AbstractThe deformation of polycrystals are modelled using three micron mechanic models; the Taylor model, the Sachs model and Hutchinson's self-consistent (SC) model. The predictions of the rigid plastic Taylor and Sachs models are compared with the predictions of the SC model. As expected, the results of the SC model is about half-way
between the upper- and lower-bound models. The influence of the elastic anisotropy is investigated by comparing the SC predictions for aluminium, copper and a hypothetical material (Hybrid) with the elastic anisotropy of copper and the Young's modulus and hardening behaviour of aluminium. It is concluded that the effect of the elastic anisotropy is limited to the very early stages of plasticity, as the deformation pattern is almost identical for the three materials at higher strains. The predictions of the three models are evaluated by neutron diffraction measurements of elastic lattice strains in grain sub-sets within the polycrystal.
The two rigid plastic models do not include any material parameters and therefore the predictions of the SC model is more accurate and more detailed than the predictions of the Taylor and Sachs models. The SC model is used to determine the most suitable reflection for technological applications of neutron diffraction, where focus is on the volume average stress state in engineering components. To be able to successfully to convert the measured elastic lattice strains for a specific reflection into overall volume average stresses, there must be a linear relation between the lattice strain of the reflection and the overall stress. According to the model predictions the 311-reflection is the most suitable reflection as it shows the smallest deviations from linearity and thereby also the smallest build-up of residual strains. The model predictions have pin pointed that the selection of the reflection is crucial for the validity of stresses calculated from the measured elastic lattice strains. |