Closed-form analysis of a thermally loaded single-layer system on a rigid foundation
A closed-form analytical model of a single layer with a linear elastic material behavior on a rigid foundation subjected to thermal loading is investigated. The closed-form analytical model is based on a higher-order displacement approach that takes the singularity exponent into account. Two applica...
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Académie des sciences
2025-01-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.268/ |
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| author | Linn, Debora Becker, Wilfried |
| author_facet | Linn, Debora Becker, Wilfried |
| author_sort | Linn, Debora |
| collection | DOAJ |
| description | A closed-form analytical model of a single layer with a linear elastic material behavior on a rigid foundation subjected to thermal loading is investigated. The closed-form analytical model is based on a higher-order displacement approach that takes the singularity exponent into account. Two applications are considered in this work. First, the interlaminar stresses are analyzed at the interface between the substrate and the material layer. These stresses are an indicator of the formation of interlaminar cracks, which cause the individual layer to peel off. Based on the interlaminar stresses, the closed-form analytical approach, which considers the singularity exponent in the displacement approach, is compared to a model with a second order displacement approach and a FEM model. In the second part, the development of transversal cracks is considered within the framework of Finite Fracture Mechanics, using a coupled stress and energy criterion. Transverse cracks often occur in thin brittle layers such as ceramic coatings and form in periodic patterns. In this work, a representative unit cell is considered – i.e. the material layer between two cracks. This unit cell is used to determine the cooling temperature at which transverse cracks develop. Furthermore, the resulting distance between two cracks can be determined when larger cooling temperatures are applied. |
| format | Article |
| id | doaj-art-9b2d6766cb0d40c3b4cf30eb6c179961 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-9b2d6766cb0d40c3b4cf30eb6c1799612025-02-07T13:49:01ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342025-01-01353G1798910.5802/crmeca.26810.5802/crmeca.268Closed-form analysis of a thermally loaded single-layer system on a rigid foundationLinn, Debora0Becker, Wilfried1Technical University of Darmstadt, Institute of Applied Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, GermanyTechnical University of Darmstadt, Institute of Applied Dynamics, Otto-Berndt-Str. 2, 64287 Darmstadt, GermanyA closed-form analytical model of a single layer with a linear elastic material behavior on a rigid foundation subjected to thermal loading is investigated. The closed-form analytical model is based on a higher-order displacement approach that takes the singularity exponent into account. Two applications are considered in this work. First, the interlaminar stresses are analyzed at the interface between the substrate and the material layer. These stresses are an indicator of the formation of interlaminar cracks, which cause the individual layer to peel off. Based on the interlaminar stresses, the closed-form analytical approach, which considers the singularity exponent in the displacement approach, is compared to a model with a second order displacement approach and a FEM model. In the second part, the development of transversal cracks is considered within the framework of Finite Fracture Mechanics, using a coupled stress and energy criterion. Transverse cracks often occur in thin brittle layers such as ceramic coatings and form in periodic patterns. In this work, a representative unit cell is considered – i.e. the material layer between two cracks. This unit cell is used to determine the cooling temperature at which transverse cracks develop. Furthermore, the resulting distance between two cracks can be determined when larger cooling temperatures are applied.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.268/Analytical modelStress predictionInterlaminar stressesTransversal cracksCrack pattern |
| spellingShingle | Linn, Debora Becker, Wilfried Closed-form analysis of a thermally loaded single-layer system on a rigid foundation Comptes Rendus. Mécanique Analytical model Stress prediction Interlaminar stresses Transversal cracks Crack pattern |
| title | Closed-form analysis of a thermally loaded single-layer system on a rigid foundation |
| title_full | Closed-form analysis of a thermally loaded single-layer system on a rigid foundation |
| title_fullStr | Closed-form analysis of a thermally loaded single-layer system on a rigid foundation |
| title_full_unstemmed | Closed-form analysis of a thermally loaded single-layer system on a rigid foundation |
| title_short | Closed-form analysis of a thermally loaded single-layer system on a rigid foundation |
| title_sort | closed form analysis of a thermally loaded single layer system on a rigid foundation |
| topic | Analytical model Stress prediction Interlaminar stresses Transversal cracks Crack pattern |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.268/ |
| work_keys_str_mv | AT linndebora closedformanalysisofathermallyloadedsinglelayersystemonarigidfoundation AT beckerwilfried closedformanalysisofathermallyloadedsinglelayersystemonarigidfoundation |