Finite Element Simulation of Selective Laser Melting process considering Optical Penetration Depth of laser in powder bed
Graphical abstract
Introduction
Additive Manufacturing (AM) is referred to technologies that fabricate directly three-dimensional objects in layer-by-layer fashion. Selective Laser Melting (SLM), as one of the powder bed fusion (PBF) AM processes, enables production of complex metallic parts from a CAD model. A schematic of a typical SLM process is depicted in Fig. 1. In this process, in order to deposit powder layers with predefined thickness, an amount of powder comes up to the build table and a roller or blade spreads powder at the build platform. Full dense parts created by scanning a high intensity laser beam in a special pattern and local consolidation of the powder bed in successive layers. A neutral gas flow, usually nitrogen or argon gas, protects molten pool from oxidation. Nowadays, the flexibility of SLM process in manufacturing complex parts with high quality has led to an increase in its applications in many industries such as aerospace, medical, automotive and even jewelry. Nonetheless, this process still faces challenges including relative density, dimensional accuracy, surface quality, and thermal residual stresses. Moving a large energy density of laser beam on powder bed causes a high thermal gradient in the part, which may result in residual stress and thermal cracking in the part [1].
Normally for fabrication of each component from the desired material, choosing a set of appropriate process parameters such as laser power, scan speed, hatch distance, and scanning pattern is necessary to produce a part with acceptable dimensional accuracy and density [2]. On the other hand, geometry of the components has a decisive role in dimensional accuracy. In other words, because of different heat transfer conditions in each layer of the part as well as negligibly of heat transfer through the powder bed [3], geometry of the part affects the melt pool size significantly [2]. In addition, the melt pool size may increase considerably in some regions of each layer such as, the first track or U-turns in zigzag pattern [4]. Accordingly predicting the melt pool size is necessary to improve dimensional accuracy of SLM parts.
In recent years, numerous numerical models have been used considerably in predicting the effect of different process parameters on the temperature and stress distribution as well as the melt pool size of SLM. For instance, Matsumoto et al., proposed a two dimensional finite element method for predicting temperature and stress distribution within a single layer [6]. Yin et al. have used element birth and death method to obtain the temperature distribution in a single layer [7].
There are, however, many challenges in modeling a complex process such as SLM. The laser beam with uneven distribution of energy strikes a surface covered with metal particles with different shape and size. There are inevitable gaps among particles that let the laser beam penetrates through the powder bed. Consequently, the absorption of the laser beam by the particles as well as the multiple reflections from the surface of the particles causes the energy of the beam to be attenuated within the powder bed. The powder shape and size, of course, has dramatic effect on the actual absorption of the laser energy by the powder and the amount of penetration depth. Considering all these features makes the simulation very tough or even impossible. Therefore, simplifying assumptions have been applied in many SLM modeling efforts. Ma et al. and Dai et al. used constant temperature to simulate the laser spot in order to analyze the temperature and stress fields [8], [9]. Xiao et al. and Antony et al. used a constant heat flux to analyze the melting of the powder bed [10], [11]. An average uniform heat generation was used by Contuzzi et al. [12] and Song et al. [13] to represent the heat source. More accurate results were reported by Hussein et al. that supposed a Gaussian volumetric heat generation to simulate the process in order to obtain the melt pool size [14]. Ilin et al. used Goldak heat source in a 2D analysis to predict the melt pool size and the temperature distribution [15].
The effect of powder size and distribution has been neglected in the mentioned references. A number of experimental based investigations have studied the effect of powder size and scanning speed on the actual laser absorption by the powder. A ray tracing algorithm has been developed to describe laser power dissipation in depth of the powder in laser micro sintering process [16]. Badrossamay et al. developed a model to predict the absorption coefficient of the powder by considering the effect of scanning speed on the absorption coefficient of three types of steel powder [17]. Energy distribution and thermal and optical penetration of the laser beam in nickel and titanium powder bed were evaluated by Fischer et al. [18].
In this paper, a 3D non-linear transient finite element model is presented to predict the temperature distribution and melt pool dimensions in a multi-tracks pattern on powder substrate. In order to improve the accuracy of the model, a practical method is introduced to estimate the Optical Penetration Depth (OPD) into the powder bed. The model is compared with the experimental results for validation. In addition, the effect of three different scanning speeds on the melt pool dimensions in various regions of a layer is discussed.
Section snippets
Finite element modelling
ANSYS® was used to simulate the heat transfer within the metal powder during the SLM process. Fig. 2 shows geometry of the model, mesh structure, and scanning strategy. A volumetric heat generation with uniform distribution was introduced to represent the laser spot (the top view can be seen in the detailed view of Fig. 2). The dimensions of the square region were chosen so that the area of the laser spot in the model is the same as the one with circular spot. A subroutine was written based on
Temperature distribution
As a result of applying laser power to the powder bed, a very high temperature gradient occurs. Fig. 6 shows the temperature distribution at the end of the forth track for three cases of 80, 100, 150 mm/s scanning speed. The color code is set so that the temperature higher than the melting point is in gray color. Therefore, the difference in the melting zone can be distinguished at the end of the forth track. The maximum temperatures at the end of the process are predicted to be 2170, 2123, and
Conclusions
In this paper, a finite element model of the SLM process was developed. The Optical Penetration Depth of the laser beam in powder bed was considered in defining the heat source. The model was used to predict the melt pool dimensions of a single layer on powder bed of material stainless steel 316 L. Experimental data were used to calibrate the effective Optical Penetration Depth. The calibrated model, then, was validated by further experiments. The modeling results indicated good agreement with
Acknowledgments
The experimentation of this work had been carried out at University of Leeds, UK, during the PhD study of one of the authors (MB) who is grateful for the support of Prof. TH.C. Childs as his supervisor, as well as the Iranian Ministry of Research, Science and Education for a scholarship.
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