Residual Deformation of Initially Curved Elasto-Plastic Bars due to Longitudinal Impact

Abstract

Behavior of a slightly curved bar under longitudinal impact with a heavy rigid hammer at a low velocity was analyzed numerically, and the residual deformation of the bar was investigated. Dynamic elasto-plastic deformation was discussed for the bar subjected to the plastic strain of the same order as the elastic one. Because of difficulty in obtaining a closed form of solution for this problem due to geometric and material nonlinearity, the solid bar was replaced by a lumped-parameter model, and the equations of motion were integrated numerically.
The stress at each point on the cross section was evaluated by taking account of a detailed deformation history of that point. The bending moment was calculated by integrating these stresses. This method has been confirmed to give more accurate results than using the conventional method for analyzing the behavior of bars of small slenderness ratios, in which the stress distribution over the cross section is highly nonlinear.
The residual deformation of the bar was evaluated by the residual axial displacement of the struck end. The effects of the following two factors on the residual axial displacement were investigated; the ratio of the mass of the rigid hammer to that of the bar, and the impact velocity of the rigid hammer. As the result, it was shown that the residual axial displacement was expressed by the product of the power function of the mass ratio and that of the impact velocity.