Precipitation strengthening of alloys by the formation of secondary particles (precipitates) in the matrix is one of the techniques used for increasing the mechanical strength of metals. Understanding the precipitation kinetics such as nucleation, growth, and coarsening of these precipitates is critical for evaluating their hardening effects and improving the yield strength of the alloy during heat treatment. To optimize the heat treatment strategy and accelerate alloy design, predicting precipitate hardening effects via numerical methods is a promising complement to trial-and-error-based experiments and the physics-based phase-field method stands out with the significant potential to accurately predict the precipitate morphology and kinetics. In this study, we present a phase-field model that captures the nucleation, growth, and coarsening kinetics of precipitates during isothermal heat treatment conditions. Thermodynamic data, diffusion coefficients, and misfit strain data from experimental or lower length-scale calculations are used as input parameters for the phase-field model. Classical nucleation theory is implemented to capture the nucleation kinetics. As a case study, we apply the model to investigate γ″ precipitation kinetics in Inconel 625. The simulated mean particle length, aspect ratio, and volume fraction evolution are in agreement with experimental data for simulations at 600 °C and 650 °C during isothermal heat treatment. Utilizing the meso-scale results from the phase-field simulations as input parameters to a macro-scale coherency strengthening model, the evolution of the yield strength during heat treatment was predicted. In a broader context, we believe the current study can provide practical guidance for applying the phase-field approach as a link in the multiscale modeling of material properties.

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