Physics-informed inverse design of heat-treatment processes for target fatigue strength in steels

Designing heat-treatment conditions for steels that achieve predictable fatigue performance remains challenging because of the complex interactions among alloy composition, processing history, and microstructure development. Despite promising results of machine-learning methods in the prediction of fatigue strength, the most existng studies focus forward prediction and provide limited support for engineering design or reliability-related process. This study presents a physics-informed inverse design framework that can be used to optimize heat-treatment processes to achieve desired fatigue strength in steels. The proposed framework operates in a metallurgical index space that incorporates physically meaningful descriptors representing tempering severity, hardening potential, diffusion-carburizing effects and microstructural integrity are the design variables. A physics-informed machine-learning model is devoloped to create the forward relationship between metallurgical indices, alloying elements, fatigue strength and predictive uncertainty. This forward model is then inverted by a constrained optimization procedure that minimizes the difference between the actual and desired fatigue strength as well as the predictive uncertainty. These optimized metallurgical index ranges are subsequently translated into feasible heat-treatment windows, which allows the determination of multiple physically consistent processing paths that can be used to reach the desired fatigue performance. The results demonstrate that the proposed framework can allow reliability-aware fatigue-based heat-treatment design while offers physically interpretable and computationally efficient framework. This approch provides a practical decisions support tool for engineering components where fatigue performance is critical.