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 \(L_2\) 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 (\(\approx \) 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. Errors correlate with proximity to grain boundaries at small (elastic) strains and with deformation-induced features (deformation bands) at large strains.

中文翻译：

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多晶有限元模拟中应力分布误差的估算

由基于晶体可塑性的有限元公式预测的应力的准确性取决于与离散化相关的误差的估计和控制。在当前的工作中，应力分布的误差是在虚拟的α相钛多晶样品（Ti-6Al-4V的六方密堆积相）中估计的。为了估计误差，使用\（L_2 \）对不具有元素间连续性的应力场进行平滑处理。投影，从而提供具有单元间连续性的连续应力分布。连续（平滑）应力场和不连续（原始）应力场之间的差异是在各个高斯正交点处计算的，并用于估计相应元素和晶粒的误差。对Voronoi镶嵌微结构，等轴微结构和两个具有变化的晶粒尺寸的微结构进行了误差估计，这些拉伸强度扩展到完全塑性状态（\（\ approx \） 5％扩展）。发现误差的大小取决于微观结构特征，特别是晶粒的形状和大小。具有晶粒尺寸变化或球形晶粒较少的样品比具有均匀尺寸的等轴晶粒的样品表现出更高的误差，并且尺寸变化具有更明显的作用。在小（弹性）应变下，误差与接近晶界有关，在大应变下，误差与由变形引起的特征（变形带）有关。