WHY A COMPLETE SOLUTION HAS NOT BEEN FOUND OF A MODE-I CRACK IN AN ELASTIC PLASTIC SOLID

No demonstrated satisfactory solution, complete or partial, has ever been found for the plastic zone of a mode I crack in an elastic plastic solid. (By complete is meant a stress strain field solution of both the crack tip plastic zone and the elastic region which surrounds it.) In this paper it is shown, as well as a negative can be shown, that it is unlikely that a solution exists for this problem if a condition on the solution is that an active plastic zone touches the crack tip and/or the crack faces behind the crack tip. The specific mode I crack problem considered is the stationary mode I crack in plane strain in an elastic perfectly plastic and incompressible solid with a plastic zone size which is small compared with the crack length (small scale yielding).