Simulation of the Selective Laser Sintering Process

ENERGY ABSORPTION AND PENETRATION IN SELECTIVE LASER SINTERING: A RAY TRACING MODEL

X.C. Wang & J.P. Kruth K. U. Leuven - Department of Mechanical Engineering - Division PMA

ABSTRACT An analytical ray tracing model is developed to simulate the energy absorption and penetration during the selective laser sintering (SLS) of metal powders. The model is applied to a Fe-Cu powder mixture. It gives an evaluation of the energy absorption and penetration and an estimation of the sintering zone dimension. The simulations will help to understand the physical phenomena involved, to identify the processing window and to optimize the SLS process.

1. INTRODUCTION

Selective laser sintering is a Material Accretion Manufacturing or Rapid Prototyping (RP) technology (1). It produces parts in a layer-by-layer fashion. The SLS technology allows a direct coupling with the CAD-model of the product, in which successive cross sections are calculated, to produce three dimensional parts without dedicated tools, like dies, as used in conventional sintering. Total production time and cost can hence be reduced.

K.U. Leuven aims at the development of the SLS process to make metal parts directly from commercially available powders, without using a polymer binder or a specially developed metal powder. Some successful applications have been made to high strength powder mixtures, like Fe-Cu, WC-Co and TiC-Ni. In order to master well the process, it is necessary to investigate the influence of processing and material parameters, such as laser power, scan speed, mixture ratio and particle size. The utilization of a new powder mixture requires extensive testing, which can be expensive and time-consuming. The development of reliable analytical and numerical tools to analyze the SLS process is important to reduce the number of tests needed. The simulations will help us not only to get a better understanding of the physical phenomena involved (temperature evolution, phase changes, fluid and mechanical problems, etc.) but also to identify the processing window and to optimize the SLS process through proper selection of some processing and material parameters.

Although several physical phenomena are involved in the process and a coupling between them exists, SLS is mainly dominated by its thermal process. The actual investigation is limited to thermal simulations. An analytical ray tracing model is developed for evaluating the total energy incoupling (the ratio between the absorbed and the total input energy) and optical penetration of the laser beam (energy absorption profile versus the depth into the powder bed) and for estimating the sintering zone dimension. The model is then applied to a Fe-Cu powder mixture, irradiated by Nd:YAG or by CO2 laser, two suitable laser sources for direct SLS of metal parts.

2. SLS PROCESS

The basic material in SLS consists of a mixture of two metal powders: a high melting

161 point metal, called the structural powder and a low melting point powder, called the binder. This mixture is spread as a thin layer, normally between 0.1 mm to 0.5 mm, on top of a container by means of a deposition system then is heated by a moving laser beam to the temperature at which the binder melts.

With liquid formation there is rapid initial bonding due to the capillary forces exerted by the wetting liquid on the solid particles. This is the first stage of liquid phase sintering (LPS), called the rearrangement stage. The second (solution precipitation) and third (solid stage sintering) stage cause further densification of the parts. Because these stages are based on migration of atoms, those densification steps require longer sintering times.

In selective laser sintering, no pre-compaction is applied to the powder bed. This allows the reuse of unsintered powders. As a result, the powder bed is very loose. Another important characteristic is that the sintering time is extremely short in SLS, because the moving laser beam supplies energy to each particle only for about 1 ms ~ 0.1 s. Due to low powder density and short sintering time, only the rearrangement stage occurs during the laser heating. Once the binder is molten and has flown into the pores between the unmolten structural powders, the system cools down. No further densification may take place in such a short time interval. This results in very low density of the green parts. For getting functional 3D parts, it is indispensable to perform a post processing by, for example, an infiltration with liquid metal.

3. PHYSICAL PHENOMENA IN SLS

SLS is a complicated process, involving several physical phenomena. These include:

 Heat generation and transfer, including the heating of the powder bed and the cooling of the sintered sample;  Microstructure evolution, including the porosity evolution and phase changes (melting and solidification of the binder);  Fluid problem (molten binder flowing in the solid lattice);  Mechanical problem (no uniformly distributed thermal strains during the cooling stage may cause residual stresses and distortions of parts produced).

In these coexisting physical phenomena, the thermal problem is dominant. Knowing the temperature distribution and evolution is essential to describe suitably the SLS process. However, the temperature distribution and evolution is influenced by other phenomena. The different physical phenomena interact at different processing stages with different importance. As a result, a coupling analysis should be performed. This may complicate our task. Fortunately, the influence of other phenomena on the temperature evolution is weak because of the extremely short sintering time. For example, there is not enough time for the molten binder flowing really in the powder bed. It shows only a flowing trend before the situation is frozen. At the same time, this extremely short time does not allow the densification of the parts. Consequently, the porosity changes rarely during the SLS process. Even the influence of the phase changes is not so important due to the limited quantity of molten powder. Finally, without a real important large mechanical deformation in the material, the mechanical problem may be studied separately using the results of the thermal study as inputs. The uncoupling of the SLS process will simplify considerably our problem. As a

162 simplification and without losing much precision, only the thermal problem is taken into consideration in this paper.

4. A RAY TRACING MODEL

4.1. Energy Absorption and Penetration

During the selective laser sintering process, the powder mixture is irradiated by a moving laser beam. This is an energy transformation process, in which the light energy of the laser beam is converted into thermal energy that causes heating of the powder bed. It is important to understand the interaction between the laser beam and the powder bed. A good understanding of this interaction helps us not only to control more easily the process (so lead to more accurate parts having enhanced mechanical properties), but also to define a set of requirements for new sintering powders (hence lead to a easier development of powders more suitable for sintering).

It is evident that not all energy contributes to the heating of the powder bed. So a parameter measuring "energy absorption" should be defined. On the other hand, unlike an opaque continuous medium, the powder bed allows a certain penetration of the light energy of the laser beam though multiple reflection into the powders. In order to describe how the energy will be absorbed in depth, an "energy penetration" parameter should be introduced.

The absorption of the powder bed is described by the total energy incoupling. It is defined as the ratio between the absorbed and the total input energy:

Absorbed energy Total Energy Incoupling  100(%) (1) Input energy

The total energy incoupling into the powder bed should be distinguished from the material absorption coefficient. It accounts for multiple reflection/absorption of the light in powders and is influenced not only by the laser source through its wavelength but also by the powder bed itself through the powder material (so its absorption coefficient), mixture ratio, mean particle sizes and shapes, etc.

The energy penetration of a laser beam is defined by the absorption profile across the powder bed depth. It measures the optical penetrance of laser light into the powder bed or, in other words, the transparency of the powder bed to a given light. It gives us an idea how the laser energy penetrates into the powder bed. The energy penetration depends also, like the energy absorption, on several processing and material parameters, of which the wavelength of the laser beam, the powder materials, the mixture ratio and the mean particle sizes are most important. Since the thermal conduction in SLS powder beds is very weak due to its very low density, taking this energy penetration into consideration becomes indispensable to get reliable result.

4.2. Assumptions of the Model

In order to evaluate energy absorption and penetration during the direct selective laser sintering of metal powders, an analytical ray tracing model is developed. The simulation model is based on the following assumptions:

163  A mixture of two powders is studied. The particles are perfect spheres. Each powder has a uniform grain diameter, but the diameters of both powders differs;  The particles of the two materials are randomly located and distributed in space;  The laser strikes the powders perpendicularly to the powder bed surface;  The powder particles have a specular reflectivity;  The absorption coefficients of the powders are equal to their solid material values. The absorptivity is independent of the incident angle and of the temperature.  The powder bed is put in vacuum. This means that the ray path will not be influenced and no energy will be lost in the pores of the powder bed.

It should be noted that any of these assumptions is indispensable. If necessary they can be easily modified or extended without difficulty. For example, some possible extension of the model can be:

 any other particle shapes may be studied if only their geometry can be described mathematically;  size non-uniformity of each powder may be taken into consideration, as is often the case in the reality;  entrance angle is easily introduced if necessary;  it is possible to take into account the incident angle dependence and the temperature dependence of the absoptivity of powder particles;  diffuse reflectivity can be used instead of specular reflectivity.

4.3. Ray Reflection and Energy Absorption

A 2D illustration of the model is shown in Fig. 1.

Figure 1. 2D illustration of light reflection of the ray tracing model

A number of rays, randomly or regular located, are emitted from the xy-plane z = 0. They are perpendicular to the powder bed surface. Each ray has a certain amount of

164 energy, calculated from the laser power, the scan speed and other parameters. At each impingement on a particle, part of the energy of the emitted ray is absorbed by this particle and the rest is reflected. This reflection is assumed to follow a specular reflection law. This procedure continues for each emitted ray until the ray is considered to "disappear", in case of either being reflected outside of the powder bed through the z = 0 or z = c surface or its energy becoming negligible after several hits against particles.

During the simulation, the energy absorbed by each particle is accumulated. At the end, the energy absorbed by all P1 and P2 particles will be used to calculate the total energy incoupling and the energy absorbed respectively by both materials.

4.4. Estimation of the Sintering Zone through Laser Beam Scanning Simulations

Before real 3D parts may be fabricated using SLS technology, one should determine the track width and the sintering thickness of a single sintered line or the thickness of a single sintered layer. Investigation of the relation between these thickness and width and the processing parameters, including the laser power and scan speed is important to chose proper settings and to determine the required scan spacing and the powder layer thickness which can be sintered.

Due to the large porosity of SLS powder beds, the contact between particles is almost punctual. This makes it possible to neglect the heat transfer between particles. The ray tracing model may be applied to estimate roughly the dimension of sintered lines in SLS.

In the laser beam scanning simulation of a single line sintering, the real laser beam is represented as a bundle of parallel rays, equally spaced. The energy of each emitted ray is calculated from the energy distribution in the irradiated zone. This distribution depends on the power density, scan speed and other parameters. It varies in y direction (perpendicular to the laser beam scanning direction). In the scanning direction x, the energy distribution is uniform. The energy distribution for the uniform distributed cylindrical laser beam is given by:

 4P d 2  4y 2 1  y  d  2 e   vd 2 (2) 1  0 y  d  2 where P is total laser power, d is the diameter of the laser beam spot and v is the scan speed of the moving laser beam. The total energy of any emitted ray is calculated by integrating the energy distribution (Equation 2) around its initial position in x-y plane according to its representing zone.

During the laser beam scanning simulation, the absorbed energy of each individual th particle is accumulated to get its total absorbed energy (Ei for i particle). At the same time, we know the energy necessary to fuse this particle, calculated respectively for both materials according to the following equation:

Em  (cp  T  cl )    V (3)

165 where cp (KJ/KgK) is the specific heat, ΔT (K) is the temperature rise needed for 3 melting, cl (KJ/Kg) is the latent melt energy, ρ (kg/mm ) the density and V the volume of the spherical particle. At the end of the simulation, a simple comparison of the absorbed energy Ei to Em will determine whether any particle absorbs enough energy to melt or not. The sintering zone dimension is evaluated from the most side- wise molten particles.

5. VALIDATION AND APPLICATION

5.1. Validation of the Model

In order to check how the simulation results fit the reality, a series of absorption simulations were realized using different values of the absorption coefficient of individual particles, varying from zero to one. Figure 2 shows the comparison between simulations and measurements (2, 3). A good agreement is found.

80% d e B

r 70% e d w

o 60% P

50% o t Íï „Sim n i 40% g Í¼>QMeas n i l p

u 30% o c n I 20%

0% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Absorption of Plain Particle Material

Figure 2. Experimental validation of the model

5.2. Energy Absorption and Penetration in a Fe-Cu Powder Mixture

The developed ray tracing model is applied to a Fe-Cu powder mixture. This is a well-described powder mixture for liquid phase sintering with attractive mechanical properties: the hard Fe lattice is dispersed in a ductile Cu matrix. Fe-Cu system is one of first powder mixtures that have been used successfully in direct laser sintering to produce 3D metal parts at PMA. Much care should however be taken for this powder mixture due to the physical characters of two materials. Their melting points are relatively close (Fe: Tm = 1535 ºC and Cu: Tm = 1083 ºC) and their absorption coefficient, on the contrary, are very different (the absorption coefficient of Cu, the binder which should be melted, is very small compared to that of Fe). If no special precautions are taken, Fe particles tend to melt before Cu particles do. This results in a complete melting, it may shut off the micro channels, which are necessary to allow the evacuation of air or infiltration of liquid metal, and make it impossible to further

166 densify the remaining porosities of green parts during post treatments. The molten parts do not have the desired composite microstructure that ensures good mechanical properties and may yield high shrinkage and distortion (4).

A Fe-Cu powder bed is constructed with the material parameters corresponding to that used in our laboratory. The diameters of two powders are respectively 50 m (Fe) and 30 m (Cu). The mixture ratio of Cu is 30wt%. The powder assemblage is constructed with 2779 Fe spheres and 4844 Cu spheres.

Nd:YAG laser and CO2 laser are used in the simulations. The absorption coefficients of Fe and Cu, when irradiated by these two laser sources, are taken from (3). They are shown in Table 1.

Table 1. Absorption coefficient of Fe and Cu for Nd:YAG laser and for CO2 laser

Absorption coefficients

Materials YAG (λ=1.06 μm) CO2 (λ=10.6 μm) Fe 0.3 0.035 Cu 0.1 0.015

The simulations consist of emitting a series of randomly located rays. For each laser source, 5 simulations (tests) are realized. The total energy incoupling and the energy absorbed respectively by the two powders are given in Table 2. We find that Nd:YAG laser is much more absorbed by the powder. The efficiency of this laser energy compared to CO2 laser is also proved by the experiments (5).

Table 2. Total energy incoupling (Etotal) and the energy absorbed respectively by two powders (EFe and ECu)

Nd:YAG Laser (λ=1.06 μm) CO2 Laser (λ=10.6 μm)

Tests Etotal (%) EFe (%) ECu (%) Tests Etotal (%) EFe (%) ECu (%) 1 65.59 53.61 11.98 1 27.99 22.00 5.994 2 66.16 52.49 13.66 2 25.71 20.31 5.339 3 65.49 53.84 11.62 3 26.79 20.88 5.910 4 65.28 53.23 12.05 4 26.89 21.10 5.791 5 67.20 55.87 11.34 5 24.81 19.45 5.361 Average 65.96 53.81 12.13 Average 26.44 20.75 5.691

The energy penetration is illustrated in Fig. 3. We compare in this figure the ratio of the accumulated energy absorbed from the powder bed surface up to a certain depth versus the total absorbed energy at full depth of 1 mm. We find an important difference between both laser sources. We observe more than 70 % of the absorbed energy is concentrated within a depth of 0.2 mm for Nd:YAG laser, but only about 42 % within this depth for CO2 laser. Almost all energy (97.5%) is absorbed within a depth of 0.5 mm for Nd:YAG laser, but only 82.4% being absorbed within this same depth for CO2 laser. This more uniform absorption profile of CO2 means that more energy will be dissipated in the powder bed depth and less energy will contribute in binder melting.

y Nd: YAG Laser g r

e 0.8 n CO2 Laser E

s 0.7 b A

a 0.6 t o T

0.5 y g r

e 0.4 n E

s 0.3 b A

. 0.2 c c A 0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Depth (mm)

Figure 3. Accumulated absorbed energy in function of the powder bed depth: comparison of two laser sources

5.3. Estimation of Sintering Zone Dimension

The sintered thickness and sintered width of a single sintered line are estimated for the same Fe-Cu powder bed presented above, irradiated by a Nd:YAG laser. Three laser powers are studied, 8.1 W, 17.9 W and 28.1 W (these are effective powers, corresponding respectively to nominative powers of 40 W, 50 W and 60 W). The scan speed varies from 3 mm/s to 25 mm/s. Figure 4 shows the sintered thickness and width compared to measurements (4). A general agreement is found even though simulations give only a rough estimation by neglecting thermal conduction in the powder bed.

Power = 8.1, 17.9 & 28.1 W - Scan Speed = 3, 5, 7.5, 10, 15, 20 & 25 mm/s 2.00

1.60 )

m 1.40 m (

h t 1.20 d i W 1.00 &

e 0.80 n k c

i Thickness Simulations

h 0.60

T Thickness Measurements 0.40 Width Simulations Width Measurements 0.20 Trendline of Simulaiton Results

0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 Energy Density (J/mm2) P Figure 4. Sintering thickness and width versus energy density ( E  ) v  d for Nd:YAG laser: comparison between simulations and measurements

168 5.4. Processing Efficiency

The process efficiency of the laser is determined as the fraction of the laser energy that is theoretically needed to sinter the part and the laser energy that effectively is used. The minimum energy, that can melt Copper, can be calculated as follows:

Cu Cu Fe (4) Emin mCu .(cp .T cl ) mFe.(cp .T)

Cu,Fe where mCu,Fe is the mass of Fe and Cu of the powder mixture, cp is the heat Cu capacity of Cu and Fe at constant pressure, cl is the latent melt energy of Cu and T is the temperature rise for melting Cu. Finally, the process efficiency is calculated:

E   min process Pd / v (5) where d is the laser beam spot diameter. The process efficiency calculated from simulation results and measurements (4) are compared in Fig. 5.

Power = 8.1, 17.9 & 28.1 W - Scan Speed = 3, 5, 7.5, 10, 15, 20 & 25 mm/s 40.00

35.00 Calculation Based on the Simulations 30.00

) Calculation based on the Measuremets %

( Trendline of Simulation Results

c 25.00 n e i c i f f 20.00 E

c 15.00 o r P 10.00

0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 Energy Indensity (J/mm2) P Figure 5. Process efficiency of the laser versus energy density ( E  ) v  d for Nd:YAG laser: comparison between simulations and measurements

Here again, a good agreement between simulations and measurements is found. From this figure, we observe a decrease strongly of this efficiency with the increase of the energy density.

6. CONCLUDING REMARKS

In order to master well the SLS technology for direct sintering of metal powders and to optimize the process through the processing and material parameters, each new material combination requires extensive testing. This can be expensive and time-

169 consuming. Developing some analytical and numerical tools to simulate the SLS process should be helpful. However, a precise evaluation of the energy absorption and penetration is indispensable for getting a reliable simulation of the process. The simulation results reported in this paper show that the developed model may give a good estimation not only to the energy absorption and penetration but also to the sintering zone dimension.

Concerning the two laser sources, it is found that the Nd:YAG laser is more efficient in the direct selective laser sintering of metal powders: it is absorbed more by the Fe- Cu powder bed and by most other metal powder mixtures and the absorbed energy concentrated more near the surface. It is this part of energy that will contribute to binder melting and sintering. While for CO2 laser, the absorbed energy contributes more to heat that is uselessly dissipated deeper into the powder bed. It may be concluded that Nd:YAG laser is at the moment the best laser for selective laser sintering of metal powders. This laser is more efficient, it has a larger processing window and results in green parts with higher density.

An inconvenience does nevertheless exist for Nd:YAG laser. The concentration of the absorbed energy near the powder bed surface leads to a larger temperature gradient in depth. This will cause a larger stress gradient in this direction during the cooling stage. The produced parts tend to curl more. If the process is not well controlled, thermal deformation will cause cracks and delaminations. This is more probable to occur especially for the first layer of powder, which may fail to stick to the base plate.

ACKNOWLEDGEMENTS

This research is supported by the Belgian national fund IUAP P4/33. The authors would like to thank all involved in the collaboration in this research project.

REFERENCES

1 J.P. Kruth: 'Material incress manufacturing by rapid prototyping techniques'. Annals of the CIRP, 40(2) 603-614, 1991

2 N.K. Tolochko, T. Laoui, Y.V. Khlopkov, S.E. Mozzharov, V.I. Titov and M.B. Ignatiev: 'Absorptance of powder materials suitable for laser sintering', Rapid Prototyping Journal, 6(3), 2000

3 W.W. Duley: Laser Processing and Analysis of Materials, Plenum press, 1983, New York

4 J.P. Kruth, B. Van der Schueren, J.E. Bonse and B. Morren: 'Basic powder metallurgical aspects in selective metal powder sintering'. Annals of the CIRP, 45(1) 183-186, 1996

5 J.P. Kruth, P. Peeters, Th. Smolderen, J. Bonse, T. Laoui and L. Froyen: 'Comparison between CO2 and Nd:YAG lasers for use with selective laser sintering of steel-copper powders', Revue International de CFAO et d'informatique graphique, 13(4-5-6), 95-112, 1998