Quantitative evaluation of Frank vector on the basis of continuous field theory of dislocation and differential geometry

Abstract

This study conducts the modeling and numerical analysis of kink deformation on the basis of continuous field theory of dislocation and differential geometry. In particular, we aim to evaluate the existence and nature of disclination which is expected to be formed at the tip of kink band. Plastic deformation due to dislocation is obtained by numerically solving the Cartan first structure equation. This result yields a Riemann - Cartan manifold which equips Riemannian metric and Levi – Civita connection. By introducing the holonomy, i.e., the integration of curvature on a closed interval, we evaluate the magnitude of Frank vector at the kink tip. The result shows quantitative agreement with those expected from the classical dislocation theory.