Aspects of the Theory of Dislocations

Various topics in the theory of dislocations in linear elastic continua are reviewed using, wherever possible, simple physical arguments to derive the mathematical results. The elastic field of a general Somigliana dislocation is derived and specialized to the physically important case where its discontinuity vector is constant. A general account of the effect of free surfaces is illustrated by some specific examples. In discussing dislocation energetics it is emphasized that once the Peach-Koehler expression describing the interaction with an externally applied stress field has been established, its extension to the case of internal stresses and image stresses follows without further mathematics. In the final Section it is demonstrated that certain solutions for uniformly and non-uniformly moving dislocations can be derived rather simply from the corresponding static solutions.