Bounds for Fully Plastic Crack Problems for Infinite Bodies

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.