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Abstract

Turbine blades which are used in the hot paths of aerospace or industrial gas turbines are usually manufactured as casted single crystalline parts. However, even though
grain boundaries are excluded, the degradation behavior of respectively developed single
crystal nickel-base superalloys, is still quite complex involving a number of very different
microscopic effects. One of these is the diffusion-limited coarsening of the
γ'-precipitates.
Long-term aging or creep loading along the <100> crystallographic orientation results in
the anisotropic coarsening of the
γ'-precipitates. In the end, the microstructure contains
quite large, irregularly shaped precipitates or plate-like precipitates aligned either parallel
(P-type rafts) or perpendicular (N-type rafts) to the loading direction. This behavior is
detrimental for the properties of these materials since their superior properties emanate
from the size, morphology and distribution of the
γ'-precipitates [R. Reed: Cambridge
University Press, (2006)]. In order to efficiently design these materials, the phenomenon
of coarsening should be known in detail to optimize the materials accurately.
On this background, the general objective of this thesis is to develop an integrated
computational approach for simulating morphological evolution in single crystal Ni-base
superalloys. As a first step towards that aim, a multi-component phase field model coupled
to inputs from CALPHAD-type and kinetic databases for the relevant driving forces was
developed based on the grand-potential formalism similar to Plapp [Phys. Rev. E, 84:
031601 (2011)]. The thermodynamic formulation of the model was validated by comparisons to ThermoCalc equilibrium calculations and DICTRA sharp-interface simulations.
Phase field approaches that allow for anisotropies of the interfacial energy sufficiently high
so that the interface develops sharp corners due to missing crystallographic orientations
were formulated. This called for a regularization that enforces local equilibrium at the
corners, and the method of Eggelston et al. [Physica D 150, 91 (2001)], generalized to
arbitrary crystal symmetries and rotations of the crystalline axes was adapted for that
context. Mechanical effects accounting for the contributions from the misfit, anisotropic
and inhomogeneous elasticity and creep loading were integrated physically consistent. The
mechanical effects are incorporated into the phase field model via the Allen-Cahn equation
based on Steinbach [Physica D, 217, 153 (2006)] and Fleck et. al [Philos. Mag., 90, 265
(2010)]. The relaxed displacement fields required to calculate the elastic driving force was
obtained by solving the mechanical equilibrium using an iterative Jacobi relaxation scheme
using a staggered grid based on the finite difference method.
Morphological evolution and kinetics in single crystal Ni-base superalloys was studied.
To gain insight in optimized alloying, a systematic computational measure to assess and
track the evolution anisotropic microstructures was integrated in the model. Previously,
focusing on the solidification behavior, Heckl et al. [Metal. and Mater. Trans. A, 41,
202 (2010)] discussed Ruthenium (Ru) as a possible Rhenium (Re) replacement-candidate
for next generation Ni-based superalloys. Employing phase field simulation studies, we
performed virtual experiments of the coarsening behavior in Re and Ru containing alloys.
The simulations revealed that the degradation of the
γ-γ' microstructure via coarsening is
considerably slower in Re-containing superalloys. We observed that an increase in the Re
content strongly reduces the
γ'-coarsening kinetics and the simulations explicitly resolved
the time dependence of that slow down beyond experiment. Likewise, it was found that Ru
variations have no significant effect on the coarsening kinetics. The simulations revealed
the mechanism by which Re reduces coarsening kinetics. The simulations showed that
Re slows interface mobility by accumulating along the path of moving γ/γ'-interfaces, a
behavior we attribute to its low diffusivity and low solubility in the
γ-precipitate. The
virtual experiments allowed for a systematic quantification of the relative contribution of
each solute in a superalloy to coarsening. This can be understood as a first step toward a
simulation-based design and optimization of alloy composition.