Particle-Size-Grouping Model of Precipitation Kinetics in Microalloyed Steels
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THE demand for steels with higher strength, ductility, and toughness is always increasing. Many alloying additions act to improve these properties through the formation of precipitate particles. In addition to precipitation strengthening, precipitates often act by pinning grain boundaries and inhibiting grain growth. These effects depend on both the volume fraction and size distribution of the precipitates.[1–4] Many small particles are more effective than a few large particles. An unfortunate side effect is a decrease in high-temperature ductility and possible crack formation during processes such as casting and hot rolling, caused by the growth of voids around precipitate particles on the weak grain boundaries. It is, therefore, important to control the spatial distribution, morphological characteristics, and size distribution of precipitates during all stages of steel processing. These parameters are generally determined by the alloy composition, and temperature history. In high-deformation processes such as rolling, they also depend strongly on strain and strain rate. The accurate modeling of precipitate growth includes at least two analysis steps: (1) supersaturation, based on equilibrium precipitation thermodynamics and (2) kinetic effects. Many models to predict equilibrium precipitation are available in commercial packages based on minimizing Gibbs free energy, including ThermoCalc (Thermo-Calc Software, Stockholm, Sweden),[5,6] FactSage (Center for Research in Computational KUN XU, Graduate Student, and BRIAN G. THOMAS, C.J. Gauthier Professor, are with the Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL 61801. Contact e-mail: [email protected] Manuscript submitted October 10, 2010. Article published online October 19, 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A
Thermochemistry, Montreal, Canada),[7] ChemSage (GTT-Technologies, Aachen, Germany),[8] JMatPro (Sente Software, Guildford, United Kingdom),[9] other CALPHAD models,[10,11] and other thermodynamic models based on solubility products in previous literature.[12–16] A recent equilibrium model predicts the stable formation of typical oxides, sulfides, nitrides and carbides in microalloyed steels efficiently by solving the fully coupled nonlinear system of solubility-product equations.[17] The model has been validated with analytical solutions of simple cases, results of a commercial package, and previous experimental results. A useful equilibrium model must predict accurately the occurrence and stability of precipitates, their equilibrium amounts, and compositions for different steel compositions, phases, and temperatures to calculate the supersaturation/driving force for a kinetic model. Theoretically, precipitates start to form when the solubility limit is exceeded, but reaching equilibrium usually takes a long time. For most steel processes, especially at lower temperatures, equilibrium is seldom approached due to limited time. Thus, kinetic models of precipitate growth are a practical neces
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