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.
Highlights
The hot deformation process is crucial for the industrial use of alloys to refine the grains, eliminate the defects and change the shape
A constitutive model is constructed based on the strain-hardening model, fractional softening model and modified Avrami kinetic equation
Various constitutive relationships have been constructed to describe the flow behavior during the hot deformation process, which are introduced as follows: Zener and Hollomon suggested that the isothermal stress-strain relation in steels depends on the strain rate ε, temperature T and activation energy Q, and concluded that the logarithm of the flow stress σ is a linear function of the logarithm of the Zener-Holloman parameter (Z parameter) which has the form: Z = ε exp( Q/RT )
Summary
The hot deformation process (e.g., forging and sheeting) is crucial for the industrial use of alloys to refine the grains, eliminate the defects and change the shape. Various constitutive relationships have been constructed to describe the flow behavior during the hot deformation process, which are introduced as follows: Zener and Hollomon suggested that the isothermal stress-strain relation in steels depends on the strain rate ε, temperature T and activation energy Q, and concluded that the logarithm of the flow stress σ is a linear function of the logarithm of the Zener-Holloman parameter (Z parameter) which has the form: Z = ε exp( Q/RT ). Among the constitutive models mentioned above, the Arrhenius-type model with sine-hyperbolic law has been successfully and widely applied for predicting the flow behavior of alloys in a hot deformation. The Avrami kinetic equation is discussed and modified to describe the kinetics of the DRX process considering the effects of strain rate and temperature. The Avrami kinetic-based constitutive model considering the effects of DRV and DRX is constructed and used to describe the flow behavior of Armco-type pure iron in hot deformation
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