Finite Dislocation Elements in Finite Media. I. Basic Theory

The interaction of finite co‐planar dislocation pieces in a finite medium is considered with special reference to the case where two partial dislocations split trapezoidally in a thin foil. The calculation is carried out on the force and moment level. The presence of the surface is taken into account by Lothe's theorem. The remaining problem of the interaction of finite pieces in an infinite medium is considered in detail. It is shown that such problems require the execution of integrals involving only the energy E of dislocations (or interaction energy of parallel dislocations) within that plane — no derivatives of E are required. Formulae suitable for numerical evaluation are derived.