It was noted that the classic theories of dislocation pile-ups, initiated by Eshelby, Frank and Nabarro, and by Leibfried, could be greatly simplified if it were recognised that the dislocations in the pile-up would experience a uniform stress if they were lodged in an ellipsoidal interface. Elementary algebra then produced the familiar results of continuum theory. It seemed to be possible that the ellipsoid construction might represent physical reality if it were taken to represent a 3-dimensional slip band. If this were so, then there were concentrated forces which spread the band perpendicular to the slip band, as well as

parallel to it. Such ellipsoids also represented mode-II and mode-III cracks, and offered a method for dealing with the more complicated mode-I cracks.

Dislocation Pile-Ups, Slip-Bands, Ellipsoids and Cracks. L.M.Brown: Materials Science and Engineering A, 2005, 400-401, 2-6