General size effect in the Hall-Petch effect and in micromechanical deformation

Abstract

This thesis is a study of the size effect. Improvements on both theoretical work and experimental design are involved in this thesis. The theoretical section focuses on the grain size effect, while the experimental section is related to the micro-foil bending test. Both classic experimental data and theories for the Hall-Petch relationship are reviewed comprehensively. The fitting of the datasets show that the inverse square-root dependence and simple inverse expressions are equally good. The fully Bayesian analysis strongly suggests that the latter is correct. Since the physical mechanism underlying the simple inverse dependence is a general size effect, the precise description of the Hall-Petch effect is that it is a manifestation of the general size effect, instead of having its own special character. Improvements on the classic Stolken and Evans’ micro-foil bending experiments are also carried out in this thesis. The smart design of the new equipment eliminates the big risk of error in the classic experiment. By using the new device, precise datasets from the elastic region through the yield point and to high plastic strain area can be obtained. The initial results correspond well with the old published data.