Recent developments in modeling of heat transfer ... - Springer Link

Int J Adv Manuf Technol (2013) 64:749–754 DOI 10.1007/s00170-012-4048-9

ORIGINAL ARTICLE

Recent developments in modeling of heat transfer during TIG welding—a review V. M. Joy Varghese & M. R. Suresh & D. Siva Kumar

Received: 27 July 2011 / Accepted: 5 March 2012 / Published online: 21 March 2012 # Springer-Verlag London Limited 2012

Abstract This paper is an attempt to list the recent developments in the area of arc welding heat transfer simulation. Fusion welding modeling is a broad area where a number of research groups were spending their efforts to get solutions for both research and industrial problems. Starting from fundamentals of arc physics, heat transfer, microstructure models, thermal stress, and modern techniques like pattern recognition comes into picture while considering the complete solution of welding-related problems. These areas are developing almost independently and there are only few efforts to couple them together as computational welding mechanics, which includes the computational fluid mechanics, magneto hydrodynamics, thermo mechanical problems, and computational material science. Here, an effort is made to list down major developments in this area and to plot the present state of research on the TIG welding heat transfer modeling by giving priority to last few years of research. Keywords Welding . Simulation . TIG . Heat transfer . Modeling

1 Introduction Welding is extensively employed as the joining technique for metals and alloys in many manufacturing industries. The

V. M. J. Varghese (*) Sree Chitra Thirunal College of Engineering, Thiruvananthapuram, India e-mail: [email protected] M. R. Suresh : D. S. Kumar Vikram Sarabhai Space Center, Thiruvananthapuram, India

strength of weld and thereby the weld efficiency is directly related to the microstructure of weld pool and heat-affected zone (HAZ). HAZ microstructure is completely controlled by the heat transfer rate during welding. Modeling the heat transfer and thereby predicting the weld quality is a topic of great interest to both researchers and industrialist for the last few decades. The high intensity welding arc makes the system a complex interaction of thermal, magnetic, electric, and fluid flow fields. Many 2D and 3D models have been developed and presented in literature in order to simulate the thermal, mechanical, and microstructural interactions during welding process. Welding arc has been modeled by many researchers, but the micromechanisms of arc heat transfer is still not completely explained, and many groups are trying to connect the developments in arc physics with the welding arc and resulting heat transfer mechanisms. The first developed heat transfer models were based on conduction mode, which would fail in and around the weld pool as these models were not considered the convection effect, which is a major mode of heat transfer inside the weld pool. During the last two decades, a number of research papers were published with convection heat transfer models. Many groups were working in the optimization of arc welding by doing experiments and by invoking the advantages of modeling and simulations. The microstructural modeling of HAZ and the prediction of thermal stress and distortions during welding is another broad area where the results of welding heat transfer research are applied. The welding robots and automation of welding process is the driving force behind the current welding research. Lindgren [1] presents a detailed review in numerical modeling of welding and the major contributions in the welding heat transfer modeling were well explained by him. This paper is concentrating only on the recent developments in this area, by listing down major papers published in the last few years.

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2 Modeling of welding arc Welding arc is a transient interaction of electric and magnetic fields. A fundamental knowledge about ionization and plasma formation is required for proper modeling of welding arc which is basically an electrical arc. Figure 1 shows the multiphysics interactions in a welding arc. Even though the plasma physics is a developed area, only limited number of group’s work for interconnecting the developments in the arc physics with welding science. During earlier developments, many authors have published both theoretical and experimental results on behavior of welding arc, effects of electrode coatings, electrode tip angle, inert gas flow rate, etc. on arc shape, arc pressure and velocity distribution. A detailed literature review about the developments in this area is presented by Biswas [2]. The welding arc can be simulated by accounting the microheat transfer mechanisms like thermionic emission, cathode jet, ionization, etc. during the formation of arc. Wu [3–5] applied the fundamentals of plasma physics to the welding arc and developed the temperature, pressure, current, and velocity distributions in the arc and over the weld surface. Later in 2002, Wu et al. [6] developed microheat transfer relations for determination of anode heat flux distribution by separately calculating conductive, convective, and radiative flux over the anode. The welding arc, which is governed by a set of physical laws, can be modeled by simultaneously solving mass, momentum, energy, and charge conservation equations, inside the computational domain, i.e., the welding arc. Recently, Wu et al. applied the conservation equations developed for a normal GTA welding arc [7] to the double-sided arc welding arc [8]. Ramirez et al. [9] presented a comparative study between magnetic and potential approaches for welding arc representations. They concluded that the potential approach is

Fig. 1 Multiphysics interactions in a welding arc [9]

Int J Adv Manuf Technol (2013) 64:749–754

superior to predict the heat flux and current densities. Shinichi et al. [10] developed a numerical model for hollow cathode arc. Murphy et al. [11] studied the weld pool behavior with considering the arc plasma in the computational domain, which is an initiative to couple the weld pool behavior with the welding arc. Traidia et al. [12] studied the interaction between welding arc and weld pool for pulsed current gas tungsten arc welding.

3 Welding heat transfer models Most of the welding research groups concentrate on the heat transfer during welding rather than the actual mechanism of heat generation in the welding arc as the later is directly related to the efficiency of welded joint. This heat transfer rate decides the microstructure thereby the strength of the weld. In order to avoid the complex interaction of electric arc and thermal fields, researchers introduced heat distribution models to represent the welding arc heat distribution, i.e., the heat source. Conduction-based models were developed at first and later convection models which are found to be more accurate even in and around the weld pool. For modeling of heat transfer during welding, different numerical and analytical methods have been applied by different authors and they have their own advantages and limitations. At present, commercial FEM software are commonly used for solving welding heat transfer. 3.1 Analytical solutions The developments in computational capabilities lead to an exponential increase in the number of publications using numerical methods. At the same time, the application of analytical approaches are still not developed and only limited number of approaches are available based on analytical methods because of complex formulations in analytical solutions. According to Klobcar et al. [13], the first technical paper in welding modeling is published by Rosenthal in 1942. He implemented many assumptions to make the problem linear and analytically solvable. He assumed that there is no heat transfer between the plates and surroundings, constant material properties throughout the process, and infinite plate dimensions. These assumptions made the problems linear but the assumptions were not valid. The moving heat source problem has been solved by many researchers and both 2D and 3D solutions are available in literature [14]. Solutions of double ellipsoidal moving heat source problems and hybrid double ellipsoid heat source that can be applied to filet joints are available in literature [15]. The major limitation of analytical approach is the use of infinite boundaries. Recently, a 2D heat transfer modeling within limited regions using moving sources is presented by Couedel


et al. [16]. They also made an attempt to study the effect of source dimensions as well as the effect of boundary on temperature distributions. The inherited complexity due to temperature-dependent material properties, and phase changes are the limiting variables for analytical solutions. 3.2 Heat distribution models A heat distribution model will generate the magnitude and direction of heat flux distribution over the weld surface. During earlier stages of research, the welding heat source was assumed to be point source and line source. According to Klobcar et al. [13], Rosenthal, in 1946, developed both line and point moving source relations and later in 1969 Pavelic introduced Gaussian form of distribution, which is used by many researchers and has been using the same because of its simplicity and accuracy of such an assumption. Goldak et al. [17] introduced double ellipsoidal distribution which is the most suitable distribution for a stationary welding source. As an extension of this work, Sapabathy et al. [18] introduced double ellipsoidal model with a differential distribution at the front and back portion of arc which is most suitable for even vibrating heat sources that can be used for modeling any type of welding technique including wave technique. The major drawback of heat distribution models are such that they require accurate determination of source dimensions, which is determined by the weld parameters and characteristics of a particular welding system like the electrode characteristics and gas flow parameters.

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of repair welding of tools which was also based on conduction model and they were able to predict the temperature profiles successfully. Goncalves et al. [22] solved 3D inverse problem of welding heat transfer using golden section technique. Those researchers who predict the thermal stress made use of conduction models in order to reduce the solution time. Since 1980, many papers were published by considering the magnetic and hydrodynamic effects inside the weld pool. The effect of various governing forces in the weld pool on pool shape, velocity distributions, surface depressions, etc. have been studied by many researchers. Initially, the simulations were based on assumed weld pool shapes, and later predicted weld pool shapes were used. Models are available for both full penetration and partial penetration. Kim et al. [23] developed 2D axisymmetric model for fluid flow and heat transfer in the weld pool with consideration of all the four driving forces of convection, electromagnetic, buoyancy, surface tension, and drag forces. Fan et al. [24] developed a numerical model for heat and fluid flow inside weld pool that can be applied to both partial penetration and full penetration. Taylor et al. [25] applied finite volume method to welding phenomenon and they were able to predict the Marangoni convection which arises because of difference in surface tension in the weld pool. Recently, the effect of an external magnetic field on the weld pool is modeled by Lin et al. [26] while a numerical model for doublesided arc welding is presented by Wu et al. [8]. 3.4 Determination of thermal stress

3.3 Welding heat transfer numerical models During initial stages of welding heat transfer modeling research, it was assumed that at base metal there is only conduction heat transfer. But conduction models fail to solve fully the heat transfer in and around the weld pool where the convection currents in the weld pool contributes more to the total heat transfer. Conduction-based models are with simple formulations to avoid complex fluid field interactions inside weld pool. Hence, even now, these models are well utilized by many groups for predicting residual stress and distortions during welding. Bag et al. [19] developed a three-dimensional thermomechanical conduction model for laser spot welding and they used the technique of adaptive heat source that need not require prior knowledge of heat source dimension. Zhu et al. [20] studied the effect of temperature-dependent material properties on welding simulation, using a conduction model and concluded that there were large variations in predicted temperatures if average values were used for simulation. Later in 2007, Gery et al. [21] studied the effects of speed and heat source dimensions on thermal history of welds using a conduction model. Klobcar et al. [13] developed FE model for thermal analysis

Prediction of residual stress and associated distortions is one of the major goals behind welding heat transfer modeling; and the numerical models have a potential role in this area because of the limitations in NDT (nondestructive testing) techniques used for experimental determination of residual stress. According to Akbari Mousavi et al. [27], Ueda and Yamakawa in 1971 used 2D finite element analysis to calculate the welding residual stresses for the first time. They analyzed the effect of geometry configuration on residual stress and compared with results from X-ray diffraction method. Many others too proposed FEM models to predict residual stresses. Owen et al. [28] presented a comparison among neutron diffraction, X-ray diffraction, synchrotron X-ray diffraction, and finite element model results of residual stress developed during welding of aluminum alloy AA2024. Deng and Murakawa [29] developed a 3D FE model for simulating residual stresses during multipass welding of a pipe. Recently, Zeng et al. [30] developed a thermoplastic elastic model and applied it for hybrid laser welding of magnesium and steel plates. Recently, Aarbogh et al. [31] predicted deformations during single-pass metal inert gas (MIG) welding of austenitic steel plate using finite element codes. A

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detailed finite element model for uncoupled thermomechanical solution of residual stress is presented by Anca et al. [32]. Most of these researches deal in heat distribution models for thermal profiles and none of them consider the convection currents in the weld pool while calculating the stress field in the weld pool boundaries. The experimental results presented by Xu et al. [33] prove that the convection in the weld pool significantly affects the penetration and weld pool shape and there by the stress distributions. Residual stress models incorporating convection effects are yet to be formulated.

generalization ability. Kuo et al. [42] applied Gery theory in neural networks to predict heat-affected zone evolved during MIG welding. Recently, Dutta et al. [43] modeled TIG welding process using convectional linear regression, a backpropagation neural network and a genetic neural network (GA-NN) and they concluded that GA-NN model can yield predictions which are more adaptive in nature and Tsai et al. [44] optimized welding and subsequent heat treatment procedure using response surface method.

3.5 Modeling using commercial software tools

5 Recent trends in welding modeling

Many welding models that are developed using commercial software like ANSYS are available in literature, and most of these models are based on conduction mode only. Both modified specific heat method and enthalpy method were utilized for including the latent heat of fusion in the models. Software like SYSWELD that are exclusively developed for commercial design of welding is also available. A few papers were published by making use of ANSYS multiphysics analysis options for modeling the convection currents inside the weld pool. Fenggui Lu et al. [34] presented an ANSYS model of TIG welding and the model was successful for a stationery welding arc. However, modifications are required to this model for considering moving heat source. Lei et al. [35] developed an ANSYS model for predicting weld pool dimensions. Later, Wang et al. [36] used ANSYS compiled program for the microstructure modeling during flash welding. Ming et al. [37] developed an ANSYS model for simulation of laser welding heat transfer by using heat distribution models. Capriccioli et al. [38] presented a multipurpose ANSYS code for welding simulation using element birth and death technique to accommodate the fusion process. Price et al. [39] conducted neutron diffraction studies for determination of residual stress on a MIG welding mild steel plate giving importance to gauge volume and compared results with the numerical results generated using a FE model developed using SYSWELD.

In the modeling of welding, arc models for double-sided arc and hollow cathode are recently developed techniques. The model for a triple wire electrode arc [45] is in the developing stage. Adaptive heat source technique, which does not need prior knowledge of weld pool dimensions, has been used by many authors [17]. Models for multipass welding still use conduction models in order to reduce the solution time, which is a major drawback in welding simulation. Duranton et al. [46] presented a 3D model for multipass welding of stainless steel pipe. They were successful in predicting the residual stress and the overlap region. They are making use of adaptive mesh technology in order to minimize the solution time, which is a major constraint in case of 3D models. The solution time is around 193 h for a complete 3D model with five passes.

4 Optimization techniques applied to welding All modern optimization theories like neural networks, genetic algorithm, etc. can be applied to welding process also. Many researchers applied neural network for the modeling of welding. Tarng et al. [40] constructed a neural network model and optimized TIG weld pool geometry by applying simulated annealing algorithm. Juang et al. [41] conducted a comparative study between backpropagation and counterpropagation networks in modeling of TIG welding. They concluded that counter propagation networks have better learning ability and back propagation networks have better

6 Conclusion The fundamental research in welding modeling began in 1942, but still the research is at a developing stage. In areas like distortion prediction, hot cracking, etc. accurate models are yet to be developed. The idea of computational welding mechanics is a new concept considering all the thermomechanical and metallurgical effect during welding, and no model is developed so far by considering all these effects. Recently, the models for prediction of microstructure are making use of convection models, but for predictions of thermal stress we are still depending upon conduction models. In the case of multipass welding, the time taken to solve the model is a major limiting criterion. Techniques like variable meshing and adaptive meshing can be applied to reduce the time.

7 Scope for future work Only limited research is carried out to interconnect the fundamentals of arc physics and welding heat transfer, in order to avoid use of assumed heat sources. Only experimental


trials are available for explaining the effect of electrode shape and size, gas flow pattern and nature of gas, etc. on welding heat transfer, and no numerical models are developed for accounting these variables. Development of a convection model for prediction of residual stress, and for multipass welding that will be most suitable for predicting the phenomenon like hot cracking in the weld yet to be developed.

References 1. Lindgren LE (2006) Numerical modeling of welding. J Comput Methods Appl Mech Eng 195:6710–6736 2. Biswas K (1993) A numerical prediction of the temperature distribution in the thermionic cathode of a welding arc. J Mater Process Technol 40:219–237 3. Wu CS, Ushio M, Tanaka M (1997) Analysis of the TIG welding arc behavior. J Comput Mater Sci 7:308–314 4. Wu CS, Ushio M, Tanaka M (1999) Modeling the anode boundary layer of high intensity argon arcs. J Comput Mater Sci 15:302–310 5. Wu CS, Ushio M, Tanaka M (1999) Determination of sheath potential of gas tungsten arcs. J Comput Mater Sci 15:341–345 6. Wu CS, Gao JQ (2002) Analysis of the heat flux distribution at the anode of a TIG welding arc. J Comput Mater Sci 24:323–327 7. Li ZY, Wu CS (1997) Analysis of the transport phenomena in the interfacial region between TIG arcs and weld pools. J Comput Mater Sci 8:243–250 8. Wu CS, Sun JS (2002) Numerical analysis of temperature field during double sided arc welding of thick material. J Comput Mater Sci 25:457–468 9. Ramirez MA, Trapaga G, McKelliget J (2004) A comparison between different numerical formulations for welding arc representations. J Mater Process Technol 155–156:1634–1640 10. Tahiro S, Tanaka M, Nakatani M, Tani K, Faurbayatani M (2007) Numerical analysis of energy source properties of hollow cathode arc. J Surf Coat Technol 201:5431–5434 11. Murphy AB, Tanaka M, Yamamoto K, Tashiro S, Lowke JJ, Ostrikov K (2010) Modeling of arc welding: the importance of including the arc plasma in the computational domain. J Vac 85:579– 584 12. Traidia A, Roger F (2011) Numerical and experimental study of arc and weld pool behavior for pulsed current GTA welding. Int J Heat Mass Transf 54:2163–2179 13. Klobcar D, Tusek J, Taljat B (2004) Finite element modeling of GTA weld surfacing applied to hot work tooling. J Comput Mater Sci 31:368–378 14. Nguyen NT, Ohta A (1999) Analytical solutions for transient temperature of semi-infinite body subject to 3D moving heat source. Weld Res Suppl AWS:265–274 15. Nguyen NT (2004) Thermal analysis of welds. WIT Press, Australia 16. Couedel D, Rogeon P, Lemasson P, Carin M, Parpillon JC, Berthet R (2003) 2D-heat transfer modeling within limited regions using moving sources: application to electron beam welding. Int J Heat Mass Transf 46:4553–4559 17. Goldak J, Chakravarti A, Bibby M (1984) A new finite element model for welding heat sources. Metall Trans B 15:299–305 18. Sabapathy PN, Wahab MA, Painter MJ (2001) Numerical models of in-service welding of gas pipe lines. Int J Mater Process Technol 118:14–21 19. Bag S, De A (2007) Three dimensional transient conduction and thermo-mechanical analysis for laser spot welding using adaptive heat source. J Sci Technol Weld Join 12:24–31

753 20. Zhu XK, Chao YJ (2002) Effects of temperature-dependent material properties on welding simulation. J Comput Struct 80:967–976 21. Gery D, Long H, Maropoulos P (2005) Effects of welding speed energy input, and heat source distribution on temperature variation in butt joint welding. J Mater Process Technol 167:393–401 22. Gonçalves CV, Carvalho SR, Guimaraes G (2010) Application of optimization techniques and the enthalpy method to solve a 3Dinverse problem during a TIG welding process. J Appl Therm Eng 30:2396–2402 23. Kim IS, Basu A (1998) A mathematical model of heat transfer and fluid flow in the gas metal arc welding process. J Mater Process Technol 77:17–24 24. Fan HG, Tasai HL, Nab SJ (2001) Heat transfer and fluid flow in a partially or fully penetrated weld pool in gas tungsten arc welding. Int J Heat Mass Transf 44:417–428 25. Taylor GA, Hughes M, Strusevich N, Pericleous K (2002) Finite volume methods applied to the computational modeling of welding phenomena. J Appl Math Model 26:309–320 26. Lin ZQ, Li YB, Wang YS, Chen GL (2005) Numerical analysis of a moving gas tungsten arc weld pool with an external longitudinal magnetic field applied. Int J Adv Manuf Technol 27:288–295 27. Akbari Mousavi SAA, Miresmaeili R (2008) Experimental and numerical analysis of residual stress distribution in TIG welding process for 304L stainless steel. J Mater Process Technol 208:383– 394 28. Owen RA, Preston RV, Withers PJ, Shercliff HR, Webster PJ (2003) Neutron and synchrotron measurements of residual strain in TIG welded aluminium alloy 2024. J Mater Sci Eng A 346:159– 167 29. Deng D, Murakawa H (2006) Numerical simulation of temperature fields and residual stress in multi-pass welds in stainless steel pipe and comparison with experimental measurements. J Comput Mater Sci 37:269–277 30. Zeng Z, Li X, Miao Y, Wu G, Zhao Z (2011) Numerical and experiment analysis of residual stress on magnesium alloy and steel butt joint by hybrid laser-TIG welding. J Comput Mater Sci 50:1763–1769 31. Aarbogh HM, Hamide M, Fjær HG, Mo A, Bellet M (2010) Experimental validation of finite element codes for welding deformations. J Mater Process Technol 210:1681–1689 32. Anca A, Cardona A, Risso J, Fachinotti VD (2011) Finite element modeling of welding processes. J Appl Math Model 35:688–707 33. Xu YL, Dong ZB, Wei YH, Yang CL (2007) Marangoni convection and weld shape variation in A-TIG welding process. J Theor Appl Fract Mech 48:178–186 34. Lu F, Yao S, Lou S, Li Y (2004) Modeling and finite element analysis on GTAW arc and weld pool. J Comput Mater Sci 29:371– 378 35. Yu-cheng LEI, Wen-xia YU, Cai-hui LI, Xiao-nong CHENG (2006) Simulation on temperature field of TIG welding of copper without preheating. Trans Nonferrous Met Soc China 16:838–842 36. Wang W, Shi Y, Lei Y, Tian Z (2005) FEM simulation on microstructure of DC flash butt welding for an ultra fine grain steel. J Mater Process Technol 161:497–503 37. Guo Ming H, Jian Z, Jian Qang L (2007) Dynamic simulation of the temperature field of stainless steel laser welding. J Mater Des 28:242–245 38. Capriccioli A, Frosi P (2009) Multipurpose ANYS procedure for welding process simulation. J Fusion Eng Des 84:546–553 39. Price JWH, Ziara-Paradowska A, Joshi S, Finlayson T, Semetay C, Nied H (2008) Comparison of experimental and theoretical residual stresses in welds: the issue of gauge volume. Int J Mech Sci 50:513– 521 40. Tarng YS, Tsai HL, Yeh SS (1999) Modeling, optimization and classification of weld quality in tungsten inert gas welding. Int J Mach Tool Manuf 39:1427–1438

754 41. Juang SC, Targ YS, Lii HR (1998) A comparison between the back-propagation and counter-propagation networks in the modeling of the TIG welding process. J Mater Process Technol 75:54–62 42. Kuo HC, Wu LJ (2002) Prediction of heat affected zone using grey theory. J Mater Process Technol 120:151–168 43. Dutta P, Pratihar DK (2007) Modeling of TIG welding process using conventional regression analysis and neural network-based approaches. J Mater Process Technol 184:56–68

Int J Adv Manuf Technol (2013) 64:749–754 44. Tsai T-C, Chou C-C, Tsai D-M, Chiang K-T (2011) Modeling and analyzing the effects of heat treatment on the characteristics of magnesium alloy joint welded by the tungsten-arc inert gas welding. J Mater Des 32:4187–4194 45. Tusek J (2004) Mathematical modeling of melting rate in arc welding with triple wire electrode. J Mater Process Technol 146:415–423 46. Duranton P, Devaux J, Robin V, Gilles P, Bergheau JM (2004) 3D modeling of multipass welding of a 316L stainless steel pipe. J Mater Process Technol 153–154:457–463