Prediction of Phase Composition and Nitrogen Concentration During the Nitriding Process in Low-Alloy Steel

Abstract

A diffusion/transformation coupled model has been developed which combines finite difference (FD) model with a phenomenological model. The composition of the different iron-nitrogen(Fe-N) hardening phase can be regard as a function of nitriding time and nitrogen concentration. The diffusion model and transformation model are linked by the limiting nitrogen solubilities and the effective diffusion coefficients. The effect of alloy elements (Cr, Mo, Mn, V, Ni etc.) is considered by introducing an alloy coefficient for limiting nitrogen solubilities and diffusion coefficient. The diffusion/transformation model can predict nitrogen concentration, phase composition and hardness distribution. The model is employed to simulate the nitriding process of SCr420H low-alloy steels. The simulated nitrogen concentration and hardness profiles are consistent with the measured ones. In addition, the predicted depth distributions of iron-nitrogen phase agree well with the available experimental results. Therefore, the comparison shows the reliability of the coupled model. It can be applied to improve the nitriding process parameters.

Keywords:
Nitriding; Low-alloy steel; Fe-N phase composition; Nitrogen concentration; Modeling

1 Introduction

The nitriding process is one of the most important thermochemical treatment processes in metallurgy for the production of case-hardened surface layers in low-alloy steel. The diffusion of nitrogen into steel leads to the formation of a nitride layer, which comprises a thin outer compound layer (white layer) and thick inner diffusion layer. The compound layer consists of the epsilon phase ($\epsilon$) and the gamma prime phase (${\gamma }^{\prime }$). The diffusion layer is composed of interstitial solid solution of nitrogen dissolved in the ferrite lattice ($\alpha$) ¹. The improvement of corrosion and wear properties can be attributed to the construct of compound layer. Therefore, it is beneficial to predict the nitrogen concentration profile and phase composition of the compound layer in the nitriding process.

To further understanding the nitriding process, numerical simulations have been employed to calculate the nitride layer growth and the nitrogen concentration profiles since 1990s ^2-13. Sun and Bell ² developed a mathematical model to simulate the plasma nitriding process of low alloy steel. Their model considered the diffusion of nitrogen in ferrite and development of iron nitride layer on the surface simultaneously. Then, Goune et al., ³ and Belmont et al., ⁴ constructed a realistic diffusion-precipitation model to describe the volume diffusion of nitrogen in ferrite and the simultaneous precipitation of fine scale alloying element nitrides in the diffusion zone. Furthermore, Kamminga, Janssen ^8,9 presented a model for the calculation of nitrogen depth profiles in nitrided steel based on precipitation and trapping, and the calculations agreed well with experimental nitrogen depth profiles for nitrided Fe–Mn (1.62 wt.% Mn) and Fe–V (0.55 wt.% V) alloy. Keddam ¹⁰ and Cavaliere et al., ¹¹ modeled the nitriding process by coupling the kinetics data of nitrogen in $\alpha$, ${\gamma }^{\prime }$and $\epsilon$ phases to the thermodynamic description of the iron-nitrogen (Fe-N) phase diagram respectively. Recently, Yang et al., ^12,13 presented a nitriding process model including the kinetics of compound layer growth and the determination of the nitrogen diffusivity in the diffusion zone. However, the prediction of Fe-N phase composition and the hardness in the nitride layer have received less attention.

The main purpose of this paper is to simulate the nitrogen concentration, (Fe-N) phase composition and hardness in the nitriding process of low alloy steel. A diffusion/transformation coupled model is developed to predict the phase compositions at the thinner compound layer by considering simultaneous the thermodynamic data and kinetics theory in the nitriding process. The simulated results are compared with the experimental ones and theoretical descriptions.

2 Model description

The knowledge of both thermodynamic and kinetics data is required in modeling the nitriding process. A large number of thermodynamic and diffusion kinetics data can be found in ^14-20. Iron-nitrogen (Fe-N) binary phase diagrams are the base to understand the phase evolution during the nitriding process. In the past decades, the iron-nitrogen phase diagram and Fe-N system has been investigated extensively ^14,15. Moreover, Lakhtin ¹⁶ reviewed the diffusion foundations of the nitriding process in carbon steel and alloy steel. Because the bonding energy in $\alpha$-phase is lower than that in the lattice of ${\gamma }^{\prime }$ and $\epsilon$-phases, the coefficient of nitrogen diffusion in $\alpha$-phase should exceed the coefficients in the ${\gamma }^{\prime }$ and $\epsilon$ by many times ¹⁷. Furthermore, the phase composition of a compound zone and growth kinetics of a diffusion zone during the nitriding of steel was investigated quantitatively ^18,19. Recently, Somers ²⁰ reviewed the development of the compound layer during gaseous nitriding of Fe-based materials.

In the development of the nitriding model, in order to simplify model, the following assumptions are made:

Firstly, the diffusion process follows Fick’s second law in a semi-infinite medium;

Secondly, the surface nitrogen concentration does not vary with the nitriding time;

Thirdly, a uniform temperature is assumed throughout the sample;

Lastly, local thermodynamic equilibrium is reached quickly at every point in the material.

2.1 Nitrogen diffusion model

The diffusion of nitrogen into ferrite phase is considered to obey Fick’s second law ²¹.

$$\frac{\partial N}{\partial t}=D_N(\frac{{\partial }^{2}N}{\partial x^2})$$ (1)

where, $N$is nitrogen concentration, $x$ is the depth, $t$ is nitriding time, $D_N$denotes the effective diffusion coefficient of nitrogen.

The numerical method is applied to solve the diffusion equation. In the present model, an alternating-direction-implicit (ADI) finite-difference formulation is used to solve equation (1).

$$C{n}_i^{t+1}=C{n}_i^t+F_i^t\ast (0.5\ast (C{n}_{i-1}^t+C{n}_{i+1}^t+C{n}_{i-1}^{t+1}+C{n}_{i+1}^{t+1})-C{n}_i^t-C{n}_i^{t+1})$$ (2)

where, $F_i^t=D_i^t*Dt/D{X}^2$, $D_i^t$ is the diffusion coefficient of location $i$ at time $t$, $Dt$ is time step, $C{n}_i^t$is the nitrogen concentration of location $i$ at time $t$.

The boundary conditions is the following

$$C(x,t){|}_{x=0}=C_N^S$$ (3)

where, $C_N^S$ is the surface nitrogen concentration.

2.2 Fe-N phase composition predicted model

By employing the Fe-N phase diagram (Fig. 1 (a)) ^14,15, it is feasible to predict the different Fe-N phases according to the limit solubility values ^10,11. In Fig. 1 (b), it is presented the composition of the different Fe-N phase as a function of nitriding time and nitrogen concentration. Based on the lever rule, a phenomenological model is developed to calculate the volume fraction of iron-nitrogen phase. The nitriding parameters are connected with the mechanisms of the nitriding process. The volume fraction of iron-nitrogen phases is defined as

$${\xi }_{{\gamma }^{\prime }}=\frac{C_N^{i,t}-C_N^{\alpha /{\gamma }^{\prime }}}{C_N^{{\gamma }^{\prime }/\alpha }-C_N^{\alpha /{\gamma }^{\prime }}},{\xi }_{\epsilon }={\xi }_{{\gamma }^{\prime }}\cdot \frac{C_N^{i,t}-C_N^{{\gamma }^{\prime }/\epsilon }}{C_N^{\epsilon /{\gamma }^{\prime }}-C_N^{{\gamma }^{\prime }/\epsilon }},{\xi }_{\alpha }=1-{\xi }_{{\gamma }^{\prime }}-{\xi }_{\epsilon }$$ (4)

where, $C_N^{i,t}$ is nitrogen concentration, $C_N^{\alpha /{\gamma }^{\prime }},C_N^{{\gamma }^{\prime }/\alpha },C_N^{{\gamma }^{\prime }/\epsilon },C_N^{\epsilon /{\gamma }^{\prime }}$ are the limiting nitrogen solubilities in Fe-N phase, as a function of temperature can be calculated by ^10,11,16

$$\begin{array}{l}{C}_N^{\alpha /{\gamma }^{\prime }}=\exp (-\frac{4575}{T}+3)\cdot {10}^{{\gamma }_{AE}^{}}\\ C_N^{{\gamma }^{\prime }/\alpha }=\frac{25.08}{4.25+{10}^{-(\frac{2341.67}{T}-1.925)}}\\ C_N^{{\gamma }^{\prime }/\epsilon }=\frac{25.08}{4.25+{10}^{-(\frac{3476.67}{T}-2.455)}}\\ C_N^{\epsilon /{\gamma }^{\prime }}=(3.01+(1.79\cdot {10}^{-2}T)-(1.54\cdot {10}^{-5}{T}^2))\cdot {10}^{{\gamma }_{AE}^{}}\end{array}$$ (5)

where, ${\gamma }_{AE}$ is the activity coefficient of nitrogen, which can be calculated by ²²

$$\begin{array}{l}{\gamma }_{AE}^{}=-(0.054\times Cmo-0.127\times Cc{r}^{0.9}+0.047\times Cmn\\ +0.083\times Cw+0.027\times Cni-0.011\times Ca{l}^{0.35})\end{array}$$ (6)

where, $C_i$ is the wt.% of i element.

Fig. 1
a Fe-N phase diagram; b schematic illustration of Fe-N phases composition in the nitriding process.

2.3 Hardness regression model

The hardness could be calculated by the experimental regression equation ^5,7

$$HV=H{V}_{st}+{\displaystyle \sum _{x=1}^{n1}{a}_x{C}_x}+{\displaystyle \sum _{y=1}^{n2}{b}_y}{\xi }_{cy}+{\displaystyle \sum _{z=1}^{n3}{c}_z{\xi }_{nz}}$$ (7)

where, $HV$is the Vickers Hardness, $H{V}_{st}$ is the Vickers Hardness of the substrate, $C_x$is the chemical compositions, ${\xi }_{cy}$is the iron-carbon phase compositions, ${\xi }_{nz}$is the Fe-N phase compositions, and $a_x$($x=Si,Mn,NiandCr$), $b_y$($y=M,B,AandF$), $c_z$($z=\epsilon ,{\gamma }^{\prime }$) are the corresponding weighting coefficients, which obtained by literature ^23-25 and experimental data. The values of coefficients are listed in Table 1.

Table 1
- The values of coefficients for hardness calculation

Coefficients	HVst	asi	aMn	aNi	aCr	bM	bF	bB	bA	Cɛ	Cγʹ
Values (HV)	196	27	11	8	16	745	212	632	201	983	886

2.4 Diffusion/Transformation coupled program

The diffusion equation and transformation equation were linked by the effective diffusional coefficients, which could be given by the mixture law ^5,6

$$D_N={\displaystyle \sum D_N^i}{\xi }_i$$ (8)

where, for each single phase,$i=1(\epsilon ),2({\gamma }^{\prime }),3(\alpha )$ , $D_N^i$ is diffusivity in various Fe-N phases, ${\xi }_i$ is volume fraction of various Fe-N phase. The diffusivity of nitrogen in different Fe-N phase could be approximately expressed in an Arrhenius form ^10,11,16,17

$$\begin{array}{l}{D}_N^{\alpha }={\eta }_{al}^{\alpha }6.6\times {10}^{-7}\exp \left(-77820/RT\right)\\ D_N^{{\gamma }^{\prime }}={\eta }_{al}^{{\gamma }^{\prime }}1.675\times {10}^{-9}\exp \left(-64000/RT\right)\\ D_N^{\epsilon }={\eta }_{al}^{\epsilon }2.1\times {10}^{-8}\exp \left(-93517/RT\right)\end{array}$$ (9)

where, ${\eta }_{al}^{\alpha }$, ${\eta }_{al}^{{\gamma }^{\prime }}$ and ${\eta }_{al}^{\epsilon }$ are the alloy coefficients, which can be determined by the formula ¹⁶

$${\eta }_{al}=\exp {\left[\sum B_i(\%AE)\right]}^{n_i/T}$$ (10)

where $(\%AE)$ is the concentration of the alloying element in the steel, $B_i$ and $n_i$, are coefficients determined on the basis of experimental data on the thickness of the nitrided layer in binary alloys. The flowchart of coupled program is shown in Fig. 2. In the present program, the diffusion and transformation are calculated respectively. On the one hand, the effective diffusion coefficients are changed with the iron-nitrogen phase fraction by equation (8); On the other hand, the iron-nitrogen fraction can be recalculated by equation (4).

Fig. 2
The flowchart of the diffusion/transformation coupled program.

3 Results and discussions

In order to validate model, the diffusion/transformation coupled model is applied to predict the nitriding process of SCr420H steel. The chemical compositions of specimens are listed in Table 2. The nitriding process parameters are shown in Fig. 3. Hardness measurements on cross sections and the surfaces of nitrided specimens were carried out with a Vickers hardness tester. For the determination of nitrogen contents, Electron Probe X-ray Microanalysis (EPMA) was performed on cross-sections of the specimens.

Table 2
- Chemical composition of SCr420H steel

Chemical elements	Fe	C	Si	Mn	Cr	P	S	N	Mo
Wt.%	94	0.21	0.19	0.80	1.15	0.0017	0.0015	0.00	0.02

Fig. 3
A schematic illustration for nitriding process in SCr420H steel.

Fig. 4 depicts the evolutions of the nitrogen concentration profiles versus depth for nitriding of SCr420H steel. The profiles show the comparison between the simulated and experimental data. Although there are detailed discrepancies, it can be seen that good agreement is achieved between the numerical results and Wavelength Dispersive (WDS) measured results. It appears that the nitrogen concentration of diffusion layer is underestimated. In the present model, the distributions of nitrogen concentration depend on the effective diffusional coefficients, which are relevant to the concentration of the alloying element (equation (9) and (10)). Therefore, the assumption that the chemical elements are uniform distribution may result in inaccurate diffusional coefficient and nitrogen concentration distribution. It is found that the nitrogen concentration gradient adjacent to the surface is very steep, while away from the surface is flat. It is indicated the diffusivity of nitrogen greatly change in different depth of sample.

Fig. 4
Nitrogen concentration simulated results in SCr420H steel.

In Fig. 5, the volume fractions of the different hardening phase are shown in SCr420H steel. It can be seen that the nitride layer is composed of the thinner compound layer (${\gamma }^{\prime }$+$\epsilon$) and inner diffusion layer ($\alpha$+${\gamma }^{\prime }$). The simulated depth distributions of ${\gamma }^{\prime }$and$\epsilon -F{e}_{2-3}N$ phases are reasonable consistent with the X-ray diffraction (XRD) phase analysis results ¹⁹ and optical micrograph. The formation of ${\gamma }^{\prime }$ phase subzone in the inner part of the compound zone may upset the balance of the nitrogen concentration between the diffusion zone and the compound zone, and may as a consequence have an influence upon the kinetics of the diffusion zone growth. The volume fraction of Fe-N phases is corresponding to the nitrogen concentration (Fig. 4). At the outer section, the nitrogen concentration is relatively high. At the inner section, nitrogen concentration is decreased rapidly to a lower value.

Fig. 5
Volume fraction of the Fe-N phase in SCr420H steel.

The hardness profiles after nitriding are calculated by experimental regression equation (4) and shown in Fig. 6 for SCr420H steel. The calculated hardness data result in good agreement with the measured ones. However, there are discrepancies between calculations and observations for the maximum hardness. The problem probably lies in the estimated hardness value of alloy nitride in regression equation, which can influence hardness in diffusion layers significantly. As shown as in Fig. 4-Fig. 6, it can be concluded that the coupled model can be employed to predict the hardening phase composition in the nitriding process quantitatively.

Fig. 6
Hardness distributions in SCr420H steel

4 Conclusions

In this paper, a diffusion/transformation coupled model has been developed to simulate nitrogen concentration distributions, iron-nitrogen phase formation and hardness by combining nitrogen diffusion and Fe-N phase composition calculation. The model is implemented to simulate nitriding process of SCr420H steel. The simulated results indicate the nitrogen concentration profiles, volume fraction of Fe-N phases and hardness distributions can be predicted quantitatively by this model. Moreover, the simulated results are in reasonable agreement with the experimentally measured ones and theoretical analysis. It shows the possibility of utilizing the model to improve the nitriding process parameters.

Acknowledgements

This research receives ongoing support from the High-tech Research Center and Open Research Center at the Saitama Institute of Technology, and sponsored by Natural Science Foundation of Tianjin (No. 13JCYBJC38900), National Natural Science Foundation of China (Project 51301121), Scientific Research Starting Foundation of Tianjin University of Technology and Education (No. KYQD12008) and Innovation Team Training Plan of Tianjin Universities and colleges (Grant No. TD12-5043).

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Publication Dates

• Publication in this collection
  05 Feb 2016
• Date of issue
  Mar-Apr 2016

History

• Received
  26 Feb 2015
• Reviewed
  26 Nov 2015
• Accepted
  21 Dec 2015