Extreme Strain Fluctuations in Polycrystalline Materials

Abstract

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.