TY  - EJOU
AU  - Bożek, Bogusław 
AU  - Sapa, Lucjan 
AU  - Tkacz-Śmiech, Katarzyna 
AU  - Danielewski, Marek 
AU  - Rybak, Janusz 

TI  - A Mathematical Model and Simulations of Low Temperature Nitriding
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2022
VL  - 130
IS  - 2
SN  - 1526-1506

AB  - 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 <i>bi</i>-velocity method. The model is formulated in any dimension, <i>i.e.</i>, a mixture is included in , <i>n</i> = 1, 2, 3. For the system in one dimension, <i>n</i> = 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.
KW  - Nitriding; expanded austenite; Maxwell solid; Darken method; Vegard rule

DO  - 10.32604/cmes.2022.017729