Simulation Of Thermal Stresses During Metal Additive Manufacturing

3D Printing of metallic parts has gained increasing attention over the last decade. Similar to prior established non-metallic 3D printing procedures [1-3], such as Stereolithography, Selective Laser Sintering (SLS) or Fused Deposition Modeling (FDM), Selective Laser Melting (SLM), Electronic-beam Melting (EBM) and Direct Metal Laser Sintering (DMLS) of metals offer all the advantages of Additive Manufacturing (AM) centered around manufacturability of very complex shapes.
  However, metal AM comes with additional challenges one has to face when preparing the design for printing. One of the biggest challenges is to create support structures which are necessary to:

• hold the part in place during printing (similar to SLS, FDM, etc.)

• facilitate heat transfer into the base plate

• prevent thermal warping due to thermal stresses

Schematic illustration of the localized melting process. Right: The laser hits and melts the powder causing thermal expansion in the peripheral volumes of the melting pool.  Left: After laser exposure the melted material cools down and solidifies causing the material to shrink and leaving residual stresses in the printed line.

To prevent the deformation due to thermal stresses, supports must be placed to :

• conduct the high temperatures more efficiently into the base plate. This will reduce the localized temperature gradients which directly effect the remaining residual stresses

• counteract the thermal warping to avoid global part distortion and to prevent contact of the part with the re-coater.

Schematic illustration of the part warping after support removal. Right: During the print the support structure holds the cantilever in place, counteracts the thermal warping and conducts heat to the base plate. Left: After support structure removal, the cantilever flanges warp due to the residual stresses ("spring-back"-effect) .

Residual stresses induced by a localized, rapid heating process (laser melts powder), and a fairly rapid cooling down process (solidification of the material) force the material to rapidly expand and contract, respectively, leaving residual stresses in each printed line [4]. For each line and each layer, the residual stresses are accumulated and will eventually cause a global deformation of the part. This "warping" may become significant enough so that the underlying support structure may yield and fail to hold the part in place, or the deformed part may touch and damage the re-coater. Both phenomena will eventually lead to printing failure. 

Finding the right support configuration to counteract is not an easy process. Often due to the complex shapes of the part designs, it is hard to predict where and how the part will deform solely based on experience. Thus, there is a need for tools that assist in the decision making process for finding the proper support structure.
  A promising technology to predict and optimize support structures is the application of thermo-mechanical simulations often realized via Finite Element Method (FEM). These tools facilitate different model techniques to predict the deformation via the manufacturing process and provide feedback to the engineers to optimize the support structures and to eventually reduce the risk of printing failure. The model techniques that are commonly being employed can be categorized in one, or in a combination of the following:

• Inherent Strain (IS) Method - fast, less accurate.   This method commonly facilitates prior analysis of a hatching-scale model to determine residual plastic strains which are then applied to the individual hatching regions in a layer by layer fashion. This is a technique that has been adapted from welding simulation and modified for SLM simulation applications and appears as promising and fast solution [5].

• Volume by Volume (VbV) or Layer by Layer (LbL) Method - slower than IS, more accurate than IS.   Here a representative Surface Heat Flux (SHFLX) or Body Heat Flux (BHFLX) are applied to a target volume (e.g.hatching volume) or an entire layer for a representative time. The magnitude of the heat fluxes and the application time depend on the machine specific laser power and scanning speed. Since this method requires transient thermo-mechanical simulation models, it is more accurate than the IS method but also slower due to the higher computational load. This method has found its application from research projects into industry and can be used with any advanced FE simulation code. It has great potential not only due to its ability to predict deformation but also to reveal volumes with higher thermal load and greater risk of accumulating thermal stresses [6,7]

• Detailed Microscopic Thermo-Mechanical Modeling - most accurate, very slow.   This method is probably the most accurate approach to predict the thermal stresses during SLM. For such models, the thermo-mechanical process is simulated for each individual laser track. Due to the very fine resolution, this simulation method requires immense computational power and thus has not yet found its way into commercial applications. Nevertheless, this is the most desired approach for simulating metal AM since it allows full insight into the microscopic accumulation of the residual stresses and their effect of global part warping. [8,9,11]

However, one of the biggest challenges that metal AM simulation applications is facing, is the right balance between model complexity, which will determine the model accuracy, and simulation time to provide feedback to the engineers for further optimization of support structures. To win the race and establish a fundamental position on the AM simulation market, commercial and non-commercial software providers are forced to speed up the simulation time of their products, without compromising the accuracy of the prediction of the AM process. Facilitating of Graphic Processing Units (GPU) [10,11] or implementing adapted FE approaches with advanced mesh facilitation [12,13] appear as promising approaches for that.

References:
[1]  Kruth, J-P., Ming-Chuan Leu, and T. Nakagawa. "Progress in additive manufacturing and rapid prototyping." CIRP Annals-Manufacturing Technology 47.2 (1998): 525-540.
[2] Frazier, William E. "Metal additive manufacturing: a review." Journal of Materials Engineering and Performance 23.6 (2014): 1917-1928.
[3] Guo, Nannan, and Ming C. Leu. "Additive manufacturing: technology, applications and research needs." Frontiers of Mechanical Engineering 8.3 (2013): 215-243.
[4] Mercelis, Peter, and Jean-Pierre Kruth. "Residual stresses in selective laser sintering and selective laser melting." Rapid Prototyping Journal 12.5 (2006): 254-265.
[5] Keller, Nils, and Vasily Ploshikhin. "New method for fast predictions of residual stress and distortion of am parts." Solid Freefrom Fabrication(2014): 1229-1237.
[6] Keller, N., et al. "Thermo-mechanical Simulation of Additive Layer Manufacturing of Titanium Aerospace structures." LightMAT Conference. Vol. 3. No. 5. 2013.
[7] Neugebauer, Fabian, et al. "Simulation of selective laser melting using process specific layer based meshing." Proc. Fraunhofer Direct Digital Manufacturing Conf.(DDMC 2014), Axel Demmer, Aachen, Germany. 2014.
[8] Kruth, Jean-Pierre, et al. "Selective laser melting of iron-based powder."Journal of Materials Processing Technology 149.1 (2004): 616-622.
[9] Fu, C. H., and Y. B. Guo. "3-DIMENSIONAL FINITE ELEMENT MODELING OF SELECTIVE LASER MELTING TI-6AL-4V ALLOY."
[10] Keller N, Ploshikhin V (2014) New method for fast predictions of residual stress and distortion of AM parts. Solid Freeform Fabrication Symposium, Austin, Texas
[11] Megahed, Mustafa, et al. "Metal additive-manufacturing process and residual stress modeling." Integrating Materials and Manufacturing Innovation 5.1 (2016): 1.
[12] Zeng, K., et al. "Comparison of 3DSIM thermal modelling of selective laser melting using new dynamic meshing method to ANSYS." Materials Science and Technology 31.8 (2015): 945-956.
[13] Pal, Deepankar, et al. "An integrated approach to additive manufacturing simulations using physics based, coupled multiscale process modeling."Journal of Manufacturing Science and Engineering 136.6 (2014): 061022.