552 research outputs found
Pattern formation during diffusion limited transformations in solids
We develop a description of diffusion limited growth in solid-solid
transformations, which are strongly influenced by elastic effects. Density
differences and structural transformations provoke stresses at interfaces,
which affect the phase equilibrium conditions. We formulate equations for the
interface kinetics similar to dendritic growth and study the growth of a stable
phase from a metastable solid in both a channel geometry and in free space. We
perform sharp interface calculations based on Green's function methods and
phase field simulations, supplemented by analytical investigations. For pure
dilatational transformations we find a single growing finger with symmetry
breaking at higher driving forces, whereas for shear transformations the
emergence of twin structures can be favorable. We predict the steady state
shapes and propagation velocities, which can be higher than in conventional
dendritic growth.Comment: submitted to Philosophical Magazin
Theory of dendritic growth in the presence of lattice strain
Elastic effects due to lattice strain modify the local equilibrium condition
at the solid-solid interface compared to the classical dendritic growth. Both,
the thermal and the elastic fields are eliminated by the Green's function
techniques and a closed nonlinear integro-differential equation for the
evolution of the interface is derived. In the case of pure dilatation, the
elastic effects lead only to a trivial shift of the transition temperature
while in the case of shear transitions, dendritic patterns are found even for
isotropic surface energy
Nonlinear Two-Dimensional Green's Function in Smectics
The problem of the strain of smectics subjected to a force distributed over a
line in the basal plane has been solved
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
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