Directional dendritic solidification of a composite slurry: Part II. Particle distribution
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I.
INTRODUCTION
IN Part I of this article,[1] the changes in the solutal and thermal field due to the presence of a foreign particle and the associated morphological changes of the solid-liquid interface have been discussed. A simple analytical model has been proposed for estimating the modified dendrite tip radius and primary arm spacing. As discussed in Part I, the two important aspects of the microstructure in a composite material are the matrix microstructure and distribution of reinforcing particles. Part II of this article deals with the distribution of reinforcing particles in the matrix. It is now well known that, during solidification, when a growing solid-liquid interface interacts with an inert particle, it can either push the particle ahead of it or it can engulf the particle into the growing solid. There have been many experimental and theoretical studies on the nature of interactions between the particle and the moving solid-liquid interface.[2–10] The predictions of these theoretical models vary widely; nevertheless, all these models have led to the following conclusions, which are of fundamental significance. (1) The interaction of an inert particle and a growing crystal alters the shape of the interface. (2) There exists a repulsive interfacial force and a viscous drag force between the particle and the moving interface. If the repulsive force is more than the drag force, the particle will be pushed; on the other hand, when the repulsive force is less than the drag force, the particle will be engulfed by the growing solid. (3) The magnitude of both these forces depends, to a large extent, on the shape of the solid-liquid interface in the vicinity of the particle.
gulfment. As shown in Part I of this article,[1] in the presence of a particle the dendrite tip radius is changed, and this change has to be considered in the postulation of a criterion for the pushing-to-engulfment transition. All the existing models proposed to date to describe the particle– solidification front interaction assume a planar interface. However, Sasikumar and Rammohan[7] have shown that, in the case of Al-Cu-SiCp composites, the plane front breaks down before the particles are engulfed, i.e., the critical velocity for particle engulfment is higher than the critical velocity for the instability of the plane front. In an earlier work,[11] the present authors have shown that the nature and magnitude of the forces on the particle are significantly different during dendritic solidification compared to those during plane front solidification. All these findings indicate that, in order to obtain a valid criterion for particle engulfment in composites, it is essential to consider the interaction of a particle with a nonplanar interface instead of a planar interface. The present work attempts to form an understanding of the interaction between a particle and a growing dendrite under directional solidification conditions. Particle distribution during directional solidification has been studied experimentally under a wide range of
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