EQUILIBRIUM CONDITION OF RESIDUAL EDGE WEDGE-TYPE NANOTWIN IN POST-DEFORMED SOLID BODY

Abstract

An equilibrium condition of residual edge wedge-type nanotwin in a deformed solid body has been derived in the paper. The condition conclusion is based on the necessity to ensure an equilibrium of force balance acting on every twinning dislocation from the side of the rest twin dislocations. In this case dislocation structure and stress condition at nanotwin mouth have not been taken into account. Results of dislocation theory obtained in the framework of elasticity theory and continuum mechanics have been used in the paper. The paper has considered a component of the resultant force acting in a twinning plane under an assumption that there is no motion of twinning dislocations in the direction which is perpendicular to the twinning plane. The following condition has been made in the model: a discrete distribution of twinning dislocations at twin boundaries. In order to reduce cumbersome calculations a limited number of twinning dislocations has been considered in the paper and an assumption has been made about small value of a helical component in the Burgers vector, in other words the paper has considered an edge nanotwin. In order to decrease a number of equations in the system of equilibrium conditions a symmetric property of a shear component in a stress tensor has been used in the paper. The paper contains description how restrictions on the order of twinning dislocation arrangement on twin boundaries have been imposed. In this case it has been assumed that an arrangement of twinning dislocation pairs in different twin boundaries is in one plane which is perpendicular to the twinning plane. It is necessary to keep in mind that only one twinning dislocation can be located in one twinning plane. Calculations have shown that it is possible to ensure a stable and unstable equilibrium of an edge nanotwin in an ideal unloaded crystal. Sustainable balance is provided by alignment of twinning dislocations in a wall. This leads to a twin disappearance due to annihilation of twin boundary dislocations with its dislocations at the mouth. In order to ensure an unstable equilibrium of a wedge edge nanotwin it is necessary that the distance between twinning dislocations along the length of the twin is equal to interplanar distance.