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 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:
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 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:
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(1) |
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:
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:
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