Relation Between Bulk and Interface Descriptions of Alloy Solidification

From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive an interface description, allowing arbitrary values of the growth velocity. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. We, moreover, discover a continuous symmetry, which appears in the low-velocity regime, and there deletes the Onsager sign and symmetry properties. An example is the generation of the sometimes negative friction coefficient in the crystallization flux-force relation

Diffusion-Induced Oscillations of Extended Defects

From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures

Capillary-Wave Description of Rapid Directional Solidification

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We, moreover, establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands, and, taking into account the Mullins-Sekerka instability, of banded structures

Capillary-Wave Model for the Solidification of Dilute Binary Alloys

Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption, and includes non-equilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability which, interfering with the Mullins-Sekerka instability, is similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure

Shape transformation of a wake following the process zone at the tip of a propagating crack

A process zone containing a new phase often forms at the tip of a crack in a quasi-brittle solid. We study such a zone engendered by the propagating crack. We show that depending on the crack speed, V, this zone has two distinct configurations. If the crack tip velocity is small, the zone takes a concave shape. As soon as V exceeds a critical value, $V_{\text{G}}$ , the zone becomes convex. A metastable remnant, the wake, forms in its rear part. It is stretched backward over a great distance and exhibits a triangle configuration with the vertex angle decreasing with speed. The morphological zone transition and the wake shape is explained by competition of the velocity of a free, plane phase front and the crack tip speed

Field-theoretical description of the formation of a crack tip process zone

The crack tip process zone is regarded as a region where the solid physical properties are altered due to high stress. They are controlled by the solid degrees of freedom existing within the zone and vanishing outside, and can be divided into two classes: (1) zones always existing at the tip and (2) those emerging as soon as certain conditions are met. We focus on the zones of the second kind and argue that they can be described analogously to phase transitions taking place locally. We report both a numerical and an analytical solution for the process zone. We find that the zone can only exist within a limited domain of the dynamic phase diagram, at one side of the phase transition line. We describe this domain and establish its dependence on the crack velocity. We show the existence of a critical crack velocity above which the zone cannot exist

Generic features of brittle crack propagation engendered by the dynamics of the process zone

We demonstrate that internal dynamics within the transformational process zone at the tip of a propagating crack gives rise to energy dissipation. It manifests itself as a velocity-dependent resistance force exerted on the crack tip. It has the effect of limiting the terminal crack speed to below the Rayleigh velocity as well as giving rise to a discontinuous dependence of the crack velocity upon the driving force