THESIS
2020
xvi, 85 pages : illustrations (chiefly color) ; 30 cm
Abstract
We present three dimensional continuum models for the energy and equilibrium
dislocation structure of low angle grain boundaries and for the dynamics of low
angle grain boundaries incorporating the dislocation structure. The orientation-dependent continuous distributions of dislocation lines on curved grain boundaries are described conveniently using the dislocation density potential functions.
In the first part, we present a continuum model to determine the dislocation
structure and energy of fixed low angle grain boundaries in three dimensions. The
equilibrium dislocation structure is obtained by minimizing the grain boundary
energy that is associated with the constituent dislocations subject to the constraint of Frank's formula. In the second part, we develop a continuum model...[
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We present three dimensional continuum models for the energy and equilibrium
dislocation structure of low angle grain boundaries and for the dynamics of low
angle grain boundaries incorporating the dislocation structure. The orientation-dependent continuous distributions of dislocation lines on curved grain boundaries are described conveniently using the dislocation density potential functions.
In the first part, we present a continuum model to determine the dislocation
structure and energy of fixed low angle grain boundaries in three dimensions. The
equilibrium dislocation structure is obtained by minimizing the grain boundary
energy that is associated with the constituent dislocations subject to the constraint of Frank's formula. In the second part, we develop a continuum model for
the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model includes
evolution equations for both the motion of the grain boundary and the evolution
of dislocation structure on the grain boundary. The critical but computationally
expensive long-range elastic interaction of dislocations is replaced by a projection
formulation that maintains the constraint of the Frank's formula describing the
equilibrium of the strong long-range interaction. This continuum model is able to
describe the grain boundary motion and grain rotation due to both coupling and
sliding effects, to which the classical motion by mean curvature model does not
apply. Comparisons with atomistic simulation results show that our continuum
models are able to give excellent predictions of the energy, dislocation structure,
and dynamics of low angle grain boundaries.
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