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 = ( σ 2 − σ r 2 ) / ( σ d s 2 − σ r 2 ) 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 σ y , saturation stress σ r s , steady stress σ d s and critical strain ε c 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.