1

Transactions of Materials and Heat Treatment, Vol. 25, No. 5, 2004, pp465-470.
14th Congress of International Federation for Heat Treatment and Surface Engineering, October 26-28, 2004, Shanghai, China

Verification of Inverse Quench-Hardening Phenomena in Bearing
Steel Specimens by Experiment and Computer Simulation
Kyozo Arimoto1, Chuanrong Jin 2, Shigeyuki Tamura 2,
Kiyoshi Funatani3, Mamoru Tajima4
1. Arimotech Ltd., Osaka, Japan
2. CRC Solutions Corp., Tokyo, Japan
3. IMST Inst., Nagoya, Japan
4. Kanagawa University, Kanagawa, Japan
Abstract: The appearance of lower hardness at the surface than at the core after through-hardening of steels is known as“inverse quench-hardening.” Pioneering work was performed in the 1970s by establishing a simple test procedure where
cylindrical specimens were cooled by air and brine sequentially to produce the effect. This phenomenon was described inrelation to the polymer quenching and its effect to the improvement in the fatigue strength of the steel in the 1990s. The
hardening mechanism in the same specimens as the pioneering work was recently examined using a finite element
simulation method. However, this work has not been completed for lack of experimental quenching cooling curves for thecomparisons. In this study, the same experiments using 20mm diameter cylindrical specimens as those of the pioneering
work were conducted to obtain cooling curves and hardness distributions for comparing simulated results. Experimental
cooling curves showed a temperature recovery as predicted by the simulation. Also the inverse quench-hardening
phenomena were found in the measured and simulated hardness distributions of the specimens.
Key words: Inverse Quench-Hardening, Heat Treatment Simulation

TYPICALLY, steel parts show full-hardening
throughout the cross-section or incomplete hardening at
the core part depending on the hardenability of the steel.
However, it was reported that some bearing steels withhigh hardenability occasionally exhibit lower hardness
at the surface than at the core after oil quenching. Thisphenomenon was designated as “inverse quenchhardening” by Shimizu and Tamura [1], since theresulting hardness distributions were inverted from theconventional behavior.
Shimizu and Tamura [1, 2] developed a simplified
experimental program using cylindrical specimens toanalyze the inverse quench-hardening phenomenon
occurring under the production conditions. The
specimens were cooled by air and brine sequentially to
produce the inverse hardening phenomenon. A
theoretical explanation of inverse hardening in thisspecimen was also proposed, using a CCT diagram
considering discontinuous cooling rates.
Liscic et al. [3, 4] reported inverse quenchhardening in their polymer quenching tests using AISI
4140 cylindrical specimens based on the Controllable
Delayed Quenching (CDQ) technology. It was notedthat this phenomenon contributes to the improvementin the fatigue strength based on their fatigue tests.
Arimoto et al. [5] simulated the experiments using
cylindrical specimens conducted by Shimizu andTamura [1, 2], and explained that the phenomenon isrelated to a pearlite transformation. The simulated
results showed that a temperature recovery in thecooling curves during air-cooling was achieved by thegeneration of latent heat during the pearlitic
transformation. However, they could not verify theirsimulated temperature recovery phenomena for lack ofexperimental cooling curves in the reports by Shimizu
and Tamura [1, 2].
In this research, the same experimental procedure as
performed by Shimizu and Tamura was used, and thecooling curves and hardness distributions on crosssections of the cylinders were measured. The coolingcurves exhibited the same temperature recovery
phenomenon that was predicted by the simulation
during the air cooling. Moreover, the inverse
quench-hardening phenomena were verified from themeasured and simulated hardness distributions in thespecimens after cooling.

1. Hardness Distributions in the Specimens
Shimizu and Tamura [1, 2] suggested that thepractical inverse quench-hardening phenomenon
occurring during oil quenching is due to the formationof the vapor blanket by the quenching oil. Lastly, asimplified experimental program was proposed toreproduce the phenomena in the laboratory bysimulating the vapor blanket stage by air-cooling andusing simple cylindrical specimens. Sizes of theircylindrical specimens were: 10, 15, 20, 25, 30, and 36
mm in diameter.
In this research, only the bearing steel specimen, 20
mm in diameter and 40 mm length, as shown in Fig. 1
was examined using the same experimental conditions
as reported by Shimizu and Tamura. The chemical

2

Table 1 Composition (mass %) of Steel Specimen
C
0.99

Si
0.21

Mn
0.4

P
0.09

S
0.04

Cr
1.51

composition of the Japanese standard bearing steel,
SUJ2, is shown in Table 1. The specimen was equipped
three holes for thermo-couples at the positions of 0, 5
and 8 mm from the center of the cylinder as shown in
Fig. 1 when measuring cooling curves.
After austenitizing at 840°C for 40 minutes, thespecimens were initially cooled in air, and finallyquenched in a 5% brine solution. In these tests, theinfluence of air-cooling on the inverse quenchhardening phenomenon was investigated by varying thecooling times from 60 to 120 s. In Fig. 2, solid curves
show the measured hardness distributions in Rockwell
C scale, HRC, on cross-sections of cylinders. The timeshown adjacent to each curve indicates the time of
air-cooling. A horizontal axis of the graph is the radial
distance from the surface of the cylinder. The inverse
quench-hardening phenomenon is found in the solid
curves for 70 to 100 s times of air-cooling.
The hardness was measured at some points along thetwo straight lines that intersect each other at rightangles at the center of the cylinder cross-section. Thismeans that hardness data was measured at four points
with an equal distance from the center. The solid curves
in Fig.2 were drawn by the fitting of the averagehardness at the four points. The dashed lines in Fig.2
show the hardness curves measured by Shimizu andTamura [1]. In their experiment, the inverse
quench-hardening phenomenon became remarkable attimes from 50 to 90 s.

2.

Simulation of the Inverse
Hardening Phenomena

ρ cT =∂  ∂T k + LIJ ξ IJ
∂xi  ∂xi (1)where T, ρ, c and k denote temperature, density,
specific heat and thermal conductivity, respectively.
ξIJ and LIJ are phase transformation rate and latent heatproduced from phase I to J transformation, respectively.
In this research, the volume fraction of the diffusion
type transformation, ξIJ , was estimated by the KJMA
(Kolmogorov –Johnson –Mehl –Avrami) [6-8]equation:ξ IJ = 1 − exp(−bt n )(2)where b and n are material constants.
Agarwal et al. [9] studied temperature and volume
fraction changes in cylinders under many coolingconditions by the simulation based on the eq. (1) and(2). Some of their simulated temperature changes werecompared with the experiments by Takeo et al. [10],while the simulated transformation changes werereported without the comparison because of lack of theexperimental data.
The research on the latent heat under transformations
has been studied for many years, and especially thedata of the latent heat in the A3 transformation of pureiron has been determined. Guillermet et al. [11]estimated the latent heat of pure iron strictly based on
past experimental data and the thermodynamic model.
However, there are few measurements on the latent
heat of carbon steels, for example, carbon steels,
containing 0.415, 0.435, 0.8, 0.84, and 1.22%C, by
70

40s

Quench-Since the simulation of the inverse quench-hardening
phenomenon is mainly for predicting hardness, stressand distortion phenomena can be disregarded. The
temperature field is therefore governed by the equationconsidering latent heat:

60

60s

60s

70s

50s

50
Hardness, HRC

Steel
SUJ2

70s
80s 90s

40

80s
90s

100s
110s

30

100s

20
This research
Shimizu & Tam ura

1000

Fig.1 Test specimen Dimensions and Location ofInstrumented Thermocouple Holes.

Fig.2

2
4
6
8
Distance from the surface, mm

Measured Hardness
Specimens.

Distribution

10

in

3

Table 2 Latent heat (kJ/kg) of pure iron andeutectoid steels
Guillermet et al
Awbery et al
Kramer et al
Krielaart et al
Tajima18.1

Eutectoid
steel (0.8%C)
43.0
75.4-77.0
85 (cooling)

16(heating), 19(cooling)

Awbery et al. [12] and eutectoid steels by Kramer et al.
[13]. The latent heat by Kramer et al. was measured
using the method proposed by Smith [14].
Recently, the latent heat of carbon steels, containing
0.17, 0.36, 0.57, or 0.8%C, was measured by Krielaart
et al. [15] using differential scanning calorimetry, DSC.
Also, Tajima [16] applied DSC to ten carbon steels
including with carbon contents of 0.001%C to 0.69%C.
Table 2 is a comparison of latent heat values in apure iron and eutectoid steels from theabove-mentioned experiments. The measured latentheats of the pure iron (0.001%C) by Tajima varied in
the heating or cooling test, as shown in Table 2. The
value of 18.1 kJ/kg by Guillermet et al. is between 16
and 19 kJ/kg determined by Tajima.
For the three eutectoid steels, the value by Awbery et
al. is the lowest. The measurement of eutectoid steel by
Kramer et al. showed a temperature arrest at the A1
transformation, while in the measurements by Krielaart
et al. and Awbery et al., the temperature was changed
continuously and not arrested. The measured values by
Kramer et al. are between 75.4 and 77.0 kJ/kg, becauseof different pearlite spacing in the prepared specimens.
Since a diffusion-type transformation progresses overa wide range of temperatures under the usual heat
treatment conditions, a temperature arrest does notoccur during cooling. In this transformation process, it
is assumed that the heat generation, which is calculated
by multiplying whole latent heat LIJ and transformation
rate ξIJ as shown in eq. (1), is produced at each timeincrement. The accuracy of the model described by eq.
(1) and (2) has not been rigorously evaluated,
especially when producing temperature recoveries dueto the latent heat.

3. Comparison between Experimental and
Simulated Results
The inverse-quenching phenomena occurring in thetest specimens of this research was simulated. We used
the simulation software that was developed based on
the finite element method for implementing the model
described by eq. (1) and (2) and verified according to
the procedure reported by Agarwal et al. [9].
The TTT diagram of the bearing steel was specified

Temperature, C

Pure Iron

600
400
200
Original curves
Shifted curves

0 -1
10

10 0

10 1

10 2
10 3
Time, s

10 4

10 5

Fig.3 Original and Shifted TTT Curves of 52100
Bearing Steel.

based on the data of 52100 steel, containing 1.02%C,
0.36%Mn, 0.2%Ni and 1.41%Cr, by US Steel [17].
However curves at the transformation start and end
were shifted along the time-axis by trial and error as
shown in Fig. 3. The performance of the transformation
is affected by shifting the curves as explained by
Arimoto et al. [5]. For the simulation, thermal physicalproperties were used from the data of BISRA [18]and/or calculated using the empirical formula by
Miettinen [19]. A latent heat of 75.8 kJ/kg was applied
for the austenite-pearlite transformation. This value wasproposed by Kramer et al. [13], and used previously by
Agarwal et al. [9] for their simulation. The heat transfer
coefficient at the surface in the air-cooling was set
based on the experimental data by Yamaguchi et al.
[20].
The 20 mm cylindrical specimen was simulated as an
axisymmetric problem using 100 finite elements along
the radial axis. Simulated temperature changes during
850

Temperature, C

Authors

800

Measured
Simulated

800
r=0

750
700
r=8

650
without latent heat

600
0

50

100

150

Time, sFig.4 Measured and Simulated Cooling Curves
during Air-cooling.

4

1

720

Temperature, C

710

Measured
50s
60s
65s
70s
75s
80s
90s
100s
110s
120s

80s
75s

700

50s 100s 70s
65s

90s

110s

690

0.8

100s

0.6

90s
80s
75s
70s

0.4
65s

0.2
0
0

60s

60s

2

4

6

8

10

Distance from the surface, mm

120s

680

110s

Pearlite volume fraction

Simulated

Fig.7 Simulated Distributions of Pearlite Volume
Fraction in Air-Cooled Cylinder.
670
0

2

4

6

8

10

Distance from the surface, mm

Fig.5

Measured and Simulated Temperature
Distributions during Air-cooling.

air-cooling at two locations, 0 and 8 mm distances fromthe center are shown by the solid curves in Fig. 4.
These curves agree with the dotted curves derived fromthe experiments precisely in the range between 840°C
and near 680°C. A temperature recovery phenomenon
is found in the cooling curves from almost 60 s after
starting of cooling. Some discrepancies are observed in
between the experimental and simulated cooling curvesin the range of the temperature recovery. When thelatent heat is not considered, simulated curves do notshow the recovery phenomenon as shown in Fig. 4.
These results suggested that the temperature recovery is
due to the latent heat. The simulated and measured
temperature distributions during its recovery period are1

Temperature, C

Volume fraction
without latent heat

0.8

800

0.6
Volume fraction
with latent heat

750

0.4

Temperature

700
650
0

r=0
r=5
r=8
r=10

0.2
50

100

Pearlite volume fraction

850

0
150

Time, sFig.6 Temperature and Pearlite Volume Fraction
Predictions in Air-Cooled Cylinder.

shown in Fig. 5 for describing the effects by the latent
heat in detail.
Simulated temperature and volume fraction of
pearlite changes at four locations, 0 5, 8 and 10 mmdistances from the center as shown in Fig. 6. The
volume fraction change shows that the transformation
at the surface part progresses faster than that at thecenter, although the temperature difference between thecenter and surface of the cylinder is relatively small.
Ultimately, the transformation at the center can be seen
to occur almost 50 s longer than that at the surface.
When simulated without the latent heat, the volume
fraction curves at different locations are parallel for theentire transformation period as shown in Fig. 6.
Agarwal et al. [9] reported the observation of thistransformation delay at the center, but did not offer an
explanation. This delay was explained by Arimoto et al.
[5] using locus curves on the plane of transformation
rate and temperature. They considered that the delay
occurs because of both the high temperaturedependency of the transformation activity and thetemperature recovery due to latent heat, even if thetemperature difference between the surface and thecenter is not large.
Simulated pearlite distribution changes during aircooling are shown in Fig. 7. Higher volume fractions ofpearlite are distributed near surface in the cooling range
between 60 and 110 s. The largest difference of thevolume fraction occurs between the surface and centerfrom 70 to 80 s. These results can be seen from thecurves of the volume fraction change at four locationsof the cylinder in Fig. 6.
In the tests, the specimens were initially cooled in air,and finally quenched in the 5% brine solution. Sincebrine quenching has high cooling ability, the retained
austenite in a specimen after the air-cooling would bealmost transformed to martensite, and the pearlite

5

110s
100s
90s

70s

750

80s
70s

700
650

Temperature 60s

600Center
Surface

550
0

0.8
0.6
0.4

60s

50

100

0.2
0
150

60s

60
50

65s

90s

70s

100s

75s

40

90s

30

80s

100s

20

110s

Time, sFig.8 Temperature and Pearlite Volume Fraction
Predictions in Air and Brine-Cooled
Cylinder.
transformation may be stopped by the rapid cooling. It
is suggested that the resulting pearlite distributions
shown in Fig. 7 would be retained after brine
quenching.
Figure 8 shows simulated temperature and volume
fraction change in the cylinder during air and brinecooling. Six different times, 60, 70, 80, 90, 100 and 110
s for air-cooling were investigated. Once the brine
quenching started, the pearlite transformation at thesurface stops suddenly, while that at the center theprocess continues for a few seconds longer.
The experimental and predicted hardness
distributions in the cylinder were compared as shown in
Fig. 9. The hardness value h was calculated by theequation:h = hPξ P + hM ξ M(3)where ξP and ξM are the volume fraction of pearlite andmaretensite, respectivly. hP and hM are the hardness for
pearlite and martensite, 24 and 66 HRC, respectively, inthis estimation.
The predicted and measured hardness exhibit similar
distribution tendencies, which indicate inverse
hardening for all cases. However, there werediscrepancies in the magnitudes and timings. One
reason for the discrepancies is most likely caused by
the non-availability of TTT data for the steel specimens
used in this research. It is believed that the process isextremely sensitive to minor differences in TTT data.
In addition, the value of latent heat used in thesimulations may not have been completely suitable forthe bearing steels analyzed in the current work.

4. Conclusions
Experimental and simulated results were comparedto verify the inverse quench-hardening phenomena in

110s
Measured
Simulated

10
0
0

Fig.9

70s

80s

60s

Hardness, HRC

80s

Volumefraction

800
Temperature, C

70

1Volume fraction transformed

850

2
4
6
8
Distance from the surface, mm

Experimental and Simulated
Distributions in Specimens.

10

Hardnessthe specimens proposed by the pioneering work. The
results obtained are summarized as follows:(1) The predicted temperature recovery was found in
the cooling curves of the specimen which produces theinverse quench-hardening phenomenon by theexperiment.
(2) The inverse quench-hardening phenomena wereverified from the experimental and simulated hardness
distributions in the specimens.
(3) The test of the inverse quench-hardening in thecylinders can be applied for observing the pearlite
transformation progress under the temperature recovery
phenomenon during slow cooling.
(4) This experiment can be used for improving theaccuracy in the model and data to describe thecharacteristics of the diffusion type transformation andits latent heat.
The thermal process simulator, FINAS/TPS,
developed by CRC Solutions Corp. was used for thesimulation in this research.
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1
2

3

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Corresponding author: Mr. Kyozo Arimoto,
Email: arimo@arimotech.com,
Mail address: 822-10 Asonaka, Kaizuka, Osaka 597-0081 Japan,
Tel & Fax: +81-724-28-0272