Limitations of Hollomon and Ludwigson stress–strain relations in assessing the strain hardening parameters

Abstract

It is shown that the deviation from the ideal Hollomon relation in describing the stress–strain behaviour is characteristic of all materials at low strains. The Ludwigson relation describing the deviation from the Hollomon relation at low strains is critically analysed and it is shown that the deviation at low strains is a consequence of some unknown ‘plastic strain equivalent’ present in the material. Stress strain curves obeying an ideal Hollomon relation as well as that of a structurally modified (prior cold worked) material were simulated and compared. The results show that the yield strength and the flow strength of a material at constant strain rate and temperature are dictated by the magnitude of the ‘plastic strain equivalent’ term. It is shown that this component need not necessarily mean a prior plastic strain present in the material due to prior cold work alone and that prior cold work strain will add to this. If this component is identified, the stress–strain behaviour can be adequately described by the Swift relation. It is shown that in both formalisms, the strain hardening index is a function of the yield strength of the material.