Modeling of dissolution, growth, and coarsening of aluminum nitride in low-carbon steels
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I. INTRODUCTION
DUE to their influence on recrystallization and grain growth during thermomechanical processing of microalloyed steels, the precipitation of nitrides, carbides, or carbonitrides of microalloying elements such as niobium, vanadium, titanium, or aluminum can have significant effects on the mechanical properties of steels. Numerous studies have been conducted to deal with the effects of these nitrides or carbides on microstructure formation and the associated mechanical properties of steels.[1–5] The size distribution of nitride or carbide precipitates is an important microstructural parameter in determining the mechanical properties of microalloyed steels after a variety of thermomechanical processing treatments. During reheating of the steels, the preexisting precipitates may dissolve due to increasing solubility. In addition, there is a tendency for the smaller particles to shrink and the larger ones to grow. This process is known as coarsening or Ostwald ripening and is driven by the minimization of the total surface free energy of the system. Although models have been developed for these two phenomena, they are often modeled as two separate processes.[6–9] In reality, dissolution and coarsening usually overlap and occur simultaneously. In such a case, neither conventional dissolution nor Ostwald ripening models can be applied. In the present work, a theoretical model is proposed to predict the dissolution, growth, and coarsening behavior of nitrides or carbides in low-carbon and microalloyed steels by using numerical integration methods on a multiparticle system. Dissolution and coarsening are treated as one continuous, simultaneous phenomenon, and the two processes are simulated in a natural sequence. This model takes into account the equilibrium thermodynamic properties of the system, the local equilibrium at the interface, curvature effects, and diffusion along grain boundaries. The size of a particular particle can be determined by simultaneously solving a set of diffusion, equilibrium, and mass-balance LEON M. CHENG, Postdoctoral Fellow, E. BRUCE HAWBOLT and T. RAY MEADOWCROFT, Professors, are with the Department of Metals and Materials Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4. Manuscript submitted December 7, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
equations for each individual particle. This model is applied to study the dissolution and coarsening behavior of aluminum nitride (AlN) in Al-killed low-carbon steels. The predicted results are then compared to experimental measurements made on the same system. II. THEORETICAL MODEL A list of symbols being used in the present model is shown in Table I. Based on the measured mean diameter and the standard deviation of the initial distribution, an assembly of n particles can be defined according to a presumed particle-size distribution. The form of the initial size distribution depends on the initial experimental conditions. However, in most cases, the distribution of nitrides or carbides in steels can b
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