On critical polyhedrons for BCC and HCP materials

The present paper deals with a new method to calculate the vertices of a cr itical polyhedron taking into account glide and twinning. This method has b een validated in the case of an extra low carbon steel and compared to that of Orlans-Joliet et al. (Orlans-Joliet, B., Bacroix, B., Monthiellet, F., Driver, J.H., Jonas, J.J., 1988. Yield surface of B.B.C, crystals for slip on the {110}[111] and {112}[111] systems. Acta Met., 36, 1365.). It has bee n applied to alpha titanium to simulate rolling textures as well as the ani sotropic Lankford coefficient R(alpha). Deformation texture calculations ha ve been performed for the triclinic symmetry of the sample. In the case of B.C.C, metals the simulated rolling texture is similar to that obtained by the Orlans-Joliet et al. (1988) method and in good agreement with the exper imental ones. Let us remark that the simulated textures have been calculate d in the homogeneous deformation assumption so as in the inhomogeneous defo rmation frame. The inhomogeneous model is an Arminjon type model (Ceccaldi, D., Yala, F., Baudin, T., Penelle, R., Royer, F., Arminjon, M., 1994. Defo rmation textures and plastic anisotropy of steels using the Taylor and nonh omogeneous models. Int. J. of Plasticity, 10 (6), 643.). (C) 1999 Elsevier Science Ltd. All rights reserved.