PSI - Issue 28

Vera Petrova et al. / Procedia Structural Integrity 28 (2020) 608–618 Author name / Structural Integrity Procedia 00 (2019) 000–000

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5. Summary A general theoretical formulation of the model for the thermal fracture analysis of functionally graded coatings on a homogeneous substrate (FGC/H) has been performed by means of integral equations. The stress intensity factors are calculated and critical stresses are obtained, using as fracture criterion the maximum hoop stresses criterion. Illustrative examples are presented to show the influence of the parameters of the problem, such as the crack sizes, the inclination angles and distances between the cracks as well as the inhomogeneity parameter of fracture toughness of FGCs, on the interaction of edge cracks with internal cracks in a weak zone as here the thermally grown oxide layer. The analysis of the parameters with respect to critical loads shows that for a system of edge and internal cracks in this weak zone, fracture starts from edge cracks in the top of the functionally graded coating, where the ceramic material predominates. It is important to consider the variation of the fracture toughness through the thickness of the FGCs. Optimal crack configurations can be determined at which the critical loads are maximal, to avoid dangerous cracks with minimal critical loads and to improve the fracture resistance of FGC/H structures. Acknowledgement The authors would like to acknowledge the financial support of the German Research Foundation under Grant SCHM 746/209-1. References Afsar, A.M., Song, J.I., 2010. Effect of FGM coating thickness on apparent fracture toughness of a thick-walled cylinder, Engineering Fracture Mechanics 77, 2919–2926. Eischen, J.W., 1987. Fracture of nonhomogeneous materials, Int. J. Fracture 34, 3-22. Erdogan, F., Gupta, G. 1972. On the numerical solution of singular integral equations, Quarterly of Applied Mathematics 29, 525-534. Jin, Z.-H., Batra, R.C., 1996. Some basic fracture mechanics concepts in functionally graded materials, Journal of the Mechanics and Physics of Solids 44, 1221–1235. Jin, X., Wu, L., Guo, L., Yu, H., Sun, Y., 2009. Experimental investigation of the mixed-mode crack propagation in ZrO2/NiCr functionally graded materials, Engineering Fracture Mechanics 76, 1800–1810. Feng, Y.Z., Jin, Z.H., 2012. Thermal shock damage and residual strength behavior of a functionally graded plate with surface cracks of alternating lengths, Journal of Thermal Stresses 35, 30–47. Kim, J.-H., Paulino, G.H., 2007. On Fracture Criteria for Mixed-Mode Crack Propagation in Functionally Graded Materials, Mechanics of Advanced Materials and Structures 14, 227–244. Lee,Y.D. Erdogan, F., 1998. Interface cracking of FGM coatings under steady-state heat flow, Engineering Fracture Mechanics 59, 361–380. Panasyuk, V., Savruk, M., Datsyshin, A. 1976. Stress Distribution near Cracks in Plates and Shells, Naukova Dumka, Kiev, pp. 270 (in Russian) Petrova, V., Schmauder, S. 2017. Modeling of thermo-mechanical fracture of FGMs with respect to multiple cracks interaction, Physical Mesomechanics 20, 241-249 Petrova, V., Schmauder, S. 2020. A theoretical model for the study of thermal fracture of functionally graded thermal barrier coatings with a system of edge and internal cracks, Theoretical and Applied Fracture Mechanics 108, 102605. Rangaraj, S., Kokini, K., 2003. Multiple surface cracking and its effect on interface cracks in functionally graded thermal barrier coatings under thermal shock, Trans. ASME J. Appl. Mech. 70, 234-245. Tohgo, K., Iizuka, M., Araki, H., Shimamura, Y., 2008. Influence of microstructure on fracture toughness distribution in ceramic–metal functionally graded materials, Engineering Fracture Mechanics 75, 4529–4541. Tohgo, K., Suzuki, T., Araki, H., 2005. Evaluation of R-curve behavior of ceramic–metal functionally graded materials by stable crack growth, Engineering Fracture Mechanics 72, 2359–2372. Zhang, Y, Guo, L., Wang, X., Shen, R., Huang, K., 2019. Thermal shock resistance of functionally graded materials with mixed-mode cracks, International Journal of Solids and Structures 164, 202–211. Zhou, Y.C., Hashida, T., 2001. Coupled effects of temperature gradient and oxidation on thermal stress in thermal barrier coating system, International Journal of Solids and Structures 38 (24-25), 4235-4264.