Dynamic buckling of elastic–plastic square tubes under axial impact—I: stress wave propagation phenomenon

The speeds of the stress waves that can propagate in an elastic–plastic medium with isotropic linear strain hardening in a plane stress state are obtained in order to analyse the influence of the transient deformation process on the initiation of buckling in square tubes under axial impact. The kinematic conditions across a surface of discontinuity were employed to obtain the stress wave propagation speeds for an initial condition [vx]=V0. It is shown that the plastic wave speeds depend on the stress state and on the direction of wave propagation. The material hardening properties have a stronger effect on the speed of the slow plastic wave, while the shear stress affects both the speeds of the fast and slow plastic waves. The magnitude of the instantaneously applied in-plane load [σxx] at t=0, which results from an impact in the direction (nx=1, ny=0), is obtained as a function of the initial velocity V0 when using the differential relationships along the characteristics. A numerical simulation of an in-plane impact on a finite plate by a large mass with an initial velocity shows that the predicted stress wave speeds from the theoretical analysis agree with the speed of the propagation of the plastic zone in the plate. It is shown that the initial buckling pattern forms within a sustained axial plastic flow and remains unchanged when large displacements develop. Therefore, it is concluded that the transient process in elastic–plastic plates subjected to an in-plane impact plays a significant role for the formation of the final buckling shape and this process can be analysed using estimates for the stress wave speeds obtained for an elastic–plastic medium in a plane stress state.