Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals

Journal Article · 18 November 2019 · Integrating Materials and Manufacturing Innovation

DOI: https://doi.org/10.1007/s40192-019-00158-z · OSTI ID:1575866

Chatterjee, Kamalika ^[1]; Carson, Robert A. ^[1]; Dawson, Paul R.  ^[1]

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1. Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering

The accuracy of the stresses predicted from crystal plasticity-based finite element formulation depends on estimation and control of the errors associated with the discretization. In the current work, the errors in the stress distribution are estimated in virtual polycrystalline samples of α-phase titanium (hexagonal close-packed phase of Ti–6Al–₄V). To estimate the error, the stress field, which does not possess inter-element continuity, is smoothed over a grain using an L₂ projection, thereby providing continuous stress distributions with inter-element continuity. The differences between the continuous (smooth) and discontinuous (raw) stress fields are calculated at individual Gauss quadrature points and used to estimate errors for corresponding elements and grains. Error estimations are performed for a Voronoi-tessellated microstructure, an equiaxed microstructure, and two microstructures with varying grain sizes for tensile loading extending into the fully plastic regime (≈ 5% extension). Magnitudes of the errors are found to depend on microstructural characteristics, particularly the shape and size of grains. Samples having variations in grain size or having less spherical grains exhibited higher errors than samples with uniformly sized, equiaxed grains, with the size variations having a more pronounced effect. In conclusion, errors correlate with proximity to grain boundaries at small (elastic) strains and with deformation-induced features (deformation bands) at large strains.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1575866
• Report Number(s): LLNL-JRNL--787804; 985546
• Journal Information: Integrating Materials and Manufacturing Innovation, Journal Name: Integrating Materials and Manufacturing Innovation Journal Issue: 4 Vol. 8; ISSN 2193-9764
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English