Stability of a crack in a cantilever beam undergoing large plastic deformation after impact
A simple model is employed to determine the dynamic response of a rigid-perfectly plastic cantilever beam with an attached tip mass and a crack, taking into account the weakening effect of the crack. The crack is assumed to be located at the base of the beam, and an initial velocity is imparted to the tip mass. The subsequent stability of the crack is considered by calculating the tearing modulus based on the J-integral associated with the deflecting beam. For the example of circumferential cracks in thin-walled piping, whose idealized geometry models some stress corrosion cracks found in service, radial propagation and instability are found to be more likely than circumferential. Once a crack penetrates the wall, however, stability in the circumferential direction is found to depend in a complex way upon loading and crack geometry. © 1984.
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