thermal modeling of electron beam additive manufacturing process–powder sintering effects

THERMAL MODELING OF ELECTRON BEAM ADDITIVE MANUFACTURING PROCESS –

POWDER SINTERING EFFECTS

Ninggang (George) ShenDr. Kevin Chou

6/6/2012

The University of Alabama-Mechanical Engineering 1

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

The University of Alabama-Mechanical Engineering

Outline of the contents

2

Why AM?


1. Introduction and research objectives

What’s the Additive Manufacturing (AM)?

3D printing

Fused Deposition Modeling

Selective Laser Sintering

Electron Beam Additive Manufacturing (EBAM)

…

Complex design

Multi-piece assembly as one component

Why EBAM?High building rate (Ti-6Al-4V: 25-50 cm3/hour [1])

Benefits based on material• High strength/density ratio (e.g. Ti-6Al-4V)• Diffi cult and expensive to process with conventional method

Complex latti ce structure within the part is available

3



Introduction

Fig. 1 Melt ball formation [2]

Fig. 2 Delamination [2]

Potential part quality problem in EBAM:• Melt ball formation

Due to complex interaction between electron beam and irradiated materials while energy dissipation

• DelaminationThe induced residual stresses are greater than the bonding ability between layers due to temperature gradients from various reasons, such as selective processing as the complex designs

4



IntroductionPowder materials• Unknown effect of porosity on heat transfer

Metallic powders are preheated and sintered before each layer deposition; porosities affect thermal properties very much

Objectives

Develop a Finite Element (FE) thermal model to:• Couple the effect of multi-physics in EBAM• Investigate the effect of various porosities on heat

transfer in EBAM• Study the molten pool geometry with various

process parameters and porosities

Fig. 3 SEM picture of Ti-6Al-4V powder

Fig 4. SEM picture of sintered Ti-6Al-4V powder

5



Heat transfer governing equation

2 2 2, ,

2 2 2

T x y z

s

T T T T

QT T T T Tv

c c t xx y z

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 , ,x y zQ - Absorbed heat flux

c - Specific heat capacityρ - Densityλ - Thermal conductivityvs - Constant speed of the moving heat source

Latent heat of fusion

fH T cdT L f 0

1

S

L S

T T

T T

f ,

,S

S L

L

T T

T T T

T T

ΔHf - latent heat of fusion Tl - liquidus temperature Ts - solidus temperature fs - solid fraction

6

• 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]

Heat source modeling

7


21

zf z

h h

Heat source equation used in our study [4]:

with

Fig. 6 Horizontal intensity distribution @ z = 0

2 2

2 2

88, , exp

s sb

E E

x x y yUIS x y z f z

If

60

2

2

1

2

0

b

E

U kV

I mA

mm

h mm

z

Max. density = 306 W/mm2


Heat source modeling

8



Fig. 7 Temperature dependent material properties of Ti-6Al-4V [5]

Solid thermal and mechanical material properties

9


1H H H SA A

2

2

0.908

1.908 2 1HA

2

2

12 3.082

11 3.082 1

S

H

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.


Emissivity [6]: Thermal Conductivity [7]:

r ck k k

316

3ck l T r bulkk k x

Porosity dependent material properties

10



Fig. 8 Flow chart of the user subroutine

DTemp > 0 DTemp < 0

Temp < Tmelting 0 0

Temp > Tmelting 0 1

Tab. 1 Truth table of material determination

†0 – powder, 1 – solid

Material state changes

11


4. FE model configuration

Fig. 9 New FE model configuration

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]

Preheat temperature, Tpreheat (°C) 760 [2]

Tab. 2 Parameters in the simulation

12

IC: 600 ºC

IC: 20 ºC

BC: 20 ºC


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

13

Comparing to a LENS study from Mississippi State University (Wang et al. 2008)



Fig. 12 Temperature fields and molten pool geometries of solid and powder top layer

Solid layer VS powder layer

14



Fig. 13 Temperature fields and molten pool geometries of powder bed of various levels of porosity

Fig. 14 Temperature histories and heating or cooling rates of center point for various levels of porosity

Effects of various porosities

15



Fig. 15 Temperature fields and molten pool geometries of various beam sizes

Various of beam diameters

16



Summary

17

Φ (mm) Material Length (µm) Width (µm) Depth (µm)

0.4

Solid 750 300 100

φ = 30% 850 400 123

φ = 45% 800 400 127

φ = 60% 750 400 134

0.2

φ = 30%

- - 130

0.7 - - 80

1.0 - - 68

Tab. 3 The simulated conditions and molten pool sizes


7. Conclusions

18

• 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.


8. Future work

Fig. 16 IR camera – MCS640 from Mikron

Fig. 20 Measurement setup of building a 1 in3 cube

Fig. 17 Contour melting Fig. 18 Hatch melting

Experimental study

Fig. 21 Comparison of measurement and simulation for Hatch melting

19


8. Future work

Experimental study

Fig. 22 Measured preheating Fig. 23 Simulated preheating

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• 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


8. Future work

Fig. 24 Molten pool geometries of solid substrate part and powder substrate part

Numerical study

21

Sponsor: NASA, No. NNX11AM11ACollaborator: Marshall Space Flight Center (Huntsville, AL),

Advanced Manufacturing Team.


Acknowledgement

22

Thank you!


Q & A

Any Question?

23

[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).


Reference

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Appendix I

EBAM ApplicationsMedical Implants (standard or custom) [1]

Aerospace [1]

25


Appendix II

Other selected conditions comparison

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thermal modeling of electron beam additive manufacturing process–powder sintering effects

Documents

molten pool geometries

material properties

molten pool

powder materials

heat transfer

latent heat

thermal conductivity

international journal