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EN
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.
EN
Purpose: The conducted research aims to describe the kinetics of Streptococcus mutans bacteria growth on the surface of Zr-C coatings with varying carbon content deposited on 316L medical-grade stainless steel substrates. Design/methodology/approach: The coatings were deposited using the MS PVD (Magnetron Sputtering Physical Vapour Deposition) technique at a constant temperature of 400°C. Varying carbon contents in the coatings were achieved by changing the flow rate of acetylene during the process. The dynamics of bacteria growth cultivated at 37°C were examined on the surface of the coatings for incubation times ranging from 0 to 72 hours. Generalised logistic functions were utilised for the mathematical description of the obtained results. Findings: The produced coatings exhibited varying carbon content, determining the structural composition ranging from a mixture of metallic Zr and ZrC through stoichiometric zirconium carbide to nanocrystalline grains of ZrC in an amorphous carbon matrix. The obtained results unequivocally demonstrate that in the case of ZrC coatings, the carbon content influences both the bacterial growth rate during the proliferation phase and the final population of bacteria. Research limitations/implications: In the conducted research on bacterial population dynamics, only a single strain of Streptococcus mutans was considered, and the mathematical description was limited to reaching a pseudo-steady state by the population. Practical implications: The proposed model can successfully be adapted to describe the dynamics of other individual strains of bacteria dwelling on metallic surfaces as well as coatings. Originality/value: The proposed model can serve as a tool for studying, among other things, inflexion points of logistic curves, which are considered as the boundary between the dominance of anabolic and catabolic processes in the bacterial population.
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