Numerical simulation and experimental characterization of a single-seam plasma wire arc additive manufacturing process for Ti-6Al-4V

Arc welding processes are increasingly being used in the additive manufacturing of metal components. Physics-based modeling of welding processes enables the study of welding parameter effects on the final weld shape, residual stress state, and distortion, helping to improve weld quality and reduce costs. However, the quality of the process simulation strongly depends on the mathematical description of the heat source. The parameters of the heat source model have a significant influence on the temperature field and, consequently, on the distortion and residual stress fields. This paper presents a trial-and-error method for determining the parameters for Goldak’s double-ellipsoidal heat source model. The transient temperature distribution and the size of the melt pool are determined through experimental studies. Numerical models are then set up in Simufact Welding 8.0 with a set of heat source parameters to reproduce the experimental trials. By comparing numerical finite element results with experimental results, the heat source parameters for a multi-pass additive manufacturing process are successfully calibrated and identified.

- DIN EN ISO/ASTM 52900:2022-03. Additive Fertigung- Grundlagen-Terminologie Additive Manufacturing-General Principles-Fundamentals and Vocabulary (ISO/ASTM 52900:2021); 2022. doi: 10.31030/3290011
- Bielik M. Thermo-Mechanical Analysis of Plasma-Based Additive Manufacturing of Ti-6Al-4V Components Using Simufact Welding. Master’s Thesis. TU Wien; 2020. Available from: https://repositum.tuwien.at/ handle/20.500.12708/15047 [Last accessed 2025 Mar 30].
- Bielik M, Meuthen J, Ariza-Galvan E, et al. Plasma Metal Deposition in Aerospace Applications Enabling a Cost- Efficient Technology for High Tech Industries. Metal Additive Manufacturing Conference (MAMC), Vienna; 2020.
- Wallis C, Neubauer E, Kitzmantel M, et al. Investigations of plasma metal deposition (PMD) of 6061 and 7075 aluminum alloys for aerospace and automotive applications. BHM Berg Hüttenmänn Monats. 2023;168(5):209-218. doi: 10.1007/s00501-023-01345-4
- Li JZ, Alkahari MR, Rosli NA, Hasan R, Sudin MN, Ramli FR. Review of wire arc additive manufacturing for 3D metal printing. Int J Autom Technol. 2019;13(3):346-353. doi: 10.20965/ijat.2019.p0346
- Gierth M, Henckell P, Ali Y, Scholl J, Bergmann JP. Wire arc additive manufacturing (WAAM) of aluminum alloy AlMg5Mn with energy-reduced gas metal arc welding (GMAW). Materials. 2020;13(12):2671. doi: 10.3390/ma13122671
- Masubuchi K. Residual stresses and distortion in welds. In: Encyclopedia of Materials: Science and Technology. Netherlands: Elsevier; 2005. p. 1-6. doi: 10.1016/B0-08-043152-6/01457-1
- Ding J, Colegrove P, Mehnen J, et al. Thermo-mechanical analysis of wire and arc additive layer manufacturing process on large multi-layer parts. Comput Mater Sci. 2011;50:3315-3322. doi: 10.1016/j.commatsci.2011.06.023
- Colegrove PA, Coules HE, Fairman J, et al. Microstructure and residual stress improvement in wire and arc additively manufactured parts through high-pressure rolling. J Mater Process Technol. 2013;213(10):1782-1791. doi: 10.1016/j.jmatprotec.2013.04.012
- Hoye N, Li HJ, Cuiuri D, Paradowska AM. Measurement of residual stresses in titanium aerospace components formed via additive manufacturing. Mater Sci Forum. 2014;777:124-129. doi: 10.4028/www.scientific.net/MSF.777.124
- Martina F, Roy MJ, Szost BA, et al. Residual stress of as-deposited and rolled wire+arc additive manufacturing Ti-6Al-4V components. Mater Sci Technol. 2016;32(14):1439-1448. doi: 10.1080/02670836.2016.1142704
- Coules HE. Contemporary approaches to reducing weld induced residual stress. Mater Sci Technol. 2013;29(1):4-18. doi: 10.1179/1743284712Y.0000000106
- Hu X, Chiu LN, Huang A, Liu M, Yan W. Application of melt pool profiles for parameter calibration of Goldak’s heat source model. Addit Manuf. 2024;92:104379. doi: 10.1016/j.addma.2024.104379
- Bayat M, Dong W, Thorborg J, To AC, Hattel JH. A review of multi-scale and multi-physics simulations of metal additive manufacturing processes with focus on modeling strategies. Addit Manuf. 2021;47:102278. doi: 10.1016/j.addma.2021.102278
- Deng D, Murakawa H. Numerical simulation of temperature field and residual stress in multi-pass welds in stainless steel pipe and comparison with experimental measurements. Comput Mater Sci. 2006;37(3):269-277. doi: 10.1016/j.commatsci.2005.07.007
- Aarbogh HM, Hamide M, Fjær HG, Mo A, Bellet M. Experimental validation of finite element codes for welding deformations. J Mater Process Technol. 2010;210(13):1681-1689. doi: 10.1016/j.jmatprotec.2010.05.014
- Karkhin VA, Pittner A, Schwenk C, Rethmeier M. Simulation of inverse heat conduction problems in fusion welding with extended analytical heat source models. Front Mater Sci. 2011;5(2):119-125. doi: 10.1007/s11706-011-0137-1
- Gu Y, Li YD, Yong Y, Xu FL, Su LF. Determination of parameters of double-ellipsoidal heat source model based on optimization method. Weld World. 2019;63(2):365-376. doi: 10.1007/s40194-018-00678-w
- Goldak J, Chakravarti A, Bibby M. A new finite element model for welding heat sources. Metall Trans B. 1984;15(2):299-305. doi: 10.1007/BF02667333
- Simufact. Infosheet Heat Source. Simufact Welding Tutorial. Hamburg, Germany: Simufact Engineering GmbH; 2018.
- Lundbäck A. Modelling of Weld Path for Use in Simulations. Master’s Thesis. Sweden: Lulea University of Technology; 2000.
- Fachinotti VD, Anca AA, Cardona A. Analytical solutions of the thermal field induced by moving double-ellipsoidal and double-elliptical heat sources in a semi-infinite body. Int J Numer Methods Biomed Eng. 2011;27(4):595-607. doi: 10.1002/cnm.1324
- Megahed M, Mindt HW, N’Dri N, Duan H, Desmaison O. Metal additive-manufacturing process and residual stress modeling. Integr Mater Manuf Innov. 2016;5(1):61-93. doi: 10.1186/s40192-016-0047-2
- Radaj D. Wärmewirkungen Des Schweißens [Thermal Effects of Welding]. Berlin, Heidelberg: Springer; 1988. doi: 10.1007/978-3-642-52297-0
- Simufact. Infosheet Boundary Conditions Thermal. Simufact Welding Tutorial. Hamburg, Germany: Simufact Engineering GmbH; 2018.
- Helbig P. Kalibrierung Von Ersatzwärmequellen Für Die numerische Simulation von Laserschweißprozessen [Calibration of Representative Heat Sources for the Numerical Simulation of Laser Welding Processes]. Master’s Thesis. Kassel: Universität Kassel; 2018.
- Xiong J, Lei Y, Li R. Finite element analysis and experimental validation of thermal behavior for thin-walled parts in GMAW-based additive manufacturing with various substrate preheating temperatures. Appl Therm Eng. 2017;126:43-52. doi: 10.1016/j.applthermaleng.2017.07.168
- Wang J, Lin X, Wang J, et al. Grain morphology evolution and texture characterization of wire and arc additive manufactured Ti-6Al-4V. J Alloys Compd. 2018;768:97-113. doi: 10.1016/j.jallcom.2018.07.235
- Abe T, Kaneko J, Sasahara H. Thermal sensing and heat input control for thin-walled structure building based on numerical simulation for wire and arc additive manufacturing. Addit Manuf. 2020;35:101357. doi: 10.1016/j.addma.2020.101357
- Sampaio RFV, Pragana JPM, Bragança IMF, Silva CMA, Nielsen CV, Martins PAF. Modelling of wire-arc additive manufacturing a review. Adv Ind Manuf Eng. 2023;6:100121. doi: 10.1016/j.aime.2023.100121
- Deyev G, Deyev D. Surface Phenomena in Fusion Welding Processes. 1st ed. United States: CRC Press; 2005. doi: 10.1201/9781420036299
- Ou W, Knapp GL, Mukherjee T, Wei Y, DebRoy T. An improved heat transfer and fluid flow model of wire-arc additive manufacturing. Int J Heat Mass Transf. 2021;167:120835. doi: 10.1016/j.ijheatmasstransfer.2020.120835
- Liu C, Wu Y, Zhou J, Wen Y, Wang L, Xie L. Effect of in situ electromagnetic field manipulation on the microstructure and hardness of titanium alloy during laser melting deposition. Mater Sci Addit Manuf. 2025;4(1):8332. doi: 10.36922/msam.8332
- Bai X, Colegrove P, Ding J, et al. Numerical analysis of heat transfer and fluid flow in multilayer deposition of PAW-based wire and arc additive manufacturing. Int J Heat Mass Transf. 2018;124:504-516. doi: 10.1016/j.ijheatmasstransfer.2018.03.085
- Belhadj M, Werda S, Belhadj A, Kromer R, Darnis P. Thermal Analysis of Wire Arc Additive Manufacturing Process. ESAFORM 2021; 2021. doi: 10.25518/esaform21.4095
- Liu S, Shin YC. Additive manufacturing of Ti6Al4V alloy: A review. Mater Des. 2019;164:107552. doi: 10.1016/j.matdes.2018.107552
- Wu B, Pan Z, Ding D, Cuiuri D, Li H. Effects of heat accumulation on microstructure and mechanical properties of Ti6Al4V alloy deposited by wire arc additive manufacturing. Addit Manuf. 2018;23:151-160. doi: 10.1016/j.addma.2018.08.004
- Hönnige J, Colegrove P, Prangnell P, Ho A, Williams S. The effect of thermal history on microstructural evolution, cold-work refinement and α/β growth in Ti-6Al-4V wire + Arc AM. Appl Phys [ArXiv Preprint]; 2018. doi: 10.48550/ARXIV.1811.02903
- Chujutalli JH, Lourenço MI, Estefen SF. Experimental-based methodology for the double ellipsoidal heat source parameters in welding simulations. Mar Syst Ocean Technol. 2020;15(2):110-123. doi: 10.1007/s40868-020-00074-4
- Yang Y, Lin H, Li Q. A computationally efficient thermo-mechanical model with temporal acceleration for prediction of residual stresses and deformations in WAAM. Virtual Phys Prototyp. 2024;19(1):e2349683. doi: 10.1080/17452759.2024.2349683
- Strobl D, Unger JF, Ghnatios C, et al. Efficient bead-on-plate weld model for parameter estimation towards effective wire arc additive manufacturing simulation. Weld World. 2024;68(4):969-986. doi: 10.1007/s40194-024-01700-0
- Wang X, Meng D, Yi H, Yan Z, Xiao J, Chen S. A novel model for directed energy deposition-arc based on in-order stacking of primitives. Virtual Phys Prototyp. 2024;19(1):e2291471. doi: 10.1080/17452759.2023.2291471
- Guo Z, Jiang H, He L, Lei Z, Bai R. CNN-empowered identification of heat source parameters from the cross-section profile of laser-welded zone. Int J Adv Manuf Technol. 2024;130(11-12):5441-5455. doi: 10.1007/s00170-024-13054-4
- Ilani MA, Banad YM. Modeling Melt Pool Geometry in Metal Additive Manufacturing Using Goldak’s Semi- Ellipsoidal Heat Source: A Data-Driven Computational Approach. Numer Anal [ArXiv Preprint]; 2024. doi: 10.48550/ARXIV.2404.08834
- Martukanitz R, Michaleris P, Palmer T, et al. Toward an integrated computational system for describing the additive manufacturing process for metallic materials. Addit Manuf. 2014;1-4:52-63. doi: 10.1016/j.addma.2014.09.002
- Simufact Infosheet Parallelization. Simufact Welding Tutorial; 2018.
- Tröger JA, Hartmann S, Treutler K, Potschka A, Wesling V. Simulation-based process parameter optimization for wire arc additive manufacturing. Prog Addit Manuf. 2025;10(1):1-14. doi: 10.1007/s40964-024-00597-x
- Wang F, Williams S, Colegrove P, Antonysamy AA. Microstructure and mechanical properties of wire and arc additive manufactured Ti-6Al-4V. Metall Mater Trans A. 2013;44(2):968-977. doi: 10.1007/s11661-012-1444-6
- Bielik M, Neubauer E, Kitzmantel M, Neubauer I, Kozeschnik E. A simulation approach for series production of plasma-based additive manufacturing of Ti-6Al-4V components. Math Model Weld Phenomena. 2022;13:361-393. doi: 10.3217/978-3-85125-968-1-20
- Graf M, Hälsig A, Höfer K, Awiszus B, Mayr P. Thermo-mechanical modelling of wire-arc additive manufacturing (WAAM) of semi-finished products. Metals. 2018;8(12):1009. doi: 10.3390/met8121009