A model for prediction of pressure and redistribution of gas-forming elements in multicomponent casting alloys
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I. INTRODUCTION
THE formation of porosity during alloy solidification affects the integrity of cast products and sometimes limits their application as structural components. Porosity is very detrimental to the mechanical properties of high-temperature superalloys because it reduces fatigue properties and stress rupture. Many modern foundries have resorted to experimental and numerical research in order to minimize, and if possible, eliminate this defect, making the prediction of porosity distribution in shaped castings a popular research topic at the present time. The two primary types of porosity occurring during solidification are shrinkage porosity and gas porosity. Shrinkage porosity develops because of a pressure drop associated with the suction of the liquid within the porous dendritic region, due to the volume contraction during the phase change. Gas porosity occurs because of segregation of gaseous solute elements such as hydrogen, nitrogen, or carbon and oxygen, which form carbon monoxide. This article addresses what is commonly called microporosity or interdendritic porosity, in which the shrinkage voids or gas pores are constrained to occupy the interdendritic spaces near the end of solidification. Large-scale shrinkage resulting from insufficient or defective liquid feeding is beyond the scope of this work. In the past 15 years, many efforts have been devoted to the modeling of porosity formation. Many of them have been oriented to aluminum-base alloys[1–6] and, in a lesser degree, to nickel-base superalloys[7,8] and steels.[9,10] The S.D. FELICELLI, Research Scientist, is with Centro Ato´mico Bariloche, 8400 S.C. de Bariloche, Argentina. D.R. POIRIER, Professor, and P.K. SUNG, Research Associate, are with the Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721. Manuscript submitted November 30, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
model presented here includes several aspects of a comprehensive one to simulate directly the formation of porosity. It is built on a robust and well-tested multicomponent macrosegregation model,[11] to which we are adding additional capabilities for predicting porosity. Emphasis is given to the calculation of gas porosity and its interaction with shrinkage, which is thought to be a major factor in the formation of microporosity.[3] This porosity arises because the solubility of gas is less in the solid than it is in the liquid metal, so that some gas is expelled into the interdendritic or intergranular liquid. If the pressure of the gaseous elements in the interdendritic liquid rises to a value sufficient to exceed the sum of the local pressure within the interdendritic liquid and the excess pressure attributed to surface tension, then microporosity results. This implies that in addition to the micro/ macrosegregation model to compute solute transport by diffusion and convection during solidification, a thermodynamic model is needed to predict the formation of the gas phase in the interdendritic liquid.[2] In its present f
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