Bifurcation into shear bands on the Bishop and Hill polyhedron. Part 2, Case of the vertices
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The present paper is the second of a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It focuses on the deformation at the vertices of the Bishop and Hill polyhedron, which are important because most of the shear bands originate at the grain boundaries where many slip systems are active. The conditions of bifurcation are analysed on the scale of the slip systems by crystallographic class of vertices. An application is given in the case of channel-die compression and it shows that the texture components are unequally liable to shear banding, the Copper one, for example, being more sensitive than Goss, as known experimentally. There is also a good agreement of the predictions with the geometry of the bands, especially the characteristic feature of the inclination at 35o with respect to the rolling axis. Considerations follow on the actual implementation, by micro-structural phenomena, of the localization whose mechanical possibility has been discussed in the article.
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