Numerical Simulation Of HCP Polycrystals Plasticity

The present work chooses HCP crystals as the object of study. Starting from the microscopic plastic deformation and hardening mechanisms of HCP crystals the micromechanic descriptions of the slip and twinning mechanisms of crystal plasticity and the boundary effects of grains are determined, and the relationship between the microscopic plastic deformation mechanisms and the macroscopic mechanical responses are established.In the thesis a viscoplastic rule is taken to describe the microscopic plastic flow, by using of van Houtte’s method twinning is treated as pseudo-slip, this means that an entire crystal is rotated when a given volume fraction of twinning in the crystal has been reached. In order to describe the boundary effects of grains a formulation with a rate-dependent term is applied, the crystal plasticity model is described in the spatial configuration, with a hardening law formulated in a power form. A self-consistent model is derived with Hill’s self-consistent method included, and a numerical algorithm is presented for transforming the single crystal plasticity into the plasticity of polycrystal.In Chapter one the status of research on the crystal plasticity is summarized. Thereafter, the plastic deformation mechanisms of crystal are described in Chapter two, whereby the mathematical equations used to describe the microscopic deformation processes of HPC crystals are formulated. In Chapter three, the kinematics of microscopic slip and twinning is presented, a constitutive equation is formulated to describe the relation between the Jaumann rate of and the elastic deformation rate, the self-consistent model is also presented in this chapter. The numerical algorithms to integrate the evolution equations are shown in Chapter four, the elasto-plastic tangent moduli are formulated in this chapter. In order to prove the validity of the theory and algorithms presented in the thesis, a plane strain extrusion of magnesium single crystals is simulated and the results are compared with those shown by Graff, it can be seen that the former results are agreement with the latter well. It should be emphasized that the algorithms and the program developed in the current work must be checked in other more complicated deformation processes of single HCP crystals and HCP polycrystals so that the effectiveness of the work is checked thoroughly, these works will be conducted in the future.