The stochastic structure of polycrystalline materials causes a high inhomogeneity of the kinematic and force fields in grains of materials and large fluctuations of these fields. The inhomogeneity and fluctuations are insignificant in some cases, but they become crucial in the study of various critical phenomena whose occurrence strongly depends on the type of material microstructure. Fluctuations mainly arise due to the elastic interaction of grains, which has a long-range effect. Therefore, it is necessary to account for the interaction of a large number of grains, which is difficult to do using conventional methods (direct computer modeling and others). In the present paper, inhomogeneous mesostrain fluctuations in grains of polycrystalline materials were estimated using a field-theoretical approach to a boundary-value problem of microheterogeneous material deformation. Particular attention is paid to the calculation of extreme fluctuations that are important for some critical phenomena, such as, e.g., crack initiation under gigacycle fatigue when the macrostress amplitude and the mean stresses in grains are much lower than the quantities included in any macroscopic damage or fatigue criteria. Phe maximum mesostrains in grains can exceed several times the macrostrains. Extreme fluctuations in a grain are generated in grain clusters of specific configuration. Phe applied approach makes it possible to predict patterns of such clusters. Extreme fluctuations in the bulk grains of a polycrystalline body are much higher than in the surface grains, due to which the behavior of the material surface layers and bulk volumes is different. Quantitative data are given for the case of uniaxial tension of polycrystalline zinc.

中文翻译：

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多晶材料中的极端应变波动

多晶材料的随机结构导致材料晶粒中运动场和力场的高度不均匀性以及这些场的大波动。在某些情况下，不均匀性和波动是微不足道的，但它们在研究各种临界现象时变得至关重要，这些现象的发生在很大程度上取决于材料微观结构的类型。波动主要是由于晶粒之间的弹性相互作用而产生的，具有长程效应。因此，需要考虑大量晶粒的相互作用，这是使用传统方法（直接计算机建模等）难以做到的。在本文中，使用场理论方法对微非均质材料变形的边界值问题进行估计，估计多晶材料晶粒中的非均匀中间应变波动。特别注意计算对某些关键现象很重要的极端波动，例如，当宏观应力幅度和晶粒中的平均应力远低于任何宏观损伤或疲劳标准。晶粒中的 Phe 最大中间应变可以超过宏观应变的数倍。颗粒的极端波动是在特定配置的颗粒簇中产生的。Phe 应用方法可以预测此类集群的模式。多晶体块体晶粒的极端波动远高于表面晶粒，因此材料表面层和体体积的行为是不同的。给出了多晶锌单轴拉伸情况下的定量数据。