A Numerical Model of Ratcheting in Thermal Barrier Systems
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A numerical model of ratcheting in thermal barrier systems
Anette M. Karlsson and Anthony G. Evans Princeton Materials Institute, Princeton University, Princeton, NJ 08540 ABSTRACT Morphological instabilities in thermally grown oxide, observed in a range of thermal barrier systems, have been simulated by developing and using a numerical code. The simulations are based on a range of phenomena and constituent properties, such as plasticity in the bond coat and growth strains in the TGO at high temperature. One of the key implications is that the incidence of reverse yielding upon reheating is a necessary condition for morphological instabilities. That is, whenever the condition for reverse yielding is satisfied during the initial cycles, the imperfection amplitude increases with thermal cycling (ratcheting). Otherwise, shakedown occurs, i.e., the imperfection amplitude stops growing. INTRODUCTION Thermal barriers are widely used in turbines for propulsion. They comprise a thermally insulating coating having sufficient thickness and durability to sustain an appreciable temperature difference between the load bearing alloy and the surface. Reviews of thermal barrier systems, including their durability and failure modes may be found in [1-6]. There are four primary constituents in a thermal barrier system. They comprise (i) the thermal barrier coating (TBC) itself, (ii) the superalloy substrate, (iii) an aluminum containing bond coat (BC) between the substrate and the TBC, and (iv) a thermally grown oxide (TGO) that forms between the TBC and the BC. The TBC is the insulator, the BC provides the oxidation protection and the alloy sustains the structural loads. The TGO is a reaction product. Each of these elements is dynamic and all interact to control the durability. The bond coat emphasized in this study comprises a Pt-modified diffusion aluminide [4]. Morphological instability of the thermally grown oxide (TGO) is a dominant failure mode in some thermal barrier systems [6, 8-13]. That is, some initial non-planarities in the TGO grow in amplitude as the system experiences thermal cycling. The growth of the undulation amplitude is associated with crack growth in the TBC, which eventually leads to large scale buckling and failure of the TBC [6]. Five fundamental factors underlie the phenomenon [9]: (1) non-elastic deformation of the bond coat, (2) a growth strain in the TGO due to the oxidation, (3) thermal cycling, (4) an initial imperfection, and (5) thermal expansion misfit between the TGO and the bond coat. The challenge is to understand how these factors interrelate and to derive mechanism-based solutions for the cyclic changes in amplitude. A numerical approach [12] is used to develop a simulation scheme capable of probing a range of mechanistic possibilities. In this paper, we discuss how some of the fundamental system-parameters effect the development of the morphological instabilities.
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THE MODEL Previous analyses of amplitude changes upon thermal cycling identified some general requirements and response
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