Michael Fleck

Brittle fracture in viscoelastic materials as a pattern-formation process.

A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are taken into account. Two different mechanism of crack propagation, a first order phase transition and surface diffusion are considered, and we discuss different loading modes. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique.

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 Greens 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.

Pattern formation during diffusional transformations in the presence of triple junctions and elastic effects

We compare different scenarios for dendritic melting of alloys with respect to the front propagation velocity. In contrast to conventional dendritic growth, selection can here be also due to the presence of a grain boundary or coherence strains, and the propagation speed is higher. The most favorable situation is partial melting, where two parabolic fronts, one melting and one solidifying interface, are moving together, since the process is then determined by diffusion in the thin liquid layer. There, and also in phase field simulations of melting in peritectic and eutectic systems, we observe a rotation of the triple junction relative to the growth direction. Finally, we discuss the role of elastic effects due to density and structural differences on solid-state phase transformations, and we find that they significantly alter the selection principles. In particular, we obtain free dendritic growth even with isotropic surface tension. This is investigated by Greens function methods and a phase field approach for growth in a channel and illustrated for the formation of a twin phase.

Elastic and plastic effects on solid-state transformations: A phase field study

Abstract We discuss a model of diffusion limited growth in solid-state transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We study the growth of a stable phase from a metastable solid in a channel geometry, and perform phase field simulations. Extensions to plastic models are discussed.

Influence of stress on interface kinetics

Non-equilibrium interface kinetics are driven by a chemical potential which sensitively depends on the elastic state of the system. We present a method to derive the chemical potential of two coherently connected linear elastic media from fundamental variational principles, also including surface tension and inertial effects. As particular applications, we perform linear stability analyses for stressed straight surfaces and interfaces, and compare them to phase field simulations.

Phase-Field Modeling of Precipitation Growth and Ripening During Industrial Heat Treatments in Ni-Base Superalloys

We develop a phase-field model for the simulation of chemical diffusion limited microstructure evolution, with a special focus on precipitation growth and ripening in multicomponent alloys. Further, the model accounts for elastic effects, which result from the lattice-misfit between the precipitate particles and the parent matrix phase. To be able to simulate particle growth and ripening in one dimension, we introduce an extra optional driving-force term, which mimics the effect of curved interfaces in one dimension. As a case study, we consider the one-dimensional (1D)

On phase-field modeling with a highly anisotropic interfacial energy

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Analysis of the dependence of spinodal decomposition in nanoparticles on boundary reaction rate and free energy of mixing

γ′-precipitation growth and ripening under the influence of a realistic multistep heat treatment in the multicomponent Ni-based superalloy CMSX-4. The required temperature-dependent thermodynamic and kinetic input parameters are obtained from CALPHAD calculations using the commercial software-package ThermoCalc. The required temperature-dependent elastic parameters are measured in-house at the chair of Metals and Alloys, using resonance ultrasound spectroscopy and high-temperature X-ray defraction. Finally, the model is applied to calculate the equilibrium shape of a single