History Reduction by Lumping for Time-Efficient Simulation of Additive Manufacturing

Abstract

Additive manufacturing is the process by which material is added layer by layer. In most cases, many layers are added, and the passes are lengthy relative to their thicknesses and widths. This makes finite element simulations of the process computationally demanding owing to the short time steps and large number of elements. The classical lumping approach in computational welding mechanics, popular in the 80s, is therefore, of renewed interest and is evaluated in this work. The method of lumping means that welds are merged. This allows fewer time steps and a coarser mesh. It was found that the computation time can be reduced considerably, with retained accuracy for the resulting temperatures and deformations. The residual stresses become, to a certain degree, smaller. The simulations were validated against a directed energy deposition (DED) experiment with alloy 625.a thermo-mechanical model where whole layers were added simultaneously when a part with 50 layers was built. This model was validated against an experiment. Keller et al. [17,18] described a model where several layers were added simultaneously. With their model they were able to predict deformation and residual stresses at the macroscopic level. In the current work the temperature and deformation evolution is studied when the passes are added transiently, and only lumped in the build direction. To the authors' knowledge there is no publication where the approach has been used in this way. The inherent strain method is another approach for fast prediction of the resulting deformation and residual stress in AM processes [19,20]. The method was first proposed for welding by Ueda and coworkers [21][22][23]. Li et al. [24,25] used the inherent strain approach, but instead of using strain, a residual stress tensor is added to each layer in the mechanical macro-scale model. The simulation was performed with a multi-scale model in three different scales. A micro-scale model was used to predict an equivalent heat source, which was the input to the meso-scale model. Because the AM process is very fast, it was assumed that the heat could be added to the whole layer simultaneously. In the thermo-mechanical meso-scale model, a residual stress tensor from one added layer was calculated.Finally, the mechanical model on the macro-scale was computed, wherein the material was added layer by layer and the pre-determined residual stress tensor was applied on each added layer. The drawback with the inherent strain method is that it often requires calibration. The inherent strains are in general sensitive to changes in the boundary conditions.The main aim of this work was to study the method lumping of welds, described above, and evaluate the error introduced in the modeling and the achieved reduction in computation time for the simulations. A detailed thermo-mechanical FE model was validated with in situ temperature and displacement measurements for directed energy deposition (DED) with alloy 625. All experimental data and results that are used for comparison with the sim...

Fast Detection of Heat Accumulation in Powder Bed Fusion Using Computationally Efficient Thermal Models

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