Sensitivity of grain-averaged elastic strain and orientation predictions on the mesh density and boundary conditions in crystal plasticity finite element simulations

TL;DR

The paper addresses how mesh density and boundary conditions influence grain-averaged predictions of elastic strain and orientation in crystal-plasticity finite-element simulations, with an eye toward robust comparisons to ff-HEDM data. Using a CPFE framework implemented in FEPX on a multi-thousand-grain polycrystal, it systematically varies mesh density and boundary-layer placement under uniaxial loading to map convergence and buffering requirements. The key finding is that roughly 250 elements per grain, coupled with a buffer layer of at least three grains, yields grain-averaged predictions within 5% of the asymptotic reference, while boundary effects extend up to the buffer distance. These results provide actionable guidelines for efficient and accurate CPFE studies and for planning HEDM experiments to ensure consistent grain-level metrics across simulations and measurements.

Abstract

Combined high-energy X-ray diffraction microscopy (HEDM) and crystal plasticity finite element (CPFE) modeling studies have emerged as a preferred paradigm to shed insight into the evolution of elasticity and plasticity at the intragrain scale of polycrystals. In particular, far-field HEDM measures the deformation response of upwards of thousands of individual grains simultaneously in situ during mechanical loading, though measurements are primarily limited, however, to the average state of each grain -- i.e., the grain's full strain tensor, crystallographic orientation, spatial location and volume. CPFE is utilized to shed information on the intragrain deformation response, via the sub-discretization of each grain into many finite elements, though the direct point of comparison to HEDM remains the grain-averaged response. We thus seek to find the minimum simulation conditions necessary to provide consistent grain-averaged predictions in an attempt to limit computational cost. In this study, we perform a suite of simulations and systematically study the effects of mesh density and boundary conditions, and consider different materials. We discuss these results and show that accurate prediction of grain-averaged elastic strains in a given region of interest typically requires a mesh with 250 elements per grain on average and a buffer layer of at least three grains between the region of interest and the control surfaces.

Figures (16)

• Figure 1: Visualizations of the tessellation representing the polycrystal utilized in the simulations with grains colored arbitrarily. Depictions of the meshes for a subset of the domain (indicated by a dashed black line on the tessellation) are shown for the six different mesh densities considered.
• Figure 2: Boundary conditions utilized in simulations, in which uniaxial tension is applied via the imposition of velocities on the nodes belonging to two opposing surfaces of the domain (i.e., the control surfaces, where one surface is fixed and the other has a constant velocity, $c$, related to the macroscopic strain rate via the gauge length), and where two nodes are further restrained on the fixed control surface to arrest rigid body translation and rotation. Gray dashed lines further indicate the central region of the sample (Section \ref{['sec:tess_and_mesh']}).
• Figure 3: \ref{['subfig:stress_strain_1']} Macroscopic equivalent stress-strain behavior for the simulations performed with mesh densities of $\bar{N}=50$ (dashed line), $\bar{N}=1000$ (solid line), and the intermediary mesh densities (gray lines), and \ref{['subfig:stress_strain_2']} detail of the behavior near 10% macroscopic strain.
• Figure 4: Grain-averaged equivalent elastic strain, $\bar{\varepsilon}^\text{e}$, plotted spatially on the deformed meshes. Results are shown for the simulation with mesh density of $\bar{N}=50$ at macroscopic strains of \ref{['subfig:mesh_strain_1']} 0.015%, \ref{['subfig:mesh_strain_2']} 0.2%, and \ref{['subfig:mesh_strain_3']} 10% (including the common scale), and for the simulation with mesh density of $\bar{N}=1000$ at macroscopic strains of \ref{['subfig:mesh_strain_4']} 0.015%, \ref{['subfig:mesh_strain_5']} 0.2%, and \ref{['subfig:mesh_strain_6']} 10%.
• Figure 5: Grain-averaged equivalent elastic strain error metric, $e$, as a function of mesh density, $\bar{N}$, at macroscopic strains of \ref{['subfig:strain_error_1']} 0.015%, \ref{['subfig:strain_error_2']} 0.2%, and \ref{['subfig:strain_error_3']} 10%. Dashed lines bound the region within $\pm$5% of the behavior predicted in the simulation performed with mesh density of $\bar{N}=1000$. Dots represent the average value at each mesh density, with whiskers representing $\pm \sigma_e$, where $\sigma_e$ is the standard deviation.