Modeling of Pack-Carburizing Route by General Factorial Design of Experiment

Modeling of Pack-Carburizing Route by General Factorial Design of Experiment

Hamed Khosravi*

PhD Candidate, Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, Tehran, Iran

Mohsen Mirzaee Sisan

Faculty of Materials Science and Engineering, K. N. Toosi University of Technology, Tehran, Iran

Zhuguo Li

Seyed Reza Elmi Hosseini

PhD Candidate, School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai, China

Mohsen Askari Paykani

PhD Candidate, Department of Materials Science and Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

Professor, School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai, China

AbstractThis work modeled the influence of Na2CO3 as an activator material in the pack-carburizing process of 1.5920 steel by General Factorial Design of Experiment (GFDE). Four different carburizing mixtures containing 0, 5, 10 and 15 wt. % of Na2CO3 at 16 experiments have been used. The samples were carburized at 925°C for different time of 3, 5, 8 and 12 hrs. The Effective Case Depth (ECD) of treated samples was measured using a micro-hardness test. The activator content and carburizing time were considered as model factors. The optimal conditions to attain the maximum ECD were predicted by GFDE. The results indicated that by using activator amount of

1. wt. %, maximum ECD could be achieved, regardless of the carburizing time. The reasons for declining of ECD corresponding to the activator amount beyond the 11.5 wt. % were also discussed.

   Keywords Pack-Carburizing; Activator; 1.5920 steel; Modeling; General factorial design of experiment.

   1. INTRODUCTION

      Surface hardening is a very important process for industrial applications. Machine components such as shafts, gears and cams often require a very hard surface that can resist wear and a soft, tough core that can withstand the impact stresses which occur during operation. An established method for the production of such a combination of hard case and soft, tough core is case hardening of steels through carburizing and quenching [1-3]. Carburizing is the addition of carbon to the surface of low carbon steels at temperatures generally between 850-950 °C (1560-1740 °F), at which austenite, with its high solubility for carbon, is the stable crystal structure. Hardening is accomplished when the high-carbon surface layer is quenched to form martensite [1,2]. As a result of this process a high-carbon martensitic case with good wear [4,5] and fatigue resistance [6,7] is superimposed on a tough low-carbon steel core.

      Carburizing steels for case hardening usually have base- carbon contents of about 0.2 wt.%, with the carbon content of the carburized layer generally being controlled between 0.8 and 1 wt.%. However, surface carbon is often limited to 0.9 wt.%, because so high carbon content can result in retained

      austenite and brittle martensite [6,8]. It has been reported [9] that the Martensite Finish Temperature (Mf) for carbon content greater than 0.65 wt.% value is below room temperature.

      It is well documented that many factors, such as time, temperature, and surface carbon influenced the final microstructure and properties of treated samples [10-15]. In contrast to the gas and liquid carburizing, solid carburizing is a minor commercial process. It requires more processing time. Obtaining greater case depths by increasing time cycles is costly due to increasing energy consumption [16]. Case depth can be increased exponentially by increasing the carburizing temperature, but this approach is also problematic in economic sense [17]. It has been reported that adding of some rock minerals [10, 18-21] or Rare Earths (RE) [22,23] in carburizer can accelerate the carburizing process. For example, Ogo et al.

      [18] observed that there was significant increase in the carburization rate of mild steel by the addition of river clam shell (mainly contains CaCO3) to charcoal. Jimenez et al. [19] reported that addition of carbonates (BaCO3 and Na2CO3) to the metallurgical coke gave rise to an increase in the carburization rate and case depth which allowed the achievement of the required carbon concentration profiles more efficiently. From the industrial point of view, it is essential to find out the best combination of carburizing parameters to attain the maximum case depth.

      One of the most common and classical approaches employed by many experimenters is One-Factor-At-a-Time (OFAT), in which one factor is varied while all other variables or factors in the experiment are fixed. The success of this approach depends on guesswork, luck, experience and intuition. Moreover, this type of experimentation requires large resources to obtain a limited amount of information about the process [24-29]. OFAT experiments often are unreliable, inefficient, time consuming [30] and may yield false optimum condition for the process. The major disadvantage of the OFAT strategy is that it fails to consider any possible interaction between the factors [24-29]. An interaction is the failure of the one factor to produce the same effect on the response at different levels of another factor [27].

      Statistical thinking and statistical methods play an important role in planning, conducting, analyzing and interpreting data in engineering experiments. When several variables influence a certain characteristic of a product, the best strategy is to design an experiment so that valid, reliable and sound conclusions can be drawn effectively, efficiently and economically [26,27,29]. This is an experimental strategy in which factors are varied together, instead of one at a time [27,29].

      It is widely accepted that the most commonly used experimental designs in experimentation are General Factorial Design of Experiment (GFDE). GFDE would enable an experimenter to study the joint effect of the factors on a response. In the present work, using GFED, an appropriate experimental procedure was designed to optimize the Effective Case Depth (ECD) of 1.5920 steel in the presence of activator material (i.e. Na2CO3). A model was then developed for predicting the ECD of this steel.

   2. EXPERIMENTAL PROCEDURE

      1. Exprimental

         The chemical composition of 1.5920 steel used in this work is listed in Table 1. To facilitate experimental works such as carburizing process and micro-hardness test, steel specimens were cut in the form of cubes with 3 cm in dimensions and thoroughly washed in acetone and allowed to dry. Pack carburizing boxes with 10×10×10 cm3 were made using low carbon steel sheets, whose thickness was 0.5 cm. An electric muffle furnace made in Iran was used.

         TABLE I. CHEMICAL COMPOSITION OF 1.5920 STEEL

         Elements	wt. %	Elements	wt. %
         C	0.210	Si	0.209
         Mn	0.900	Ni	1.823
         Cr	0.911	Cu	0.149
         Mo	0.027	Al	0.024
         P	0.011	S	0.004
         V	0.004	Fe	Rem.

         To prepare carburizing mixture, the used activator material (i.e. Na2CO3) was solved in hot water and then graphite powder was added to the solution. By agitation, the mixture was converted to gass form. Then, the mixture was subjected to sunlight until humidity was totally removed. In the present research, the mixtures were prepared with 0, 5, 10 and 15 wt.

         % pure Na2CO3. A single specimen was placed in the center of each box and the remaining space was filled carefully with the carburizing mixture. The box was covered with a lid and sealed with the fireclay to prevent air infiltration into the box during carburization. The box containing the test specimen was then placed in the central zone of the furnace, which was already at the required temperature of 925°C. Carburizing durations of 3, 5, 8 and 12 hrs were also used. At the end of each test, the box was taken out of the furnace and the sample was quenched in oil. Each test was repeated for at least three times. Vickers micro-hardness testing machine (model MHT.1; No: 8331) made by Matsuzawa Seiki Co Ltd of Japan was used. The carburized specimens were cut from the central region. The samples were then prepared for the micro- hardness test. The micro-hardness test was performed

         employing a Knoop indenter at every 0.1 mm from the edge of the samples to the center according to ASTM E384-99 standard. ECD was defined as the distance below the surface where the hardness was equal to 550 VHN [31,32].

      2. Design of experiment

      After a brainstorming session, two factors and their levels were chosen as independent input factors: Carburizing time and weight percent of Na2CO3. GFDE was selected as the experimental design method to identify the factors which have the sequence of significance of each effect. Factors and their levels are shown in Table 2. The experiments were performed in random order to ensure that uncontrolled factors did not influence the results [30,33,34]. The response variable of interest was to reach the maximum ECD. The design and statistical analysis of experiments was done by Design-Expert 7 (State-Ease, Inc., Trial version) software.

      TABLE II. SELECTED FACTORS AND THEIR LEVELS

      Factor	Symbol	Unit	Level 1	Level 2	Level 3	Level 4
      Carburizing time	A	hrs	3	5	8	12
      Na2CO3	B	wt. %	0	5	10	15

   3. RESULTS AND DISCUSSION

      Fig. 1 represents the hardness profiles as a function of distance from edge at various carburizing times and different amounts of the activator material. The values of ECD for different conditions extracted from these graphs are given in Table 3.

      Fig. 1. The hardness-distance curves for carburized samples with different amounts of energizer material (a) 0, (b) 5, (c) 10 and (d) 15 wt.%

      The results of the GFDE are presented in Analysis of Variance (ANOVA) table (Table 4) with a Confidence Interval (CI) of 99% for model. In statistics, CI is a kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. The level of confidence

      of CI would indicate the probability that the confidence range captures this true population parameter given a distribution of samples [26-28]. By considering half normal plot and normal

      plot (not show here), two main effects and one two-factor interactions all with CI over 90% were selected as significant

      In this model, t and E are time (hrs) and Na2CO3 wt. %, respectively. To convert from actual units to coded units the following equation (Eq. 2) must be used.

      X X

      factors for modeling. The effect of a factor is defined as the change in response produced by change in level of factor. This

      X coded Actual

      ( X Hi X Low ) / 2

      (2)

      is frequently called a main effect because it refers to primary

      factors of interest in the experiment [29]. ANOVA results for ECD shows a significant model with adequate precision of 65.105.

      TABLE III. GFED, EXPERIMENTAL SEQUENCES AND EXPERIMENTAL RESULTS

      Standard Order	Run Order	Factor A Carburizing time (hrs)	Factor B Na2CO3 wt.%	Response ECD (mm)
      1	9	3	0	0.14
      2	4	5	0	0.19
      3	16	8	0	0.25
      4	7	12	0	0.32
      5	12	3	5	0.18
      6	2	5	5	0.24
      7	14	8	5	0.32
      8	7	12	5	0.42
      9	8	3	10	0.65
      10	1	5	10	0.76
      11	5	8	10	0.80
      12	3	12	10	0.89
      13	11	3	15	0.47
      14	6	5	15	0.57
      15	15	8	15	0.64
      16	13	12	15	0.74

      TABLE IV. ANOVA TABLE WITH CI OF OVER 90% FOR FACTORS

      Source	Sum of squares	Degree of freedom	Mean square	F value	P-value Prob> F
      Model	0.93	5	0.19	504.66	<0.0001
      A	0.11	1	0.11	309.35	<0.0001
      B	0.44	1	0.44	1205.48	<0.0001
      AB	0.0014	1	0.0014	3.83	0.0787
      B2	0.055	1	0.055	149.86	<0.0001
      B3	0.023	1	0.023	627.17	<0.0001
      Residual	0.0036	10	0.00036	—–
      Cor Total	0.93	15	—-

      Adequate precision compares the range of the predicted values at the design points to the average prediction error. On the other hand, adequate precision measures the signal to noise ratio and a ratio greater than 4 is desirable [25]. Here, the value of the ratio is greater than 4, and then it represents the adequate model for predicting the results within design space without doing any further experiments. The analysis of the regression coefficients of the polynomial model describing the relationship between the response and factors, in terms of coded forms, is shown as Eq. 1.

      Where X Actual , , X ,X Hi , X Low are actual, mean, higher and lower values of the levels [25].

      Sum of Squares (SS) of each factor quantifies its

      importance in the process and as the value of the SS icreases the significance of the corresponding factor in the undergoing process also increases. As shown in ANOVA table (Table 4), the effect of factor B is the strongest and then B3, A, B2 and interaction of A and B (AB), respectively. If we consider the model equation in actual terms, one can found that effect of A, AB and B2 are positive (synergistic effect). B and B3 have negative (antagonism) effect on ECD. For increasing ECD, the positive effect should be ascended and negative effect should be descended.

      The quality of fittings of the equations was expressed by the coefficient of regression "Adjusted R-squared" or in better way by "Predicted R-squared". The "Adjusted R-squared" values indicate variability in the observed response values which can be explained by the experimental factors and their interactions. The "Predicted R-Squared" and "Adjusted R- Squared" values are closer to 1, the better fitting is achieved [35]. The "Predicted R-Squared" of 0.9896 is in reasonable agreement with the "Adjusted R-Squared" of 0.9941. The Model F-value of 504.66 implies that the model is significant (Fmodel = 504.66 >> Ftable (5,10) = 10.48) and there is only a 0.01% chance that a "Model F-Value" could occur due to noise. F-Value is the test for comparing the variance associated with that term with the residual variance. It is the mean square for a term divided by the mean square for the residual. This term should be as large as possible [25]. Tables of F-value (a,b) for different confidence intervals exist in statistical references [24], where, the first number in parenthesis is the parameter or model degree of freedom and the second one is errors degree of freedom. To categorize the parameter or the model as a significant value, calculated F- value must be more than its value in the statistical tables. If the calculated value of F is greater than that in the F table at a specified probability level, a statistically significant factor or interaction will be obtained [27]. This model (Eq. 1) can be used to navigate the design space. The relationship between the actual and predicted values that are shown in Fig. 2 is a confirmation for navigation power of the model. As can be seen in Fig. 2, level 2 and 3 of the factor B resulted in higher and less scattered data than other levels. The perturbation plots (not shown here) also confirm these results.

      Fig. 3 shows the 3D plot of ECD, as a function of time and Na2CO3 wt. %. The surface plot allowed the whole range of conditions to be explored, including the combinations that were not experimentally demonstrated. A greater ECD, in practice, may follow a longer analysis time, which the results show that is not very important factor in our work. In this

      ECD(mm) 0.56 0.11t 0.8E 0.017t.E 0.13E2 0.60E3

      (1)

      work, the optimum condition was achieved at Na2CO3 content

      of 11.5 wt. %., and in this range, time had not so important effect.

      The confirmation experiments were conducted at A: 12 hrs

      Na2CO3 as an activator material is decomposed at elevated temperatures and produces CO2 (reaction 6).

      and B: 11.5 wt. % for 3 times. From these experiments, the amount of ECD was obtained equal to 0.96 mm. If the average

      Na2CO3 Na2O CO2

      (6)

      of the results of the confirmation is within the limits of the CI, then the significant factors as well as the appropriate levels for obtaining the desired results are properly chosen [26-29]. The predicted range of ECD is 0.98 ± 0.05 mm, then the response (ECD = 0.96 ± 0.01 mm) is in 99% CI range and this model can be used to navigate within the design space.

      By producing CO2 in the pack, the pressure of CO2 increases. According to reaction 4, CO2 reacts with carbon atoms present in the pack and produces CO. Fig. 4 shows the equilibrium diagram for reaction 5 at any temperature [1].

      Fig. 4. Equilibrium pressure of CO and CO2 for

      Fig. 2. Predicted vs. actual values. Numbers indicate the level of factor B. For example, number 2 indicates that the amount of factor B is 5 wt.%.

      2CO CO2 Catom reaction [1]

      Fig. 3. Graphical representation of the ECD as a function of carburizing time) and Na2CO3 wt. %.

      The carburizing pack contains some air. The oxygen in the pack's air combines with carbon at elevated temperatures and produces CO2 (reaction 3). Then CO2 reacts with carbon atoms present in the pack, and CO is produced (reaction 4). CO decomposes on the steel surface into atomic carbon and CO2 (reaction 5). The atomic carbon (Catom) is quickly absorbed at the metal surface and diffuses into the metal. Again, according to reaction 4, the re-produced CO2 reacts with more carbon to produce more CO [12,18].

      According to Fig. 4, if the ratio of CO to CO2 at a constant temperature is more than the equilibrium ratio of CO to CO2, reaction 5 goes in the right direction, and the carburizing phenomenon happens. However, when the ratio of CO to CO2 at a constant temperature is less than the equilibrium ratio of CO to CO2, reaction 5 goes in the left direction, and the decarburizing phenomenon happens. When carbon diffuses into steel, the carbon content in the surface increases compared to the core of the steel, so that after quenching the steel in the oil, the hardness of the surface increases and the core remains flexible. According to Fig. 3 by increasing activator material up to 11.5 wt. %, ECD value was increased and then declined. In other words, up to 11.5 wt.% activator, the pressure ratio of CO to CO2 in the carburizing box is more than the equilibrium ratio of CO to CO2. In fact, up to this amount, the activator material decomposes continuously and according to reaction 6, the pressure of CO2 in the carburizing pack increases continuously. The produced CO2 gas reacts with the carbon atoms within the pack according to reaction 4 and CO gas is produced. CO causes carburizing phenomenon on exceeds this amount, decarburizing phenomenon happens and the case depth decreases. In this situation, more Na2CO3 is decomposed, and more CO2 gas is produced. A small amount of CO2 gas enters reaction 4 and produces CO, and a tremendous part of this gas causes oxidation in the box

      C O2 CO2

      CO2 C 2CO

      2CO CO2 Catom

      (3)

      (4)

      (5)

      environment. As a result, CO2 attracts atomic carbon from the surface of steel according to reaction 7.

      CO2 Catom 2CO

   4. CONCLUSIONS

(7)

1. S.R. Elmi Hosseini, The effect of carburizing time on the case layer depth of AISI 8620 cemented steel, 4th National Symposium of Heat Treatment, Isfahan, Iran, 2009.

2. S.R. Elmi Hosseini, The effect of various processes of surface hardening on the hardenability of DIN 18CrNi8 steel, 12th National Conference of Surface Engineering, Isfahan, Iran, 2011.

3. M.F. Yan, T.W. Pan, and Z. Liu, The effect of rare earth catalyst on

Pack-carburization of 1.5920 cementation steel in the presence of Na2CO3 as an activator material was investigated using General Factorial Design of Experiment (GFDE). The conclusions drawn from the results can be summarized as follows:

1. The optimum condition was achieved when Na2CO3 11.5wt.% and in this range, time had not so important effect.

2. The maximum ECD was obtained using 11.5 wt. % activator materials (Na2CO3) for the carburizing time of 12 hrs.

3. At the constant time, by increasing the Na2CO3 content from 5 to 11.5 wt. %, the Effective Case Depth (ECD) increases due to the carburizing phenomenon and afterwards decreases due to the decarburizing phenomenon.

REFERENCES

1. G. Krauss, Microstructure and properties of carburized steel, In: Metals handbook, Heat treating, vol. 4. Materials Park, OH: ASM International, 1991, pp. 363-375.

2. G. Parrish, Carburizing: microstructures and properties, Materials Park, OH:ASM International, 1999.

3. T.M. Loganathan, J. Purbolaksono, J.I. Inayat-Hussain, and N. Wahab, Effects of carburization on expected fatigue life of alloys steel shafts, Mater. Des., vol. 32, pp. 3544-3547, 2011.

4. M. Izciler, and M. Tabur, Abrasive wear behavior of different case depth gas carburized AISI 8620 gear steel, Wear, vol. 260, pp. 90-98, 2006.

5. L. Ceschini, C. Chiavari, E. Lanzoni, and C. Martini, Low- temperature carburized AISI 316L austenitic stainless steel: Wear and corrosion behavior, Materi. Des., vol. 38, pp. 154-160, 2012.

6. O. Asi, A.C. Can, J. Pineault, and M. Belassel, The effect of high temperature gas carburizing on bending fatigue strength of SAE 8620 steel, Mater. Des., vol. 30, pp. 1792-1797, 2009.

7. O. Asi, A.C. Can, J. Pineault, and M. Belassel, The relationship between case depth and bending fatigue strength of gas carburized SAE 8620 steel, Surf. Coat. Technol., vol. 201, pp. 5979-5987, 2007.

8. M.M.A. Bepari, and K.M. Shorowordi, Effects of molybdenum and nickel additions on the structure and properties of carburized and hardened low carbon steels, J. Mater. Proc. Technol., vol. 155-156, pp. 1972-1979, 2004.

9. D.S. Clark, W.R. Varney, Physical Metallurgy for Engineers, Second Ed., Van Nortland Company, New York, 1962.

10. A. Oyetunji, and S.O. Adeosun, Effects of Carburizing Process Variables on Mechanical and Chemical Properties of Carburized Mild Steel, J Basic & Applied Sci., vol. 8, pp. 319-324, 2012.

11. M. Tsujikawa, S. Noguchi, N. Yamauchi, N. Ueda, and T. Sone, Effect of molybdenum on hardness of low-temperature plasma carburized austenitic stainless steel, Surf. Coat. Technol., vol. 201, pp. 5102-5107, 2007.

12. S.R. Elmi Hosseini, and H. Khosravi, Determination of Case Layer Depth of a Low Carbon Steel after Carburizing Process by Numerical Method, International Conference on Materials Heat Treatment, Islamic Azad University, Majlesi Branch, Isfahan, Iran, 2010.

13. M. Erdogan, and S. Tekeli, The effect of martensite particle size on tensile fracture of surface carburized AISI 8620 steel with dual phase core microstructure, Mater. Des., vol. 23, pp. 597-604, 2002.

carburizing kinetics in a sealed quench furnace with endotermic atmosphere, Applied Surf. Sci., vol. 173, pp. 91-94, 2001.

1. G. Parrish, Carburizing: Microstructure and Properties, ASM International, 1999.

2. D.U.I. Ogo, T. Ause, and E.J. Ibangal, The Use of River Clam Shells as an Energizer in Case Carburization of Mild Steels, ISIJ Int., vol. 44, pp. 865-868, 2004.

3. H. Jimenez, M.H. Staia, and E.S. Puchi, Mathematical modeling of a carburizing process of a SAE 8620H steel, Surf. Coat. Technol., vol. 120-121, pp. 358-365, 1999.

4. S.R. Elmi Hosseini, and H. Khosravi, The effect of sodium carbonate content as energizer material on the case depth of 1.5920 low carbon steel, Majlesi J Mater. Eng., vol. 3, pp. 51-58, 2009.

5. S.R. Elmi Hosseini, H. Khosravi, and E. Ghaderi, Comparison between the effect of excess air and the activator material on the hardenability of DIN 18CrNi8 steel in solid carburizing process, Majlesi J. Mater. Eng., vol. 3, pp. 49-57, 2009.

6. Z.X. Yuan, Z.S. Yu, P. Tan, and S.H. Song, Effect of rare earths on the carburization of steel, Mater. Sci. Eng. A, vol. 267, pp. 162-166, 1999.

7. M.F. Yan, Study on absorption and transport of carbon in steel during gas carburizing with rare-earth addition, Mater. Chem. Phys., vol. 70, pp. 242-244, 2001.

8. M.J. Anderson, and P.J. Whitcomb, DOE Simplified: Practical Tools for Effective Experimentation, First Ed., Portland: Productivity Inc, New York, 2000.

9. Software helps Design-Expert Software, Version 7.1, User's guide, Technical Manual, Stat-Ease Inc., Minneapolis, MN, 2007.

10. J. Antony, Design of Experiment for Engineers and Scientists, First Ed., Elsevier Science & Technology Books, 2003.

11. D.C. Montgomery, Design and Analysis of Experiments, Fifth Ed., John Wiley & Sons Inc., New York, 2000.

12. A. Dean, and D. Voss, Design and Analysis of Experiments, First Ed. Springer text in statics, 1999.

13. [29] Gottipati R., Mishra S., Process optimization of adsorption of Cr(VI) on activated carbons prepared from plant precursors by a two- level full factorial design, Journal of Chemical Engineering 160, 2010, 99-107.

14. Y. Song, D. Kim, and Y. Park, Statistical optimization of Rhodamine B removal by factorial design using reaction rate constant in electrochemical reaction, J. Chem. Eng., vol. 28, pp. 156-163, 2011.

15. L.D. Liu, and F.S. Chen, The influences of alloy elements on the carburized layer in steels using vacuum carburization in an acetylene atmosphere, Mater. Chem. Phys., vol. 82, pp. 288-294, 2003.

16. S.R. Elmi Hosseini, Simulation of Case Depth of Cementation Steels According to Fick's Laws, J Iron and Steel Res., Int. vol. 19, pp. 71- 78, 2012.

17. Metals Handbook Welding, Brazing and soldering ASM, vol. 6, 9th Ed., Metals Park, Ohio, 1989.

18. T. Alizadeh, An imprinted polymer for removal of Cd2+ from water samples: optimization of adsorption and recovery steps bye experimental design, J. Polymer Sci., vol. 29, pp. 658-669, 2011.

19. S. Costa, M. Barroso, A. Castanera, and M. Dias, Design of experiments, a powerful tool for method development in forensic toxicology: application to the optimization of urinary morphine 3- glucuronide acid hydrolysis, Anal. Bioanal. Chem., vol. 396, pp. 2533-2542, 2010.