A Critical Assessment of Three Usual Equations for Strain Hardening and Dynamic Recovery

Abstract

The Laasraoui-Jonas (LJ), Kocks-Mecking (KM), and power law (PW) stress–strain equations pertaining to hot working of metals within the range of moderate strains (i.e., before the occurrence of dynamic recrystallization) are compared. It is shown that it is not possible to select the “best” one to fit a given experimental flow curve, neither in the σ − e nor in the \( {{{\text{d}}\rho } \mathord{\left/ {\vphantom {{{\text{d}}\rho } {{\text{d}}\varepsilon - \rho }}} \right. \kern-0pt} {{\text{d}}\varepsilon - \rho }} \) diagram. Noting that each of the three laws depends on two constitutive parameters, transformation formulae are then derived allowing the parameters of one law to be derived from the parameters of any of the two others. The fit of a given LJ equation by a PW law is then discussed. Finally, the transformation formulae are used to estimate the current rate of dynamic recovery when the flow rule is known in the form a PW law. The above theoretical derivations are illustrated by the specific case of a Fe-C alloy in the ferritic phase domain. However, they suggest that the conclusions are widely applicable to hot working of metals and alloys.