Inverse Analysis of Eutectic Nucleation and Growth Kinetics in Hypoeutectic Al-Cu Alloys
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MANY commercially relevant casting alloys have significant fractions of eutectic phase in their microstructures. Differences in the size, shape, and distribution of the eutectic grains affect the mechanical performance of the cast component. Additionally, the differences in eutectic structure can affect feeding during solidification leading to porosity formation. For example, Knuutinen et al.[1] showed a strong correlation between the amount and distribution of porosity and the eutectic solidification mode in aluminum alloy A356. Therefore, understanding the eutectic nucleation and growth mode is crucial in casting models for accurate defect prediction. With the development of advanced numerical techniques and the improved understanding of the mechanisms governing microstructure development, substantial progress has been made in the field of microstructural modeling. For instance, on the one hand, the phase field method has been applied widely to improve our knowledge in the area of solidification.[2] However, one major challenge that must be addressed when employing phase field models is running realistic or relevant problems with current computational resources. Stochastic models, on the other hand, are more computationally efficient. Brown and Spittle[3,4] EHSAN KHAJEH, PhD Candidate, and DAAN M. MAIJER, Associate Professor, are with the Department of Materials Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada. Contact e-mails: [email protected]; ehsan.khajeh@ gmail.com Manuscript submitted May 15, 2010. Article published online October 5, 2010 158—VOLUME 42A, JANUARY 2011
were one of the first to develop a stochastic model, based on the Monte Carlo (MC) technique, to predict the grain structure in a casting. Since this initial application, MC models have been shown to predict the grain structure observed in real castings accurately. However, models based solely on the MC technique do not account properly for the physical phenomena observed during the growth of dendritic or eutectic phases.[5,6] To address this, physically based modeling techniques such as the cellular automaton (CA) technique have been developed.[6] The CA technique was first developed by Hesselbarth and Gobel[7] to simulate recrystallization. In this method, the computational domain is divided into cells with associated state data (phase, orientation, etc.) and calculated fields (temperature, composition, etc.). A cell changes state based on transition rules, which can be probabilistic or deterministic and often incorporate neighboring cell states.[6] Several researchers have used the CA technique to describe solidification processes.[5,8] Rappaz and Gandin[8] and Gandin et al.[9] developed a CA model to predict the grain structure during the solidification of an Al-Si alloy and a Ni-based superalloy, respectively. Rappaz et al.[5] coupled a CA growth model with a probabilistic nucleation relationship and a finite element (FE) heat transfer model to create the CAFE modeling technique. Charbon and Rappaz[10] adapted
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