Open Access

ARTICLE

A Mathematical Model and Simulations of Low Temperature Nitriding

Bogusław Bożek¹, Lucjan Sapa^1,*, Katarzyna Tkacz-Śmiech², Marek Danielewski², Janusz Rybak²

1 AGH University of Science and Technology, Faculty of Applied Mathematics, Cracow, 30-059, Poland
2 AGH University of Science and Technology, Faculty of Materials Science and Ceramics, Cracow, 30-059, Poland

* Corresponding Author: Lucjan Sapa. Email:

Computer Modeling in Engineering & Sciences 2022, 130(2), 777-803. https://doi.org/10.32604/cmes.2022.017729

Received 02 June 2021; Accepted 10 September 2021; Issue published 13 December 2021

Abstract

Low-temperature nitriding of steel or iron can produce an expanded austenite phase, which is a solid solution of a large amount of nitrogen dissolved interstitially in fcc lattice. It is characteristic that the nitogen depth profiles in expanded austenite exhibit plateau-type shapes. Such behavior cannot be considered with a standard analytic solution for diffusion in a semi-infinite solid and a new approach is necessary. We formulate a model of interdiffusion in viscoelastic solid (Maxwell model) during the nitriding process. It combines the mass conservation and Vegard’s rule with the Darken bi-velocity method. The model is formulated in any dimension, i.e., a mixture is included in , n = 1, 2, 3. For the system in one dimension, n = 1, we transform a differential-algebraic system of 5 equations to a differential system of 2 equations only, which is better to study numerically and analytically. Such modification allows the formulation of effective mixed-type boundary conditions. The resulting nonlinear strongly coupled parabolic-elliptic differential initial-boundary Stefan type problem is solved numerically and a series of simulations is made.

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