Morphological Changes in Rod-Shaped Precipitates With Internal Boundaries: Finite Difference Analysis
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MORPHOLOGICAL CHANGES IN ROD-SHAPED PRECIPITATES WITH INTERNAL BOUNDARIES: FINITE DIFFERENCE ANALYSIS JUN-HO CHOY, S. A. HACKNEY AND J. K. LEE Dept. of Metallurgical & Materials Engineering, Michigan Technological University, Houghton, MI 49931
ABSTRACT Shape evolution of rod-shaped precipitates due to surface diffusion has been studied under the conditions of constant volume and isotropic interfacial free energy. The shape evolution depends strongly on both the initial aspect ratio and the grain boundary groove angle. For a finite rod with one grain boundary, the morphology evolves into an equilibrium shape made of spherical portions if its aspect ratio and the groove angle are small. Increase in the aspect ratio causes a boundary splitting. For an infinite rod with periodic boundaries, three types of morphological evolutions are observed. When the relationship between the aspect ratio and the groove angle satisfies a certain critical condition, the shape evolves into an equilibrium. If the relationship deviates significantly from this condition, an ovulation process takes place at each location of the internal grain boundaries. When the deviation is intermediate, the morphology undergoes an oscillation in a quasi-dynamic state between the process toward an equilibrium shape and the ovulation process. The ovulation process due to internal grain boundaries is found to precede the Rayleigh spheroidization process.
INTRODUCTION The shape stability of a fibre in a composite material at elevated temperature is an important metallurgical factor that affects mechanical property of the composite[l]. Since the theory of surface diffusion and the grain boundary grooving was developed[2,3], many investigations have been focused on the interphase boundary instability mechanisms of fibres or rod eutectics that have cylindrical geometries[1,4]. The classical work of Nichols and Mullins[5] offers a background for this instability mechanism known as Rayleigh spheroidization for which an infinitely long cylinder breaks up into a series of spheres. If internal boundaries(grain boundaries) exist in the rod, the instability mechanism will be different since the grain boundary grooving will influence the instability of the interphase boundary. In addition, the equilibrium shape of the grain can be sought in the non-linear analysis. In this analysis finite difference method is applied to the study of the interphase boundary instability mechanism in the polycrystalline bamboo structure. Under the constant volume condition, it will be assumed that the interfacial properties are isotropic. The migration of grain boundaries and the process of volume diffusion will not be considered in this analysis.
BACKGROUND In order to study the 3-dimensional morphological changes of a rod precipitate, the rod with its internal boundaries perpendicular to the precipitate-matrix boundary is considered, as illustrated in Fig. 1. Two cases are considered; a rod of finite length with a single internal Mat. Res. Soc. Symp. Proc. Vol. 237. 01992 Materials
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