A constitutive model for the high-temperature creep of particle-hardened alloys based on the θ projection method

The theta projection method is a procedure for the interpolation and extrapolation of creep properties. It works by describing the shape of conventional creep curves by suitable mathematical functions and then by projecting those curves to different stresses and temperatures. It involves techniques for the collection of data that enable large amounts of information to be summarized and this paper explores the possibility that this information-rich method can be extended to give a constitutive creep relationship for component analysis. A general framework involving a variety of hardening, recovery and damage mechanisms is evolved and the relationships between the required experimental parameters and the theta values are derived. The collection of data is illustrated with respect to a wrought superalloy (Waspaloy), creep tested in uniaxial and multiaxial stress conditions. The material is shown to be isotropic with a creep potential function equal to the second deviatoric stress invariant and the resulting flow rule, together with the constitutive relationship, is applied to the creep of notched bars by a finite-element procedure. The analysis incorporates a stress-dependent failure criterion and is shown to predict the experimentally observed notch hardening successfully. In addition, it correctly describes the failure paths in this quasi-static situation. The implications of the relationships with regard to design methods which use skeletal stresses are discussed.