Formation of Cottrell atmosphere studied by Langevin equation coupled with the first strain gradient elasticity

Abstract

This study investigate the formation of Cottrell atmosphere around a dislocation on the basis of Langevin equation coupled with the first strain gradient elasticity (SGE) of Cauchy type. Following to the eigen strain theory of Eshelby, we introduced a straight edge dislocation at the center of a two-dimensional rectangular SGE medium. Non-singular stress field around the dislocation is obtained using the isogeometric analysis (IGA) solved with the 3rd-order NURBS basis functions. Long-time diffusion of solute atoms is governed by the overdamped Langevin equation which equips the Peach-Koehler potential, obtained from stress field around the dislocation, in addition to the conventional thermal noise. Present numerical analysis revealed the formation process of Cottrell atmosphere in a realistic time scale.