# Phase-field simulations of coherent precipitate morphologies and coarsening kinetics

Abstract (Summary)

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The primary aim of this research is to enhance the fundamental understanding of
coherent precipitation reactions in advanced metallic alloys. The emphasis is on a particular
class of precipitation reactions which result in ordered intermetallic precipitates
embedded in a disordered matrix. These precipitation reactions underlie the development
of high-temperature Ni-base superalloys and ultra-light aluminum alloys. Phasefield
approach, which has emerged as the method of choice for modeling microstructure
evolution, is employed for this research with the focus on factors that control the precipitate
morphologies and coarsening kinetics, such as precipitate volume fractions and
lattice mismatch between precipitates and matrix.
Two types of alloy systems are considered. The first involves L12 ordered precipitates
in a disordered cubic matrix, in an attempt to model the ?? precipitates in
Ni-base superalloys and ?? precipitates in Al-Li alloys. The effect of volume fraction on
coarsening kinetics of ?? precipitates was investigated using two-dimensional (2D) computer
simulations. The temporal evolution of precipitate morphologies and coarsening
kinetics were characterized by the time-dependence of average aspect ratios of precipitates,
average particle size, and precipitate size distributions. With increase in volume
fraction, larger fractions of precipitates were found to have smaller aspect ratios in the
late stages of coarsening, and the precipitate size distributions became wider and more
positively skewed. The most interesting result was associated with the effect of volume
fraction on the coarsening rate constant. Coarsening rate constant as a function of volume
fraction extracted from the cubic growth law of average half-edge length was found
to exhibit three distinct regimes: anomalous behavior or decreasing rate constant with
volume fraction at small volume fractions (20%), volume fraction independent or constant
behavior for intermediate volume fractions (?20-50%), and the normal behavior or
increasing rate constant with volume fraction for large volume fractions (50%). The
simulation results are in agreement with the experimental results of Ardell and coworkers
in Ni-Al, Ni-Ti and Ni-Si alloys. Based on non-linear growth law fit to the coarsening
data, the growth exponent in the presence of coherency stress was found to be ?3 for
the average precipitate size, while the exponents were ?4 for the average spacing between
the aligned precipitate arrays. The effect of simulation dimension (2D and 3D) on
the coarsening kinetics was compared for stress-free ?? precipitates in Al-Li alloys and
stressed ?? precipitates in Ni-base alloys, at 20% volume fraction. The main difference
in the kinetics from 2D and 3D simulations was the increase in coarsening rate constant
with the simulation dimension.
The second alloy system considered was Al-Cu with the focus on understanding
precipitation of metastable tetragonal ??-Al2Cu in a cubic Al solid solution matrix. In
collaboration with Chris Wolverton at Ford Motor Company, a multiscale model, which
involves a novel combination of first-principles atomistic calculations with a mesoscale
phase-field microstructure model, was developed. Reliable energetics in the form of bulk
free energy, interfacial energy and parameters for calculating the elastic energy were
obtained using accurate first-principles calculations. With the help of anisotropies incorporated
in the multiscale model based on first-principles calculations, the equilibrium
precipitate morphology of ?? was found to be governed by the combination of interfacial
and elastic energy anisotropy. Quantitative results from the model in the form of
length, thickness and aspect ratio of precipitates were comparable with the experimental
results. With sufficient large-scale simulations, which will become possible in the coming
years, this multiscale model can be used to provide quantitative precipitation kinetics
and coarsening information, which are very useful in designing the processing parameters
of these alloys.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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