Cloud native EDA tools & pre-optimized hardware platforms
Simpleware software was used to generate high quality unstructured meshes for the microstructure RVEs being analyzed. The multi-label mask feature in the software was able to easily convert grain labels provided into a finite element compatible mesh. Simpleware software was able to mesh grains of very disparate sizes/shapes while maintaining the lowest number of elements possible when other meshing programs failed to generate a mesh at all. Capturing the smooth features of grains in a microstructure through an unstructured mesh is paramount to make accurate predictions of stress/strain within a grain.
Robert Saunders and the Naval Research Laboratory for permission to publish this case study under the following:
DISTRIBUTION A: Approved for Public Release, Distribution is Unlimited
R. Saunders et al., Influence of Grain Size and Shape on Mechanical Properties of Metal AM Materials. Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference (2018, Austin, TX)
Metal powder-based additive manufacturing (PAM) processes typically produce microstructures with different grain sizes and aspect ratios, which affects the mechanical properties of the material. This research looked to better represent the local granular stress fields within the microstructure in a workflow using Simpleware software. The study built on previous constitutive models of a microstructure-informed model based on crystal plasticity. This work was based on a synthetic microstructure representative volume element (RVE) that was numerically generated.
When cubic hexahedral elements are used for discretizing the sample RVE (structured mesh), there is insufficient resolution to capture the grain boundary due to the stair stepped surfaces. The new model developed with Simpleware software tackled this problem by generating a smooth, watertight and multi-domain volumetric Finite Element (FE) mesh, which ensures that the grain boundary is accurately captured.
Comparison of conforming interfaces for grains from Simpleware meshing (left) with structured mesh showing gaps (right)
The results of the new unstructured mesh RVE were then compared to the previous results that used a structured mesh RVE while using simulation time and predicted RVE mechanical properties to determine the efficacy of the new method. This new method allows the local stress intensification to be better captured in the vicinity of the grain boundary, helps with the prediction of defects and void formation in the material and informs future insights into better understanding the performance of complex parts produced using PAM.
An RVE of a synthetic microstructure was generated to simulate grain evolution within 3D domains. The matrix data was converted to a bitmapped voxel image containing grey scale values equal to the grain labels, before being imported to Simpleware ScanIP for processing. The synthetic data was segmented to create a surface representation of each grain, and then exported as a surface and volume mesh. One problem of structured hexahedral meshes are their “stair stepping” effect, which produces a degradation in model accuracy. This was solved in the new model through Simpleware’s anti-alias and smoothing tools, ensuring smooth contours along grain boundaries.
The Simpleware mesh generated with Simpleware FE module was better able to capture the size of small grains at a suitable resolution, compared to the structured mesh. Furthermore, Simpleware’s meshing algorithm was used to convert the segmented boundaries of the mesh into a triangulated surface representation, before applying a multi-part surface decimation algorithm and Delaunay tessellation with tetrahedral elements. The non-uniform meshing scheme results in a more accurate representation of grain geometry, while also reducing total degrees of freedom in the model. This has the effect of decreasing computational cost without significantly affecting result quality.
Unstructured Simpleware mesh with 200k 10-noded tetrahedral elements with ~700k degrees of freedom (left) compared to structured mesh with 40x40x40 grid of 20-noded brick elements with ~810k degrees of freedom (right)
Specific boundary conditions and constitutive model definitions were added to the mesh, based on a microstructure-informed constitutive model. Simulation was carried out in Abaqus/Standard to subject the RVE sample to a uniaxial tensile load, using properties from the literature. The properties of the constitutive model were defined using different equations to represent grain shape, while periodic boundary conditions were enforced on all external faces of the RVE.
The new workflow was tested by running a taste case with an RVE of a single grain using the structured and hexahedral mesh. The same material properties, grain orientation, loading and boundary conditions, and dimensions were used. Results showed that the homogeneous normal stress-strain behavior in the loading direction produced identical results. The accuracy of the unstructured mesh was then tested using the RVE of a polycrystal material.
Homogenized stress-strain behavior of the microstructure RVE using hexahedral and tetrahedral FE meshes: Tetrahedral mesh better able to capture small grains than hexahedral mesh
Simulations showed differences in results, based on both grain orientation in the constitutive model, and more detailed capturing of stress concentration effects in the unstructured mesh. These results are due to the hexahedral mesh using equal element sizes that omit some small regions in the model to save on computational cost, leading to a misrepresentation of grain characteristics such as volume, size, and shape. In addition, this mesh introduces artificial stress intensification. By contrast, the tetrahedral meshes show the highest stresses in the grain due to being able to capture sharp corners in the geometry.
Mises stress contours of two selected grains within the RVE microstructure: Simpleware tetrahedral mesh (left) captures grain boundaries more accurately than a structured mesh (right)
The use of Simpleware software in this project to create a more accurate RVE mesh of the PAM results in a better understanding of local stress fields within grains, compared to previous structured models. While in agreement on homogenized behavior, the unstructured mesh showed a significant difference in results for local stress determination, which can be determined much more accurately using a well-refined unstructured mesh. Future work will focus on improving analysis of differences in grain orientation assignment, as well as testing of as-built AM microstructures to validate shape effects, studies of aspect ratio, grain boundary effects, load direction, and material point implementation.
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