Avrami kinetic-based constitutive relationship for armco-type pure iron in hot deformation

Abstract

The work presents a full mathematical description of the stress-strain compression curves in a wide range of strain rates and deformation temperatures for Armco-type pure iron. The constructed models are based on a dislocation structure evolution equation (in the case of dynamic recovery (DRV)) and Avrami kinetic-based model (in the case of dynamic recrystallization (DRX)). The fractional softening model is modified as: X=(σ2−σ2r)/(σ2ds−σ2r) considering the strain hardening of un-recrystallized regions. The Avrami kinetic equation is modified and used to describe the DRX process considering the strain rate and temperature. The relations between the Avrami constant k∗, time exponent n∗, strain rate ε˙, temperature T and Z parameter are discussed. The yield stress σy, saturation stress σrs, steady stress σds and critical strain εc are expressed as the functions of the Z parameter. A constitutive model is constructed based on the strain-hardening model, fractional softening model and modified Avrami kinetic equation. The DRV and DRX characters of Armco-type pure iron are clearly presented in these flow stress curves determined by the model.