Scripta METALLURGICA Vol. 23, pp. 1301-1306, 1989 Pergamon Press plc Printed in the U.S.A. All rights reserved MODELLING THE ORIENTATION DEPENDENCE OF TERTIARY CREEP IN SINGLE CRYSTAL SUPERALLOYS R N Ghosh 1,2 and M McLean I 1. 2. Division of Materials Applications, National Physical Laboratory, Teddington, Middlesex, UK National Metallurgical Laboratory, Jamshedpur-831007, Bihar, India (Received April 27, 1989) (Revised May 17, 1989) Introduction Single crystal superalloys are now extensively used in critical components in modern aero-gas-turbines. Several studies of the orientation dependence of the mechanical behaviour of these materials have shown that axially stressed <001> oriented crystals have a good combination of creep and thermal fatigue behaviour, although the creep strength of <111> can be substantially greater than that of <001> crystals (1-3). MacKay et al (1) have attempted to map the stress rupture performance of single crystal Mar M247 for all possible orientations. This type of information has been valuable in providing a broad basis for the selection of the optimum crystallographic orientation for the manufacture of turbine blades. However, it is not sufficient to allow effective design incorporating the complex stress states that are likely to occur in a typical air-cooled turbine blade. Here a constitutive description of the deformation of the material taking into account the inherent crystallographic anisotropy is required and this type of information has not been available. The creep behaviour of single crystal superalloys, like that of the simpler equiaxed wrought and cast versions, is dominated by a progressively increasing creep rate (ie tertiary creep) over most of the creep life. Dyson and McLean (4) have shown that, for nickel-base superalloys, this extensive tertiary-creep behaviour is a result of strain softening, probably due to the accumulation of mobile dislocations. This concept has been utilised by Ion et al (5) and Barbosa et al (6) to develop a physics-based method of analysing creep data to represent creep strain as a function of time and to allow extrapolation or interpolation to arbitrary stress/temperature conditions. The formalism used by Ion et al (5) and Barbosa et al (6) has been expressed in terms of axial loads and strains, and implicitly assumes material isotropy. The purpose of the present paper is to extend this approach to account for the inherent crystallographic anisotropy of single crystal superalloys. Development of the Model Ion et al (5) discuss two variants of the strain softening model that are associated with either linear or exponential accumulations of damage with creep strain. Recently, Maldini and Lupioc (7) have suggested that the linear strain softening model is more appropriate to single crystal superalloys and this conclusion is supported by Curtis et al (8) from analysis of an extensive creep database for a single crystal superalloy. Consequently, the following discussion will be restricted to extending the linear strain softening model. The exponential strain softening model can be similarly modified if required. The variation in uniaxial creep rate e with increasing creep strain e can be represented by the following equation (4,5):- - ~i (1 + c 3 e) (1) where e i (a,T) is the initial creep rate, a is the applied axial stress, T is the. temperature and C 3 is the strain softening coefficient. Curtis et al (8) have shown that for <001> crystals e i (a,T) is well described by an exponential, rather than power law, formulation of creep. Consequently, Equation 1 can be expressed more fully in the following form:- • .% e - C 1 exp (C 2 a - ) (1 + C3 e) (2) 1301 0036-9748/89 $3.00 + .00 Copyright (c) 1989 Pergamon Press plc