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Quantitative InfraRed Thermography Journal

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Thermoelastic stress analysis with a compact low-cost microbolometer system

Nik Rajic & David Rowlands

To cite this article: Nik Rajic & David Rowlands (2013) Thermoelastic stress analysis with acompact low-cost microbolometer system, Quantitative InfraRed Thermography Journal, 10:2,135-158, DOI: 10.1080/17686733.2013.800688

To link to this article: http://dx.doi.org/10.1080/17686733.2013.800688

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Published online: 25 Jun 2013.

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Thermoelastic stress analysis with a compact low-costmicrobolometer system

Nik Rajic* and David Rowlands

Defence Science and Technology Organisation, Fishermans Bend, VIC 3207, Australia

(Received 17 January 2013; final version received 26 March 2013)

This article describes the development and validation of a novel thermoelastic stressanalysis (TSA) system based on a low-cost microbolometer device. The use of amicrobolometer for a highly synchronous and delicate temperature measurementbreaks a longstanding and exclusive reliance on high performance, cooled photondetectors for thermoelastic applications. It is shown that despite markedly inferiornoise equivalent temperature detectivity and dynamic response specifications, mic-robolometers are capable of achieving comparable levels of stress measurement per-formance. The practical implications for experimental stress analysis are significant.Microbolometers are relatively low in capital cost, small in size, have good toleranceto shock and vibration and consume less power than their photon counterparts, attri-butes that confer enormous practical advantages. It is argued that the emergence ofTSA systems that are more affordable and better suited to in-service applicationcould help to promote a much broader use of this powerful technique in applicationsacross the life cycle of high value civil, maritime and aerospace assets, from thevalidation of finite element modelling for design to in-service structural integrityassessment. A full-scale fatigue test of a flight-critical aircraft structural componentis employed as a case study to demonstrate important aspects of the capability.Future directions in the development and application of low-cost miniaturisedsystems are also discussed.

Keywords: thermoelastic stress analysis; experimental mechanics; microbolometer;infrared imaging

1. Introduction

Thermoelastic Stress Analysis (TSA) is one of the only few methods capable of furnish-ing a full-field measurement of mechanical stress. Yet, despite the commercial availabil-ity of TSA systems for over 30 years, and the advent of rapid staring array systemsalmost 20 years ago (e.g. [1,2]), the contemporary use of TSA is not as widespread asmight have been reasonably anticipated by those involved in the early stages of itsdevelopment. Indeed, awareness of the method within the broader engineering commu-nity seems to be low relative to optical techniques including electronic speckle patterninterferometry and in particular, digital image correlation (DIC). Admittedly, a reviewof such techniques would reveal a number of advantages over TSA such as a lowercapital cost in relation to DIC and an ability to furnish measurements under static load-ing, however, TSA offers several fundamental practical advantages that will ensure that

*Corresponding author. Email: nik.rajic@dsto.defence.gov.au

Quantitative InfraRed Thermography, 2013Vol. 10, No. 2, 135–158, http://dx.doi.org/10.1080/17686733.2013.800688

� 2013 Crown CopyrightThis is an Open Access article. Non-commercial re-use, distribution, and reproduction in any medium, provided the originalwork is properly attributed, cited, and is not altered, transformed, or built upon in any way, is permitted. The moral rights ofthe named author(s) have been asserted.

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it remains an important experimental tool well into the future. The precise reasons forthe modest uptake of TSA remain a matter for conjecture and debate, however, twocontributing factors are reasonably clear: (1) the relatively high capital cost ofcommercial TSA systems, a point acknowledged by previous authors (e.g. [3,4]) and(2) a general perception outside the research community that the technique can bedifficult to use.

Hardware affordability has improved significantly over the past decade (by at least afactor of two), thanks largely to a decline in the cost of staring array photon detectors.However, the improvement has occurred incrementally and to some extent has goneunnoticed within the broader engineering community. Recent advances in microbolome-ter technology provide an opportunity for a more radical reduction in cost as wellimprovements in practicality that together have the potential to transform TSA into amuch more affordable mainstream technique. That objective forms the primary motiva-tion of the present article which describes the development, validation and applicationof a TSA system developed using a compact low-cost microbolometer device. The sys-tem, named MiTE,1 was first reported in [5], however, that article was brief and con-tained few technical details. The present article provides a comprehensive account of itsdevelopment, validation and application. A brief review of thermoelastic theory is fol-lowed by a description of a signal-processing methodology that eliminates the need fordedicated signal processing hardware, thereby helping to achieve a relatively lowsystem cost, as well as a degree of portability and ruggedness that cannot be matchedby systems employing cooled photon detectors.2 A validation of the system is achievedby means of a comparison between measured results and theoretical as well as numeri-cal predictions relating to two standard mechanical test coupons. Finally, a combataircraft full-scale fatigue test (FSFT) is used as a case study to highlight key aspects ofthe capability and its potential to furnish important information across the life cycle ofan engineering structure, from design to through-life maintenance. The example willalso be used to highlight some possible future directions for the development and appli-cation of this capability.

2. Thermoelasticity

Detailed reviews of the thermoelastic effect and TSA are available in the existing litera-ture (e.g. [6–8]), so only a brief summary of the fundamentals is necessary here. Thethermoelastic effect describes a small reversible change in the temperature of an objectas it undergoes an elastic deformation. A theoretical description was reported by LordKelvin in 1853 [9]. The relationship is given in [6] as

dT ¼ �aT T drq Cp

; ð1Þ

where dT is the change in temperature produced by a change in the sum of the princi-pal stresses dr, T is the absolute temperature, aT is the coefficient of thermal expan-sion, q is the mass density and Cp is the specific heat at constant pressure. Equation (1)exposes a number of important properties. Firstly, as the sum of the principal stressesrelate to the dilatational component of the deformation, it follows that states of pureshear produce no thermoelastic response. Secondly, a positive change in stress (increas-ingly tensile) produces a negative change (drop) in temperature and vice versa. Thirdly,

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the relation describes a reversible phenomenon meaning that a material deformed andthen released recovers its initial thermal state exactly. However, for that to occur, thedeformation must take place adiabatically. Since strain gradients produce temperaturegradients, and loading rates are invariably finite, adiabatic conditions are never strictlyattained in practice. A good working approximation can, however, be achieved in manycases by increasing the loading rate, which stems diffusion by limiting the time avail-able for it to occur. At the other extreme, static loading represents a limiting case wherethe thermoelastic response is extinguished by diffusion. The reader interested in furtherdetails on any of these aspects should consult the review articles cited previously. Forthose that are unfamiliar with the technique, these properties could create a sense of atechnique with rather restrictive limitations, however, for a great many roles, these poselittle problem. Indeed, the literature is full of examples of highly successful practicalapplications (e.g. [10–12]).

The final remark to be made here is that the temperature variations produced by thethermoelastic effect are relatively small. For example, at the elastic limit of the Al andTi alloys listed in Table 1, the variations are seen to approach 1 K. In the majority ofpractical cases, however, the variations are much smaller. A non-contact measurementin this context is not trivial and indeed, it was well over a century after Lord Kelvin’smathematical description before a radiometric measurement of the effect was achieved[13]. Fifty years on that task still poses an experimental challenge, which is perhapsbest appreciated by considering the sort of sensitivity that can be achieved from a rawmeasurement furnished by a modern high-performance cooled infrared imaging device.Take a mid-wave Indium Antimonide (InSb) array. Such a device might have a nominalsensitivity (expressed as the noise equivalent temperature detectivity (NETD)) of15 mK or thereabouts. In a subject made of the aluminium alloy listed in Table 1, thiswould equate to a change in stress of approximately 5 MPa, which is equivalent toabout 70 l�. Anyone accustomed to using electrical resistance strain gauges is likely tofind that unimpressive. Fortunately, it turns out that much better can be done withappropriate signal processing, a fact demonstrated long ago by the developers of SPATE(Stress Pattern Analysis by Thermal Emission) [14].

3. Microbolometer detectors

A microbolometer is a thermal detector that relies on absorption and thermal conduc-tance for the transduction of radiant energy to an electrical signal. Compared withphotodetection, thermal detection has two fundamental disadvantages in relation to themeasurement of small-scale rapid temperature oscillations. The process time constant(integration time equivalent) is much longer (by about an order of magnitude) and theNETD is notionally at least 3 times higher. Superficially at least, these seem like goodreasons to avoid microbolometers for such a task. However, a comparison of this sort

Table 1. Thermoelastic response of several engineering materials.

MaterialaT q Cp dT=dr

(10�6 K�1) (kg m�3) (J kg�1 K�1) (mK MPa�1)

Al alloy (Al2024) 22.8 2770 875 �2.76Ti alloy (Ti6Al4V) 8.6 4430 526.3 �1.09Steel (AISI1005) 12.6 7872 481 �0.98

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overlooks several key points. Firstly, the raw performance specifications of a detector,and particularly the rated NETD, provide an insufficient basis for a precise forecast ofstress measurement performance, a point we re-examine later. Secondly, the experienceof the Australian Defence Science and Technology Organisation (DSTO) suggests thatthe performance levels achieved by even low-grade microbolometer devices are adequatefor many (and one might argue most) industrial applications. And finally, microbolome-ters are vastly superior to photon detectors on just about every measure of practicality.They are lower in capital cost, are more compact in size, have a better tolerance to shockand vibration and should be more reliable than cooled detectors employing closed cyclerefrigerators. The authors contend that these latter factors are significant enough to out-weigh minor shortfalls in performance for a great many applications. If this assertionproves correct, microbolometers could pave the way for a much broader utilisation ofthis powerful stress analysis technique, as remarked in the introduction.

The TSA system described in the present article was developed using a FLIRA20M (see Figure 1), a low-grade commercial microbolometer camera that exemplifiesthe poor raw performance comparison mentioned in the previous paragraph. This devicecontains a 160(H) � 120(V) Vanadium Oxide (VOx) array with a nominal NEDT of120 mK, which is nearly an order of magnitude higher than that of an InSb array, andover twice that of newer microbolometer devices. Output is in 16-bit digital form and issupplied at a fixed frame rate of 50 Hz.

4. Sensitivity enhancement

An NETD of 120 mK equates to a stress measurement noise floor of approximately44 MPa, a value that suggests a poor basis for a precise stress measurement capability.It is not the case. As the developers of SPATE showed, providing the load signal isknown and the noise in the radiometric signal is chiefly temporal and random, thethreshold stress measurement sensitivity of the detector can be improved significantlywith signal processing. Consider an applied load that varies harmonically in time, viz.

Figure 1. TSA of a plate using the MiTE system.

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LðtÞ ¼ Lo e jxt; ð2Þ

where Lo is the load amplitude and x is the circular frequency. Equation (1) is linear,so the thermoelastic response should occur at the same frequency.3 It follows that if theloading is sufficiently rapid to negate the effects of diffusion, the thermoelastic responsecan be written as [16]

Tðx; y; tÞ ¼ Aðx; yÞ � ðLðtÞ � LÞ þ Bðx; yÞ; ð3Þ

where L is the temporal average of the load, B accounts for any background infraredemission uncorrelated with the load, and the constant of proportionality A is a functionof the material properties, which are normally known and the stress amplitude which issought. A least squares estimate for the constant A is obtained by minimising the func-tion,

v ¼XNk¼1

ðTn;mk � An;mLk � Bn;mÞ2; ð4Þ

where the subscript k is an index to time, the superscripts n;m identify the detector cell,N is the number of temporal samples and L is the oscillatory component of the load (i.e.stripped of its offset). This produces the set of equations

PL2k

PLkP

Lk

P1

� �An;m

Bn;m

� �¼

PLkT

n;mkP

Tn;mk

� �: ð5Þ

Since Lk varies about a zero mean, it follows that,

An;m ¼P

Lk Tn;mkP

L2k

: ð6Þ

An;m represents the linear correlation between the radiometric and load signals, and forconvenience is referred to as the correlation signal hereon. A cross-correlation of thistype works well in removing noise. Indeed, where the noise in the measurement Tn;m is

random Gaussian, the process leads to a 1=ffiffiffiffiN

pdecline in the standard deviation of

An;m. The implication is that cross-correlation can achieve a sensitivity that has no limit,which seems unrealistic and it is. The central reason is that measurement noise is notalways uncorrelated. A variety of causes exist, however, an important source in the con-text of staring arrays is fixed pattern noise (FPN) relating to variations in the offset andgain characteristics of detector elements across the array [17]. Variations in the latterare the most relevant since these are indistinguishable from variations in the thermoelas-tic response in the scene (i.e. are correlated with the load signal), and appear as a biasin the estimate An;m. Modern photon cameras are susceptible and typically include a‘non-uniformity correction’ facility in the system firmware to deal with it [18].Although effective, some degree of non-uniformity always remains. This discussionraises an important cautionary point about the NETD, the chief figure of merit fordetector performance and a value that makes no distinction between the two types ofnoise. The upshot is that based on NETD alone, a photon detector should alwaysoutperform a microbolometer in terms of stress sensitivity, however, the latter point

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suggests that this need not necessarily be the case, or at the very least, the margin inperformance might not be as great as the difference in NETD would suggest.

5. System implementation

Equation (6) assumes a synchronous acquisition of the infra-red data stream and the loadreference signal. This is easily achieved in practice with a frame-grabber. However, theuse of dedicated hardware was ruled out for the present implementation because ofthe adverse impact on the affordability, size and ruggedness of the system, as well as theadded future risk of obsolescence. Those considerations led to a decision to basedevelopment on an off-the-shelf notebook computer. Only two specific requirementswere imposed: the availability of an IEEE1394 interface to allow for a direct acquisitionof the digital infrared signal from the A20M and a PCMCIA slot to accommodate ananalogue to digital converter (ADC) for the acquisition of the load reference.Incidentally, this ADC is the only peripheral device in the system dedicated to the TSAprocess.

The pursuit of a low-cost and compact hardware configuration raises some technicalchallenges. As anticipated, an analysis of the load and infrared signals acquired using thisarrangement revealed the presence of significant time delays. This finding, along withother considerations, meant that a real-time computation of the correlation sums wasimpractical. A pseudo-real-time approach was used instead. The sums were calculatedoff-line in a piecewise continuous sense using stored blocks of data and then recursivelyaveraged as a final step. The approach takes marginally longer than a real-time computa-tion, but the difference is largely negligible, since at the loading frequencies typicallyemployed in TSA (� 1� 20 Hz) data acquisition accounts for the bulk of the total analy-sis time.

The process was tested using an experimental apparatus comprising a small Peltiercell driven sinusoidally by a function generator. A relatively low drive frequency of1:5 Hz was required to accommodate the slow thermal response time of the Peltier cell.The value An;m was computed for an arbitrary detector cell ðn;mÞ as a function of thenumber of temporal samples or image frames. Figure 2 plots the decline in signal noise.The trend is approximately log-linear and the improvement in sensitivity after 10,000samples is nearly two orders of magnitude which is roughly consistent with theory. Thisimprovement in the noise floor obviously translates to a significant difference in theapparent stress measurement sensitivity. For the hypothetical aluminium structure con-sidered earlier, this value improves to less than 1 MPa One should recall that this relatesto a single pixel and so excludes the influence of FPN.

Recall from Equation (1) that an adiabatic thermoelastic response is precisely anti-phase relative to the load signal. In practice, some deviation in that phase relationshipwill invariably occur due to the effects of heat transfer, mainly conduction within thesample. However, in the present system, the load and infrared signals are skewed by anunknown system delay, which adds an extraneous phase variation. In fact, three delaysare present. These can be conveniently expressed in terms of an adjustment to the phaseof the load signal, viz.

Ln;mðtÞ ¼ Lo ejxt e�/tc e�/td e�/n;m

sd ; ð7Þ

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where /tc denotes a phase delay due to the detector integration process, /td refers to atransport delay between sampling of the load and infrared signals, and /sd describes ascan delay between detector cells in the array. Each delay has a significant influence onthe correlation process as explained in the following.

5.1. Scan delay

The integration and readout of the detector array occurs sequentially such that eachdetector observes the scene at a slightly different time in the loading sequence. Theeffect is shown in Figure 3 which maps the argument of the correlation signal (Equation(6)) from a nominally uniform scene where the infrared emittance was varied harmoni-cally at 40 Hz. The experimental apparatus used to produce this result is describedlater.

In the absence of a scan delay, the argument should be uniform, so the result inFigure 3 confirms a significant delay and implicates the vertical scan as the main cause.The delay associated with the horizontal scan rate is negligibly small in comparison.The vertical scan rate is readily deduced from the variation in argument in Figure 3 andwas found to be approximately 131 ls per vertical line. This corresponds to a delaybetween the integration of the first and last pixels in an image of 15:7 ms, or marginallybelow the reciprocal of the frame rate. Interestingly, the analysis revealed a bottom-upintegration for the present detector – i.e. the scan commences at the bottom of the array.A second A20M was found to have a top-down integration suggesting that at least twodifferent imaging cores were used in the A20 product line.

5.2. Detector dynamics

A photon detector accumulates photons over a prescribed interval of time, so its dynam-ics are consistent with that of an ideal integrator. A bolometer behaves differently. Itrelies on infra-red absorption and thermal conduction, so its dynamics are fixed by atime constant that depends on the thermal properties and physical dimensions of the

100 101 102 103 104 105

10−3

10−2

10−1

total frames

stan

dard

dev

iatio

n ( ° C

)

Figure 2. Improvement in sensitivity with processing time.

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detector element. The dynamic response can be described approximately by the first-order differential equation

a@T

@tþ T ¼ FðtÞ; ð8Þ

where a is the time constant, T is the detector temperature and FðtÞ is a forcing termthat relates to the incoming photon flux. The impulse response follows by settingFðtÞ ¼ dðtÞ, viz.,

TðtÞ ¼ 1

ae�

ta for t P 0: ð9Þ

This leads to the following frequency response function:

HðxÞ ¼ 1

a

Z 1

0

e�ta e�jxt dt ð10Þ

¼ 1� jxa1þ x2a2

; ð11Þ

jHðxÞj ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ x2a2

p ; ð12Þ

\HðxÞ ¼ arctanð�axÞ: ð13Þ

The time constant of the A20M detector was unknown and had to be determinedby means of an experiment. The apparatus constructed for that purpose is shown in

Camera horizontal direction

Cam

era

verti

cal d

irect

ion

Figure 3. Linear greyscale image of the phase distribution measured across a notionally uniformscene. The spiral-shaped object is an artefact unrelated to the scan delay and can be ignored.

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Figure 4. It comprises of a rotating infrared polarising filter in front of a blackbody areasource held at constant temperature. Viewed through the filter, the scene has a uniformintensity that modulates as the filter rotates. Figure 5 plots the response spectrum of thedetector measured for modulation frequencies in the range 1–50 Hz.

The time constant can be deduced from either the phase or magnitude spectrum.The latter was preferred here since the measured phase includes the effect of thetransport delay mentioned previously, which is yet to be determined. The time constantwas found by minimising the following objective function:

minfa;CgXi

jHmðxiÞj � Cffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ x2

i a2p

!2

; ð14Þ

Microbolometer

IR Polarising Filters

Motor

Blackbody

NotebookComputer

PhotodiodeMotorController

FunctionGenerator

(Rotating) (Fixed)

Figure 4. Schematic diagram of experimental apparatus used for dynamic responsecharacterisation.

100 101 102−15

−10

−5

0

phas

e (ra

dian

s)

frequency (Hz)

0.5

1

1.5

2

mag

nitu

de (K

)

Figure 5. Detector frequency response spectrum.

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where jHmj is the measured frequency response magnitude, and C is an unknownconstant. The summation was taken over the frequency range 0–50 Hz. Choosing anarbitrary detector element in the array, a Nelder–Mead Simplex algorithm was appliedto solve for the unknowns, yielding a time constant of 7.78ms. Figure 6 confirms anexcellent model fit.

5.3. Transport delay

The transport delay stems from the skewed acquisition of the radiometric and loadreference signals. The effect of the delay is significant, as illustrated in Figure 7, whichcompares the measured phase spectrum with a prediction based on the first-order modelpreviously validated by the result in Figure 6. Assuming the scan delay has beenaccounted for, the phase variation in the detector signal can be expressed by the model,

/̂ ¼ arctanð�axÞ þ xdþ /0; ð15Þ

which consists of the delay due to the detector dynamics, the unknown transport delayd, and some phase offset u0. Again, least squares is used to solve for the unknowns,viz.

min d; /0

Xi

ð/i � /̂iÞ2; ð16Þ

which results in the following pair of linear equations:

Pi x

2i

Pi xiP

i xi

Pi 1

� �d/0

� �¼

Pi xið/i � arctanð�axiÞÞP

i /i � arctanð�axiÞ� �

: ð17Þ

0 10 20 30 40 500.6

0.8

1

1.2

1.4

1.6

1.8

2

frequency (Hz)

mag

nitu

de (K

)α = 7.78 ms

modelmeasured

Figure 6. Measured magnitude spectrum and first-order model fit.

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Solving these over the frequency range 1–50 Hz, yields values of d ¼ �18:27 msand /0 ¼ 64:9 mr. Figure 8 compares the measured spectrum to the phase model usingthese values. The agreement is excellent which confirms the accuracy of both the pro-posed phase model and the estimates themselves.

In summary, four corrections need to be implemented in the present system toproduce an accurate thermoelastic response measurement. These comprise three phasecorrections; for the scan delay, detector time constant and system transport delay, andan amplitude correction for the time constant. The computational expense involved inimplementing these is negligible and the process is opaque to the user. The parameters

0 10 20 30 40 50−4

−3

−2

−1

0

1

2

3

4

frequency (Hz)

phas

e (ra

dian

s)modelmeasured

Figure 7. Measurements and first-order model predictions of the phase spectrum.

0 10 20 30 40 50−14

−12

−10

−8

−6

−4

−2

0

frequency (Hz)

phas

e (ra

dian

s)

δ = −37.22 msφ0 = 51.16 mr

modelmeasured

Figure 8. As in Figure 4 but for the corrected phase model.

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need to be only determined once for a given camera and can be included as part of thesystem firmware.

The gain and offset spatial uniformity and stability of an array were previouslydescribed as factors essential to the achievement of a low noise-floor. For the A20M,this is accomplished by means of an internal calibration applied automatically throughthe camera firmware. In the present implementation of MiTE, a calibration is forcedprior to the capture of each data block. The duration of these blocks is also kept rela-tively short to minimise the effect of any drift in the detector characteristics.

6. Experimental validation

In the absence of any prior experience in the use of a microbolometer for stress analy-sis, validation of the new facility was an important step and therefore given close atten-tion. Two separate test cases were considered in the evaluation. Both involved relativelystraightforward coupon geometries; a uniaxially-loaded plate containing a circular holeand a beam exposed to four-point bending. These were selected chiefly on the groundsthat the stress distributions are relatively simple and readily deduced by either analyticalor numerical means.

6.1. Plate with a hole – validation against finite element analysis

The specimen was a rectangular plate of aluminium alloy approximately 2mm thick,100mm wide and 400mm long with a circular hole 12.35mm in diameter at its centre.A thin coating of matt-black paint was applied to the specimen to ensure a high anduniform emissivity. Testing was done under uniaxial sinusoidal loading at constantamplitude.

Figure 9 shows the in-phase and quadrature components of the measured signalafter one minute of processing at a frequency of 10Hz. Dark shades in the left imagecorrespond to a negative correlation or a tensile bulk stress, and light shades to apositive correlation or a compressive bulk stress. A non-zero quadrature componentconfirms the presence of heat diffusion, which, as expected, is strongest near the edgeof the hole where the stress gradients are the largest. The inferred stresses in theseregions are consequently biased. This is best appreciated by comparing the measuredin-phase component to the actual stress distribution as deduced by finite element analy-sis (FEA), which for the simple geometry at hand, can be expected to furnish reason-able accuracy.

Figure 9. In phase (left) and quadrature (right) signals at 10Hz.

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Figure 10 provides a comparison between the measured in-phase signal and thecorresponding bulk-stress predictions along the horizontal line of symmetry, where theorigin is at the hole edge. Thermoelastic response measurements are shown for loadingfrequencies in the range 1–16Hz. As expected, an increase in frequency leads toimproved agreement with the model prediction. The measurement at 16Hz is largelycoincident with the prediction suggesting firstly that pseudo-adiabatic conditions havebeen attained and secondly that the system is behaving as it should in thiscircumstance.

6.2. A beam in four-point bending – analytical solution

Despite the convincing nature of the comparison shown in Figure 10, the result pro-vides only a qualified basis for validation since the solution furnished by FEA is notexact. A second test case was developed to provide an independent and arguably morerigorous basis for comparison. The case chosen is a beam in pure bending which is anattractive problem for two reasons. The depthwise strain profile is linear and with anappropriate loading configuration, the heat diffusion is confined to one spatial dimen-sion. This allows the thermoelastic response of the beam to be derived analytically,which confers another advantage. The availability of an analytical solution helps toclarify an important practical point regarding heat conduction that we explore a littlefurther on.

6.2.1. Theory

The general non-adiabatic thermoelastic response of a body is described by theheat-diffusion equation with an appropriate source term, viz.

qCv@h@t

� kr2h ¼ �qCvcTo@de@t

; ð18Þ

0 5 10 15 20 25 30 35 40

0.4

0.6

0.8

1

distance from hole edge (mm)

norm

alis

ed b

ulk

stre

ss (a

.u.)

0.4

0.6

0.8

1

norm

alis

ed b

ulk

stre

ss (a

.u.) FE

1Hz2Hz5Hz10Hz

FE16Hz

Figure 10. Bulk stress distributions furnished by TSA and FEA for a plate containing a circularhole.

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where

c ¼ 3aTKqCv

; ð19Þ

k is the thermal conductivity and h is the change in temperature relative to an initialtemperature To. Pure bending results in a linear strain distribution, and if the load oscil-lates harmonically, the strain across a beam of depth L can be written as:

�ðx; tÞ ¼ �o 2x

L� 1

� �sinðxt þ /Þ ð20Þ

where x : 0 ! L, with the origin taken at the compressive surface of the beam, �o is thestrain magnitude at that point, and / is an arbitrary phase offset. By condensing someof the terms associated with the thermoelastic source strength in a constant Qo, andobserving that for a four-point bend configuration, the source only varies as a functionof x, then the governing equation becomes,

@h@t

� j@2h@x2

¼ Qo�ox 2x

L� 1

� �cosðxt þ /Þ; ð21Þ

where j is the thermal diffusivity. In practice, heat transfer to the environment isnormally negligibly small (see [6]). Consequently, adiabatic conditions are a reasonableassumption for the boundaries x ¼ 0; L. Under these conditions, Equation (21) has thefollowing solution

hðx; tÞ ¼ 2Qo�oxqCvL2

X1m¼1

1

b2mðj2b4

m þ x2Þ

ð2 cos bmLþ bmL sin bmL� 2Þ � cos bmx ð22Þ

ðjb2m cosðxt þ /Þ þ x sinðxt þ /Þ � e�jb2mtðjb2

m cos/þ x sin/ÞÞ;

bm ¼ m pL

; m ¼ 1; 2; 3; . . . ;1: ð23Þ

In the absence of heat conduction, the solution simplifies to

hðx; tÞ ¼ Qo

qCv� ¼ Qo�o

qCv2x

L� 1

� �sinðxt þ /Þ: ð24Þ

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6.2.2. Experiment

The specimen was machined from 6 mm thick Al2024 plate stock to side dimensions of400 mm� 30 mm. Figure 11 illustrates the loading arrangement. As in the previouscase, matt-black paint was applied to the surface of interest.

The thermoelastic response of the beam was measured under a sinusoidal loadapplied at frequencies in the range 0.5–5Hz. Values along the vertical line of symmetryAA′ (see Figure 11) were compared with theoretical predictions furnished by Equation(22) using the following material properties [19]: j ¼ 49:7 mm2 s�1, q ¼ 2780 kg m�3

and Cv ¼ 875 J kg�1 K�1. Figure 12 shows the comparison for the 0.5 and 5Hz cases.The agreement at both frequencies is seen to be excellent. A slight discrepancy

occurs in the in-phase component on the compressive side of the neutral axis(0 mm\�\15 mm), however, this can be explained in part by the effects of frictionand localised plastic deformation at the loading points.

6.3. Remarks on the effects of heat conduction

The 0.5Hz result underscores the need for caution in applying the adiabatic expressionfor the thermoelastic effect to experimental data. The strain profile derived from themeasured response would in this case contain a significant bias resulting in a conserva-tive estimate of the strains at the extreme surfaces of the beam. One should note a simi-lar effect in the results shown in Figure 10. The pattern is no coincidence. Thisconservative tendency is a feature of heat conduction that needs to be kept in mind,especially in applications such as airframe structural lifing where a small conservativebias in a peak stress estimate has the potential to erode the conservatism factored into afatigue life prediction.

This problem can be dealt with in two main ways. The first and preferred option isto ensure that the loading rates are high enough to render diffusion effects negligible.Where that is not possible, modelling may provide a solution. In fact, Equation (18)creates the impression of a straightforward inverse problem. This could not be furtherfrom the truth as even small amounts of experimental noise render an inverse solutionintractable. A known functional form for the strain distribution is an enormousadvantage [20], as in the present example, but this sort of knowledge is seldom avail-able in practice.

Heat conduction can, in theory, be dealt with in a more generalised sense using ahybrid analytical/experimental approach. Measurements of the thermoelastic response ofa structure across a range of frequencies, whether obtained by means of a frequencysweep or a sufficiently rich loading spectrum, should, with an appropriate model for

A

A’

90 mm

250 mm

xx=0

Xx=L=30 mm

Figure 11. Schematic illustration of a simply supported beam loaded in four-point bending.Measurements were taken along the line AA′.

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heat conduction, allow for the determination of an adiabatic response. Work along theselines has appeared in the literature. For example, in [21], an approach is describedwhere the bulk stress distribution is locally approximated by a power law which is usedin the heat diffusion equation to relate the attenuation caused by conduction to a corre-sponding phase shift. The method was shown to perform quite well under relativelycomplex test conditions.

FEA offers another avenue for tackling complex conduction problems, and provides,arguably, the most general and powerful approach to the issue. Use of FEA in this con-text might appear cumbersome, but one should note that for many high value engineer-ing structures, finite element (FE) models will already be available, if not for the entirestructure, then certainly for known critical areas. Where the model is structural, anadaptation to a thermal model should not be difficult. At the modulation frequenciesemployed in TSA (generally < 20Hz), a harmonic heat diffusion problem would requireonly a relatively coarse mesh, and since thermal transients are irrelevant, the analysisitself is quasi-static. In cases where TSA is applied to validate or refine FE models, theapproach is intuitive and might proceed as follows: a prediction of the stressdistribution furnished by a structural FE model serves as the heat source for a corre-sponding thermal analysis yielding a non-adiabatic thermoelastic response predictionthat can be compared directly with the TSA result. Iterative refinement of the modelcontinues until the predicted response matches4 the TSA measurement. Generally, abroad-band thermoelastic response measurement (i.e. a measurement taken at multiplefrequencies) would help the process resolve the effects of conduction from spatial varia-tions in the source (or bulk stress) and thereby help with rates of convergence. Anapproach of this type has other advantages which will be discussed shortly.

7. Application to aircraft component lifing – a case study

As part of a mid-life structural upgrade [22] for the RAAF F/A-18 fleet, an extensiveFSFT programme was carried out on the critical centre-barrel structure of the airframe.

0 5 10 15 20 25 30−1.5

−1

−0.5

0

0.5

1

corre

latio

n su

m (n

orm

.)

0 5 10 15 20 25 30−1.5

−1

−0.5

0

0.5

1

corre

latio

n su

m (n

orm

.)

depthwise position (mm)

Figure 12. In-phase (solid line) and quadrature (dashed line) profiles at 0.5Hz (top) and 5Hz(bottom). Lines correspond to theory and markers to measurements from the MiTE system.

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The centre-barrel consists of three main bulkheads which connect to the wings andlanding gear and react the primary flight and landing loads into the fuselage of the air-craft. It is a highly stressed structure and is prone to fatigue. The main idea of the FSFTis to understand well ahead of time, where and when fatigue failure is likely to occur inservice. Failures in test articles are extensively studied using a combination of experi-mental (strain gauges), predictive (FE modelling) and analytical (fractography) tools butTSA has also had an important role in a number of facets of these tests. One of the firstwas in validating FE predictions of the stresses in a critical region in the lower part ofthe aft bulkhead, close to where failure of the centre-barrel normally first occurs. Thearea of broad interest has been painted black in the test article shown in Figure 13,however, the examination in this case focused on a smaller area in the vicinity of thehole arrowed in the close-up.

In initial deliberations on the problem, the authors were concerned by two aspectsin particular. The first was that the loading rates were low by TSA standards, about100mHz in the course of full flight-spectrum loading and no more than 1.0Hz under aconstant amplitude loading at 8% of the peak spectrum load which was the conditionunder which the test was eventually done. The second concern related to the displace-ment of the structure under load which was large enough (many mm’s) to rule out afixed observation, at least without some form of motion compensation. It was in dealingwith this particular issue that the notional practical superiority of a microbolometer wasdemonstrated in a most emphatic way. The simplest and most effective remedy for themotion was to attach the detector to the loaded structure. The approach was highly

Figure 13. TSA of the aft bulkhead in an F/A-18 centre-barrel. Top-right photograph shows aclose-up of the hydraulic hole under inspection (arrowed). Bottom-right photograph shows aclose-up of the A20M fixed to the bulkhead by means of a small articulated arm.

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unconventional and there was no precedent for it at DSTO, where photon-based TSAsystems of various persuasions have been applied to aerospace problems for over twodecades. However, the solution seemed obvious and a compact low-cost device made itstraightforward, both from the viewpoint of the engineering required to fix the device tothe bulkhead, and from a risk perspective in that in the eventuality of a major structuralfailure, the financial loss incurred would be low.

Figure 14 compares the stress distribution furnished by MiTE with the correspond-ing FEA prediction for the region surrounding the hydraulic hole. The agreement isexcellent, with peak tensile and compressive stress values matching remarkably well. Anoticeable quadrature signal confirmed the presence of heat conduction which wasentirely anticipated given the low loading rate, however, the effect was evidently slight,helped no doubt by the scaling effect of the large hole (� 57 mm). No analysis wasdone of the errors caused by heat conduction in this case, in part because of the excel-lent agreement but mainly because of lack of time. The omission is regrettable as aconfidence interval on the measurement would have furnished a more rigorous basis for

Figure 14. Bulk stress distribution around the hydraulic hole arrowed in Figure 13, as measuredby MiTE (top) and predicted by FEA (bottom). Bottom-scale is in MPa. Measured stresses werederived from an experimental calibration using a biaxial strain-gauge reading.

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assessing the FE result. It is speculation now but the FE model available for this struc-ture could possibly have been applied for this purpose, broadly in line with the strategyoutlined previously.

8. Variable amplitude loading

A constant amplitude sinusoidal loading offers an experimentally convenient basis forTSA, and is preferred for most laboratory investigations, but it is not a necessity.Indeed, the cross-correlation process at the core of the MiTE system can be applied ingeneral to any load sequence that can be expressed as a sum of harmonic terms of thetype in Equation (2). In this sense, MiTE is no different to commercial systems andcopes easily with a variable-amplitude load sequence. We illustrate with an example.

Consider the coupon shown in Figure 15, which replicates the main details of struc-tural significance in a small fatigue-critical section of the lower wing-skin of the F-111C aircraft, in a location referred to as FASS 281.28.5 The coupon was manufacturedfrom Al2024-T851 alloy to match the actual wing-skin construction material. The fea-ture of chief interest here is a depression in the main integral stiffener, the purpose ofwhich is to facilitate fuel-flow between adjacent bays of the wing-box fuel tank. Inmeeting its primary function however, the design introduces a stress concentration thatleads ultimately to premature fatigue cracking [23].

The variable amplitude loading applied to the coupon was derived from an F-111Cflight-load sequence. This sequence contains relatively large compressive load excur-sions which pose a buckling risk for the coupon, which in flexure is far less rigid thanthe actual wing skin because of the absence of spars and other supporting members.The requisite flexural stiffness can be achieved by fitting anti-buckling restraints to thecoupon. However, it proved far more convenient to simply strip compressive loads fromthe sequence. Figure 16 shows part of the modified sequence measured at the load-cellduring an actual test, along with the corresponding amplitude spectrum. The load-points

Figure 15. Close-up of an F-111 lower wing-skin coupon (left) with an arrow highlighting afatigue-critical feature under examination by MiTE (right).

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in the sequence were applied to the coupon at a rate of two per second. As a bench-mark for comparison, a thermoelastic scan was also done under pure sinusoidal loadingat an equivalent frequency (1Hz) and rms equivalent amplitude. Figure 17 shows themeasured stress distributions. The results are virtually identical. The test duration wasapproximately 6min in both cases.

It is worth noting that an analysis confined to the primary frequency in a variableamplitude load sequence ignores potentially valuable information contained elsewhere inthe spectrum. At the most basic level, the inclusion of response components close to theprimary frequency should foster some improvement in the signal-to-noise ratio of astress measurement. There are, however, potentially more significant opportunities. Abroad-band measurement of the thermoelastic response offers information that might

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

load

(nor

mal

ised

)

time (s)

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

mag

nitu

de (n

orm

alis

ed)

frequency (Hz)

Figure 16. Representative sample of the modified flight-load sequence (top) applied to the F-111C coupon, along with the corresponding magnitude spectrum (bottom).

Figure 17. Comparison of TSA results obtained under a variable amplitude flight-load spectrum(left) and pure sinusoidal loading (middle). Also shown is the quadrature component from a rear-side (external wing-surface) inspection (right).

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help to retrieve an adiabatic response – a possibility noted previously in this article. Con-ceivably, the process used to achieve that could also furnish information about stressesbeneath the near-surface layer providing a virtual through-thickness probing capability.

Exploiting heat conduction as a means of measuring internal stresses is not a newidea and was first raised in [24]. Its major appeal is that it might provide a way ofaddressing problems where access for a customary line-of-sight inspection is not avail-able. The present example serves as an excellent case in point and is worth discussing alittle further. The inside surface of the wing skin is inaccessible to inspection, other thanperhaps visibly with a borescope, which means the results presented in Figure 17 couldnot have been achieved in an in-service scenario, nor for that matter, in an FSFT of awing. The external wing surface is of course accessible, but an adiabatic inspectionfrom that side would, by definition, yield no information about the stress state at theinside surface of the stiffener depression. In this context, heat diffusion can play a con-structive role. If the loading rate is appropriately low, the thermal response measured atthe external surface will include contributions from stresses beneath the surface. Arough estimate of the frequency required to permit diffusion through the wing-skin isobtained by setting the diffusion length (l) equal to the skin thickness, which is approx-imately 4mm, i.e.

l ¼ffiffiffiffiffiffi2jx

r¼ 4� 10�3; x ¼ 6:25 r s�1; ð25Þ

where the thermal diffusivity j has been assigned a value of 50� 10�6 m2 s�1. This fre-quency happens to coincide with the primary component of the load sequence, which sug-gests that evidence of the stress state at the depression should be apparent in aninspection of the rear side of the coupon. Figure 17 provides confirmation of that, notingthat the quadrature component is shown instead of the in-phase component to emphasisethe importance of conduction to this type of probing inspection. It is surmised that suchexperimental information, augmented with similar information derived from otherfrequencies contained in the load spectrum (Figure 16), should permit an estimate of thefar-side stress distribution. A study exploring this possibility is currently underway.

It is to be noted that constructive uses of heat diffusion in TSA have been demon-strated before. As well as the example in [24], the principle was used in [25] to developa way of decomposing individual strain components in polymer composite laminates,and in [26] to investigate internal surface flaws.

9. Future directions

The overarching objective in developing the MiTE system was to create a facility thatwould enable a broader utilisation of TSA. The present article has addressed the centralpart of that objective which is the development and validation of the capability itself. Inproviding adequate coverage of that aspect however, little space has been left to canvassthe practical implications of the capability, which are thought to be significant. Such adiscussion is planned for a sequel to the present article however, it would be remisshere not to at least briefly outline one of the more ambitious possibilities, whichinvolves structural health monitoring (SHM).

Interest in SHM has steadily grown over the years in response to an increasingawareness of the infrastructure sustainment challenges emerging across the aerospace,

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maritime and civil sectors. The central idea in SHM is integrated sensing and for themost part, the types of sensor technologies that have attracted the greatest interest havebeen those that are most amenable to structural integration, i.e. contact sensors such asoptical fibres, electrical resistance strain gauges and solid state piezoelectric devices.Each has its virtues, but notably none has the capacity to furnish a full-field measure-ment of stress which provides in principle an unrivalled basis for the diagnostic and/orprognostic assessment of structures susceptible to load-induced failure [27]. Theconnection with the capability described in the present article should be clear. If oneexamines the centre-barrel application described previously, it will be noticed that allbut one of the key elements of structural health monitoring were there. What was miss-ing was persistent or periodic observation, however adding that it involves nothingmore than leaving the systems in place.

The idea of a nexus between TSA and SHM is an attractive prospect which couldhave significant implications for high-value structural asset management. Indeed, currentefforts at DSTO in developing the next generation of the MiTE system have beenshaped with this in mind. Initial work along these lines has focused on the integrationof the most recent crop of microbolometer devices which are considerably moreadvanced than the A20M. Figure 18 illustrates some preliminary results from recenttesting of two such devices; the FLIR-A325 and the FLIR-A35. Both are based onVOx detector technology and have almost identical performance specifications; anNETD of approximately 50 mK, arrays of 320� 240 and 320� 256 respectively, and aframe rate of 60Hz. All else being equal these improved specifications should translate

FLIR - A325

FLIR - A35

Figure 18. Thermoelastic scan results (bulk stress) from FLIR-A325 and A35 microbolometerimagers. The photograph shows the latter inspecting a plate loaded uniaxially at 5 Hz. An Austra-lian 20-cent coin is included for scale (� 28:5 mm in diameter).

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to better stress measurement performance. Whether this has been achieved will beknown shortly once the relevant evaluations are completed, however regardless of theoutcome, the results in Figure 18 are significant in verifying that these newer devicesare capable of rendering a useful stress measurement. The result for the A35 is espe-cially encouraging as this device is considerably smaller6 than the A20M and is one ofa growing class of miniature microbolometer devices that create a positive outlook forthe development of an in situ structural monitoring capability based on TSA.

10. Conclusion

This article has given a detailed account of the development, validation and applicationof a novel TSA system based on a compact low-cost microbolometer device. Validationof the system was approached by comparing measurements with predictions furnishedby FEA and analytical modelling for two standard coupon geometries. An experimentalcase study was then employed to underscore the key points of practical differencebetween this new capability and existing photon-detector-based commercial tools. It ishoped that the emergence of TSA systems that are more affordable and better suited toin-service application will foster a much broader use of this powerful technique inapplications across the civil, maritime and aerospace sectors.

AcknowledgementsThe authors dedicate the article to Dr Sami Weinberg, who turned some roughly written notesinto the elegant and robust computer code, underpinning the capability described in this article.The contribution of Mr Matt Pelosi to the mechanical testing of the F-111 coupon is alsogratefully acknowledged as is the effort of Mr Chris Brooks in achieving the results in Figure 18.

Notes1. Microbolometer ThermoElasticity.2. This includes all previous and present commercial TSA systems.3. A response also occurs at the second harmonic [15], but is much weaker and can be ignored

for most cases.4. In a least-squares error sense.5. Forward Auxillary Spar Station.6. By a factor of five in volume and three in mass.

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