THESIS
2013
xviii, 116 pages : illustrations (some color) ; 30 cm
Abstract
This thesis is concerned with the continuum modeling and simulations of the
structure, energy and dynamics of grain boundaries and dislocation arrays in
crystalline materials.
In the first part of the thesis, the structure and energy of (111) twist boundaries
in fcc Al, Cu and Ni are studied systematically by atomistic simulations with
EAM potentials and generalized Peierls-Nabarro models. Compared with atomistic
simulations, the generalized Peierls-Nabarro models work excellently for low
angle grain boundaries and near twin grain boundaries. In these two regimes,
dislocations and fault regions can be identified, based on which analytical energy
expressions are derived, respectively. For the intermediate grain boundaries, a
simple polynomial expression is proposed to fit the e...[
Read more ]
This thesis is concerned with the continuum modeling and simulations of the
structure, energy and dynamics of grain boundaries and dislocation arrays in
crystalline materials.
In the first part of the thesis, the structure and energy of (111) twist boundaries
in fcc Al, Cu and Ni are studied systematically by atomistic simulations with
EAM potentials and generalized Peierls-Nabarro models. Compared with atomistic
simulations, the generalized Peierls-Nabarro models work excellently for low
angle grain boundaries and near twin grain boundaries. In these two regimes,
dislocations and fault regions can be identified, based on which analytical energy
expressions are derived, respectively. For the intermediate grain boundaries, a
simple polynomial expression is proposed to fit the energy from atomistic simulations.
The resulting analytical energy formulas for twist boundaries over the full
range of twist angles are in excellent agreement with atomistic simulations.
In the second part of the thesis, a continuum model is presented for the core
relaxation of incoherent twin boundaries based on the Peierls-Nabarro framework,
incorporating both the long-range strain field and the local atomic structure. The
continuum model is employed to study the finite size effect of twin boundaries
and interactions of dislocations with twin boundaries. Simulation results obtained
using this continuum model agree well with those of experiments and atomistic
simulations. This model provides a basis for quantitative study of structures and
collective behaviors of twin boundaries within the continuum framework.
Finally in this thesis, a simulation method for the dynamics of dislocation arrays
is presented. In this numerical method, dislocation arrays are considered as continuous
surfaces in three dimensions, represented using the level set framework.
The level set representation of the surfaces has the advantage of automatically
handling the topological changes occurring during the evolution, and simple implementation
using standard accurate finite difference schemes on a uniform grid.
The driving force of the evolution of the dislocation array surfaces comes from
both the long-range interaction of the constituent dislocations and their local
curvature effect. The long-range interaction is calculated efficiently using the fast
Fourier transform (FFT) method. Simulations are performed for dislocation arrays
bypassing different particles under applied stress. The long-range nature of
the stress fields of nonplanar infinite dislocation arrays is shown to be essentially
different from that by a single dislocation.
Post a Comment