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IN turbine airfoil systems, there is a superposition of centrifugal and vibratory stresses with thermal stresses that arise due to internal air cooling.[1] The impingement of hot gases on the surface of the airfoil and the constraint caused by the cooler inner surfaces typically results in surface compressive stresses.[2–4] Under these conditions, the failure of nickel-base single crystals subjected to thermomechanical fatigue typically occurs by surface crack initiation and subsequent propagation inward through the coating into the substrate.[3–5] This damage growth process is influenced by oxidation of the superalloy, or intermetallic coating when present.[3–6] When a ceramic yttria-stabilized zirconia top layer is considered, cracking can either occur below the ceramic, or occurs following local spallation of the top layer, enabling enhanced local oxidation and crack initiation at the surface of the bond coat, followed by propagation into the superalloy. Material degradation is further accelerated by sustained compressive holds present in the fatigue cycle.[5,7,8] Sustained peak low-cycle fatigue (SPLCF) with compressive dwells has been examined both experimentally[5,8–10] and via finite element (FE) models.[2,11–13]

M.A. LAFATA, M.Y. HE, and T.M. POLLOCK are with the Materials Department, University of California, Santa Barbara, Bldg. 503, Rm. 1355, Santa Barbara, CA 93106-5050. Contact e-mail: [email protected] L.H. RETTBERG is with Pratt & Whitney, 400 Main Street, M/S 114-41, East Hartford, CT 06108. Manuscript submitted June 8, 2017.

METALLURGICAL AND MATERIALS TRANSACTIONS A

During SPLCF cycling, single-crystal superalloys are found to form discontinuous rafts, as well as undergo coarsening and topological inversion. TEM analyses of the bulk superalloy indicate an evolution of dislocation activity as a function of various cycling times. Patil et al. describe evidence of early plastic deformation and initially high dislocation densities, followed by an intermediate stage where significant dislocation annihilation has occurred.[13] Specimens at later stages of life show higher dislocation densities and increased pairwise shearing of c0 . Interestingly, Patil et al. also observed slip lines ahead of SPLCF crack tips, in a converging configuration when crack depths were less than 75 lm, indicative of a thermally grown oxide (TGO) pushing into the superalloy. This correlates well with the crack propagation mechanism originally proposed by Evans et al.[2] Longer cracks produce diverging slips lines, typical of tensile crack growth. Detailed finite element analyses of the oxide-assisted crack growth process have been conducted.[2,3,12] Two versions of a fatigue model have previously been developed for the oxide on the superalloy: one is a creep version where creep properties are explicitly considered and a second is a plasticity version where an equivalent plasticity analysis is implemented for numerical efficiency.[12] These models demonstrate an important role for the substrate and/or bond coat oxide g