Introduction

In a variety of industrial sectors, longevity, wear resistance and dimensional stability of mechanical components are essential, especially when these components are subjected to cyclic loads. To achieve these objectives, various surface hardening treatments have been developed. Since the surface layer of a part strongly influences its service life, the goal is to enhance its functional properties to differentiate them from those of the core. Within this framework, thermochemical treatment plays a crucial role by utilizing thermal diffusion to incorporate chemical elements into the material's surface, thereby altering its properties and microstructure.

Nitriding is a well-established thermochemical treatment with industrial use beginning in the 1950s1. It involves the diffusion of nitrogen atoms into the skin of a material, forming a hard surface while keeping the core ductile. Gas nitriding is performed at moderate temperatures, generally between 500°C and 600°C, and commonly uses ammonia gas as the nitrogen source, although salt bath and plasma-based methods are also possible2. Steels containing elements like chromium, aluminum, and molybdenum are most suitable for nitriding, as these form hard stable nitrides with the diffused nitrogen. Unlike carburizing techniques, no quenching is required after nitriding (ferritic matrix), which greatly reduces the risk of distortion or cracking3.

This thermochemical treatment offers multiple advantages including high surface hardness, enhanced wear and fatigue resistance, minimal dimensional distortion, and excellent thermal stability of the hardened layer4. Nitrided layers maintain their hardness at temperatures where carburized layers would begin to soften, making this method ideal for components subject to both mechanical and thermal stress. Common parts treated are gears4,5, crankshafts6, dies7 and tools.

During nitriding, nitrogen accumulates locally in the steel matrix. When its solubility limit in ferrite or alloying elements is exceeded, nitride precipitates form and grow8. This leads to the consumption of a fraction of nitrogen in precipitation while the remainder continues diffusing inward until thermodynamic equilibrium is reached. Simultaneously, local plastic deformations increase dislocation density, which provides faster diffusion pathways, necessitating adjustments to the diffusion coefficient8. Moreover, grain boundaries act as natural diffusion irregularities and frequently host nitride or carbide precipitates. It is important to note that during nitriding, carbon diffusion must be considered alongside nitrogen diffusion, even in the absence of external carbon input, as carbon retro-diffusion can influence the microstructural evolution and, consequently, the surface properties9.

These intertwined physical processes and coupled diffusion phenomena add to the complexity of chemical element transport in alloy steels. Therefore, accurate modelling of nitrogen and carbon diffusion and control of the composition gradients are fundamental for achieving desired hardness and optimizing the overall outcome of the nitriding process.

In this article, we demonstrate the ability of the finite element simulation software FORGE® to predict the diffusion profiles of chemical elements by integrating thermodynamic equilibrium data into the modeling to account for precipitation processes. 

Modelling of the Nitriding process of the 32CDV13 steel

In collaboration with SAFRAN, we studied the nitriding process of a 32CDV13 steel cylindrical part with a drill hole. 32CDV13 is a high-performance low-alloy steel widely used in the aerospace industry for mechanically demanding components such as helicopter transmissions and turbine engine accessory drives10. It is valued for its high fatigue strength, thermal resistance, and dimensional stability. In its untreated state, this steel offers good machinability. When nitrided, it develops a hard surface layer with surface hardness values exceeding 1000 HV11. This significantly enhances wear and fatigue resistance while preserving core ductility.

The aim of this study is to analyze nitrogen and carbon diffusion in 32CDV13 in order to predict the resulting concentration profiles after nitriding. These predictions serve as a basis for adjusting treatment parameters to achieve targeted surface characteristics.

Nitriding involves several key parameters that must be carefully controlled to achieve the desired surface properties. These include temperature which affects diffusion rates, time which influences case depth, and in gas nitriding, the nitriding potential linked to the ammonia dissociation rate.

These factors govern the formation of two distinct zones:

  • a compound layer (also called white layer), generally 10 to 20 µm thick, composed of ε-Fe₂₋₃N and γ′-Fe₄N phases. This layer is not considered in the modeling, but it plays an essential role in stabilizing the nitrogen potential at the surface once it has formed;
  • a diffusion zone, which can reach depths on the order of 1 mm8, where nitrogen is dissolved in the ferritic matrix and interacts with alloying elements.

To effectively control these parameters, the finite element simulation software FORGE® offers a chemical diffusion/precipitation module, allowing to model nitrogen and carbon diffusion during the process. The evolution over time of mass concentration in percentage (or rate), of a chemical element C, in a material of diffusivity D, is expressed by the following diffusion equation:

The diffusivity of a chemical element in a material is difficult to predict. It can vary significantly, depending on temperature, the nature and structure of the material, or even the concentration of the chemical element in the material itself.

Three different types of boundary conditions can be defined. The first, corresponding to perfect exchange between the atmosphere and the workpiece, involves directly imposing the chemical potential on the surface of the workpiece (Dirichlet boundary condition). The potential of a chemical element for a metal-atmosphere pair is defined as the concentration of the chemical element that would be obtained in the metal if it were immersed for an infinite time in the considered atmosphere.

The second, more realistic type, corresponds to a transfer coefficient between the atmosphere and the part, due to parasitic chemical reactions on the surface of the part or a boundary layer effect caused by poor furnace mixing. The exchange model is defined by specifying the chemical potential of the atmosphere as a mass percentage, along with an alpha transfer coefficient. A flux is imposed proportional to the difference between the surface concentration of the part and the chemical element potential of the atmosphere (Robin boundary condition).

The final type is the imposed-flux type, corresponding to a Neumann boundary condition, where a specific flux of the chemical species is applied at the interface.

A typical nitriding cycle consists of three main stages as illustrated in Figure 1, namely a heating stage, a diffusion stage in which the part is exposed to a nitrogen-containing atmosphere, and finally a cooling stage in which the part is cooled in a controlled manner. In our model, we introduce a simplification by decoupling the mechanical response from the diffusion of nitrogen. This approach treats stress evolution as a separate post-processing step rather than modeling it concurrently with nitrogen diffusion. This strategy can reduce computational costs and complexity but does not reflect the physical reality of the process in which stress development arises simultaneously with nitrogen uptake due to lattice expansion, phase formation, and concentration gradients.

While in nitriding residual stress is primarily the result of precipitation phenomena, in carburizing, the main source of residual stress and distortion is associated with the martensitic transformation induced by quenching. This difference generally leads to more limited distortion and residual stress levels in nitrided components.

In nitriding, the matrix phase remains ferritic throughout the treatment due to the relatively low operating temperatures, unlike carburizing, which is carried out in the austenitic phase at higher temperatures. As a consequence, no phase transformation occurs during nitriding, and quenching becomes obsolete since it has no significant effect.

Carbonitriding, on the other hand, introduces both carbon and nitrogen and may involve quenching depending on the application.

nitriding

Figure 1: Chained simulation of the nitriding cycle using FORGE®.

 

The process involves simultaneous diffusion of nitrogen and carbon into the material. This diffusion leads to phase transformations that require thermodynamic calculations to predict8. Using JMatPro®, we conducted thermodynamic equilibrium calculations in the nitriding temperature range of 500°C - 600°C to determine the precipitation behavior of various nitrides (see Figure 2). Although true thermodynamic equilibrium is rarely achieved during treatment, these calculations provide valuable insight into the nature of the phases likely to form.

During nitriding of 32CDV13 steel, the microstructure is primarily composed of ferrite (α-Fe), which serves as the diffusion medium for interstitial nitrogen. As nitrogen penetrates the ferritic matrix, it reacts with strong nitride-forming elements such as chromium, vanadium, and molybdenum to form stable nitrides. Initially present carbides, particularly M23C6-type carbides, tend to dissolve due to the higher thermodynamic stability of nitrides, leading to the precipitation of corresponding nitrides and the release of carbon into the sub-surface region. This results in local carbon enrichment beneath the nitrided layer, a phenomenon commonly observed in nitrided low-alloy steels8,12,13. This mechanism is commonly referred to as carbon back-diffusion (or retro-diffusion).

jmatpro calculationm23c6 carbides evolution

Figure 2: JMatPro® calculations of (a) precipitates ratio and (b) M23C6 carbides evolution, as a function of nitrogen content at 550°C, and with a fixed carbon content.

 

From the thermodynamic equilibrium, we can then calculate the volume expansion related to the rate of precipitates in order to calculate the distortions associated with precipitation. These results were then fed into our chemical element diffusion model to simulate nitrogen and carbon profiles during a 120 h nitriding process at 550°C, taking into account the precipitation phenomena in the material, as well as their effects on the geometrical variations of the nitrided component. The results obtained are illustrated in Figure 3, as well as experimental profiles measured by IRT-M2P13. A good tendency is observed between simulated and experimental profiles for both nitrogen and carbon. Nevertheless, a slight shift of the simulated profiles towards the material’s surface can be noted in comparison to the experimental profiles. One possible solution to this could be the refinement of the diffusion coefficient data for the two elements.

The increase in carbon content beneath the nitrided layer is also noted and is explained by the precipitation of nitrides at the expense of pre-existing carbides when the nitrogen solubility in ferrite is exceeded during the treatment.

nitrogen

Figure 3: Nitrogen and Carbon profiles as a function of depth simulated using FORGE® considering precipitation, in comparison to experimental measurements.

 

Conclusion

This study proposes an advanced simulation approach aimed at modeling the coupled diffusion of nitrogen and carbon during nitriding, while incorporating precipitation phenomena and the mechanical deformations they induce in the treated component.

The objective is to obtain a more realistic representation of the process by accounting for the influence of precipitations on the diffusion mechanisms of chemical elements. These interactions directly affect the evolution of concentration profiles and the final geometry of the component.

Starting from version 5.0 of the FORGE® software, diffusion modeling will include the precipitation option, allowing precise control and optimization of the nitriding process parameters. This enhancement will improve the reliability and reproducibility of thermochemical treatment simulations while contributing to a significant reduction in industrial process development time.

References

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