A pragmatic model for selective laser melting with evaporation
Introduction
Selective Laser Melting (SLM) is a rapid manufacturing technique in which three-dimensional parts of complex shape are produced in a layer-by-layer fashion, typically in small series. Examples of applications of this technology are biomedical implants [1], [2] and casting molds with sophisticated internal cooling channels [3], [4].
A typical configuration of a SLM machine is shown in Fig. 1. Most machines are equipped with a Nd-yttrium aluminum garnet (YAG) fiber-laser or a CO2-laser. The laser beam is deflected by galvano mirrors, which control the movement of the laser source over the surface of the powder bed. In each layer the laser beam follows a certain scanning path. Upon absorption of the laser radiation, the powder particles heat up and after melting and solidifying, a solid structure is formed. In this way, SLM allows functional parts with near full density to be produced directly, in contrast to selective laser sintering (SLS) where post-processing is needed to obtain fully dense parts [5]. When a layer is scanned, the build cylinder moves down one step—typically between 30 and 100 μm—and the next powder layer is placed upon the previous one by means of a powder coater mechanism. After all layers have been deposited, the powder which has not been scanned can be removed and the produced part can be taken out of the machine.
SLM is a complex process, giving rise to a multitude of physical phenomena. The laser beam interacts with the material, which is initially powder, but then melts to become liquid. The heat transfer in the material will be drastically different in the low-conductivity powder and in the densified metal parts. Temperature gradients in the liquid pool can give rise to convection—both natural convection and Marangoni. Surface tension effects may lead to wetting or balling of the liquid pool, depending on the circumstances.
A good understanding of the aforementioned phenomena is of crucial importance to be able to control the properties of the produced parts, such as microstructure, porosity and residual stress. Mathematical models can help to achieve this goal. In the past, considerable research has been performed to acquire insight into the SLM process and the related SLS technique, a process in which the powder does not melt but merely sinters, through numerical simulations. In what follows, we briefly discuss an illustrative selection. Kandis, Bergman and co-workers [6], [7] used a constitutive relation based on experimental measurements to account for the density change caused by sintering in SLS, and compared their simulations on polymer powders with experimentally produced parts. Their work was extended to three-dimensional parts and two-component metal powders by Zhang and co-workers [8], [9], [10], [11], [12], [13], taking into account fluid flow caused by capillary and gravity forces through Darcy’s law [8] or through the Navier–Stokes equations [13], investigating the effect of the powder layer thickness [9] and of the substrate [12], studying partial shrinkage [11]. The group of Childs developed a finite-element model for SLS/SLM using a similar viscous sintering law as Kandis and Bergman [6] to study the behavior of amorphous polymer powders [14], crystalline and glass-filled crystalline polymer powders [15], and stainless and tool steel powders [16]. Gusarov and co-workers studied in detail the phenomena related to the radiative heat transfer in powders and the interaction with the substrate. They investigated the contact conductivity in a powder bed [17] and developed a penetration heat transfer model for a powder layer on a fully [18] and partially [19], [20] reflecting substrate.
This work differs from most of the previous models in a number of respects. Where most of the aforementioned models study the quasi-steady-state solution of the heat transfer problem by employing a reference frame moving along with the heat source, we deliberately choose not to do so to obtain a model to study the effect of changing substrate structure, e.g. from a dense metal substrate to a deep powder bed. In our enthalpy formulation of the heat transfer equation, we take into account the various phase transitions exhibited by the investigated material, i.e. Ti6Al4V, including evaporation. The vapor phase is assumed to be taken away by the inert gas flow over the bed. Our goal is to obtain a simple and pragmatic, but versatile, model, grasping the essential physics in order to be useful in process control. For the time being, we hereby neglect certain important phenomena, such as Marangoni convection and surface tension driven shape evolution of the liquid bath. Through comparison with experimentally produced parts, we will show, however, that our model reproduces the essential features.
The remainder of this paper is organized as follows. In Section 2, the model formulation will be discussed. The results obtained with the model are given and discussed in Section 3. Section 4 concludes the paper.
Section snippets
General setup
Four phases are considered, namely the solid, liquid and vapor phase and a fourth pseudo-phase, the powder phase. In every computational cell, the phase distribution is given by the phase fractions . The algorithm consists of a sequential solution of the heat transfer equation, the translation of the new enthalpies in the new temperature field and phase distributions, the calculation of the shrinking in the new time step, and an update of the material properties. These various steps will be
Results and discussion
Fig. 6 shows for every value of the power input considered an example of an experimental melt pool cross-section. Fig. 7 shows the comparison of the simulated cross-section widths in both options, with and without evaporation, with the experimentally determined width. Fig. 8 shows the same plot for the remelting depth, i.e. the depth to which the substrate material has been remolten by the process. Fig. 9 compares the obtained cross-sections for both options. The case without evaporation is
Conclusions
We have presented an engineering model to study the SLM process, and we have studied the influence of incorporating or neglecting the effects of evaporation. From the results, it is clear that, for the energy density inputs used in this work, evaporation occurs. The bath temperatures achieved when neglecting the evaporation phenomenon are unrealistic. Although the model is relatively simple and contains certain limiting assumptions, insight can be gained in the SLM process by analyzing the
Acknowledgments
The authors thank Dr. A. Gusarov and Dr. M. Rombouts for insightful discussions. F.V. acknowledges the financial support of the Research Foundation—Flanders (FWO—Vlaanderen) through a postdoctoral fellowship. T.C. acknowledges the financial support from the KU Leuven IOF-project IOF-KP/06. J.H. acknowledges the financial support from the IWT Grant SB-73161. L.P. acknowledges the financial support from the IWT Grant SB-61446. The simulations were performed on the computer cluster of the HPC
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