A software tool for lifetime prediction of thermal barrier coating systems E. P. Busso, H. E. Evans, L. Wright * , L. N. McCartney, J. Nunn and S. Osgerby Thermal barrier coatings (TBCs) are widely used to extend the lifetime of key components within gas turbines, and so the ability to predict the lifetime of TBCs is a high priority for gas turbine users. A complete model of TBC failure requires characterisation of the coating system, identification of the main failure mechanisms, quantitative description of stress evolution in the key areas within the coating system and robust failure criteria for each failure mechanism. Thus lifetime prediction invariably requires a massive effort both in terms of determining the appropriate input parameters for the model and in computing the solution. In order to reduce the need for extensive calculation, a software tool has been developed that interpolates the key stresses for each failure mechanism from a matrix of previously calculated values. The matrix of values is generated using a recently developed finite element (FE) model of TBC lifetime of an IN738/MCrAlY/ EB-PVD YSZ system. The stress distribution predicted by this model is dependent on exposure time and temperature as well as the morphology of the bond coat/ceramic interface and requires FE calculation for each specific set of conditions. The software tool interpolates the FE results with respect to time, temperature and a geometric parameter to predict key stresses that drive failure, and coating system lifetime. This paper describes the principles behind the development of the algorithms implemented in the software tool. Validation of the approach is in progress through comparison of predictions with non-destructive measurements on the coating system. 1 Introduction In modern gas turbines, thermal barrier coatings (TBCs) provide the essential technology controlling the performance and lifetime of key high temperature components. It is therefore critical to be able to understand the mechanisms controlling the failure of TBCs and to predict these events. A typical TBC system, particularly for land-based gas turbines, is made of a top layer of yttria stabilised zirconia (YSZ, the insulating layer) and an MCrAlY (where M is a combination of Ni and Co) low pressure plasma sprayed (LPPS) bond coat. During exposure to high temperatures, the metallic bond coat forms a thermally grown oxide (TGO) that consists predominantly of alumina. Most current approaches relate TBC failure to stress generation at or near the TGO (e.g. see [1–5]). Methods for predicting spallation and failure in TBCs have generally followed two main approaches. The first approach uses empirical fatigue life models that link the life of the TBC to the total amount of damage caused by oxidation and mechanical straining [6–8]. This approach has merit in that interpolation may be made within the database but its phenomenological and mechanistic processes are generally not considered. The second approach uses dela- mination models to consider edge cracking and buckling [9]. This approach neglects the fact that there is generally a lengthy period of sub-critical crack formation and growth prior to the delamination stage which, largely, determines the life of the TBC system. The work reported here investigates the local stresses that drive the crack formation and growth within a TBC system, and the use of these stresses within a software tool for predicting lifetime of a coating system. The approach is based on linking models of TGO formation, continuum mechanics (including thermal stresses, viscoplasticity and sintering) and measurements of the properties of a coating system (material properties of the individual components, morphological properties of its internal microstructure and damage behaviour prior to coating failure). The models of TGO formation and continuum mechanics are solved using a finite element (FE) method. FE methods [10] have a well-established history of use in the field of continuum mechanics. The methods solve partial differential equations by  subdividing the region of interest into non-overlapping smaller regions (the ‘elements’ or ‘mesh’, with the element corners being the ‘nodes’),  approximating the variables of interest, in this case displacements, within each element using simple para- metric functions such as linear variations interpolating the values at the nodes,  applying the governing partial differential equations at each point to generate a large set of simultaneous equations linking the unknown values at the nodes,  solving the simultaneous equations, using an appropriate numerical algorithm, to calculate the values of the 556 DOI: 10.1002/maco.200804138 Materials and Corrosion 2008, 59, No. 7  E. P. Busso Centre des Mate ´riaux, Mines Paris, Paristech, UMR CNRS 7633, 91003 Evry (France) H. E. Evans Department of Metallurgy and Materials, University of Birmingham, Edgbaston Birmingham B15 2TT (UK) L. Wright, L. N. McCartney, J. Nunn, S. Osgerby National Physical Laboratory, Teddington, Middlesex TW11 0LW (UK) E-mail: louise.wright@npl.co.uk S. Osgerby Present address: Alstom Power, Rugby (UK) www.wiley-vch.de/home/wuk ß 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim