Keywords

1 Introduction

Metal additive manufacturing also known as MAM demonstrated remarkable ability in the fabrication of metal objects with complex geometry [1]. The geometric versatility of MAM stems from the layer-by-layer scanning of a heat source, which generally melts the metal powder or wires [2]. Among the different MAM processes flourishing, selective laser melting (SLM) offers advantages in developing fully dense, near-net-shape metallic parts [3]. The high-energy laser scans the previously placed powder layer, melting the powder particles beneath the beam, which leads to the creation of a melt pool [4]. A fine track of solid metal is developed as the laser beam travels, and by repeating these scans, the entire part is fabricated [5].

Nickel-based superalloys have become more prevalent in pivotal industries like aerospace, marine, and nuclear [6]. Due to its potential to retain its high strength at elevated temperatures, Inconel 718 (IN718) has gained acceptance in many applications [7]. SLM fabrication of IN718 components has addressed many of the challenges associated with conventional manufacturing methods [8]. However, the challenge regarding the process-induced defects, microstructure, and property relationships with process parameters and dimensional accuracy is still there for SLMed parts [9].

One viable approach for limiting or eliminating SLM defects and achieving higher build quality is to determine the temperature of melt pool during printing and control it accordingly. Further, the resulting microstructure and properties of SLMed parts are strongly influenced by temperature distribution, as it governs the solidification characteristics and grain growth [10]. The thermal history is also shown to have a strong effect on melt pool geometry and hence the dimensional accuracy of the SLMed parts [11]. Temperature distribution is also used in residual stress evaluation, grain growth estimation, and process parameter optimisation, in addition to assessing and limiting defects [12]. Thus, it is evident that temperature distribution plays an important role in realising defect free SLM builds, and therefore, an efficient framework is desired that can predict temperature distribution with a given set of process parameter condition. Several researchers incorporated different frameworks to obtain temperature profiles using experimental, analytical, and numerical approaches [13].

In the experimental domain, researchers started to monitor thermal history with the help of various sensors to observe in situ control of build quality [14]. Incorporating various monitoring sensors into the SLM setup and analysing the generated data is both costly and time intensive [15]. Therefore, developing rapid and cost-effective numerical modelling approaches to predict temperature distribution is so critical in the context of SLM.

Various multiscale modelling frameworks are also developed to study the temperature distribution in SLM builds [16]. These numerical models seem to be reliable to predict the thermal history in SLM because they also reveal the underlying physics of the process [17]. Studies using numerical modelling techniques for various combinations of process parameters on various material systems are documented in the literature [18, 19]. A numerical model with a Gaussian heat source is developed for a single bead print to predict the effect of important process conditions on SLM build [20]. In another study, a thermal simulation model is employed to assess the influence of scan speed on the developed solidification characteristics in the SLM parts [21]. The thermal model is useful to predict the temperature distribution as well as to develop the linkage between process parameters and the developed thermal history [22]. Zhao [23] used a FEM-based numerical model to foresee the residual stresses based on the thermal history during the printing of titanium alloy. Tan [24] proposed a thermo-microstructural model to determine the temperature history and grain growth for various SLM process parameters.

It is evident from the literature that several studies have been conducted on predicting the thermal history as a signature for various outcomes, including grain growth, distortion, residual stress, and quality control. But the point-wise temperature distribution or nodal thermal history is not yet fully explored by numerical modelling, and hence there is a need for an efficient approach to model temperature distribution in SLM builds. In this study, the multi-track, multi-layer SLM builds of IN718 were simulated using a three-dimensional FEM model. The temperature distribution on printed layers was evaluated, after which thermal profiles from simulated layers were extracted and the permissible limit exercise was performed to identify potential hotspots. Additionally, the impact of the layer rotation angle or scan pattern on the simulated thermal history was investigated. Figure 1 depicts the framework employed in the study.

Fig. 1
A flow diagram depicts the modeling framework. It begins with the material system and machine configuration as input, then leads to the thermal history simulation of modeling, further leads to the simulated results of layer wise temperature distribution, and ends at interpretation with hotspots.

Modelling framework used in the study

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2 Material and Methods

For thermal analysis, some physical assumptions related to the SLM process were taken into account. The physical characteristics of the powder particles were homogeneous, and the powder bed was regarded as a continuous media. The numerical modelling takes into account the material's temperature-dependent thermophysical properties. The convective heat transfer coefficient for the powder bed was assumed to be constant. The material data for IN718 with thermophysical properties was taken from the ANSYS mechanical engineering data source.

2.1 Governing Equations

Various key SLM process parameters such as laser power (P), scanning speed (v), hatch spacing (h), and layer thickness (t) are related to laser energy density (Ed) as:

$${E}_{d}=\frac{P}{v.t.h} \mathrm{J}/{\mathrm{mm}}^{3}$$
(1)

The partial differential equation for the transient heat transfer satisfied by the temporal and spatial distribution of the temperature field is given by [25]:

$$\rho c\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left(k\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(k\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(k\frac{\partial T}{\partial z}\right)+ Q$$
(2)

where T is the temperature, t is the interaction time, and ρ, c, k are material density, heat capacity, and thermal conductivity, respectively. Q represents the volumetric heat generation.

The initial state of the temperature distribution can be written as-

$${T\left(x,y,z,t\right)}_{t=o}={T}_{0}$$
(3)

where T0 is the ambient temperature. The following is a representation of the natural boundary condition with energy balance:

$$k\frac{\partial T}{\partial z}+h\left(T-{T}_{0}\right)+\sigma \varepsilon ({T}^{4}-{T}_{0}^{4})=Q$$
(4)

where h is the coefficient of convective heat transfer, ε is the emissivity of the surface, and σ represent the Stefan–Boltzmann constant.

It was assumed that the surface heat flux distribution throughout the powder bed follows a Gaussian distribution and is expressed by [26]

$$Q_{0} = \frac{32 AP}{{\pi D^{2} }} \exp \left( {\Delta \frac{{2r^{2} }}{{D^{2} }}} \right)$$
(5)

where A, P, and D represent the energy absorption coefficient, laser power, effective laser spot diameter. Further, r represents the radial distance between a point on the powder bed and laser spot.

2.2 Thermal History Simulation

The thermal history in the SLM builds was simulated by generating elemental temperature distributions on individual layers of the build. In this approach, results from a coaxial average sensor were simulated, comprising the temperature distribution for an arbitrary layer within the build with a given material system and process parameter combination. A simulated map of the instantaneous temperatures was generated within a circular field of view centred around the laser at the top surface of the build. Temperatures were averaged over the field of view radius, which was defined by the sensor radius, an input parameter. The average temperature will generally decrease as the sensor radius is increased since the thermal gradients are strongest in the melt pool vicinity.

First, a 3 mm cube was designed using 3D CAD modelling software, Ansys SpaceClaim, and imported into the numerical simulation module. The designed cube and considered layer for temperature distribution are shown in Fig. 2. Then a thermal model was employed with all the input process parameters given in Table 1. Sensor radius of 0.2 mm and the layer at 2 mm height from the bottom was considered for temperature distribution modelling.

Fig. 2
A 3 d and a 2 d diagram of a cube. Left, a 3 d cube. Right, a 2 d with a height of 3 millimeters from the base has a square layer inside the cube. The layer is at a height of 2 millimeters from the base. An upward arrow on the right is labeled build direction.

Representation of a 3 mm cube and b the layer at 2 mm from the bottom considered for the temperature distribution

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Table 1 Process parameters used for thermal simulation
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To further study the influence of the scan pattern or layer rotation angle, three adjacent layers, starting from the bottom layer, were simulated. As the layer start angle and layer rotation angle are 57° and 67°, the first three layers have starting angles of 57°, 124°, and 181°, respectively. The centre point on the individual layer was considered for the comparison, and the temperature at that point is taken as Tpoint. Moreover, the maximum temperature on each individual layer (Tmax) was also used to compare the thermal history of these layers. The individual layer results and comparative study are discussed in the next section.

3 Results and Discussions

3.1 Thermal History

By analysing the output visualisation toolkit files, the temperature distribution on the printed layer was predicted. The temperature distribution outputs for a layer at 2 mm from the bottom are shown in Fig. 3. Figure 3a depicts the temperature distribution over the whole layer, whereas Fig. 3b shows the fluctuations in the temperature as the layer is printed.

Fig. 3
A contour graph and a line graph. On the left, a schematic of a layer for temperature. On the right, a line graph of temperature versus time step plots a fluctuating line for temperature.

Representation of a thermal history and b variation of temperature with time during print

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Further, domains from the individual layer were extracted, and the permissible limit exercise was performed to find out the potential hotspots. The extracted domain from the layer at 2.0 mm height from the base is shown in Fig. 4, along with spots where the local temperature surpasses 1050 °C.

Fig. 4
A contour graph depicts multiple temperature hotspots on the 2 millimeter layer lines. The temperature ranges from 1050.37 to 1088.40 degrees Celsius at all the hotspots.

2 mm layer from the bottom showing hotspots where local temperature exceeds 1050 °C

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3.2 Effect of the Scan Pattern on the Thermal History

Individual layer results from three adjacent layers starting from the bottom layer are shown in Table 2. The temperature at the centre point of the layers (Tpoint) is increasing as the next layer is printed. Tpoint for the first layer is 988.5 °C, whereas for second layer it is significantly increased to 1049.3 °C (Figs. 5 and 6). This is due to the additional heating provided by the previously deposited layer. Similarly, the temperature of the third layer is increased to 1077.8 °C (Fig. 7). The thermal impact of the residual heat from deposited layers can also be seen in the maximum temperature (Tmax), which is also increasing as second and third layers are printed.

Table 2 Effect of scan pattern on thermal history
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Fig. 5
A contour graph and a line graph. On the left, a schematic of a layer depicts a temperature hotspot of 988.56 degrees Celsius. On the right, a graph plots a fluctuating line for temperature.

Temperature distribution on the first layer from base with Tpoint

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Fig. 6
A contour graph and a line graph. On the left, a schematic of a layer depicts a temperature hotspot of 1049.34 degrees Celsius. On the right, a graph plots a fluctuating line for temperature.

Temperature distribution on the second layer from with Tpoint

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Fig. 7
A contour graph and a line graph. On the left, a schematic of a layer depicts a temperature hotspot of 1077.87 degrees Celsius. On the right, a graph plots a fluctuating line for temperature.

Temperature distribution on the third layer from base with Tpoint

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The individual layer scans show how the layer rotation angle alters the number of tracks on a layer and also the length of an individual track. It demonstrates that any arbitrary point on the layer experiences a significantly different temperature history depending on the layer start and rotation angles. The effects of this altered temperature distribution can be seen in the developed residual stresses and distortion, but these outcomes are not in the scope of current study.

4 Conclusion

In this work, a numerical modelling approach was employed to study the temperature distribution in multi-track, multi-layer SLMed IN718. The simulated thermal history, corresponding to SLM process parameters, was further utilised in conducting permissible limit exercise and potential hotspots identification. These hotspots where the local temperature exceeds the permissible limit can be attributed to the potential process-induced defects commonly found in SLMed parts. Hence, this thermal history simulation can be utilised prior to the actual printing of SLMed parts to assess the temperature distribution and hotspots and optimise the SLM input parameters accordingly. Further, the effect of the scan pattern was also analysed by considering the temperature at the centre point and the maximum temperatures of individual adjacent layers. The different thermal histories in these layers are attributed to residual heat from previous layers and a change in the length of scan vectors due to different layer start and rotation angles.