Surface and Coatings Technology 184 (2004) 331–337 0257-8972/04/$ - see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2003.09.068 Residual stress relaxation processes in thermal barrier coatings under tension at high temperature M. Lugovy *, V. Slyunyayev , V. Teixeira a, a b Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, 3 Krzhizhanovsky str., 03142 Kiev, Ukraine a Physics Department Functional Coatings Group, Institute of Materials, University of Minho, Campus de Gualtar, 4700 Braga, Portugal b Received 13 September 2003; accepted in revised form 26 September 2003 Available Online 27 November 2003 Abstract A model of failure is considered that can be applied to n-phase brittle materials (in particular to thermal barrier coatings (TBCs)). The authors attempt to solve a physical problem of the description of failure of a microscopically inhomogeneous solid as stochastic process of the cracking of individual structural elements. The above mentioned model is applied to describe the mechanical behavior of single-phase ceramic-based coatings with given statistical distribution of grains sizes. The failure process is found to have several stages. If the stage of the catastrophic microcracking is reached, the microcracking process in a TBC reaches saturation when the average distance between cracks approximately equals the lamella thickness of 4–5 mm. Large multigrain cracks with sizes within the range 1–32 mm are observed in the TBC after thermal cycling. These microcracks can be explained by the model proposed. They are the result of unstable microcracking during the fourth stage of the stochastic failure process. In such a way, the model proposed provides a means to describe some features of thermal stress relaxation in a TBC during thermal cycling.  2003 Elsevier B.V. All rights reserved. Keywords: Reliability models; Elastic properties; Scanning electron microscopy; Zirconium oxide; Microcracking 1. Introduction Multilayered coatings are commonly used as protec- tive coatings for advanced power engineering applica- tions to improve performance, e.g. thermal barrier coatings (TBCs) deposited by plasma spraying tech- niques are currently applied on gas turbine blades and diesel engine components. Demands for increased per- formance in gas turbines are met in part by increasing combustion temperatures and reducing cooling systems. Temperature increases within the engine lead to the service limits of current superalloys. Therefore, the TBC concept provides a means of raising the operating temperature by enabling the underlying metallic com- ponents to operate at lower temperature due to the temperature gradient across the thick ceramic coating, and thus permit performance increases without requiring major alloy development w1–8x. *Corresponding author. Tel.: q380-44-457-4890. E-mail address: lugovy@viptelecom.net (M. Lugovy). TBCs, traditionally, consist of a thick stabilized ZrO top coating (plasma sprayed (PS) top coat) com- 2 monly deposited by atmospheric plasma spraying on superalloys previously coated with a metallic bond layer (typically MCrAlY where M is Ni or yand NiCo) pro- duced by vacuum plasma spraying (VPS) w1,3x. Another coating concept is to substitute the metallic VPS bond layer by a thinner, dense ceramic coating (ZrO coating 2 stabilized by Y O and yor Al O ) deposited by reactive 23 23 magnetron sputtering (PVD bond coating) or electron beam sputtering (EB-PVD bond coating) w4x. The idea of using a thin PVD bond coating resides on the fact that the coating microstructures achieved by PVD pro- cesses are dense and columnar, so this structure may act as some diffusion gas barrier and controls the oxidation of a metallic substrate w5x. The thermal strain tolerance and thus the thermal shock resistance are improved due to the segmented nature of PVD coatings. Residual stress within the PS coatings occurs due to a mismatch between the coefficients of thermal expansion of metal-