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Monitoring of the diffusion processes during carburizing automotive steel parts
Iva Nová1, Jiri Machuta1
1Faculty of Mechanical Engineering, Technical University of Liberec, Studentská 2, 461 17 Liberec 1, Czech Republic.
Email: iva.nova@tul.cz, jiri.machuta@tul.cz
The article deals with the prediction of diffusion process of steel components, respectively diffusion of carbon
during carburizing. The calculation was made on the basis of the solution diffusion in semiinfinite space. For the
calculation there was used the II. Fick's law. For the reason that the transfer medium is formed at the interface
environments diffusion boundary layer, for the more accurate calculations, it is necessary to consider the
coefficient of transfer of atoms of carbon. For the calculation of the diffusion coefficient D was used Arrheni
us´s equation, which is based on the rate of diffusion processes (diffusion). It was calculated the time for diff usion
of carbon to achieve the concentration of 0.8% C. There was also made a calculation of carbon diffusion in the
gear from material EN DIN 1.7142 (DIN 14221). Diffusion was performed at 950 ° C, the initial concentration of
carbon was 0.2%. Carburizing carbon concentration was 1.1% C and carburizing time was 1, 3 and 6 hours.
Keywords: Carburizing, Diffusion, Carbon, Gearwheel, Calculation
1 Introduction
Nowadays are in the automotive industry more and more applied methods which are necessary for improving the
quality and utility properties of products. These products include shafts and gears of cars gearboxes. To ensure high
hardness of the gear flanks is currently used carburizing, followed by rapid cooling in a suitable medium. Carburizing is
among the methods of chemical and thermal processing, which uses the process of diffusion of carbon. The purpose of
carburizing is to increase the hardness of the surface of components and simultaneously ensuring tough inner parts of
the material. The material must have increased resistance to wear out and tear cyclic fatigue. Therefore, for these
purposes are used steels with low carbon content to about 0.2% [1].
In the process of chemical heat treatment of steels, respectively carburizing used penetration capability atoms diffusing
element, in this case carbon into the surface layer under conditions of relatively high operation temperatures of about
950 °C. Active atoms of carbon, which are arising through dissociation of molecules of chemical compounds on the
saturated steel surface. Active carbon atoms, which penetrate on the surface of the steel by diffusion, here they are
absorbed, relocate from the surface into the interior of the diffusion layer in accordance with the laws of diffusion. [2],
[3].
2 Theory of the diffusion
Diffusion of the active carbon atoms from the surface to the middle part is the process that determines the depth of
saturation of the layer. The depth of the diffusion layer depends on temperature, time and on the material, where the
diffusion takes place and on the diffusing element.
For efficient progress of diffusion is needed a sufficient concentration of diffusing carbon on the surface of the metal
throughout the process and heat the metal to a sufficiently high temperature to allow thermal motion of carbon atoms.
The diffusion of carbon describes II. Fick's law. This law is valid for nonstationary diffusion conditions. The rate of
change of concentration at a given point caused by the diffusion is proportional to the concentration gradient at that
point. The constant of proportionality (D) is called the diffusion coefficient [4], [5].
If the diffusion coefficient (D) is constant, it is possible to calculate the diffusion by using this equation:
(1)
If the diffusion coefficient (D) depends on the concentration c and position x, it is necessary to calculate by using this
form of the equation [6], [7], [8]:
(2)
Where:
c/t … Concentration change versus time (rate of change of concentration),
x
c
D
ct
c
2
2
xc
D
t
c
D… Diffusion coefficient,
2c/x2…Curvature concentration profile at a given point x,
c/x… Concentration profile at a given point x.
Solving equations (1) and (2) for diffusion in a semiinfinite medium (0 < x < ∞) during initial conditions before
diffusion: (t = 0) is the concentration c0 at each point (x > 0); boundary condition: in the planar interface at the point
(x = 0) is maintained constant concentration c1 throughout (t > 0), we can write:
, (3)
Where:
c… Concentration in a particular location of the material,
c0…Inicial concentration of carbon,
c1…Maximal concentration of carbon,
t …Time of diffusion,
erf …Gauss integral errors.
Because of the transfer of the medium form sat the interface environment diffusion boundary layer. For this reason it is
necessary to consider a more accurate calculation coefficient sharing of carbon
atoms [5]. The value of x from equa
tion (4) can then determine:
(4)
Where:
… Coefficient of transfer carbon atoms [ms1],
h…Depth carbon diffusion,
x…Total depth carbon diffusion.
The right side of equation (3) by substituting equation (4) can be expressed as:
(5)
The coefficient of sparing carbon atoms [8] for the carburizing proces is 1.30107 to 2.70107 [m.s1], [5].
Diffusion coefficient D can be determined by using the Arrheni´s equation, which details the speed of diffuse processes
(diffusion) [9],[10]. Within growing activation energy decreases the rate of diffusive happening. The diffusion supports
the temperature, which contributes to increasing the mobility of atoms. Arrheniu´s equationin puts to the centext the
speed of move of the atoms with the activation energy of atoms [4]:
(6)
Where:
D…Diffusion coefficient [m2.s1],
D0…Frequencyfactor [m2.s1],
HD…The activation energy of diffusion [Jmol1],
R… Gas constant 8314 [J.kmol1.K1],
T…Absolute temperature [K].
Into the equation (4) may be necessary to substitute the values from the Tab. 1. There are the selected values of
variables for calculating the diffusion coefficient (D) in Table 1.
Tab. 1 The values for calculating of the diffusion coefficient in diferent metals [4]
Diffusion
element
Diffusion
environment
D0
[m2s.1]
Hd [kJmol
1]
Rangeoftemperature
T [K]
t [°C]
H
Fe
2.0107
12.1
2931173
20900
tD
x
erf
cc
cc
2
1
01
0
D
hx
)(1
2
1
01
0zerf
tD
D
h
erf
cc cc
TRH
DD d
exp
0
H
Fe
6.7107
45.1
6231323
3501050
C
Fe
2.0106
6.2107
84.1 [4]
80.0 [3]
2931123
20850
C
Fe
4.0105[4]
2.3105[3]
140.0 [4]
148.0 [3]
7731373
5001100
Mn
Fe
7.6105
225.0
10631173
790900
Mn
Fe
1.8105
264.0
11731153
9001300
Fe
Fe
2.0104
241.0
6731473
4001200
Fe
Fe
5.0105
284.0
7731373
5001100
3 Diffusion calculations of carbon during carburizing
Calculation of time t to obtain the necessary concentration of carbon in the carburizing components
Diffusion coefficient D was calculated according to the Arrheniu´s equation (6), by substituting you can write:
(7)
Calculation of the time t of the diffusion of carbon, to obtain the necessary concentration of the carbon steel at various
locations at a distance x below the surface, done by applying II. Fick's law, see equation (1), the equation for the solu
tion is derived from the concentration ratio and the Gaussian´s error integral (5). After achieving concentrations and
calculated diffusion coefficient (4.1921011 [m2s1]).
(8)
On the based calculation erf (z) = 0.33 and a curve, see in Fig. 1, can be determined that the argument (z):
(9)
From this relationship can be expressed in time t: (10)
].[10192.4
1223314.8 140000
exp100.4 12115
)(
smD Fe
C
t
D
h
erf 11
10192.42
1
20.010.1 20.080.0
t
D
h
erf 11
10192.42
167.0
;33.0
2
tD
D
h
erf
36.0
2
tD
x
][5011)
36.010475.62 00033,0
(2
6st
Fig. 1 Context between argument (z) and Gaussian´s error integral erf (z)
To achieve a concentration of 0.80% of C under the surface layer of 0.33 mm, it is necessary the diffusion for about
5011 [s]. Tab. 2 gives the calculated values of time t for various values of x (0.1; 0.33 and 1.0 mm) below the surface of
the cemented material.
Tab. 2 Calculated value of time for the various layers of carburizing
Calculation of t [s] required to obtain a concentration of 0.80 % carbon in the carburizing in the
various layers below the surface D = 4.1921011 [m2s1]
Layer x
below the surface [m]
Carburizing
time [s]
0.00010
0.33
0.36
460
0.00033
0.33
0.36
5011
0.00100
0.33
0.36
46010
4 Determination of the distribution of the concentration of carbon in the gearwheel
The gearwheel was made from steel, see in Fig. 3. There is a chemical composition of the gearwheel in Tab. 3.
Chemical composition was monitored by spectrometer Q 4 TASMAN (fa. Bruker Elemental GmbH). The steel is
manganesechromium, very good ductility by heat. The steel is intended for chemical heat treatment. Carburizing was
performed by termical dissociation of CH4.
Tab. 3 Chemical composition of steel 1.7142
Chemical composition steel 1.7142, 20MnCr5 (ČSN 14 221)
C
Mn
Si
Cr
Ni
Mo
S
P
0.170.22
1.001.30
0.170.37
1.001.30


0.035
0.035
The calculation of the distribution of concentration of carbon in the carburized steel. To calculate these values were
considered carburizing  temperature 950 ° C, initial concentration of carbon in the steel of 0.20% C, carburizing con
centration at the surface of 1.1% C and the time of carburizing 1, 3 and 6 hours.When solving the diffusion of carbon in
the steel forging blank consider solutions in a compact semiinfinite material. The solution maybe performed by a
tD
x
erf 2
tD
x
2
Gaussian´s error integral (6). The calculated concentration of carbon in the steel incertain locations x below the surface
are shown in Tab. 4. In Fig. 2 is shown the dependence of difussing concentration of difussing carbon on distance in the
cementing of the gearwheel.
Tab. 4 The calculated values of carbon concentration in the carburizing of the gear
Distance from sur
face [mm]
Concentration of carbon [wt %]
3600 s (1 hour)
10 800 s (3 hours)
21 600 s (6 hours)
0
0.98
0.98
0.98
0.5
0.47
0.63
0.71
1.0
0.24
0.40
0.49
1.5
0.21
0.26
0.37
2.0
0.20
0.22
0.31
2.5
0.20
0.20
0.24
3.0
0.20
0.20
0.21
3.5
0.20
0.20
0.20
4.0
0.20
0.20
0.20
Fig.2 Dependence of carbon difussing concentration on distance
On the Fig. 3a is the observed gearwheel after carburazing. On the Fig. 3b there is shown an example of carburazing
surface layer of the gearwheel. On the Fig. 3c is the metallographic structure of the gearwheel after the heat treatment,
which was identificated on the light microscope.
Fig. 3 Carburazing gearwheel(a), carburizing layer(b), and structure after heat treatment(c)
5 Conclusion
Prediction of diffusion process has significant application in the chemical and thermal processing of metals. Diffusion
of carbon has a considerable importance during carburizing automobile parts, e.g. during carburizing gears of gear
boxes of cars. In industrial practice, it is used in a carburizing gas mixture (40% nitrogen, 20% hydrogen and 20% of
water, CO and CO2). In the automotive industry is recently used the vacuum carburizing gas atmosphere of pure
hydrocarbon. The advantage of the vacuum carburizing is a quick process, reduced deformation and tension in the
gears. It is supposed that the layer of carbon in the surface region of the gear is 0.8 to 1% carbon. After heat treatment 
hardening, it is assumed that hardness (microhardness) on the gearwheels surface is 550 HV 30. Calculation of diffusion
of carbon in the low carbons steel or carburization was conducted to determineted in diffusion time t. Initial concentra
tion of the carbon c0 was 0.20 wt. % C, carburizing temperature T = 950 °C. The surface of steel has been exposed to
carburizing atmostphere which formed on the carbonated surface a concentration of carbon c1 = 1.1wt % C.
Calculated time t is required to obtain a desired carbon concentration c = 0,80 wt% C in the depth x below the surface
(x = 0.1 mm, 0.33 mm a 1 mm) .
By carburizing hardening process is steel heated at 950 °C in a state Fe. At first it was calculated the diffusion
coefficient DC(Fe). Calculation required values are shown in Table 1. Frequency factor D0C(Fe) = 4,0.105 m2.s1 and
HD(Fe) = 140000 J mol1.
This article is financially supported by Ministry of Education Youth and Sports of Czech Republic through the
project SGS.
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