Interactive Failure of Two Impacting Beams

A complete analysis of an inelastic beam-to-beam impact is presented. Both beams are of solid, rectangular cross-sections. The problem is formulated based on the momentum conservation and the kinematic and dynamic continuity conditions at the moving wavefront. Closed-form solutions are obtained for transient transverse velocities, deflection profiles, and tensile strains based on the moderately large deflection theory of the beam. Three different regimes of the solution are distinguished, depending on relative values of mass ratios and wave speed ratios. Critical impact velocities to break either of the beams are determined for both the striking and struck beams by assuming both beams fail by tensile necking. However, location of the fracture point depends on relative values of various parameters. It can be right in the contact zone or away from it. It is also shown that after one beam breaks, the other beam will deform further without breaking.