Size effect on the statistical distribution of stress and strain in microforming

Abstract

The frequency distribution of local stress or strain across the micromechanical field in plastic deformation tends to universally follow a normal or lognormal distribution, regardless of the variety of microstructural inhomogeneity. However, it has not been reported how size effect (SE) influences the grain-scale statistical distribution of stress and strain in microforming, and thus an in-depth investigation is further needed. Taking the polycrystalline Cu sheets with thickness t = 0.1–1.5 mm and t/d = 1–29 as the case materials, this study implements the full-field CPFE simulation incorporated with a size-dependent dislocation-based constitutive model and statistical analyses to explore the influence of SE on the frequency distribution of grain-scale stress and strain in micro-scaled plastic deformation. With increasing t/d, the stress frequency consistently follows a normal distribution. In contrast, the frequency distributions of strain and dislocation density undergo a transformation from a lognormal distribution to an approximately normal distribution. The results indicate that the distribution law of stress is dominantly influenced by the dislocation density, while that of strain is determined by a multiplicative process of slip activities. The established knowledge will help to elucidate the nature of the distribution law of stress or strain, and to seek for effective approaches to alleviate the scatter and uncertainty of deformed part geometry during a microforming process.