Development of a Prediction Method for Carbonitrided Surface Carbon

ISIJ International, AdvanceISIJ PublicationInternational, by AdvanceJ-STAGE, Publication DOI: 10.2355/isijinternational.ISIJINT-2020-050 by J-STAGE ISIJ International, J-Stage AdvancedISIJ International,Publication,ISIJ International, DOI: Advance http://dx.doi.org/10.2355/isijinternational.ISIJINT-2015-@@@ Vol. Publication 60 (2020), No.ISIJby J-Stage 9International, Vol. 60 (2020), No. 9, pp. 1–8

Development of a Prediction Method for Carbonitrided Surface Carbon and Nitrogen Contents by Computational Thermodynamics and Validation by Carbonitriding for Pure Iron

Kenta TSUJII,1)* Marian Georg SKALECKI,2) Matthias STEINBACHER2) and Hans-Werner ZOCH2)

1) Corporate Research & Development Center, Daido Steel Co., Ltd, 30, 2-Chome, Minami-ku, Nagoya, Aichi, 457-8545 Japan. 2) Leibniz-Institut für Werkstofforientierte Technologien – IWT, Badgasteiner Straße 3, Bremen, 28359 Germany. (Received on January 31, 2020; accepted on March 23, 2020; J-STAGE Advance published date: May 25, 2020)

In this study, a new method for predicting carbon and nitrogen contents of a carbonitrided surface using computational thermodynamics with Thermo-Calc was developed. The nitrogen content of alloyed steel, which is in equilibrium between the steel surface and the atmosphere, was predicted using the nitriding potentials and Thermo-Calc, and the experimental and calculated results were compared using pure iron. For lower nitrogen levels, the accuracy of prediction was sufficient. However, for higher nitrogen levels, the experimental nitrogen content was lower than the calculated value, which was attributed to pore formation. Through a comparison of the described method with the conventional one, it was confirmed that our novel prediction method exhibits sufficient accuracy to predict the nitrogen content following carbonitriding.

KEY WORDS: carbonitriding; carbon; nitrogen; simulation; CALPHAD; pores.

als, e.g. in contaminated lubricants.9) In contrast, an excess 1. Introduction of retained austenite results in decreased hardness and Carbonitriding is a thermochemical surface hardening strength.10) Therefore, in carbonitriding, control of the carbon treatment, which is similar to carburizing. In the gas car- and nitrogen contents is of particular importance, and thus, to burizing process, carbon is transferred from the atmosphere increase the application of this method, prediction techniques onto steel surfaces, and this reaction occurs in equilibrium for the resulting carbon and nitrogen contents are required. between the atmosphere and the steel surface. More specifi- Previously, hardware was developed at the IWT (Leibniz- cally, it relies on the so-called Boudouard reactions.1) Dur- Institut für Werkstofforientierte Technologien) for measure- ing this process, control of the carbon content is relatively ment of the nitriding potential for carbonitriding.4,5) More facile. In addition, through the carburization and hardening specifically, measurement of the nitrogen potential of the of steel components, certain properties, such as the wear atmosphere was performed by means of an ammonia sensor resistance, strength, and fatigue, can be altered, and thus, in the exhaust gas, and the carbon potential of the atmo- this technique is widely employed in industry. sphere was controlled using a conventional oxygen probe. In contrast, during the gas carbonitriding process, both The use of such devices therefore allowed simultaneous carbon and nitrogen are absorbed into steel surfaces simul- control of the nitrogen and carbon potentials of the atmo- taneously, and compared to carburizing, this process can sig- sphere during carbonitriding.4,5) nificantly increase wear resistance.2,3) As a result, although In addition, numerous prediction methods have been considerable research has been carried out in this field,1–8) reported for the carbon and nitrogen contents of alloyed the target carbon and nitrogen contents have been difficult steels through use of the carbon and nitrogen potentials of to achieve using controlled processes due to the interactions the atmosphere.11,12) In these methods, the effects of alloy- of carbon and nitrogen during the process, in addition to ing elements on the equilibrium contents were also taken the lack of a sufficient control system for automatic control into account, and these methods were proven to exhibit suf- of the nitrogen potential in the atmosphere. Carbonitrided ficient accuracy to predict the carbon and nitrogen contents components contain high amounts of both carbon and nitro- in the carbonitriding of alloyed steels under specific condi- gen, which leads to higher volume fractions of the retained tions.11,12) However, the influence of the alloying elements austenite.2) In this context, 20–35% of retained austenite has can vary with the temperature and the constituent phases; been proven to increase the wear properties of the materi- therefore, a more effective method is required. In contrast, computational thermodynamics has recently * Corresponding author: E-mail: [email protected] gained increasing attention in the context of nitriding, which DOI: https://doi.org/10.2355/isijinternational.ISIJINT-2020-050 is also a commonly employed surface hardening treatment.

More specifically, a prediction method for the constituent where the unit is Pa −1/2 or atm −1/2. phase was developed by Yang and Hiraoka’s groups using Thermodynamic calculations for predicting the nitro- computational dynamics.13,14) In their study, the Lehrer dia- gen content were carried out according to the CALPHAD grams of pure iron and alloyed steels were calculated using methodology,16) which has been under development since the CALPHAD methodology, and the calculation results the early 1970s. In this study, Thermo-Calc, which is a were proven to agree with the experimental results.13,14) This commercially available software, was used in combination method therefore also exhibited potential to be an effective with the TCFE7 database to calculate the thermodynamic tool for the prediction of carbon and nitrogen contents dur- properties.17) ing carbonitriding. Through the combined use of Thermo-Calc and TCFE7, However, to date, the use of CALPHAD to predict the the thermodynamic parameters of the solid solutions (e.g., carbon and nitrogen contents during carbonitriding has yet the Gibbs energy) were calculated using the sub-lattice to be reported. Thus, we herein report the application of model between the FCC phase and the M (C,N) carbonitride computational thermodynamics in the carbonitriding pro- phases, based on the amounts of carbon and nitrogen.17) cess for prediction of the nitrogen content. The prediction During the carbonitriding process, samples are heated to accuracy is also considered and compared with experimental 1 123 K, resulting in the absorption of carbon and nitrogen, observations. Moreover, the validity of this method is exam- and adoption of the FCC phase. The relationship between ined by comparison with the conventional method. the nitrogen content and the thermodynamic properties (e.g., the chemical potential and activity) can be calculated using these methods. Furthermore, we note that the nitrid- 2. Prediction Method for the Nitrogen Content Based ing potential, K , during the carbonitriding process can be on Computational Thermodynamics N controlled using hardware such as sensors;4,5,12) hence, the During carbonitriding, both the carburizing reaction and nitrogen content can be accurately predicted. the nitriding reaction occur simultaneously. In terms of the nitriding reaction in the nitriding atmosphere, the chemi- 3. Experimental Procedure cal potential of nitrogen, μN, thermodynamically defines the nitridability.15) At the thermodynamic equilibrium, the 3.1. Sample Material chemical potential in the steel surface, μN,s, equals that in Table 1 presents the chemical composition of the foil 1 employed for this study. The foil, which is essentially pure the nitriding atmosphere, µNg2 , , as described by Eq. (1): 2 iron, was used to prepare test samples of 50 μm thickness 1 to ensure that the samples reached their equilibrium carbon Ng,, Ns...... (1) 2 2 and nitrogen contents within a short period of treatment in the carbonitriding atmosphere. This set-up allowed the The chemical potential of nitrogen in the steel can there- equilibrium carbon and nitrogen contents to be measured. fore be related to the nitrogen activity, aN, by:

C S 3.2. Heat Treatment Conditions 1 0 1 pN2 0 RT lnD T Ns, RT ln aN ...... (2) Figure 1 presents the carbonitriding conditions employed 2 Ng2 , 2 D p0 T E N2 U herein, and further details are given in Table 2. For the purpose of this study, the gaseous carburizing atmosphere where R is the gas constant; T is the temperature; pN2 is the 0 furnace employed herein had dimensions of 300 mm × 300 partial pressure of nitrogen; and p is the partial pressure N2 mm × 300 mm. The inlet nozzle was located on the upper of nitrogen in the standard state. wall, and the analyzed gas was pumped upwards from Since the chemical potential of nitrogen is extremely low in N2 and relatively high in ammonia, ammonia is used as the principal constituent of the nitriding atmosphere. The nitriding reaction by ammonia can be represented by: Table 1. Chemical compositions of the foil samples employed herein. 3 NH32 []NH...... (3) (Mass%) 2 C Si Mn Cu Ni Cr Mo Al N Nb where [N] represents nitrogen dissolved in the steel surface. Foil 0.03 0.03 0.18 0.03 0.02 0.04 <0.01 0.035 0.006 <0.01 For the local equilibrium between N in the gas phase and N in the steel surface, the activity of nitrogen, aN is given by:

pNH3 12/ aKN = p0 ...... (4) p32/ H2 15) where K is the equilibrium constant of the reaction, p0 is the total pressure, and pNH3 and pH2 are the partial pres- sures of the ammonia and hydrogen gases, respectively. Moreover, the nitriding potential, KN, is defined by Eq. (5):

PNH3 KN = ...... (5) P32/ H2 Fig. 1. Carbonitriding conditions.

Table 2. Carbonitriding conditions.

3 Target Measured Target NH3 Measured Measured No. CHOH (l/h) N2 (m /h) KN CP (mass%) CP (mass%) (ppm) NH3 (ppm) H2 (%) 1 0.26 0.20 0.6 0.61 276 273 37.4 0.0012 2 0.36 0.05 0.6 0.58 350 271 50.5 0.0008 3 0.36 0.05 0.6 0.58 450 448 51.0 0.0012 4 0.36 0.05 0.6 0.59 604 607 52.1 0.0016 5 0.26 0.20 0.6 0.61 604 603 38.4 0.0025 6 0.36 0.05 0.6 0.58 850 845 50.5 0.0024 7 0.36 0.05 0.6 0.58 1 250 1 247 51.1 0.0034 8 0.26 0.20 0.6 0.59 1 250 1 245 37.6 0.0054 9 0.26 0.20 0.6 0.60 1 250 1 247 37.9 0.0053 10 0.36 0.05 0.6 0.59 1 600 1 599 50.6 0.0044 11 0.26 0.20 0.6 0.61 1 811 1 809 40.3 0.0071 12 0.36 0.05 0.6 0.59 1 811 1 800 52.3 0.0048 13 0.26 0.20 0.6 0.61 2 500 2 489 40.0 0.0098 14 0.36 0.05 0.6 0.59 2 929 2 926 53.6 0.0075 15 0.26 0.20 0.6 0.59 3 019 3 066 41.2 0.0116 16 0.26 0.20 0.6 0.60 0 0 37.0 0 under the wall. All processes were carried out at 1 123 K 4. Experimental Results and Discussion over 120 min. The hydrogen and carbon monoxide gases employed herein were generated from CH3OH, while nitro- 4.1. Trend Data during Carbonitriding gen and ammonia (>99.99% purity) were also employed Figure 2 shows an example of trend data obtained from for introduction to the furnace. A non-dispersive infrared the gases during the carbonitriding process along with the (NDIR) sensor, with which the hydrogen, ammonia, carbon calculated parameters (No. 11). In the carburizing reaction, monoxide, and carbon dioxide gas contents could be mea- a carburizing equilibrium reaction exists with the Boud- sured, was used along with a conventional oxygen probe to ouard reaction as shown below:12) control the atmosphere. Liquid methanol and nitrogen gas ...... (6) were used as the carrier media, whereby the amounts of 2CO = []C CO2 liquid methanol and nitrogen gas were adjusted to alter the where [C] represents the carbon content, which is dissolved hydrogen gas content in the furnace. Propane was used as an into the steel surfaces. The carburizing potential of reaction enriching gas. The carbon potential was fixed to focus on the (6) can be described as follows: varying nitrogen contents in the steel samples. In addition, 2 PCO the carbon potential was fixed using hardware to prevent KC = ...... (7) P decreases caused by dilution in the atmosphere through CO2 the addition of ammonia gas. The flow rate of the NH3 gas where PCO is the partial pressure of carbon monoxide and was controlled to maintain a target NH3 gas content in the PCO2 is the partial pressure of carbon dioxide. In Fig. 2, as furnace. The nitriding potentials, KN, are given in Table 2, the CO gas content decreases slightly over time, the CO2 gas and these values were calculated according to Eq. (5) using content also decreases similarly. Therefore, the carburizing the average values of both the analyzed NH3 gas content and potential and the carbon potential stay constant during the the analyzed hydrogen gas content from the final 10 min of process because the amount of enriching gas was adjusted treatment. The nitrogen content was then calculated using using hardware to ensure a constant carbon potential. More- the obtained KN values. over, the NH3 gas content fluctuated at the beginning of the process, but became constant relatively quickly to allow 3.3. Analysis and Observation Methods its use as a target content. The H2 gas content also stayed The nitrogen and carbon contents of the foils after carbo- constant during the process. Therefore, according to Eq. (5), nitriding were measured by the gas analysis method, where the nitriding potential KN was also constant. calibration was carried out using samples in which the real carbon and nitrogen contents were known. Cross-sections 4.2. Influences of KN, NH3, and H2 on the Nitrogen of select treated foil samples obtained under different Content carbonitriding conditions were also observed by optical Figure 3 shows the relationship between the retained microscopy to confirm whether pore formation took place NH3 gas content and the nitrogen content in the foils after during the process (Fig. 9). All specimens for observation carbonitriding. As demonstrated in previous works,4,5) the were prepared by grinding and mirror polishing without nitrogen content correlates to the retained NH3 gas content, etching. and as the retained NH3 gas content increases, the nitro-

Fig. 2. An example of a gas trend during a carbonitriding process: No. 11. (a) CO gas content, %, (b) CO2 gas content, %, (c) Carburizing potential, Kc, (d) Carbon potential in the atmosphere, mass%, (e) NH3 gas content, ppm, (f) H2 gas content, %, and (g) Nitriding potential, KN. (Online version in color.)

Fig. 3. Relationship between the retained NH3 gas content and the Fig. 5. Relationship between the nitriding potential and the N N content in the foil. (Online version in color.) content in the foil. (Online version in color.)

gen content also increases. However, as observed, even when the NH3 gas content remained constant, the nitrogen content differed in some data. In addition, Fig. 4 shows the relationship between the H2 gas content and the nitrogen content, where symbols of the same shape represent the same NH3 gas content. Thus, although the NH3 gas content remained constant, an increase in H2 gas content resulted in a decrease in the nitrogen content. Therefore, 12) as demonstrated previously, both the NH3 and H2 gas contents affect the nitrogen content after carbonitriding. Furthermore, Fig. 5 shows the reorganized data obtained using the nitriding potential, KN. As shown, the nitrogen content in the foil correlates to the nitrogen potential, and little variation is observed in the lower nitriding potential region, i.e., <0.005. In contrast, a greater deviation was observed at higher nitriding potentials.

Fig. 4. Relationship between the H2 gas content and the N content in the foil. (Online version in color.)

4.3. Accuracy of the Computational Thermodynamics of carbon. Thus, Fig. 7 shows the relationship between the Calculation Method recalculated nitrogen content and the experimental nitrogen As described above, the nitrogen content after carboni- content. In this calculation, it was considered that the carbon triding can be calculated by computational thermodynamics. content of all the samples would be 0.6 mass% based on Thus, to confirm the accuracy of this method, the calculated their target carbon potential. Although the carbon content nitrogen content was compared to the experimental nitrogen used in the calculation must be taken from the real carbon content. For this calculation, the KN values listed in Table 2 content after carbonitriding, the accurate carbon content were employed. Thus, Fig. 6 shows the relationship between could not be measured due to decarburizing during trans- the calculated nitrogen content and the experimental nitro- portation from the carburizing chamber to the quenching gen content, whereby the calculation was performed for the chamber. To confirm the degree of surface decarburization, binary iron-nitrogen system, and the influences of carbon the carbon and nitrogen contents of the foils were measured and other alloying elements on the nitrogen activity were using an electron probe micro-analyzer (EPMA), and the not considered. In this figure, the black line represents a results are presented in Fig. 8. As shown, the surface carbon 1:1 ratio, and it is apparent that the relationship between the content decreased compared to the inner carbon content, calculated nitrogen content and the experimental nitrogen likely due to decarburization. Therefore, in further studies, content does not fit this line. This was attributed to the fact that these calculations do not consider the influence of carbon on the nitrogen activity. However, as the steel surfaces absorb both carbon and nitrogen from the atmosphere simultaneously during the carbonitriding process, this absorption must be considered. If a constant activity is set in the atmosphere during carbonitriding, different equilibrium nitrogen contents of Nalloy and NP result in the alloy steel and in the pure iron, as described in Eq. (8),

FeN Fe N alloy afNN **NfPN* fNN alloy ...... (8) Fe−N alloy where fN is the activity coefficient, and fN is the ratio alloy between the nitrogen activity of aN in the alloyed steel Fe−N alloy and aN in the binary iron-nitrogen system. fN can be defined as outlined in Eq. (9):

alloy alloy aN fN FeN ...... (9) aN Fig. 7. Relationship between the calculated and experimental alloy nitrogen contents. This calculation considers the influence In addition, fN can be calculated using Thermo-Calc, and of the carbon content (0.6 mass%) on the nitrogen activity. so the influence of an alloy element such as carbon on the (Online version in color.) nitrogen content can be also calculated. Through use of Eq. (9), recalculation for prediction of the nitrogen content was performed by considering the influence

Fig. 6. Relationship between the calculated and experimental Fig. 8. Carbon and nitrogen content distributions within the foil nitrogen contents. This calculation does not consider the determined using EPMA. (a) Carbon, and (b) Nitrogen. (c) influence of any alloying elements on the nitrogen activity. Backscattered electron image (Treatment No. 11). (Online (Online version in color.) version in color.)

5 © 2020 ISIJ ISIJ International, Advance Publication by J-STAGE ISIJ International,ISIJ International, Advance Vol. Publication 60 (2020), No.by J-Stage9 decarburization must be prevented during treatment, and dissolved in the austenite begins to decrease at a certain the real carbon content must be measured. However, as the point due to the presence of pores. He reports that if the nitrogen content was uniformly distributed, it could be con- nitrogen content is >0.4 mass%, the correlation with the firmed that analysis of the nitrogen content by gas analysis calculated nitrogen potential is lost. We therefore consid- was accurate. ered that the lower experimental values compared to the Therefore, the effect of the carbon content on the cal- calculated values could be attributed to pore formation. culated nitrogen content was confirmed, and the variation However, as it is known that practical alloy steel contains of this influence was measured. However, by comparing virtually no pores in the high density nitride area after car- calculations carried out using assumed carbon contents of bonitriding compared to pure iron, further studies into the 0.5 and 0.6 mass%, no significant influence on the -calcu effect of pore formation using our method are required for lated nitrogen content was found. In this context, we note practical alloys. that during carbonitriding, the nitrogen content also affects the carbon content of the alloyed steel, and this influence 4.5. Accuracy Compared to the Conventional Calcula- can decrease the level of carbon. In the calculation above, tion Method 0.5 mass% carbon was selected for comparison because the To determine the accuracy of our prediction method, maximum amount of influence that the nitrogen content can it was compared to the previously reported conventional have on the carbon content is 0.1 mass% of the foil con- method,10,11) whereby the nitrogen potential in the atmo- tent.11) It was therefore assumed that the carbon content of sphere was calculated by: all samples would be 0.6 mass%. From Fig. 7, the calculated C PNH3 S 2 210 values were found to correlate highly to the experimental log(NP )l ogD T 39. 1...... (10) P 32/ T values in the lower nitrogen content region, i.e., up to 0.45 E H2 U mass%, and the accuracy of prediction was considered sufficient. However, in the higher nitrogen content region, the prediction accuracy remained low, thereby suggesting that other factors are also responsible for determining the nitrogen content in the higher nitrogen region.

4.4. Pore Formation Figure 9 shows the optical microscopy images of cross- sections of the various carbonitrided samples. As reported previously, it is well known that when excess nitrogen is absorbed into steel surfaces, pores form within the steel.18) We found obvious pore formation in sample No. 15, which was due to the recombination of atomic nitrogen to give molecular nitrogen along the austenite grain boundaries. Since the nitrogen contents of Nos. 11 and 14 were ~0.5 mass%, no obvious pore formation took place, but it is still Fig. 10. Nitrogen contents of the foils vs. the nitrogen potential of possible that small pores were present. Figure 10 presents 18) the atmosphere as calculated from the composition of the data reported by Slycke, whereby the nitrogen content atmosphere, according to a previously reported model.14) (Online version in color.)

Fig. 11. Relationship between the calculated nitrogen content Fig. 9. Optical micrographs after carbonitriding. (a) No. 5: (using a previously reported method6)) and the experi- KN= 0.0025, (b) No. 11: KN= 0.0071, (c) No. 14: mental nitrogen content. This calculation considers the KN= 0.0075, and (d) No. 15: KN= 0.0116. (Online version in influence of the carbon content (0.6 mass%) on the nitro- color.) gen activity. (Online version in color.)

Fig. 12. Comparison of the prediction accuracies of the 2 methods. (a) Calculation results obtained using computational thermodynamics, and (b) calculation results obtained using a previously reported method.6) Horizontal error bars: Margin of error of the analyzed value of the ammonia sensor. (Online version in color.)

According to the relationship between the nitrogen potential method exhibits sufficient accuracy for predicting the nitro- and the nitrogen content in alloyed steels (Eq. (9)), Nalloy can gen content in carbonitriding. be represented by:

NP 5. Conclusions Nalloy = ...... (11) f alloy N We herein reported the development of a novel predic- We also note that studies have been carried out into the tion method for carbonitrided surface carbon and nitrogen effect of individual alloying elements on the activity,10,19–21) contents based on the use of computational thermodynamics alloy and the logarithmic alloy-dependent activity factor fN with Thermo-Calc. To confirm the prediction accuracy of can be calculated according to Eq. (12): this method, a number of trials were conducted, and it was found that the equilibrium nitrogen content could be pre- log( fealloy )* B w ...... (12) N Nj j dicted using the nitriding potential values and Thermo-Calc. where eNj represents the interaction parameters of the alloy- In addition, the prediction accuracy increased when the ing elements, and wj represents the content (mass%) of the effect of carbon on the nitrogen activity was taken into alloying elements. account. Furthermore, we found that the experimental Figure 11 shows the relationship between the nitrogen nitrogen content became lower than the calculated nitrogen content calculated using the previous method and the experi- content in the higher nitrogen content region, likely due to mentally obtained nitrogen content. In this calculation, the the formation of small pores within the structure. Through carbon contents of all samples were hypothesized to be 0.6 comparison of our method to the conventional method, we mass%, and reference interaction parameters10) were used to confirmed that this novel prediction method exhibits suf- calculate the effect of the carbon content on the calculated ficient accuracy to predict the nitrogen content in carboni- nitrogen content. Indeed, it was found that the calculated triding. We note that for our study, the carbon potential, the values correlated to the experimental values. temperature, and the time were fixed at 0.6 mass%, 1 123 K, and 120 min, respectively. However, to confirm the accu- 4.6. Comparison between the Two Prediction Methods racy of our method, further studies are required to examine To confirm the accuracy of our developed prediction higher and lower carbon potential regions, in addition to a method, it was compared to the previously described con- wider range of temperatures. Moreover, the effect of alloy- ventional method (see chapter 4.5). As shown in Fig. 12, ing elements on the nitrogen content must also be examined bars representing the margins of error were added to both for further method validation. the calculated nitrogen content and the experimental nitrogen content. The horizontal error bars show the margins of REFERENCES error of the analyzed values, and so any deviation in the 1) T. Naito: Shintanyakiirenojissai, 2nd ed., The Nikkan Kogyo ammonia analyzer is included. Based on a margin of error of Shimbun, Ltd., Tokyo, (1999), 11 (in Japanese). ±200 ppm, the calculated nitrogen content was recalculated. 2) Y. Watanabe, N. Narita, S. Umegaki and Y. Mishima: Tetsu- to-Hagané, 84 (1998), No. 12, 902 (in Japanese). https://doi. The deviation of the analyzed NH3 gas values strongly influ- org/10.2355/tetsutohagane1955.84.12_902 ences the calculated nitrogen content. These results indicate 3) M. Nagahama, K. Iwasaki and S. Abe: Kobe Steel Eng. Rep., 56 that improved sensors are required in such systems. In the (2006), No. 3, 53 (in Japanese). 4) S. Bischoff, H. Klümper-Westkamp, F. Hoffmann and H.-W. Zoch: context of our new method, if the higher nitrogen content HTM J. Heat Treat. Mater., 65 (2010), No. 3, 141. region can be excluded from the data due to possible pore 5) S. Bischoff, H. Klümper-Westkamp, F. Hoffmann and H.-W. Zoch: HTM J. Heat Treat. Mater., 67 (2012), No. 3, 217. formation, the prediction accuracy is superior to that of the 6) C. Ohki: Tetsu-to-Hagané, 93 (2007), No. 3, 220 (in Japanese). previous method, thereby confirming that our developed https://doi.org/10.2355/tetsutohagane.93.220

2 7) J. Slycke and T. Ericsson: J. Heat Treat., 2 (1981), No. 2, 97. (g/mm /s), βc represents the carbon transfer coefficient (g/ 8) M. G. Skalecki, H. Klümper-Westkamp, M. Steinbacher and H.-W. 2 Zoch: HTM J. Heat Treat. Mater., 74 (2019), No. 4, 215. mm /s), CA represents the carbon potential of the atmo- 9) H. Komata, Y. Iwanaga, T. Ueda, K. Ueda and N. Mitamura: Tribol. sphere, and CS represents the surface carbon content of the schmierungstech., 62 (2015), 54 (in German). steel. The diffusion is simulated using Fick’s second law, 10) T. Naito: Shintanyakiirenojissai, 2nd ed., The Nikkan Kogyo Shimbun, Ltd., Tokyo, (1999), 182 (in Japanese). as shown below: 11) K.-M. Winter: J. Mater. Eng. Perform., 22 (2013), No. 7, 1945. 12) M. G. Skalecki, H. Klümper-Westkamp, M. Steinbacher and H.-W. C C C S Zoch: HTM J. Heat Treat. Mater., 73 (2018), No. 2, 80. D D T ...... (14) 13) M. Yang, B. Yao, Y. H. Sohn and R. D. Sisson, Jr.: Int. Heat Treat. tx E x U Surf. Eng., 5 (2011), No. 3, 122. 14) Y. Hiraoka, Y. Watanabe and O. Umezawa: Netsu Shori (J. Jpn. Soc. Heat Treat.), 54 (2014), No. 6, 313 (in Japanese). https://doi. where D represents the diffusion coefficient, which was org/10.14940/netsushori.54.313 obtained from the literature.22) For calculation purposes, the 15) E. J. Mittemeijer and J. T. Slycke: Surf. Eng., 12 (1996), No. 2, 152. 16) N. Saunders and A. P. Miodownik: Calphad (Calculation of Phase following parameters were applied: temperature, 1 123 K; Diagrams): A Comprehensive Guide, Pergamon, Oxford, (1998), 478. decarburizing time, 10 s; carbon potential of outer atmo- 17) J. O. Andersson, T. Helander, L. Höglund, P. F. Shi and B. Sundman: Calphad, 26 (2002), 273. sphere, 0 mass%; carbon transfer coefficient, 0.05. Figure 18) J. Slycke and T. Ericsson: Heat Treatment ‘81, The Metal Society, 13 shows the EPMA results and the calculation result, Birmingham, (1983), 185. whereby similar results were obtained, thus confirming that 19) H. J. Grabke, D. Grassl and F. Hoffmann: Die Prozessregelung beim Gasaufkohlen und Einsatzharten (Process Control in the Gas decarburization takes place due to transportation from the Carburizing and Case Hardeing), ed. by AWT-Fachausschuss 5 and carburizing chamber to the quenching chamber. Arbeitskreis 4, Expert, Renningen, (1997), 3 (in German). 20) D. Liedtke and F. Neumann: HTM Haerterei-Tech. Mitt., 49 (1994), No. 2, 83. 21) K.-H. Sauer, M. Lucas and H. J. Grabke: HTM Haerterei-Tech. Mitt., 43 (1988), No. 1, 45. 22) C. Wells, W. Batz and R. F. Mehl: Trans. AIME, 188 (1950), 553.

Appendix As described in Section 4.3, decarburization occurs during transportation from the carburizing chamber to the quenching chamber. Thus, a simulation decarburizing model was constructed and the degree of decarburization was calculated:

qCCC ()ASC ...... (13) Fig. 13. Carbon distribution within the foil. (a) EPMA result, and where qC represents the velocity of decarburization (b) Calculation result. (Online version in color.)