AN IMAGE FORCE THEOREM FOR A SCREW DISLOCATION NEAR A CRACK IN NONLOCAL ELASTICITY

Using the non-local elasticity theory developed by Kroner, Eringen and some others, the interaction between a finite-length crack and a straight screw dislocation parallel to the crack plane is investigated. The following theorem is proved: 'In isotropic, non-local elastic media, the force exerted on a screw dislocation by the other defects is proportional to the gradient of the energy of the dislocation', which is correct in classical elasticity. With the theorem, the non-local image force on a screw dislocation due to a finite-length crack is calculated. The result shows that there is no singularity of the classical image force and there is a maximum of the force at the crack tip.