Prediction of Cooling Curves for Controlled Unidirectional Solidification Under the Influence of Shrinkage: A Semi-analy
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DIRECTIONAL single crystal growth has many applications related to production of high-frequency turbine blades, solar absorber materials, photovoltaic materials, and many more. Crystal growth is the fundamental phenomenon that defines the grain structure during solidification processes. Favorable mechanical properties such as strength and hardness of cast products can be achieved by controlling grain structure.[1–3] Attempts have been made to refine micro-structure of castings by adding refiner and modifier to the melt, in order to improve the mechanical strength of cast products.[4] One of the most important factors that influence the growth of micro-structure is the cooling rate (K/s).[5–7] Zhuang and Langer[5] achieved fine equiaxed grain structure of Co-Cr-Mo alloys by employing fast cooling rate during casting. Zhang et al.[7] ANIKET D. MONDE and PRODYUT R. CHAKRABORTY are with the Department of Mechanical Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342037, India. Contact e-mail: [email protected] Manuscript submitted March 20, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS B
studied a fast cooling technology using a copper mold for solidification of Al356 alloy. Hosseini et al.[8] also studied the effect of cooling rate on mechanical properties, solidification parameters and micro-structures of LM13 alloy. Zhang et al.[7] and Hosseini et al.[8] concluded that higher cooling rate and shorter solidification time causes further refinement of micro-structures, resulting segregation-free micro-structures with homogeneous distribution of micro-porosity. Boettinger et al.[9] reported prevalence of conventional dendritic or eutectic structures at low crystal growth rate condition. Boettinger et al.[9] also suggested the possibility of obtaining micro-segregation-free single phase structures at higher crystal growth rates. Sarreal and Abbaschian[10] and Taha et al.[11] reported existence of optimal cooling rate for achieving maximum amount of non-equilibrium eutectic (NEE) phase in the directionally solidified sample of non-eutectic alloys. Sarreal and Abbaschian[10] and Taha et al.[11] interpreted this phenomenon as a result of back diffusion, dendrite tip under-cooling, and eutectic temperature depression. Eskin et al.[12] and Du et al.[13] studied the effect of cooling rate on non-eutectic Al-Cu alloy casts, and made similar conclusion on the existence of an optimum cooling rate. Kasperovich et al.[14] investigated non-eutectic Al-Cu alloy solidification under the large range of
cooling rates (0.01 to 20,000 K/s) to conclude the similar trend. Kasperovich et al.[14] also used 2-D pseudo-front tracking (PFT) model developed by Du and Jacot[15] to predict the eutectic fractions, and validated the numerical results with experimental data. Uncontrolled cooling rate causes inhomogeneous distribution of grain-size and micro-porosity which may lead to severe casting defects.[7,8] Challenge of determining appropriate cooling curve to ensure desired crystal growth rate received considerable attention from several
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