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Alloy Dependence of the Diffusion Coefficient of Carbon in Austenite and Analysis of Carburization Profiles in Case Hardening of Steels
J. Gegner1,a, A. A. Vasilyev2,b, P.-J. Wilbrandt3,c and M. Kaffenberger1,d 1University of Siegen, Institute of Material Science, Paul-Bonatz-Straße 9-11, 57068 Siegen,
Germany
2St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, 195251, St. Petersburg, Russia
3University of Göttingen, Institute of Material Physics, Friedrich-Hund-Platz 1, 37073 Göttingen, Germany
[email protected], [email protected], [email protected], [email protected]
Keywords: Case hardening engineering, alloy dependent carbon diffusivity, modeling of diffusion coefficients, gas carburizing experiments, secondary ion mass spectroscopy.
ABSTRACT
The simulation of carburization profiles for online computer aided control of carburizing processes
and offline case hardening engineering represent the most important technical application of
carbon diffusion coefficients in austenite. The question of whether substitutional alloying elements
such as Cr, Mn, Mo, Ni or Si, at low concentrations around 1 wt.% typical of the used steels
influence the diffusivity considerably, is increasingly raised recently. In the present paper, the
materials science tool SimCarb Diffusivity is introduced as one module of the stand-alone SimCarb
program package for the numerical simulation of case hardening. The Windows expert software
suite comprises the process steps of carburizing, quenching and tempering. The new program
SimCarb Diffusivity calculates alloy dependent diffusion coefficients of carbon in the austenite of,
e.g., case hardening steels for SimCarb simulations. The implemented physically based model is
described in detail. A numerical process study indicates a crucial alloy related effect of the
diffusivity on the resulting carburization and hardness profiles, even within the specification of
individual steel grades. Carburizing experiments on 18NiCrMo14-6 and 15NiCr13 are evaluated.
The carbon distributions are measured by secondary ion mass spectroscopy. Strong evidence is
found that the diffusion coefficient of carbon in austenite depends significantly on the steel
composition, which should be taken into account in the process control of carburizing.
Introduction
Case hardening is the most commonly applied heat treatment of steel. The high hardness, fatigue
strength and wear resistance of the carbon enriched edge material is combined with the good shock
load capacity from the ductile tough core microstructure. Journals, bolts, screws, shafts, gears,
bearings, cams, crown wheels, spindles, levers and tools, for instance, are frequently case hardened.
The service performance of the produced parts and the economic efficiency of the heat treatment
depend on a high process quality. As main target parameter, the (case) carburization depth, CCD,
taken at a carbon concentration 0.35 wt.%, should not deviate more than ±0.1 mm from the desired
value [1]. In current practice, however, a discrepancy of ±0.25 mm already represents a good heat
treatment result [2], which is often actually not achieved [3]. The sufficiently precise predictability
of the carburization profile requires an adequate knowledge of the diffusion coefficient of carbon in
the austenite phase of the used steel. Alloy dependent expressions are provided by the new software
SimCarb Diffusivity introduced in the present paper [4]. Accurately simulated carbon distributions
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are the prerequisite for the correct prediction of the resulting hardness profiles. The corresponding
main process target parameter is the case hardening depth, CHD, taken at 550 HV or 52.5 HRC.
Fundamentals of Case Hardening of Steel
The first step of case hardening is the thermochemical process of diffusion of carbon usually from
controllable gas mixtures of thermally decomposed hydrocarbons into the near-surface zone of the
steel at temperatures between 800 and 1100 °C, mostly from 850 to 980 °C. Fast oxygen-containing
atmospheres reach high mass transfer coefficients β of 1×10−5
to 4×10−5
cm/s. Today's industry
standard is two-step boost-diffuse normal pressure gas carburizing. Fig. 1 illustrates this process. In
the boost stage, the carbon potential, cp, is adjusted as high as possible below the carbide and soot
limit, usually between 0.8 and 1.3 wt.% C, to achieve maximum enrichment depth at minimum
annealing time. The subsequent diffuse period equalizes the steep concentration gradient in the edge
zone. The carbon potential is reduced to 0.55 to 0.95 wt.% C. The diffuse treatment takes about a
quarter of the boost time. The final surface concentration usually amounts to 0.6 to 0.85 wt.% C.
The basic carbon content, c0, of steels for case hardening ranges from 0.07 to 0.30 wt.%.
Fig. 1.
Carbon concentration profiles after the
boost and subsequent diffuse stage of a two-
step carburizing process and evaluation of
the respective case carburization depth,
CCD.
The carburized parts are hardened by quenching with suitable cooling rate, e.g. in oil or water.
Direct, single and double hardening can be applied. Tempering commonly occurs between 150 and
200 °C for 2 to 4 h. Typical hardness profiles are shown in Fig. 2. The desired carburization and
case hardening depths vary from 0.05 to 10 mm, frequently from 0.5 to 4 mm. Target values of the
surface hardness are 58 to 65 HRC, whereas 30 to 50 HRC in the core are generally appropriate.
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Fig. 2. Hardness distributions after quenching and tempering of the carburized workpiece of Fig. 1
and evaluation of the respective case hardening depth, CHD.
Case Hardening Engineering
To realize the indicated potential for optimization, a systematic procedure of process analysis and
simulation is required. Case hardening engineering involves the accurate computational prediction,
experimentally verified calibration and parameter study based strategy development of the heat
treatment. Continuous monitoring finally ensures the stability of optimized processes.
Process analysis
The case hardening parameters must be known. The time dependent properties of the endothermic
carburizing gas, i.e. the carbon potential and the mass transfer coefficient, are measured by the foil
method. An example is shown later in Fig. 19. The heat transfer coefficient during quenching is
deduced from cooling curves. The alloy factor, carbon diffusivity and hardenability are governed by
the steel composition. It is determined by chemical check analysis. The influence of the alloying
elements on the carbon diffusion coefficient (CDC) in austenite is examined in detail in the follow-
ing. The hardenability of the steel can be considered, e.g., by time-temperature-transformation
diagrams for continuous cooling or Jominy curves. The carburization and hardness profiles have to
be measured with high accuracy to allow reliable nominal/actual value comparisons. The quenching
microstructure can be characterized with reasonable significance by the retained austenite content.
Part of case hardening engineering is, moreover, the development and application of appropriate
experimental methods. The alloy factor of a certain steel, for instance, can be derived from through
carburized foils by comparing the total carbon content with reference samples of binary Fe–C. The
microstructure should be adjusted representatively. Isothermal powder pack decarburization is
suitable for determining the concentration dependent diffusion coefficient of carbon in austenite of
the non- or low-alloyed steels. Completely through carburized samples or model materials, such as
Fe–1 wt.% Cr–1 wt.% C, can be used. Hollomon-Jaffe parameters or carbon dependent diminution
factors of martensite evaluated experimentally allow the prediction of the tempering hardness.
Process simulation
Computer aided case hardening engineering is based on an efficient simulation tool. The SimCarb
program suite used in the present paper is outlined in the section after next. Expert software allows
the simulation of complex carburizing case hardening processes. Systematic nominal/actual value
comparisons form the basis for status analyses. The approach is particularly illustrated by carbon
depth profiles later in Figs. 21, 23, 27 and 28. Also, fundamental process understanding becomes
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available, e.g. by computational parameter studies, that is not or only with much effort accessible in
the experiment.
Alloy Dependence of the Diffusion Coefficient of Carbon in Austenite
The prediction of carburization depths for case hardening represents the most important practical
application of the diffusivity of carbon in austenite [5]. Experimental data on multi-component iron
based systems are rare. The general statement in the literature, however, is that the small amounts of
maximal few wt.% of alloying elements, such as Cr or Si, typical of steels for case hardening do not
significantly influence the carbon diffusion coefficient [6–8]. Expressions on binary Fe–C austenite
are therefore used in state-of-the-art furnace control software for online simulations of carburization
profiles [9]. On the other side, a noticeable dependence of the carbon diffusivity in austenite on the
alloy composition is indicated, for instance, by decarburization experiments [10–13]. These findings
are supported by recent metal physics based analyses [4, 14, 15]. The question addressed in this
paper of how alloying elements in case hardening steels change the diffusion coefficient and profile
of carbon as well as particularly the carburization depth is of essential importance for achieving the
required high process reliability.
SimCarb Diffusivity in the Sequence of the Stand-Alone SimCarb Software Suite
Advanced expert simulation tools provide a deeper insight into heat treatment processes of steels
and disclose optimization potentials in terms of quality and productivity, energy as well as resource
efficiency. The commercial SimCarb software suite for offline computer aided case hardening engi-
neering in industry and research consists of three interacting Windows programs. The carburizing
module SimCarb, introduced at the MMT-2006 conference [16], allows the numerical simulation of
carbon profiles for complex user-defined multi-stage or continuously controlled isothermal and
temperature programmed carburization processes by the finite difference method. The software also
includes a basic hardness calculation. In addition to the relevant SimCarb library of 18 entries, the
extension module SimCarb Diffusivity, introduced in the present paper, provides steel specific
carbon diffusion coefficients in austenite containing substitutional alloying elements (SAE). The
expressions of exponential concentration dependence, which are derived from the quantitative
physically based model described in the next section [4], serve as optional manual SimCarb input.
The simulation of case hardening is completed by the advanced microstructure prediction and
hardness computation of SimCarb QuenchTemp. Carbon depth distributions calculated by SimCarb
are directly importable but arbitrary carburization profiles can be programmed in an implemented
subroutine and entered by the user as well. The quenching process is simulated by the finite
difference method, based on continuous cooling (time-temperature-) transformation diagrams. The
tempering hardness is deduced from experimentally determined Hollomon-Jaffe parameters.
SimCarb QuenchTemp is also introduced at the MMT-2012 conference in a separate paper.
SimCarb Diffusivity Model of Alloy Dependent Carbon Diffusion Coefficients in Austenite
The model for calculating the carbon diffusion coefficient, DC, in complexly alloyed austenite [4],
implemented in the SimCarb Diffusivity software, is based on a microscopic analysis of the
diffusion of carbon atoms. The approximation of average energies is used [17]. The following
formula holds for the CDC in Fe–C–Xi austenite [4], where Xi is a substitutional alloying element:
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T
yyyyUyyyyU
T
TLyTLyyyDyyTD
iiiiiiii
i
i
i
i
i
R
γα)(exp
R
γα)(θexp
R
)()(1121),,(
XXCXXCCXXCXXCC
XVaC,X
XVaC,X
CC0C,XCC
(1)
The concentrations of the carbon and Xi atoms are respectively expressed as site fractions yC and
iyX . Furthermore, ΔUC(yC)=ΔUC,0+αCyC represents an effective activation energy for the migration
of carbon atoms in Fe–C austenite, iLX
Va,C(T) is a thermodynamic parameter and DC,0, ΔUC,0, αC, θ,
iXα as well as iXγ are empirical quantities. The model parameters DC,0, ΔUC,0, αC and θ are deter-
mined, utilizing the experimental CDC data for the Fe–C alloys [6, 18], on the basis of minimization
of the average relative deviation, δ , of the theoretical results from the experimental data:
exp
D
1exp
,C
exp,C,C
thC
expD
),(1δ
N
j j
jjj
D
DyTD
N (2)
Here, expDN is the number of elements in the database, Tj and yC,j are respectively the temperature
and carbon concentration corresponding to the j-th experimental CDC value. The experimental and
theoretical carbon diffusion coefficients obtained using the formula of Eq. (1) are accordingly
denoted exp,C jD and ),( ,C
thC jj yTD .
The core of the experimental database is represented by the data on CDC investigations carried
out for temperatures between 800 and 1305 °C in the range of carbon concentration from 0.22 to
1.35 wt.%, i.e. 0.01<yC<0.06 [6]. The most reliable and self-consistent CDC values are selected.
Some data, which are obviously out of the general trend of the diffusivity change with temperature,
and also the data, obtained for samples with rather high SAE (Mn, Si and, especially, Cr) content,
are excluded from consideration. The performed selection of the diffusion data minimizes the effect
of distortion of the values of the model parameters for binary Fe–C alloys caused by experimental
errors and the systematic SAE influence on carbon diffusivity.
The CDC data from Ref. [6] are enlarged by including the additional data obtained in Ref. [18]
for the temperatures of 1000, 1100 and 1200 °C and the carbon concentrations of 0.2, 0.4 and 0.7
wt.%, i.e. site fractions yC of about 0.009, 0.019 and 0.033. As a result, a database consisting of 75
experimental CDC values is utilized at the first stage of the model calibration.
Table 1 lists the optimal model parameters values and the corresponding data used in the well-
known model of Ågren [5]. As may be seen from this comparison, the derived values of the carbon
diffusion activation energy in γ iron, ΔUC,0, and of the parameter αC, determining the rate of
activation energy decrease with increase of the carbon concentration, are considerably lower than
suggested by Ågren. According to Fig. 3, all CDC values from Ref. [6] agree well with the calcula-
tions, as well as the data from [18]. The later is rather important in view of the further use of the
CDC investigation results in the Fe–C–Хi alloys [19–22], which are deduced with the application of
the same experimental approach.
Table 1. Two sets of the model parameters for binary Fe–C austenite.
Model DC,0×107 in m
2/s ΔUC,0 in J/mol αC in J/mol θ×10
4
SimCarb Diffusivity [4] 1.41 137772.1 −231000 2.588
Ågren [5] 4.53 147714.8 −219789 2.221
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On the basis of the obtained results, one may conclude that the SimCarb Diffusivity model
predicts CDC of Fe–C alloys throughout the whole studied interval of temperatures and carbon
concentrations much more precisely than the Ågren model [5], as well as recently suggested
alternative approaches [14, 15].
Fig. 3.
Correlation between the measured and calculated
CDC values for the binary Fe–C alloys. The
accuracy bars correspond to ±7% from the meas-
ured value [6, 18].
At the second stage of model calibration, the values of the parameters iXα and
iXγ , describing
the effect on CDC caused by an additional alloying with the substitutional element Xi, are evaluated
according to Table 2. These parameters are determined, utilizing experimental investigation data on
the carbon diffusivity in the ternary alloys Fe–C–Xi (Xi=Cr, Mn, Mo, Ni, Si, Al, W, Co) with differ-
ent carbon and SAE contents [19–22]. The appropriate data are available for the three temperatures
of 1000, 1100 and 1200 °C and carbon concentrations of 0.2, 0.4 and 0.7 wt.%. Data for alloys
containing SAE in the following amounts are utilized: 1.0 and 2.5 wt.% Cr; 1.0 and 12.0 wt.% Mn;
0.9 and 1.55 wt.% Mo; 4.0 and 9.5 wt.% Ni; 1.6 and 2.55 wt.% Si; 0.7, 1.7 and 2.45 wt.% Al; 0.5,
1.05 and 1.95 wt.% W; 6.0 and 11.0 wt.% Co.
Table 2. Some values of the model parameters, determining the effect of substitutional alloying
elements on the diffusion coefficient of carbon in Fe–C–Хi austenite.
Element Xi iXα , J/mol iXγ , J/mol
Si ↓ 192650 –4044000
W 2080000 –27820000
Cr (< 2.5 wt.%) 1041871 –2117897
Co –41340 –1702000
According to Fig. 4, the results of the CDC calculation agree rather well with the experiment for
all ternary alloys. The obtained accuracy of the experimental data reproducing is much higher than
for the alternative models calibrated using the same experimental data set [14, 15, 23]. Such a
difference is related to the fact that the major (exponential) effect of the CDC change in the ternary
alloys is caused by a variation of the diffusion frequency factor due to the corresponding change in
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the effective energy of the carbon diffusion that is more precisely taken into account in the SimCarb
Diffusivity model.
The developed model allows to describe a slowing down of the diffusion of carbon owing to the
carbide forming elements (Cr, Mn, Mo, Al, W), which reduce its activity in an austenite, as well as
diffusion acceleration by elements (Ni, Co) raising the carbon activity. The main part of the effect
of the SAE is caused by their influence on the effective activation energy of diffusion. Additional
alloying by Cr, Mn, Mo, Al and W results in an increase of the activation energy (iXα > 0), whereas
additions of Ni and Co reduces this energy (iXα < 0).
A synergetic effect on the diffusion activation energy, which occurs when the austenite simulta-
neously contains the carbon and substitutional alloying elements Xi, is described by means of the
iXγ parameter. A negative value of iXγ for the carbide formers (see Table 2) corresponds to a de-
crease of the activation energy with an increase of carbon content or, accordingly, to a depression of
their slowing down effect. This parameter is also negative for such elements as Ni and Co (cf. Table
2). Therefore, the synergetic effect is the opposite for them.
Assuming the additivity of SAE effects on the thermodynamic factor and the effective activation
energy of the carbon diffusion, the formula of Eq. (1) for CDC in ternary Fe–C–Хi alloys may be
generalized for the case of a multi-component alloy Fe–C–Х1–…–XN, containing a number (X1, …,
XN) of SAE. In this case the carbon diffusion coefficient may be calculated as follows:
T
yyyyUyyyyU
T
TLyTLy
yyDyyyTD
N
i
N
i
N
i
N
i
N
i
N
i
iiiiiiii
i
i
i
i
N
R
γα)(
expR
γα)(
θexp
R
)()(1
121),...,,,(
1XXC
1XXCC
1XXC
1XXCC
XVaC,
1X
XVaC,
1X
CC0C,XXCC 1
(3)
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Fig. 4. Correlation between measured and calculated CDC values for the ternary Fe–C–Xi alloys
(Xi=Cr, Mo, Ni, Si). The accuracy bars correspond to ±7% from the measured value.
According to experimental data [22], the effect of Si on the carbon diffusivity depends on the
temperature. Above 1000 °С, Si decreases the diffusivity of carbon (Si ↓, see Fig. 4), whereas below
this temperature, on the contrary, it significantly increases the diffusion coefficient (Si ↑). The set of
values of model parameters determining the effect of Si on CDC at low temperatures is evaluated,
according to Fig. 5a, on the basis of data given in Ref. [24] by processing experimental carbon
profiles of carburizing AISI 8620 steel containing 0.19 wt.% Si, 0.87 wt.% Mn, 0.57 wt.% Cr, 0.21
wt.% Mo and 0.42 wt.% Ni. As per the obtained results, Si should have an intense accelerating
effect on carbon diffusion at low temperatures Т<1000°С: iXα = –777300,
iXγ = 700200 J/mol. As
illustrated in Fig. 5b, the version of the model used in SimCarb Diffusivity with an accelerating
influence of Si predicts a significant increase in CDC by alloying with 0.2 to 0.3 wt.% of this
element, which represents a typical content of Si in many case hardening and other practically
important steels (see also next section, Fig. 8).
It is worth noting that the CDC calculations, according to the SimCarb Diffusivity model [4],
correlate with existing experimental data substantially better than predictions of the alternative
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models [5, 14, 15, 23]. Therefore, it is recommended for the simulation of carburization profiles in
case hardening (see below) and several other technological applications, such as decarburization.
Fig. 5. Calculated CDC dependences on carbon concentration for alloys of different compositions.
a) AISI 8620 steel; b) illustration of the acceleration effect (Si ↑) of Si alloying.
Influence of Main Steel Alloying Elements on the Carbon Diffusion Coefficients of Austenite
According to the model outlined above, substitutional alloying elements significantly change the
bulk diffusion coefficient of carbon in austenite, DC, even at the usual low concentrations around 1
wt.% of steels for case hardening. The predictions of SimCarb Diffusivity at different temperatures
are further discussed in this section by means of Figs. 6 to 8. The carbon concentration cC of 0 to
1.4 wt.% covers the common range of carburizing. The relevant additions of the main alloying
elements Cr, Mn, Mo, Ni and Si are considered.
Fig. 6.
SimCarb Diffusivity prediction of the effect
of typical Cr, Ni and Mo contents (in wt.%)
on the concentration dependent diffusion
coefficient of carbon in ternary austenite at
900 °C.
Carbide formers tend to reduce the carbon diffusivity. This is evident for Mo up to 1.1 wt.% C
and particularly for Cr at 900 and 970 °C from Figs. 6 and 7, respectively. Both tendencies agree
with literature statements [10, 12, 13, 25]. The predicted influence of Cr is higher than indicated in
previous sources [10, 25]. An alloy addition of 0.5, 1, 1.5 and 2 wt.% Cr at 900 °C (cf. Fig. 6), for
instance, approximately corresponds to the carbon diffusion coefficient in binary Fe–C austenite at
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868, 837, 810 and 782 °C, respectively. The effect of 0.5 to 2 wt.% Cr is thus comparable with a
temperature reduction of about 30 to 120 °C. The influence of Mn can practically be neglected. In
the relevant ranges of temperature from 850 to 1100 °C and carbon concentration between 0 and 1.4
wt.%, technically common contents of up to 2 wt.% Mn result in a DC change of only around ±3%.
Fig. 7.
SimCarb Diffusivity prediction of the effect
of typical Cr, Ni and Mo contents (in wt.%)
on the concentration dependent diffusion
coefficient of carbon in ternary austenite at
970 °C.
The austenite stabilizers Ni and Si are also analyzed. The tendency of these alloying elements is
to increase the carbon diffusivity. Ni shows the expected effect, reported in the literature [12], in the
whole temperature range relevant to carburizing, as indicated at 900 and 970 °C respectively in
Figs. 6 and 7. The predicted influence of Si is more complex, as discussed in the previous section.
At most common carburizing temperatures up to 980 °C, Si greatly increases the diffusion coeffi-
cient of carbon in austenite. According to Fig. 8, a rise of over 20% and about 50% corresponds to
usual alloying additions of 0.2 and 0.4 wt.% Si, respectively, at 900 and 970 °C. A transition occurs
around 1000 °C. At higher temperatures, a slight reversed effect on the carbon diffusivity, e.g. at
1050 °C in Fig. 8, of −5% to +1% at 0.2 wt.% Si and −9% to +2% at 0.4 wt.% Si, again compared
with binary Fe–C austenite, is obtained. This prediction should attract more interest in the future.
Fig. 8. SimCarb Diffusivity prediction of the temperature dependent Si effect (typical alloying con-
tents) on the carbon diffusion coefficient in Fe–C–Si austenite at 900, 970 and 1050 °C.
Carbon Diffusivity in Case Hardening Steels in Relation to the Result of Carburizing
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By entering the chemical composition into the input mask and pressing the button to start the
calculation, SimCarb Diffusivity provides the SimCarb user with the predicted concentration
dependent expression of the diffusion coefficient of carbon in the austenite of the alloy concerned.
Fig. 9 demonstrates on the example of six conventional case hardening steel grades at the typical
carburizing temperature of 900 °C that large differences occur.
Fig. 9. SimCarb Diffusivity prediction of the concentration dependent diffusion coefficient of car-
bon in the austenite of the indicated steels at 900 °C and binary Fe–C for comparison.
The mean chemical compositions of the materials are considered according to the standard speci-
fication. The concentrations i
cX of the main substitutional alloying elements Xi, the individual
effects of which on the carbon diffusivity arise from Fig. 6, are summarized in Table 3. Compared
in Fig. 9 with binary Fe–C austenite, the diffusion coefficient DC is increased by up to about 65%
(±12%) in X12Ni5 and reduced by up to 69% (±6%) in 18CrNi8. Einstein’s equation, ‹x›2=2Dt,
suggests a square root dependence of the carburization depth upon the carbon diffusivity. Here, ‹x›
and t respectively denote the average diffusion distance and the time.
Table 3. Designation, material number and chemical composition of the steels of Fig. 9. The case
carburization depths calculated for the gas carburizing process of Fig. 10 are also given.
Steel Designation Mat. No. Cr, wt.% Mn, wt.% Mo, wt.% Ni, wt.% Si, wt.% CCD, mm
18CrNi8 1.5920 1.95 0.50 0 1.95 0.275 2.00
18NiCrMo14-6 1.3533 1.45 0.55 0.20 3.50 0.20 2.38
17Cr3 1.7016 0.85 0.75 0 0 0.20 2.87
15NiCr13 1.5752 0.75 0.55 0 3.25 0.20 3.11
Fe–C (reference) --- 0 0 0 0 0 3.54
C15 1.0401 0 0.45 0 0 0.20 3.92
X12Ni5 1.5680 0 0.55 0 5.00 0.35 4.53
Carburizing of different steel grades
To estimate the impact on the resulting carbon depth profiles, the conventional isothermal 80 h two-
step boost-diffuse gas carburizing process of Fig. 10 is analyzed. At the assumed temperature of
900 °C, the predicted diffusivities of Fig. 9 can be applied. The carbon potential of 1.0 wt.% in the
boost or saturation stage of 64.5 h is lowered linearly during 30 min to 0.6 wt.% in the diffuse step.
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The mass transfer coefficient simultaneously rises from 2.0×10−5
to 2.5×10−5
cm/s. A decrease of
the carburizing speed β in the equalization phase due to the changing gas composition is unlikely.
The SimCarb simulations of this typical process are displayed in Fig. 11. To achieve direct com-
parability, a uniform initial carbon content, c0=0.17 wt.%, is assumed for the binary Fe–C reference
material as well as for all steels in Table 3. Only for X12Ni5, this value slightly exceeds the specifi-
cation limits by 0.02 wt.% C. A unity alloy factor, ka=1, simply accounts for the actual adjustment
of the carbon potential to the target parameters (surface C concentration), material and process con-
ditions [16].
Fig. 10.
Process conditions for a numerical
analysis of gas carburizing of the
steels of Fig. 9. The carbon
potential and the mass transfer
coefficient are plotted as a function
of time.
The differing diffusion coefficients of Fig. 9 result in strongly deviating concentration profiles.
From Fig. 11, the main process target value of the carburization depth, CCD, is indicated for all
simulated case hardening steels in the diagram and correspondingly included in Table 3. Compared
with CCD=3.54 mm for binary Fe–C austenite, an increase by 0.99 mm (28%) and a reduction by
1.54 mm (44%) is found in X12Ni5 and 18CrNi8, respectively. The alloy dependent carburization
depths vary widely from 2.00 to 4.53 mm (cf. Fig. 11). This finding clarifies the recommendations
in the literature that the chemical composition of the steel must be considered in the calculation of
the carbon diffusivity in austenite and that certain grades should be carburized separately [24, 26].
Fig. 11.
Carburization profiles for the process of Fig.
10 simulated for the steels of Fig. 9 of initial
carbon content c0=0.17 wt.%. A uniform
alloy factor of ka=1 allows direct comparabil-
ity.
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Admissible variations in the chemical composition of individual steel grades
The alloy composition can differ from batch to batch within the specification limits of the standard.
It is therefore of particular interest to assess the effect of such admissible variations on the diffusion
coefficient of carbon in austenite and resulting carburization profiles. The two-step process of Fig.
10 is studied. The case hardening steel grades 17Cr3 and 18NiCrMo14-6 are chosen for the simula-
tion. The contents of the substitutional alloying elements corresponding to the minimum (min.),
average (avg.) and maximum (max.) carbon diffusivity DC are given in Table 4.
Fig. 12 reveals the predicted diffusion coefficients. The maximum and minimum values deviate
upwards and downwards from the average alloy compositions, also shown in the diagram, respec-
tively by about 40% and 30%.
Table 4. Steel composition of minimum, average and maximum carbon diffusivity for 17Cr3 and
18NiCrMo14-6. The carburization and case hardening depths refer to actual alloy factors.
Designation DC Cr, wt.% Mn, wt.% Mo, wt.% Ni, wt.% Si, wt.% CCD, mm CHD, mm
18NiCrMo14-6
min. 1.60 0.70 0.25 3.25 0 2.18 2.43
avg. 1.45 0.55 0.20 3.50 0.20 2.48 2.75
max. 1.30 0.40 0.15 3.75 0.40 2.81 3.15
17Cr3
min. 1.00 0.90 0 0 0 2.70 2.68
avg. 0.85 0.75 0 0 0.20 3.06 3.05
max. 0.70 0.60 0 0 0.40 3.46 3.42
Fig. 12.
SimCarb Diffusivity prediction of alloy de-
pendent carbon diffusion coefficients of
17Cr3 and 18NiCrMo14-6 steel for
average composition and at specification
limits according to Table 4.
The carburization profiles for the two-step process of Fig. 10 are plotted in Fig. 13. In this simu-
lation, the actual alloy factors ka are used in accordance with the default of the SimCarb library [9].
The values also vary within the different steel compositions from 1.036 (at max. DC) to 1.132 (min.
DC) for 17Cr3 and from 0.997 (max. DC) to
1.106 (min. DC) for 18NiCrMo14-6, which
is reflected in the surface carbon content
[16]. Again, the initial concentration c0 is
set at 0.17 wt.% C.
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Fig. 13.
Carburization profiles for the process of Fig. 10 simulated for the steels of Fig. 12 by considering
the SAE dependent actual alloy factor ka [9].
The carburization depths, evaluated in Fig. 13, are added in Table 4. The large deviations from
the mean alloy composition (avg. DC) to higher and lower values by more than 10% amount to
+0.40 and −0.26 mm for 17Cr3 as well as +0.33 and −0.30 mm for 18NiCrMo14-6, respectively.
The differing carburization profiles also lead to deviating hardness distributions. Quenching of
long cylinders of 50 mm diameter in mildly agitated oil is exemplarily simulated by means of
SimCarb QuenchTemp. Single hardening of 17Cr3 and 18NiCrMo14-6 steel from an austenitizing
temperature of 870 and 830 °C, respectively, is considered. The ASTM austenite grain size number
[27], KASTM, is assumed to be 8. The microstructural composition is calculated as well.
Fig. 14 reveals the simulation results for the three variants of 17Cr3 steel of Fig. 13. Note that
the carburization and case hardening depths indicated in Table 4 are almost identical. The volume
fractions vi of the occurring phases i are also plotted in Fig. 14 as a function of depth. The steel con-
tains quite small additions of alloying elements so that only little retained austenite of maximum 3%
(min. DC) remains in the edge zone of carbon content around 0.65 wt.%. The limited hardenability
of 17Cr3 is manifested in the drop of the martensite amount in the region of falling carbon con-
centration. Bainite and particularly ferrite is formed increasingly with distance from surface. The
martensite content at the case hardening depth is slightly above 70% for each variant.
Fig. 14.
SimCarb QuenchTemp simulation of
quenching results of 17Cr3 steel
according to Fig. 13. The depth de-
pendent hardness (CHD indicated)
and microstructural composition are
displayed. The phase contents vi of
martensite, retained austenite, bainite
and ferrite are predicted.
The SimCarb QuenchTemp simulation results for the three 18NiCrMo14-6 steel compositions
are shown in Fig. 15. The predicted retained austenite content in the edge zone of this much better
hardenable grade, enriched to about 0.65 wt.% C, equals up to 11%. The amount of martensite
remains above 90% even far below the depth where the core hardness is reached. No ferrite occurs.
The case hardening exceeds the carburization depth by more than 10%, as evident from Table 4.
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Fig. 15. Simulated quenching results of 18NiCrMo14-6 steel according to Fig. 13 (cf. Fig. 14).
Experimental Procedure
Carburizing experiments are evaluated to verify and analyze the predictions of the physically based
model of calculating alloy dependent diffusion coefficients of carbon in austenite implemented in
the new SimCarb Diffusivity software. The applied processes, steels and testing methods are briefly
described in the following.
Carburizing case hardening experiments
Isothermal boost-diffuse gas carburizing treatments are performed at the same temperature of 970
°C. Diameter and height of the cylindrical samples are large compared to the depth of the diffusion
zone. Two case hardening steel grades are chosen, for which the predicted carbon diffusivity differs
significantly (cf. Fig. 9). For 18NiCrMo14-6, a shorter (about 13 h) and a longer (44 h) carburizing
time are applied in experiment N° 1 and N° 2, respectively. Different chemical compositions within
the specification limits are used. For 15NiCr13, a carburizing period of about 50 h, i.e. quite similar
to the longer process time for 18NiCrMo14-6, is chosen in experiment N° 3. The carbon potential in
the boost and diffuse step is consistently set at 1.20 and 0.79 wt.%, respectively.
Quenching in still oil and tempering at 200 °C for 2 h are exemplarily examined in experiment
N° 2. The hardness depth profiles and the composition of the microstructure are measured and
simulated. The diameter and height of the sample cylinders respectively amount to 90 and 90 mm,
40 and 80 mm as well as 30 and 100 mm in experiment N° 1, N° 2 and N° 3.
Experimental and measurement methods
Carbon potential and mass transfer coefficient in the boost and diffuse process step of carburizing
are determined by means of the foil method using thin pure Fe–C sheets (c0=0.1 wt.% C) of 100 µm
thickness. The evaluation is demonstrated below for experiment N° 1 in Fig. 19. The concentration
of the substitutional alloying elements of the used case hardening steels is analyzed by optical
emission spectrometry. The carbon content, e.g. of the foils or in the core of the cylindrical samples
(initial value c0), is measured by applying the dry combustion method.
The carburization profiles are determined by secondary ion mass spectroscopy (SIMS) on pol-
ished sections of central disks [13]. The required data calibration is performed by means of a carbon
reference value in the core or, as c0 is rather low, in the enriched near-surface zone.
The distributions of the micro hardness are measured by Vickers indentation technique. The
HV1 values are converted to HRC. The retained austenite content is deduced from an X-ray dif-
fraction (XRD) phase analysis applying Mo Kα radiation. The XRD line broadening correlates with
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the hardness. It is determined as full width at half maximum (FWHM) intensity by applying Cr Kα
radiation.
Reference Data of the Diffusion Coefficient of Carbon in Binary Fe–C Austenite
For analyzing the carburization profiles produced in the case hardening test steels in terms of
literature data of the carbon diffusivity in binary Fe–C austenite by comparative simulations, the
widely accepted work of Tibbetts is used [8]. This reference, which represents the default of the
corresponding SimCarb library [16], agrees well with earlier findings [6]. The investigated
concentration and temperatures range from 0.2 to 1.3 wt.% C and 975 to 1075 °C, respectively, is
suitable for the applied conditions of the carburizing processes (see above).
The data of Tibbetts, deduced from steady-state diffusion coefficient measurements, are chosen
because they are based on AISI 1010 steel (similar to St34-2, Mat. No. 1.0032). The predictions of
SimCarb Diffusivity for this low Mn alloyed grade and binary Fe–C austenite do not differ signifi-
cantly from each other. The chemical composition of AISI 1010 test steel is not reported in Ref. [8].
The customary additions of substitutional alloying elements are given in Table 5. The graphical
representation of the concentration dependence of the diffusion coefficient of carbon in austenite at
the experimental carburizing temperature of 970 °C in Fig. 16 refers to the mean steel composition
(0.45 wt.% Mn). The diagram reveals that the deviations remain small even if a Si content of 0.05
wt.% is considered.
Table 5. Designation, UNS (unified numbering system) number and specified chemical composi-
tion of AISI 1010 and AISI 4130 steel considered in the analysis of the carbon diffusivity.
Steel Designation UNS No. C, wt.% Cr, wt.% Mn, wt.% Mo, wt.% Ni, wt.% Si, wt.%
AISI 1010 G10100 0.08–0.13 0 0.30–0.60 0 0 ≤ 0.10
AISI 4130 G41300 0.28–0.33 0.80–1.10 0.40–0.60 0.15–0.25 ≤ 0.25 0.15–0.35
Fig. 16. Carbon diffusion coefficient of Tibbetts and predicted by SimCarb Diffusivity for binary
Fe–C and AISI 1010 steel without (coincident with Fe–C) and with Si addition at 970 °C.
It is worth mentioning that Tibbetts includes diffusivity data of AISI 4130 steel (similar grade to
34CrMo4, Mat. No. 1.7220) at 1075 °C in the evaluation. Thus, Fig. 17 shows the correspondingly
extended comparison of Fig. 16 at this temperature, where again the mean chemical composition
according to Table 5 is used for modeling. Above 1000 °C, the Si effect is small (cf. Fig. 8) and can
be neglected for AISI 1010 steel. Note that the data of Tibbetts for the carbon diffusion coefficient
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agree well with the predictions of SimCarb Diffusivity for binary Fe–C austenite in the whole
temperature range from 975 to 1075 °C. This is another reason of the choice made for the following
reference simulations of the carburization profiles.
Fig. 17. Diffusion coefficient of carbon in austenite at 1075 °C according to the data of Tibbetts
and predicted by SimCarb Diffusivity for binary Fe–C, AISI 1010 and AISI 4130 steel.
In Fig. 17, however, SimCarb Diffusivity predicts a considerably lower carbon diffusion coeffi-
cient in austenite of AISI 4130 steel at 1075 °C. Small Ni additions within the specification of up to
0.25 wt.% do not change the dot-and-dashed line in the diagram significantly. Note that AISI 4130
steel contains a rather high amount of Cr, for which indication of a decreasing effect on the carbon
diffusivity in austenite from the literature is discussed above.
Chemical Composition of the Test Steels and Predicted Carbon Diffusivity in Austenite
The determined basic carbon content, c0, and the concentrations of the substitutional alloying
elements are summarized in Table 6 for the test steels used in the carburizing case hardening
experiments N° 1 to N° 3. The typical measuring accuracy is better than 5%.
The predictions of the concentration dependent diffusion coefficient of carbon in the austenite of
these test steels and of binary Fe–C at 970 °C by SimCarb Diffusivity are compared with the data of
Tibbetts in Fig. 18. The differing DC values of the two alloys of 18NiCrMo14-6 are clearly lowest.
A less deep carburization profile as expected from the reference data of Tibbetts is thus suggested.
Due to the effect of Ni and Si at reduced Cr content, the carbon diffusivity in 15NiCr13 is not much
smaller than in binary Fe–C austenite, according to the predictions of SimCarb Diffusivity. The data
of Tibbetts lie in the same range.
Table 6. Designation, experiment number and measured chemical composition of the test steels.
Steel Designation Experiment C, wt.% Cr, wt.% Mn, wt.% Mo, wt.% Ni, wt.% Si, wt.%
18NiCrMo14-6 N° 1 0.165 1.533 0.599 0.166 3.229 0.228
18NiCrMo14-6 N° 2 0.180 1.366 0.446 0.180 3.318 0.261
15NiCr13 N° 3 0.150 0.690 0.418 0.069 3.323 0.291
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Fig. 18.
Carbon diffusion coefficient of Tibbetts and
predicted by SimCarb Diffusivity for the test
steels 18NiCrMo14-6 (two compositions) and
15NiCr13 as well as binary Fe–C at 970 °C.
Carburizing Experiment N° 1 on 18NiCrMo14-6
Carbon potential cp and mass transfer coefficient β are determined during the carburizing process by
means of the foil method. An example of the evaluation of the measurements is shown in Fig. 19 for
the boost stage of experiment N° 1. As for the thin Fe–C sheets of thickness d=100 µm, βd<<DC is
valid, the carbon content of the foil, foilCc , increases with exposure time, t, from the initial concen-
tration, foil0c , toward the cp saturation level according to the following relationship [9]:
t
dccctc
β2exp)( foil
0ppfoilC (4)
Fig. 19. Total carbon content of six foils as a function of the respective carburizing time.
The mass transfer coefficient β is obtained as fitting parameter from Eq. (4). The complete two-
step scheme of the carburizing process of experiment N° 1 is illustrated in Fig. 20. The carbon
potential and the mass transfer coefficient in the boost and diffuse stage are respectively denoted by bpc and βb as well as
dpc and βd. The applied values are given in the diagram.
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Fig. 20. Conditions of isothermal two-step boost-diffuse gas carburizing of experiment N° 1 re-
vealing the development of the carbon potential and mass transfer coefficient with time.
Fig. 21 shows the SIMS data points of the spatially resolved determination of the carbon con-
centration. The results of two independent measurements performed at different locations of the
sectioned cylindrical disk fall within the respectively indicated scatter bars of 10% of the absolute
value, which illustrates the accuracy of the method. The carburization depth, CCD, is taken from
the SIMS data to be about 1.7 mm. The carbon profiles simulated by SimCarb for the predictions of
SimCarb Diffusivity for binary Fe–C and the specific 18NiCrMo14-6 steel composition (N° 1 in
Table 6) as well as for the DC reference of Tibbetts are also plotted in Fig. 21. The alloy factor, ka,
according to the AWT recommendation (Association for Heat Treatment and Materials Technology,
Bremen, Germany) is used [9], which represents the default entry of the SimCarb library. The
carburization depths are evaluated at 0.35 wt.% C in the diagram.
Fig. 21. Measured and simulated carburization profiles (CCD indicated) of experiment N° 1.
As suggested by Fig. 18, the carbon distance curves based on the diffusion coefficients of
Tibbetts and SimCarb Diffusivity for Fe–C austenite reveal a very similar progression with
CCD≈2.2 mm. The SIMS analysis, however, demonstrates a clearly flatter actual carburization
profile. The simulation for the carbon diffusion coefficient in the austenite of 18NiCrMo14-6 steel
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(N° 1) calculated by SimCarb Diffusivity is close to the measurement. With a deviation of about 0.1
mm from the SIMS result of CCD≈1.7 mm, the obtained value of CCD≈1.6 mm can be regarded as
accurate prediction of the carburization depth.
Carburizing Case Hardening Experiment N° 2 on 18NiCrMo14-6
On the example of this experiment, quenching and tempering are also analyzed by measurements
and simulations. Apart from the correspondingly calculated carburization profile at the end of the
boost stage, the depth distributions shown in Figs. 1 and 2 represent fitting curves of the measured
carbon (SIMS) and hardness data.
Carburizing process
The applied two-step treatment is defined in Fig. 22. The time courses of cp and β are plotted.
Fig. 22. Gas carburizing conditions of experiment N° 2, again determined by the foil method.
For both evaluated diffusion coefficients of carbon in austenite, predicted by SimCarb Diffusivity
for the actual chemical composition of the used 18NiCrMo14-6 steel (N° 2 in Table 6) and reported
by Tibbetts for binary Fe–C, an analysis of the effect of the alloy factor ka on the resulting carburi-
zation profile is performed. The SimCarb simulations are displayed in Fig. 23 together with the
SIMS measuring points. The central carbon distributions for the AWT recommendation are respec-
tively enclosed by the limiting concentration profiles based on the minimum (Sauer et al., [28]) and
maximum (Neumann et al., [29]) versions of the SimCarb library of the alloy factor ka.
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Fig. 23. Measured carburization profile of experiment N° 2 and simulations, including ka analysis.
The interpretation of the results summarized in Table 7 proves to be less clear than in experiment
N° 1. However, the alloy dependent carbon diffusion coefficient calculated by SimCarb Diffusivity
again predicts the actual carburization depth of 3.55 mm better than the reference data of Tibbetts.
Table 7. Carburization depth, CCD in mm, for the indicated SimCarb simulations of Fig. 23 based
on the given alloy factors ka. The SIMS carbon measurement provides CCD≈3.55 mm.
Sauer et al., [28] AWT, [9] Neumann et al., [29]
ka=0.9461 ka=1.0371 ka=1.0819
SimCarb Diffusivity 3.07 3.28 3.39
Tibbetts, [8] 4.01 4.27 4.39
The application of Einstein’s equation to the outcome of experiment N° 1, CCD≈1.7 mm, yields
CCD≈3.05 mm for the longer process of Fig. 22 (43.7 h compared to 13.55 h). The actual value of
3.55 mm exceeds this simple estimation, at similar basic carbon contents, by 0.5 mm, which corre-
sponds to an extension of 15 h or 35%. A higher diffusion coefficient in experiment N° 2 is thus
suggested, in agreement with the prediction of SimCarb Diffusivity in Fig. 18.
The influence of the alloy factor on the carbon profile is noticeable. This finding of Fig. 23
underlines the usefulness of supporting steel specific ka measurements, e.g. by means of the foil
method, in case hardening engineering.
Single hardening
After carburizing, the test cylinder is slowly cooled to room temperature (hydrogen desorption
anneal irrelevant in this context). The hardening result is simulated by SimCarb QuenchTemp.
Austenitizing at 830 °C (KASTM=8, relatively fine microstructure) is followed by quenching in still
oil of 53 °C. Final tempering occurs at 200 °C for 2 h. The micro hardness profiles are measured.
The values are converted in HRC in Fig. 24. The case hardening depth at 52.5 HRC, CHD, after
quenching and tempering amounts to 4.24 and 3.85 mm, respectively (cf. Fig. 2). The simulations
are based on the SIMS data of the carbon distribution of Fig. 23 (see diffuse curve in Fig. 1). The
profile of the quenching hardness Hq is well predicted by the software. The corresponding case
hardening depth of 4.02 mm is indicated in Fig. 24.
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Fig. 24. Measured quenching and tempering hardness of experiment N° 2 and corresponding simu-
lations by means of SimCarb QuenchTemp. The case hardening depth, CHD, is indicated.
Calculating the tempering from the simulated quenching hardness provides CHD=3.51 mm. The
difference of 0.34 mm to the measurement result mainly stems from the slightly deviating Hq values
at x≥3.5 mm (see Fig. 24). Using the determined quenching hardness, the SimCarb QuenchTemp
simulation yields visibly better agreement with the experimental tempering data. With CHD=3.75
mm, a deviation of only 0.1 mm remains in Fig. 24.
The volume content of retained austenite, vRA, and the XRD peak width, FWHM, are measured
in the tempered condition. Fig. 25 compares the results with the prediction of the composition of the
microstructure by SimCarb QuenchTemp. The bainite fraction is denoted vB (no pearlite and ferrite).
Fig. 25. Measured retained austenite content and prediction of the microstructural composition by
means of SimCarb QuenchTemp. The obtained XRD peak width profile is also plotted.
The simulated retained austenite amount in the edge zone is just over 5 vol.% lower than deter-
mined. The effect of this deviation on the hardness is evidently small. From 3 mm on, as drawn in
Fig. 25, a slightly increasing volume fraction of bainite, vB, is computed by the software (cf. Fig.
15), which would be suppressed by stronger quenching, e.g., in agitated water. At the tempering
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temperature of 200 °C, only minor retained austenite decomposition occurs. The XRD peak width is
sensitive to the hardness. It is thus reduced by tempering. The decrease of the hardness from a depth
of 2.5 mm on is clearly reflected in the FWHM profile.
Carburizing Experiment N° 3 on 15NiCr13
Fig. 26 reveals the time course of the carbon potential, cp, and the mass transfer coefficient, β, for
experiment N° 3. A conventional two-stage boost-diffuse gas carburizing process is applied.
Fig. 26.
Time course of the carbon
potential and the mass transfer
coefficient in the gas carburizing
process of experiment N° 3,
determined in the boost and diffuse
stage by the foil method.
The virtually coincident carburization profiles simulated by using the diffusion coefficients of
SimCarb Diffusivity for the test steel composition in Table 6 and the Fe–C reference of Tibbetts (see
Fig. 18) agree quantitatively with the SIMS measurement in Fig. 27. The CCD values of both calcu-
lated concentration distance curves are indicated in the diagram.
A comparison of Figs. 21 and 27 provides strong evidence that the diffusion coefficient of car-
bon in austenite depends significantly on the alloy composition of the steel. It is recommended to
include this correlation in the process control of carburizing [30].
Fig. 27.
Measured and simulated carburization pro-
files of experiment N° 3.
An influence analysis of deviations of
the mass transfer coefficient, e.g. due to measurement inaccuracies, is conducted in Fig. 28 for the
carburization profile simulated on the basis of the SimCarb Diffusivity data. A considerable
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variation of the β value of 2.5×10−5
cm/s, determined in both carburizing stages (cf. Fig. 26), of
±1.0×10−5
cm/s is assumed. The resulting small deviation of the carburization depth within ±0.1
mm, indicated in Fig. 28, reflects the fast surface reactions in oxygen-containing industrial gas
mixtures.
Fig. 28. Measured carburization profile of experiment N° 3 and simulation based analysis of the
effect of varying mass transfer coefficient for the CDC predicted by SimCarb Diffusivity.
The result of this evaluation is graphically illustrated in Fig. 29 also for the carbon diffusivity in
austenite according to Tibbetts. The carburization depth is plotted as a function of the mass transfer
coefficient over the whole typical range from 1×10−5
to 4×10−5
cm/s. Conventional carburizing pro-
cesses are mainly controlled by carbon diffusion.
Fig. 29.
Case carburization depth as a function of
the mass transfer coefficient according to
Fig. 28.
Conclusions
Advanced simulation tools provide a deeper insight into the heat treatment processes of steels and
optimization potential in terms of quality and productivity, energy or resource efficiency. The
stand-alone SimCarb software suite for offline computer aided case hardening consists of the three
interacting Windows programs SimCarb, SimCarb Diffusivity and SimCarb QuenchTemp. The
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mathematical analysis of carburizing, quenching and tempering is based on physical material and
process models. The expert software represents the key element of case hardening engineering.
The present paper introduces the program SimCarb Diffusivity. This software provides steel
specific exponentially concentration dependent carbon diffusion coefficients in austenite containing
substitutional alloying elements in the mathematical form of the manual SimCarb input expression
for the simulation of carburization profiles. The implemented quantitative physically based model is
described in detail.
By applying the new tool, the fundamental question is analyzed theoretically and experimentally
of whether low alloying additions of, e.g., Cr, Mn, Mo, Ni or Si around 1 wt.% typical of case hard-
ening materials significantly influence the carbon diffusion coefficient in austenite. A numerical
study of a two-step boost-diffuse gas carburizing treatment of several steels is performed based on
SimCarb Diffusivity calculations. A considerable effect of the alloy composition on the resulting
carbon profile and particularly on the main process target quantity of the carburization depth, taken
at 0.35 wt.% C, is indicated, even within the specification of individual grades.
Three carburizing case hardening experiments are carried out on 18NiCrMo14-6 and 15NiCr13
steel. The carburization profiles are measured by secondary ion mass spectroscopy on polished
microsections of the test cylinders. The evaluation provides strong evidence that the diffusion
coefficient of carbon in austenite depends significantly on the steel composition. It is indicated to
also include this correlation in the computer aided process control of carburizing. The SimCarb
Diffusivity prediction that carbon diffusion occurs faster in the austenite of 15NiCr13 than of
18NiCrMo14-6 is confirmed by the experiments. The hardening processes of quenching and tem-
pering are investigated by means of SimCarb QuenchTemp.
References
[1] Wünning, J.: Grundlagen der rechnergesteuerten Aufkohlung, in: Einsatzhärten, edited by J.
Grosch and J. Wünning, Association for Heat Treatment and Materials Technology (AWT),
Berlin, 1989, pp. 154–171, in German.
[2] Parrish, G.: Carburizing – Microstructures and Properties, ASM International, Materials Park,
Ohio, 1999.
[3] Gegner, J.: Analytical Modeling of Carbon Transport Processes in Heat Treatment Technology
of Steels, Proc. 3rd
Int. Conf. on Mathematical Modeling and Computer Simulation of
Materials Technologies (MMT), Ariel, Israel, 6th
–10th
September 2004, College of Judea and
Samaria, 2004, Chap. 1, pp. 95–106.
[4] Vasilyev, A. A.: Carbon Diffusion Coefficient in Complexly Alloyed Austenite, Proc. Conf.
on Materials Science and Technology (MS&T), Detroit, Michigan, 16th
–20th
September 2007,
ASM International, Materials Park, Ohio, 2007, pp. 537−551.
[5] Ågren, J.: A Revised Expression for the Diffusivity of Carbon in Binary Fe–C Austenite.
Scripta Metall., 20 (11), 1986, 1507–1510.
[6] Wells, C., Batz, W. and Mehl, R. F.: Diffusion Coefficient of Carbon in Austenite. Trans.
AIME, 188 (3), 1950, 553–560.
[7] Hartl, M. and Wever, H.: Ermittlung der Aktivität des Kohlenstoffs im System Eisen–Chrom–
Kohlenstoff mittels des Diffusionsverfahrens. Arch. Eisenhüttenwes., 43 (8), 1972, 609–612.
[8] Tibbetts, G. G.: Diffusivity of Carbon in Iron and Steels at High Temperatures. J. Appl. Phys.,
51 (9), 1980, 4813–4816.
1-286
[9] Grabke, H. J., Grassl, D., Hoffmann, F., Liedtke, D., Neumann, F., Schachinger, H., Weissohn,
K.-H., Wünning, J., Wyss, U. and Zoch, H.-W.: Die Prozessregelung beim Gasaufkohlen und
Einsatzhärten, expert publisher, Renningen, Germany, 1997, in German.
[10] Hajduga, M. and Kučera, J.: Decarburization of Fe–Cr–C Steels during High-Temperature
Oxidation. Oxid. Met., 29 (5/6), 1988, 419–433.
[11] Kučera, J., Hajduga, M., Glowacki, J. and Brož, P.: Decarburization and Hardness Changes of
Fe–C–Cr–Mn–Si Steels Caused by High Temperature Oxidation in Ambient Air. Z. Metallkd.,
90 (7), 1999, 514–521.
[12] Adamaszek, K., Bro, P. and Kučera, J.: Decarburization and Hardness Changes in Carbon
Steels Caused by High-Temperature Surface Oxidation in Ambient Air. Defect and Diffusion
Forum,194–199, 2001, 1701–1706.
[13] Wilbrandt, P.-J., Gegner, J. and Kirchheim, R.: On the Application of SIMS for the Determina-
tion of Carbon Depth Profiles, in: Physics meets Industry, edited by J. Gegner and F. Haider,
expert publisher, Renningen, Germany, 2007, pp. 58–74.
[14] Lee, S.-J., Matlock, D. K. and van Tyne, C. J.: Carbon Diffusivity in Multi-Component
Austenite. Scripta Mater., 64 (9), 2011, 805–808.
[15] Lee, S.-J., Matlock, D. K. and van Tyne, C. J.: An Empirical Model for Carbon Diffusion in
Austenite Incorporating Alloying Element Effects. ISIJ Int., 51 (11), 2011, 1903–1911.
[16] Gegner, J. and Bontems, N.: First Purchasable High-End FDM Software for Advanced Case
Hardening Technology of Steels, Proc. 4th
Int. Conf. on Mathematical Modeling and Computer
Simulation of Materials Technologies (MMT), Ariel, Israel, 11th
–15th
September 2006, College
of Judea and Samaria, 2006, Vol. 1, Chap. 2, pp. 1–20.
[17] Smirnov, A. A.: Theory of Diffusion in Interstitial Alloys, Naukova Dumka, Kiev, 1982, in
Russian.
[18] Blanter, M. E.: Carbon Diffusivity in Austenite. J. Tech. Phys., 17, 1947, 1331‒ 1339, in Rus-
sian.
[19] Blanter, M. E.: Effect of Nickel on Carbon Diffusion in Austenite. J. Tech. Phys., 20, 1950,
217–221, in Russian.
[20] Blanter, M. E.: Effect of Cobalt on Carbon Diffusion in Austenite. J. Tech. Phys., 20, 1950,
1001–1004, in Russian.
[21] Blanter, M. E.: Effect of Manganese on Carbon Diffusion in Austenite. J. Tech. Phys., 21,
1951, 818–821, in Russian.
[22] Krishtal, M. A.: Diffusion Processes in Iron Alloys, Publishing House of the Literature on Fer-
rous and Nonferrous Metallurgy, Moscow, 1963.
[23] Babu, S. S. and Bhadeshia, H. K. D. H.: Diffusion of Carbon in Substitutionally Alloyed
Austenite. J. Mater. Sci. Letters, 14 (5), 1995, 314–316.
[24] Rowan, O. K. and Sisson Jr., R. D.: Effect of Alloy Composition on Carburizing Performance
of Steel. J. Phase Equilib. Diffus., 30 (3), 2009, 235–241.
[25] Blazek, K. E. and Cost, J. R.: Carbon Diffusivity in Iron–Chromium Alloy. Trans. JIM, 17
(10), 1976, 630–636.
[26] Eckstein, H.-J.: Technologie der Wärmebehandlung von Stahl, Deutscher Verlag für Grund-
stoffindustrie, Leipzig, Germany, 1987, 468, in German.
1-287
[27] ASTM E112: Standard Test Methods for Determining Average Grain Size, ASTM Internation-
al, West Conshohocken, Pennsylvania, 2006.
[28] Sauer, K. H., Lucas, M. and Grabke, H. J.: Kohlenstofflöslichkeit, Legierungsfaktoren und ma-
ximale Löslichkeit in Einsatzstählen bei 950 °C. HTM, 43 (1), 1988, 45–53, in German.
[29] Neumann, F. and Person, B.: Beitrag zur Metallurgie der Gasaufkohlung – Zusammenhang
zwischen dem Kohlenstoffpotential der Gasphase und des Werkstückes unter Berücksichti-
gung der Legierungselemente. HTM, 23 (4), 1968, 296–310, in German.
[30] Gegner, J.: Verfahren zum Aufkohlen eines Eisenwerkstoffes. German Patent DE 10 2010 039
941 B4, 2012, in German.