Thermal modeling of directed energy deposition additive manufacturing using graph theory
Abstract
Purpose: The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach: Here, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings: The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications: This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermalmore »
- Authors:
-
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Univ. of Nebraska, Lincoln, NE (United States)
- Univ. of Nebraska, Lincoln, NE (United States)
- Publication Date:
- Research Org.:
- Univ. of Nebraska, Lincoln, NE (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1907973
- Grant/Contract Number:
- SC0021136
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Rapid Prototyping Journal
- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 2; Journal ID: ISSN 1355-2546
- Publisher:
- Emerald Group Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Thermal Modeling; Directed Energy Deposition; Titanium Alloy; Graph Theory
Citation Formats
Riensche, Alex, Severson, Jordan, Yavari, Reza, Piercy, Nicholas L., Cole, Kevin D., and Rao, Prahalada. Thermal modeling of directed energy deposition additive manufacturing using graph theory. United States: N. p., 2022.
Web. doi:10.1108/rpj-07-2021-0184.
Riensche, Alex, Severson, Jordan, Yavari, Reza, Piercy, Nicholas L., Cole, Kevin D., & Rao, Prahalada. Thermal modeling of directed energy deposition additive manufacturing using graph theory. United States. https://doi.org/10.1108/rpj-07-2021-0184
Riensche, Alex, Severson, Jordan, Yavari, Reza, Piercy, Nicholas L., Cole, Kevin D., and Rao, Prahalada. Fri .
"Thermal modeling of directed energy deposition additive manufacturing using graph theory". United States. https://doi.org/10.1108/rpj-07-2021-0184. https://www.osti.gov/servlets/purl/1907973.
@article{osti_1907973,
title = {Thermal modeling of directed energy deposition additive manufacturing using graph theory},
author = {Riensche, Alex and Severson, Jordan and Yavari, Reza and Piercy, Nicholas L. and Cole, Kevin D. and Rao, Prahalada},
abstractNote = {Purpose: The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach: Here, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings: The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications: This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermal camera data from large parts. Practical implications: The DED process is particularly valuable for near-net shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation. Originality/value: This paper presents a new mesh-free computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.},
doi = {10.1108/rpj-07-2021-0184},
journal = {Rapid Prototyping Journal},
number = 2,
volume = 29,
place = {United States},
year = {Fri Aug 12 00:00:00 EDT 2022},
month = {Fri Aug 12 00:00:00 EDT 2022}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Correlation of Microstructure and Mechanical Properties of Metal Big Area Additive Manufacturing
journal, February 2019
- Shassere, Benjamin; Nycz, Andrzej; Noakes, Mark
- Applied Sciences, Vol. 9, Issue 4
Invited review article: Metal-additive manufacturing—Modeling strategies for application-optimized designs
journal, August 2018
- Bandyopadhyay, Amit; Traxel, Kellen D.
- Additive Manufacturing, Vol. 22
Computational heat transfer with spectral graph theory: Quantitative verification
journal, July 2020
- Cole, Kevin D.; Yavari, M. Reza; Rao, Prahalada K.
- International Journal of Thermal Sciences, Vol. 153
Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of Ti–6Al–4V
journal, January 2015
- Heigel, J. C.; Michaleris, P.; Reutzel, E. W.
- Additive Manufacturing, Vol. 5
Benchmarking build simulation software for laser powder bed fusion of metals
journal, December 2020
- Peter, Noha; Pitts, Zachary; Thompson, Spencer
- Additive Manufacturing, Vol. 36
A new physics-based model for laser directed energy deposition (powder-fed additive manufacturing): From single-track to multi-track and multi-layer
journal, January 2019
- Huang, Yuze; Khamesee, Mir Behrad; Toyserkani, Ehsan
- Optics & Laser Technology, Vol. 109
Part-scale thermal simulation of laser powder bed fusion using graph theory: Effect of thermal history on porosity, microstructure evolution, and recoater crash
journal, June 2021
- Yavari, Reza; Smoqi, Ziyad; Riensche, Alex
- Materials & Design, Vol. 204
Simulation of metallic powder bed additive manufacturing processes with the finite element method: A critical review
journal, August 2016
- Schoinochoritis, Babis; Chantzis, Dimitrios; Salonitis, Konstantinos
- Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 231, Issue 1
Anisotropic properties of directed energy deposition (DED)-processed Ti–6Al–4V
journal, October 2016
- Wolff, Sarah; Lee, Taekyung; Faierson, Eric
- Journal of Manufacturing Processes, Vol. 24
Multi-sensor investigations of optical emissions and their relations to directed energy deposition processes and quality
journal, May 2018
- Stutzman, Christopher B.; Nassar, Abdalla R.; Reutzel, Edward W.
- Additive Manufacturing, Vol. 21
Toward the digital twin of additive manufacturing: Integrating thermal simulations, sensing, and analytics to detect process faults
journal, January 2020
- Gaikwad, Aniruddha; Yavari, Reza; Montazeri, Mohammad
- IISE Transactions, Vol. 52, Issue 11
Temperature distribution in laser-clad multi-layers
journal, August 2004
- Jendrzejewski, R.; Kreja, I.; Śliwiński, G.
- Materials Science and Engineering: A, Vol. 379, Issue 1-2
Application of Directed Energy Deposition-Based Additive Manufacturing in Repair
journal, August 2019
- Saboori, Abdollah; Aversa, Alberta; Marchese, Giulio
- Applied Sciences, Vol. 9, Issue 16
Thermal Modeling in Metal Additive Manufacturing Using Graph Theory: Experimental Validation With Laser Powder Bed Fusion Using In Situ Infrared Thermography Data
journal, September 2020
- Reza Yavari, M.; Williams, Richard J.; Cole, Kevin D.
- Journal of Manufacturing Science and Engineering, Vol. 142, Issue 12
Modeling forced convection in the thermal simulation of laser cladding processes
journal, February 2015
- Gouge, Michael F.; Heigel, Jarred C.; Michaleris, Panagiotis
- The International Journal of Advanced Manufacturing Technology, Vol. 79, Issue 1-4
Experimental comparison of residual stresses for a thermomechanical model for the simulation of selective laser melting
journal, October 2016
- Hodge, N. E.; Ferencz, R. M.; Vignes, R. M.
- Additive Manufacturing, Vol. 12
Residual Strain Predictions for a Powder Bed Fusion Inconel 625 Single Cantilever Part
journal, July 2019
- Yang, Yangzhan; Allen, Madie; London, Tyler
- Integrating Materials and Manufacturing Innovation, Vol. 8, Issue 3
Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by Directed Energy Deposition: Modelling and experimental calibration
journal, March 2019
- Lu, Xufei; Lin, Xin; Chiumenti, Michele
- Additive Manufacturing, Vol. 26
Additive manufacturing of metallic components – Process, structure and properties
journal, March 2018
- DebRoy, T.; Wei, H. L.; Zuback, J. S.
- Progress in Materials Science, Vol. 92
Graph characteristics from the heat kernel trace
journal, November 2009
- Xiao, Bai; Hancock, Edwin R.; Wilson, Richard C.
- Pattern Recognition, Vol. 42, Issue 11
Understanding the Microstructure Formation of Ti-6Al-4V During Direct Laser Deposition via In-Situ Thermal Monitoring
journal, January 2016
- Marshall, Garrett J.; Young, W. Joseph; Thompson, Scott M.
- JOM, Vol. 68, Issue 3
Modeling metal deposition in heat transfer analyses of additive manufacturing processes
journal, September 2014
- Michaleris, Panagiotis
- Finite Elements in Analysis and Design, Vol. 86
Residual Stress Measurement of Laser-Engineered Net Shaping AISI 410 Thin Plates Using Neutron Diffraction
journal, October 2008
- Pratt, P.; Felicelli, S. D.; Wang, L.
- Metallurgical and Materials Transactions A, Vol. 39, Issue 13
Heat and fluid flow in additive manufacturing—Part I: Modeling of powder bed fusion
journal, July 2018
- Mukherjee, T.; Wei, H. L.; De, A.
- Computational Materials Science, Vol. 150
3D spatial reconstruction of thermal characteristics in directed energy deposition through optical thermal imaging
journal, July 2015
- Kriczky, Dennis A.; Irwin, Jeff; Reutzel, Edward W.
- Journal of Materials Processing Technology, Vol. 221
An improved prediction of residual stresses and distortion in additive manufacturing
journal, January 2017
- Mukherjee, T.; Zhang, W.; DebRoy, T.
- Computational Materials Science, Vol. 126
Graph spectral image smoothing using the heat kernel
journal, November 2008
- Zhang, Fan; Hancock, Edwin R.
- Pattern Recognition, Vol. 41, Issue 11
Microstructural evolution in laser-deposited multilayer Ti-6Al-4V builds: Part II. Thermal modeling
journal, June 2004
- Kelly, S. M.; Kampe, S. L.
- Metallurgical and Materials Transactions A, Vol. 35, Issue 6
Finite element modeling and validation of thermomechanical behavior of Ti-6Al-4V in directed energy deposition additive manufacturing
journal, October 2016
- Yang, Qingcheng; Zhang, Pu; Cheng, Lin
- Additive Manufacturing, Vol. 12
Digitally twinned additive manufacturing: Detecting flaws in laser powder bed fusion by combining thermal simulations with in-situ meltpool sensor data
journal, December 2021
- Yavari, R.; Riensche, A.; Tekerek, E.
- Materials & Design, Vol. 211
Distortion minimization of laser‐processed components through control of laser scanning patterns
journal, December 2002
- Dai, K.; Shaw, L.
- Rapid Prototyping Journal, Vol. 8, Issue 5
A survey of finite element analysis of temperature and thermal stress fields in powder bed fusion Additive Manufacturing
journal, May 2018
- Luo, Zhibo; Zhao, Yaoyao
- Additive Manufacturing, Vol. 21
Thermal Modeling in Metal Additive Manufacturing Using Graph Theory
journal, May 2019
- Yavari, M. Reza; Cole, Kevin D.; Rao, Prahalada
- Journal of Manufacturing Science and Engineering, Vol. 141, Issue 7
Mechanistic models for additive manufacturing of metallic components
journal, February 2021
- Wei, H. L.; Mukherjee, T.; Zhang, W.
- Progress in Materials Science, Vol. 116
On thermal modeling of Additive Manufacturing processes
journal, January 2018
- Foteinopoulos, Panagis; Papacharalampopoulos, Alexios; Stavropoulos, Panagiotis
- CIRP Journal of Manufacturing Science and Technology, Vol. 20
The metallurgy and processing science of metal additive manufacturing
journal, March 2016
- Sames, W. J.; List, F. A.; Pannala, S.
- International Materials Reviews, Vol. 61, Issue 5
Modelling of metal deposition
journal, October 2011
- Lundbäck, Andreas; Lindgren, Lars-Erik
- Finite Elements in Analysis and Design, Vol. 47, Issue 10
Process Maps for Predicting Residual Stress and Melt Pool Size in the Laser-Based Fabrication of Thin-Walled Structures
journal, March 2006
- Vasinonta, Aditad; Beuth, Jack L.; Griffith, Michelle
- Journal of Manufacturing Science and Engineering, Vol. 129, Issue 1
Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges
journal, December 2015
- King, W. E.; Anderson, A. T.; Ferencz, R. M.
- Applied Physics Reviews, Vol. 2, Issue 4
Residual stresses in LENS-deposited AISI 410 stainless steel plates
journal, November 2008
- Wang, Liang; Felicelli, Sergio D.; Pratt, Phillip
- Materials Science and Engineering: A, Vol. 496, Issue 1-2
Heat diffusion: Thermodynamic depth complexity of networks
journal, March 2012
- Escolano, Francisco; Hancock, Edwin R.; Lozano, Miguel A.
- Physical Review E, Vol. 85, Issue 3
Modelling of temperatures and heat flow within laser sintered part cakes
journal, October 2016
- Josupeit, Stefan; Ordia, Lavish; Schmid, Hans-Joachim
- Additive Manufacturing, Vol. 12
In-situ monitoring of melt pool images for porosity prediction in directed energy deposition processes
journal, March 2018
- Khanzadeh, Mojtaba; Chowdhury, Sudipta; Tschopp, Mark A.
- IISE Transactions, Vol. 51, Issue 5
Metal additive manufacturing: Technology, metallurgy and modelling
journal, September 2020
- Cooke, Shaun; Ahmadi, Keivan; Willerth, Stephanie
- Journal of Manufacturing Processes, Vol. 57
Distortion prediction and compensation in selective laser melting
journal, October 2017
- Afazov, Shukri; Denmark, Willem A. D.; Lazaro Toralles, Borja
- Additive Manufacturing, Vol. 17
Process-structure relationship in the directed energy deposition of cobalt-chromium alloy (Stellite 21) coatings
journal, January 2021
- Smoqi, Ziyad; Toddy, Joshua; Halliday, Harold (Scott)
- Materials & Design, Vol. 197
Impact of Interlayer Dwell Time on Microstructure and Mechanical Properties of Nickel and Titanium Alloys
journal, June 2017
- Foster, B. K.; Beese, A. M.; Keist, J. S.
- Metallurgical and Materials Transactions A, Vol. 48, Issue 9
A pragmatic part scale model for residual stress and distortion prediction in powder bed fusion
journal, August 2018
- Williams, Richard J.; Davies, Catrin M.; Hooper, Paul A.
- Additive Manufacturing, Vol. 22
Temperature and composition profile during double-track laser cladding of H13 tool steel
journal, December 2009
- He, X.; Yu, G.; Mazumder, J.
- Journal of Physics D: Applied Physics, Vol. 43, Issue 1
Data indicating temperature response of Ti–6Al–4V thin-walled structure during its additive manufacture via Laser Engineered Net Shaping
journal, June 2016
- Marshall, Garrett J.; Thompson, Scott M.; Shamsaei, Nima
- Data in Brief, Vol. 7
Numerical Analysis of Residual Stresses in Parts Produced by Selective Laser Melting Process
journal, January 2020
- Marques, Bruno M.; Andrade, Carlos M.; Neto, Diogo M.
- Procedia Manufacturing, Vol. 47
Thermal modeling in metal additive manufacturing using graph theory – Application to laser powder bed fusion of a large volume impeller
journal, May 2021
- Yavari, Reza; Williams, Richard; Riensche, Alex
- Additive Manufacturing, Vol. 41
Review on Computational Modeling of Process–Microstructure–Property Relationships in Metal Additive Manufacturing
journal, November 2019
- Gatsos, Theofilos; Elsayed, Karim A.; Zhai, Yuwei
- JOM, Vol. 72, Issue 1
Heterogeneous sensor-based condition monitoring in directed energy deposition
journal, December 2019
- Montazeri, Mohammad; Nassar, Abdalla R.; Stutzman, Christopher B.
- Additive Manufacturing, Vol. 30
The development of temperature fields and powder flow during laser direct metal deposition wall growth
journal, May 2004
- Pinkerton, A. J.; Li, L.
- Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 218, Issue 5
A framework to link localized cooling and properties of directed energy deposition (DED)-processed Ti-6Al-4V
journal, June 2017
- Wolff, Sarah J.; Lin, Stephen; Faierson, Eric J.
- Acta Materialia, Vol. 132
Thermal Behavior and Microstructural Evolution during Laser Deposition with Laser-Engineered Net Shaping: Part I. Numerical Calculations
journal, June 2008
- Zheng, B.; Zhou, Y.; Smugeresky, J. E.
- Metallurgical and Materials Transactions A, Vol. 39, Issue 9
Review on thermal analysis in laser-based additive manufacturing
journal, October 2018
- Yan, Zhaorui; Liu, Weiwei; Tang, Zijue
- Optics & Laser Technology, Vol. 106
Heat-flow simulation of laser remelting with experimenting validation
journal, February 1991
- Hoadley, A. F. A.; Rappaz, M.; Zimmermann, M.
- Metallurgical Transactions B, Vol. 22, Issue 1
Thermal and microstructural analysis of laser-based directed energy deposition for Ti-6Al-4V and Inconel 625 deposits
journal, February 2018
- Lia, Frederick; Park, Joshua Z.; Keist, Jayme S.
- Materials Science and Engineering: A, Vol. 717
A new finite element model for welding heat sources
journal, June 1984
- Goldak, John; Chakravarti, Aditya; Bibby, Malcolm
- Metallurgical Transactions B, Vol. 15, Issue 2