Mathematical modeling of particle segregation during centrifugal casting of metal matrix composites
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casting of metal matrix composites, segregation of particles occurs due to centrifugal force, either at the inner or the outer periphery of the casting, depending on the relative densities of the particles and the melt, resulting in particle-reinforced functionally gradient composites. The extent of segregation depends on various process parameters including cast geometry, pouring temperature of the melt, solidification time, density difference between matrix and reinforced particles, and rotational speed. Kang and Rohatgi[1] have described the results of a heattransfer analysis of centrifugal casting of metal matrix composites by one-dimensional analysis considering the thermophysical properties due to particles moving as a function of temperature. In their investigations, the positions of the dispersed particles at a given instant of time are analyzed as a first step. Then, the temperature distributions in the mold and the solidifying metal are analyzed at different time intervals. Using these temperature distributions, time taken for solidification of casting at different rotational speeds, initial mold temperatures, and pouring temperatures of molten metal are estimated. Siva Raju and Mehrotra[2] have presented a more realistic model wherein the volume fraction of the particles across the thickness of the casting varies with time. Their formulation is based on oneEMILA PANDA, Scientist, and S.P. MEHROTRA, Director, are with the National Metallurgical Laboratory, Jamshedpur-831007, Jharkhand, India. Contact e-mail: [email protected] or [email protected] DIPAK MAZUMDAR, Professor, is with the Department of Materials & Metallurgical Engineering, Indian Institute of Technology, Kanpur208016, U.P., India. Manuscript submitted June 24, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS
dimensional heat-transfer analysis incorporating variations in thermophysical properties due to particle movement in the matrix. It also considers variations in the heat-transfer coefficient and latent heat release. The present investigation is an attempt to further improve that analysis. At the outset, there are two principal differences between the present investigation and that of Siva Raju and Mehrotra, (1) Both Kang and Rohatgi[1] and Siva Raju and Mehrotra[2] in their models neglected the repulsive force term in their equations for force balance on particles. In the present investigations, the repulsive force that a particle experiences when it approaches a solid wall/solidification front is taken into consideration and characterized by an appropriate expression, the details of which are given in a later section of this article, and (2) Siva Raju and Mehrotra took into consideration the variation of the volume fraction of particles with time by ensuring the conservation of the total mass of particles at all times. In their approach, the volume of particulates in between two consecutive nodal points always remains the same, but the length of the segment varies with time as do the nodes as they depend on the constant volume fractio
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