Comparison of Viscoplastic Modeling of an Equiaxed and Directionally Solidified Ni-Base Superalloy

Abstract

Abstract Engine components are subjected to both high temperatures and cyclic loads resulting in fatigue and creep effects. Directionally-solidified (DS) Ni-base superalloys were developed in order to produce favorable creep properties in the primary stress axis of turbine blades by casting the grains longer along this axis. Doing so causes the material to exhibit anisotropic behavior, which allows for improved fatigue and creep strength but also adds complexity to modeling the material. To predict the life of components accurately, it is necessary to use a high-fidelity constitutive model to relate the loading and the deformation of the material. The dual-phase microstructure of these DS superalloys evolves with time, rendering the yield surface of the material a challenge to track. Furthermore, components made from these materials are subjected to complex loading conditions, often seeing cycling temperature in addition to loads, known as thermomechanical fatigue (TMF), and cyclic loads with dwells, known as creep-fatigue (CF). Viscoplasticity models are able to capture the complex behaviors of these materials under complex loading conditions, including the hysteresis effects, rate-dependence, and stress relaxation, etc., making them attractive models to use with critically heated and loaded parts. These models, originally designed for equiaxed materials, have been adapted for use with anisotropic materials, such as DS superalloys. An isothermal anisotropic viscoplasticity model and parameter identification framework has been calibrated within a dedicated parameter identification framework. Principally, the constitutive model is based on the Chaboche viscoplasticity model featuring Armstrong-Frederick kinematic hardening. The performance of a preliminary model is presented for both an equiaxed (i.e., conventionally cast, CC) and DS materials within the same strength class, though more data is needed for validation. With regard to the stress relation associated with creep-fatigue, a fitting-technique for the static recovery model that has shown promise in isotropic materials is expanded to capture the behavior of the DS alloy. Previously developed methods for finding kinematic hardening constants for isotropic material based on Ramberg-Osgood constants at various orientations are expanded to an anisotropic case. These techniques allow for the capturing of more complex loading conditions with a limited number of tests, allowing for cost savings when developing the constitutive model. The model is implemented with three non-linear kinematic hardening terms with static recovery, allowing for the capture of rate and hold time effects, and non-linear isotropic hardening, allowing for the capture of cyclic hardening. The ability to capture the low cycle fatigue (LCF) behavior of both the equiaxed and DS alloys are examined through comparisons with test data.