An image force theorem for a dislocation near a crack in an anisotropic elastic medium

Abstract

Using the sextic formalism developed by Stroh (1958, 1962), and Malen and Lothe (1970), the interaction between a semi-infinite crack and a straight dislocation parallel to the crack plane is treated. The following theorem is proved: If r' is the radial distance from the crack tip to the dislocation, then the image (interaction) force exerted by the crack on the dislocation is given by F_r=-E^infinity /r' where E^infinity is the prelogarithmic energy factor of the same dislocation in the infinite uncracked medium. The image force is thus independent of the dislocation's angular position. Anisotropy influences the image force only through E^infinity . This result is of importance in estimating the local plastic deformation near the tip of a crack.