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Why a Complete Solution Has not Been Found of a Mode I Crack in an Elastic Plastic Solid
Author(s) -
Weertman J.
Publication year - 1992
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221720105
Subject(s) - materials science , crack tip opening displacement , crack closure , plasticity , plane stress , crack growth resistance curve , stress field , mode (computer interface) , stress intensity factor , mechanics , plane (geometry) , composite material , structural engineering , fracture mechanics , geometry , mathematics , physics , computer science , engineering , finite element method , operating system
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).