OBTAINING TEMPERATURE FIELDS AS A FUNCTION OF EFFICIENCY IN TIG WELDING BY NUMERICAL MODELING

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1 OBAINING EMPERAURE FIELDS AS A FUNCION OF EFFICIENCY IN IG WELDING BY NUMERICAL MODELING P. B. Guimaães a,b, P. M. A. Pedosa b, Y. P. Yadava b, A. V. Siqueia Filho b, J. M. A. Babosa b, and R. A. S. Feeia b a Instituto Fedeal de Penambuco Depatamento de Mecânica Cidade Univesitáia CEP , Recie, Penambuco, Basil pabloguimaaes@ecie.ipe.edu.b b Univesidade Fedeal de Penambuco Depatamento de Engenhaia Mecânica Cidade Univesitáia CEP , Recie, Penambuco, Basil as@upe.b ABSRAC he tempeatue ield seves as the basis o pedicting levels o esidual stess in a welded joint. he aspects elated to the mathematical modeling o complex welding pocedues wee pondeed with the FEM: vaiations in the physical and mechanical popeties o the mateials as a unction o the tempeatue, the tansience and the speed o the welding pocess, the mateial phase tansomations, the dieent mechanisms o heat exchange with the envionment (convection and adiation), all them associated with a high level o nonlineaity. he heat souce used in this analytical model o heat supply was the double ellipsoid model poposed by Goldak (005), in which a 60 mm x 50 mm and 3 mm ectangula ASM AH36 steel plate was used o the IG pocess simulations. It was made a compaison o tempeatue ields o thee dieent values o pocess eiciency (60%, 70% and 80%). he esults showed many dieences in the tempeatue ields ollowing changes in the levels o esidual stesses which will be detemined in uthe studies. Keywods: empeatue Field, Residual Stess, IG Welding. NOMENCLAURE a a length o the weld pool beoe the toch, m length o the weld pool ate the toch, m b semi-width o the weld pool, m c depth o usion zone, m c p speciic heat at constant pessue, J/kg.ºC depatments o enegy beoe the toch depatments o enegy ate the toch h convective heat tanse coeicient, W.m /ºC h p thickness o the plate, m K themal conductivity, W.m/ºC K 0 modiied Bessel unction I electical cuent, A U voltage, V 0 initial tempeatue, ºC tempeatue, ºC ν welding speed, m/s Geek symbols α themal diusivity, m /s ε emissivity σ Stean-Boltzmann s constant, W.m -.ºC -4 INRODUCION he IG (ungsten Inet Gas) welding technique begins with the ceation and maintainance o the electic ac between a non-consumable tungsten electode and a base metal (Modenesi et al., 006; Gonçalves et al., 006). his welding pocess was ist developed by the aeonautical industy duing the Wold Wa II to make easie the weld pocess o light mateials such as aluminum and magnesium. Ate the impovement, IG became a pocess o high quality and elatively high cost used in vaious applications (Maques et al., 007). In this study, the tempeatue ields wee numeically developed consideing thee dieent levels o electical cuent in ode to obtain the esidual stesses o a welded joint subsequently. his numeical model is based on the coupling o dieent physical phenomena in themal, mechanical and metallugical natues, always pesent in a welding opeation. In the 4 th decade o the twentieth centuy, an analytical method was poposed by Rosenthal (1941) to solve the themal poblem, taking into consideation a concentated heat souce (punctual o linea). Fo the analytical solutions Rosenthal poposed the ollowing simpliying assumptions (Ramanzini et al., 006 and Goyal et al., 009): he heat souce (punctual, linea) moving at a constant speed along a plate; the physical popeties o the medium (pat) ae constant; heat loss though the suace (convection) ae negligible; welding is long enough to each the quasi-steady state (constant tempeatue distibution to the obseve placed at the heat souce) and the phase tansomations ae negligible. Fo the modeling o thin plates, the 50 Engenhaia émica (hemal Engineeing), Vol. 10 No June and Decembe 011 p

2 Guimaães et al. Obtaining empeatue Fields as a tempeatue distibution is constant o the obseve who moves along a linea heat souce with constant velocity, as shown in Figue 1. ηui 3x 3y 3z q ( x, y, z) = 6 3 exp exp exp a bc a b c π π ηui 3x 3y 3z q = ( x, y, z) 6 3 exp exp exp a bc a b c π π () (3) Figue 1. Heat souce o linea analysis o twodimensional heat low. Consideing that thee is no low in the plate thickness diection and shiting the oigin o coodinates o the plate o the linea heat souce, the heat conduction takes place in the x and y diections, eatuing a bi-diectional low (Binda et al., 004; Gonçalves et al., 006). P / hp = 0 + e πk v x α v K0 α x + y (1) aking as eeence the coodinates, the tempeatue o a point at a distance (x, y) has a solution given by Equation (1). whee α is the themal diusivity, k is the themal conductivity, h is the thickness o the plate and v is the welding speed. Accoding Depadeux (003), these analytical models ae well suited only when the size o the usion is consideed a zone vey small as compaed with the dimensions o the piece. New analytical solutions have been poposed, in which take into account a heat souce distibuted (Fassani and evisan, 003). Fo modeling the heat souce poposed by Goldak, conduces to an analytical solutions that is cuently the most suitable o IG pocesses, whee is consideed a 3D inite Gaussian ove a double ellipsoid, as shown in Figue. his souce is deined analytically by Equation () and Equation (3) (Goldak and Chakavati, 1984; Goldak and Akhlaghi, 005). Whee q and q ae the volumetic enegy distibutions beoe and ate the toch [w/m 3 ]; and ae the depatments o enegy beoe and ate the toch; a and a ae the length o the weld pool beoe and ate the toch [m]; b is the semi-width o the weld pool [m] and c is the depth o usion zone [m] as shown in Figue. he U and I paametes ae linked diectly to the welding pocedue, while b and c ae the geometical paametes o the souce, which may be detemined by metallogaphic examination. = (4) + a = (5) a + a a = (6) a + a he othe paametes a, a, and, ae obtained by helping o paametes b and c which ae elated in the bibliogaphy, as shown on Equations (4), (5) and (6) (Gey et al., 005; Goldak and Akhlaghi, 005). EXPERIMENS Fo the simulation o esidual stesses, a 60mm x 50mm and 3mm ectangula ASM AH36 steel plate was used, consideing the use o a IG (tungsten inet gas) in the welding pocess. able 1 shows the chemical composition o the alloy. able 1. Chemical composition o the sample o ASM AH36. C C Mn Ni Si V Al Cu S P Sn Nb Figue. Schematic epesentation o the double ellipsoid heat souce. Numeical simulations wee peomed with a sotwae pogam (Abaqus) based on the inite element method (FEM). he boad was divided into elements type DC3D8 sum to a total o elements. his mesh pesented moe einement in the usion zone and in the heat aected zone (HAZ), because those wee the aeas whee the most impotant phenomena in the welding pocess Engenhaia émica (hemal Engineeing), Vol. 10 No June and Decembe 011 p

3 Guimaães et al. Obtaining empeatue Fields as a occued. his mesh einement is shown in Figue 3 and in able. Heat exchange by convection and adiation was expessed by Eq. (8) (Newton's law) and Eq. (9) (Stean Boltzmann s law), espectively. Whee h is the convection coeicient, σ is the Stean-Boltzmann s constant and ε epesents emissivity. Liteatue values wee used to model heat exchange and the assumed convection aound the boad. he ambient tempeatue consideed was 5 C and emissivity 0.7. he values used o the convection coeicient (h), speciic heat (C p ) and themal conductivity (k) ae shown in Figue 5 (sikas et al. 003) as a unction o tempeatue. Figue 3. Mesh and egions used o poblem solving themal and mechanical. able. Elements that make up the mesh o the FEM calculation. Region 1 Region Region 3 Numbe o Elements hese elements ae continuous - 3D o linea omulation and each one o them contains 8 nodes (Figue 4). Fo all elements, edges along the 0,75mm thick wee always used, emaining ou elements along the thickness o the plate. K x Figue 4. Element DC3D8-8 nodes and linea omulation (Hibbit et al., 007). x + K y y + K z z +. q = ρc t (7) he solution o the themal poblem is given by Equation (7). Fo the themal bounday conditions, the exchange o convection and adiation was consideed duing the welding pocess. hese bounday conditions wee impoted to the model. Five sides o the plate wee welded, except the lowe suace, which ested on the table duing the welding opeation. q R q c ( ) = h (8) ( ) = σ ε (9) Figue 5. Vaiation o mateial popeties as a unction o tempeatue (tsikas et al., 003). he souce used in this study was the double ellipsoid model poposed by Goldak, shown in Figue. he geometic paametes a, a, b, c and the enegy paametes and wee obtained with the suppot o the elationships ound in eeences suggested by Gey et al (005) and Goldak et al. (005) (able 3). Duing the modeling, a FORRAN DFLUX suboutine (Hibbit et al. 007) was developed to displace the heat souce. his unction detemines the toch position vesus time, and calculates the heat input in all points o the boad. Only one mechanical bounday condition was established because the plate was attached though a 4 mm diamete hole, as shown in Figue (Danis et al. 008). able 3. Geometical paametes and enegy om the heat souce (Goldak & Akhlaghi, 005; Danis, 008). Paamete Value a 0.005m a 5m b 0.005m c 0.003m Fo the numeical simulations peomed, in this study the value o the voltage and electical cuent wee kept constant and equal to V and 15 A espectively. he vaiations in eiciency souce wee applied, as shown in able 4. 5 Engenhaia émica (hemal Engineeing), Vol. 10 No June and Decembe 011 p

4 Ciência/Science Guimaães et al. Obtaining empeatue Fields as a able 4. Paametes o heat input used in the numeical simulation. Cuent Voltage Eiciency Speed (A) (V) (%) (m/s) RESULS AND DISCUSSION he vitual welding lasted 50s. he evolution o tempeatue ield o eiciency souce o 60%, 70% and 80% ae shown in the Figues 6, 7 and 8 espectively. Figue 8. Evolution o the tempeatue ield [ºC] o eiciency souce o 80% as a unction o the Figue 6. Evolution o the ield o tempeatue [ºC] o eiciency souce o 60% as a unction o the he evolution o the tempeatue ield is inluenced by the paametes o the heat souce and the heat input welding. he contous o this ield ae diectly inluenced by the welding speed and the physical popeties o the mateial. Fo simulations, a welding speed o 1 mm/s was used. Unde these conditions (Figues 6, 7 and 8), the Heat Aected Zone (HAZ) is highe o the cuent o 16A, due to the incease in heat input. I the speed o welding inceases the contous o the isothems tend to stetch moe towads the opposite diection to welding, thus aecting a smalle aea (Chon and Chin, 1993), howeve the welding speed in this wok was kept constant. In this model the tempeatue emains nealy constant ove the thickness, accoding to the poblem solution o thin plate poposed by Rosenthal (1941). he maximum tempeatue achieved o the welding eiciency o 60% was 177 C, o the welding eiciency o 70% was 184º C and o the eiciency o welding o 60% was 09º C. In liteatue, models that do not take into account the phase tansomations (γ-α) o mateial can be easily ound, but they pesent poo accuacy in esults concening the tempeatue ield. In this study, phase tansomations wee consideed but these simulated esults ae in accodance with expeimental esults (Guimaães, 010). CONCLUSIONS Figue 7. Evolution o the tempeatue ield [ºC] o eiciency souce o 70% as a unction o the he detemination o the tempeatue ield in welding poduced by IG can be simulated by using the Abaqus code in which both themal and mechanical eects can be consideed as well. Consideing the phase tansomation (γ α) duing Engenhaia émica (hemal Engineeing), Vol. 10 No June and Decembe 011 p

5 Guimaães et al. Obtaining empeatue Fields as a vitual welding, the model pesented consistent esults unde the expeiment. he detemination o the tempeatue ield can be used eithe o the optimization o welding pocedues in utue woks o in educing the levels o esidual stess in dieent industial ange, such as in the petochemical and shipbuilding industies. ACKNOWLEDGEMENS We would like to thank FACEPE (Penambuco State Foundation o Science and echnology) o the inancial suppot to this study. REFERENCES Binda, B., Capello, E. and Pevitali, B., 004, A semi-empiical model o the tempeatue ield in the AISI 304 lase, welding Jounal o Mateials Pocessing echnology. Vol. 155, pp Chon, L.. and Chin, M.., 1993, Heat Flow in Fusion Welding - Paametic Eects, ASM HANDBOOK. Vol. 6, pp Danis, P. Y., 008, Étude de la soudabilité d um supealliage base nickel otement chage em éléments ducissants titane et aluminium: l inconel 738, Doctoal hesis, L Univesité Bodeaux 1, Fance. Depadeux, L. and Jullien, J. F., 003, Expeimental and numeical simulation o themomechanical phenomena duing a IG welding pocess, In: Intenational Coneence on hemal Pocess Modelling and Compute Simulation. Nancy, Fance, pp Fassani, R. N. S. and evisan, O. V., 003, Analytical Modeling o Multipass Welding Pocess with Distibuted Heat Souce, Jounal o the Baz. Soc. o Mech. Sci. & Eng. Vol. XXV, No. 3, pp Gey, D., Long, H. and Maopoulos, P., 005, Eects o welding speed, enegy input and heat souce distibution on tempeatue vaiations in butt joint welding, Jounal o Mateials Pocessing echnology. Vol. 167, pp Goldak, J. A. and Akhlaghi, M., 005, Computational Welding Mechanics, Sping, New Yok. Gonçalves, C. V., Vilainho, L. O., Scotti, A. and Guimaães, G., 006, Estimation o heat souce and themal eiciency in GAW pocess by using invese techniques, Jounal o Mateials Pocessing echnology. Vol. 17, pp Goyal, V. K., Ghosh, P. K. and Saini, J. S., 009, Analytical studies on themal behaviou and geomety o weld pool in pulsed cuent gas metal ac welding, Jounal o mateials pocessing technology. Vol. 09, pp Guimaães, P. B., 010, Estudo do Campo de empeatua Obtido Numeicamente paa Posteio Deteminação das ensões Residuais em uma Liga de Aço ASM AH36, Doctoal hesis, Univesidade Fedeal de Penambuco, Bazil. (in Potuguese) Hibbit, Kalsson & Soenson Inc., 007, Abaqus Use Suboutines Reeence Manual vesion 6.7, USA. Hibbit, Kalsson & Soenson Inc., 007, Abaqus Getting Stated with Abaqus Inteactive Edition vesion 6.7, USA. Maques, P. V., Modenesi, P. J., Bacaense, A.Q., 007, Soldagem: Fundamentos e ecnologia. Ed. UFMG, Belo Hoizonte, Bazil. (in Potuguese) Modenesi, P. J., Maques, P. V. and Santos, D. B., 006, Intodução à Metalugia da Soldagem. Univesidade Fedeal de Minas Geais. DEM, Belo Hoizonte, Bazil. (in Potuguese) Ramanzini, R. and Pauca Casas, W. J., 006, Distibuição do Campo de empeatuas num Potótipo Vitual de Junta Soldada Multipasse, in: 17º CBECiMat - Congesso Basileio de Engenhaia e Ciência dos Mateiais. PR, Bazil. pp (in Potuguese) Rosenthal, D., 1941, Mathematical theoy o heat distibution duing welding and cutting, Weld. J. Vol. 0, pp sikas, S. A., Papanikos, P. and Kemanidis,.H., 003, Numeical Simulation o the Lase Welding Pocess in butt-joint specimens, Jounal o Mateials Pocessing echnology. Vol. 134, pp Engenhaia émica (hemal Engineeing), Vol. 10 No June and Decembe 011 p