Stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel
Highlights
► The model considers the stress-diffusion interaction during nitriding process of ASS. ► The stress induced diffusion with D(CN) model was applied to nitrided AISI 316L ASS. ► Effects of nitrogen diffusivity dependence on stresses and CN in ASS are analyzed.
Introduction
Austenitic stainless steels (ASS) are often used in structural applications for their excellent corrosion resistance due to an inherent and self-healing passive film on the surface. However, their poor tribological and mechanical properties in terms of abrasion resistance, high and unstable friction qualities and a significant tendency to adhesive wear or galling have restricted their applications in a number of engineering fields [1], [2], [3], [4]. The nitriding of ASS at temperatures between 300 °C and 400 °C by nitrogen ion beam implantation [5], [6], low-temperature gas and plasma nitriding [7], [8], [9], or nitrogen plasma immersion ion implantation (PIII) [10], [11], [12], [13] results in formation of a modified layer with outstanding hardness together with high wear resistance, while the excellent corrosion resistance is still preserved. The insertion of nitrogen into the surface of austenitic stainless steel leads to the formation of expanded austenite, characterized by rather rapid nitrogen diffusion, a nitrogen content of up to 20 at.% and an expansion of the interplanar spacing that can reach 12% [14], [15].
It is well known that nitrogen diffusion in austenitic stainless steel is a complicated process and still not fully understood. The nitrogen depth profiles in nitrided ASS exhibit plateau-type shapes slowly decreasing from the surface, followed by a rather sharp leading edge (which cannot be explained by the classical diffusion models). In addition, the nitrogen diffusivity is faster than expected from classical diffusion. Various earlier publications discuss the calculation of nitrogen depth profiles in nitrided ASS and several models were proposed to explain the shape of nitrogen depth profile and the high diffusivity in ASS: (1) the nitrogen diffusion model [16] with trapping–detrapping at Cr sites; (2) the model based on Fick's laws and nitrogen diffusion coefficient dependence of nitrogen concentration [17]; (3) the model combining those two models (1) and (2) [18]; (4) the model proposed by Pranevicius and co-workers [19], [20] based on the study of the stochastic mixing of atoms ‘‘ballistically” displaced by incident ions and the flow of atoms into grain boundaries responding to irradiation induced increase in the surface chemical potential.
It is known that diffusion of atoms in materials could lead to the evolution of local stresses, which has been referred as diffusion-induced stresses or chemical stresses [21]. Nitriding processes are accompanied by changes of stainless steel volume, since interstitial nitrogen causes an expansion of the crystal lattice of the solid matrix. This phenomenon implies the occurrence of local stresses, induced by nitrogen concentration gradients within the solid, and influences nitrogen transport in the steel. Stress is one of the factors determining the chemical potential of components of solid systems. Therefore, self-stress resulting from the gradient of the nitrogen concentration affects the diffusion mechanism of nitrogen in ASS.
The purpose of the present work is to provide a real time nitrogen diffusion model, which describes the nitrogen distribution in ASS during plasma nitriding process at temperatures around 400 °C. The model considers the concentration dependent diffusion of nitrogen in presence of internal stresses gradient induced by penetrating nitrogen as the next driving force of diffusion after concentration gradient, i.e. this model is developed taking into account the stress-diffusion interaction during the nitriding process of ASS.
Section snippets
Basic equations
The mathematical description of nitrogen transport in ASS under presence of internal stresses can be formulated by solving the diffusion equation based on gradient of chemical potential. According to the Onsager theory [22] the diffusion flux of nitrogen JN being proportional to the gradient of chemical potential μ(CN,T,p) can be expressed as,where L is the Onsager coefficient. Chemical potential in general case is the function of concentration CN, temperature T and pressure p.
Modelling results and discussion
The experimental nitrogen depth profiles were fitted by using proposed stress induced diffusion model. The experimental results (Fig. 1 points) are taken from Ref. [31] where plasma nitridation of a polycrystalline AISI 316L ASS samples was considered. The 316L SS sample was exposed to the following plasma nitriding conditions [31] (which were used for our calculations): (1) a gas composition of 60% N2 + 40% H2; (2) a working pressure of 7.5 Pa and RF power of 700 W; (3) a substrate temperature
Conclusions
The stress induced diffusion model with a concentration dependent diffusion coefficient D(CN) = f(1/CN) is developed to account for stress and diffusion interaction in the nitriding of an austenitic stainless steel. Nitrogen depth profiles fitted on the basis of non-Fickian diffusion model, which considers the diffusion of nitrogen in presence of internal stresses as driving force of diffusion, are in good agreement with experimental nitrogen depth profiles. The diffusion coefficient D(CN) for
Acknowledgement
This research was funded by a grant (No. TAP-46/2010) from the Research Council of Lithuania.
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