Advancing Vacuum Carburizing Simulation: Calibration and Implementation of a Carbon-Level-Dependent Diffusion Model for AISI 9310 Steel

Abstract

Understanding the behavior of carbon diffusion in austenite is critical to the design and optimization of heat treatment processes such as vacuum carburization of alloy steels. The carburization process is complex due to the intricate surface chemical reactions, resulting in a carbon content distribution curve that typically exhibits an inverse-S shape—a phenomenon that traditional carbon diffusion models fail to explain. Alternately, the carbon-level-dependent carbon diffusion model suggests that local carbon concentration impacts the carburization rate, implying that carburization parameters should be considered functions of carbon concentration. In this research, a forward analysis was first conducted by leveraging the analogy between the carburizing process and the heat transfer process to establish an efficient finite element modeling. A custom user subroutine, UMATHT, was developed, enabling the integration of the carbon-level-dependent diffusion model within abaqus-based analysis. Subsequently, an inverse analysis framework was formulated to facilitate the parametric identification of the carbon-level-dependent diffusion model. Combining the model prediction with a simulated annealing stochastic optimization algorithm, we identified the coefficients in the carbon diffusion model by minimizing the difference between experimental measurements and finite element simulations under various conditions within the parametric space. Our results have demonstrated that the carbon-level-dependent model not only offers smaller prediction errors in AISI 9310 steel but also accurately reproduces the characteristic inverse-S carbon distribution curve which traditional models cannot achieve. This research provides new insights into the vacuum carburization characterization of alloy steels.