Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation - Yan Zhang; Qichao Fan; Xiaofeng Zhang; Zhaohui Zhou; Zhihui Xia; Zhiqiang Qian (Metals, 2019)
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: <semantics> X = ( σ 2 − <msubsup> σ r 2 </msubsup> ) / ( <msubsup> σ d s 2 </msubsup> − <msubsup> σ r 2 </msubsup> ) </semantics> 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 <semantics> k ∗ </semantics> , time exponent <semantics> n ∗ </semantics> , strain rate <semantics> <mover accent="true"> ε ˙ </mover> </semantics> , temperature <semantics> T </semantics> and <semantics> Z </semantics> parameter are discussed. The yield stress <semantics> σ y </semantics> , saturation stress <semantics> σ r s </semantics> , steady stress <semantics> σ d s </semantics> and critical strain <semantics> ε c </semantics> are expressed as the functions of the <semantics> Z </semantics> 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.