Origin of bent ridge-kink based on disclination relaxation

In this study, we have developed a geometric model for bent kinks by introducing sequences of ortho-connected kink bands into ridge-kinks to provide insights into the possible reasons why kinks are bent and the resulting geometry when they are bent. We first formulated the Frank angles and coordinates of the disclinations formed in the bent kinks, which enable our discussion on the influence of the introduction of ortho-kinks on the Gibbs energy by utilizing Romanov’s disclination model. It turns out that the introduction of ortho-kinks can relax the elastic strain energy and thus reduce the Gibbs energy of the system under compression states with lower external stresses. On the other hand, the introduction of ortho-kinks increases the Gibbs energy at higher compression stresses, implying sharp ridge-kinks are preferred under such conditions. This trend resembles the experimental observations reported by previous studies that the shapes of newly formed kinks tend to transition from pre-kinks with bent shapes to ridge-kinks with sharp shapes as the compression test progresses. The smoothly bent kink with smoothly distributed misorientation, formed by increasing the number of introduced ortho-kinks, can further reduce the Gibbs energy at lower applied stresses. Subsequently, based on the Rank-1 condition for the connection of kink bands, we further analyzed the geometry of such smoothly bent kinks and derived the analytical equations for the constraints on the orientation distribution. Finally, we conducted EBSD measurements on bent kinks observed in directionally solidified (DS) LPSO-Mg alloys and confirmed that the derived equations for the orientation distribution are in good agreement with the experimental results.