Meso-deformation And Constitutive Relations Of Sliding Polycrystals

When subject to a loading environment, the deformation of a polycrystalline aggregate is generated by both the slipping within the grains and the sliding along the grain boundaries. The meso-deformation and constitutive relations for the polycrystals with anticipated grain boundary sliding, henceforth referred as sliding polycrystals, are explored in the present thesis from a combined viewpoint of micro-optical observation and micromechanics analysis.The first chapter aims at revealing various meso-deformation characteristics, such as crystalline slip and grain boundary slide, which are recorded under scaning electronic microscope for high purity aluminum tensile specimen at room temperature. These experimental data provide us direct evidence for shear localization near the grain boundary network via multi-directional grain boundary slide. The nonuniform deformation induced in the interior of grains would have decisive effect on the plastic flow and failure of polycrystalline materials.An approximate theoretical framework suitable for inhomogeneities of arbitrary shape, called as domain averaging inclusion method, is advanced in the second chapter. By means of domain averaging quantities over the inclusion, such as averaged eigenstrain, etc., the present approach enables us to generalize the self consistent scheme of Hill applicable for uniform eigenstrains within ellipsoidal inclusions to inclusions, either adhered or sliding, of arbitrary shape. An error estimate for the present scheme is also provided for its numerical justification. This scheme is tested by a self consistent calculation for polycrystals ensambled by cubic grains. Due to the integrity of the polycrystal aggregate so constructed, the model based on cubic grains gives better simulation on the constitutive behaviour of actual polycrystals. The difference of constitutive simulation between spheric grain and cubic grain scheme is revealed to be insignificant, justifying the legitimation and usefulness of the averaged self-consistent scheme based on domain-averaging inclusion method.In the third chapter, the domain averaging inclusion method is applied to sliding polycrystals. The kinematic relations for the volume averaging (macroscopic) deformation rate tensor are established, which clearly indicates the additive nature for the macroscopic velocity gradient contributed from the grain interior and along the grain boundaries. The same additive rules are also observed for the rate of stretching and for the spin. The reduction of material rigidity caused by grain boundary slidings which might take place in part or whole grain boundary network is investigated by utilizing the established averaged self-consistent scheme. Not only the overall constitutive moduli, but also the anticipated value of grain boundary sliding, are obtained through this process.