A methodology that integrates the phase field model with simpler models was developed to study the early stages of microstructural development in nickel base superalloys under non-isothermal conditions, allowing for faster, more comprehensive examination of the experimental system. Additionally, the parameters required for calibrating a phase field model were examined for uncertainty, and a comprehensive method for linking experimental data to a model was developed.
The methodology developed was applied to analyze the formation of bimodal particle size distributions during linear continuous cooling. The dynamic competition for supersaturation by growth of existing precipitates and nucleation of new particles was modeled. The nucleation rate was calculated according to classical nucleation theory as function of local supersaturation and temperature. The depletion of matrix super-saturation by growth of existing particles was calculated from fully diffusion-controlled
precipitate growth in an infinite matrix. Phase field simulations of γ' precipitation in a binary Ni-Al alloy were performed under continuous cooling conditions. Then the average and maximum matrix supersaturations were calculated and plotted onto the contours of nucleation rate and growth rate in concentration and temperature space. These methods were used iteratively to identify the window for bimodal particle size distributions. Combining the models of different complexities produced a much more comprehensive understanding of the competing dynamics involved early in microstructure formation.
A systemic method for calibrating a model to experimental alloy systems was
developed. Calibrated to isothermal aging data along with literature, database and parametric values, a phase field model reproduced the precipitation kinetics. Quantitative phase field modeling techniques were developed to control the influence of uncertainty in the original data sources for model inputs. Using more data sources than simulation targets allows for over-constraining, thus limiting the effect of uncertainty from any single source. Using directly measurable data and other low uncertainty sources allows for a higher degree of representation to be achieved. Sensitivity studies to optimize the simulation parameters were also used to obtain better agreement between simulation predictions and experimental observations.