Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Metals |
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| Online Access: | https://www.mdpi.com/2075-4701/9/3/365 |
| _version_ | 1811238610348802048 |
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| author | Yan Zhang Qichao Fan Xiaofeng Zhang Zhaohui Zhou Zhihui Xia Zhiqiang Qian |
| author_facet | Yan Zhang Qichao Fan Xiaofeng Zhang Zhaohui Zhou Zhihui Xia Zhiqiang Qian |
| author_sort | Yan Zhang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T12:45:39Z |
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| id | doaj.art-01892f96f9ce45aca9de251bf6c84c84 |
| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-04-12T12:45:39Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Metals |
| spelling | doaj.art-01892f96f9ce45aca9de251bf6c84c842022-12-22T03:32:38ZengMDPI AGMetals2075-47012019-03-019336510.3390/met9030365met9030365Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot DeformationYan Zhang0Qichao Fan1Xiaofeng Zhang2Zhaohui Zhou3Zhihui Xia4Zhiqiang Qian5Institute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaInstitute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaInstitute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaInstitute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaInstitute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaInstitute of Machinery Manufacturing Technology, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaThe 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.https://www.mdpi.com/2075-4701/9/3/365Avrami kineticconstitutive modeldynamic recoverydynamic recrystallizationhot deformationpure iron |
| spellingShingle | Yan Zhang Qichao Fan Xiaofeng Zhang Zhaohui Zhou Zhihui Xia Zhiqiang Qian Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation Metals Avrami kinetic constitutive model dynamic recovery dynamic recrystallization hot deformation pure iron |
| title | Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation |
| title_full | Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation |
| title_fullStr | Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation |
| title_full_unstemmed | Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation |
| title_short | Avrami Kinetic-Based Constitutive Relationship for Armco-Type Pure Iron in Hot Deformation |
| title_sort | avrami kinetic based constitutive relationship for armco type pure iron in hot deformation |
| topic | Avrami kinetic constitutive model dynamic recovery dynamic recrystallization hot deformation pure iron |
| url | https://www.mdpi.com/2075-4701/9/3/365 |
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