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For cracks in infinite bodies it is shown that modified principles of complementary potential energy and potential energy can be used to generate upper and lower bounds to the J-integral of the deformation theory of plasticity. These principles are used to obtain relatively tight numerical bounds on J for two basic plane strain problems: the finite crack in an infinite plane and the edge-crack in a semi-infinite plane. In both problems the material is incompressible with a pure power relation between stress and strain. Upper bounds for the plane stress problems are also given.
nonlinear fracture mechanics, fully plastic crack problems, J-integral, bounds, elastic-plastic fracture
Researcher, Institute of Mechanics, Chinese Academy of Sciences, Beijing,
Professor of applied mechanics, Division of Applied Sciences, Harvard University, Cambridge, Mass.