Extended solid solution and nonequilibrium phase diagram for Ni-Al alloy formed during laser cladding
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I.
INTRODUCTION
L A S E R technology provides a unique way of modifying the surface chemistry of materials. Due to the inherent rapid heating and cooling rate in laser alloying and cladding processes, it is often possible to obtain novel metastable materials with extended solid solution. Recently, laser cladding technique has been applied to increase the solid solubility of reactive elements such as Hf in nickel superalloyrll for improved high temperature properties. The mechanism of extended solubility encompasses the energy, momentum, and mass transport of solute atoms. The heat transfer equation governs the heating and cooling rates while the momentum and mass transport equations govern the extent of mixing and the redistribution of solute atoms in the molten cladding pool. This paper uses a mathematical model to predict the composition of solute in the extended solid solution of Ni-AI binary alloy which is usually formed during laser cladding. The model also allows us to construct a nonequilibrium phase diagram of a given system from its equilibrium phase diagram. In the available literature, there is very little information on mathematical models for laser cladding and surface alloying with rapid cooling rate. As mentioned earlier, the composition of a rapidly solidified metastable alloy depends greatly on the rate of solidification. Three-dimensional heat transfer models for various material processings with continuous wave laser have been presented by several authors, t2-51It has been found experimentally that convection arises in laser melted pools due to variation of surface tension with temperature. This aspect was modeled by Chan e t a l . t61 They studied the effects of surface tension on the cooling rate, surface velocity, surface temperature,7 and the pool shape. Chande and Mazumder I1 examined the distribution of solute by diffusion and convection in a laser melted pool after delivering the solute powder into the pool. Thermodynamic variables such as free energy and chemical potential have been used for the problem of exA. KAR. Visiting Research Assistant Professor, and J. MAZUMDER, Professor, are with the Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801. Manuscript submitted October 9, 1987. METALLURGICAL TRANSACTIONS A
tended solid solution during rapid solidification. Baker and Cahn tsj examined the thermodynamics of nonequilibrium solidification. Boettinger and Perepezko tg] discussed the process of rapid solidification from a thermodynamics point of view. Boettinger et a l J 1~ also used the response function approach of Baker and Cahn fsj and stability analysis for microsegregation-free solidification. Further details on rapidly solidified materials can be found in References 11 and 12. In a recent paper, tlaj the authors have presented a model for extended solid solution during laser cladding by considering the cladding pool and the solid substrate semi-infinite and the freezing point of the cladding me
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