Micro-Scale Effect On Cyclic Plasticity And Its Discrete Dislocation Simulation In Crystal Materials

Classic Constitutive Relation of Continuum Mechanics has achieved great success in mechanics, aerospace, building construction, electric power, traffic vessel and other traditional engineering field. With the rapid development of the computer science and technology, finite element methods have been widely used in structure strength checking, optimal design, safety life evaluation and analysis of structure reliability, which greatly improved the technology used both in product design and science research. It is of no doubt that the traditional continuum mechanics theory has been successful in macro scale. However, the recent micro-nano technology is at the ascendant. Micro-structure apparatus, micro mechanical electronic, micro electromechanical systems and those photoelectric apparatus with optoisolator, optical conductor, photo semiconductor as the representatives emerged in secession and has been widely employed. These apparatus usually work under cyclic loading. On the other hand, with the material size down to micron or even below, their mechanical behaviors show great micro size effect, thus strength analysis based on traditional mechanical constitutive relations is no longer applicable. Therefore, research on the cyclic plastic behaviors of polycrystal materials under micro-scale and its underlying mechanism is not only of great significance in mechanic theory but also of important material value in real engineering projects. Toward this end, the main research contents and results acquired are as follows:(1) The cyclic plastic response of a single crystalline thin beam subject to combined cyclic tension and bending is analyzed using two-dimensional discrete dislocation plasticity. In this contribution, special attention is paid to the difference in the inherent mechanism of the size effect for different cyclic loads. Results show that the cyclic plastic response has a strong size effect for both cyclic pure tension-compression and pure bending. However, the inherent mechanisms are different. The dislocation starvation mechanism dominates the cyclic tension-compression while the geometrically necessary dislocation dominates the cyclic pure bending. When the combined cyclic tension and bending are applied to the thin beam, the cyclic moment-rotation response shows strong size effect while the stress-strain response shows weak or even no size effect. In addition, it is also found that the cyclic loading paths have considerable influences on the shape of the cyclic stress-strain loops.(2) To simulate the dislocation transmission across grain boundary, a dislocation-grain boundary penetration model is proposed and then integrated into the two-dimensional discrete dislocation dynamics (DDD) framework by Giessen and Needleman (1995). By this extended DDD technology, cyclic plastic response of polycrystals is analyzed. Special attentions are paid to significant influence of dislocation-penetrable grain boundaries (GBs) on micro-plastic cyclic responses of polycrystals and the underlying dislocation mechanisms. Results show that, when GBs are penetrable to dislocations, continual dislocation accumulation and enhanced dislocation-dislocation interactions give rise to the cyclic hardening behavior; on the other hand, when a dynamic balance among dislocation nucleation, penetration and annihilation is approximately established, cyclic stress gradually tends to saturation. In addition, other factors, including the grain size, cyclic strain amplitude and its history, have considerable influences on the cyclic hardening and saturation.(3) The cyclic plastic response of periodic crystalline material subjected to non-proportional loads are analyzed using two-dimensional discrete dislocation plasticity. It is found thatâ‘ the additional hardening presents for both the single crystal and polycrystals;â‘¡the cyclic plastic response has a weak dependence of cell size but a strong grain size effect;â‘¢the load radios have a significant influence on cyclic plastic deformation. With different load radios, it can lead to either strain hardening or strain softening;â‘£under the nonproportional loads, the cyclic hardening behavior is not present obviously.