This document summarizes research on modeling the thermal effects of the electron beam additive manufacturing process, specifically how powder sintering affects temperature distribution and melt pool geometry. Key findings from simulations include higher temperatures and deeper melt pools with increasing powder porosity. Larger beam sizes produced shallower melt pools. Future work is proposed on modeling overhang structures, thermal effects at solid/powder interfaces, and thermo-mechanical analysis.

1. THERMAL MODELING OF ELECTRON BEAM
ADDITIVE MANUFACTURING PROCESS –
POWDER SINTERING EFFECTS
Ninggang (George) Shen
Dr. Kevin Chou
6/6/2012
The University of Alabama-Mechanical Engineering 1

2. Outline of the contents
1. Introduction & research objectives
2. Heat transfer and heat source modeling
3. Material properties & state changes
4. FE mode configuration
5. Model validation
6. Simulation results
7. Conclusions
8. Future work
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3. 1. Introduction and research objectives
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4. 1. Introduction and research objectives
Fig. 1 Melt ball formation [2]
Fig. 2 Delamination [2] 4
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5. 1. Introduction and research objectives
Fig. 3 SEM picture of Ti-6Al-4V powder
Fig 4. SEM picture of sintered Ti-6Al-4V powder
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6. 2. Heat transfer and heat source modeling
Assumption: Negligible molten flow within molten pool
Temperature distribution given by heat conduction within process domain
Radiation considered as boundary condition
No convection between part and surroundings due to vacuum
T - Temperature
2 2 2 
Q Q
T T T T x, y,z T T x , y , z - Absorbed heat flux
2 2 2
vs c - Specific heat capacity
c x y z c t x
T T T T
ρ - Density
λ - Thermal conductivity
vs - Constant speed of the moving heat source
Latent heat of fusion
0 T TS , ΔHf - latent heat of fusion
T TS
H T cd T Lf f f TS T TL , Tl - liquidus temperature
TL TS Ts - solidus temperature
T TL
1 fs - solid fraction
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7. 2. Heat transfer and heat source modeling
• The cross sectional geometry of keyhole is usually idealized as a cone
• The intensity distribution is considered as a conical source:
 Horizontal – Gaussian distribution
 Vertical – Decaying with increasing of penetration depth
Fig. 5 Actual keyhole example and idealization [3]
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8. 2. Heat transfer and heat source modeling
Heat source equation used in our study [4]:
2 2
8 UIb 8 x xs y ys
2 z
S x, y, z f z 2
exp 2 with f z 1
E E
h h
Max. density = 306 W/mm2
U 6 0 kV
Ib 2mA
If E
2mm
1
h 2mm
z 0
Fig. 6 Horizontal intensity distribution @ z = 0
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9. 3. Material properties & state changes
Fig. 7 Temperature dependent material properties of Ti-6Al-4V [5]
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10. 3. Material properties & state changes
Emissivity [6]: Thermal Conductivity [7]:
AH H
1 AH S
2 k kr kc
1
S
2 3 .0 8 2
2
0.908 16
AH 2 H 2 kc l T
3 kr k b u lk x
1.908 2 1 1
1 3 .0 8 2 1 3
S
εS – Emissivity of solid material
εH – Emissivity of the hole among adjacent powder particles
f – Fraction of total cavity surface
AH – The area fraction of the surface that is occupied by the radiation emitting holes
d – Mean pore diameter
D – Particle size
φ – Fractional porosity of the bed
l – Mean photon free path between scattering events, the particle diameter in this study
σ – Stefan-Boltzmann constant,
T – Temperature
x = b/R – Ratio of neck radius to particle radius
Λ – Normalized contact conductivity for the three packing structures.
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11. 3. Material properties & state changes
Tab. 1 Truth table of material determination
DTemp > 0 DTemp < 0
Temp < Tmelting 0 0
Temp > Tmelting 0 1
†0 – powder, 1 – solid
Fig. 8 Flow chart of the user
subroutine
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12. 4. FE model configuration
Tab. 2 Parameters in the simulation
Parameters Values
Solidus temperature, TS ( C) 1605 [8]
Liquidus temperature, TL ( C) 1665 [8]
Latent heat of fusion, Lf (kJ/Kg) 440 [8]
Electron beam diameter, Φ (mm) 0.2, 0.4, 0.7, 1.0
Absorption efficiency, η 0.9 [2]
Scan speed, v (mm/sec) 400 [2]
Acceleration voltage, U (kV) 60 [2]
Beam current, Ib (mA) 0.002 [2]
Powder layer thickness, t-layer (mm) 0.1 [2]
Porosity, φ 0, 0.3, 0.45,0.6
Beam penetration depth, dP (mm) 0.1[2]
Fig. 9 New FE model configuration
Preheat temperature, Tpreheat ( C) 760 [2]
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13. 5. Model validation
Fig. 10 Model geometry, ICs and BCs [9]
Fig. 11 Simulation results comparison with Wang et al [9]:
a) Temperature contour; b) Temperature distribution along beam center scan pass
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14. 6. Simulation results
Fig. 12 Temperature fields and molten pool geometries of solid and powder top layer
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15. 6. Simulation results
Fig. 13 Temperature fields and molten pool Fig. 14 Temperature histories and heating or cooling
geometries of powder bed of various levels of porosity rates of center point for various levels of porosity
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16. 6. Simulation results
Fig. 15 Temperature fields and molten pool geometries of various beam sizes
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17. 6. Simulation results
Tab. 3 The simulated conditions and molten pool sizes
Φ (mm) Material Length (µm) Width (µm) Depth (µm)
Solid 750 300 100
φ = 30% 850 400 123
0.4
φ = 45% 800 400 127
φ = 60% 750 400 134
0.2 - - 130
0.7 φ = 30% - - 80
1.0 - - 68
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18. 7. Conclusions
• Higher molten pool temperature is caused by to the high thermal resistance of
powder materials. The higher the porosity is, the higher molten pool temperature
will be and molten pool becomes deeper but shorter. The width of molten pool has
less correlation with porosity.
• A longer, wider and deeper melt pool with the powder top layer applied.
• Heat is generally trapped in the scanned region even if powder materials are
changed to solid after solidification,
• Cooling rate increases drastically due to greater temperature gradients around the
melt pool, even the thermal conductivity is low.
• A larger electron beam diameter → shallower molten pool, less the temperature
gradients, and a lower cooling rate. For the tested electron beam power level, the
beam size around 0.4 mm could be an adequate choice.
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19. 8. Future work
Fig. 17 Contour melting Fig. 18 Hatch melting
Fig. 16 IR camera – MCS640 from Mikron
Fig. 20 Measurement setup of
building a 1 in3 cube Fig. 21 Comparison of measurement and
simulation for Hatch melting
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20. 8. Future work
Fig. 22 Measured preheating Fig. 23 Simulated preheating
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21. 8. Future work
• Thermal process of manufacturing a part with overhang structure
(i.e. two kinds of substrate under a unique scan, both solid and powder substrate)
• Effects of the solid/powder interface in substrate on thermal process
• Thermo-mechanical analysis
Fig. 24 Molten pool geometries of solid substrate part and powder substrate part
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22. Acknowledgement
Sponsor: NASA, No. NNX11AM11A
Collaborator: Marshall Space Flight Center (Huntsville, AL),
Advanced Manufacturing Team.
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23. Q&A
Thank you!
Any Question?
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24. 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] Rouquette, S., Guo, J., and Le Masson, P., 2007, "Estimation of the parameters of a Gaussian heat source by
the Levenberg-Marquardt method: Application to the electron beam welding," International Journal of
Thermal Sciences, 46(2), pp. 128-138.
[5] 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.
[6] Sih, S. S., and Barlow, J. W., 2004, "The prediction of the emissivity and thermal conductivity of powder beds,"
Particulate Science and Technology, 22, pp. 291-304.
[7] Kolossov, S., Boillat, E., Glardon, R., Fischer, P., and Locher, M., 2004, "3D FE simulation for temperature
evolution in the selective laser sintering process," International Journal of Machine Tools and Manufacture,
44(2-3), pp. 117-123.
[8] Boyer, R., Welsch, G., and Collings, E. W., 1998, "Materials Properties Handbook: Titanium Alloys," ASM
InternationalMaterials Park, OH, USA, pp. 483-636.
[9] Wang, L., Felicelli, S., Gooroochurn, Y., Wang, P. T., and Horstemeyer, M. F., 2008, "Optimization of the LENS
process for steady molten pool size," Materials Science & Engineering A (Structural Materials: Properties,
Microstructure and Processing), 474, pp. 148-156.
[10] Hofmeister, W., Wert, M., Smugeresky, J., Philliber, J. A., Griffith, M., and Ensz, M. T., 1999, "Invesitigation of
solidification in the Laser Engineered Net Shaping (LENS) process," JOM, 51(7).
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25. Appendix I
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26. Appendix II
Other selected conditions comparison
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