An Analytical Stress-Strain Hysteresis Model for a Directionally-Solidified Superalloy Under Thermomechanical Fatigue

Cyclic plasticity and creep are the primary design considerations of 1^st and 2^nd stage gas turbine blades. Directionally-solidified (DS) Ni-base materials have been developed to provide (1) greater creep ductility and (2) lower minimum creep rate in solidification direction compared to other directions. Tracking the evolution of deformation in DS structures necessitates a constitutive model having the functionality to capture rate-, temperature-, history-, and orientation-dependence. Historically, models rooted in microstructurally-based viscoplasticity simulate the response of long-crystal, dual-phase Ni-base superalloys with extraordinary fidelity; however, a macroscopic approach having reduced order is leveraged to simulate LCF, creep, and creep-fatigue responses with equally high accuracy. This study applies uncoupled creep and plasticity models to predict the TMF of a generic DS Ni-base, and an anisotropic yield theory accounts for transversely-isotropic strength. Due to the fully analytic determination of material constants from mechanical test data, the model can be readily tuned for materials in either peak- or base-loaded units. Application of the model via a parametric study reveals trends in the stabilized hysteresis response of under isothermal fatigue, creep-fatigue, thermomechanical fatigue, and conditions representative of in-service components. Though frequently considered in design and maintenance of turbine materials, non-isothermal fatigue has yet to be accurately predicted for a generalized set of loading conditions. The formulations presented in this study address this knowledge gap using extensions of traditional power law constitutive models.