Elstic energy changes accompanying gamma-prime rafting in nickel-base superalloys
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Samuel M. Allen Massachusetts Institute of Technology, Center for Materials Science and Engineering, Cambridge, Massachusetts 02139 (Received 7 February 1991; accepted 14 May 1991)
Eshelby's equivalent inclusion method is applied to the case of a single, inhomogeneous, ellipsoidal precipitate in an infinite matrix to study the morphological changes of the gamma-prime precipitates in nickel-base superalloys due to the influence of lattice constant misfit, elastic inhomogeneity and anisotropy, applied stress, and interfacial energy. The energy-minimizing inclusion shapes depend very sensitively on the degree of elastic inhomogeneity, on the sense and magnitude of the applied stress, and on the sense of the lattice constant misfit. The interfacial energy contribution can dominate that of elastic strain energy for small precipitate sizes, elastically compliant systems, nearly homogeneous alloys, and/or nearly isotropic materials. Calculations are carried out for two well-characterized nickel-base alloys: a Ni-13.5A1 alloy (positive misfit, elastically hard inclusions) studied by Miyazaki et al. and CMSX-3 (negative misfit, elastically soft inclusions) studied by Pollock. The Eshelby energy calculations correctly predict the precipitate morphologies observed by Miyazaki et al. and by Pollock.
I. INTRODUCTION In Ni-base superalloys, changes in precipitate morphology due to an applied uniaxial stress at elevated temperature (rafting) profoundly influence creep properties.1"3 For a Ni-13Al-9Mo-2Ta single crystal,1 the creep rupture life of a rafted specimen was four times greater than that for a conventionally heat treated crystal and the creep rate was an order of magnitude lower for tests conducted at 1311 K, 207 MPa, and [100] stress axis orientation. Nathal and Ebert4'5 found similar results for single crystal alloys based on MAR-M247. In both cases, the gamma-prime precipitates coarsened into platelets, or rafts, with the broad faces normal to the applied stress axis. The increased creep rupture life and reduced creep rate were attributed to these microstructural changes. Rafting has been observed frequently during creep testing of superalloys. Most commonly, alloys of negative misfit (gamma-prime lattice constant is less than that of gamma) have been creep tested. In such alloys, rafts generally develop with their broad faces normal to the tensile stress axis. The rafts have approximately {100} orientation, although the raft interface is no longer smoothly planar. The gamma-prime rafting phenomenon has been observed most often in single-crystal superalloys containing a high volume fraction of gamma-prime.6 In certain uniaxial creep tests, gamma-prime rafting has occurred to form fine platelets oriented perpendicular to J. Mater. Res., Vol. 6, No. 9, Sep 1991
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the applied stress axis.1'2'4'5 This appears to improve the creep properties of the materials.
II. SCOPE OF THIS PAPER This paper presents an elasticity-based predictive model that describes the elastic
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