Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures
This paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Ceramics |
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| Online Access: | https://www.mdpi.com/2571-6131/6/1/15 |
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| author | Vera Petrova Siegfried Schmauder Alexandros Georgiadis |
| author_facet | Vera Petrova Siegfried Schmauder Alexandros Georgiadis |
| author_sort | Vera Petrova |
| collection | DOAJ |
| description | This paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such structures include edge cracks, internal cracks, and edge/internal cracks. The material properties and fracture toughness of the FGC were modeled by formulas based on the rule of mixtures. The FGC comprised two constituents, a ceramic on the top and a metal as a homogeneous substrate, with their volume fractions determined by a power law function with the power coefficient λ as the gradation parameter for the FGC. For this study, the method of singular integral equations was used, and the integral equations were solved numerically by the mechanical quadrature method based on the Chebyshev polynomials. Attention was mainly paid to the determination of critical loads and energy release rates for the systems of interacting cracks in the FGCs in order to find ways to increase the fracture resistance of FGC/H structures. As an illustrative example, a system of three edge cracks in the FGC was considered. The crack shielding effect was demonstrated for this system of cracks. Additionally, it was shown that the gradation parameter λ had a great effect on the fracture characteristics. Thus, the proposed model provided a sound basis for the optimization of FGCs in order to improve the fracture resistance of FGC/H structures. |
| first_indexed | 2024-03-11T06:48:10Z |
| format | Article |
| id | doaj.art-f387116f764b4638b38f52dc5d6f16ac |
| institution | Directory Open Access Journal |
| issn | 2571-6131 |
| language | English |
| last_indexed | 2024-03-11T06:48:10Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Ceramics |
| spelling | doaj.art-f387116f764b4638b38f52dc5d6f16ac2023-11-17T10:14:40ZengMDPI AGCeramics2571-61312023-01-016125526410.3390/ceramics6010015Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of MixturesVera Petrova0Siegfried Schmauder1Alexandros Georgiadis2Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, GermanyInstitute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, GermanyInstitute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, GermanyThis paper is devoted to the problem of the thermal fracture of a functionally graded coating (FGC) on a homogeneous substrate (H), i.e., FGC/H structures. The FGC/H structure was subjected to thermo-mechanical loadings. Systems of interacting cracks were located in the FGC. Typical cracks in such structures include edge cracks, internal cracks, and edge/internal cracks. The material properties and fracture toughness of the FGC were modeled by formulas based on the rule of mixtures. The FGC comprised two constituents, a ceramic on the top and a metal as a homogeneous substrate, with their volume fractions determined by a power law function with the power coefficient λ as the gradation parameter for the FGC. For this study, the method of singular integral equations was used, and the integral equations were solved numerically by the mechanical quadrature method based on the Chebyshev polynomials. Attention was mainly paid to the determination of critical loads and energy release rates for the systems of interacting cracks in the FGCs in order to find ways to increase the fracture resistance of FGC/H structures. As an illustrative example, a system of three edge cracks in the FGC was considered. The crack shielding effect was demonstrated for this system of cracks. Additionally, it was shown that the gradation parameter λ had a great effect on the fracture characteristics. Thus, the proposed model provided a sound basis for the optimization of FGCs in order to improve the fracture resistance of FGC/H structures.https://www.mdpi.com/2571-6131/6/1/15thermal fracturesystem of cracksfunctionally graded coatingsfracture toughnessrule of mixtures |
| spellingShingle | Vera Petrova Siegfried Schmauder Alexandros Georgiadis Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures Ceramics thermal fracture system of cracks functionally graded coatings fracture toughness rule of mixtures |
| title | Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures |
| title_full | Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures |
| title_fullStr | Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures |
| title_full_unstemmed | Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures |
| title_short | Thermal Fracture of Functionally Graded Coatings with Systems of Cracks: Application of a Model Based on the Rule of Mixtures |
| title_sort | thermal fracture of functionally graded coatings with systems of cracks application of a model based on the rule of mixtures |
| topic | thermal fracture system of cracks functionally graded coatings fracture toughness rule of mixtures |
| url | https://www.mdpi.com/2571-6131/6/1/15 |
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