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Carbonitriding—Fundamentals, Modeling and Process Optimization
Report 13-02
Research Team: Liang He [email protected]
Yuan Xu [email protected]
Xiaolan Wang [email protected]
Mei Yang [email protected] (508) 353-‐8889
Richard D. Sisson, Jr. [email protected] (508) 831-‐5335
Focus group:
1. Project Statement
Objectives Develop a fundamental understanding of the process in terms of:
• The diffusion of nitrogen in the steel depends on the nitrogen gradients as well as the carbon and other alloying element concentrations and gradients. The carbon content and gradients will have a significant influence on the nitrogen activity and therefore diffusivities. A fundamental understanding of the thermodynamics of solutions of carbon and nitrogen in alloyed austenite is necessary as well as the effects on diffusion of carbon and nitrogen.
• The effect of nitrogen on the hardenability of carburized steels will be determined. Nitrogen stabilizes austenite and increases the hardenability by moving the TTT diagram to longer times. The effects of nitrogen content on these phenomena will be determined.
• Determine the process control requirements for Carbonitriding in terms of temperature, atmosphere composition measurement and times based on the precision and accuracy required to control the process.
Develop a computational model to determine the carbon and nitrogen concentration profiles in the steel in terms of temperature, atmosphere composition (ENDOGAS + NH3), steel surface
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condition, and alloy composition. This tool will be designed to predict the carbon and nitrogen profiles based on the input of the process parameters of temperature (time), and atmosphere composition (time). Boost and diffuse cycles will be included.
• CarbTool© will be modified to create CarboNitrideTool©, a software that will simulate the carbonitriding process, by adding the nitrogen absorption and diffusion in austenite with concomitant carbon uptake and diffusion. The fundamentals of these phenomena as described above will be used for the model generation. The model will include multiple cycles.
• Verify the model by comparison with experimental results. The verification will initially be conducted by comparison with results in the literature and results from CHTE member companies. Selected experiments will also be conducted to test the model’s accuracy and capabilities.
• Develop a model-based optimization process to determine the optimum process parameters for several process goals: minimum cycle time, minimum cost, maximum productivity, and minimum gas consumption.
Strategy The objectives will be achieved by completing the following tasks.
• Task 1. Literature review
o Carbonitriding practices in industry o NH3 – endogas thermodynamics o Diffusivities of carbon and nitrogen in steel o N adsorption, decomposition and absorption o Hardenability of steels as a function of nitrogen and carbon contents o Control of carbonitriding systems
• Task 2. Determine the boundary conditions and diffusivities of nitrogen and carbon for
simulation tool development
o Flux o Mass transfer coefficient o Diffusivities of nitrogen and carbon in steel
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• Task 3. Modify Carbtool© for carbon and nitrogen absorption and diffusion to create CarboNitrideTool©
• Task 4.Verify computer model
o Literature data o Selected experiments
• Task 5.Develop optimization methods for Carbonitriding
o Minimum cycle time o Minimum cost
• Task 6. Test optimization methods
Deliverables • Literature review
• CarboNitrideTool©
• Optimization method
2. Executive Summary
The increased understanding of the carbonitriding process when combined with the new process model (i.e. CarboNitrideTool©) will provide the heat treater with new opportunities to determine the process parameters and control strategy to minimize cycle times and cost while enhancing the quality of the products. The recommendations for measurement techniques of atmosphere content and steel surface condition will provide the opportunity for improved quality and productivity of the carbonitriding process.
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3. Achievements in this semester
o Performed the microhardness profile measurement of all samples; o Improved CarboNitrideTool©; o Finished the final project report.
3.1 Carbonitriding experiments
3.1.1 Experimental Plans and Procedures
The AISI 8620 and AISI 1018 steels were used in the experiments. Both steels are commonly
used for carburizing and carbonitriding case-hardened processes. Table 1 shows the chemical
compositions of these two steels.
Table 1: Compositions of AISI 8620 and AISI 1018 (in wt %)
C Mn P S Si Ni Cr Mo
8620 0.18-0.23 0.7-0.9 0.035(max) 0.04(max) 0.15-0.3 0.4-0.7 0.4-0.6 0.15-0.25
1018 0.15-0.20 0.60-0.90 0.04 (max) 0.05(max) ---- ---- ---- ----
The samples were made from cylindrical steel bar by cutting it into disks with a diameter of
1.25 inches and thickness of 0.4 inch. The surface of samples were grinded with sand paper
before carbonitriding, to remove rust on the surface, and after grinding the samples were washed
by acetone to remove any organic compounds.
Both AISI 8620 and AISI 1018 samples were placed in the furnace with an endothermic
enriched atmosphere and carbonitriding atmosphere at 850℃ or 800℃ for 2 hours. The carbon
potential of endothermic gas was maintained at 0.9% for the entire process. During the last 15 or
45 minutes, ammonia was introduced into the furnace. The processes are shown in Figure 1
According to the experimental plan, 14 groups of samples for each steel, i.e., totally 28 groups of
samples have been prepared, and every group has 5 samples (Table 2).
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Figure 1 Experimental Process
Table 2: Experiments design for each steel
3.1.2 Experimental results Carbon concentration and nitrogen concentration were analyzed with SPECTRO MAXX and microhardness was measured with SHIMADZU HMV-2000 and BUEHLER 1600-6300. Surface
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retained austenite was analyzed with Panalytical PIXcel3D X-ray diffraction instrument. Also, the weight gain during carbonitriding process was measured with the scale, Mettler H54AR, with an accuracy of 0.1mg. Samples were weighed before and after carbonitriding. 3.1.2.1 Optical Emission Spectroscopy (OES) results
The OES was used to measure the concentration of carbon and nitrogen. The depth of each OES burn is approximately 40 µm. The depth of carbon diffusion is approximately 500 µm and the depth of nitrogen diffusion depends on the intensity and time of ammonia addition.
The measurement results are listed in Appendix A. From the measurement results, it can be concluded that 1) more nitrogen will be introduced into the steel surface with more and longer ammonia addition into the furnace atmosphere; 2) more carbon will be transferred into the steel surface with more nitrogen in the steel surface; 3) higher temperature helps the absorption of carbon and nitrogen into the steel surface.
3.1.2.2 Microhardness measurement results
All the measurement results for the microhardness are shown in Appendix B. Figure 2 presents some microhardness measurement results. It can be seen that more and longer ammonia addition increases sample hardness.
Figure 2 Microhardness (HV) and C&N concentrations (wt%) vs depth from sample surface (µm)
(Material: AISI 1018 Temperature: 850°C)
0
100
200
300
400
500
600
700
800
900
1000
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500 600
Vickers h
ardn
ess
Weight p
ercent of carbo
n or nitrogen
Carbon -‐ 0% NH3
Nitrogen -‐ 0% NH3
carbon -‐ 5% NH3 15min
Nitrogen -‐ 5% NH3 15min
Carbon -‐ 15% NH3 45min
Nitrogen -‐ 15% NH3 45min
Hardness -‐ 0% NH3
Hardness -‐ 5% NH3 15min
Hardness -‐ 15% NH3 45min
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From Figure 2, the microhardness of first test point is always smaller than the measurement result of the second test point. The possible reasons are: 1) during the microstructure hardness test, the edge part always takes larger deformation with the load pressure because of edge effect; and 2) in steel, nitrogen and carbon are always considered as the austenite stabilizers, and there are more carbon and nitrogen at the sample surface, which help to produce more retained austenite and decrease the surface microhardness.
3.1.2.3 Discussion on retained austenite at the sample surface
The heat treatment of steels by quenching and tempering to produce a martensitic structure involves three basic steps which include: 1) Austenitizing – The process in which the steel is heated into the red-heat temperature range where it will become a single-phase mixture of face-centered cubic iron with the carbon dissolved into solution. This phase of steel is known as austenite and important parameters during this stage include heating rate, final holding temperature and time at temperature. 2) Quenching – The stage in which the austenite is quickly cooled to room temperature or below. This stage is designed to convert the austenite to a new single-phase of carbon in iron known as martensite. The crystal structure of martensite is body centered tetragonal and its formation is diffusion controlled phases such as bainite, and important parameters include cooling rate and final quench temperature. 3) Tempering – The process of heating the martensitic steel to temperatures below its critical temperature for the purposes of decomposing the martensitic structure. Changes that take place during this step include stress relief of the microstructure, decomposition of the martensite to tempered martensite and transformation of retained austenite to other products.
While austenite is the stable phase of steel at high temperature, it is an unstable phase at room temperature where it is termed to as retained austenite. Retained austenite is most often produced during the heat treatment of plain carbon steels with carbon contents greater than 0.4% or in alloy steels with significant alloy contents. Typically most of the austenite transforms to martensite upon quenching. In practice, however, this does not always happen with some steels, as the steel must be quenched to below a certain characteristic temperature known as the martensite finish temperature, Mf, in order to complete the austenite to martensite transformation. The martensite finish temperatures in many steels such as high carbon and/or alloy steels is often low enough to retain some of this austenite at room temperature.
In general, the amount of retained austenite that will exist in a martensitic structure quenched to a given temperature is dependent on the martensite finish temperature of the alloy and the lowest temperature to which it was quenched. An often used expression for the amount of retained austenite is given by:
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% RA =exp-0.011(Ms-Tq)×100%[16] where Tq is the temperature of quench in degrees centigrade and Ms is the martensite start temperature which is often given by:
Ms(degree C)=539-423(%C)-30.4(%Mn)-12.3(%Cr)-17.7(%Ni)-7.5(%Mo) [16] where % is the weight percent of the alloy elements.
There are some other Ms temperature calculation methods:
Stevens and Haynes Ms(degree C)= 561-474(%C)-33(%Mn)-17(%Ni)-17(%Cr)-21(%Mo) [17] Stuhlmann For high alloy and medium alloy steels Ms(degree C)=550-350(%C)-40(%Mn)-20(%Cr)-10(%Mo)-17(%Ni)-8(%W)-35(%V)
-10(%Cu)+15(%Co)+30(%Al) [17] For the relationship between RA percent and Ms, Fig. 3 gives two methods from ref [16] and
ref [17].
Figure 3 Relations which allow estimation of the amount of retained austenite from the chemical composition for different
steels [17]
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Figure 4 Surface XRD test results on the carbonitrided AISI 1018 samples
In order to determine the retained austenite at the sample surface, XRD analysis method was
performed. Some of the XRD measurement results on sample surface for AISI 1018 at 850℃ with Cr radiation are shown in Figure 4, and the scan range (2θ) is from 60° to 163°. By using the direct comparison method, the percentages of retained austenite for different samples were calculated and listed in Figure 4.
From the XRD measurement results, it could be conclude that the effect from nitrogen should not be ignored for carbonitrided steel and need to be considered in the prediction of microstructure and hardness during the carbonitriding process of steels.
3.1.2.4 Weight gain measurement results
0
2000
4000
6000
8000
10000
12000
14000
16000
60 80 100 120 140
Inte
nsity
(cou
nt)
2θ (degrees)
No Ammonia Addition (RA: 37%)
15min of 10% Ammonia Addition (RA: 45%)
45min of 15% Ammonia Addition (RA: 53%)
(111γ）
(110α）
(200γ） (200α） (220γ）
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The weight gain during carbonitriding was measured by using the scale, Mettler H54AR, with an accuracy of 0.1mg. Samples were weighed before and after carbonitriding. Test group number is listed in Table 3.
Table 3: Test group number
Test Group Number Process Parameters 1 0 NH3 addition 2 5% NH3 addition in 15 min 3 5% NH3 addition in 45 min 4 10% NH3 addition in 15 min 5 10% NH3 addition in 45 min 6 15% NH3 addition in 15 min 7 15% NH3 addition in 45 min
Figure 5 and Figure 6 present the comparisons of total weight gains with various nitriding
intensity and time. From the weight gain measurement results, it can be seen that more and longer ammonia addition brings more weight gain. Higher temperature is helpful to increase the weight gain. Also, no obvious difference is found with same ammonia addition condition for different steels and it presents that the carbonitriding process is more like boundary condition controlled process. The measurement results were used to help the determination of boundary conditions for the diffusion simulation in carbonitriding process.
Figure 5 Weight gain comparison for different steels at the same temperatures.
0
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7
850℃
800℃
1018 Weight gain (g)
Test group number
0
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7
850℃
800℃
8620 Weight gain (g)
Test group number
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Figure 6 Weight gain comparison for same steel at 800℃ and 850℃ .
3.2 Tempering process To investigate the post carbontiriding treatment, a series of tempering experiments were
conducted (see Table 4). Two carbonitriding samples, i.e. 10% NH3 addition in 15mins and 15% NH3 addition in 45mins, were tempered at 300°F, 350°F, and 400°F for 2h to investigate the effects of temperature on the hardness of the carbonitrided samples. The tempering processes at 350°F for two 2hrs were also conducted to investigate the time effect of the tempering process.
Table 4 : The tempering experiments for carbonitrided samples
Material Carbonitriding
Tempering
Temperature (°F)
Time (hours)
AISI 8620
10% NH3 addition in 15MIN 15% NH3 addition in 45MIN
300 2
350 2
2+2
400 2
0
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7
850℃ Weight gain (g)
Test group number
0
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7
800℃ Weight gain (g)
Test group number
12
The carbon and nitrogen concentration profiles were measured for the carbonitrided samples. And the microhardness profiles were also measured for the tempered samples.
The microhardness profiles were plotted in Figure 7. It shows that tempering process decreases the hardness for the same depth with the tempering temperature increasing. The hardness decreases further with the increase of the tempering time. This is due to transformation from Martensite to ferrite and carbides during the tempering process. Surface carbon and nitrogen concentrations can be measured by spectral analysis on the OES (Optical Emission Spectroscopy). The carbon and nitrogen concentration profiles are obtained by removing thin layer (60-80µμm) of the sample as shown in Figure 8. The 3-D carbon and nitrogen concentration profiles were shown in Figure 9 plotted with MATLAB.
Based on the hardness profiles nitrogen, concentration profile, and carbon concentration profiles, the 3-D microhardness profiles as the function of carbon and nitrogen concentration can be plotted as shown in Figure 10, which were plotted with MATLAB.
The 3-D carbon and nitrogen concentration profiles were shown in Figure 11 plotted with MATLAB. The 3-D carbon and nitrogen concentration profiles were shown in Figure 12 plotted with MATLAB.
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Figure 7 The microhardness profiles for 10%NH3 15minutes and 15%NH3 45minutes carbonitrided AISI 8620 samples with
tempering at 300°F for 2 hours, 350°F for 2 hours, 400°F for 2 hours and 350°F for 2 hours + 350°F for 2 hours
300
400
500
600
700
800
900
0 200 400 600 800 1000
Vickers H
ardn
ess
Depth (micrometer)
AISI 8620 10% NH3 15MIN
Origin
300F
350F
400F
350F+350F
300
400
500
600
700
800
900
0 200 400 600 800 1000
Vickers H
ardn
ess
Depth (micrometer)
AISI 8620 15% NH3 45MIN
Origin
300F
350F
400F
350F+350F
for 2 hrs
for 2 hrs
for 2 hrs
350F for 2 hrs+350F for 2 hrs
for 2 hrs
for 2 hrs
for 2 hrs
350F for 2 hrs+350F for 2 hrs
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Figure 8 The nitrogen and carbon concentration profile for 10%NH3 15minutes and 15%NH3 45minutes carbonitrided AISI
8620 samples.
0 100 200 300 400 500 6000.2
0.4
0.6
0.8
wt%
C
Depth (micrometer)
10% NH3 15MIN Concentration
0 100 200 300 400 500 6000
0.05
0.1
0.15
wt%
N
0 50 100 150 200 250 300 350 400 450 5000
0.5
1
wt%
C
Depth (micrometer)
15% NH3 45MIN Concentration
0 50 100 150 200 250 300 350 400 450 5000
0.2
0.4
wt%
N
15
Figure 9 The 3-‐D nitrogen and carbon concentration profile for 10%NH3 15minutes and 15NH3 45minutes carbonitrided AISI
8620 samples.
00.05
0.10.15
0.2
0.20.3 0.4
0.50.6
0.7
0
100
200
300
400
500
600
wt% N
10% NH3 15MIN Concentration
wt% C
Dept
h (m
icro
met
er)
00.1
0.20.3
0.4
0.20.3
0.40.5
0.60.7
-500
0
500
1000
1500
wt% N
15% NH3 45MIN Concentration
wt% C
Dept
h (m
icro
met
er)
16
Figure 10 The 3-‐D microhardness profile as the function of nitrogen and carbon concentration for 10%NH3 15minutes and
15%NH3 45minutes carbonitrided AISI 8620 samples.
00.05
0.10.15
0.2 0.2 0.3 0.4 0.5 0.6 0.7
450
500
550
600
650
700
750
800
850
wt% C
10% NH3 15MIN Hardness vs. Concentration
wt% N
Mic
roha
rdne
ss H
V
0 0.1 0.2 0.30.4 0.5 0.2
0.4
0.6
0.8
1
300
400
500
600
700
800
wt% C
15% NH3 45MIN Hardness vs. Concentration
wt% N
Mic
roha
rdne
ss H
V
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Figure 11 The microhardness profiles as the function of nitrogen and carbon concentration for 10%NH3 15minutes and
15%NH3 45minutes carbonitrided AISI 8620 samples with tempering at 300°F for 2 hours, 350°F for 2 hours, 400°F for 2
hours and 350°F for 2 hours + 350°F for 2 hours.
0
0.1
0.2 0.2 0.3 0.4 0.5 0.6 0.7
400
450
500
550
600
650
700
750
800
wt% C
10% NH3 15MIN Hardness vs. Concentration
wt% N
Mic
roha
rdne
ss H
V300F
350origin400F
350+350
0 0.1 0.2 0.3 0.4 0.5 0
0.5
1350
400
450
500
550
600
650
700
750
wt% C
15% NH3 45MIN Hardness vs. Concentration
wt% N
Mic
roha
rdne
ss H
V
350F+350F300F
350F
400Forigin
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Figure 12 The 3-‐D microhardness profiles as the function of nitrogen and carbon concentration for 10%NH3 15minutes and
15%NH3 45minutes carbonitrided AISI 8620 samples with tempering at 300°F for 2 hours, 350°F for 2 hours, 400°F for 2
hours and 350°F for 2 hours + 350°F for 2 hours.
00.1
0.20.2 0.3 0.4 0.5 0.6 0.7
400
450
500
550
600
650
700
750
800
850
900
wt% Nwt% C
10% NH3 15MIN Hardness vs. Concentration
Mic
roha
rdne
ss H
V
origin
300
350
400
350+350
0 0.1 0.2 0.3 0.4 0.500.5
1300
400
500
600
700
800
900
wt% N
15% NH3 45MIN Hardness vs. Concentration
wt% C
Mic
roha
rdne
ss H
V
origin300F
350F400F
350F+350F
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3.2 CarboNitrideTool© Development
3.2.1 CarboNitrideTool©
CarboNitrideTool© is an extension of CarbTool©. The user interfaces are presented in Figure
13 and Figure 14. The carbon and nitrogen concentration profiles can be predicted based on the
user-defined initial conditions and the process parameters.
Figure 13 Material properties Figure 14 Process parameters
3.2.2 Surface boundary conditions
In CarboNitrideTool©, the carbon boundary condition will be the flux balance at the interface
with a surface mass transfer coefficient used in CarbTool© for gas carburizing. The boundary
condition for the calculation of nitrogen diffusion is assumed to be a constant flux condition.
These conditions are presented in Figure 15.
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Figure 15 Schematic representation of carbon & nitrogen transport in CarboNitrideTool©
The gas carbonitriding process of steel is analogous to diffusion in vapor-solid diffusion
couple, and was modeled using parabolic governing PDE for carbon and nitrogen diffusion in
steel:
!"!"= !
!"𝐷 !"!"
(Eq 1)
where D is the coefficient of carbon diffusion in steel, x is the distance from the surface.
The boundary condition is specified by assuming a mass balance at the steel surface:
𝛽 𝐶! − 𝐶! = −𝐷 !"!"
(Eq 2)
where ∂C ∂x is the carbon concentration gradient at the surface and β is the mass transfer
coefficient (in centimeters per second), CP is the carbon potential in the gas phase, and CS is the
carbon concentration in the solid.
To model the carbon diffusion process, Eq 1 was solved numerically using flux balance
condition (Eq 2). The mass transfer coefficient, as defined in Eq 2 accounts for all of the
phenomena at the phase boundary between gas atmosphere and steel. Therefore, the two primary
Atmosphere
PC
NJ
SC
XC
OCSN
XNON
x
β
Interface
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parameters governing carburizing are the mass transfer coefficient (𝛽) and carbon diffusivity (D)
in austenite.
From the flux balance condition at the steel interface and the continuity equation of the mass
accumulation within the solid, the rate at which the total mass of the solid changes per unit cross
section area is:
𝐶 𝑥, 𝑡 𝑑𝑥 = 𝐽𝑑𝑡!!!!
= ∆!!
!!!!
(Eq 3)
where m is the mass and A is the surface area of the workpiece.
The total quantity of the species diffusing through the surface is found by integrating the
concentration profile over the depth of the carburized layer. Further differentiation of the total
weight gain by the steel over the carburizing time yields the following expression for the total
flux of carbon atoms through the vapor-solid interface:
𝐽! = ! ∆! !!"
= 𝛽 𝐶! − 𝐶!! (Eq 4)
Assuming a time-dependent nature for the process, the mass transfer coefficient can be found
as:
𝛽! =!!" ! !,! !"!!
!!!!!!!
! =∆! ! |!!→!! !!!!!
! (Eq 5)
If weight gain is expressed in grams per square centimeter, time in seconds, and carbon
concentration in grams per cubic centimeter, the calculated mass transfer coefficient is expressed
in centimeters per second. From Eq 5, the data needed for the calculation include: total carbon
obtained over process time; and time evolution of the surface carbon concentration. In order to
develop CarboNitrideTool©, a series of experiments were designed. From the experiment results,
the mass transfer coefficient, β, for the specific carbonitriding furnace used for the experiments
is calculated to be 4.0×10!!cm/s.
For nitrogen absorption, nitrogen potential in carbonitriding furnace atmosphere cannot be
calculated according to the chemical thermodynamics. The mass flux on the atmosphere-steel
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interface is used in CarboNitrideTool. The flux is determined with the process temperature and
atmosphere composition. The following equation is used to define the boundary:
J!|!!! = −D|!!! ∙!!!!|!!! (Eq 6)
where JN is the constant nitrogen inflow flux at the surface during the carbonitriding process.
It is assumed that the amount of nitrogen produced by the surface reactions is equal to the mass
flow rate for diffusion described by Fick’s first law. JN was acquired by integrating the nitrogen
concentration profile and is affected by temperature and furnace atmosphere composition. The
calculated results are listed in Table 5 and it can be concluded that higher temperature helps to
get higher nitrogen inflow flux and the ammonia percentage in furnace atmosphere also increases
the nitrogen inflow flux.
Table 5: Calculated nitrogen fluxes (g/cm2/s) from experiment results
Ammonia addition conditions AISI 1018 AISI 8620 800OC 850OC 800OC 850OC
No NH3 addition 0 0 0 0 5% NH3 addition in 15 min 1.14E-07 1.58E-07 1.21E-07 1.80E-07
10% NH3 addition in 15 min 1.17E-07 1.89E-07 1.13E-07 1.91E-07 15% NH3 addition in 15 min 1.12E-07 1.97E-07 1.37E-07 2.18E-07
3.2.3 Interaction between carbon and nitrogen in steel[1-12]
When both carbon and nitrogen are dissolved in austenite, these two interstitial atoms will
interact and affect the activity of one another. The diffusion coefficient for carbon in austenite
has long been known to be strongly dependent on the carbon content. J. Slyske and T. Ericsson[2]
studied the interaction mechanism between carbon and nitrogen in steel carbonitriding process
and presented the diffusivity calculation equations.
An approximate value of the diffusion coefficient for carbon in Fe-C-N austenite is obtained
by taking the material thermodynamics study into account:
23
D!! = 4.84 ∙ 10!! ∙ 𝑒𝑥𝑝 − !""###
!"∙ 𝑒𝑥𝑝 !"####!!"#∙!
!"∙ 𝑥! + 0.72 ∙ 𝑥! ∙ !!!!!
!!! !!!!!𝑚!/𝑠 (Eq 7)[2]
At higher nitrogen contents and in the presence of high carbon contents this value will be
altered. The resulting equation for the diffusion coefficient for nitrogen in austenite as a function
of temperature and composition in the (Fe-N-C) system would then become:
𝐷!! = 9.1 ∙ 10!! ∙ 𝑒𝑥𝑝 − !"#"$$
!"∙ 𝑒𝑥𝑝 !"####!!"#∙!
!"∙ 𝑥! + 0.72𝑥! ∙ !!!!!
!!! !!!!!𝑚!/𝑠 (Eq 8)[2]
DICTRA is a general software package for simulation of Diffusion Controlled
TRAnsformations in multicomponent systems. Any number of components may be treated
(provided that necessary thermodynamic and kinetic data are available). The program is based on
a numerical solution of the multicomponent diffusion equations in the various regions of a
material assuming that thermodynamic equilibrium holds locally at all phase interfaces. During
the development of CarboNitrideTool©, DICTRA is also used to help calculating diffusivities of
carbon and nitrogen in steel.
Table 6: Diffusivity calculation results from Eq 8 and DICTRA
Temperature (OC)
Composition (wt%) Diffusivity (cm2/s)
C N DC DN Equation (3) DICTRA Equation (5) DICTRA
850
0.2 0 3.83506E-08 3.97E-08 1.60067E-08 1.32E-08 0.2 0.1 4.09673E-08 4.25E-08 1.74478E-08 1.35E-08 0.2 0.2 4.37645E-08 4.54E-08 1.90275E-08 1.38E-08 0.2 0.3 4.67548E-08 4.86E-08 2.076E-08 1.41E-08 0.4 0 4.97806E-08 4.98E-08 1.97603E-08 1.31E-08 0.4 0.1 5.3236E-08 5.33E-08 2.15632E-08 1.34E-08 0.4 0.2 5.69365E-08 5.70E-08 2.35425E-08 1.36E-08 0.4 0.3 6.09002E-08 6.10E-08 2.57172E-08 1.39E-08 0.6 0 6.4789E-08 6.23E-08 2.43941E-08 1.29E-08 0.6 0.1 6.9371E-08 6.66E-08 2.66524E-08 1.32E-08 0.6 0.2 7.42883E-08 7.13E-08 2.91362E-08 1.35E-08 0.6 0.3 7.95669E-08 7.63E-08 3.18705E-08 1.38E-08 0.8 0 8.45712E-08 7.76E-08 3.01146E-08 1.28E-08 0.8 0.1 9.06762E-08 8.30E-08 3.29474E-08 1.31E-08 0.8 0.2 9.72432E-08 8.89E-08 3.60696E-08 1.34E-08 0.8 0.3 1.0431E-07 9.51E-08 3.95142E-08 1.37E-08
Table 6 shows the calculation results of the carbon diffusivity in austenite (steel: AISI 8620,
temperature: 850°C) when carbon concentration is 0.2% ~ 0.8% and nitrogen concentration is 0
24
~ 0.3% with Eq 7 and DICTRA. From the comparison it, can be seen that the DC calculation results agree very well but the DN from DICTRA has an unexpected continuous decrease with carbon growth.
In CarboNitrideTool©, Eq 7 and Eq 8 are used to calculate the diffusion coefficients of carbon
and nitrogen in steels. With Eq 7 and Eq 8, the effects of other alloy elements are not included.
In order to simulate the diffusion processes for different with CarboNitrideTool, DICTRA was
also used to study these effects. Table 1 gives the compositions of AISI 1018 and AISI 8620, and
it can be noticed that Cr and Ni are the main alloy elements in AISI 8620 comparing with AISI
1018. With 0.4% of C and 0.6% of N, the calculations on diffusivities of C and N at 800 OC with
different wt% of Cr and Ni were performed with DICTRA. Table 5 shows the calculation results
for diffusivities.
Table 7: Diffusivity calculation results from DICTRA with Cr and Ni (with 0.4% C and 0.2% N)
Composition (wt%) Diffusivity (cm2/s) Cr Ni DC DN
0.0 0.0 2.8243339E-08 5.8971029E-09 0.4 0.4 2.8440595E-08 5.8961250E-09 0.4 0.5 2.8489404E-08 5.8958804E-09 0.4 0.6 2.8538008E-08 5.8956363E-09 0.4 0.7 2.8586408E-08 5.8953911E-09 0.5 0.4 2.8440595E-08 5.8961250E-09 0.5 0.5 2.8489404E-08 5.8958804E-09 0.5 0.6 2.8538008E-08 5.8956358E-09 0.5 0.7 2.8586408E-08 5.8953911E-09 0.6 0.4 2.8440595E-08 5.8961250E-09 0.6 0.5 2.8489404E-08 5.8958804E-09 0.6 0.6 2.8538008E-08 5.8956358E-09 0.6 0.7 2.8586408E-08 5.8953911E-09 1.0 1.0 2.4268175E-08 5.7549907E-09
From the calculation results in Table 7, it can be concluded that there is no obvious effects of
Cr and Ni on the diffusivities of C and N for AISI 8620 (In AISI 8620, Cr is between 0.4% and
0.6, Ni is between 0.4% and 0.7%). In the current version of CarboNitrideTool, the same
diffusivity calculation equations are used for different steels.
However, if there is more alloy elements in the steel, the diffusivities of C and N will be
changed significantly (In Table 7, the diffusivities of C and N with 1.0% Cr and 1.0% Ni are
given). Therefore, more calculation and experiments should be performed in the future study on
the establishment of material database for more steels with carbonitriding process.
25
3.2.4 Model calibration and validation
In the previous study, two diffusivity calculation methods are used and we need to choice the
better method for CarboNitrideTool by running some validation receipts and comparing with the
experiment results. The Equation (7) and Equation (8) are used in the current version of
CarboNitrideTool© to determine the diffusivities of carbon and nitrogen. The calculated results
from experiments in Table 3 are used to determine the boundary conditions for nitrogen transfer
into the steel. Fig.10 presents the comparison between experiment and simulation results for
AISI 1018 at 850OC with 45min of 10% ammonia addition.
Figure 16 Comparison between experiment results and simulation results
3.2.4 Study on the relationship between microhardness and C&N concentration
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600 700 800
Car
bon
& N
itrog
en C
once
ntra
tion
wt%
depth /µm
C_1018_0_ammonia C_1018_5_ammonia_45min N_1018_5_ammonia_45min C_1018_15_ammonia_45min N_1018_15_ammonia_45min Simulation_C_1018_0_ammonia Simulation_C_1018_5_ammonia_45min Simulation_N_1018_5_ammonia_45min Simulation_C_1018_15_ammonia_45min Simulation_N_1018_5_ammonia_45min
26
The microhardness was measured with every group of carbonitrided samples and the results
are listed in Appendix B. From the measurement results, some simple prediction equations for
microhardness from Carbon and Nitrogen concentrations are established with MATLAB:
1) Microhardness=622*C%+5239*N%+305.2 for AISI 1018 at 800 OC (R2=0.8503)
2) Microhardness=704*C%+4358*N%+334.4 for AISI 1018 at 850 OC (R2=0.4506)
3) Microhardness=648*C%+1149*N%+356.9 for AISI 8620 at 800 OC (R2=0.9168)
4) Microhardness=720*C%+2419*N%+371.6 for AISI 8620 at 850 OC (R2=0.7241)
With the fitting equations, the function of predicting surface microhardness profiles could be
included in CarboNitrideTool© in the future.
References [1] J. Slyske, T. Ericsson, A Study of Reactions Occurring during the Carbonitriding Process, J.
Heat Treating, 1981, Vol.2, No.1, 3-19
[2] J. Slyske, T. Ericsson, A Study of Reactions Occurring during the Carbonitriding Process, J.
Heat Treating, 1981, Vol.2, No.2, 97-112
[3] H. Kurabe, Some Behaviors of Ammonia Gas in Carbonitriding, Tetsu-to-Hagane, 1973, Vol.
59, No. 9, 1251-1260
[4] H. J. Grabke, Arch. Eisenhuttenwes., 1975, Vol. 46, 75-81
[5] H. J. Grabke, Ber. Bunsenges., 1968, Vol. 72, 541-548
[6] J. Pomey, Rev. Met., 1950, Vol. 47, 727-738
[7] C. Wells, W. Batz, and R.F. Mehl, Trans. AIME, 1950, Vol. 188, 553-560
[8] R.P. Smith, Acta Met., 1953, Vol. 1, 578-587
[9]. R.M. Asimow, Trans. Met. Soc. AIME, 1964, Vol. 230, 611-613
[10] R. Collin, S. Gunnarson, and D. Thulin, J. Iron Steel Inst., 1972, 785-789
[11] P. Grieveson and E.T. Turdogan, Trans. Met. Soc. A1ME, 1964, Vol. 230, 407-414
[12] R. Davies and C.G. Smith, A Practical Study of the Carbonitriding Process, Metal Progress,
1978, No.9, 40-53
[13] Olga Karabelchtchikova, Calculation of gas carburizing kinetics from carbon concentration
profiles based on direct flux integration. Defect and Diffusion. 2007, Vol.266, 171-180
27
[14] Olga Karabelchtchikova, Carbon Diffusion in Steels – a Numerical Analysis Based on
Direct Flux Integration, Journal of Phase Equilibria and Diffusion, 2006, Vol.26, 598-604
[15] Marcel A. J. Somers and Eric J. Mittemeijer. Layer-growth on Gaseous Nitriding of Pure
Iron: Evaluation of diffusion coefficients for nitrogen in iron nitrides, Metallurgical and
Materials Transaction A. 1994, Vol. 26A, 57-74
[16] B.M. Wilson, W.N. Weins. Retained Austenite and Tooling Failure Case Studies, 20th ASM
Heat Treating Society Conference Proceedings, 9-12 October 2000, St. Louis, MO, ASM
International, 2000, 566-573
[17] Charlie R. Brooks. Principles of the Heat Treatment of Plain Carbon and Low Alloy Steels,
The Materials Information Society, ASM International, Materials Park, OH, USA, 1996
28
Appendix A OES Measurement Results of Carbon and Nitrogen Concentration
Fig.A-1 Carbon and nitrogen concentration (wt%) profiles v.s. depth (µm)
for the C concentration and for the N concentration in AISI 8620 at 800 OC with x% NH3 addition
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
15min of 5% NH3 addition 0% NH3 addition
15min of 10% NH3 addition 45min of 5% NH3 addition
15min of 15% NH3 addition 45min of 10% NH3 addition
45min of 15% NH3 addition
29
Fig.A-2 Carbon and nitrogen concentration (wt%) profiles v.s. depth (µm)
for the C and for the N concentration in AISI 8620 at 850 OC with x% NH3 addition
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 700
15min of 5% NH3 addition 0% NH3 addition
15min of 10% NH3 addition 45min of 5% NH3 addition
15min of 15% NH3 addition 45min of 10% NH3 addition
45min of 15% NH3 addition
30
Fig.A-3 Carbon and nitrogen concentration (wt%) profiles vs depth (µm)
for the C and for the N concentration in AISI 1018 at 800 OC with x% NH3 addition
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
45min of 15% NH3 addition
15min of 15% NH3 addition 45min of 10% NH3 addition
15min of 5% NH3 addition
45min of 5% NH3 addition 15min of 10% NH3 addition
0% NH3 addition
31
Fig.A-4 Carbon and nitrogen concentration (wt%) profiles vs depth (µm)
for the C and for the N concentration in AISI 1018 at 850 OC with x% NH3 addition
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600 0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
0 100 200 300 400 500 600
15min of 5% NH3 addition 0% NH3 addition
15min of 10% NH3 addition 45min of 5% NH3 addition
15min of 15% NH3 addition 45min of 10% NH3 addition
45min of 15% NH3 addition
32
Appendix B Microhardness Measurement Results
8620 0 NH3 0min 850c 1007
8620 5% NH3 15min 850c 1012
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 0 NH3 0min 850c
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 5% NH3 15min 850c
HK
HK
33
8620 5% NH3 45min 1020
8620 10% NH3 15min 850c 1023
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 5% NH3 45min
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 10% NH3 15mins 850℃
HK
HK
34
8620 10% NH3 45min 850c 1031
8620 15% NH3 15min 850c 1032
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 10% NH3 45mins 850℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 15% NH3 15mins 850℃
HK
HK
35
8620 15% NH3 45min 850c 1043
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
cm
8620 15% NH3 45mins 850℃ HK
36
8620 0% NH3 0min 800c 1049
8620 800c 5%N 15min 1056
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 0% NH3 800℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 5% NH3 15mins 800℃ HK
HK
37
8620 800c 5%N 45min 1062
8620 800c 10%N 15min 1067
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.01 0.02 0.03 0.04 0.05 0.06
wt%
depth cm
8620 5% NH3 45min 800'C concentraaon
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 10% NH3 15mins 800℃ HK
HK
38
8620 800c 10%N 45min 1075
8620 800c 15%N 15min 1078
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 10% NH3 45mins 800℃
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 15% NH3 15mins 800℃ HK
HK
39
8620 800c 15%N 45min 1085
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
8620 15% NH3 45mins 800℃ HK
40
1018 0%N 0min 850c 2006
1018 5%N 15min 850c 2013
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 0% NH3 850℃
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 5% NH3 15mins 850℃ HK
HK
41
1018 5%N 45min 850c 2017
1018 10%N 15min 850c 2022
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 5% NH3 45mins 850℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 10% NH3 15mins 850℃ HK
HK
42
1018 10%N 45min 850c 2028
1018 15%N 15min 850c 2034
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 10% NH3 45mins 850℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 15% NH3 15mins 850℃ HK
HK
43
1018 15%N 45min 850c 2038
0
100
200
300
400
500
600
700
800
900
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 15% NH3 45mins 850℃ HK
44
1018 0%N 0min 800c 2043
1018 5%N 15min 800c 2048
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 0% NH3 800℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 5% NH3 15mins 800℃ HK
HK
45
1018 5%N 45min 800c 2059
1018 10%N 15min 800c 2063
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 5% NH3 45mins 800℃
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 10% NH3 15mins 800℃ HK
HK
46
1018 10%N 45min 800c 2070
1018 15%N 15min 800c 2072
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06
wt %
depth cm
1018 10%N 45min 800c
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Axis Title
cm
1018 15%N 15min 800c HK
HK
47
1018 15%N 45min 800c 2078
0
100
200
300
400
500
600
700
800
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.01 0.02 0.03 0.04 0.05 0.06
%wt
depth cm
1018 15% NH3 45mins 800℃ HK
