A new analytical model for process-microstructure-hardness relationships of directed energy deposited nickel alloys

Developing a Process-Structure-Properties (P–S–P) integrated model for directed energy deposition (DED) is essential for optimizing microstructures and enhancing material properties. However, existing numerical models are associated with high computational costs and lengthy processing times, while data-driven models frequently lack interpretability, with their predictive accuracy dependent on the quantity and quality of training data. To address these challenges, an analytical model of Process-Microstructure-Hardness (P–S–H) is developed based on the continuous growth restriction factor Q C , which integrates both Interdependence and Hall-Petch models. The results indicate that the model effectively delineates the effects of laser power P and scanning speed v s on solidification microstructure, while clarifying the intricate relationships among process parameters, grain size, and microhardness in DED nickel-based alloys. Furthermore, its predictions exhibit a strong correlation with experimental data, with an approximate prediction error of 10.6 % for the average grain size , and the predicted microhardness values falling within a narrower 95 % confidence interval. Consequently, this model offers a novel technological approach to predicting microstructure and properties, as well as facilitating online real-time control and optimization in DED processes .