Some Unification of Creep Theories Based on Internal Time Concept

Summary

Among the constitutive equations for high strain rate properties of materials under dynamic loading, the’ Overstress Model’ of Malvern[l] and Perzyna[2] is well known because of its simplicity and ability. This model has been widely extended for describing the quasi-static creep behavior under high temperature environment by Chaboche[3], Robinson[4], Bruhns[5], Krempl, McMahon & Yao[6] and Sahashi, Imatani & Inoue[7]. On the other hand,’ Endochronic Model’ of Valanis[8] received attensions because of its ability to predict time-independent plastic deformation under complex loading histories. This model is applied for time-dependent deformations, such as dynamic loading and quasi-static creep behaviors. Wu & Yip[9] applied this model for the dynamic behavior of materials, and Chang, Sugiura & Lee[10] proposed an alternate theory of high strain rate problems. In this’ Endochronic Model’ for dynamic problems, the current stress exists beyond the yield surface, and inelastic strain becomes larger as the stress goes away from the boundary of the static yield surafce. Watanabe & Atluri[11,12] applied’ Endochronic Model’ for quasi-static creep behaviors, where the current stress is confined within the yield surface, and inelatic strain rate will become infinite as the stress approaches to the boundary of yield surface.

This paper gives some theoretical unification of the rate dependent constitutive modeling for dynamic and quasi-static problems developed in’ Overstress Model’ and’ Endochronic Model’. By introducing a new intrinsic time derived from the fundamental stress-strain relation in the integral form,’ Endochronic Model’ is shown to be general enough to relate closely to the previous’ Overstress Model’.