Simple phenomenological expression for plastic deformation of pure metals and single-phase alloys to high strains

Abstract

Recent studies on the deformation of metals indicate that at relatively high strains the flow stress does not increase with further strain. The mathematical expressions usually used to derive the relationship between stress and strain (generally the Ludwik or Hollomon equations) do not predict such a plateau. A new expression (σ = K1mn(tanh ε/m)n is proposed, where K and n have the same values as the original Hollomon equation and m is an additional disposable parameter. The new expression reduces to the Hollomon equation at low strains but, by adjusting the value of m, can be made to correspond to the high-strain behaviour. For copper and silver, using values of n = 0·5 and m = 2, the ratio of the flow stresses at unit strain to the saturation flow stresses corresponds to those observed experimentally.MST/455