A further study of plastic shear failure of impulsively loaded clamped beams

As early as in 1973, Menkes and Opat (Exp Mech 1973; 13:480–6) conducted an experimental investigation on the dynamic plastic response and failure of fully clamped metal beams subjected to a uniformly distributed impulsive loading and identified three basic failure modes: large inelastic deformation (Mode I), tensile tearing (Mode II) and transverse shear failure at the supports (Mode III). A rigid-plastic analysis was later carried out by Jones (Trans ASME J Eng Ind 1976; 98 (B1): 131–6), in which an elementary failure criterion was adopted to estimate the threshold impulsive velocities at the onset of Mode II or Mode III failure. A deep understanding of these three basic failure modes is of fundamental importance to failure analyses of various structures under intense dynamic loading. The present paper re-examines the plastic shear failure (Mode III) of impulsively loaded clamped beams, with focus on two effects: (i) the interaction between the shear force and bending moment; and (ii) the weakening of the sliding sections during the failing process. A dimensional analysis is first performed to obtain a general form of the threshold impulsive velocity, which overlooks succeeding concrete analyses. The elementary failure criterion is then modified to incorporate the sliding sections’ weakening effect. Interaction between the shear force and the bending moment at the supporting ends is considered by using circular yield curve (Robinson, Int J Solids Struct 1973; 9:819), Hodgeʹs curve (J Appl Mech 1957; 24:453–6), or a yield condition based on slip-line solutions. By taking into account the variation with time of the shear force and the bending moment over the failing cross-sections, the plastic deformation and failure process of the beams are traced and the ratio of plastic shear dissipation to the total plastic dissipation is thus calculated. This is followed by a discussion on a shear strain failure criterion. Finally, the predictions from various approaches are compared with each other as well as with relevant experimental results.