This document summarizes simulations of the thermo-mechanical characteristics of electron beam additive manufacturing (EBAM). A 3D finite element model was developed to investigate thermal response, residual stress, and deformation. The model considers conical heat flux, Gaussian intensity distribution, and linear heat decay. Temperature, stress, and deformation results are presented from simulations of single-line scans and multi-layer crossed raster patterns. Peak tensile stresses occur at the solidification front, and maximum deformation follows the beam path. Future work will focus on simulating hatch melting patterns.

1. SIMULATIONS OF THERMO-MECHANICAL
CHARACTERISTICS IN ELECTRON BEAM
ADDITIVE MANUFACTURING (EBAM)
Ninggang (George) Shen
Dr. Kevin Chou
11/14/2012
The University of Alabama-Mechanical Engineering 1

2. Outline of the contents
1. Introduction
2. Thermo-mechanical modeling
3. FE model application
4. Thermo-mechanical analysis
5. Conclusions
6. Future work
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3. 1. Introduction and research objectives
What’s Electron Beam Additive Manufacturing (EBAM)?
• Metallic powders melt by electron beam
• Rapid self-cool to solidify
• Produced in layer-building fashion
Why EBAM?
• Be able to build full-density functional metallic products
• Eco-friendly
• High building rate (Ti-6Al-4V: 25-50 cm3/hour [1])
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4. 1. Introduction and research objectives
Powder materials
• Study of porosity effects on heat transfer
Metallic powders are preheated to slightly sintered before each deposition;
Porosities in powder bed affect thermal response very much
Fig. 1 SEM picture of Ti-6Al-4V powder Fig 2. SEM picture of sintered Ti-6Al-4V powder
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5. 1. Introduction and research objectives
Potential part quality problem in EBAM:
• Delamination
The induced residual stresses are greater than the bonding ability between layers
Fig. 3 Delamination [2]
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6. 1. Introduction and research objectives
A 3D Finite Element (FE) thermo-mechanical model
was developed to:
• Investigate the thermo-mechanical response in EBAM
• Behavior of thermal and residual stress
• Deformation analysis
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7. 2. Thermo-mechanical modeling
Assumptions:
• Conical volumetric body heat flux
• Gaussian intensity distribution in deposition plane
• Linear decay along penetration
Fig. 4 Actual keyhole example and idealization [3] Fig. 5 Horizontal intensity distribution @ z = 0
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8. 2. Thermo-mechanical modeling
Fig. 4 Thermal & mechanical bulk material materials [4,5] Fig. 5 Thermal conductivity of both bulk and powder
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9. 2. Thermo-mechanical modeling
Tab. 1 Truth table of material determination
DTemp > 0 DTemp < 0
Temp < Tmelting 0 0
Temp > Tmelting 0 1
†0 – powder, 1 – solid
• Latent heat of fusion is considered as well
Fig. 6 Flow chart of the user subroutine
coupled UMATH and DFLUX
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10. 3. FE model application
Tab. 2 Parameters in the melting simulation
Parameters Values
Solidus temperature, TS ( C) 1605
Liquidus temperature, TL ( C) 1665
Latent heat of fusion, Lf (kJ/Kg) 440
Electron beam diameter, Φ (mm) 0.4
Absorption efficiency, η 0.9
Scan speed, v (m/sec) 0.4
Acceleration voltage, U (kV) 60
Beam current, Ib (mA) 2
Powder layer thickness, t-layer (mm) 0.1
Porosity, φ 30%
Beam penetration depth, dP (mm) 0.1
Fig. 7 New FE model configuration
Preheat temperature, Tpreheat ( C) 750
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11. 3. FE model application
Fig. 8 Schematic of the cross-raster scan pattern
applied in the multi-layer EBAM thermal
analysis.
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12. 4. Thermo-mechanical analysis
Fig. 10 the simulated residual stress profile comparison
Fig. 9 the simulated temperature contour comparison
Fig. 11 the simulated residual stress distribution comparison
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13. 4. Thermo-mechanical analysis
Fig. 12 Simulated temperature fields and molten pool Fig. 13 Simulated temperature fields and molten pool
geometry. geometry for raster scan: a) the temperature fields of
layer-1; b) the cross sectional view of the field in a).
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14. 4. Thermo-mechanical analysis
Fig. 14 Simulated temperature history and thermal
stress histories close the beam center starting point. Fig. 15 Simulated thermal stress fields of single straight scan
just before cooling: a) Longitudinal stress; b) Transverse stress.
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15. 4. Thermo-mechanical analysis
Fig. 16 Simulated residual stress fields of single straight
scan: a) Longitudinal stress; b) Transverse stress.
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16. 4. Thermo-mechanical analysis
Fig. 17 Simulated thermal stress and its cross sectional view.
Fig. 18 Simulated thermal stress fields and their cross
sectional views at the end of the 10 sec break between
two sequential layers: a) Longitudinal stress; b)
Transverse stress.
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17. 4. Thermo-mechanical analysis
Fig. 19 Simulated residual stress fields and their cross
sectional views: a) Longitudinal stress; b) Transverse
stress.
Fig. 20 Simulated deformations (mm) for: a) Single straight
scan; b) Multi-layer crossed raster scan.
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18. 5. Conclusions
• The raster scan pattern affects the temperatures and molten pool due to the
residual heat from previous adjacent scan
• Thermal stress histories on top (for both longitudinal and transverse)
Compressive – just before beam coming; Tensile - solidified
• Vertical thermal stress distribution (for both longitudinal and transverse)
Tensile in solidified and the compressive just beneath the tensile
• Vertical residual stress distribution (for both longitudinal and transverse)
Max. tensile in solidified and it decreases to the compressive for a certain penetration.
• The largest deformation follows the track of beam center
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19. 6. Future work
Fig. 21 Hatch melting
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20. Acknowledgement
Sponsor: NASA, No. NNX11AM11A
Collaborator: Marshall Space Flight Center (Huntsville, AL),
Advanced Manufacturing Team.
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21. Q&A
Thank you for your attention!
Any Question?
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22. Reference
[1] Available from: http://www.arcam.com/.
[2] Zaeh, M. F., and Lutzmann, S., 2010, "Modelling and simulation of electron beam melting," Production
Engeering. Research and Development, 4, pp. 15-23.
[3] Lampa, C., Kaplan, A. F. H., Powell, J., and Magnusson, C., 1997, "An analytical thermodynamic model of laser
welding," Journal of Physics D: Applied Physics, 30(9), p. 1293.
[4] Yang, J., Sun, S., Brandt, M., and Yan, W., 2010, "Experimental investigation and 3D finite element prediction
of the heat affected zone during laser assisted machining of Ti6Al4V alloy," Journal of Materials Processing
Technology, 210(15), pp. 2215-2222.
[5] Liu, C., Wu, B., and Zhang, J., 2010, "Numerical Investigation of Residual Stress in Thick Titanium Alloy Plate
Joined with Electron Beam Welding," Metallurgical and Materials Transactions B, 41(5), pp. 1129-1138.
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