Crystal Visco-Plastic Model for Directionally Solidified Ni-Base Superalloys Under Monotonic and Low Cycle Fatigue
Authors: Wijeyeratne Navindra , Irmak Firat , Gordon Ali P. 
Published: September 2021

Abstract
Nickel-base superalloys (NBSAs) are extensively utilized as the design materials to develop turbine blades in gas turbines due to their excellent high-temperature properties. Gas turbine blades are exposed to extreme loading histories that combine high mechanical and thermal stresses. Both directionally solidified (DS) and single crystal NBSAs are used throughout the industry because of their superior tensile and creep strength, excellent low cycle fatigue (LCF), high cycle fatigue (HCF), and thermomechanical fatigue (TMF) capabilities. Directional solidification techniques facilitated the solidification structure of the materials to be composed of columnar grains in parallel to the &lt;001&gt; direction. Due to grains being the sites of failure initiation the elimination of grain boundaries compared to polycrystals and the alignment of grain boundaries in the normal to stress axis increases the strength of the material at high temperatures. To develop components with superior service capabilities while reducing the development cost, simulating the material’s performance at various loading conditions is extremely advantageous. To support the mechanical design process, a framework consisting of theoretical mechanics, numerical simulations, and experimental analysis is required. The absence of grain boundaries transverse to the loading direction and crystallographic special orientation cause the material to exhibit anisotropic behavior. A framework that can simulate the physical attributes of the material microstructure is crucial in developing an accurate constitutive model. The plastic flow acting on the crystallographic slip planes essentially controls the plastic deformation of the material. Crystal Visco-Plasticity (CVP) theory integrates this phenomenon to describe the effects of plasticity more accurately. CVP constitutive models can capture the orientation, temperature, and rate dependence of these materials under a variety of conditions. The CVP model is initially developed for SX material and then extended to DS material to account for the columnar grain structure. The formulation consists of a flow rule combined with an internal state variable to describe the shearing rate for each slip system. The model presented includes the inelastic mechanisms of kinematic and isotropic hardening, orientation, and temperature dependence. The crystallographic slip is accounted for by including the required octahedral, cubic, and cross slip systems. The CVP model is implemented through a general-purpose finite element analysis software (i.e., ANSYS) as a User-Defined Material (USERMAT). Uniaxial experiments were conducted in key orientations to evaluate the degree of elastic and inelastic anisotropy. The temperature-dependent modeling parameter is developed to perform non-isothermal simulations. A numerical optimization scheme is utilized to develop the modeling constant to improve the calibration of the model. The CVP model can simulate material behavior for DS and SX NBSAs for monotonic and cyclic loading for a range of material orientations and temperatures.