Heat source model for electron beam welding of nickel-based superalloys
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Torsten Jokisch
Dipl.-Ing. (FH) IWE Torsten Jokisch, born in 1973, achieved mechanical engineer degree at the HTW Dresden and obtained a postgraduate degree in international welding engineering at the TU Dresden. After working as R&D Senior Engineer responsible for welding in the automotive industry he has been a Senior Research Engineer for materials, joining and additive systems at Siemens Energy Berlin since 2008 and has studied joining and simulation at the Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany.
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Nikolay Doynov
Dr.-Ing. IWE Nikolay Doynov, born in 1967, graduated in Material Processing Technologies – Welding at TU Sofia f. Plovdiv, Bulgaria and later received his International Welding Engineer qualification. In 2003 he received his PhD in Welding Simulation. After graduation, he worked at the Research Institute of Laser Processing Technologies in Sofia, Bulgaria and later as Research Associate at the Institute of Metal Science at the Bulgarian Academy of Sciences. Since 2005, he has been working as a Research Associate in the Department of Joining and Welding Technology at BTU Cottbus-Senftenberg, Germany, focusing on topic mathematical modeling and simulation of welding processes and as leader of a research group Welding Simulations.
Dr.-Ing. Ralf Ossenbrink, born in 1969, studied Mechanical Engineering at the Technical University of Braunschweig, Germany. He worked as a Research Associate at the Technical University of Braunschweig, Germany, and the Fraunhofer Institute for Mechanics of Materials, Freiburg, Germany. Currently, he is Group Leader and Senior Engineer in the Department of Joining and Welding at the Brandenburg University of Technology Cottbus-Senftenberg, Germany where he also received his Doctoral Degree. His fields of research expertise include the numerical simulation of welding processes, welding metallurgy and materials testing.
Prof. Dr.-Ing. habil. Vesselin Michailov, born in 1953, graduated with a specialization in physical metallurgy and welding technology in 1979, defended his PhD thesis in the field of Technical Sciences in 1983 and obtained his DSc Degree in Technical Sciences at the Leningrad Polytechnic Institute, Russia, in 1997. He habilitated at the Technical University of Braunschweig, Germany in 2001. At present, he is Head of the Joining and Welding Department of Brandenburg University of Technology Cottbus-Senftenberg, Germany, Director of the Lightweight Materials Center “Panta Rhei” in Cottbus, Germany. He has many years of experience in the fields of industry, science and education and is author or co-author of over 200 scientific articles, books and patents.
Abstract
An adapted heat source model is developed for transient thermal numerical analysis of electron beam welded nickel-based alloy with increased susceptibility to hot cracking. The model enables the consideration of heat redistribution due to beam deflection phenomena. The modeling concept is validated by the appropriate theoretical models and in addition, experimental studies especially performed for this purpose. Special attention is given to the calibration of heat source model parameters. The calibration procedure is based on a statistical approach involving a combination of novel analytical solutions and quasi-steady state finite element models. The model parameter field is statistically analyzed, and a prediction algorithm is developed using optimization algorithms from the six sigma theory. The reliability and practicability of the model is demonstrated by validation weldments. The work is dedicated to precisely calculating the temperature field in the high temperature region around the weld pool and thus to provide a more detailed explanation of the formation of hot cracks when welding turbine materials commonly used in industry and aircraft constructions.
About the authors
Dipl.-Ing. (FH) IWE Torsten Jokisch, born in 1973, achieved mechanical engineer degree at the HTW Dresden and obtained a postgraduate degree in international welding engineering at the TU Dresden. After working as R&D Senior Engineer responsible for welding in the automotive industry he has been a Senior Research Engineer for materials, joining and additive systems at Siemens Energy Berlin since 2008 and has studied joining and simulation at the Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany.
Dr.-Ing. IWE Nikolay Doynov, born in 1967, graduated in Material Processing Technologies – Welding at TU Sofia f. Plovdiv, Bulgaria and later received his International Welding Engineer qualification. In 2003 he received his PhD in Welding Simulation. After graduation, he worked at the Research Institute of Laser Processing Technologies in Sofia, Bulgaria and later as Research Associate at the Institute of Metal Science at the Bulgarian Academy of Sciences. Since 2005, he has been working as a Research Associate in the Department of Joining and Welding Technology at BTU Cottbus-Senftenberg, Germany, focusing on topic mathematical modeling and simulation of welding processes and as leader of a research group Welding Simulations.
Dr.-Ing. Ralf Ossenbrink, born in 1969, studied Mechanical Engineering at the Technical University of Braunschweig, Germany. He worked as a Research Associate at the Technical University of Braunschweig, Germany, and the Fraunhofer Institute for Mechanics of Materials, Freiburg, Germany. Currently, he is Group Leader and Senior Engineer in the Department of Joining and Welding at the Brandenburg University of Technology Cottbus-Senftenberg, Germany where he also received his Doctoral Degree. His fields of research expertise include the numerical simulation of welding processes, welding metallurgy and materials testing.
Prof. Dr.-Ing. habil. Vesselin Michailov, born in 1953, graduated with a specialization in physical metallurgy and welding technology in 1979, defended his PhD thesis in the field of Technical Sciences in 1983 and obtained his DSc Degree in Technical Sciences at the Leningrad Polytechnic Institute, Russia, in 1997. He habilitated at the Technical University of Braunschweig, Germany in 2001. At present, he is Head of the Joining and Welding Department of Brandenburg University of Technology Cottbus-Senftenberg, Germany, Director of the Lightweight Materials Center “Panta Rhei” in Cottbus, Germany. He has many years of experience in the fields of industry, science and education and is author or co-author of over 200 scientific articles, books and patents.
Abbreviations
- a
thermal diffusivity
- A
area
- b
heat exchange parameter
- [C]
capacity matrix
- Cm
thermo couple table
- c p
specific heat capacity
- cTm
current measured temperature
- Dmax
difference of approximated and measured maximum temperatures
- Ib
beam current
- K0(u)
modified Bessel function of second kind and null order of argument u
- Mss
temperature distribution matrix
- MΔy
y-difference matrix
- q2
effective heat flux
- q2m
maximum effective heat flux
- q3
effective heat generation rate
- q3m
maximum effective heat generation rate
- qeff
effective heat flow rate
- {q3}
nodal vector of heat generation rate
- re2
surface distribution width
- re3
volume distribution width
- rek
surface distribution reduction
- r ez
volume distribution depth
- SS
sensor temperature table
- {T}
nodal temperature vector
- T0
initial temperature
- ta
approximated time step
- Th
homologues temperature
- TL
liquidation temperature
- tm
measured time step
- Tm
measured point table
- TRange
thermo couple temperature range
- Ts
simulated point table
- TT
temperature tolerance
- Ub
accelerating voltage
- {v}
velocity vector
- V
volume
- vx
weld velocity in x-direction
- [W]
conductivity matrix
- x, y, z
cartesian coordinates
- ym
measured y position
- za
volume domain boundary
- η
overall efficiency coefficient
- ηa
approximated efficiency coefficient
- ψk
weight coefficient of volume heat sources
- αr
heat transfer coefficient
- ε
emissivity
- Φz
domain boundary factor
- σ
Stefan-Boltzmann constant
- λ
thermal conductivity
- ρ
density
Acknowledgments
The authors would like to thank Aleksej Senger from the Fraunhofer Institute (ISF) Aachen and Prof. Peter Petrov from the Institute of Electronics of the Bulgarian Academy of Sciences for supporting these experimental investigations and Prof. Andreas Neidel from Siemens Energy for support in material and data analysis.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany
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Articles in the same Issue
- Frontmatter
- Overview
- Technology in the 21st Century – The role of materials and materials testing
- Materials testing for welding and additive manufacturing applications
- Effect of laser inclination angle on mechanical properties of Hastelloy X processed by selective laser melting
- Component-Oriented testing
- Heat source model for electron beam welding of nickel-based superalloys
- Materialography
- Effects of Ti-bearing inclusions on intragranular ferrite nucleation
- Mechanical testing/Materialography
- Effect of extruded low-density polyethylene on the microstructural and mechanical properties of hot-press produced 3105 aluminum composites
- Production-Oriented testing/Additive manufacturing
- 10.1515/mt-2020-0004
- Materialography
- Effect of austenitizing temperatures on the microstructure and mechanical properties of AISI 9254 steel
- Materials testing for production technologies/Non-destructive testing
- Automation of pipe defect detection and characterization by structured light
- Wear testing
- Wear resistance of HVOF sprayed NiSiCrFeB, WC-Co/NiSiCrFeB, WC-Co, and WC-Cr3C2-Ni rice harvesting blades
- Materials testing for welding and additive manufacturing applications
- Effect of heat treatment on mechanical properties of 3D printed polylactic acid parts
- Wear testing
- Friction and wear properties of heavy load truck composite brake linings
- Mechanical testing/Wear testing
- Effect of Lanthanum on mechanical and wear properties of high-pressure die-cast Mg-3Al-3Sn-3Sb alloy
- Production-Oriented testing
- A novel graphene-based Fe3O4 nanocomposite for magnetic particle inspection
- Materials testing for welding and additive manufacturing applications
- Effect of shielding gas combination on microstructure and mechanical properties of MIG welded stainless steel 316
