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Inspection of an end quenched 0.15% –0.2% C, 0.6%–0.9% Mn steel
jominy bar with photothermal radiometric techniques
Yue Liu, Natalie Baddour, Andreas Mandelis, and Chinhua Wang
Center for Advanced Diffusion Wave Technologies, Department of Mechanical and Industrial Engineering,
University of Toronto, 5 King’s College Road, Toronto, Ontario, M5S 3G8, Canada
(Received 17 February 2004; accepted 20 May 2004)
The effect of the cooling rate on hardness and thermal conductivity in a metallurgical Jominy bar
made of 0.15%–0.2% C, 0.6% –0.9% Mn (AISI 1018)steel, by means of a water end-quenched
heat treatment process without diffusion-controlled case depth, is studied with photothermal
radiometry (PTR). It is concluded that our two PTR techniques, common-mode rejection
demodulation and conventional 50% duty-cycle square-wave frequency scan, are sensitive to low
hardness values and gradients, unlike the high values all previous photothermal studies have dealt
with to-date. Both PTR methods have yielded an anticorrelation between thermal conductivity and
microhardness in this case as in previous cases with heat-treated and diffusion-controlled case depth
profiles. It is shown that the cooling rate strongly affects both hardness and thermal conductivity in
the Jominy-bar heat-treating process. © 2004 American Institute of Physics.
[DOI: 10.1063/1.1771478]
I. INTRODUCTION
In recent years, a number of photothermal applications
to hardness measurements in metals have been reported in
the literature. Establishing a quantitative correlation between
the microhardness and thermal conductivity or thermal dif-
fusivity is a key issue to performing reliable photothermal
hardness measurements. Various independent research
groups have reported a well-established anticorrelation be-
tween thermal diffusivity/thermal conductivity and micro-
hardness. Jaarinen and Luukkala1made the first attempt to
study the properties of surface hardness of steel in terms of
an inverse process and developed a numerical technique
based on the solution of the thermal-wave equation using a
two-dimensional finite difference grid. Lan et al.2used a
mathematical reconstruction technique3to obtain the thermal
conductivity depth profile of quenched steels, and found a
close anticorrelation between depth dependent thermal con-
ductivity and conventionally measured Vickers hardness.
Munidasa et al.4applied the thermal harmonic oscillator5
(THO)method on quenched steels and found an anticorrela-
tion between thermal diffusivity and microhardness. Later,
Mandelis et al.6showed that the results from investigated
cold-work depth profiles in rail track samples illustrated the
potential of photothermal depth profilometry as a nonde-
structive, noncontact inspection methodology of rail deterio-
ration as a function of length of service in the train transpor-
tation field. From this wealth of evidence it is now
established that the diffusivity depth profiles obtained for
case-hardened steels anticorrelate, at least qualitatively, with
destructive microhardness measurements. Fournier et al.7
used a photoreflectance setup as well as a photothermal ra-
diometric (PTR)setup to reconstruct the thermal diffusivity
depth profiles of hardened steel samples. They, too, showed
that there was an anticorrelation between hardness and ther-
mal diffusivity. Walther et al.8used two different experimen-
tal methods to determine the relation between hardness and
thermal diffusivity: the common laser flash technique to es-
timate the thermal diffusivity of a set of fully hardened, ho-
mogeneous specimens with different hardness produced by
appropriate heat treatments; and lateral scanning photother-
mal microscopy to estimate the thermal diffusivity depth pro-
file from localized measurements that was compared with the
hardness depth profile obtained by microindentation. In gen-
eral, despite the thermal-wave inverse problem types of re-
constructions applied to steels and the anticorrelation trends
observed between thermal diffusivity and hardness, no physi-
cal interpretation of the anticorrelated thermophysical and
mechanical depth profiles (mostly for quenched steels)has
been attempted. Only very recently attempts have been made
to offer physical interpretations of photothermally recon-
structed hardness depth profiles in processed steels. Nico-
laides et al.9concluded that the depth distribution of the
thermal diffusivity profile in a hardened low-alloy Mn, Si,
Cr, Mo Steel (AISI 8600)is dominated by carbon diffusion
during carburization, while the absolute thermal diffusivity
values are dominated by microstructural changes that occur
during quenching. The authors also pointed out that the va-
lidity of these conclusions for other types of steel is uncer-
tain. Most investigations to-date have focused on samples
heat treated in the presence of conventional elements, such as
carbon or nitrogen, to form a concentration gradient which
subsequently defines the hardness case depth profile after
quenching. The effect of heat treatment on the hardness and
conductivity is a combination of specific gas exposure in a
furnace and cooling rate. The relationship between hardness
and thermal diffusivity in carburized and carbonitrided steels
has been investigated by Nicolaides et al.9and Liu et al.10,11
JOURNAL OF APPLIED PHYSICS VOLUME 96, NUMBER 4 15 AUGUST 2004
0021-8979/2004/96(4)/1929/5/$20.00 © 2004 American Institute of Physics1929
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However, the type of relationship between hardness and ther-
mophysical properties resulting from the cooling rate of steel
still remains unclear. Nevertheless, in order to perform reli-
able photothermal hardness tests, the sensitivity of the pho-
tothermal techniques to hardness variation is very important.
To our best knowledge, all previous works2,4,7–9 have con-
cluded that photothermal techniques are sensitive to high
hardness (maximum ⬎800 HV and minimum ⬎200 HV)
and large hardness gradient (hardness case depth ⬍2mm).
The applicability of photothermal methods to low hardness
values 共⬍200 HV兲and gradients (case depth ⬎2mm)has
not been studied.
In this work we used laser infrared photothermal radi-
ometry (PTR)to explore this issue. A Jominy bar12 made of
AISI 1018 steel 共0.15% –0.2 % C, 0.6% –0.9% Mn兲was
end-quenched to form a mild hardness profile with continu-
ously varied cooling rate along the bar with maximum hard-
ness less than 14 HC 共⬇140 HV兲. Two types of PTR signal
generation techniques were used: conventional 50% duty-
cycle square-wave modulation and common-mode rejection
demodulation (CMRD).13,14 Vertical spatial scans along the
side of the end-quenched Jominy bar were performed, and
local hardness and thermal conductivity were measured.
Measurement results from the two methods and the relation-
ships between thermal conductivity and hardness profiles ob-
tained from destructive mechanical measurements will be
presented.
II. LASER-BEAM MODULATION WAVEFORMS
The two-pulse configuration of the CMRD scheme is
shown in Fig. 1. It has been shown13,14 that the in-phase and
quadrature demodulated lock-in outputs from any experi-
mental system driven by such a bimodal periodic pulse ex-
citation with period Tare given by
YIP共f兲
=− 2I0
冦
cos
冉
⌬
T
冊
冋
sin
冉
1
T
冊
+ sin
冉
2
T
冊
册
Re关S共f兲兴
+ sin
冉
⌬
T
冊
冋
sin
冉
1
T
冊
− sin
冉
2
T
冊
册
Im关S共f兲兴
冧
,
共1兲
YQ共f兲
=2I0
冦
sin
冉
⌬
T
冊
冋
sin
冉
1
T
冊
− sin
冉
2
T
冊
册
Re关S共f兲兴
− cos
冉
⌬
T
冊
冋
sin
冉
1
T
冊
+ sin
冉
2
T
冊
册
Im关S共f兲兴
冧
,
共2兲
where f=1/Tis the CMRD wave-form repetition frequency,
1and
2are the two pulse widths, and S共f兲is the corre-
sponding signal response of the experimental system to
single-pulse excitation at the same frequency. ⌬is the center-
to-center time delay.
The configuration of a conventional square-wave excita-
tion is shown in Fig. 2. The one dimensional thermal-wave
signal response is given by15
S共f兲=I0共1−R兲共1−i兲
冑keff
c
⬀1
冑keff ,共3兲
where
,crepresent the material density and specific heat,
respectively; I0is intensity of the laser beam; Ris the reflec-
tivity of the measured surface;
=2
f, and keff represents
the depth-variable effective thermal conductivity in the range
of the thermal diffusion length
and is given by
keff =1
冕
0
k共x兲dx.共4兲
From the above expressions it is clear that the corresponding
signal response of the experimental system to photothermal
excitation at a fixed frequency is in inverse proportion to the
effective thermal conductivity, regardless of the excitation
waveform.
FIG. 1. Optical excitation wave form consisting of a bimodal pulse applied
to the photothermal CMRD system. The horizontal time units are expressed
as a percentage of a full repetition period T;
1and
2are the corresponding
square pulse widths; ⌬is the center-to-center time delay. Only one repetition
period is presented for clarity.
FIG. 2. Optical excitation applied to conventional 50% duty-cycle square-
wave modulation in photothermal radiometry. Only one repetition period is
presented for clarity.
1930 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Liu
et al.
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III. SAMPLE PREPARATION AND EXPERIMENTAL
SETUP
A. End quenching
For the end-quenching heat treatment, a portion of the
1018 AISI steel bar was cut into the form of a Jominy bar.12
This bar was cylindrical in shape, half an inch in diameter,
and 4 in. long. A flat portion was ground on one side of the
bar to ensure a flat area for laser photothermal probing. The
end-quench test, also referred to as a Jominy test, is widely
used in the steel industry to simply and effectively determine
the hardenability of a particular steel.12 This test provides a
convenient and reproducible method of quenching steel bars
and determining the effect of cooling rate on the resulting
hardness and microstructure. In this instance, the Jominy bar
was heated in an oven at 900°C to austenitize it for one-half
hour and was then quickly transferred to a quenching jig,
which directs a controlled jet of water at one end of the bar.
Heat exchange between the hot steel and the water jet and
heat flow occurs primarily along the length of the bar, so that
the cooling rate varies from a high value at the quenched end
to a low value at the far end, thus forming a continuum of
hardness along the length of the bar. The Jominy curve was
obtained by making Rockwell C hardness measurements
along the length of the bar. The sideways flat portion was
carefully polished after the quenching to keep the surface
optically uniform.
B. Experimental setup
The experimental system for PTR scans is shown in Fig.
3. Ahigh-power 20 W diode laser (Jenoptik JOLD-X-CPXL-
1L)was current-modulated using a Thor Labs high power
laser driver, which accepted the voltage modulation wave
form from the signal function generator to modulate the laser
driving current. The largely anisotropic multimode laser
beam was expanded, collimated, and then focused on the
surface of the sample with ⬇1 mm diameter spotsize. The
infrared (Planck)radiation from the optically excited sample
surface was collected and collimated by two silver-coated,
off-axis paraboloidal mirrors and then focused onto a liquid
nitrogen-cooled HgCdTe (mercury-cadmium-telluride)de-
tector (EG&G Judson Model J15016-M204-S01M-WE-60).
The heated area of the sample was at the focal point of one
mirror positioned near the sample and the detector was at the
focal point of the other mirror. The HgCdTe detector is a
photoconductive element that undergoes a change in resis-
tance proportional to the intensity of the incident infrared
radiation. Our detector had an active square-size area of
1mm⫻1 mm and spectral bandwidth of 2–12
m. An an-
tireflection coated germanium window with a transmission
bandwidth of 2–14
m was mounted in front of the detector
to block any direct radiation from the laser. Prior to being
sent to the digital lock-in amplifier (EG&G Instruments
Model 7265), the PTR signal was amplified by a low-noise
preamplifier (EG&G Judson PA101), specially designed for
operation with the HgCdTe detector. The lock-in amplifier,
which was interfaced with a PC, received and demodulated
the preamplifier output. For CMRD measurements, the
thermal-wave in-phase and quadrature lock-in signals were
obtained as a function of
1,
2, and time delay ⌬. In con-
ventional 50% duty-cycle square-wave PTR measurements,
thermal-wave amplitude and phase were obtained. The pro-
cess of data acquisition and storage was fully automated.
IV. EXPERIMENTALRESULTS AND DISCUSSION
As a first step, conventional PTR frequency scans were
performed on the end-quenched Jominy bar. The scans were
performed upwards from the quenched end, and along the
bar every 0.5 cm to the middle of the bar, and then every
1 cm up to the other end of the bar. The modulated laser
beam was focused at each measurement point, and the fre-
quency was varied from 1 Hz to 2 kHz. Comparison of the
full photothermal frequency scan results showed that the
largest amplitude response variations in the entire frequency
range appeared ⬇100 Hz. The sensitivity of the technique to
changes in the thermophysical properties of the steel depends
on both magnitude of the thermophysical change and on ge-
ometry. When the Jominy bar was quenched, heat was trans-
ferred along the bar axially and laterally. The cooling rate at
any location inside the bar was a combination of cooling
rates in these two directions. Spots closest to the surface
experience higher lateral cooling rate than deeper spots, due
to the larger temperature gradient near the outer surface.
Since the cooling rate is the dominant factor in the hardness
profile formation when the chemical composition of the steel
does not change, the hardness of the surface is always higher
than that of the interior. Therefore, a hard surface layer
(“case”)is formed surrounding the bulk. From thermal-wave
calculations, the frequency range corresponding to peak PTR
sensitivity to hardness variations is expected to also corre-
spond to a thermal diffusion length range commensurate with
the mean case depth: At 100 Hz the thermal diffusion length
is ⬇200
m when the thermal diffusivity is 14 mm2/s.16
Based on the foregoing results, spatial scan experiments
were performed with a fixed frequency of 100 Hz.
FIG. 3. Experimental setup.
J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Liu
et al.
1931
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Given that the CMRD signal is a function of time delay
⌬when the pulse widths
1,
2are fixed, Fig. 1, time delay
scans with 100 Hz repetition rate along the Jominy bar were
performed to optimize the sensitivity of the CMRD PTR
signal with respect to time delay before scanning the length
of the Jominy bar side. The pulse widths were fixed at
1
=5% and
2=25% and the center-to-center time delay ⌬was
varied from 15% to 85%. Upon comparison of the ⌬-scan
results, both in-phase and quadrature signals were found to
exhibit combined optimal sensitivity at ⌬=17%. So we
chose ⌬=17% for further experiments.
Comparisons of in-phase and quadrature CMRD signal
scan profiles along the side of the Jominy bar with the hard-
ness profile from a destructive hardness test are shown in
Figs. 4 and 5. Both in-phase and quadrature signals were
normalized with respect to the reflectivity at each measure-
ment spot. Both Figs. 4 and 5 show that there is a strong
correlation between PTR signal and hardness. Typical error
bars for both CMRD and square-wave PTR signals were es-
timated at 2%. Since the real (in-phase)and imaginary
(quadrature)parts of the CMRD PTR signal are inversely
proportional to the square root of the mean thermal conduc-
tivity as shown in Eq. (4), an anticorrelation between hard-
ness and thermal conductivity can be obtained.
Figure 6 shows the results from the conventional 50%
duty-cycle square-wave spatial scans compared with the in-
dependently measured hardness profile. A good correlation
between the photothermal and mechanical profiles is appar-
ent. The extent of correlation between thermal wave and
hardness profiles is comparable between the CMRD and con-
ventional square-wave scans, Figs. 4–6. The PTR phase did
not exhibit as good a correlation as the amplitude, perhaps
due to the very small extent of the hardness gradient normal
to the surface. To reconstruct the thermal conductivity from
either PTR signal, it was assumed that the thermophysical
properties beyond 8 cm away from the quenched bottom of
the Jominy bar were not affected by the quenching process
and the thermal conductivity remained at the prequenching
value of 51.9 W/mK.17 This was based on the fact that it
was not possible to obtain any measurable hardness by me-
chanical means (indenter)beyond 5.5 cm away from the bot-
tom. Nevertheless, the sensitivity of PTR techniques to
minute values of hardness shows a profile that keeps on de-
creasing past that point in Figs. 4–6. Using Eq. (3)and the
PTR signal shown in Fig. 6, the effective thermal conductiv-
ity profile along the side of the Jominy bar was recon-
structed. The results and comparison with the hardness pro-
file are shown in Fig. 7. An anticorrelation between the
thermal conductivity and hardness is observed, as expected.
The remaining curve in Fig. 7 is the average of the thermal
conductivity reconstructions of all three profiles shown in
Figs. 4–6. The PTR signal definitely exhibits improved sen-
sitivity to very low hardness profiles (⬍2RC)compared to
the conventional mechanical hardness measurement.
V. CONCLUSIONS
Overall, it can be concluded that the rate of quenching of
this particular type of steel (AISI 1018)through cooling, in
the absence of hardening through heat treating and element
(carbon, nitrogen)diffusion, affects both local hardness and
thermal conductivity at distances of several centimeters away
from the quenched end. Experimental results from a Jominy
FIG. 4. Comparison of CMRD in-phase spatial scan with hardness profile.
Pulse repetition rate: 100 Hz.
FIG. 5. Comparison of CMRD quadrature spatial scan with hardness profile.
Pulse repetition rate: 100 Hz.
FIG. 6. Comparison of amplitude spatial scan with hardness profile. Modu-
lation frequency: 100 Hz.
1932 J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Liu
et al.
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bar showed that there exists an expected anticorrelation be-
tween thermal conductivity and hardness. The anticorrelation
is not perfect, and this conclusion is consistent with earlier
depth profilometric work from our group4,6 and other
groups.2,8 Noncontact photothermal methods such as conven-
tional square-wave PTR and common-mode rejection de-
modulation PTR can be very sensitive monitors of the case-
depth-averaged local variation of hardness as a result of
quenching, provided they are used judiciously by adjusting
frequency and/or pulse repetition rate for matching case
depth and thermal diffusion length. It is concluded that PTR
techniques are sensitive to low hardness values and mild gra-
dients, in addition to the high hardness values and steep gra-
dients reported in all previous photothermal studies to-date.
ACKNOWLEDGMENTS
The authors wish to acknowledge the support of Materi-
als and Manufacturing Ontario through a Collaborative Con-
tract to A.M.
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FIG. 7. Comparison of reconstructed thermal conductivity with hardness
profile along the side of the Jominy bar. “Thermal conductivity 1” represents
thermal conductivity profile reconstructed from amplitude spatial scan. “Av
thermal conductivity” represents the average reconstructed profile from both
CMRD spatial scans and the amplitude spatial scan.
J. Appl. Phys., Vol. 96, No. 4, 15 August 2004 Liu
et al.
1933
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