Mathematical modelling of gas nitriding process of steel using cellular automata

Purpose: The primary aim of this research was to develop a mathematical and computational model of the nitriding process for steel using CA cellular automata theory, which enables the modelling of spatial hardness distributions and nitrogen concentrations within the material. Design/methodology/approach: The proposed mathematical model consists of two interacting cellular automata: one representing the surface layer of the nitride material and the other describing the spatial distribution of nitrogen. The developed algorithm and model based on CA were implemented in the MATLAB environment, enabling more effective and efficient testing of the created model and its further use. Findings: The developed computer model enabled, by changing the values of the CA model parameters, which correspond to the nitrogen diffusion coefficient in alloy steel, nitrogen solubility in iron and the enthalpy of formation and decomposition of iron nitrides, to adapt the model to the description of the nitriding process of 1.2343 (WCL) steel. The model was experimentally verified by comparing predicted hardness profiles with those measured after nitriding. Research limitations/implications: The main limitation of the developed model is the size of the material fragment in which the nitriding process is simulated. Practical implications: High compliance of the results of numerical calculations with the results obtained by experimental measurements was obtained, which predestines the potential usage of CA-based models for scientific and practical applications. The model can be used as part of an optimisation procedure for designing hybrid composite layers for tribological applications, comprising a nitride layer and a coating deposited via Physical Vapor Deposition (PVD) techniques. Originality/value: The added value of the developed model of the nitriding process, based on the concept of CA, is the author’s modification of the transition rules (both for cells in the Moore and von Neumann neighbourhood) in the automaton related to the structural and phase transformations in the nitride material.