Motivation — The detailed knowledge on the evolution of dendritic microstructures is essential for the ability to systematically influence the quality of cast products. As the dendrite tips grow into the undercooled melt, at a short distance behind the development of sidebranches leads to a complex morphology of the solid-liquid interface. At a certain distance behind the dendrite tip a slower evolution sets in, which is taking place close to phase equilibrium. At this stage interface dynamics are mainly determined by capillarity and slow solidification. The major part of published research is concerned with purely capillarity-driven coarsening. However, most practical cases imply the concurrent effect of slow solidification, which constitutes an important aspect in the quantitative understanding of the involved mechanisms. This project is concerned with the evolution of integral geometrical properties such as the specific interface area as well as evolution scenarios of single sidebranches. The specific interface area is a key ingredient in volume-averaged models of solidification which are related e.g. with the permeability of the mush-zone and microsegregation. On the other hand, single sidebranches are subject to different evolution scenarios depending on the geometrical and thermal conditions: retraction towards the parent stem, pinch-off and fragmentation or coalescence with a neighboring sidearm. A particular importance is associated with the pinch-off of sidebranches as the generated fragments act as a potential source of equiaxed dendrites in the free melt. This provides a "natural" mechanism for archiving a fine-grained microstructure with desirable technological properties.
Methods — The studies of solidification processes in binary alloys are based on a phase-field model. The partial differential equations associated with the phase-field model are solved with the help of an open finite element library. This allows for high efficiency and scalability of the models due to available techniques such as adaptive mesh refinement and parallel computing on high performance computing infrastructures. Large 3D models on the dendrite scale were used to study various aspects regarding the evolution of the complex interface morphology during growth and coarsening. However, due to high computation costs examinations are restricted to selected cases. Therefore, an idealized, axisymmetric model of a single sidearm is utilized to more generally understand the evolution of sidebranches.
Results — The evolution of the dendrite interface area is characterized by a rapid increase during the growth of sidebranches which is followed by a decrease due to capillarity and coalescence of adjacent structures. Although there exist separate models for both of the latter effects, their combined operation is still lacking a systematic examination. Our recent collaboration with Prof. C. Beckermann (University of Iowa) is concerned with a generalisation of the existing models towards arbitrary cooling rates by including 3D phase-field simulation in comparison with in-situ observations from X-ray tomography experiments. Based on the simplified sidearm model we were able to obtain a general characterisation of the pinching dynamics and conditions for the occurrence of the different evolution scenarios. We have found that pinch-off only occurs over limited ranges of geometrical parameters and cooling rates and is generally bounded by sidearm retraction and coalescence regimes. In order to identify more general boundaries between the particular scenarios we have examined important limiting cases and performed automated searches throughout the 2D parameter space.