A uniaxial viscoplastic model based on total strain and overstress

Abstract

A previously proposed, uniaxial differential constitutive equation (E.R. C ernocky and E. K rempl, 1979a, b), nonlinear in the Cauchy stress and the engineering strain but linear in the stress and strain-rates, is specialized to an overstress model. It is shown by qualitative arguments that the solutions correspond to typical room-temperature viscoplastic behavior of AISI type 304 stainless steel. Two unknown coefficient functions are determined by extrapolation of room temperature relaxation data for this steel. The stiff first-order nonlinear differential equations are then numerically integrated for a variety of test histories. These include strain control with strain-rates from 10 −6 to 800s −1, stress control with stressrates from 1.95 kPa s −1 to 19.5 MPa s −1, instantaneous large changes in strain-rate and stress-rate, and partial unloading and reloading in strain and stress control and tension-tension cyclic creep. The computed results show good qualitative agreement with tests. Based on these results we consider that the model is a good representation of metal deformation behavior as long as the overstress does not change sign.