A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals
Plastic deformation in metals is heavily influenced by the loading direction. Studies have explored its effects on multiple mechanisms by analysing individual dislocations, but there is currently no systematic way of rationalising the cooperative behaviour of the different slip systems for arbitrary...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/10/6/445 |
| _version_ | 1797566547663781888 |
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| author | Fernando Daniel León-Cázares Catherine Mary Fiona Rae |
| author_facet | Fernando Daniel León-Cázares Catherine Mary Fiona Rae |
| author_sort | Fernando Daniel León-Cázares |
| collection | DOAJ |
| description | Plastic deformation in metals is heavily influenced by the loading direction. Studies have explored its effects on multiple mechanisms by analysing individual dislocations, but there is currently no systematic way of rationalising the cooperative behaviour of the different slip systems for arbitrary stress tensors. The current study constitutes the foundation of a new orientation analysis framework for face-centred cubic crystals by introducing “stress orientation maps”, graphical tools to simultaneously analyse the effects of loading orientation on the stress state of the <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mi>a</mi> <mn>2</mn> </mfrac> <mrow> <mo>〈</mo> <mn>1</mn> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mn>0</mn> <mo>〉</mo> </mrow> <mrow> <mo>{</mo> <mn>111</mn> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mi>a</mi> <mn>6</mn> </mfrac> <mrow> <mo>〈</mo> <mn>112</mn> <mo>〉</mo> </mrow> <mrow> <mo>{</mo> <mn>111</mn> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula> slip systems in a comprehensive, yet intuitive way. Relationships between the Schmid and Escaig stresses are described from geometrical constraints of the slip systems in the crystal structure, linking the dislocation behaviour on a slip plane with the stress tensor via a one parameter description. The case of uniaxial loading along different orientations within the fundamental sector of the unit cell is explored to describe the physical basis, properties and capabilities of this framework. The stress normal to the slip plane is then considered in the analysis via an extension of the Mohr’s circles. The orientation dependence of two twin nucleation mechanisms from the literature are examined as examples of how the stress orientation maps can be used. |
| first_indexed | 2024-03-10T19:28:27Z |
| format | Article |
| id | doaj.art-2cc4b5f4788e4f5981d51bf38b117cdc |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-10T19:28:27Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-2cc4b5f4788e4f5981d51bf38b117cdc2023-11-20T02:18:55ZengMDPI AGCrystals2073-43522020-05-0110644510.3390/cryst10060445A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic MetalsFernando Daniel León-Cázares0Catherine Mary Fiona Rae1Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Rd, Cambridge CB3 0FS, UKDepartment of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Rd, Cambridge CB3 0FS, UKPlastic deformation in metals is heavily influenced by the loading direction. Studies have explored its effects on multiple mechanisms by analysing individual dislocations, but there is currently no systematic way of rationalising the cooperative behaviour of the different slip systems for arbitrary stress tensors. The current study constitutes the foundation of a new orientation analysis framework for face-centred cubic crystals by introducing “stress orientation maps”, graphical tools to simultaneously analyse the effects of loading orientation on the stress state of the <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mi>a</mi> <mn>2</mn> </mfrac> <mrow> <mo>〈</mo> <mn>1</mn> <mover> <mn>1</mn> <mo>¯</mo> </mover> <mn>0</mn> <mo>〉</mo> </mrow> <mrow> <mo>{</mo> <mn>111</mn> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mfrac> <mi>a</mi> <mn>6</mn> </mfrac> <mrow> <mo>〈</mo> <mn>112</mn> <mo>〉</mo> </mrow> <mrow> <mo>{</mo> <mn>111</mn> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula> slip systems in a comprehensive, yet intuitive way. Relationships between the Schmid and Escaig stresses are described from geometrical constraints of the slip systems in the crystal structure, linking the dislocation behaviour on a slip plane with the stress tensor via a one parameter description. The case of uniaxial loading along different orientations within the fundamental sector of the unit cell is explored to describe the physical basis, properties and capabilities of this framework. The stress normal to the slip plane is then considered in the analysis via an extension of the Mohr’s circles. The orientation dependence of two twin nucleation mechanisms from the literature are examined as examples of how the stress orientation maps can be used.https://www.mdpi.com/2073-4352/10/6/445face-centred cubic crystalsorientationnon-Schmidplastic deformationdeformation twinningstress analysis |
| spellingShingle | Fernando Daniel León-Cázares Catherine Mary Fiona Rae A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals Crystals face-centred cubic crystals orientation non-Schmid plastic deformation deformation twinning stress analysis |
| title | A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals |
| title_full | A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals |
| title_fullStr | A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals |
| title_full_unstemmed | A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals |
| title_short | A Stress Orientation Analysis Framework for Dislocation Glide in Face-Centred Cubic Metals |
| title_sort | stress orientation analysis framework for dislocation glide in face centred cubic metals |
| topic | face-centred cubic crystals orientation non-Schmid plastic deformation deformation twinning stress analysis |
| url | https://www.mdpi.com/2073-4352/10/6/445 |
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