The yield surface of single crystals at arbitrary strain

With the current state as reference, the initial and subsequent yield surfaces of a single crystal are constructed under finite deformation in both Kirchhoff stress and its conjugate strain space. In both cases the yield condition of a slip system is characterized by a quadric surface rather than by a linear yield plane. As consequences of Drucker's and Ilyushin's postulates, these quadric surfaces are necessarily convex; so is the yield surface of the crystal. The translation and rotation of each quadric surface and the distortion of the yield surface are determined following an incremental loading. The loading criterion, its associated flow rule and the normality structure in connection with a yield surface at finite strain are also rigorously analyzed from physical grounds.