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 <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.
Highlights
Nitriding is a thermochemical surface treatment carried out below eutectoid temperature
A plateau appears at the nitrogen concentration profile, Figs. 1–3, 5–7, which is according to the expectations. Such a choice agrees with the supposition that the diffusion in the expanded austenite is faster that it is expected from chemical diffusion [18]
Low and intermediate-temperature nitriding of iron and stainless steel can cause a formation of expanded austenite phase
Summary
Nitriding is a thermochemical surface treatment carried out below eutectoid temperature. Known as S phase or γN phase, is a metastable supersaturated solid solution of nitrogen (or carbon) in austenite that forms as a case by diffusion [31,32] It provides high hardness and high resistance against wear, corrosion and fatigue, which is a consequence of compressive residual. Galdikas et al [40] considered a simple case, namely the diffusion flux of nitrogen JN being proportional to the gradient of chemical potential μN(cN, T, p), depending on the nitrogen concentration cN, temperature T, and pressure p They examined a degenerated situation when the pressure p in solids is proportional to internal stresses: p = −σ. They neglected the interdiffusion in Fe-N system, a drift was not analyzed and ignore plastic deformation (in our work we consider the Maxwell solid) They had different, mathematically complicated boundary conditions on the nitrogen concentration cN given by a suitable differential equation. A comparison of our numerical simulations with simulations obtained with the use of some known physically simpler models, for example given in [40], we will present in our future papers
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