The onset of nonlinear effects in metals, such as plasticity and damage, is strongly influenced by the heterogeneous stress distribution at the grain level. This work is devoted to studying the local stress distribution in fcc polycrystals using FFT-based solvers. In particular, we focus on the distribution of shear stresses resolved in the slip systems as the critical driving force for plastic deformations. Specific grain orientations with respect to load direction are investigated in the linear elastic regime and at incipient plastic deformations based on a large ensemble of microstructures. The elastic anisotropy of the single crystal is found to have a crucial influence on the scatter of the stress distribution, whereas the Young’s modulus in the respective crystal direction governs the mean stress in the grain. It is further demonstrated that, for higher anisotropy, the shear stresses deviate from the normal distribution and are better approximated by a log-normal fit. Comparing the full-field simulations to the Maximum Entropy Method (MEM), reveals that the MEM provides an excellent prediction up to the second statistical moment in the linear elastic range. In a study on the spatial distribution of shear stresses, the grain boundary is identified as a region of pronounced stress fluctuations and as the starting point of yielding during the elastic–plastic transition.

金属中非线性效应的开始，例如塑性和损伤，受到晶粒级异质应力分布的强烈影响。这项工作致力于使用基于 FFT 的求解器研究 fcc 多晶中的局部应力分布。特别是，我们专注于在滑动系统中解决的剪应力分布，作为塑性变形的关键驱动力。相对于载荷方向的特定晶粒取向在线性弹性状态和基于大量微观结构的初始塑性变形中进行了研究。发现单晶的弹性各向异性对应力分布的分散具有至关重要的影响，而各个晶体方向上的杨氏模量决定了晶粒中的平均应力。进一步证明，对于更高的各向异性，剪应力偏离正态分布，并通过对数正态拟合更好地近似。将全场模拟与最大熵方法 (MEM) 进行比较，发现 MEM 提供了一个很好的预测，直到线性弹性范围内的第二个统计矩。在一项关于剪应力空间分布的研究中，晶界被确定为具有明显应力波动的区域，并且是弹塑性转变过程中屈服的起点。