Daniel Schneider

Calibration of a multi-phase field model with quantitative angle measurement

Over the last years, the phase-field method has been established to model capillarity-induced microstructural evolution in various material systems. Several phase-field models were introduced and different studies proved that the microstructure evolution is crucially affected by the triple junction (TJ’s) mobilities as well as the evolution of the dihedral angles. In order to understand basic mechanisms in multi-phase systems, we are interested in the time evolution of TJ’s, especially in the contact angles in these regions. Since the considered multi-phase systems consist of a high number of grains, it is not feasible to measure the angles at all TJ’s by hand. In this work, we present a method enabling the localization of TJ’s and the measurement of dihedral contact angles in the diffuse interface inherent in the phase-field model. Based on this contact angle measurement method, we show how to calibrate the phase-field model in order to satisfy Young’s law for different contact angles.

Concepts of modeling surface energy anisotropy in phase-field approaches

To simulate the growth of geological veins, it is necessary to model the crystal shape anisotropy. Two different models, classical and natural models, which incorporate the surface energy anisotropy into the objective functional of Ginzburg–Landau type, are presented here. Phase-field evolution equations, considered in this work, are derived using the variational approach, and correspond to the conservative Allen–Cahn-type equation. For three characteristic anisotropy formulations, we show what kind of difficulties arise in the simulations for the presented models. Particularly, if the anisotropy becomes strong, the phase-field evolution equations become ill-posed. Thus, we present regularized phase-field models and discuss the corresponding simulation results. Furthermore, in the scope of the grain growth simulation, we extend the original two-phase models to multiphases.

Understanding the Influence of Neighbours on the Spheroidization of Finite 3-Dimensional Rods in a Lamellar Arrangement: Insights from Phase-Field Simulations

Understanding the microstructural phenomena during the production chain of steels is essential to improve the characteristic material properties. Besides experimental investigations, numerical methods have proven to be a powerful tool to yield property delineations. Therefore, a phase-field model incorporating free energies from CALPHAD database is employed to analyse curvature-driven shape-instabilities, in the absence of any phase transformations. Owing to the instabilities, morphological evolution occurs. In this study, previous works [1, 2] are extended to capture the influence of the neighbouring rods on the volume-diffusion governed transformation of finite 3-dimensional facetted rods. It is identified that the terminal rods strongly influence the carbon redistribution. Furthermore, we observe, in the later stages of transformation, that the neighbouring rods introduce a reverse mass transfer towards the terminal rods. The interplay of those two aforementioned effects causes a shift of the critical aspect ratio (\(w/t_p\)) of the rods, above which the spheroidization is accompanied by the breaking-up of rods (‘ovulation’).

On the Volume-Diffusion Governed Termination-Migration Assisted Globularization in Two-Phase Solid-State Systems: Insights from Phase-Field Simulations

Morphology of the constituent phase in a microstructure influences the mechanical properties of the materials similar to the chemical composition, crystal structure and volume fraction of the phases. Often to enhance the mechanical properties, heat treatment techniques that exclusively facilitate the morphological evolution without any phase transformation are adopted. In the present work, the mechanism and the kinetics of this morphological transformation governed by the inherent curvature-difference introduced by the shape, referred to shape instabilities, are analysed through phase-field simulations. By monitoring the temporal evolution of the elliptical plate, a finite three-dimensional structure associated with two-phase titanium alloys, it is observed that the transformation is dictated by the recession of the edges, or termination migration. It is identified that the elliptical structure transforms to a rod before assuming an ellipsoidal shape at the midpoint and ultimately, evolves into a spheroid. The results of this work are compared with the existing analytical approach and the deviations introduced by the geometrical approximations of the theoretical study are discussed. Furthermore, for the first time, it is shown that the hitherto assumed monotonic decrease in the driving force is interrupted by a series of ‘aberrations’ predominantly in the first half of the transformation, which intensifies with increase in aspect ratio. An analytical prediction which includes this non-monotonic evolution of the curvature is presented from the outcomes of the simulation.

Phase-Field Study of Electromigration-Induced Shape Evolution of a Transgranular Finger-Like Slit

Electromigration damage due to void propagation in thin films has garnered much attention due to its implications for efficient design of interconnects. Voids can drift along the line, preserving its shape, or evolve into various time-dependent configurations, which are governed by the interplay between the capillarity and electron wind force. We have employed the phase-field method to elucidate the transition of a circular void to a finger-like slit. Following an initial transient regime, the void attains an equilibrium shape with a narrow parallel slit-like body, which contains a circular rear end, and a parabolic tip. The subsequent drift of the void is characterized by shape invariance along with a steady-state slit width and velocity, which scale with the applied electric field as

Co-existence of strongly and weakly localized random laser modes

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Combined crystal plasticity and phase-field method for recrystallization in a process chain of sheet metal production

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