WORST-CASE CRACKS IN DUCTILE CANTILEVERS STRUCK TRANSVERSELY AT THE TIP.
Given a ductile cantilever beam subject to dynamic forces acting transversely at its tip, what crack location and orientation will result in the greatest likelihood of instability? Such a question arises in assessing the integrity of a cracked piping loop under pipe whip or impact loading, and the influence of the crack on the mode of deformation makes the answer less than obvious. While it may be clear that the worst-case crack orientation will be one for which the crack front experiences the greatest tensile stress, where along the beam such a crack will undergo the greatest crack-opening displacement may be less trivial a question. The cantilever beam with attached tip mass is a familiar configuration in applied mechanics, and its analysis provides fundamental insight into such important practical problems as damage due to impact and pipe whip.