| Summary: | 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: <inline-formula> <math display="inline"> <semantics> <mrow> <mi>X</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>σ</mi> <mn>2</mn> </msup> <mo>−</mo> <msubsup> <mi>σ</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mo stretchy="false">)</mo> <mo>/</mo> <mo stretchy="false">(</mo> <msubsup> <mi>σ</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> <mn>2</mn> </msubsup> <mo>−</mo> <msubsup> <mi>σ</mi> <mi>r</mi> <mn>2</mn> </msubsup> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>k</mi> <mo>∗</mo> </msup> </mrow> </semantics> </math> </inline-formula>, time exponent <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>n</mi> <mo>∗</mo> </msup> </mrow> </semantics> </math> </inline-formula>, strain rate <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </semantics> </math> </inline-formula>, temperature <inline-formula> <math display="inline"> <semantics> <mi>T</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula> parameter are discussed. The yield stress <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>σ</mi> <mi>y</mi> </msub> </mrow> </semantics> </math> </inline-formula>, saturation stress <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>r</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula>, steady stress <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> and critical strain <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>ε</mi> <mi>c</mi> </msub> </mrow> </semantics> </math> </inline-formula> are expressed as the functions of the <inline-formula> <math display="inline"> <semantics> <mi>Z</mi> </semantics> </math> </inline-formula> 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.
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