Abstract
Two types of higher-order stresses work-conjugate to slip gradient in single crystals are investigated to analyze the grain-size dependent yield behavior of polycrystals. The first is the higher-order stress due to the self-energy of geometrically necessary dislocations (GNDs). The second higher-order stress examined is an extension based on the non-recoverable energy that is postulated to be proportional to the accumulated density of incrementally defined GNDs. It is shown that the second higher-order stress is co-directional with the in-plane gradient of slip-rate and consequently causes isotropic hardening, whereas the first higher-order stress is co-directional with the in-plane gradient of slip. These higher-order stresses are incorporated into a strain gradient plasticity theory of single crystals. Subsequently, using a finite element method, 2D model polycrystals are analyzed to demonstrate the influence of the two types of higher-order stresses on the grain-size dependent yield behavior under loading, unloading and reverse loading.
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