THERMOELASTIC STRESS ANALYSIS BY MEANS OF A STANDARD
THERMOCAMERA AND A 2D-FFT BASED LOCK-IN TECHNIQUE
G. Pitarresi, L. D’Acquisto, F. Lo Nigro and A. M. Siddiolo
Dipartimento di Meccanica (DIMA)
Università degli Studi di Palermo, Viale delle Scienze, 90128 Palermo (IT)
pitarresi@dima.unipa.it
ABSTRACT
An IR thermographic experimental set-up has been proposed and evaluated towards the capability to acquire thermoelastic
effect induced temperature changes. A standard infrared thermocamera with a nominal Noise Equivalent Temperature
Difference (NETD) resolution of 0.12 K has been employed to measure the temperature from unidirectional GRP tensile
coupons under cyclic sinusoidal loads. The raster scanning mode of the camera single detector is such to produce a temporal
delay in acquiring the signal from two succeeding pixels on the same row, and from consecutive scanned rows. By making an
opportune use of this acquiring dwell times, it was possible to produce and observe thermoelastic fringes on the thermal maps
from the tensile coupons. The acquired raw data have then been post-processed with a lock-in algorithm implemented in
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MATLAB , and based on a 2d Fast Fourier Transform analysis. The filtered thermoelastic component from the lock-in analysis
showed a good linearity with the load applied, up to values of the temperature change an order of magnitude lower than the
NETD resolution limits of the thermocamera, proposing the present experimental set-up and processing methodology as a
potential low cost tool for TSA investigations.
Introduction
The thermoelastic effect in a generic orthotropic body under adiabatic and linear elastic stress conditions induces small and
reversible temperature changes that can be correlated with the stress field by means of linear relationships [1]. In the case of a
orthotropic homogeneous material the corresponding thermoelastic law can be written as follows [2]:
ΔT = − T ⋅
α LL
α
⋅ (Δσ LL + TT Δσ TT ) = −T ⋅ K 1 ⋅ (Δσ LL + K 2 Δσ TT )
ρC p
α LL
(1)
where T is the absolute temperature, ρ and Cp are the density and the specific heat of the material, αLL,TT are components of
the tensorial coefficient of thermal linear expansion, K1,2 are two orthotropic thermoelastic constants and the LL,TT subscripts
indicate the material principal orthotropic directions.
Infrared techniques are mainly used to measure temperature changes on the component surface [3], while adiabatic conditions
are generally achieved by applying cyclic loads above a threshold frequency. The resolution in the measurement of the
thermoelastic signal that is possible to achieve by implementing a Thermoelastic Stress Analysis (TSA) based technique
depends on the resolution of the IR system and on the features of the signal post-processing analysis. State of the art infrared
detectors have NETD values ranging between 0.1 and 0.01 K. In order to further enhance the resolution and to filter out noisy
components affecting the small temperature changes induced by the thermoelastic effect, the most employed signal
processing technique is a lock-in analysis [4]. This results in a narrow-band filter where the components of the measured
signal at frequencies different from a reference one are identified and rejected. If the reference frequency is the loading
frequency, the harmonic filtered is the one carrying the amplitude and phase information of the thermoelastic signal.
A major reason which has slowed down a more widespread adoption of TSA based techniques is the cost of commercial
infrared differential thermocameras [4-6]. These systems, fully equipped to perform measurements of the thermoelastic signal,
generally comprise a high resolution thermocamera and an analogic or digital lock-in amplifier for signal correlation. While
thermographic systems are now available at ever cheaper prices, the purpose of this work is to set up a system able to
perform TSA by using a standard average performances infrared thermocamera and a custom developed lock-in algorithm in
order to achieve a resolution adequate for investigating various key aspects concerning the thermoelastic effect. While the
great majority of TSA related works in the literature make use of fully integrated commercial differential IR systems, a different
approach was proposed by Audenino et al. [7], who employed a standard IR camera, whose single detector scanning mode
was able to suitably detect the thermoelastic signal in specimen under a uniform stress field.
A similar approach is adopted in this work, where the measuring dwell time of a raster scanning single detector IR camera is
exploited to acquire the specimen surface temperature at a sampling rate suitable for reproducing the thermoelastic signal on a
point wise and line wise domain (in the case of generic 2D stress fields) and on a full field domain (in the case of a onedimensional stress field [7]). The sampled temperature signal was subsequently post-processed by means of a lock-in algorithm
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implemented in MATLAB , and based on a 2D FFT analysis, to further enhance the thermoelastic signal to noise ratio.
Experimental tests have been carried out on glass reinforced plastic (GRP) tensile coupons, sinusoidally loaded at various
stress amplitudes and frequencies. The acquired and post-processed values of the thermoelastic signal were plotted against
the peak to peak amplitude of the principal stress component. The experimental results fit well the linear trend predicted by the
thermoelastic effect law (Eq. 1), up to values of temperature change an order of magnitude smaller then the resolution limits of
the IR camera employed. The adopted analysis is hence proposed as an effective technique for thermographic investigations
involving the thermoelastic effect.
Experimental setup
The proposed procedure for the measurement of the thermoelastic signal consists of two steps: a first one where the pure
thermographic (not differential) signal is collected, digitized and stored as a 2D matrix frame, and a subsequent one where the
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collected data are post-processed by a lock-in algorithm in MATLAB .
In this work the thermographic signal was recorded with a Varioscan 3022 system (by JENOPTIK Laser, Optik, Systeme
GmbH), equipped with a single MCT sensor that collects data frames up to 300×240 pixels on a 30°(H)×20°(V) scanned field
of view. The nominal NETD resolution for such system is 0.12 K. The raster scanning mode of the detector is the key factor
exploited to sample the thermographic signal in a way suitable for detecting the thermoelastic signal from cyclically loaded
components. The detector horizontal and vertical scanning is driven by two hinged mirrors oscillating at two different
frequencies. The horizontal scanning mirror oscillates at a frequency of 135 Hz. In the first half cycle (1/270 of a second) the
mirror swaps an horizontal line from left to right, with the detector acquiring the signal from 300 equally spaced pixels. In the
second half of the cycle the mirror can swap the same line (vertical scanning mirror off) or a different line (vertical scanning
mirror rotated of one angular step), from right to left, with the detector acquiring the signal on the same number of pixels. A full
frame is built up after 240 rows have been collected, in about 0.9 s. A further time gap of about 60 ms is spent between the
scanning of two succeeding frames, to allow the vertical mirror to reverse its scanning direction, as it scans even frames
downwards and odd frames upwards. Overall the camera frame rate is then about 1 Hz.
In the case of a specimen under cyclic loads, giving rise to values of thermoelastic effect induced temperature changes high
enough to be not completely buried in noise, the scanning mode of the Varioscan 3022 system is such to produce visible
isothermal fringes. Since the main source of temperature variation is the thermoelastic effect, such fringes can be regarded
and will hereinafter be referred to as thermoelastic fringes. The genesis and information carried by such fringes is somewhat
different according to which scanning mode is being adopted: 1) vertical scanner on (different rows in each grabbed frame are
referred to different vertically shifted lines on the scanned image scenery), 2) vertical scanner off (different rows in each
grabbed frame are referred to the same line on the scanned image scenery).
The vertical scanner on mode can give rise to thermoelastic fringes only when the component scanned area has a uniform
stress field, such as the case of a tensile sample. The formed fringes are a result of the varying temperature due to the
thermoelastic effect, during a frame grabbing. Since the horizontal scanning is very rapid (much faster than the loading
frequency), the temperature acquired along the same scanned row can be assumed constant. The result is then a number of
straight fringes, parallel to the horizontal axis of the camera. Figure 1.a shows the thermographic maps acquired in this
scanning mode from a tensile GRP sample. The different orientation of the fringes in Figure 1.c and d was the result of tilting
the camera by an angle of 30° and 90°. This confirms that the fringes on the sample surface are a result of a varying
temperature with time. The vertical scanner on mode uses a full field domain to collect the information, with the thermal data in
each row collected at different geometric positions and at different times. This also means that the thermoelastic signal
measured can be affected by geometric and material non-homogeneities on the component surface.
In the vertical scanner off mode all the 240 rows composing a frame are referred to the same line in the image scenery, and a
measured temperature in a given pixel position along the rows, is referred to the same geometric point of the component
(assuming that its motion due to deformation is negligible), but taken at different time intervals. Each column in a frame collects
the signal from a single point (fixed in space) versus time. In this way the presence of a uniform stress field is no longer required.
Examples of thermal maps acquired on tensile samples with the vertical scanner off mode are shown in Figure 1.b and Figure 2.
In the case of a tensile sample cyclically loaded in traction, the number of “thermoelastic fringes” acquired in a single frame is
not dependent on the scanned sample area (i.e. on the zoom level, compare Figure 1a and 1b, where the sampled area is
different but the applied loading frequency was the same). For both the two scanning modes described the relationship giving
the number of thermoelastic fringe periods appearing in a frame, p, is given by:
p=
N rows
240
⋅ f load ≈
⋅ f load
f rows
270
(2)
where Nrows is the number of rows in a frame (240), frow is the frequency at which rows are acquired (≈270 Hz), and fload is the
loading frequency (Figure 2 shows some thermal maps acquired at different values of frequency from the same sample). The
sampling frequency fs, i.e. the number of acquired pixels per a thermoelastic fringe cycle, is given by fs = frows / fload. From this
relation it is possible to estimate the maximum loading frequency useful to sample the thermoelastic signal, i.e. the Nyquist
frequency which is around 135 Hz that is half the value of frow. This value is well higher than the usual loading frequencies
applicable with standard servo-hydraulic testing machines, and higher than the range of 5-20 Hz within which the majority of TSA
applications are performed when high loading frequency is not an issue. For such applications the values of fs determine a
favourable oversampling in light of the likely presence of high frequency noise components in the thermographic signal acquired.
Figure 1. a) Vertical scanner on mode, peak to peak load amplitude 10 kN - 6 Hz; b) vertical scanner off mode, peak to peak load
amplitude 10 kN – 6 Hz (higher zoom level than in a); c) IR camera 30° tilted, vertical scanner on mode (5 Hz loading frequency); d) IR
camera 90° tilted, vertical scanner on mode (5 Hz loading frequency)
Figure 2. Scanned frames with the vertical scanner off mode (peak to peak load amplitude 8 kN, a) 2 Hz; b) 6 Hz, c) 10 Hz
It has to be mentioned that sampled pixels along a vertical line are not equally spaced in the time domain, as the horizontal
scanning detector is slower at the edges of the acquiring row and faster in the middle, and its scanning direction is opposite
between even and odd rows.
The number of thermoelastic signal cycles (p) collected in a single frame is somewhat limited, and increases with increasing
loading frequency. A better noise reduction is in theory achievable with a greater number of thermoelastic signal cycles as this
is a parameter equivalent to the integration time in real time IR focal plane array systems. A limit is therefore represented by
the loading frequency that can be applied, given by the sampling frequency and depending on the loading system capabilities.
In order to increase the number of thermoelastic cycles, it would be ideal to gather information from various acquired frames.
This is not made difficult due to the time gap between two succeeding frames, and the alternate upward and downward
scanning direction of the vertical mirror, which is such to loose the mechanical continuity of the component stress field
between different frames. Algorithms to restore the continuity among full frames acquired in successive time instants are
currently being considered. One strategy at the moment under investigation is based on optimizing the frequency content of
the image resulting from the composition, finding the shift parameter that reduce the spectrum band of the whole signal. It is
believed that in this way, a better accuracy in the measurement of the thermoelastic signal will be gained.
The vertical scanner on mode earlier described was also the modality adopted in [7] to acquire the thermoelastic signal on
tensile steel samples. The camera system employed in [7] had however a better resolution (0.03 K) than the one used here.
Another major difference is the row scanning frequency of the two cameras, with the one used in [7] being much higher (2500
Hz). In this case, in order to collect a useful number of cycles p in a single frame, a much higher specimen loading frequency,
possibly above 100 Hz, has to be employed. While this would force the use of specific testing facilities (Electromagnetic
vibrophores, shakers, etc..), it is not possible in this conditions to apply TSA to plastic or plastic reinforced materials, due to the
high strain rate levels introduced.
Material choice and manufacturing of the specimens
A main requirement in this work, for what concerned the material choice and specimen design, was to establish the conditions
giving rise to a high-level thermoelastic signal, i.e. a value of ΔT (as defined in Eq. 1) of the order of a few tenths of kelvin. This
can be achieved by considering materials with: high values of the thermoelastic constants and a good linear elastic behaviour
up to high stress values. Different materials were assed towards the above requirements, and it was concluded that the best
compromise was offered by unidirectional GRP samples. In particular for a glass reinforced polyester sample with 35% in
-6
-1
volume of fibres, adopting traditional rule of mixture formulas, a thermoelastic constant K1≈6.2×10 MPa was estimated. So
in the case of a unidirectional tensile sample and at room temperature, according to Eq. 1, a peak to peak stress amplitude of
ΔσLL=600 MPa would give rise to a temperature variation of ΔT≈1 K.
2
The sample tested in this work was cut from a [0]6 laminate manufactured with a hand lay-up technique, employing a 300 g/m
unidirectional glass fabric, and a room temperature cured polyester resin, and having the properties summarized in Table 1.
Sample
name
Thickness
[mm]
Width
[mm]
Fibres
volume %
Measured Young
modulus E [GPa]
2.1
18.6
38.7
26.4
GRP
ΔσLL [MPa] at a tensile
load of 16 kN
410
Table 1. Dimensions and properties of the tested tensile samples GRP.
The GRP sample was proof-load tested by an electrostatic testing machine, measuring the stress-strain curve up to an applied
tensile load of 16 kN. A very good linear elastic behaviour was observed, with the linear regression line fitting the experimental
points having correlation coefficients around 0.999. No onset of static failure was detected in the sample. The measured curve
was useful to establish the values of minimum and maximum forces in the dynamic tests.
Experimental and measurement procedure
The GRP sample was dynamically tested in a servo-hydraulic MTS testing machine, digitally and remotely controlled by the
FlexTest TM unit and the software Series 793 (both by MTS). The machine was operated in load control, applying tractiontraction sinusoidal loads. The loading parameters for the various acquired scans are summarized in Table 2. Four different
zones were investigated (see Figure 3). The signal from the three lines was measured in the vertical scanner off mode. The
three lines where: one close to the upper grip (which was fixed with the testing machine chassis), one close to the bottom grip
(which was attached on the moving actuator) and one vertical line along the sample axis (acquired by tilting laterally the IR
camera by 90°). Due to the high loads applied and the relatively low Young modulus of GRPs, the sample motion due to axial
deformation was quite consistent near the bottom grip. The choice of scanning the three differently positioned lines was
determined in order to investigate possible influences of the sample motion on the measured and processed signal.
As polymer resins have high values of IR emissivity, the IR signal was acquired on the samples bare surface, i.e. no paint was
applied to enhance emissivity.
The GRP sample was also instrumented with a T-type thermocouple (Cu-CuNi), bonded on the face opposite to the one scanned
with the IR camera. The tests summarized in each line of Table 2, at varying load amplitudes, were all performed during the same
session, according to the following procedure: 1) the sample was statically pre-loaded to the average load value, 2) it was then
progressively and rapidly loaded with the maximum load amplitude at the prescribed frequency, 3) the signal from the
thermocouple was in the meanwhile monitored until observing the formation of a plateau following a rapid initial warming up, 4)
after the plateau was formed the IR signal was acquired by the thermocamera, 5) as soon as the signal for one loading value had
been collected, the following lower loading amplitude was set up and the IR signal acquired subsequently, 6) the previous point
was repeated until all the prescribed load amplitude values had been applied and the corresponding IR signal acquired. An
example of a temperature profile versus time recorded by the thermocouple during one session is reported in Figure 4.
test
Average
load [kN]
GRP - UP
6
GRP - DW
6
GRP - VR
6
GRP - FF
6
Load
Amplitudes [kN]
5-4.5-4-3.5-32.5-2-1.5-1-0.5
5-4.5-4-3.5-3-2.52-1.5-1-0.5
5-4.5-4-3.5-3-2.52-1.5-1-0.5
5-4.5-4-3.5-3-2.52-1.5-1-0.5
Load
Frequency [Hz]
6
6
6
6
Table 2. Loading parameters for all acquired thermal maps
Figure 3. GRP gripped sample with the marked
scanned lines and areas
The profile shown in Figure 4 (acquired at 6 Hz loading frequency) was similar for all the experiments, although it was
observed that the plateau was established at values of ΔT increasing with the loading frequency, and decreasing with the
sample width.
The initial rise of temperature in variable amplitude mode in FRP materials has been already observed and reported in the
literature as due to irreversible rate-dependent hysteretic heating and viscoelastic phenomena [8-9]. The plateau is generally
formed when during the fatigue loading a balance is achieved between the irreversible heat produced and the heat dissipated
through the air and through the grips.
Figure 4. Temperature versus time curve from the thermocouple during the testing of GRP-VR
It is known that any variation of the absolute temperature will in theory influence the value of the temperature change
determined by the thermoelastic effect. This influence is already implicit in Eq. 1, where the absolute temperature will have a
direct influence proportional to its first power. Given the very small values of the thermoelastic constant K1, a few degrees
change in the absolute temperature will usually give a negligible effect. It is important to observe that also the radiometric
calibration of the detector in the IR camera can be affected by the absolute temperature. Furthermore this influence is usually
proportional to a higher power of the absolute temperature [10]. It will then be important to take into account the rise of the
absolute temperature of the component during a test when an uncalibrated IR camera is used. Such precaution though is not
necessary in this work since the output of the Varioscan camera used is already internally calibrated.
Raw data, which are acquired and digitized with a 16 bit resolution, are not exportable for further external data processing. The only
exportable format is a 8-bit grey tone or 24-bit RGB bitmap, the used to visualize the thermal maps. It is then essential to optimize the
brightness and contrast of the bitmap representing the acquired frame (i.e. the average value and the width of the display range), in
order to have the maximum resolution for the information to be post-processed, i.e. the sample surface temperature.
Signal Lock-in post-processing
A signal post-processing technique – named Phase Lock-in Amplifier (PLA) – was numerically implemented to enhance the
thermoelastic signal. This technique represents a most widely utilized method to recover signals of interest deeply buried in a
noisy environment. In this section, after a brief review of the general concepts about the technique, the ad hoc developed PLAbased algorithm will be presented in some details.
Signals acquired by means of thermocameras in standard PLA analyses are essentially sinusoids; data are generally
corrupted by noise. The information of interest is represented by its amplitude (A) and phase (ϕ). For a general scheme of the
classical PLA, see the sketch in Figure 5. The signal to noise ratio of these signals is usually too low to allow standard bandpass filtering operations; hence, more refined algorithms are required. The technique generally makes use of an independent
reference signal (RS). The RS is characterized by a cyclic signal having known initial phase and a frequency value equal to the
one characterizing the thermoelastic signal. The Phase-Locked Loop (PLL) generates two signals (F and G) oscillating at the
same frequency of the signal S: the former in-phase and the latter in-quadrature with S. By mixing the S signal with F and G
respectively, two new signals are obtained. Being S, F and G characterized by the same oscillating frequency, the spectra of
these signals retain - in the low-frequency area – information related to the A and ϕ components of the original S signal.
Moreover, other undesired components are localized far away from the low-frequency zone; hence, it appears relatively easy
the design of a low-pass filter to retain just the desired data. Finally, properly combining the results (X and Y) of the low-pass
filtering operations, the A and ϕ components are gained.
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The algorithm developed in MATLAB allows the generation of the RS by the thermoelastic data itself (this being one of its
peculiar characteristic), given the previously stated nature of the acquired thermo-image. In what follows, thermoelastic data
acquired in vertical scanner off mode will visually support the algorithm explanation.
Figure 5. General concepts of PLA
The code makes use of an algorithm – originally developed by the authors [12] – which extends the initial fringe domain
beyond its borders (Figure 6.c), in order to reduce the edge distortions near the image boundaries. In a few words, the
frequency energy localized around the first order lobe is utilized to analytically extend the domain data. It is worth to notice that
data added are noiseless and can be fruitfully utilized to accurately and automatically estimate the frequency position of the
first order lobe, as we will be shown later. Afterwards, the signal to noise ratio is enhanced through few steps here listed:
•
interactive or automatic design of a 2D low-pass filter to measure – and then subtract – the low variable component;
•
automatic design of a 2D band-pass filter. The design starts with a binarization of the image spectrum. The threshold
value is statistically chosen by analysing a region of the spectrum far enough from the signal of interest. The further
processing of the binary image obtained in this way allows the optimum design of a filter able to retain the in-phase
information (see Figure 6.d). In this way the offset and the high frequency components are rejected.
Figure 6. Data pre-processing. a) Acquired data; b) cropped domain; c) data with fringe extension to reduce edge
effects; d) noiseless thermoelastic fringes
Data added beyond the original domain are automatically processed to obtain the in-phase (F) and in-quadrature (G) signals
(Figure 7.a and b). Therefore, according to the classical PLA, enhanced thermoelastic data (Figure 6.d) are point-wise
multiplied by F and G; the results of this step are shown in Figure 7.c and d, respectively. The desired information is now
differently coded as a low-frequency component. A straightforward low pass filter is – at this point – designed and applied; the
amplitude A of the temperature oscillation is measured for each point of the scanned horizontal line. In particular, since we get
the envelope of the thermoelastic signal, in the vertical scanner off mode the amplitude oscillation is finally gained averaging
each column vector (Figure 7.e-f). Due to the nature of the experimental case-studies investigated in this work, there is no
further interest in deriving also the phase information ϕ, even if this quantity is actually measured and available.
Figure 7. Results (c and d) of the point-wise multiplication of the signal S with a) F and b) G; e) final temperature map; f)
Summarizing plot of PLA algorithm (noisy and noiseless data; temperature amplitude)
Analysis of results
For each value of applied average load, load amplitude and frequency (see tab. 2), a frame was acquired and its data
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imported in MATLAB and post-processed as previously described. The result of the lock-in analysis for each processed frame
is ΔT value representing the thermoelastic effect induced temperature change. All ΔT values resulting from processing the
frames acquired on the same sample line or area, and at different load amplitude values, should then follow a linear trend
versus the load amplitude (and hence the stress amplitude) as predicted by Eq. 1. Figure 9 shows the plots of the values of ΔT
versus the peak-to-peak Δσ. Each plot has a value of ΔT-Δσ for each value of load amplitude applied, and the four plots are
referred to the different zones of the sample as shown in Figure 3.
Figure 9. Filtered signal versus applied peak to peak stress amplitude on a) lines DW and UP, b) line VR and area FF.
2
The plot legends show also the values of the linear fitting slope coefficient and the correlation parameters R
2
It is first of all observed that the four plots are well fitted by a linear curve (high values of the R correlation parameter). The worst
linear correlation is found for the full field scan, and this might be due to a higher level of noise introduced by scanning a wider area.
The slopes of the four linear fitting curves are all similar, with variations that can be justified by the local variation of the
physical properties on the composite sample. In fact the glass fabric texture and the technique employed to manufacture the
sample are such to give rise to local macroscopic non-homogeneities (fibre or resin rich areas, surfacing weaving weft ties,
fibre bundles crimping, resin rich layers, are some sources of potential disturb). It is though observed that the slope of plots on
the VR and DW line and FF area have more similar values than that found for the UP line. The UP line in the sample is placed
near the still grip. In this region the motion due to deformation is very small, so the signal acquired on the UP line is very much
coming from the same points on the sample. In the case of the DW line, placed near the moving grip, the motion due to axial
deformation is very consistent (due to the high loads and the low rigidity of the sample). So the scanned points on the sample
in the case of the DW line are likely belonging to an area around the DW line. In conclusion the results for the DW line, the VR
line and the FF area are all coming from a widespread number of points. The somewhat different slope found in the UP line
could then be explained by the higher sensitivity to material local properties (the acquired results are averaged upon a smaller
area). It has to be remarked that since the sample has a uniform stress field that depends only on time, there are no pseudosignals generated by the sample motion, and hence no need of motion compensation correction.
By considering the average slope from the DW and VR scans a value of the thermoelastic constant K1 is found to be around
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-1
7.7×10 MPa , which is not far from the theoretical estimation reported in the previous Material Choice section ( a value of
absolute temperature T=300 K has been considered in the calculation). The smallest applied peak to peak Δσ was around 26
MPa. From Eq. 1 it comes out that the corresponding theoretical thermoelastic effect induced temperature change is ΔT=
0.006 K. This value is smaller than the resolution capabilities of the IR camera employed by approximately an order of
magnitude; therefore it was completely buried in noise (no visible thermoelastic fringes could be detected in the displayed map
of this scan). The lock-in analysis implemented was able to detect such values of ΔT, which fitted well the linear trend
determined by all experimental points.
Conclusions
An experimental-numerical methodology is presented in this work, allowing the analysis of thermoelastic effect induced
temperature changes, by means of a standard low resolution single detector IR thermocamera. The raster scanning mode of
the camera detector is in particular exploited to suitably sample the temperature on dynamically loaded samples having
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uniform and non-uniform stress fields. The acquired thermal maps are then post-processed in MATLAB by a lock-in algorithm
to enhance the thermoelastic signal.
The presented methodology was adopted to measure the thermoelastic signal from tensile unidirectional GRP samples
undergoing traction-traction sinusoidal loads. Results have shown that the obtained thermoelastic induced temperature
changes have a good linear trend with the peak to peak stress amplitude applied. Furthermore it was possible to detect ΔT
values about one order of magnitude smaller than those measurable by the IR camera resolution.
Further developments of this work will consist of: the use of higher thermal resolution IR cameras in order to evaluate the
effectiveness of the lock-in procedure adopted, the application of the proposed methodology to non-uniform stress fields (by
using the vertical scanner off mode described in the paper), the simplification of the lock-in analysis in order to make it more
user friendly and faster to perform. It is believed that the presented methodology could help to foster research on various
topics of TSA through the use of cheaper standard IR equipment and more flexible customized data processing routines.
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