High-Temperature Static Coarsening of Gamma-Prime Precipitates in NiAlCr-X Single Crystals
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thermomechanical processing (TMP) of nickel-base alloys typically focuses on the control of various microstructural features such as the size (and size distribution) of grains, strengthening precipitates, and structure-control phases. The precipitate size/size distribution and volume fraction are particularly important because they affect plastic flow and recrystallization during subsolvus hot working, grain growth following dissolution during supersolvus heat treatment, and mechanical properties such as strength, creep, and fatigue during service.[1] A number of phase transformations affect precipitate evolution during TMP. These include (1) dissolution during solution treatment and (2) nucleation, growth, and coarsening during cooling or isothermal subsolvus holding following solution treatment. Because of the S.L. SEMIATIN, E.J. PAYTON, and J.S. TILEY are with the AFRL/RXCM, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, OH, 45433. Contact e-mail: [email protected] N.C. LEVKULICH and A.R.C. GERLT are with UES, Inc., Dayton, OH, 45432. F. ZHANG is with CompuTherm LLC, Middleton, WI, 53562. R.A. MACKAY, R.V. MINER, and T.P. GABB are with the NASA Glenn Research Center, Cleveland, OH, 44135. Manuscript submitted November 5, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
importance of such phenomena, extensive work has been performed to both quantify kinetics and develop descriptive models. For example, the modeling of dissolution has been performed using one of three broad types of approaches, phenomenological,[2–5] analytical,[6–8] and phase field.[9] In addition, the homogeneous nucleation and growth of precipitates have also been treated extensively[10–19] Precipitate coarsening is frequently controlled by bulk diffusion for which the analyses introduced by Lifshitz, Slyosov, and Wagner (‘‘LSW’’)[10,20–23] are usually relied upon to quantify kinetic behavior. Derived for an infinitesimal fraction of precipitates in a two-component system, such approaches have been extended for multi-component alloys with a finite volume fraction of precipitates whose composition is not a terminal solid solution.[24–31] Coarsening kinetics and associated models for c¢-strengthened, nickel-base superalloys have received considerable attention in the literature, e.g., the overview by Baldan.[32] In the vast majority of cases, behavior is controlled by bulk diffusion of solute(s) through the c matrix, yielding a cubic dependence of the average c¢-precipitate size on time. The corresponding analytical descriptions fall into one of three categories: (i) those which are purely phenomenological in nature,[33,34] (ii) those based on the LSW analysis without consideration of volume fraction or non-terminal solid-solution effects,[35–42] and (iii) modified LSW (MLSW) analyses
which incorporate such influences.[5,43,44] The three different descriptions of coarsening kinetics thus rely on expressions of the following forms to describe the average three-dimensional (3D) radius of th
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