Why a Complete Solution Has not Been Found of a Mode I Crack in an Elastic Plastic Solid

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Abstract
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).

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