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POROSITY-RELATED defects are a major cause of casting rejection and rework in the casting industry. They are typically caused by a lack of feeding of the shrinkage that occurs during solidification or by excessive levels of gas species dissolved in the melt. Modeling of porosity formation has been attempted by many researchers, dating back to the early one-dimensional (1-D) work of Piwonka and Flemings[1] and the seminal two-dimensional (2-D) work of Kubo and Pehlke.[2] An extensive review of the research progress in porosity modeling, from these early studies up to the work done in 2000, is provided by Lee et al.[3] Recent examples of porosity models for aluminum alloy castings, including the effect of dissolved hydrogen, can be found in Sabau and Viswanathan[4] and Pequet et al.[5] These models assume that the local diffusion of hydrogen in the melt is infinitely fast. In a series of experimental and theoretical studies, Lee and co-workers[6–10] have shown that diffusion of hydrogen through the supersaturated liquid (inside the mushy zone) to the pores can be a ratecontrolling factor in pore growth for aluminum alloys. KENT D. CARLSON, Research Engineer, ZHIPING LIN, Graduate Research Assistant, CHRISTOPH BECKERMANN, Professor, are with the Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242. Contact e-mail: [email protected]. This article is based on a presentation made in the symposium ‘‘Simulation of Aluminium Shape Casting Processing: From Design to Mechnacial Properties’’ which occured March 12–16, 2006, during the TMS Spring meeting in San Antonio, Texas, under the auspices of the Computational Materials Science and Engineering Committee, the Process Modelling, Analysis and Control Committee, the Solidification Committee, the Mechanical Behavior of Materials Committee, and the Light Metal Division/Aluminium Committee. Article published online February 27, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B

Lee and Hunt[6,7] experimentally observed porosity formation in aluminum alloys using an X-ray temperature gradient stage. They found the pressure drop caused by shrinkage to be negligibly small. They developed a microscale model of hydrogen diffusioncontrolled growth by considering a single pore inside the mushy zone. The model does not compute the pressure field in the mushy zone; rather, the pressure is an input variable. Atwood et al.[8,9] applied this model to an Al7Si alloy, and Hamilton et al.[10] incorporated it into a heat flow model for complex-shaped castings, still neglecting pressure variations. Hence, a comprehensive porosity model that simultaneously accounts for hydrogen diffusion and shrinkage is still lacking. Figure 1 shows porosity percentages resulting from directional solidification experiments performed by several researchers using unmodified aluminum alloy A356.[11–14] Note that in every study, covering a range of initial hydrogen concentrations C0, the pore volume decreases as the cooling rate during solidification increases. If the poros