Strain rate sensitivity and yield point behavior in mild steel

Abstract

An empirical description of the rate sensitive behavior of mild steel based on a logarithmic dependence of flow stress on strain rate is examined in detail. It is shown that the law provides a good representation of the material response for strains up to about 5.0 percent. The delayed yield phenomenon, which is a striking characteristic of mild steel behavior is included and a mechanism previously found to be accurate in representing the delay time under constant stress is used to determine the delay time under complex stress histories. The relaxation from the upper yield point resulting from the delay time in a constant strain rate situation is prescribed by the rate sensitive behavior of the material.It is shown that the response of the material is a functional of the stress history and has a fading memory in strain as well as time. The characteristic memory strain is found to be small so that for large strains the influence of the history is small and an equation-of-state representation is appropriate. For small strains and strain histories of rapidly changing type the integral representation must be used.The theory is applied to the prediction of the response of a beam subject to constant rate of curvature and the predicted response compared with published experimental data. In addition, the transverse impact of a mass on a beam is investigated and the theory is used to predict the onset of yielding in the beam. This problem is of importance in the design of highway guard-rails.