A full-range stress-strain model for metallic materials depicting non-linear strain-hardening behavior

Abstract

Ramberg-Osgood (R-O) type stress-strain models are commonly employed during elasto-plastic analysis of metals. Recently, 2-stage and 3-stage R-O variant models have been proposed to replicate stress-strain behavior under large plastic deformation. The complexity of these models increases with the addition of each stage. Moreover, these models have considered deformation till necking only. In this paper, a simplistic multi-stage constitutive model is proposed to capture the strain-hardening non-linearity shown by metals including its post necking behavior. The constitutive parameters of the proposed stress-strain model can be determined using only elastic modulus and yield strength. 3-D digital image correlation was used as an experimental tool for measuring full-field strains on the specimens, which were subsequently utilized to obtain the material parameters. Our constitutive model is demonstrated with an aerospace-grade stainless steel AISI 321 wherein deformation response averaged over the gauge length (GL) and at a local necking zone are compared. The resulting averaged and local material parameters obtained from the proposed model provide interesting insights into the pre and post necking deformation behavior. Our constitutive model would be useful for characterizing highly ductile metals which may or may not depict non-linear strain hardening behavior including their post necking deformations.