Rate-dependent inelastic constitutive equation: the extension of elastoplasticity

Abstract

A rate-dependent inelastic constitutive equation is formulated by extending the elastoplastic constitutive equation so as to retain the latter's mathematical structure and thus reduce to the latter equation at an infinitesimal rate of deformation. That structure differs substantially from that of the over-stress model, the best-known rate-dependent inelastic constitutive model. The proposed constitutive model is a type of superposition model, which is premised on the additive decomposition of the inelastic strain rate into the plastic and creep strain rates. The plastic strain rate is formulated so as to become suppressed as the rate of deformation increases but is induced even at the infinite rate of deformation. This is the distinguishing features of this model from the existing superposition models. The present model can describe realistically the rate-dependent inelastic deformation for a wide range of strain rates. On the other hand, the over-stress model cannot predict appropriately the difference of mechanical response due to the rate of deformation, especially being inapplicable to the description of deformation at high rate of deformation as known from the unrealistic prediction of the infinite strength at an infinite rate of deformation. The proposed model is applied to various metals, and its adequacy is verified through comparisons with various test data under a wide variety of strain rates and temperatures.