This subject was explored by using an analysis which was based upon the Peierls model, as interpreted by Rice. A slight modification was introduced here in order to identify the pure linear elastic response of a material. New governing equations were derived which were different to those used by Beltz and Rice. The stress field and dislocation density field could be expressed in terms of the first and second Chebyshev polynomial series, respectively. The opening and slip displacements could then be expanded as a trigonometric series. The Newton-Raphson method was used to solve a set of non-linear algebraic equations. The new equations permitted the extension of the analysis to the case of dislocation emission. Detailed calculations were presented for pure shearing, pure tension and combined tension and shear loading.

Dislocation Nucleation and Emission from a Crack Tip. T.C.Wang: International Journal of Fracture, 1995, 69[4], 295-306