Different behaviors of mechanics are manifested in solids at the length scale of micron or submicron with at the macron scale. The discrepancy of mechanics behaviors due to different size scales is often referred to as the size effect. On the modeling of the size effect, since conventional elastic-plastic theory does not include any length scale parameters inside it, one can not predict the size effect phenomenon using it. Although the strain gradient plasticity theory includes some length parameters and can be used to model the size effect well, the physical meaning of the length parameters in the strain gradient plasticity theory is a little ambiguous. Although great deal of researches for material plastic behaviors have been preformed in past decades directly based on the microscopic dislocation theory, employing the dislocation theory for studying size effect is still lacking. Intention of the present research is focused on modeling the strong size effect displayed in the fundamental micro-scale experiments (torsion and bend), by adopting the combination method of discrete dislocation theory with elastic finite element method. Firstly, for the basic mechanics problems (micro-bend and micro-torsion), a one-dimensional model, by which the size effect can be characterized, is derived out by using the Mura's one-dimensional formula. Secondly, based on the experimental results and measurements, propose that an elastic core exists within the central zone of beam and bar when they undergo the micro-bending and micro-torsion, respectively. Through analysis based on the model, stress-strain relations of the micro-bend and micro-torsion are attained. The results show that when specimen size decreases and attains to a small value a strong size effect is displayed in the micro-bend and micro-torsion tests. A successful modeling for the known experimental results is realized. Based on the researches of Needleman and his collaborators, two-dimensional plane strain problems are used to model the effects of the slip-plane location, dislocation obstacle density, dislocation source density and specimen size on the micro-bend beam results. In the results, the size effect is displayed in the results. Based on the rigorous boundary conditions for pure bend, we obtain the dislocation distribution different from that of Needleman et al. However our result is comparable with the experimental observation of Hsia. Furthermore, the three- or four-point bend experiments for Cu and for Al-alloy specimens are preformed in the present research. Through observing the distribution of slip-lines on the surface, the existence of the elastic core within the central zone of beam is verified.
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