基于FFT的面心立方多晶体剪切应力分布研究
FFT-based investigation of the shear stress distribution in face-centered cubic polycrystals
摘要：
金属中非线性效应的发生，如塑性和损伤，强烈地受晶粒水平上的非均匀应力分布的影响。本文研究了作为塑性形变临界驱动力的滑移系中剪切应力的局部应力分布。特定的晶粒取向相对于负载方向进行了研究，在线性弹性制度，并在初始塑性形变的基础上的一个大的合奏微观结构。发现单晶的弹性各向异性对应力分布的分散有至关重要的影响，而在相应的晶体方向上的杨氏模量支配晶粒中的平均应力。它进一步表明，对于更高的各向异性，剪切应力偏离正态分布，更好地近似对数正态拟合。比较全场模拟的最大熵方法（MEM），揭示了MEM提供了一个很好的预测的第二个统计时刻的线弹性范围。在剪切应力的空间分布的研究中，晶界被确定为一个区域的显着的应力波动，并作为在弹塑性转变过程中屈服的起点。
英文摘要：
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 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.
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