Experimental Investigation on the Rheological Behavior of Hypereutectic Al-Si Alloys by a Precise Rotational Viscometer
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INTRODUCTION
THE functionally graded material (FGM) concept is spreading in material production. As a result, there are many various techniques for producing FGM materials.[1] In casting techniques, centrifugal,[2] electromagnetic,[3] or gravitational[4] forces are frequently used for formation of particle concentration gradient within solidifying slurries. Also, some researchers have tried to simulate the motion of solid particles in molten metals and the gradient of reinforcing particles within FGMs.[5–7] For simulation of particle motion, Stokes’ equation (Eq. [1]) is frequently used as a basic equation for predicting the velocity of particles in molten slurries.[5,7,8] Existence of so many particles in a fluid leads to an increase in the drag force on a particle, and consequently, the moving of particles in the fluid hinders. Therefore, the velocity of particles may be more accurately predicted by Stokes’ law (Eq. [1]) in which the viscosity of fluid replaces the viscosity of slurry (g) for prediction of hindered velocity (Vh):[5,7] qp q gdp2 ½1 Vh ¼ 18g where dp is the diameter of particles; and qp and q are, respectively, the density of particles and fluid. As can be D. SOHRABI BABA HEIDARY, M.Sc., and F. AKHLAGHI, Professor, are with the School of Metallurgy and Materials Engineering, Faculty of Engineering, University of Tehran, P.O. Box 111554563, Tehran, Iran. Contact e-mail: [email protected] Manuscript submitted March 17, 2010. Article published online September 28, 2010 METALLURGICAL AND MATERIALS TRANSACTIONS A
inferred from Eq. [1], for calculating the hindered velocity, all the terms of Eq. [1] can be measured easily except the viscosity. As a result, determining the viscosity of slurry can be a key factor in the simulation of particle motion. Some equations have been developed to estimate the viscosity of slurries such as Brinkman’s[9] or Richardson’s[10] equations. However, the direct measurement of viscosity can be the most valid technique to determine the exact amount of viscosity. The viscosity of semisolid metal alloys depends on a number of parameters and can be generally represented by the following equation:[11,12] _ C0 g ¼ f c_ ; t; T; T; ½2 where c_ is the shear rate, t is the shear time, T is the temperature of semisolid alloy, T_ is the cooling rate to T, and C0 is the alloy composition. Mada et al.’s study[13] showed that at a constant shear rate, the apparent viscosity (g) decreases as a function of the duration of shear (t) according to Eq. [3]: g ¼ ge þ ðg0 ge Þ expðktÞ
½3
where k is constant; and ge and g0 are the viscosity at dynamic equilibrium and initial condition, respectively. The correlation of the equilibrium viscosity with the shear rate has been studied by a number of researchers on aluminum alloys.[14–16] Their results have been fitted to the empirical power law equation g ¼ C_cm
½4
where C is the material consistency; and m is the power law index, which is constant over a wide range of shear rate conditions. Equation [4] is derived from VOLUME 41A, DECEMBE
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