Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields
Abstract A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional di...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-04-01
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| Series: | Materials Theory |
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| Online Access: | http://link.springer.com/article/10.1186/s41313-020-00020-2 |
| _version_ | 1818684504080908288 |
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| author | Yejun Gu Jaafar A. El-Awady |
| author_facet | Yejun Gu Jaafar A. El-Awady |
| author_sort | Yejun Gu |
| collection | DOAJ |
| description | Abstract A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations. Using this model, it is shown that a nano-hydride can form in the tensile region below a dissociated edge dislocation at hydrogen concentration as low as χ 0=5×10−5, and its formation induces a localized hydrogen elastic shielding effect that leads to a lower stacking fault width for the edge dislocation. Additionally, the model also predicts the segregation of hydrogen at Σ109(13 7 0)/33.4∘ symmetric tilt grain boundary dislocations. This segregation strongly alters the magnitude of the shear stresses at the grain boundary, which can subsequently alter dislocation-grain boundary interactions and dislocation slip transmissions across the grain boundary. Moreover, the model also predicts that the hydrogen concentration at a mode-I central crack tip increases with increasing external loading, higher intrinsic hydrogen concentration, and/or larger crack lengths. Finally, linearized approximate closed-form solutions for the solute concentration and the interstitial solute-induced stress field were also developed. These approximate solutions can effectively reduce the computation cost to assess the concentration and stress field in the presence of solutes. These approximate solutions are also shown to be a good approximation when the positions of interest are several nanometers away (i.e. long-ranged elastic interactions) from stress singularities (e.g. dislocation core and crack tip), for low solute concentrations, and/or at high temperatures. |
| first_indexed | 2024-12-17T10:51:41Z |
| format | Article |
| id | doaj.art-bdfb5375ff5947e6b4dd0fae6588c502 |
| institution | Directory Open Access Journal |
| issn | 2509-8012 |
| language | English |
| last_indexed | 2024-12-17T10:51:41Z |
| publishDate | 2020-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Materials Theory |
| spelling | doaj.art-bdfb5375ff5947e6b4dd0fae6588c5022022-12-21T21:51:58ZengSpringerOpenMaterials Theory2509-80122020-04-014112210.1186/s41313-020-00020-2Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fieldsYejun Gu0Jaafar A. El-Awady1Department of Mechanical Engineering, Whiting School of Engineering, The Johns Hopkins UniversityDepartment of Mechanical Engineering, Whiting School of Engineering, The Johns Hopkins UniversityAbstract A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations. Using this model, it is shown that a nano-hydride can form in the tensile region below a dissociated edge dislocation at hydrogen concentration as low as χ 0=5×10−5, and its formation induces a localized hydrogen elastic shielding effect that leads to a lower stacking fault width for the edge dislocation. Additionally, the model also predicts the segregation of hydrogen at Σ109(13 7 0)/33.4∘ symmetric tilt grain boundary dislocations. This segregation strongly alters the magnitude of the shear stresses at the grain boundary, which can subsequently alter dislocation-grain boundary interactions and dislocation slip transmissions across the grain boundary. Moreover, the model also predicts that the hydrogen concentration at a mode-I central crack tip increases with increasing external loading, higher intrinsic hydrogen concentration, and/or larger crack lengths. Finally, linearized approximate closed-form solutions for the solute concentration and the interstitial solute-induced stress field were also developed. These approximate solutions can effectively reduce the computation cost to assess the concentration and stress field in the presence of solutes. These approximate solutions are also shown to be a good approximation when the positions of interest are several nanometers away (i.e. long-ranged elastic interactions) from stress singularities (e.g. dislocation core and crack tip), for low solute concentrations, and/or at high temperatures.http://link.springer.com/article/10.1186/s41313-020-00020-2Interstitial solutesHydrogen embrittlementSegregationDislocation dynamicsSolute diffusion |
| spellingShingle | Yejun Gu Jaafar A. El-Awady Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields Materials Theory Interstitial solutes Hydrogen embrittlement Segregation Dislocation dynamics Solute diffusion |
| title | Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields |
| title_full | Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields |
| title_fullStr | Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields |
| title_full_unstemmed | Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields |
| title_short | Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields |
| title_sort | theoretical framework for predicting solute concentrations and solute induced stresses in finite volumes with arbitrary elastic fields |
| topic | Interstitial solutes Hydrogen embrittlement Segregation Dislocation dynamics Solute diffusion |
| url | http://link.springer.com/article/10.1186/s41313-020-00020-2 |
| work_keys_str_mv | AT yejungu theoreticalframeworkforpredictingsoluteconcentrationsandsoluteinducedstressesinfinitevolumeswitharbitraryelasticfields AT jaafaraelawady theoreticalframeworkforpredictingsoluteconcentrationsandsoluteinducedstressesinfinitevolumeswitharbitraryelasticfields |