195 research outputs found
Phase Field Modeling of Fracture and Stress Induced Phase Transitions
We present a continuum theory to describe elastically induced phase
transitions between coherent solid phases. In the limit of vanishing elastic
constants in one of the phases, the model can be used to describe fracture on
the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting
from a sharp interface formulation we derive the elastic equations and the
dissipative interface kinetics. We develop a phase field model to simulate
these processes numerically; in the sharp interface limit, it reproduces the
desired equations of motion and boundary conditions. We perform large scale
simulations of fracture processes to eliminate finite-size effects and compare
the results to a recently developed sharp interface method. Details of the
numerical simulations are explained, and the generalization to multiphase
simulations is presented
Nonlinear evolution of surface morphology in InAs/AlAs superlattices via surface diffusion
Continuum simulations of self-organized lateral compositional modulation
growth in InAs/AlAs short-period superlattices on InP substrate are presented.
Results of the simulations correspond quantitatively to the results of
synchrotron x-ray diffraction experiments. The time evolution of the
compositional modulation during epitaxial growth can be explained only
including a nonlinear dependence of the elastic energy of the growing epitaxial
layer on its thickness. From the fit of the experimental data to the growth
simulations we have determined the parameters of this nonlinear dependence. It
was found that the modulation amplitude don't depend on the values of the
surface diffusion constants of particular elements.Comment: 4 pages, 3 figures, published in Phys. Rev. Lett.
http://link.aps.org/abstract/PRL/v96/e13610
Influence of Strain on the Kinetics of Phase Transitions in Solids
We consider a sharp interface kinetic model of phase transitions accompanied
by elastic strain, together with its phase-field realization. Quantitative
results for the steady-state growth of a new phase in a strip geometry are
obtained and different pattern formation processes in this system are
investigated
Modeling Elasticity in Crystal Growth
A new model of crystal growth is presented that describes the phenomena on
atomic length and diffusive time scales. The former incorporates elastic and
plastic deformation in a natural manner, and the latter enables access to times
scales much larger than conventional atomic methods. The model is shown to be
consistent with the predictions of Read and Shockley for grain boundary energy,
and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure
Crack growth by surface diffusion in viscoelastic media
We discuss steady state crack growth in the spirit of a free boundary
problem. It turns out that mode I and mode III situations are very different
from each other: In particular, mode III exhibits a pronounced transition
towards unstable crack growth at higher driving forces, and the behavior close
to the Griffith point is determined entirely through crack surface dissipation,
whereas in mode I the fracture energy is renormalized due to a remaining finite
viscous dissipation. Intermediate mixed-mode scenarios allow steady state crack
growth with higher velocities, leading to the conjecture that mode I cracks can
be unstable with respect to a rotation of the crack front line
Finite to infinite steady state solutions, bifurcations of an integro-differential equation
We consider a bistable integral equation which governs the stationary
solutions of a convolution model of solid--solid phase transitions on a circle.
We study the bifurcations of the set of the stationary solutions as the
diffusion coefficient is varied to examine the transition from an infinite
number of steady states to three for the continuum limit of the
semi--discretised system. We show how the symmetry of the problem is
responsible for the generation and stabilisation of equilibria and comment on
the puzzling connection between continuity and stability that exists in this
problem
On a classical spectral optimization problem in linear elasticity
We consider a classical shape optimization problem for the eigenvalues of
elliptic operators with homogeneous boundary conditions on domains in the
-dimensional Euclidean space. We survey recent results concerning the
analytic dependence of the elementary symmetric functions of the eigenvalues
upon domain perturbation and the role of balls as critical points of such
functions subject to volume constraint. Our discussion concerns Dirichlet and
buckling-type problems for polyharmonic operators, the Neumann and the
intermediate problems for the biharmonic operator, the Lam\'{e} and the
Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape
Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27
September 201
Stress-driven phase transformation and the roughening of solid-solid interfaces
The application of stress to multiphase solid-liquid systems often results in
morphological instabilities. Here we propose a solid-solid phase transformation
model for roughening instability in the interface between two porous materials
with different porosities under normal compression stresses. This instability
is triggered by a finite jump in the free energy density across the interface,
and it leads to the formation of finger-like structures aligned with the
principal direction of compaction. The model is proposed as an explanation for
the roughening of stylolites - irregular interfaces associated with the
compaction of sedimentary rocks that fluctuate about a plane perpendicular to
the principal direction of compaction.Comment: (4 pages, 4 figures
Stability of Solid State Reaction Fronts
We analyze the stability of a planar solid-solid interface at which a
chemical reaction occurs. Examples include oxidation, nitridation, or silicide
formation. Using a continuum model, including a general formula for the
stress-dependence of the reaction rate, we show that stress effects can render
a planar interface dynamically unstable with respect to perturbations of
intermediate wavelength
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