Geometry of kink microstructure analysed by rank-1 connection

Abstract

The kinematical relationships among the geometric quantities that characterise kink bands, ridge kinks, and ortho kinks and the existence of disclinations in connecting kink bands were revealed based on the rank-1 connection, which is a condition of the continuity of deformation. Owing to the simple geometry of the kinks, the kink plane and the crystallographic rotation of the kink band were obtained in analytic forms as functions of the magnitude of the shears inside kinks. The geometry of the kink band predicted by the rank-1 connection agreed well with literature experimental data. Ridge kinks and ortho kinks were treated as the rank-1 connection of two kink bands. Positive and negative partial wedge disclinations were inevitably formed in any kink band connections when the junction plane of the kink bands did not reach the surface of the body. The Frank vector of the disclinations was also obtained as a function of the shear magnitudes in the kink bands. There exist compatible kink microstructures in which the disclinations are cancelled. Modes of complete relaxation and annihilation of disclinations by combinations of kinks or slip deformations were revealed. The nature of the kink microstructure and kink strengthening was discussed based on the formation and annihilation of disclinations.