Modeling of feeding behavior of solidifying Al-7Si-0.3Mg alloy plate casting
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I.
INTRODUCTION
THE formation of porosity in aluminum alloy is well known as a problem relating to its good thermal conductivity, long freezing range, and large decrease of hydrogen solubility from liquid state to solid state. This inevitable casting defect greatly deteriorates the soundness of casting. As such, numerous efforts have been carried out in an attempt to understand the feeding process of aluminum alloy by thermal measurement and to explore its feeding behavior by numerical analysis. The importance of interdendritic fluid flow for the pore formation in solidification was pioneered by Piwonka and Flemings t~] and later by other investigators, t2-8] Davies t9J derived an equation which involves solidus velocity to calculate the capillary feeding distance for plate castings according to the Hagen-Poiseuill equation; however, the structural effect of the dendritic network was ignored. Niyama et al. t~~ and later Minakawa et al., Em working on steel, postulated the same parameter G / V ~ , the thermal gradient divided by the square root of cooling rate, based on Darcy's law; the parameter verified that shrinkage decreased with increasing solidification time. The basis of this result is rationalized as the permeability of the dendritic network for capillary fluid flow increasing with increasing dendrite arm spacing which is proportional to solidification time. I4,7JLecomte-Beckers ~21 took into consideration alloying elements in a superalloy and proposed a microporosity index also based on Darcy's law; in essence, this work agrees with the previous work of Davies, t9~ Niyama et al., t~~ and Minakawa et al. tlq On the contrary, Poirier et al.,t~3! in modeling the feeding behavior of A1-4.5 pct Cu, found that the porosity content decreased with increasing solidification rate and thermal gradient because of the smaller interdendritic spaces. In studying the same alloy, a similar
was reached by Kubo and Pehlke, t141 although the latter authors also considered Darcy's law which governs the interdendritic fluid flow through porous media. This school of thinking was further supported by Entwistle et al., [~51who evidenced the parallel relationship between porosity content and local solidification time for aluminum alloys. In an attempt to reconcile the disagreement, Pathak and Prabhakar l~rl postulated for aluminum alloys that the feeding efficiency is determined by both the pasty zone factor, feeding efficiency as influenced by pasty zone (FEP), and the interdendritic feeding time, feeding efficiency as influenced by the time allowed during the last stage of solidification (FET). However, contradiction exists as these two so-defined parameters, i . e . , FEP and FET, cannot be satisfied simultaneously; if the solidification rate is increased to improve the FEP, the FET will be sacrificed and vice v e r s a . The dilemma was also noticed by Bachelet and Lesoult t~71 in studying a superalloy, but no solution was attempted. One of the reasons for failure to solve the above disputes, from the present authors' view,
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