An analysis of the relationship between grain size, solute content, and the potency and number density of nucleant parti
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I. INTRODUCTION
GRAIN refinement has many benefits in direct chill casting operations including reduced hot tearing susceptibility, reduced homogenization time, and improved mechanical properties.[1] The amount and type of grain refiner addition required for effective grain refinement of a particular alloy has previously been determined on a trial and error basis or, as is more often the case, one type of master alloy addition is used for all alloys cast. From previous work, it is known that for effective grain refinement, both nucleant particles and solute are required.[2,3] Nucleating substrates provide heterogeneous sites for nucleation of the primary solid phase at low undercooling, while the solute elements provide constitutional undercooling to restrict the growth of grains and facilitate nucleation. Recent work[4] indicates that the effect of alloy content on grain size is well understood and predictable for a fixed particle addition. However, the effects of nucleant particle addition rate, differences in potency for different types of master alloy, and cooling rate on grain size are not well understood. In this article, the effects of nucleant particle additions and solute content are investigated as part of a research program that aims to develop a relationship that allows the prediction of grain size and morphology in any casting for any alloy and grain refiner addition. To characterize and quantify the effect of nucleant particles on grain size, the contribution made by solute content needs to be established. Experimental evidence[3–6] and theMARK EASTON, CRC for Cast Metals Manufacturing (CAST), is with the School of Physics and Materials Engineering, Monash University, Melbourne, Australia. Contact e-mail: [email protected] DAVID StJOHN, CRC for Cast Metals Manufacturing (CAST), is with the Division of Materials Engineering, University of Queensland, Brisbane, Australia. Manuscript submitted January 27, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS A
ory[7,8] have shown that the growth restriction factor Q is the best factor to use as a measure of the effect of solute on grain refinement. It was found[3–6] that grain size is related to solute content by a semiempirical relationship: da
b Q
[1]
where d is the grain size and a and b are constants. Theoretically, Q was originally derived to be inversely proportional to the growth rate of the primary phase.[9] More recently, it has been defined as the initial rate of development of constitutional undercooling with respect to fraction solid[7,8] and can be estimated using the sum of mc0(k 1) of the individual elements present in most wrought alloy systems, where m is the slope of the liquidus, c0 is the concentration of the element, and k is the partition coefficient. However, if the elements in the alloy react or change their partition coefficients, then this simple relationship breaks down as in the case of titanium additions to Al-Si foundry alloys.[10] In these cases, thermodynamic packages can be used to calculate Q.[4,11]. For a
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