Generalization of the Ramberg–Osgood Model for Elastoplastic Materials

Abstract

The paper dwells upon two plastic material models: the “inverse” and the modified Ramberg–Osgood laws. What makes the modified law different is that it postulates the existence of a strictly linear nonzero portion on a deformation curve, limited by the elastic limit point. The plastic strain portion begins beyond this point and ends with the ultimate stress point, which is another characteristic point of the strain curve. Strain curves corresponding to the inverse law and to the modified law have ben plotted on a sample consisting of 30 experimental Russian 20HGR-steel (Grade 900M SAE/USA) strain curve points. Standard error for the inverse law is sinvers = 0.45, while that for the modified law is an order of magnitude lower: smodif = 0.02. It is proven that the inverse law is a strict limit case of the modified law, where the elastic limit point converges to the origin and contracts the linear strain portion to a point, while the entire strain curve becomes a plastic strain curve.