An image force theorem for dislocations in anisotropic bicrystals

Using a formalism developed by Stroh (1962), a simple image force theorem for a dislocated anisotropic bicrystal is derived. An extension of the Stroh formalism, shows that the prelogarithmic energy factors depend only on the crystallographic directions of the dislocation line and its Burgers vector relative to each medium constituting the bicrystal. In addition, a formula is developed which allows one to obtain the prelogarithmic energy factor by simple numerical integration. A previous result of Dundurs and Sendeckyj (1965) for the net integrated tractions on any plane parallel to the interface of a dislocated bicrystal is extended to the anisotropic case. Finally, an intimate relation between dislocations moving parallel to the bicrystal interface and Stoneley waves in anisotropic bicrystals is developed.