Yield vertices for {123}〈111〉 multiple slip

Abstract

The single-crystal yield surfaces of bcc crystals for slip on {123}͗111͘ systems have been analyzed systematically and derived based on the Taylor/Bishop-Hill theory. It is found that there are 338 stress states altogether. All the stress states are classified according to the crystal symmetry. The results demonstrated that there are 14 groups of yield vertices, which activate five, six, or eight slip systems, depending on the crystallographically nonequivalent groups. In addition, the four groups of yield vertices that Chin and Wonsiewicz [15] did not consider have been obtained (there are 126 stress states). Among all these vertices, the fraction of vertices for which there is slip ambiguity (more than five active slip systems) is reduced considerably to 146/338 (Ϸ43 pct). By means of the stress states obtained by Chin et al. and by the present authors, respectively, the plastic flow for axially symmetric deformation and three-axial deformation have been analyzed. In the case of axially symmetric deformation, the results are the same using the two different kinds of stress states. The obtained new stress states are necessary in order to analyze the three-axial deformation.

Analysis for twinning and slip in face-centered cubic crystals under axisymmetric co-deformation

“…It means that, for different orientations with the same deformation, the greater the M value is, the more difficult the deformation will be. Using the maximum work principle of Bishop-Hill and all the possible yield stress states (including slip or/and twinning yield stresses), the 5 dimensional yield stress states (the definition of notations is seen in reference [15] ) and corresponding active slip or/and twinning systems (the definition of notations is seen in ref. [11]) for arbitrary orientations in the standard stereographic triangle of cubic crystal orientations under axisymmetric ξ > , as shown in Table 1), the results show that the standard stereographic triangle (it can represent all tension or compression axial orientations when symmetry is considered) can be divided into 5 certain regions, each of them is activated by a specific yield stress states respectively.…”