Evolution of δ phase precipitates in Inconel 625 superalloy additively manufactured by laser powder bed fusion and its modeling with fuzzy logic

Experimental and modeling studies of the evolution of plate-like δ phase precipitates in Inconel 625 superalloy additively manufactured by the laser powder bed fusion process are performed. The maximum Feret diameter and the number of particles per unit area are used as parameters describing the size and distribution of the δ phase precipitates. On the basis of microstructural analysis and quantitative image analysis, the effect of time and temperature on the development of δ phase precipitates is determined. The distinct differences in the intensity of precipitation, growth, and coarsening of the δ phase precipitates during annealing at temperatures of 700 and 800 °C up to 2000 h are shown. The experimental results are compared with computational data obtained by thermodynamic modeling. Using the experimentally determined parameters of the δ phase precipitates in different variants of annealing, a fuzzy logic-based phase distribution model is designed. Since the quantity of available data was too small to train a model with the machine learning approach, expert knowledge is used to design the rules, while numerical data are used for its validation. Designed rules, as well as reasoning methodology are described. The proposed model is validated by comparing it with the experimental results. It can be used to predict the size and number density of the δ phase precipitates in the additively manufactured Inconel 625, subjected to long-term annealing at temperatures of 700–800 °C. Due to limited experimental data, the quality of assurance is not perfect, but warrants preliminary research. Graphical abstract