A uniformly valid asymptotic solution of Hart's equations for constant, nonelastic, extensional strain rate (Q1058355)

A uniformly valid approximate solution of \textit{E. W. Hart}'s constitutive equation [e.g. J. Eng. Materials Technol. 98, 193-202 (1976)] is presented in this paper for the special case of a constant, nonelastic strain rate tensile test. The method of matched asymptotics is used in the analysis. A principal result is that for sufficiently low temperature or high nonelastic strain rate, the ''viscoplastic limit'' is a good approximation to the solution of Hart's equations. The combined effect of temperature and strain rate on the behavior of these equations is shown to be characterized by two nondimensional parameters \(\epsilon_ 1\) and \(\epsilon_ 2\). It is found that with a judicious choice of these parameters, the numerical integration of Hart's equation can be easily carried out. The numerical results validate the viscoplastic approximation. A comparison of numerical results and the analytic solution is presented.