Phase Field Modeling of Fast Crack Propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.Comment: 5 pages, 11 figure

Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects

Liquid-liquid phase transition in flow systems

Liquid-liquid phase transition is occurring in many chemical engineering processes either as a desired phenomenon or as an undesired side effect. Typically, the phase split is modeled by neglecting all non-equilibrium effects. Here, a simple non-equilibrium situation is considered. Convective flow of a liquid along a decreasing temperature profile in a cooled channel is studied analytically. Three different scenarios for the transition process with two typical phase diagrams for binary mixtures are examined. For a phase diagram with critical concentration, phase segregation occurs via spinodal decomposition as a convective instability. For a cigar-shaped phase diagram the phase transformation is shown to evolve in analogy to directional solidification. Finger-like structures may be established under certain circumstances. (C) 2002 Elsevier Science Ltd. All rights reserved

Kristallzucht im Weltraum

Anlaß zu dieser Studie war die Frage, ob unter Schwerelosigkeit /63/ Kristalle größerer Perfektion als unter Erdschwere gezüchtet werden können. Dieses Problem wurde im ad-hoc Ausschuß des Bundesministeriums für Forschung und Technologie "Möglichkeiten der industriellen Forschung, Entwicklung und Produktion im Weltraum" und von der Gesellschaft für Weltraumforschung aufgeworfen im Hinblick auf eine sinnvolle Nutzung des zukünftigen Weltraumlabors "Space Lab" /64/ auf dem Gebiet der Materialwissenschaften. Im Institut für Festkörperforschung der Kernforschungsanlage Jülich wird experimentell und theoretisch auf dem Gebiet desKristallwachstums und der Kristallzucht gearbeitet /65, 66/. Aufgrund dieser Erfahrungen wurde versucht, in der relativ kurzen Zeit von November 1974 bis Januar 1975 möglichst originelle und kritische Meinungen zu einigen Aspekten der Kristallzucht unter Schwerelosigkeit zu entwickeln. Dabei galt es, zahlreiche theoretische und experimentelle Arbeiten auf diesem Gebiet, die vor allem in den USA publiziert wurden /67, 68, 69, 70, 71, 72,149, 73/, zu analysieren und zu berücksichtigen

vorgelegt von Diplom-Physiker

This thesis describes the behavior of cracks and pores under the influence of elastic and curvature effects. In a continuum theory approach, these structure deformations are treated as free moving boundaries. Our investigation start with well established sharp interface equations for which no fully dynamical solutions exist so far. The equations include only linear dynamical elasticity, surface energy and non-equilibrium transport theory. By proper use of the phase-field concept, we are now able to tackle the fully time-dependent free moving boundary problem to describe crack propagation in a fully self-consistent way. We concentrate on two material transport processes, namely surface diffusion and phase transition dynamics. We show analytically that the intuitive and widely used approach for constructing a phase-field model for surface diffusion fails, since it does not reduce to the desired sharp interface equations, providing an uncontrolled approximation to the dynamics. We then develop two completely new models that ensure the correct asymptotic behavior and support our analytical findings by numerical simulations, which are are computationally very demanding due to the high order equations that have to be solved