transverse depth-profilometric hardness photothermal phase imaging of heat treated steels

JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 9 1 NOVEMBER 2003

Transverse depth-profilometric hardness photothermal phase imagingof heat treated steels

Yue Liu, Natalie Baddour,a) and Andreas MandelisDepartment of Mechanical and Industrial Engineering, Center for Advanced Diffusion-Wave Technologies,University of Toronto, 5 King’s College Road, Toronto ON M5S 3G8, Canada

~Received 2 June 2003; accepted 5 August 2003!

A method to image near-surface hardness profiles of heat-treated case-hardened steels using laserinfrared photothermal radiometric phase imaging is described. It is shown that thermophysical andmechanical transverse inhomogeneity profiles in industrial case hardened steel samples are wellcorrelated. Phase surface scanning imaging leads to a practical criterion for assessing transversehardness homogeneity. A simple method based on phase imaging is proposed as a quantitativecriterion to determine which steel samples should be rejected for thermal-wave depth-profilometricreconstruction of thermal diffusivity or conductivity. ©2003 American Institute of Physics.@DOI: 10.1063/1.1613808#

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INTRODUCTION

Industrial steels are often treated by the addition of cbon and nitrogen, followed by a quenching process in orto produce parts with a tough case. During the heat-treaprocess, it is possible that a particular sample developsdesired lateral~transverse! hardness inhomogeneities, in adition to the desired depth inhomogeneity.

Much work has been done on the non-destructive evation of metals using thermal waves. The field of nondestrtive evaluation with thermal waves has been reviewedBusse.1 In another review, Busse and Walther reviewedphotothermal nondestructive evaluation of variomaterials.2 In particular, thermal waves have been useddetermine the depth of structures in metals, for the detecof faults and also for determining thicknesses and properof hardened layers. Jaarinenet al.3 determined the variationof thermal diffusivity with depth. For metals, the evaluatioappear to be limited to detection of areas of prior deformtion, fault inspection, profile analysis of seams, and deprofiling. It was also shown that photoacoustic phase anscanning can be used to measure subsurface structumetals.4 The scanning methodology used permitted the idtification of small holes hidden under a carefully ground sface of an aluminum sample. While the use of thermal wato investigate various properties of metals is not new,present imaging method to investigate the degree of traverse hardness homogeneity in a metal and to use itcriterion to define thermomechanical homogeneity doesappear to have been previously considered.

EXPERIMENTAL AND RESULTS

The experimental setup for photothermal radiome~PTR! hardness imaging is shown in Fig. 1. It consists ohigh-power semiconductor laser the output of whichcurrent-modulatedI (v). The beam is expanded, collimate

a!Author to whom correspondence should be addressed; [email protected]

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and then focused onto the surface of the sample with asize of 1 mm. The harmonically modulated infrared~Planck!radiation from the optically excited sample surface is clected and collimated by two off-axis paraboloidal mirroand then focused onto a HgCdTe detector. The signal frthe detector is amplified by a low-noise preamplifier and thsent to a lock-in amplifier which is interfaced with a PCCylindrical samples 1 in. in diameter and 1 cm thick wecut from a bar of AISI 1018 steel. The chemical compositiof this steel is 0.15%–0.2% C and 0.6%–0.9% Mn. Tsurfaces of the samples were ground with a 44, 54, 60sand-wheel. The samples were subsequently carbonitrand thermally quenched. The samples were treated in aface Combustion Super 30 allcase furnace, equipped witop cool chamber for slow cooling processes. For the carnitriding process, a base atmosphere consisting of nitroand methanol was used. The aim was to produce a nomcarrier gas composition consisting of 40% nitrogen, 40%drogen, and 20% CO. To this base atmosphere an additioenriching methane (CH4) and ammonia (NH3) gas was usedThe ammonia was present throughout the entire cycle.

A photograph of a carbonitrided 1018 steel sampleshown in Fig. 2. It is clear from the photograph that tsurface of this particular sample contains some nonuniforties in color. These optical nonuniformities were generatedlocations which were in contact with the basket supportthe steel samples during the furnace processing cycle. Thfore, the question arises as to whether this inhomogeneipurely optical ~confined to the surface! or if it representshardness inhomogeneities at greater depths. To this endsurface of the sample was scanned at 10 Hz using infraphotothermal radiometry. The results were mapped andshown in Fig. 3. Since the amplitude of the signal is proptional to (12R), whereR is the surface reflectance,5 varia-tions in the signal amplitude over the sample surfacesemble the shape of the discolored region of Fig.However, alongside the variation in signal amplitude ovthe sample surface there is a variation in signal phase as wThe photothermal phase is independent of the factoril:

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5544 J. Appl. Phys., Vol. 94, No. 9, 1 November 2003 Liu, Baddour, and Mandelis

2R)2 and thus is independent of the optical properties ofsurface. The contrast in the phase scan of Fig. 3 suggestpossibility of thermophysical and/or mechanical inhomogneities across the sample.

Over a range of phase angles, the exact relationshiptween surface value of the thermal wave field and therdiffusivity, a, for a homogeneous semi-infinite solid is giveby

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FIG. 1. Instrumental setup.

FIG. 2. Example of a nonhomogeneous AISI 1018 steel sample and boaries of PTR mapping range. The dashed line indicates the locations ofand mechanical hardness scans as shown in Figs. 8 and 9.


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e-alsmall range of phases such as those found in the phase mthe relationship between the phase ofT and thermal diffusiv-ity, a, can be accurately represented as being linearg$T(a;v0)%5c1a1c2, wherec1 and c2 can be found by asimple linear fitting. This is accomplished by plotting thphase of Eq.~1!, given a particular frequency and beam sizagainst a small range of thermal diffusivity centered arounchosen reference thermal diffusivity value. In this work, tmeasured value of thermal diffusivity of the bulk was useThe linearity can be exploited to quickly determine tchange inaveragethermal diffusivity across the surface ofsample. At the chosen points, this gives a measure ofmean thermal diffusivity within a thermal diffusion length.surface map of average thermal diffusivity of the sampleFig. 3 is shown in Fig. 4. A change in the chosen referenthermal diffusivity value will change the absolute thermdiffusivity values as given in Fig. 4 but will preserve threlative changes in thermal diffusivity.

For comparison purposes, a similar phase/amplitumapping was performed on a visually homogeneous samand is presented in Fig. 5. From the very small signal~am-plitude and phase! variations across this map, the homogneity of the sample is obvious. Figures 6 and 7 show adtional surface scans performed on yet another sample.sample is made of AISI 8620 steel, carburized and quencin a heat treatment similar to that for the 1018 steel. Tchemical composition of AISI 8620 steel contains 0.18%0.23% C, 0.70%–0.90% Mn, 0.40–0.70 Ni, 0.40%–0.60

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FIG. 3. PTR surface maps of framed area in Fig. 2 with 10 Hz modulabeam~nonhomogeneous sample!.


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5545J. Appl. Phys., Vol. 94, No. 9, 1 November 2003 Liu, Baddour, and Mandelis

Cr, and 0.15%–0.25% Mo. This sample is inhomogeneand this can be seen quite well in the phase mappingsformed at both 10 Hz and 1 kHz. It should be noted thlow-frequency phase variations of up to 2° constitute sevnear-surface thermophysical inhomogeneity and possstrong hardness inhomogeneity, Figs. 3, 6, and 7, whephase variations of less than 0.5° are benchmarks of amophysically and possibly mechanically homogeneo

FIG. 4. Average thermal diffusivity surface map of framed area in Fig.

FIG. 5. PTR surface maps of a homogeneous AISI 1018 steel sample10 Hz modulated beam.


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sample, Fig. 5. Figures 6 and 7 show that amplitude scare dominated by changes in optical reflectance and thusages obtained at different frequencies vary little. On the othand, phase images can vary significantly as they are donated by thermophysical properties within depths on theder of the thermal diffusion length. Although optical inhomogeneities ~amplitude images! can be indicators ofthermomechanical inhomogeneities~phase images! as in Fig.3, this is not always the case~e.g., Figs. 6 and 7!.

To illustrate the foregoing observations and correlmechanical and thermal-wave image profiles, PTR radialscans were performed on a fixed radius of the sample of2 at three different frequencies: 10, 100, and 1000 Hz.each frequency, a 1 mmsize beam was employed and mesurements were made at eight different points across thedius indicated by dashed lines in Fig. 2. The PTR amplituand phase signal results are shown in Fig. 8. The shape osignal amplitude across the scanned diameter remains etially the same for the three frequencies, an indication tthe surface optical reflectance dominates the PTR amplituHowever, the shape of the signal phase changes withquency and thus points to changing thermal properties ofsample across the transverse scan. The implication hethat PTR phase imaging such as shown in Figs. 3~b!, 6~b!,and 7~b! is capable of yielding subsurface depth profilomric hardness images at different frequencies.

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FIG. 6. PTR surface map of a nonhomogeneous AISI 8620 steel samwith 10 Hz modulated beam.


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To demonstrate this claim, the corresponding surfacecrohardness tests of the same sample were made alondashed line of Fig. 2 with an indenter and are presenteFig. 9, confirming that the chosen sample does indeed ctain a transverse inhomogeneity. In particular, there is a ccorrelation between the diameter hardness test perforwith a 1 kg load @Fig. 9~a!# ~which thus indents deeper intthe steel! and the phase portion of the line scan performed10 Hz. This corresponds to a thermal diffusion lengthroughly 700mm, assuming a thermal diffusivity value for thAISI 1018 steel of 131025 m2/s ~Ref. 2, Table I, p. 219!.There is also a good correlation between the transverse hness test performed with a 300 g load~shallower indentation!and the phase of the line scan at 1000 Hz which prowithin a thermal diffusion length of approximately 70mm.For further evidence of transverse inhomogeneity, a samwas chosen for destructive microhardness depth measments to be performed at various locations along the dieter, as indicated in the inset of Fig. 10. The results of ttest are shown in Fig. 10. From this figure, it is clear thatmicrohardness at a particular depth is not uniform acrosssample, varying as much as 120 HV. Therefore, the samcontains a transverse hardness inhomogeneity, the profiwhich is well correlated with the thermophysical inhomogneity profile imaged by the PTR phase, Fig. 8. In view of testablished correlation between thermophysical scan profi

FIG. 7. PTR surface map of a nonhomogeneous AISI 8620 steel sawith 1 kHz modulated beam.


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represented by the thermal-diffusion-length/depth-averathermal diffusivity and the hardness scan profiles, Figs. 89, it can be concluded that the PTR phase images of F3–7 can be used as hardness images. The changes obsbetween the low-frequency phase image, Fig. 6, andhigh-frequency image, Fig. 7, can therefore be interpretedvariations in hardness profiles, roughly averaged overthermal diffusion length.

DISCUSSION

The present experimental results show that thermal-wphase hardness scanning imaging at a fixed modulationquency constitutes a powerful criterion for transverse homgeneity assessment within one thermal diffusion lengthhardened steels. Among many potential uses of such a crion, from the photothermal point of view it can be appliedselecting suitable candidates for thermal diffusivity andconductivity depth profile reconstructions in case hardesteels.7 Depth profilometry is a thermal-wave inverse prolem where thermal diffusivity depth profiles are recostructed from surface experimental data as a functionmodulation frequency. Theoretically, the problem requione dimensionality and thus a large incident beam spotis used so that lateral diffusion can be neglected. Numeralgorithms exist that allow for the reconstruction of the thmal diffusivity depth profiles from surface frequency depedent measurements.8,9 Since most thermal-wave inversproblem numerical algorithms developed to date are apcable to the one-dimensional problem only, a ondimensional geometry is required experimentally, includisamples with material inhomogeneity in the depth direct

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FIG. 8. PTR line scan across a particular sample of AISI 1018 steel: Molation frequency:~a! and~b! --10 Hz,~c! and~d! --100 Hz,~e! and~f!—1000Hz.


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5547J. Appl. Phys., Vol. 94, No. 9, 1 November 2003 Liu, Baddour, and Mandelis

only. Transversely inhomogeneous case hardened samare not suitable candidates for the one-dimensional recstruction as thermal diffusivity inversions can lead to inacurate depth profile reconstructions.7,8

Hardness imaging criteria based on this work candeveloped and used for determining if a sample is a suita

FIG. 9. Microhardness test results measured across the surface of the csample of Fig. 8 with~a!—1 kg load; and~b! --300 g load.

FIG. 10. Carbonitrided AISI 1018 sample 9~0.04 in. case depth! backsurface hardness depth profile with seven different measured spots.


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candidate for reconstruction. Transverse line scansformed on each of the carbonitrided and quenched 1018 ssamples at three different frequencies, 10, 100, and 1000were employed. At each frequency, the mean and variancthe data sets over the entire amplitude and phase lateralwere calculated and the results plotted in a histogram.amplitudes, the quotient of variance and mean at a particfrequency was plotted and for phase, the variance ofmeasurements taken at a particular frequency was ploThe results of one such test are shown in Fig. 11. Thhistograms permitted the immediate identification of the lehomogeneous samples. For example, from the histogramFig. 11, and application of the criterion that a steel samplmechanically homogeneous if PTR phase variations acrosurface scan are less than 0.5°, it is obvious that sampland 9 are far less homogeneous than other samples ogroup and thus should not be used in thermal diffusivreconstructions. By using this line scan method of rejectthe less transversely homogeneous samples, a significanprovement in depth profilometric data inversion has beachieved.10

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FIG. 11. Histogram of~a! amplitude and~b! phase line scans of a group oAISI 1018 steel samples.


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CONCLUSIONS

We have shown that industrial case hardened ssamples often contain thermophysical and mechanical trverse inhomogeneities which are well correlated. By scning the surface using photothermal radiometry, an imagthe mean thermal diffusivity down to a depth fixed by tthermal diffusion length of carbonitrided or otherwise haened samples can be produced. Phase imaging of hardinhomogeneities can be used effectively as a criterionstrongly inhomogeneous steels to be excluded from thermwave depth-profilometric reconstruction of thermal diffusity or conductivity. A simple method has been proposed aquantitative criterion to determine which samples shouldchosen or rejected for such thermal-wave reconstructioSubsequent satisfactory performance or failure in the fiof such inhomogeneously hardened parts remains an oquestion.


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ACKNOWLEDGMENT

The support of Material and Manufacturing Ontar~MMO! is gratefully acknowledged.

1G. Busse, inSpringer Series Topics in Current Physics, edited by P. Hess~Springer, Heidelberg, 1989!, p. 251.

2G. Busse and H. G. Walther, inProgress in Photothermal and Photoacoustic Science and Technology, edited by A. Mandelis~Elsevier, NewYork, 1992!, Vol. 1, Chap. 5.

3J. Jaarinen, A. Lehto, and M. Luukkala, Proc.-IEEE Ultrason. Symp. ,~1983!.

4G. Busse, Appl. Phys. Lett.35, 759 ~1979!.5G. Busse, inOptics in Biomedical Sciences, edited by G. von Bally and P.Greguss~Springer, Berlin, 1982!, p. 34.

6A. Mandelis,Diffusion Wave Fields~Springer, New York, 2001!, Chap. 5.7L. Nicolaides, A. Mandelis, and C. Beingessner, J. Appl. Phys.89, 7879~2001!.

8A. Mandelis, F. Funak, and M. Munidasa, J. Appl. Phys.80, 5570~1996!.9J. F. Power, Rev. Sci. Instrum.73, 4057~2002!.

10Y. Liu, N. Baddour, and A. Mandelis, J. Appl. Phys.~submitted!.


transverse depth-profilometric hardness photothermal phase imaging of heat treated steels

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