Lawrence Livermore National Laboratory

This simulation shows laser energy interacting with three successive layers of powder. The transformation from blue to red indicates the material has changed from powder to a consolidated form. The red contour line represents the melt pool, where outside the contour line the material has begun to solidify.

Predicting material properties of printed parts

The effective medium model is used to computationally predict the properties of metal parts additively manufactured using selective laser melting, a process where layers are melted together to produce a fully dense part.

Part of the internally funded strategic initiative to accelerate the certificaiton of additively manufactured metals, it models the fabrication of a complete additively manufactured part to gain an understanding of residual stress, density, and strength in three dimensions. The model treats the metal powder as a low-density, low-strength solid, and the interaction of the laser and powder is treated using an energy source term. In a simulation that covers as long as several hours of activity and a length scale of centimeters, the model seeks to capture such processes as melting, solidification, and solid-state phase transformations leading to the final, as-manufactured configuration of the part.

Modeling Approach

A Lagrangian thermo-mechanical capability is appropriate for this part-scale simulation. This approach also creates a ready path to downstream analysis for annealing warpage (residual stress relief) and perhaps the effects of machining material removal.

Successive melting sites are represented as individual voxel-like elements (or small group of elements), with a mesh that is nominally conformal to the intended blank outline. The simulation domain must also include "skin layers" to represent the effects of nearby, unmelted powder.

'Boundary conditions on those outer layers represent the effects of the bulk powder bed. The continuum treatment of the unconsolidated powder and boundary conditions applied thereon will eventually be informed by mesoscale modeling of the powder that generates effective media properties. Pending those efforts, expert judgment will be used to identify plausible ranges.

The mesh is only "active" for the current layer and those below that datum. As defined by the desired laser path, successive individual voxels receive energy as prescribed by an energy source term due to Gusarov et al. (citation below). The resulting temperature excursion drives a continuum hypo-elastic-plastic material model through a time-phase trajectory intended to notionally represent the porosity consolidation while melted and the local "lock-up" of the material as it re-solidifies.

Representing aggregate behavior

The research goal is to represent aggregate behavior and configuration of the fabricating part through the successive and collective response of these voxel transformations. The element activation approach is similar to that used by Zaeh et al. (Zaeh et al.: 2010) Their work is limited to a global model that smears the energy deposition over broader surface areas and has only been applied to relatively simple part geometries. With Lawrence Livermore's parallel codes and massive computer resources, resolution to more precise laser paths may be investigated for relatively complicated parts. Our effective medium modeling approach and assumptions are being validated against, and refined by, a series of test fabrications for notional geometries and their subsequent characterizations. The objectives are true part-scale modeling and prediction of residual stress, density, and deformation.


  • Spatial discretization strategies with adequate fidelity and tractable computational complexity. This may include approaches such as coarsening strategies (reverse adaptive mesh refinement) away from the vicinity of the most recently heat-effected zone, or potentially an advection of material from a near-process fine mesh toward a suitably coarser mesh.
  • Interchange with the powder/melt pool (mesoscale) modeling as to the adequacy of homogenized media properties and boundary conditions and their performance on target geometries of growing complexity.
  • Appropriate validation metrics leveraging the available characterization techniques and consistent with the system response quantities that are found to be indicative of eventual material and part performance.

Bob Ferencz


    Group Leader, Methods Development

    Bob Ferencz


    Group Leader, Methods Development