Abstract In the present study we elucidate the nature of local strain statistics evolution during tensile deformation in polycrystalline materials. A rate-independent formulation was implemented within a crystal plasticity framework by the means of representative volume element (RVE) analysis. Local elastic strain, as well as stress, were found to obey a normal distribution, whereas the statistics of local plastic strain conforms to a lognormal distribution. In line with experimental observations, the plastic strain becomes progressively localised and the local regions of large strains make significant contribution to the overall average strain increase. The results reveal the nature of strain inhomogeneity at the microscale and emphasize the fact that in metallic materials the elastic strain accumulation represents an additive process, whereas plastic deformation is a multiplicative process.

中文翻译：

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为什么局部应力统计是正态的，而应变是对数正态的？

摘要 在本研究中，我们阐明了多晶材料拉伸变形过程中局部应变统计演变的性质。通过代表性体积元素 (RVE) 分析，在晶体塑性框架内实施了与速率无关的公式。发现局部弹性应变以及应力服从正态分布，而局部塑性应变的统计符合对数正态分布。根据实验观察，塑性应变逐渐局部化，大应变的局部区域对整体平均应变的增加做出了重大贡献。结果揭示了微观尺度上应变不均匀性的本质，并强调了这样一个事实，即在金属材料中，弹性应变积累代表了一个累加过程，