Crystal Visco-Plastic Model for Ni-Base Superalloys Under Thermomechanical Fatigue
Authors: Wijeyeratne Navindra , Irmak Firat , Gordon Ali P. , Jeon Jun-Young 
Published: January 2021

Abstract
Gas turbine blades are subjected to complex mechanical loading coupled with extreme thermal loading conditions which range from room temperature to over 1000°C. Nickel-base superalloys exhibit high strength, good resistance to corrosion and oxidation, long fatigue life and is capable of withstanding high temperatures for extended periods of time. Consequently, Ni-base superalloys (NBSAs) are highly suitable as blading materials. The cyclic strains due to mechanical as well as thermal cycling leads to Thermomechanical fatigue (TMF). Damage from TMF takes the form of microstructural material cracking which consequently lead to the failure of the component. In order to increase the service life and reliability and reduce operating costs, development of simulations that accurately predict the material behavior for TMF is highly desirable. To support the mechanical design process, a framework consisting of theoretical mechanics, experimental analysis and numerical simulations must be used. Capturing the effects of thermomechanical fatigue is extremely important in the prediction of the material behavior and life expectation. Single crystal (SX) Ni-base superalloys exhibit anisotropic behavior. A modeling framework which is capable of simulating the physical attributes of the material microstructure is essential. Crystallographic slip along the slip planes controls the microstructural evolution of the material Crystal Visco-Plasticity (CVP) theory captures anisotropic behavior as well as the slip along the slip planes. CVP constitutive models can capture rate-, temperature, and history-dependence of these materials under a variety of conditions. Typical CVP formulations consist of a flow rule, internal state variables, and parameters. The model presented in the current study includes the inelastic mechanism of kinematic hardening and isotropic hardening which are captured by the back stress and drag stress, respectively. Crystallographic slip is accounted for by the incorporation of twelve octahedral six cubic slip systems. An implicit integration scheme which uses Newton-Raphson iteration method is used to solve the required solutions. The CVP model is implemented through a general-purpose finite element analysis software (i.e., ANSYS) as a User-Defined Material (USERMAT). A small batch of uniaxial experiments were conducted in key orientations (i.e., [001], [011], and [111] to assess the level of elastic and inelastic anisotropy. Modeling parameters are expressed as temperature-dependent to allow for simulation under non-isothermal conditions. An optimization scheme based in MATLAB utilizes this experimental data to calibrate the CVP modeling constants. The CVP model has the capability to simulate material behavior for monotonic and cyclic loading coupled with in phase and out phase temperature cycling for a variety of material orientations, strain rates, strain and temperature ranges. A CVP model that predicts SX behavior across various rates, orientations, temperatures and load levels have not been presented before now.