermal conductvty (W/(cm. )) Specfc (J/(g. )) Densty (g/cm 3 ) The materal physcal propertes are dffcult to obtan n hgh temperature. Therefore lnear nterpolaton approach s used to calculate the propertes n hgh temperature. Frstly, the slope can be calculated n formula (1). X ( F F ) / ( T T ) (1) k 1 1 X k s the slope, F s the th propertes, T s the th temperature. Then the ntercept s calculated n formula (2). B F T X (2) 1 1 k B s the ntercept. Other materal physcal propertes can be fnally obtaned n formula (3). C TX k B (3) C s the fnal propertes. The propertes wll be changed by thermal-phase transformaton coupled model. The lnear nterpolaton results are shown n Fg.3.

3 3 z -- The Z coordnates of body re -- The radus of top surface r -- The radus of body Fgure 3 Materal propertes wth lnear nterpolaton. 2.3 Heat Source Model The combned models of Gauss surface and Cone body model are employed to smulate the nal-head shape of laser weldng. The coordnate system of heat source model s shown n Fg.4. r0 -- The radus of dfferent surface n body 2.4 Phase Transformaton Model The startng temperature of β to α can be determned as 850 centgrade degree and fnshng temperature s 750 centgrade degree durng coolng process, whle n heatng process the phase transformaton s α to β. These parameters can be obtaned from the approxmate CCT dagram of TA15 n Fg. 5 whch was drew by Kujng Song et al. (Song et al., 2015; Song et al., 2013). Fgure 4 Combned heat source model of Gauss surface and Cone body. For the surface: S 2 3.0m 3r exp( ) (4) 2 2 Mr Mr For the cone body: V Pe 1 3r exp( ) ( e 1) ( z z )( r r r r ) r Where: e e e 0 S -- The heat of surface Mr -- The radus of Gauss surface V -- The heat of body -- The effectve of laser weldng ze -- The Z coordnates of top surface (5) Fgure 5 CCT dagram of TA15 Based on the CCT dagram, then the JMAK model s employed to calculate the phase transformaton fracton. n f 1exp( bt ) (6) Where f s sothermal phase transformaton fracton, b s constant of temperature and n s constant of crystallzaton nucleaton. However, ths f equaton fts to sothermal phase transformaton. For the weldng, non-sothermal process, the JMAK model s modfed by Elmer (Elmer, Palmer, Zhang, Wood, & DebRoy, 2003) shown n formula (7). f( t ) 1 exp{ [ k0 exp( ) ( t )] n } (7) F RT Where parameters k 0, and n are three knetc constants whch can be assumed to be ndependent of temperature. R s the unversal gas constant. F s the equlbrum volume fracton of the product phase

4 4 at th tme step and s complex functon whch s shown n formula (8). f( t ) F k0 exp( ) RT n 1 ln[1 ] (8) As n formula (8) s used to calculate the C-Mn steel, t was modfed by Malnov (S. Malnov, 2001) to ft ttanum knetc theory, whch s shown n formula (9). ln[1 f( t )] n 1 (9) k Therefore the Malnov s s also used n ths paper. Addtonally, the base metal phase composton s mportant for TA15 ttanum, by ntroducng base metal phase composton to Elmer s model, the fnal phase transformaton s presented as formula (10). n f ( t) {1 exp[ ( k0 exp( ) ( t )) ]} F y m(10) RT Where y m s the base metal phase composton and the default s 1.0 for TA15 ttanum, t s modfed as Thermal-phase transformaton coupled Model As so far, the temperature and the phase transformaton can be calculated. We now can change the materal model wth thermal-phase transformaton coupled model nstead of lnear nterpolaton. The model s used mxture rule as shown below. C TP = ycc (11) T Where the y c s the th teraton step phase volume fracton, whch s obtaned from phase transformaton model, C s the materal propertes. 2.6 FEM of Temperature feld Fourer heat conducton dfferental equaton s used to smulate the temperature feld and FEM s employed to solve t. The formula (12) s organzed n matrx form. T T T T [ k X ] [ k Y ] [ k Z ] G C P (12) X X Y Y Z Z t Where K s the thermal conductvty, Cp s specfc heat and s densty. G s nternal heat source whch s zero n our model. It may have to cast nto form as formula (13). T [ C]{ } [ K]{ T} { f } (13) t Where [ C] NN jcpd N N j N N j N N j [ K1] [ k X ky kz ] d x t Y t Z t [ K ] hn N d 2 q 1 2 j q [ K] [ K ] [ K ] { f } N Gd qn d ht N d q a q q q Where N and Nj are shape functon of element and j, h s the heat transfer coeffcent, Ta s the room temperature and q s the boundary heat flux. 2.7 Weldng Parameters The mportant weldng parameters whch nfluence temperature felds of laser weldng are weldng velocty, laser power and defocusng value. The weldng parameters are shown n table 2. Table 2 Weldng parameters of TA15 laser weldng Weldng Velocty (m/mn) Laser Power (W) defocusng value (mm) Results and dscusson 3.1 Temperature Feld The smulated results of laser weldng process are shown n Fg. 6. Owng to the combned heat source model, the concentrated laser beam can be observed lke a nal-head. At tme 5s and 10s, the peak temperature s about 2200 centgrade degree. Snce the fuson pont of TA15 ttanum s about 1600 centgrade degree, whch s far lower than the peak temperature, the deep penetraton s formed n molten pool.

5 5 t=1s t=5s t=10s Fgure 6 Temperature feld of dfferent tme durng laser weldng The weld bead morphology s further proofread wth the experment, whch s shown n Fg.7. The nflecton pont poston of nal-head s lower than experment as shown n Fg.7.c (pont A and B). The major error may be caused by overlookng weld resdual hgh n model. (a) n Fg.9. They are begnnng area, stable area and termnal area respectvely. At begnnng and at the end, phase transformaton s not stable, whle between them, the stable phase transformaton was formed. (a) Fgure 9 Dfferent areas of phase transformaton zone At the coolng process of laser weldng, the correspondng β to α phase transformaton s shown n Fg.10. It just lke α to β, the max phase transformaton s stll not 100% but 95%. Ths may be the character of TA15 ttanum phase transformaton. (c) Fgure 7 Comparng weld bead between modelng and experment 3.2 Phase Transformaton Volume Fracton The phase transformaton volume fracton of heat process durng laser weldng s shown n Fg.8. It s noted that the ntal β s 5% not 0% because TA15 ttanum s approxmate α alloy. The heat affect zone (HAZ) can be estmated based on the volume fracton dstrbuton n Fg.8. At tme 10s, the volume fracton s 95% near weld bead as shown n Fg.8.(c). However t exsts a narrow zone wth observng n Fg.8.(d). Obvously t s HAZ, and the phase volume fracton changes from 0.35 to HAZ s lmted nto a mesh element, and then ts sze was estmated smaller than 0.25cm. (a) (a) (c) t=1s t=5s t=10s Fgure 10 Phase transformaton of dfferent tme durng coolng process 3.3 Interacton between Temperature and phase transformaton The thermal cycles along penetraton drecton are exacted, whch s shown n Fg.11. It llustrates the gradent s very large n laser weldng. It could be found that the deep penetraton s formed and the peak temperature of Z drecton wth small dstncton. Then the coolng stage s able to be observed. Ths coolng stage llustrates at the temperature durng 750 centgrade degree to 850 centgrade degree, the phase transformaton behavor has effect on the temperature value, as the thermal-phase transformaton coupled model s adopted. (c) t=1s (d) t=5s (d) t=10s Fgure 8 Phase transformaton of dfferent tme durng heatng process If the phase transformaton zone s taken along X, then three dfferent areas can be observed as shown Fgure 11 Thermal cycle of dfferent ponts along penetraton drecton

6 6 The smulated results wth coupled thermal-phase transformaton model are compared wth uncoupled model shown n Fg.12. Frstly, the dfference occurs at peak temperature. The temperature wth the coupled model s about 2000 centgrade degree whle the temperature wth the uncoupled one s about 2200 centgrade degree. Accordng to the expermental results, the coupled model s more accurate than uncoupled one. The gradent of heatng process s smlar between two models, whle t s dfferent n coolng process. The temperature n the uncoupled model s a lttle hgher than the one n the coupled model. The more essental reason may be that the crystal of dfferent phase determnes the dfferent materal propertes. It s shown n Fg.14 (Leyens, 2003). The α phase s wth HCP, whle the β phase s wth BCC. If the volume fracton s dfferent of these structures materal propertes change. However, the mcrostructure s too complex to solve wth the model n the paper now. Fgure 14 Crystal structure of α and β phase Fgure 12 Comparng thermal cycle between coupled and uncoupled model As we know, the coupled model changes materal thermal propertes. It rases the propertes n phase transformaton as shown n Fg.13. Accordng the FEM formula (12), {T} can be solved as formula (13) T [ C]{ } [ K]{ T} { f } t In formula (13), f the other parameters are taken as constant, then wth the materal propertes rsng up, the temperature s slowng down. Ths s why the temperature of coupled model s smaller than uncoupled model. 4. Conclusons A coupled thermal-phase transformaton model s developed to predct the temperature feld and volume fracton of TA15 ttanum durng laser weldng. The conclusons are concluded as three objects. (1) The peak temperature was 2000 centgrade degree n coupled model whle 2200 centgrade degree n uncoupled model, whch drops down a lttle n coupled model compared wth uncoupled one. (2) The phase transformaton of α to β s smulated durng heatng process. The ntal phase volume fracton of α s 0.95 and the change ranges are from 0.35 to 0.95 n HAZ. The correspondng model fts n coolng process. (3)The materal thermal propertes are modfed by coupled mode nstead of lnear nterpolaton. It could be found that materal thermal propertes rsng up n coupled model compared wth the uncoupled one. Fgure 13 Materal propertes n phase transformaton zones and lnear nterpolaton ACKNOWLDEGEMENT The authors gratefully acknowledge a Project Funded by the Prorty Academc Program Development of Jangsu Hgher Educaton Insttutons (PAPD) and the fnancal support of the project from the Fundamental Research Funds for the Central Unverstes NP and Natonal Natural Scence Foundaton of Chna (Grant no ).

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