1 Department of Solid Mechanics, Technical University of Denmark
The uniaxial deformation of polycrystals are modelled using three incremental rate-insensitive micro-mechanic models; the Taylor model, the Sachs model and Hutchinson’s self-consistent model. The predictions of the two rigid plastic upper- and lower-bound models (Taylor and Sachs) are compared with the predictions of the elastic-plastic self-consistent model. As expected, the results of the self-consistent model is about half-way between the upper- and lower-bound models. The average number of active slip systems is about 3.6 compared to the ﬁve active slip systems in the Taylor model and the one active slip system in the Sachs model. The average m-factor is about 2.6 compared to the 3.06 in the Taylor model and the 2.23 in the Sachs model. The predicted rotation pattern of the self-consistent model is closest to the Taylor model, but the orientation distribution of the m-factor is closest to the Sachs model. The inﬂuence of the elastic anisotropy is investigated by comparing the self-consistent predictions for aluminium, copper and a hypothetical material (hybrid) with the elastic anisotropy of copper and the Young’s modulus and work hardening behaviour of aluminium. It is concluded, that the eﬀect of the elastic anisotropy is limited to the very early stages of plasticity (εP < ∼0.1%), 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 mea-surements of elastic lattice strains in grain sub-sets within the polycrystal. In the evaluation of the rigid plastic Taylor and Sachs models, the ’elastic’ strain is determined as the calculated stress divided by the diﬀraction elastic constants (cal-culated as the Kr¨oner elastic stiﬀnesses for the grain sub-sets). The comparison of calculated and measured lattice strains are made for three diﬀerent materials; alu-minium, copper and austenitic stainless steel. The predictions of the self-consistent model is more accurate and detailed than the predictions of the Taylor and Sachs models, though some discrepancies are noted for some reﬂections. The self-consistent model is used to determine the most suitable reﬂection for technological applications of neutron diﬀraction, where focus is on the volume av-erage stress state in engineering components. To be able to successfully 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 lattice strains. Below 5% deforma-tion the deviations from linearity and the residual strains are below the normal strain resolution of a neutron diﬀraction measurement. The model predictions have pinpointed, that the selection of the reﬂection is crucial for the validity of stresses calculated from the measured elastic lattice strains. The calculations are limited to uniaxial tension with an initially random texture, and in normal measurements with unknown stress state and texture, the complexity of the measurements increases. If the stress state is unknown, there will not be a unique solution to the macroscopic stress state, and the introduction of texture will inherently change the intergranular stresses and strains within the material, and therefore it might not be the 311-reﬂections, that is the most suitable reﬂection under all conditions.