Thermal Operating Window in Selective Laser Melting Processes

The laser additive manufacturing (AM) approach includes processes such as selective laser sintering (SLS) and selective laser melting (SLM) and is a repetitive, multilayer manufacturing process wherein a laser beam melts the material in a powder bed according to the slices of a corresponding threedimensional (3D) computer-aided design (CAD) model. Stepwise production reduces complex 3D geometries into simpler 2D manufacturing steps, thus also reducing manufacturing restrictions. Because of the high geometric freedom that it provides, AM facilitates new impulses for the design of functional parts by having the potential to manufacture geometries that are impossible to manufacture using other processes. For these reasons, AM is now widely accepted as a new paradigm for the design and production of high-performance components for aerospace, medical, energy and automotive applications. Aerospace examples include complex fuel injector nozzles that previously required assembly of multiple parts and lightweight engineered structures that result in significant cost savings.

For example, the General Electric Company has successfully certified and implemented GE9X engine components such as T25 sensor housing, fuel nozzle tip and low-pressure turbine blades made using AM technologies (Fig. 1).

Figure 1.

SLM is a three-step layer-based process using a powder bed: (1) a thin layer of metal powder is placed on a platform using a mechanical coating system; (2) a focused laser beam selectively melts the topmost layer of the powder bed; and (3) after solidification, the platform is lowered by the layer thickness, and the cycle begins again. Complex parts can be built up, typically using thousands of layers.

In AM, processes comprise two stages, which include the following:

the data preparation stage;

The schematic diagram of these stages is shown in Fig. 2.

Figure 2.

The schematic diagram of selective laser melting (SLM) and the various phenomena occurring during the process and that affect both the physical behaviour of the material and the final result of production are shown in Fig. 3.

Figure 3.

Particularly, the most important physical phenomena are powder melting, molten metal pool formation, keyhole formation, thermal fluid dynamics, vapourisation, spattering of powder and liquid/ molten material, Marangoni effect, capillary effect, gaseous diffusion, instability of the pool, occurrence of powder particles and powder particles partially molten, remelting, excess heating, reheating and cooling, solidification, microstructural phase transformation, bending and shrinkage [3–10].

All these multiple physical processes and effects are highly influenced by several dozen process parameters, particularly laser power (P), laser spot size (d), scanning speed (V), path distance (P_d), layer thickness (h), energy density (E_d) and scanning strategy.

Improper parameters may lead to severe part-quality issues, such as defects in the manufactured part’s structure.

Moreover, the manufacturer’s recommended processing parameters often become obsolete with the introduction of new materials, technology upgrades and new SLM machines. Preparatory trial-and- error experiments are time-consuming and laborious. Therefore, fast screening of the proper process parameters is highly desirable for the SLM process, in pursuance of desired part quality, shortened design cycle and reduced production cost.

In the selection of SLM/SLS conditions, it is important to determine the range of operating parameters settings, called as the manufacturing process parameters window or operating window, which will ensure process stability and consequently avoid defects in the manufactured products [10, 18, 21].

The operating window of SLM processes is most often presented in the form of a set of points on the plane of parameters, such as plane {scan speed V, laser beam power P }.

The instability of the process means undesirable phenomena occurring during melting, evaporation and solidification, which lead to splashing of the material in a liquid state, balling effect, increase in porosity and poor interlayer cohesion, cracks and other defects.

In most of the works conducted to determine the process parameter window, experiments were carried out with a large number of samples. Based on the results of porosity or specific density measurements of the samples, a window of optimal parameters was determined. Based on statistical models, the relationship between the porosity or specific density of the product and the energy density used in the manufacturing process was determined [17]. In a previous study [18], a numerical tool based on the fluid dynamic model is presented to predict laser power and scan speed window to manufacture pore-free printed parts without lack of fusion and keyhole pores.

In this paper, an approximate method for determination of the process parameter window is presented based on the thermal limitations of the SLM processes.

If the energy of the laser beam indenting on the powder layer surface is sufficient, melting begins, and the solid–liquid interface is formed and propagates into the powder layer. The temperature and phase changes during the heat input are illustrated on Fig. 4. The thermal limitations of the SLM process are presented by points A and B.

Figure 4.

The upper thermal limit relates to the possibility of occurrence of boiling, vaporising and injecting of the molten metal. Therefore, in this case, the isotherm (here, T_B) must be lower than the boiling point (Fig. 4).

The lower thermal limit guarantees that the powder layer is completely molten and, partially, the underlying layer is remelting to ensure proper bonding between the layers.

The SLM/SLS conditions that drive to these limits can be considered as critical and can be defined as the thermal operating window.

Comprehensive reviews of the thermal problems, modelling, computer simulations and experimental investigations of the SLM/SLS processes have been presented in numerous works [3–15].

The determination of process windows from within a vast parameter space is a difficult task, especially for a large variety of feedstock powders used in SLM. The process window for each type of metal powder is typically determined through a sequential and time-consuming trial-and-error approach.

The paper presents the approximate approach for the determination of the critical conditions of the process and the operating window based on a simple thermodynamic model, in addition to its verification by means of computer simulation and experimental tests. The model has been developed with the basic idea of adequately representing the process within a simplified approach in order to reduce the computational time for practical use. For this reason, the model contains simplifications of the complex reality (surface tension effects, evaporation and thermo-flow dynamics are not simulated), aiming for a simplified simulation of heat transfer, leading to a reliable prediction of the operating window.

To find a relationship between the process parameters and the material’s temperature, the simple model based on balance of the input energy and melt enthalpy of powder material is proposed in this section.

Let us consider the melting process of a single track, as shown in Fig. 5.

Figure 5.

In mathematical modelling, the following assumptions were made in order to approximately determine the thermal operating window of SLM:

The powder phase is a quasi-homogenised continuum described by means of effective, i.e. spatially averaged, thermal and mechanical constant properties, without resolving the individual powder grains.

Let us make an energy balance for a unit of time; in this case, the mass of the powder melted by the laser beam is equal to: 2M=ρVA$$M = \rho VA$$

After considering the cross-sectional profile of the path, we have: 3M=ρkpwhtV$$M = \rho {k_p}w{h_t}V$$

Based on the mass conservation equation and taking into account the remelting of the underlying layer, we get the following: 4ht=(1−β)h+Δh$${h_t} = (1 - \beta )h + \Delta h$$ where β is the porosity of powder layer, h is the powder layer thickness and Δh is the thickness of the remelted material of the underlying layer.

The example of a typical cross-section of a track is shown in Fig. 6.

Figure 6.

The shape of the cross-sectional profile can be approximated by a parabolic curve (Fig. 7), where the coefficient profile k_p = ⅔, or by an elliptical profile, where k_p = π/4.

Figure 7.

Let us introduce the process efficiency coefficient being defined as η =P_m /P, where power P_m is the energy needed for melting over unit time and P is the laser beam power. The value of η depends on the laser energy transfer efficiency η_a and the melting efficiency η_m. The laser energy transfer efficiency is the ratio of energy that is being absorbed by the powder over the incident total laser energy, η_a = P_a /P. The second term is the melting efficiency η_m which describes the amount of energy that is used to create a molten pool in relation to the energy absorbed by the powder, i.e. η_m =P_m /P_a. Therefore, the process efficiency coefficient η = (P_a /P)(P_m /P_a) = η_a η_m.

The value of the energy transfer efficiency is determined experimentally, whereas the melting efficiency can be determined by computer simulation. A review of all the possible factors affecting the process efficiency is far beyond the scope of this paper.

Based on Figs 4 and 5 and the given assumptions, the energy balance for the lower and upper thermal limits is described as follows:

Point A – lower thermal limit (P_l): 5ηPldt=kpρwVdt[(1−β)h+Δh][ cs(Tm−T0)+Lm ]$$\eta {P_l}dt = {k_p}\rho wVdt[(1 - \beta )h + \Delta h]\left[ {{c_s}\left( {{T_m} - {T_0}} \right) + {L_m}} \right]$$

Point B – upper thermal limit (P_u): 6ηPudt=kpρwVdt[(1−β)h+Δh][ cl(TB−T0)+Lm ]$$\eta {P_u}dt = {k_p}\rho wVdt[(1 - \beta )h + \Delta h]\left[ {{c_l}\left( {{T_B} - {T_0}} \right) + {L_m}} \right]$$ where T_B = T_b – ΔP_B, the upper temperature limit for the thermal operating window (Fig. 3).

The temperature margin ΔT_B was introduced into the energy balance equation, Eq. (6), to prevent the molten material from boiling during the process, which may cause product defects.

The thickness of the remelted material Δh should be selected taking into account the structural integrity of the product.

The thermal limitations and processing window parameters of SLM are described by Eqs (5) and (6). The acceptable range of laser power from the point of view of product quality is as follows: 7kpρwVη[(1−β)h+Δh][ cs(Tm−T0)+Lm ]≤P≤kpρwVη[(1−β)h+Δh][ cl(TB−T0)+Lm ]$${{{k_p}\rho wV} \over \eta }[(1 - \beta )h + \Delta h]\left[ {{c_s}\left( {{T_m} - {T_0}} \right) + {L_m}} \right] \le P \le {{{k_p}\rho wV} \over \eta }[(1 - \beta )h + \Delta h]\left[ {{c_l}\left( {{T_B} - {T_0}} \right) + {L_m}} \right]$$

The relationship in Eq. (7) describes the initial prediction of the SLM thermal operating window on the plane {scanning speed V, laser beam power P}. It is a useful method for selection of the initial process conditions applying the software used in SLM practice, which is based on more accurate models. This approach significantly reduces the labour and time spent on the selection of SLM conditions.

In order to determine the degree of compliance of the given approach with the real SLM process, a computer simulation was carried out using the COMSOL Multiphysics software developed by COMSOL, Inc. [19,20].

The software used in models more adequately describes and provides insight into the complex phenomena underlying the mechanisms of powder bed melting, transient thermo-fluid dynamics and solidification. It allows to take into account the influence of surface tension on molten metal conventions, as well as the evaporation and gas-cooling effects.

The general equation governing heat transfer during powder heating used in the COMSOL Multiphysics simulation is as follows: 8∂(ρcpT)∂t+∇(ρcpT⋅v→)=∇(ke⋅∇T)+q$${{\partial \left( {\rho {c_p}T} \right)} \over {\partial t}} + \nabla \left( {\rho {c_p}T \cdot \vec v} \right) = \nabla \left( {{k_e} \cdot \nabla T} \right) + q$$ where ρ is the density, ρ_cp is the specific heat at constant pressure, T is the temperature, v represents the velocity field, k_e is the effective thermal conductivity of the powder layer and q is the internal volume heat generation. Here, k_e is calculated in COMSOL as the combination of thermal conductivities of the metal and the protective atmosphere (N₂). For the needs of the mathematical model and computer simulation, an individual coefficient β (porosity) was determined for each layer’s thickness, i.e. h = 25 μm, 30 μm and 35 μm. The porosity coefficient (β) of the powder was determined using CATIA V5 software developed by Dassault Systèmes based on the 3D model of the analysed powder bed.

The transport equations are applied to mass and momentum to describe velocity field of molten material.

Energy absorption depends on the heat source characteristicsThe laser beam power density distribution q_e for the SLM/SLS is assumed to be axisymmetric Gaussian.

9qe=2ηaPπre2exp(−2r2re2)$${q_e} = {{2{\eta _a}P} \over {\pi r_e^2}}\exp \left( { - {{2{r^2}} \over {r_e^2}}} \right)$$ where P is the laser power, r is the radial distance from the source’s centre, r_e is the effective laser beam radius at which the energy density is reduced to 1/e² at the centre of the laser spot.

The boundary conditions for Eq. (8) were assumed as shown in Fig. 8:

Figure 8.

Figure 8 shows the simplified geometry as applied to the present boundary conditions for the mathematical model.

The boundary conditions for walls A, B, C, D, E and F were as follows: 10ke∂T∂n=−σsε(T4−Ta4)−αk(T−Ta)$${k_e}{{\partial T} \over {\partial n}} = - {\sigma _s}\varepsilon \left( {{T^4} - T_a^4} \right) - {\alpha _k}\left( {T - {T_a}} \right)$$ where n is the direction normal to the considered wall, σ_S is the Stefan–Boltzmann constant, ε is the emissivity; α_k is the convective heat transfer coefficient and T_a is the ambient temperature.

11melting kl∂T∂n−ke∂T∂n=ρLdnsldt solidification ks∂T∂n−kl∂T∂n=ρLdnsldt$$\matrix{ {{\rm{\;melting\;}}{k_l}{{\partial T} \over {\partial n}} - {k_e}{{\partial T} \over {\partial n}} = \rho L{{d{n_{sl}}} \over {dt}}} \hfill \cr {{\rm{\;solidification\;}}{k_s}{{\partial T} \over {\partial n}} - {k_l}{{\partial T} \over {\partial n}} = \rho L{{d{n_{sl}}} \over {dt}}} \hfill \cr } $$ where n_sl is the displacement of the moving solid–liquid interfaces along their normal direction n.

The 3D models of the powder bed were made in CATIA V5 software in the Part Design module.

For the purposes of the simulation, three variants of the bed layer models were created representing thicknesses h = 25 m, 30 m and 35 m with a grain diameter of 20 m.

The experiment was performed in the New Manufacturing Technologies Department at Lukasiewicz Research Network – Institute of Aviation.

The test samples were produced on the 3D Printer SISMA MySint 100. The machine has a laser with a spot diameter 2 r_e = 55 m and a wavelength of 1,070 nm. During fabrication, the working chamber in the machine was filled with nitrogen gas to prevent oxidation of the fabricated specimens. The experiments were carried out using Mediloy S-Co powder (Co63.9Cr24.7W5.4Mo5.0Si) produced by BEGO GmbH & Co.

The physical properties of the powder were provided by manufacturer.

In the simulation, we assumed a change in the thermal conductivity coefficient of the powder material with temperature shown in Fig. 9.

Figure 9.

The thermophysical properties and other parameters used in the simulation are given in Table 1.

The surface absorptivity of molten material strongly depends on its chemical composition and on the interaction with the surrounding atmosphere. For example, oxidation of the surface of the liquid material can cause a significant increase of absorptivity. However, in this study, we assume that the surface oxidation is negligible. This assumption is justified since the SLM process was performed under a protective atmosphere (nitrogen N₂).

The SLM process parameters used in the experiment and simulation are shown in Table 2.

The physics-controlled meshing for the 3D model of the powder bed body is shown in Fig. 10A. An example of the simulation results is presented in Fig. 10B.

Figure 10.

The temperature distribution for the first layer is shown in Fig. 11, where the laser scanning direction is perpendicular to the drawing plane. The temperature isotherm curve is a series of quasi-ellipses. The position of the melting isotherm curve shows that the conditions are critical to the lower thermal limit due to the risk of incomplete melting of the powder layer.

Figure 11.

Computer simulations of the unstable process using parameters outside the process window and a stable process using parameters inside the window were carried out. The plane of parameters {scan speed V, laser beam power P} are shown in Fig. 12.

Figure 12.

The result of simulation after exceeding the upper thermal limit is illustrated in Fig. 13, where the occurrence of ejection molten material, which leads to spatter, is shown. This result has been confirmed experimentally as shown in Fig. 14.

Figure 13.

Figure 14.

The determined SLM operating window assuming a parabolic cross-sectional profile and the results of computer simulations and experimental tests are shown in Figs 12 and 15.

Figure 15.

Figure 16 shows, as examples, the results of SLM processes carried out under conditions presented by points (1) and (2) in Fig. 15. In condition (1), outside the operating window, the quality of the sample is low, in particular, the (side) surface roughness parameters are Rz = 110 μm and Ra = 23 μm.

Figure 16.

The SLM process carried out under condition (2), i.e. in the operating window, is characterised by products of a much higher quality, in particular, the surface roughness is many times lower, namely Rz = 23.6 μm and Ra = 6 μm.

Experimental studies have shown a fairly good agreement between the results of the approximate SLM model and the results of experiments and simulations. SLM processes performed with parameters from the approximate operating window were stable and showed acceptable product quality.

The paper presents an approximate determination of the operating window of the SLM process while maintaining thermal limitations. The determined thermal limits were confirmed by computer simulation and experiments. This allows to conclude about the usefulness of the approximate determination of the operating window for the preliminary selection of SLM conditions. In addition, it should be emphasised that all process parameters and material properties can be easily changed in the simulation code. This can be very helpful when trying to quickly determine a window of optimal process parameters for new materials.