Mixed-mode loading of the structural elements with defect
In the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in t...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2015-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20479/16726 |
| _version_ | 1811330270985453568 |
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| author | Larisa V Stepanova Ekaterina M Yakovleva |
| author_facet | Larisa V Stepanova Ekaterina M Yakovleva |
| author_sort | Larisa V Stepanova |
| collection | DOAJ |
| description | In the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numeric solution of the nonlinear eigenvalue problem formulated is obtained. The power of the distance from the crack tip is the eigenvalue of the nonlinear eigenvalue problem considered whereas the angular distributions of the stress components are the eigenfunctions. The new eigenvalues different from the eigenvalues of the Hutchinson-Rice-Rosengren are found. It is shown that the new asymptotic solution can be interpreted as the self-similar intermediate asymptotics of the stress field in the vicinity of the crack tip at distances which are very small compared to the crack length or the size of the specimen and at distances which are large compared to the length of the completely damaged zone. The developed method allows us to construct the geometry of the completely damaged zone in vicinity of the crack tip. |
| first_indexed | 2024-04-13T15:58:45Z |
| format | Article |
| id | doaj.art-73275dd412c44fa888babf1401a8a7ec |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:58:45Z |
| publishDate | 2015-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-73275dd412c44fa888babf1401a8a7ec2022-12-22T02:40:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812015-06-0119235838110.14498/vsgtu143217899Mixed-mode loading of the structural elements with defectLarisa V Stepanova0Ekaterina M Yakovleva1Samara State UniversitySamara State UniversityIn the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numeric solution of the nonlinear eigenvalue problem formulated is obtained. The power of the distance from the crack tip is the eigenvalue of the nonlinear eigenvalue problem considered whereas the angular distributions of the stress components are the eigenfunctions. The new eigenvalues different from the eigenvalues of the Hutchinson-Rice-Rosengren are found. It is shown that the new asymptotic solution can be interpreted as the self-similar intermediate asymptotics of the stress field in the vicinity of the crack tip at distances which are very small compared to the crack length or the size of the specimen and at distances which are large compared to the length of the completely damaged zone. The developed method allows us to construct the geometry of the completely damaged zone in vicinity of the crack tip.https://journals.eco-vector.com/1991-8615/article/viewFile/20479/16726nonlinear eigenvalue problemstress-strain state near the crack tipmixed-mode loadingmixity parameterperturbation technique |
| spellingShingle | Larisa V Stepanova Ekaterina M Yakovleva Mixed-mode loading of the structural elements with defect Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki nonlinear eigenvalue problem stress-strain state near the crack tip mixed-mode loading mixity parameter perturbation technique |
| title | Mixed-mode loading of the structural elements with defect |
| title_full | Mixed-mode loading of the structural elements with defect |
| title_fullStr | Mixed-mode loading of the structural elements with defect |
| title_full_unstemmed | Mixed-mode loading of the structural elements with defect |
| title_short | Mixed-mode loading of the structural elements with defect |
| title_sort | mixed mode loading of the structural elements with defect |
| topic | nonlinear eigenvalue problem stress-strain state near the crack tip mixed-mode loading mixity parameter perturbation technique |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20479/16726 |
| work_keys_str_mv | AT larisavstepanova mixedmodeloadingofthestructuralelementswithdefect AT ekaterinamyakovleva mixedmodeloadingofthestructuralelementswithdefect |