Single‐crystal yield surface for trigonal lattices: Application to texture transitions in calcite polycrystals

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Abstract
Assuming that deformation is caused solely by dislocation glide and mechanical twinning, with negligible strain rate sensitivity, the plastic behavior of crystals is described by a polyhedron in stress space, the single‐crystal yield surface (SCYS). Each facet of the SCYS represents the yielding condition on one slip or twinning system, and the distance from the origin to a facet is proportional to the critical resolved shear stress (CRSS) on that system. Changes in the various CRSS, for example, due to temperature variations, will be accompanied by topological shape transitions of the SCYS and by changes in the activity of the deformation systems. Thus the final polycrystal deformation texture depends on the particular topology of the SCYS. In this work we analyze the topology changes and the associated texture transitions for calcite based upon the Taylor‐Bishop‐Hill criterion, assuming homogeneous strain. Although the topological changes are very complex, only a few transitions are associated with sharp texture transitions related to major changes in the activity of the different deformation systems. The Taylor‐Bishop‐Hill model agrees with experimental plane strain and pure shear deformation textures at various temperatures even though the model neglects strain rate sensitive process and heterogeneous strain. By comparing simulations with experiments we can infer the relative importance of the different deformation systems as a function of the temperature.