Elastic and plastic fields induced by a screw dislocation in a nanowire within Mindlin’s second strain gradient theory

Abstract

Due to the wide applications of nanowires as a main component of nano-scale electronic devices, a lot of attentions have thus far been paid to study their relevant problems. Knowing that the presence of dislocations in nanowires affects their mechanical properties, this paper is dedicated to the determination of analytical expressions for the elastic displacement, elastic strains, and plastic distortion developed in a nanowire due to a screw dislocation, as well as the image force acting on the dislocation core, within the framework of Mindlin’s second strain gradient theory. Expecting that the size effect plays an important role in such a problem, this theory seems an appropriate continuum approach for its addressing. Furthermore, utilizing the adopted theory leads to the removal of all classical singularities in the elastic displacement, strain, stress, and plastic distortion fields, as well as the image force. It is, in addition, seen that the elastic double- and elastic triple-strains are regularized. Furthermore, the results evidently illustrate the size effect, i.e. the effect of the ratio between the radius of the nanowire and the characteristic lengths of its constituent material.