PSI - Issue 23

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Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000

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Procedia Structural Integrity 23 (2019) 407–412

9th International Conference on Materials Structure and Micromechanics of Fracture A theoretical model for the study of thermal fracture of functionally 9th International Conference on Materials Structure and Micromechanics of Fracture A theoretical model for the study of thermal fracture of functionally

graded thermal barrier coatings Vera Petrova a,b, *, Siegfried Schmauder a a IMWF, University of Stuttgart, Pfaffenwaldring 32, D-70569 Stuttgart, Germany b Voronezh State University, University Sq.1, Voronezh 394006, Russia graded thermal barrier coatings Vera Petrova a,b, *, Siegfried Schmauder a a IMWF, University of Stuttgart, Pfaffenwaldring 32, D-70569 Stuttgart, Germany b Voronezh State University, University Sq.1, Voronezh 394006, Russia

Abstract Abstract

© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the ICMSMF organizers © 201 9 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Th problem of fracture of functionally gra ed coatings (FGC ) on omogeneous substrate (a s mi-infinit medium) is investi a d under t influence of thermal and/or mechanical loads (e.g. a heat flux, r sidual hermal stresse caused by cooling hea ing, tension). The e loads refle t the most importa cases, which aris during the exploitation of FGC s ructures. The FGC contains pre-exist g systems of cracks, such as edge, internal and interface cracks. The mat matical descript on of the model is based on singular in egral equations. The properties of he FGC are continuous functions of th thickness coordinat . Furthe more, the non-hom gen ity of the unctionally graded material is rev ale in the form of corresponding inhomogeneous tr ction distributions on the surfaces of cracks. T is method is approximat a d used with the s umption, that the gradation of material properties of the FGC w th he depth of the layer is not abrupt. The nfluenc f r sidual st ess s c used by temperature ch ng s on ΔT (cooling) is investigated in det il. Differ t crack patterns (which are r por ed in experiments d available n the literature) a e studied by carrying out numerical experiments with respect to stress intensity fact rs, fracture angles (a deviation of cracks fr the i itial direction of ropagation) nd critical loads, when th propagation of cracks starts. The propos d mod l in combinati n with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous systems. © 201 9 The Authors. Published by Elsevier B.V. This is an open acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. The problem of fracture of functionally graded coatings (FGCs) on a homogeneous substrate (a semi-infinite medium) is investigated under the influence of thermal and/or mechanical loads (e.g. a heat flux, residual thermal stresses caused by cooling heating, tension). These loads reflect the most important cases, which arise during the exploitation of FGC structures. The FGC contains pre-existing systems of cracks, such as edge, internal and interface cracks. The mathematical description of the model is based on singular integral equations. The properties of the FGC are continuous functions of the thickness coordinate. Furthermore, the non-homogeneity of the functionally graded material is revealed in the form of corresponding inhomogeneous traction distributions on the surfaces of cracks. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The influence of residual stresses caused by temperature changes on ΔT (cooling) is investigated in detail. Different crack patterns (which are reported in experiments and available in the literature) are studied by carrying out numerical experiments with respect to stress intensity factors, fracture angles (a deviation of cracks from the initial direction of propagation) and critical loads, when the propagation of cracks starts. The proposed model in combination with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous systems. Keywords: Thermal fracture; functionally graded coatings; thermal residual stresses; systems of cracks; singular integral equations Keywords: Thermal fracture; functionally graded coatings; thermal residual stresses; systems of cracks; singular integral equations

* Corresponding author. Tel.: +49 711 685 63339; fax: +49 711 685 67779. E-mail address: Vera.Petrova@mpa.uni-stuttgart.de * Correspon ing author. Tel.: +49 711 685 63339; fax: +49 711 685 67779. E-mail address: Vera.Petrova@mpa.uni-stuttgart.de

2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

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