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 () and the gamma prime phase (). The diffusion layer is composed of interstitial solid solution of nitrogen dissolved in the ferrite lattice () 11 Pye D. Practical nitriding and ferritic nitrocarburizing. Materials Park, OH: ASM International; 2003.. 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 22 Sun Y, Bell T. A numerical model of plasma nitriding of low alloy steels. Materials Science & Engineering A. 1997;224(1): 33-47.doi:10.1016/S0921-5093(96)10561-X
https://doi.org/10.1016/S0921-5093(96)10...
3 Goune M, Belmonte T, Fiorani JM, Chomer S, Michel H. Modelling of diffusion–precipitation in nitrided alloyed iron. Thin Solid Films. 2000;377-378:543-549.doi:10.1016/S0040-6090(00)01305-5
https://doi.org/10.1016/S0040-6090(00)01...
4 Belmonte T, Gouné M, Michel H. Numerical modeling of interstitial diffusion in binary systems: Application to iron nitriding. Materials Science & Engineering A. 2001;302(2): 246-57.
5 Liu CC, Ju DY, Inoue T. A numerical modeling of metallo-thermo-mechanical behavior in both carburized and carbonitrided quenching processes. ISIJ International. 2002;42(10): 1125-1134.doi:10.1016/S0924-0136(03)00378-9
https://doi.org/10.1016/S0924-0136(03)00...
6 Ju DY, Liu CC, Inoue T. Numerical modeling and simulation of carburized and nitrided quenching process. Journal of Materials Processing Technology. 2003;143-144:880-885.doi:10.1016/S0924-0136(03)00378-9
https://doi.org/10.1016/S0924-0136(03)00...
7 Krukovich MG. Simulation of the nitriding process. Metal Science and Heat Treatment. 2004;46(1):25-31.
8 Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided Fe-Mn and Fe-V. Surface & Coatings Technology. 2006;200(20):909-912.
9 Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided multi-component ferritic steel. Surface & Coatings Technology. 2006; 200(20-21): 5896-5901.doi:10.1016/j.surfcoat.2005.09.002
https://doi.org/10.1016/j.surfcoat.2005....
10 Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
https://doi.org/10.1016/j.msea.2006.02.4...
11 Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35.
12 Yang M, Yao B, Sohn YH, Sisson Jr RD. Simulation of the ferritic nitriding proces. International Heat Treatment and Surface Engineering. 2011;5(3):122-126. DOI: http://dx.doi.org/10.1179/174951411X12956208225186
https://doi.org/10.1179/174951411X129562...
-1313 Yang M, Zimmerman C, Donahue D, Sisson Jr RD. Modeling the gas nitriding process of low alloy steels. Journal of Materials Engineering and Performance. 2013;22(7):1892-1898.. Sun and Bell 22 Sun Y, Bell T. A numerical model of plasma nitriding of low alloy steels. Materials Science & Engineering A. 1997;224(1): 33-47.doi:10.1016/S0921-5093(96)10561-X
https://doi.org/10.1016/S0921-5093(96)10...
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., 33 Goune M, Belmonte T, Fiorani JM, Chomer S, Michel H. Modelling of diffusion–precipitation in nitrided alloyed iron. Thin Solid Films. 2000;377-378:543-549.doi:10.1016/S0040-6090(00)01305-5
https://doi.org/10.1016/S0040-6090(00)01...
and Belmont et al., 44 Belmonte T, Gouné M, Michel H. Numerical modeling of interstitial diffusion in binary systems: Application to iron nitriding. Materials Science & Engineering A. 2001;302(2): 246-57. 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 88 Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided Fe-Mn and Fe-V. Surface & Coatings Technology. 2006;200(20):909-912.,99 Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided multi-component ferritic steel. Surface & Coatings Technology. 2006; 200(20-21): 5896-5901.doi:10.1016/j.surfcoat.2005.09.002
https://doi.org/10.1016/j.surfcoat.2005....
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 1010 Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
https://doi.org/10.1016/j.msea.2006.02.4...
and Cavaliere et al., 1111 Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35. modeled the nitriding process by coupling the kinetics data of nitrogen in , and phases to the thermodynamic description of the iron-nitrogen (Fe-N) phase diagram respectively. Recently, Yang et al., 1212 Yang M, Yao B, Sohn YH, Sisson Jr RD. Simulation of the ferritic nitriding proces. International Heat Treatment and Surface Engineering. 2011;5(3):122-126. DOI: http://dx.doi.org/10.1179/174951411X12956208225186
https://doi.org/10.1179/174951411X129562...
,1313 Yang M, Zimmerman C, Donahue D, Sisson Jr RD. Modeling the gas nitriding process of low alloy steels. Journal of Materials Engineering and Performance. 2013;22(7):1892-1898. 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 1414 Wriedt HA, Gokcen NA, Nafziger RH. The Fe-N (Iron-Nitrogen) system. Bulletin of Alloy Phase Diagrams. 1987;8:355-377.
15 Voorthuysen EH, Boerma DO, Chechnin NC. Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram. Metallurgical and Materials Transactions A. 2002;33(8):2593-2598.
16 Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279.
17 Somers MA, Mittemeijer EJ. Layer-growth kinetics on gaseous nitriding of pure iron: Evaluation of diffusion coefficients for nitrogen in iron nitrides. Metallurgical and Materials Transactions A. 1995;26(1):57-74.
18 Hernandez M, Staia MH, Puchi-Cabrera ES. Evaluation of microstructure and mechanical properties of nitrided steels. Surface & Coatings Technology. 2008;202(10):1935-1943. doi:10.1016/j.surfcoat.2007.08.018
https://doi.org/10.1016/j.surfcoat.2007....
19 Ratajski J. Relation between phase composition of compound zone and growth kinetics of diffusion zone during nitriding of steel. Surface & Coatings Technology. 2009; 203(16):2300-2306.DOI: 10.1016/j.surfcoat.2009.02.021
https://doi.org/10.1016/j.surfcoat.2009....
-2020 Somers MA. Development of compound layer during nitriding and nitrocarburising; current understanding and future challenges. International Heat Tretament and Surface Engineering. 2011;5(1):7-16.. 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 1414 Wriedt HA, Gokcen NA, Nafziger RH. The Fe-N (Iron-Nitrogen) system. Bulletin of Alloy Phase Diagrams. 1987;8:355-377.,1515 Voorthuysen EH, Boerma DO, Chechnin NC. Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram. Metallurgical and Materials Transactions A. 2002;33(8):2593-2598.. Moreover, Lakhtin 1616 Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279. reviewed the diffusion foundations of the nitriding process in carbon steel and alloy steel. Because the bonding energy in -phase is lower than that in the lattice of and -phases, the coefficient of nitrogen diffusion in -phase should exceed the coefficients in the and by many times 1717 Somers MA, Mittemeijer EJ. Layer-growth kinetics on gaseous nitriding of pure iron: Evaluation of diffusion coefficients for nitrogen in iron nitrides. Metallurgical and Materials Transactions A. 1995;26(1):57-74.. Furthermore, the phase composition of a compound zone and growth kinetics of a diffusion zone during the nitriding of steel was investigated quantitatively 1818 Hernandez M, Staia MH, Puchi-Cabrera ES. Evaluation of microstructure and mechanical properties of nitrided steels. Surface & Coatings Technology. 2008;202(10):1935-1943. doi:10.1016/j.surfcoat.2007.08.018
https://doi.org/10.1016/j.surfcoat.2007....
,1919 Ratajski J. Relation between phase composition of compound zone and growth kinetics of diffusion zone during nitriding of steel. Surface & Coatings Technology. 2009; 203(16):2300-2306.DOI: 10.1016/j.surfcoat.2009.02.021
https://doi.org/10.1016/j.surfcoat.2009....
. Recently, Somers 2020 Somers MA. Development of compound layer during nitriding and nitrocarburising; current understanding and future challenges. International Heat Tretament and Surface Engineering. 2011;5(1):7-16. 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 2121 Crank J. The mathematics of diffusion. Oxford: Clarendon Press; 1956..
where, is nitrogen concentration, is the depth, is nitriding time, 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).
where, , is the diffusion coefficient of location at time , is time step, is the nitrogen concentration of location at time .
The boundary conditions is the following
where, is the surface nitrogen concentration.
2.2 Fe-N phase composition predicted model
By employing the Fe-N phase diagram (Fig. 1 (a)) 1414 Wriedt HA, Gokcen NA, Nafziger RH. The Fe-N (Iron-Nitrogen) system. Bulletin of Alloy Phase Diagrams. 1987;8:355-377.,1515 Voorthuysen EH, Boerma DO, Chechnin NC. Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram. Metallurgical and Materials Transactions A. 2002;33(8):2593-2598., it is feasible to predict the different Fe-N phases according to the limit solubility values 1010 Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
https://doi.org/10.1016/j.msea.2006.02.4...
,1111 Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35.. 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
where, is nitrogen concentration, are the limiting nitrogen solubilities in Fe-N phase, as a function of temperature can be calculated by 1010 Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
https://doi.org/10.1016/j.msea.2006.02.4...
,1111 Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35.,1616 Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279.
where, is the activity coefficient of nitrogen, which can be calculated by 2222 Lakhtin YU, Kogan YA, Bulgach AA. Effect of alloying elements on the thermodynamic activity and solubility of nitrogen in phases of a nitrided case. Metal Science and Heat Treatment. 1982;24(4):15-18.
where, is the wt.% of i element.
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 55 Liu CC, Ju DY, Inoue T. A numerical modeling of metallo-thermo-mechanical behavior in both carburized and carbonitrided quenching processes. ISIJ International. 2002;42(10): 1125-1134.doi:10.1016/S0924-0136(03)00378-9
https://doi.org/10.1016/S0924-0136(03)00...
,77 Krukovich MG. Simulation of the nitriding process. Metal Science and Heat Treatment. 2004;46(1):25-31.
where, is the Vickers Hardness, is the Vickers Hardness of the substrate, is the chemical compositions, is the iron-carbon phase compositions, is the Fe-N phase compositions, and (), (), () are the corresponding weighting coefficients, which obtained by literature 2323 Yakhnina VD, Nikitin VV. Development of the hardness of the nitrided case. Metal Science and Heat Treatment. 1975;17(1-2):125-128.
24 Lakhtin YU, Kogan YA, Sharlat ES. Nitriding of low- and medium-carbon steels surface-alloyed with nitride-forming elements. Soviet Materials Science. 1976; 13(5):514-517.-2525 Glushchenko VN, Goryushin VV, Kondrashova GA, Duka ME. Effect of alloying on the structure and properties of the nitrided case on medium-carbon steels. Metal Science and Heat Treatment. 1980;22(9):638-643. and experimental data. The values of coefficients are listed in Table 1.
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 55 Liu CC, Ju DY, Inoue T. A numerical modeling of metallo-thermo-mechanical behavior in both carburized and carbonitrided quenching processes. ISIJ International. 2002;42(10): 1125-1134.doi:10.1016/S0924-0136(03)00378-9
https://doi.org/10.1016/S0924-0136(03)00...
,66 Ju DY, Liu CC, Inoue T. Numerical modeling and simulation of carburized and nitrided quenching process. Journal of Materials Processing Technology. 2003;143-144:880-885.doi:10.1016/S0924-0136(03)00378-9
https://doi.org/10.1016/S0924-0136(03)00...
where, for each single phase, , is diffusivity in various Fe-N phases, 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 1010 Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
https://doi.org/10.1016/j.msea.2006.02.4...
,1111 Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35.,1616 Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279.,1717 Somers MA, Mittemeijer EJ. Layer-growth kinetics on gaseous nitriding of pure iron: Evaluation of diffusion coefficients for nitrogen in iron nitrides. Metallurgical and Materials Transactions A. 1995;26(1):57-74.
where, , and are the alloy coefficients, which can be determined by the formula 1616 Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279.
where is the concentration of the alloying element in the steel, and , 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).
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.
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.
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 (+) and inner diffusion layer (+). The simulated depth distributions of and phases are reasonable consistent with the X-ray diffraction (XRD) phase analysis results 1919 Ratajski J. Relation between phase composition of compound zone and growth kinetics of diffusion zone during nitriding of steel. Surface & Coatings Technology. 2009; 203(16):2300-2306.DOI: 10.1016/j.surfcoat.2009.02.021
https://doi.org/10.1016/j.surfcoat.2009....
and optical micrograph. The formation of 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.
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.
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).
References
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1Pye D. Practical nitriding and ferritic nitrocarburizing. Materials Park, OH: ASM International; 2003.
-
2Sun Y, Bell T. A numerical model of plasma nitriding of low alloy steels. Materials Science & Engineering A. 1997;224(1): 33-47.doi:10.1016/S0921-5093(96)10561-X
» https://doi.org/10.1016/S0921-5093(96)10561-X -
3Goune M, Belmonte T, Fiorani JM, Chomer S, Michel H. Modelling of diffusion–precipitation in nitrided alloyed iron. Thin Solid Films. 2000;377-378:543-549.doi:10.1016/S0040-6090(00)01305-5
» https://doi.org/10.1016/S0040-6090(00)01305-5 -
4Belmonte T, Gouné M, Michel H. Numerical modeling of interstitial diffusion in binary systems: Application to iron nitriding. Materials Science & Engineering A. 2001;302(2): 246-57.
-
5Liu CC, Ju DY, Inoue T. A numerical modeling of metallo-thermo-mechanical behavior in both carburized and carbonitrided quenching processes. ISIJ International. 2002;42(10): 1125-1134.doi:10.1016/S0924-0136(03)00378-9
» https://doi.org/10.1016/S0924-0136(03)00378-9 -
6Ju DY, Liu CC, Inoue T. Numerical modeling and simulation of carburized and nitrided quenching process. Journal of Materials Processing Technology. 2003;143-144:880-885.doi:10.1016/S0924-0136(03)00378-9
» https://doi.org/10.1016/S0924-0136(03)00378-9 -
7Krukovich MG. Simulation of the nitriding process. Metal Science and Heat Treatment. 2004;46(1):25-31.
-
8Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided Fe-Mn and Fe-V. Surface & Coatings Technology. 2006;200(20):909-912.
-
9Kamminga JD, Janssen GC. Calculation of nitrogen depth profiles in nitrided multi-component ferritic steel. Surface & Coatings Technology. 2006; 200(20-21): 5896-5901.doi:10.1016/j.surfcoat.2005.09.002
» https://doi.org/10.1016/j.surfcoat.2005.09.002 -
10Keddam M. Surface modification of the pure iron by the pulse plasma nitriding: Application of a kinetic model. Materials Science & Engineering A. 2007;462(1): 169-173. doi:10.1016/j.msea.2006.02.459
» https://doi.org/10.1016/j.msea.2006.02.459 -
11Cavaliere P, Zavarise G, Perillo M. Modeling of carburizing and nitriding processes. Computational Materials Science. 2009;46(1): 26-35.
-
12Yang M, Yao B, Sohn YH, Sisson Jr RD. Simulation of the ferritic nitriding proces. International Heat Treatment and Surface Engineering. 2011;5(3):122-126. DOI: http://dx.doi.org/10.1179/174951411X12956208225186
» https://doi.org/10.1179/174951411X12956208225186 -
13Yang M, Zimmerman C, Donahue D, Sisson Jr RD. Modeling the gas nitriding process of low alloy steels. Journal of Materials Engineering and Performance. 2013;22(7):1892-1898.
-
14Wriedt HA, Gokcen NA, Nafziger RH. The Fe-N (Iron-Nitrogen) system. Bulletin of Alloy Phase Diagrams. 1987;8:355-377.
-
15Voorthuysen EH, Boerma DO, Chechnin NC. Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram. Metallurgical and Materials Transactions A. 2002;33(8):2593-2598.
-
16Lakhtin YU. Diffusion foundations of the nitriding process. Metal Science and Heat Treatment. 1995;37(7):276-279.
-
17Somers MA, Mittemeijer EJ. Layer-growth kinetics on gaseous nitriding of pure iron: Evaluation of diffusion coefficients for nitrogen in iron nitrides. Metallurgical and Materials Transactions A. 1995;26(1):57-74.
-
18Hernandez M, Staia MH, Puchi-Cabrera ES. Evaluation of microstructure and mechanical properties of nitrided steels. Surface & Coatings Technology. 2008;202(10):1935-1943. doi:10.1016/j.surfcoat.2007.08.018
» https://doi.org/10.1016/j.surfcoat.2007.08.018 -
19Ratajski J. Relation between phase composition of compound zone and growth kinetics of diffusion zone during nitriding of steel. Surface & Coatings Technology. 2009; 203(16):2300-2306.DOI: 10.1016/j.surfcoat.2009.02.021
» https://doi.org/10.1016/j.surfcoat.2009.02.021 -
20Somers MA. Development of compound layer during nitriding and nitrocarburising; current understanding and future challenges. International Heat Tretament and Surface Engineering. 2011;5(1):7-16.
-
21Crank J. The mathematics of diffusion. Oxford: Clarendon Press; 1956.
-
22Lakhtin YU, Kogan YA, Bulgach AA. Effect of alloying elements on the thermodynamic activity and solubility of nitrogen in phases of a nitrided case. Metal Science and Heat Treatment. 1982;24(4):15-18.
-
23Yakhnina VD, Nikitin VV. Development of the hardness of the nitrided case. Metal Science and Heat Treatment. 1975;17(1-2):125-128.
-
24Lakhtin YU, Kogan YA, Sharlat ES. Nitriding of low- and medium-carbon steels surface-alloyed with nitride-forming elements. Soviet Materials Science. 1976; 13(5):514-517.
-
25Glushchenko VN, Goryushin VV, Kondrashova GA, Duka ME. Effect of alloying on the structure and properties of the nitrided case on medium-carbon steels. Metal Science and Heat Treatment. 1980;22(9):638-643.
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