The elasticity-theory boundary-value problem, for a screw dislocation near to a triple junction between phases having different elastic moduli, was solved by using a modified method that was based upon virtual surface dislocations. The exact analytical expressions for the dislocation stress fields were analyzed in Mellin space. In the limiting case, where the Inter-phase boundaries made contact at right angles, Mellin transforms were found for the distribution functions of virtual surface dislocations. This made it possible to transform the dislocation stress fields back into the real coordinate space in an analytical manner and to obtain them in explicit form.

Elastic Behavior of Screw Dislocations near to Triple Junctions. M.J.Gutkin, A.E.Romanov, E.C.Aifantis: Materials Science Forum, 1996, 207-209, 605-8