``Mutual'' attraction of a dislocation to a bimetallic interface and a theorem on ``proportional'' anisotropic bimetals (Q675358)

A straight dislocation parallel to the interface of two perfectly bonded dissimilar linear elastic half-spaces experiences a Peach-Koehler image force tending to move the dislocation toward or away from the interface. As a rough rule, the dislocation is repelled from the interface when it resides in the elastically softer of the two half-spaces and is attracted to the interface when it resides in the stiffer half-space. Here we prove that this rough rule holds exactly for ``proportional'' anisotropic bimetals, i.e. two perfectly joined half-spaces for which \(C_{ijkl} (2)= \lambda C_{ijkl} (1)\), where the constant \(\lambda\) is positive, so that for a dislocation in medium (1) repulsion occurs when \(\lambda>1\) and attraction occurs when \(\lambda<1\).