Part VII - Communications - The Importance of Twinning for the Ductility of CPH Polycrystals

WHILE single crystals of most materials with cph lattice structure show essentially unlimited ductility, polycrystalline specimens of the same materials exhibit the entire range of ductilities. A difference between the ductility of single crystals and polycrystals may be associated with the special stress concentrations to be expected, for example, at the intersections of slip bands or twin lamellae with grain boundaries. Whether such stress concentrations prove catastrophic depends on the cleavage strength of the material, the size of the stress concentrations, and the speed with which they are formed. Thus, the ductility may vary in degree from material to material. Another possible reason for differences in ductility between single crystals and polycrystals is that a sufficient number of independent deformation modes must be available to insure compatibility between the macroscopic strains in neighboring grains.''2 This criterion is often taken to be a necessary condition for any polycrystal ductility whatsoever, not as one that determines different degrees of ductility; thus, a material with an insufficient number of independent deformation modes would have to be brittle as a polycrystal. The "sufficient number" is five if every grain is to accommodate arbitrary shape changes ("von Mises criterion "). We should like to argue that fewer than five independent modes may be sufficient to satisfy compatibility conditions; and that the internal stresses set up when the plastic strains are not compatible reach the theoretical fracture stress only after a significant amount of macroscopic strain has taken place which may vary in magnitude from case to case, allowing an influence on the degree of ductility. Experimental evidence for these statements is taken from the following review of the number of independent deformation modes observed in the various cph