Lawrence Livermore National Laboratory

The local SLM process is an extreme, thermally driven material transformation, as illustrated in the discussion of modeling at the powder scale. At the part scale, the goal is to capture the aggregate influence of the SLM process on the macroscopic state of the part during and at the completion of its fabrication. By choosing to ignore flow dynamics in the melt pool, the simulation can be cast as the thermo-mechanical response of a nonlinear solid continuum. Within that perspective, the powder can be represented as a reduced-density, low-strength solid. The deposition of the laser energy into the powder can then be represented by a volumetric energy source term. The spatial distribution derived by Gusarov et al.(Gusarov et al.: 2009) is one possible choice, which represents the heating in terms of parameters that naturally describe the physical problem. Gusarov introduces a simple knockdown factor to the total nominal laser power to acknowledge the effects of reflected radiation and metal evaporation. Melting can be represented thermally through a latent heat and mechanically as a near-total loss of strength. Having the temperature-dependent strength rise as temperature falls below Tsolidus is currently our only acknowledgement of the complex behavior in the "mushy zone" at the melt pool boundary.

With an effective medium model such as discussed here, the geometry of powder particles is not resolved. It is indeed a choice as to what powder volume is directly represented in the computational domain. For true part-scale spatial domains, the common modeling practice to date is to largely ignore the adjacent regions of un-melted powder, at most perhaps representing their thermal interaction with the part through some Neumann boundary condition. We have analyzed Representative Volume Element domains consisting of a cubic millimeter of material. (Hodge et al.: 2014) In this case, successive 50 µm layers of powder are initialized and scanned by moving the energy source location. To model the gross loss of porosity due to powder melting, an irreversible 'phase strain' was introduced into the thermo-mechanical constitutive model that is activated during the material's first excursion above Tsolidus. This 'phase strain' magnitude was simply assigned to result in a net volume associated with full-density material. If future powder-scale modeling can identify a phenomenological evolution law for porosity, e.g., based upon the local history of temperature and temperature gradients, then the part scale model could adaptively assign the appropriate local phase strain or at least output a map of regions likely to have unacceptable porosity.

Our approach to thermo-mechanical modeling of SLM fabrication is being pursued in the context of the computational perspective and resources at a national laboratory. Some of the present authors are involved in adapting the in-house, general purpose implicit nonlinear finite element code Diablo,(Solberg et al.: 2014) capable of effectively utilizing commodity parallel-processing platforms. Early efforts focused on developing SLM modeling and algorithmic approaches in the context of 50 μm layer-resolved simulations for representative volumes comprising 1 mm3.(Hodge et al.: 2014) That paper provides a detailed description of the balance laws, boundary conditions and material models utilized. These coupled thermo-mechanical simulations utilize the laser deposition model of Gusarov directed in a serpentine pattern with alternating layer orientations. These calculations typically used 32 to 128 processors simultaneously, eventually taking less than two days. Peak heating and cooling rates of O(105 K) are observed, as also reported in Schilp et al.(Schilp et al.: 2014) Importantly, these simulation highlight that it is misleading to think merely in terms of the temperature history of the material in the active powder layer. These simulations clearly show that the material located several or more layers below the active work surface is still undergoing significant temperature excursions, which will contribute to continued evolution of the local microstructure.

Watch a technical presentation on the effective medium model by Neil Hodge at the National Academy of Sciences Workshop on Predictive Theoretical and Computational Approaches for Additive Manufacturing that was held Wednesday, October 7 and Thursday, October 8, 2015.

Modeling approach

Modeling approach:

  • Treats powder as an under-dense, low strength solid. Laser material interaction treated using an energy source term
  • Models effects of melting, solidification, and solid state phase transformations. Includes material strength
  • Covers time scale to hours and length scales to centimeters
Contact: Neil Hodge

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