A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation
The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="normal">sin</mi><mo>²</mo></mrow><mo></mo><mrow><m...
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| Format: | Article |
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MDPI AG
2024-01-01
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| Series: | Metals |
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| Online Access: | https://www.mdpi.com/2075-4701/14/1/62 |
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| author | Ewann Gautier Pierre Faucheux Bruno Levieil Laurent Barrallier Sylvain Calloch Cédric Doudard |
| author_facet | Ewann Gautier Pierre Faucheux Bruno Levieil Laurent Barrallier Sylvain Calloch Cédric Doudard |
| author_sort | Ewann Gautier |
| collection | DOAJ |
| description | The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="normal">sin</mi><mo>²</mo></mrow><mo></mo><mrow><mi>ψ</mi></mrow></mrow></mrow></semantics></math></inline-formula> method is the general method for analyzing X-ray diffraction stress measurements. This method relies on the estimation of a parameter known as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula>, which is generally considered as a material constant. However, various studies have shown that this parameter can be affected by plastic deformation leading to proportional uncertainties in the estimation of stresses. In this paper, in situ X-ray diffraction measurements are performed during a tensile test with unloads on a low-carbon high-strength steel. The calibrated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula> parameter varies from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula> MPa<sup>−1</sup> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.5</mn><mo> </mo><msup><mrow><mo>×</mo><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula> Mpa<sup>−1</sup>, depending on the surface condition and on the plastic strain state, leading to a maximum error on the stress level of 40% compared to reference handbook values. The results also show that plastic strain is responsible for 6 to 14% of the variation, depending on the initial surface sample condition. A method is then proposed to correct this variation based on the fit of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula> evolution with respect to the peak diffraction width, the latter being an indication of the plasticity state. It is shown that the proposed methodology improves the applied stress increment prediction, although the absolute stress value still depends on pseudo-macrostresses that also vary with plastic strain. |
| first_indexed | 2024-03-08T10:40:32Z |
| format | Article |
| id | doaj.art-91871d2efdbb4226a04561607f42de8b |
| institution | Directory Open Access Journal |
| issn | 2075-4701 |
| language | English |
| last_indexed | 2024-03-08T10:40:32Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
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| series | Metals |
| spelling | doaj.art-91871d2efdbb4226a04561607f42de8b2024-01-26T17:41:04ZengMDPI AGMetals2075-47012024-01-011416210.3390/met14010062A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width VariationEwann Gautier0Pierre Faucheux1Bruno Levieil2Laurent Barrallier3Sylvain Calloch4Cédric Doudard5ENSTA Bretagne, IRDL—UMR CNRS 6027, 2 Rue François Verny, 29200 Brest, FranceENSTA Bretagne, IRDL—UMR CNRS 6027, 2 Rue François Verny, 29200 Brest, FranceENSTA Bretagne, IRDL—UMR CNRS 6027, 2 Rue François Verny, 29200 Brest, FranceMSMP Arts et Métiers Institute of Technology, HESAM Université, F-13617 Aix-en-Provence, FranceENSTA Bretagne, IRDL—UMR CNRS 6027, 2 Rue François Verny, 29200 Brest, FranceENSTA Bretagne, IRDL—UMR CNRS 6027, 2 Rue François Verny, 29200 Brest, FranceThe <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mrow><mi mathvariant="normal">sin</mi><mo>²</mo></mrow><mo></mo><mrow><mi>ψ</mi></mrow></mrow></mrow></semantics></math></inline-formula> method is the general method for analyzing X-ray diffraction stress measurements. This method relies on the estimation of a parameter known as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula>, which is generally considered as a material constant. However, various studies have shown that this parameter can be affected by plastic deformation leading to proportional uncertainties in the estimation of stresses. In this paper, in situ X-ray diffraction measurements are performed during a tensile test with unloads on a low-carbon high-strength steel. The calibrated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula> parameter varies from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula> MPa<sup>−1</sup> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5.5</mn><mo> </mo><msup><mrow><mo>×</mo><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></semantics></math></inline-formula> Mpa<sup>−1</sup>, depending on the surface condition and on the plastic strain state, leading to a maximum error on the stress level of 40% compared to reference handbook values. The results also show that plastic strain is responsible for 6 to 14% of the variation, depending on the initial surface sample condition. A method is then proposed to correct this variation based on the fit of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msubsup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>h</mi><mi>k</mi><mi>l</mi></mrow></msubsup></mrow></semantics></math></inline-formula> evolution with respect to the peak diffraction width, the latter being an indication of the plasticity state. It is shown that the proposed methodology improves the applied stress increment prediction, although the absolute stress value still depends on pseudo-macrostresses that also vary with plastic strain.https://www.mdpi.com/2075-4701/14/1/62X-ray elastic constantsplastic strainpseudo-macrostress |
| spellingShingle | Ewann Gautier Pierre Faucheux Bruno Levieil Laurent Barrallier Sylvain Calloch Cédric Doudard A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation Metals X-ray elastic constants plastic strain pseudo-macrostress |
| title | A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation |
| title_full | A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation |
| title_fullStr | A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation |
| title_full_unstemmed | A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation |
| title_short | A Simple Calibration Method to Consider Plastic Deformation Influence on X-ray Elastic Constant Based on Peak Width Variation |
| title_sort | simple calibration method to consider plastic deformation influence on x ray elastic constant based on peak width variation |
| topic | X-ray elastic constants plastic strain pseudo-macrostress |
| url | https://www.mdpi.com/2075-4701/14/1/62 |
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