Multi-Scale Crystal Plasticity Model of Creep Responses in Nickel-Based Superalloys

Abstract

The current study focuses on the modeling of two-phase γ-γ′ nickel-based superalloys, utilizing multi-scale approaches to simulate and predict the creep behaviors through crystal plasticity finite element (CPFE) platforms. The multi-scale framework links two distinct levels of the spatial spectrum, namely, sub-grain and homogenized scales, capturing the complexity of the system responses as a function of a tractable set of geometric and physical parameters. The model considers two dominant features of γ′ morphology and composition. The γ′ morphology is simulated using three parameters describing the average size, volume fraction, and shape. The sub-grain level is expressed by a size-dependent, dislocation density-based constitutive model in the CPFE framework with the explicit depiction of γ-γ′ morphology as the building block of the homogenized scale. The homogenized scale is developed as an activation energy-based crystal plasticity model reflecting intrinsic composition and morphology effects. The model incorporates the functional configuration of the constitutive parameters characterized over the sub-grain γ-γ′ microstructural morphology. The developed homogenized model significantly expedites the computational processes due to the nature of the parameterized representation of the dominant factors while retains reliable accuracy. Anti-Phase Boundary (APB) shearing and, glide-climb dislocation mechanisms are incorporated in the constitutive model which will become active based on the energies associated with the dislocations. The homogenized constitutive model addresses the thermo-mechanical behavior of nickel-based superalloys for an extensive temperature domain and encompasses orientation dependence as well as the loading condition of tension-compression asymmetry aspects. The model is validated for diverse compositions, temperatures, and orientations based on previously reported data of single crystalline nickel-based superalloy.

Advanced Computational Analysis of Cobalt-Based Superalloys through Crystal Plasticity

“…In the realm of single crystals of superalloys, two distinct length scales can be delineated. The smaller scale, known as the sub-grain scale, involves an explicit representation of the γ-γ ′ phases, where the larger scale, or the homogenized grain scale, has implicit effects of morphology through parametric constitutive equations [27,28]. Two constitutive models are proposed for each scale, tailored to address dislocation mechanisms occurring either below or above the peak temperature, typically around 850 • C, where the maximum flow stress is observed.…”

“…Conversely, a larger average size for the same volume fraction increases channel width, thereby reducing the gradient of plastic deformation. As a result, the densities of parallel and forest dislocations can be expressed in terms of scalar SSDs and vectorial GNDs, influencing the mobile dislocation density ρ α m as described [27].…”

“…Instead, they glide just inside the channel of the γ phase [14,33,34]. This glide in the channel typically continues by climbing along the precipitates, as illustrated in Figure 4, giving rise to a glide-climb dislocation mechanism [27,29]. Accordingly, two constitutive models are employed to address the distinct dislocation mechanisms.…”

“…The rate of plastic shear strain for a given slip system can be calculated in terms of the morphology of γ-γ ′ and the composition of γ-γ ′ using the Orowan-based constitutive model, as outlined in [27] by…”