Phase Change with Density Variation and Cylindrical Symmetry: Application to Selective Laser Melting

In this paper we introduce an analytical approach for predicting the melting radius during powder melting in selective laser melting (SLM) with minimum computation duration. The purpose of this work is to evaluate the suggested analytical expression in determining the melt pool geometry for SLM processes, by considering heat transfer and phase change effects with density variation and cylindrical symmetry. This allows for rendering first findings of the melt pool numerical prediction during SLM using a quasi-real-time calculation, which will contribute significantly in the process design and control, especially when applying novel powders. We consider the heat transfer problem associated with a heat source of power Q' (W/m) per unit length, activated along the span of a semi-infinite fusible material. As soon as the line heat source is activated, melting commences along the line of the heat source and propagates cylindrically outwards. The temperature field is also cylindrically symmetric. At small times (i.e., neglecting gravity and Marangoni effects), when the density of the solid material is less than that of the molten material (i.e., in the case of metallic powders), an annulus is created of which the outer interface separates the molten material from the solid. In this work we include the effect of convection on the melting process, which is shown to be relatively important. We also justify that the assumption of constant but different properties between the two material phases (liquid and solid) does not introduce significant errors in the calculations. A more important result; however, is that, if we assume constant energy input per unit length, there is an optimum power of the heat source that would result to a maximum amount of molten material when the heat source is deactivated. The model described above can be suitably applied in the case of selective laser melting (SLM) when one considers the heat energy transferred to the metallic powder bed during scanning. Using a characteristic time and length for the process, we can model the energy transfer by the laser as a heat source per unit length. The model was applied in a set of five experimental data, and it was demonstrated that it has the potential to quantitatively describe the SLM process.

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Transient Powder Melting in SLM Using an Analytical Model with Phase Change and Spherical Symmetry in a Semi-Infinite Medium

Journal of Manufacturing and Materials Processing ◽

10.3390/jmmp3020050 ◽

2019 ◽

Vol 3 (2) ◽

pp. 50

Author(s):

Marios M. Fyrillas ◽

Loucas Papadakis

Keyword(s):

Heat Transfer ◽

Heat Source ◽

Phase Change ◽

Square Root ◽

Spherical Coordinates ◽

Laser Melting ◽

Finite Radius ◽

Element Analysis ◽

Analytical Expression ◽

Melt Pool

In this work, we introduce an analytical expression for approximating the transient melting radius during powder melting in Selective Laser Melting (SLM) assumed with a stationary laser heat source. The purpose of this work is to evaluate the suggested analytical approach in determining the melt pool geometry during laser processing, by considering heat transfer and phase change effects. This will allow for the rendering of the first findings on the way to a quasi-real time calculation of the melt pool during laser melting, which will contribute significantly to the process design and control, especially when new powders are applied. Initially, we consider the heat transfer process associated with a point heat source, releasing a continuous and constant power (in a semi-infinite powder bed. On the point of the heat source the temperature is infinite, and the material starts to melt spherically outwards, creating an interface that separates the solid from the molten material; we assume different properties between the two phases. Unlike the cases of the cartesian and cylindrical coordinates, (in a cartesian coordinate the heat source is over a plane, i.e., W/m2, and in cylindrical along a line, i.e., W/m), where the melting process is proportional to the square root of time, in spherical coordinates the melting stops at a finite radius, i.e., a maximum radius, which depends only on the heat source, the conductivity of the solid and the difference between the far-field temperature and the melting temperature of the material. Here we should also point out that to achieve continuous melting in spherical coordinates the power of the source must increase with the square root of the time. The obtained analytical expression for the maximum melting radius and the approximate expression for its dependence on the time compare well with the numerical results obtained by a finite element analysis.

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A Comparative Study Between Selective Laser Melting and Electron Beam Additive Manufacturing Based on Thermal Modeling

Volume 1: Advances in Aerospace Technology ◽

10.1115/imece2018-86428 ◽

2018 ◽

Cited By ~ 1

Author(s):

M. Shafiqur Rahman ◽

Paul J. Schilling ◽

Paul D. Herrington ◽

Uttam K. Chakravarty

Keyword(s):

Electron Beam ◽

Additive Manufacturing ◽

Heat Source ◽

Selective Laser Melting ◽

Thermal Modeling ◽

Maximum Temperature ◽

Full Density ◽

Rate Variation ◽

Laser Melting ◽

Melt Pool

Selective Laser Melting (SLM) and Electron Beam Additive Manufacturing (EBAM) are two of the most promising additive manufacturing technologies that can make full density metallic components using layer-by-layer fabrication methods. In this study, three-dimensional computational fluid dynamics models with Ti-6Al-4V powder were developed to conduct numerical simulations of both the SLM and EBAM processes. A moving conical volumetric heat source with Gaussian distribution and temperature-dependent thermal properties were incorporated in the thermal modeling of both processes. The melt-pool geometry and its thermal behavior were investigated numerically and results for temperature profile, cooling rate, variation in specific heat, density, thermal conductivity, and enthalpy were obtained with similar heat source specifications. Results obtained from the two models at the same maximum temperature of the melt pool were then compared to describe their deterministic features to be considered for industrial applications. Validation of the modeling was performed by comparing the EBAM simulation results with the EBAM experimental results for melt pool geometry.

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Finite Element Thermal Analysis of Melt Pool in Selective Laser Melting Process

Volume 1A: 38th Computers and Information in Engineering Conference ◽

10.1115/detc2018-85701 ◽

2018 ◽

Author(s):

Zhibo Luo ◽

Yaoyao Fiona Zhao

Keyword(s):

Heat Source ◽

Selective Laser Melting ◽

Computational Cost ◽

Melting Process ◽

Point Heat Source ◽

Laser Melting ◽

Line Heat Source ◽

Powder Bed ◽

Melt Pool ◽

Gaussian Point

Selective laser melting is one of the powder bed fusion processes which fabricates a part through layer-wised method. Due to the ability to build a customized and complex part, selective laser melting process has been broadly studied in academic and applied in industry. However, rapidly changed thermal cycles and extremely high-temperature gradients among the melt pool induce a periodically changed thermal stress in solidified layers and finally result in a distorted part. Therefore, the temperature distribution in the melt pool and the size and shape of the melt pool directly determine the mechanical and geometrical property of final part. As experimental trial-and-error method takes a huge amount of cost, different numerical methods have been adopted to estimate the transient temperature and thermal stress distribution in the melt pool and powder bed. The most existing research utilizes the moving Gaussian point heat source to model the profile of the melt pool, which consumes a significant amount of computational cost and cannot be used to implement the part-level simulation. This research proposes a new line heat source to replace the moving point heat source. Some efforts are applied to reduce the computational cost. Specifically, a relatively large step size is used for the line heat source to reduce the number of time steps. In addition, a mesh refinement scheme is adopted to reduce the number of cells in each time step by refining the mesh close to the heat source and coarsening the mesh far away from it. On the other hand, efforts are implemented to increase the accuracy of the simulation result. Temperature-dependent material properties are considered in this FE framework. In addition, material transition among powder, liquid, and solid are incorporated in the developed FE framework. In this study, temperature simulation of one scanning track based on self-developed FE code is applied for Stainless Steel 316L. The simulation results show that the temperature distribution and history of melt pool within line heat source are comparable to that of the moving Gaussian point heat source. While the simulation time is reduced by more than two times depending on the length of line heat input. Therefore, this FE model can be used to numerically investigate the process parameters and help to control the quality of the final part.

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Selective Laser Melting of Pre-Alloyed NiTi Powder: Single-Track Study and FE Modeling with Heat Source Calibration

Materials ◽

10.3390/ma14237486 ◽

2021 ◽

Vol 14 (23) ◽

pp. 7486

Author(s):

Stanislav V. Chernyshikhin ◽

Denis G. Firsov ◽

Igor V. Shishkovsky

Keyword(s):

Heat Source ◽

Thermal Behavior ◽

Selective Laser Melting ◽

Process Parameters ◽

Laser Power ◽

Scanning Speed ◽

Fe Modeling ◽

Single Track ◽

Laser Melting ◽

Melt Pool

Unique functional properties such as the low stiffness, superelasticity, and biocompatibility of nickel–titanium shape-memory alloys provide many applications for such materials. Selective laser melting of NiTi enables low-cost customization of devices and the manufacturing of highly complex geometries without subsequent machining. However, the technology requires optimization of process parameters in order to guarantee high mass density and to avoid deterioration of functional properties. In this work, the melt pool geometry, surface morphology, formation mode, and thermal behavior were studied. Multiple combinations of laser power and scanning speed were used for single-track preparation from pre-alloyed NiTi powder on a nitinol substrate. The experimental results show the influence of laser power and scanning speed on the depth, width, and depth-to-width aspect ratio. Additionally, a transient 3D FE model was employed to predict thermal behavior in the melt pool for different regimes. In this paper, the coefficients for a volumetric double-ellipsoid heat source were calibrated with bound optimization by a quadratic approximation algorithm, the design of experiments technique, and experimentally obtained data. The results of the simulation reveal the necessary conditions of transition from conduction to keyhole mode welding. Finally, by combining experimental and FE modeling results, the optimal SLM process parameters were evaluated as P = 77 W, V = 400 mm/s, h = 70 μm, and t = 50 μm, without printing of 3D samples.

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