Line defects in the (110)plane of a cubic crystal  an outstanding problem solved by the integral formalism
Abstract
Anisotropic theory of a line defect (dislocation or line force) is numerical because the displacement and stress fields around a defect of arbitrary orientation involve the roots of a sextic equation, which cannot be obtained analytically. For certain orientations of defects in crystals exhibiting symmetry, the sextic reduces to a cubic or simpler polynomial equation, the roots of which can be expressed in analytic form. In this paper, we obtain, via the integral formalism, analytic expressions for the fields of defects situated in the (110)planes of cubic crystals.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 2003
 DOI:
 10.1098/rspa.2003.1118
 Bibcode:
 2003RSPSA.459.2033W