**Numerical-Experimental Study of the Consolidation Phenomenon in the Selective Laser Melting Process with a Thermo-Fluidic Coupled Model**

**Francisco Cordovilla 1,\*, Ángel García-Beltrán 1, Miguel Garzón 2, Diego A. Muñoz <sup>3</sup> and José L. Ocaña <sup>1</sup>**


Received: 4 July 2018; Accepted: 9 August 2018; Published: 12 August 2018

**Abstract:** One of the main limiting factors for a widespread industrial use of the Selective Laser Melting Process it its lack of productivity, which restricts the use of this technology just for high added-value components. Typically, the thickness of the metallic powder that is used lies on the scale of micrometers. The use of a layer up to one millimeter would be necessarily associated to a dramatic increase of productivity. Nevertheless, when the layer thickness increases, the complexity of consolidation phenomena makes the process difficult to be governed. The present work proposes a 3D finite element thermo-coupled model to study the evolution from the metallic powder to the final consolidated material, analyzing specifically the movements and loads of the melt pool, and defining the behavior of some critical thermophysical properties as a function of temperature and the phase of the material. This model uses advanced numerical tools such as the Arbitrary Lagrangean–Eulerian formulation and the Automatic Remeshing technique. A series of experiments have been carried out, using a high thickness powder layer, allowing for a deeper understanding of the consolidation phenomena and providing a reference to compare the results of the numerical calculations.

**Keywords:** Selective Laser Melting; thermo fluidic; phase change; consolidation; Arbitrary Lagrangean–Eulerian Method; metallic powder

#### **1. Introduction**

In the Selective Laser Melting Process (SLM), the objective, in an industrial context, is to manufacture continuous solid components layer by layer. It uses a laser beam to consolidate the metallic powder at each of the steps in the growth of the workpiece [1]. The layer-by-laser philosophy of production theoretically eliminates the geometrical complexity of the part as a restriction for the manufacturing process. This circumstance provides the additive manufacturing technologies with large advantages to face geometrically complicated designs and a high flexible demand, in comparison with conventional techniques [2].

As is well known, productivity is one of the main limiting factors for a wide use of the additive manufacturing technologies [3], restricting their industrial application to only high added value parts, such as aeronautical parts [4] or medical implants [5].

The use of high thickness powder layers in the SLM process can contribute to improve productivity by reducing the number of steps for a given height of the desired component. There are multiple

works, of theoretical or experimental nature, where the thickness of the powder layer and the diameter of the laser beam lies on the microscale. In reference [6], a layer of 30 μm is used to carry out an experimental parametrization of the process. Reference [7] calculates the evolution of the temperature during the SLM process considering a beam diameter of several tens of microns. If the thickness of the layer is turned into a scale ranging from several hundred microns up to 1 mm, and, the laser beam is adjusted to a diameter of several mm, the productivity of the process necessarily experiences a dramatic increase.

Although the relation between the size of the powder layer and the beam diameter with the productivity is extremely clear, there is neither significant research nor industrial usage of large beams and thicknesses for the SLM process. It can be associated with the more complex behavior of the melt pool, when a larger amount of material is involved, which makes the process more difficult to be governed.

Although most of the relevant phenomena in the consolidation of the material are present with small bed thicknesses, such as limited diffusivity associated to poor particle contact, phase changes, and, for the liquid metal, gradients of surface tension associated with Marangoni convection, or even recoil pressure; in the case of large thicknesses these factors strongly influence the size and shape of the melt pool leading to a relatively high degree of curvature of the geometry of the consolidated material.

There are different approaches to study the consolidation of the material during the SLM process. The work of [8], highlights very important aspects of the consolidation, such as the evolution of the material throughout several phases, powder, liquid and solid. The relevance of considering the evolution of the melt pool, with explicit use of the fluidic properties of the liquid metal, such as dynamic viscosity or surface tension, is emphasized. However, the use of a discrete particle model forces the representation of the domain to be at the scale of the metallic particles (several microns) and makes it difficult, from a computational point of view, to project the behavior of the melt pool on the final dimension of the consolidated material in a real process.

A totally different approach is carried out on the models based on the activation of layers of finite elements when they are reached by the laser beam, reproducing in this way the manufacturing of the part layer by laser [9]. These models depart from the final design of the part that is going to be manufactured, study the evolution of the temperature, and, in some cases, estimate the residual stresses in the bulk of consolidated material. No analysis of the phase change or the melt pool is performed. While this approach can provide interesting results, at little computational cost, associated to processes with a very low layer thickness, where the movements of the melt pool are very small, in the case of normal or high thickness of the powder bed, the simulation cannot depart from the final design of the part since, in these cases, the final shape of the consolidated material cannot be predicted with only thermal or mechanical stress considerations. For instance, in reference [10], it can be seen that the initial powder has given rise, as a consequence of the SLM process, to a drop-like profile in the cross section of the consolidated material. It can only be due to the surface tension when the metal was in liquid state.

The present work proposes the use of a coupled thermo-fluidic model in the frame of a moving mesh, in combination with experimental test of the process with a powder bed of 1 mm thickness. When a large thickness of the powder bed is considered, there is such an amount of liquid metal submitted to the effect of the surface tension that the differences between the original flat domain representing the powder bed and the arising droplet forces the domain not only to move but also to recursively experience re-meshing. The droplet formation process happens in a time scale of milliseconds. The model considers the evolution of the material during the different phases, powder, liquid and solid, associating some critical thermo-physical properties, such as thermal conductivity, dynamic viscosity or surface tension, with the temperature and the phase of the material, making specific considerations to describe phase change. The concatenation of the thermo-fluidic properties to describe two different phase changes, powder to liquid and liquid to solid, must be adapted to the characteristics of each process in particular. Sigmoid functions are proposed to describe the evolution

of the thermo-physical properties during the different states of the matter. The use of this explicit formulation for the phase change introduces an innovative way of dealing with it, which does not have high computational requirements. The application of the finite element method on domains representing the powder bed and the substrate, makes the study of the consolidation happen at a scale where the final macroscopic dimensions of the material can be predicted, thus favoring, in this way, its application to real industrial situations. The so-called Arbitrary Lagrangean–Eulerian formulation [11] is used to allow the movement of the mesh to be performed, which, along with some specific numerical tools, like Automatic Remeshing techniques, enables the movements of the melt pool to be fully represented. A series of experimental tests was carried out using a 1 mm thickness powder bed. These tests were used, in the first place, to understand some critical aspects associated to the use of large thicknesses. Finally, theoretical and experimental cross sections were compared, showing a good degree of agreement.
