54 research outputs found
Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy
We present a unified description of interface kinetic effects in phase field
models for isothermal transformations in binary alloys and steps dynamics in
molecular-beam-epitaxy. The phase field equations of motion incorporate a
kinetic cross-coupling between the phase field and the concentration field.
This cross coupling generalizes the phenomenology of kinetic effects and was
omitted until recently in classical phase field models. We derive general
expressions (independent of the details of the phase field model) for the
kinetic coefficients within the corresponding macroscopic approach using a
physically motivated reduction procedure. The latter is equivalent to the
so-called thin interface limit but is technically simpler. It involves the
calculation of the effective dissipation that can be ascribed to the interface
in the phase field model. We discuss in details the possibility of a non
positive definite matrix of kinetic coefficients, i.e. a negative effective
interface dissipation, although being in the range of stability of the
underlying phase field model. Numerically, we study the step-bunching
instability in molecular-beam-epitaxy due to the Ehrlich-Schwoebel effect,
present in our model due to the cross-coupling. Using the reduction procedure
we compare the results of the phase field simulations with the analytical
predictions of the macroscopic approach
Fast crack propagation by surface diffusion
We present a continuum theory which describes the fast growth of a crack by
surface diffusion. This mechanism overcomes the usual cusp singularity by a
self-consistent selection of the crack tip radius. It predicts the saturation
of the steady state crack velocity appreciably below the Rayleigh speed and tip
blunting. Furthermore, it includes the possibility of a tip splitting
instability for high applied tensions
Achieving realistic interface kinetics in phase field models with a diffusional contrast
Phase field models are powerful tools to tackle free boundary problems. For
phase transformations involving diffusion, the evolution of the non conserved
phase field is coupled to the evolution of the conserved diffusion field.
Introducing the kinetic cross coupling between these two fields [E. A. Brener,
G. Boussinot, Phys. Rev. E {\bf 86}, 060601(R) (2012)], we solve the
long-standing problem of a realistic description of interface kinetics when a
diffusional contrast between the phases is taken into account. Using the case
of the solidification of a pure substance, we show how to eliminate the
temperature jump at the interface and to recover full equilibrium boundary
conditions. We confirm our results by numerical simulations
Viscoelastic Fracture of Biological Composites
Soft constituent materials endow biological composites, such as bone, dentin
and nacre, with viscoelastic properties that may play an important role in
their remarkable fracture resistance. In this paper we calculate the scaling
properties of the quasi-static energy release rate and the viscoelastic
contribution to the fracture energy of various biological composites, using
both perturbative and non-perturbative approaches. We consider coarse-grained
descriptions of three types of anisotropic structures: (i) Liquid-crystal-like
composites (ii) Stratified composites (iii) Staggered composites, for different
crack orientations. In addition, we briefly discuss the implications of
anisotropy for fracture criteria. Our analysis highlights the dominant
lengthscales and scaling properties of viscoelastic fracture of biological
composites. It may be useful for evaluating crack velocity toughening effects
and structure-dissipation relations in these materials.Comment: 18 pages, 3 figure
Melting of alloys along the inter-phase boundaries in eutectic and peritectic systems
We discuss a simple model of the melting kinetics along the solid-solid
interface in eutectic and peritectic systems. The process is controlled by the
diffusion inside the liquid phase and the existence of a triple junction is
crucial for the velocity selection problem. Using the lubrication approximation
for the diffusion field in the liquid phase we obtain scaling results for the
steady-state velocity of the moving pattern depending on the overheating above
the equilibrium temperature and on the material parameters of the system,
including the dependences on the angles at the triple junction
Frictional shear cracks
We discuss crack propagation along the interface between two dissimilar
materials. The crack edge separates two states of the interface, ``stick'' and
``slip''. In the slip region we assume that the shear stress is proportional to
the sliding velocity, i.e. the linear viscous friction law. In this picture the
static friction appears as the Griffith threshold for crack propagation. We
calculate the crack velocity as a function of the applied shear stress and find
that the main dissipation comes from the macroscopic region and is mainly due
to the friction at the interface. The relevance of our results to recent
experiments,
Baumberger et al, Phys. Rev. Lett. 88, 075509 (2002), is discussed
Theory of unconventional singularities of frictional shear cracks
Crack-like objects that propagate along frictional interfaces,
i.e.~frictional shear cracks, play a major role in a broad range of frictional
phenomena. Such frictional cracks are commonly assumed to feature the universal
square root near-edge singularity of ideal shear cracks, as predicted by Linear
Elastic Fracture Mechanics. Here we show that this is not the generic case due
to the intrinsic dependence of the frictional strength on the slip rate, even
if the bodies forming the frictional interface are identical and predominantly
linear elastic. Instead, frictional shear cracks feature unconventional
singularities characterized by a singularity order that differs from the
conventional one. It is shown that depends on the
friction law, on the propagation speed and on the symmetry mode of loading. We
discuss the general structure of a theory of unconventional singularities,
along with their implications for the energy balance and dynamics of frictional
cracks. Finally, we present explicit calculations of and the associated
near-edge fields for linear viscous-friction -- which may emerge as a
perturbative approximation of nonlinear friction laws or on its own -- for both
in-plane (mode-II) and anti-plane (mode-III) shear loadings.Comment: 15 pages, 2 figure
Fracture and Friction: Stick-Slip Motion
We discuss the stick-slip motion of an elastic block sliding along a rigid
substrate. We argue that for a given external shear stress this system shows a
discontinuous nonequilibrium transition from a uniform stick state to uniform
sliding at some critical stress which is nothing but the Griffith threshold for
crack propagation. An inhomogeneous mode of sliding occurs, when the driving
velocity is prescribed instead of the external stress. A transition to
homogeneous sliding occurs at a critical velocity, which is related to the
critical stress. We solve the elastic problem for a steady-state motion of a
periodic stick-slip pattern and derive equations of motion for the tip and
resticking end of the slip pulses. In the slip regions we use the linear
viscous friction law and do not assume any intrinsic instabilities even at
small sliding velocities. We find that, as in many other pattern forming
system, the steady-state analysis itself does not select uniquely all the
internal parameters of the pattern, especially the primary wavelength. Using
some plausible analogy to first order phase transitions we discuss a ``soft''
selection mechanism. This allows to estimate internal parameters such as crack
velocities, primary wavelength and relative fraction of the slip phase as
function of the driving velocity. The relevance of our results to recent
experiments is discussed.Comment: 12 pages, 7 figure
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