Article

A finite volume alternate direction implicit approach to modeling selective laser melting

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Abstract

Over the last decade, several studies have attempted to develop thermal models for analyzing the selective laser melting process with a vision to predict thermal stresses, microstructures and resulting mechanical properties of manufactured products. While a holistic model addressing all involved phenomena is yet to emerge, the existing partial models have already become computationally heavy. This is observed to go hand-in-hand with a trend across literature for the usage of finite element (FE) formulations for developing implicit 3D models. However, the 3D implicit FE models, though able to accurately simulate the process, are constrained by either the size or scale of the model domain. A second challenging aspect involves the inclusion of non-linear material behavior into the 3D implicit FE models. An alternating direction implicit (ADI) method based on a finite volume (FV) formulation is proposed for modeling single-layer and few-layers selective laser melting processes. The ADI technique is implemented and applied for two cases involving constant material properties and non-linear material behavior. The ADI FV method consume less time while having comparable accuracy with respect to 3D implicit FE models. Drawing on the comparative results, appropriate models are recommended for different scenarios and modeling domains.

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... The above thermal equations can then be solved using any of the different numerical techniques. [226][227][228][229][230] One of the most common material property for which an equivalent value is required when using a conductive heat transfer formulation is the emissivity of the powder bed. The current work is based on the predictive models proposed by Sih and Barlow 231-233 wherein a combination of the emissivity of the particles and the emissivity of the cavities in the powder bed is used ...
... The above governing equations and constitutive models are sufficient to develop a continuum model of the thermal conditions during SLM. 228,230,[234][235][236][237] The internal state variable approach 238 is well suited to the development of models for non-isothermal microstructural evolution. In general, a microstructure may be defined by different state variables such as grain size, volume fraction of grains, fraction of solid in solidification. ...
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... F is called the view factor, and can be chosen as a function of the emissivity of the powder bed leading to í µí²Œí µí²Œ í µí²“í µí²“ =The 3D finite volume alternate direction implicit model is a high-fidelity model developed for faster thermal calculations while still preserving accuracy (the accuracy is similar to Crank-Nicholson method). The theoretical basis can be found in[24]while the application of it in modelling selective laser melting can be found in[5]. ...
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... In the hybr main while th be combined n study with [19]. As refe at transfer d become owever, in w wherein s, thereby he pseudo- model [13] of discrete on implicit preserving [18] ). el with the algorithm rid model, he 3D FV in various respect to l 600 μm X rence, the problem implemen model, an mesh wit FVADI m local dom as transfe Figure 2pseudoan than the molten an [22] is implement nted hybrid m nd a 5 μm cu th the pseudo model, which main around th erred to the gl QUS on a 10 cubic mesh fo roblem is first the local 3DF alculate the tem l are saved on implementa this case, the s e laser meltin espectively. ...
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