CLOSED-FORM SOLUTIONS FOR THE ELASTIC FIELDS DUE TO THEMOTION OF A SCREW DISLOCATION AT A CONSTANT VELOCITYALONG A LINEAR PATH WITH AN ARBITRARY DIRECTION

The present study aims to investigate the elastic elds induced due to the motion of a screw dislocation that moves along a linear path with an arbitrary direction in an in nitely extended isotropic medium. This inves- tigation was performed based on the assumption that the dislocation moves at a constant velocity less than the speed of shear waves in the medium. In the present analysis, from the viewpoint of micromechanics, the dis- location was described using the concept of eigenstrain. The expression of such an eigenstrain eld includes a constant to be determined in the sequel of the analysis by applying the jump condition of the displacement on the slip plane of the dislocation. Following the repre- sentation of the governing eld equations of the prob- lem, a two-dimensional Fourier transform was utilized and then, the closed-form solutions were obtained for the displacement and elastic strain elds of the delin- eated problem, for the rst time. Subsequently, two special cases of the problem, the one pertinent to the motion of the dislocation along its slip plane and the other associated with its motion perpendicular to such plane were addressed. The derived expressions showed that the strain eld of the problem has a singularity at the dislocation core. The obtained results demonstrated that at di erent velocities and in di erent motion direc- tions, the displacement eld of the problem su ers from constant discontinuity on the slip plane of the disloca- tion. Moreover, it was shown that at distances far away from the slip plane of the dislocation, the components of the strain eld vanish. The presented results, in addi- tion, exhibited the e ect of the direction of the motion of the dislocation and its velocity on the induced elastic elds. Speci cally, it was shown that with an increase in the velocity of the dislocation, the magnitudes of the components of the induced strain eld become larger.