Journal of Mechanics Engineering and Automation 5 (2015) 623-634 doi: 10.17265/2159-5275/2015.11.005
Using Thermoelastic Stress Analysis to Detect Damaged
and Hot Spot Areas in Structural Components
Freire J. L. F.1, Waugh, R. C.2, Fruehmann, R.2 and Dulieu-Barton, J. M.2
1. Mechanical Engineering Department, Pontifical Catholic University of Rio de Janeiro, PUC-Rio, Rio de Janeiro 22453-900 Brazil
2. Faculty of Engineering and Environment, University of Southampton, Southampton SO17 1BJ, UK
Abstract: This paper discusses the suitability of using TSA (thermoelastic stress analysis) as an advanced tool to detect damaged areas and highly stressed (hot spot) areas in structural components. Such components can be, for example, parts of large structural panels built of welded metallic or composite materials. Besides detecting hot spot areas, it is expected that stresses in these areas can be suitably quantified and processed in order to predict crack initiation and propagation due to in-service loads. The paper starts with references to selected review and application articles on the subject. Two simple laboratory experiments are presented which illustrate the quality of the results that can be achieved using TSA. In the first experiment, a stainless steel T-joint designed to model a welded structural component is analysed. The T-joint had a machine-notched crack-like flaw close to the component’s weld toe. The qualitative and quantitative experimental results determined along four specified areas of the T-joint model showed that TSA can indeed be used as a tool to detect loaded cracks and hot spots in large metallic structures, and that stresses can be accurately evaluated. In the second experiment, a prismatic bar made of CFRE (carbon fibre-reinforced-epoxy) was tested to locate three subsurface areas of damage introduced beforehand into the component. Two of these inside damaged areas were detected to be 3.1 mm and 7.1 mm from the observed surface. The positive results achieved with the two lab experiments, along with a review of the selected research publications, indicate that TSA application can be extended to the real-world field of structural components. Topics to be addressed in this research field should have to do with components that work under random or quasi-cyclic service loading, problems where adiabatic conditions do not prevail, and reduction of the cost of infra-red cameras.
Key words: TSA, stress distribution, NDT, stress distribution, stress concentration, crack, T-joint, infra-red.
1. Introduction
TSA (thermoelastic stress analysis) or
Thermoelasticity is an experimental stress analysis
technique based on the thermoelastic effect. The
thermoelastic effect is defined as the change in
temperature at a point on a body due to its elastic
deformation under adiabatic conditions. The
thermoelastic effect was reported by Weber in 1830
and its associated theory was published by Lord
Kelvin in 1853 [1-3].
The thermoelastic effect causes a point on a body
under cyclic loading to undergo a reversible change in
temperature that is proportional to the first stress
invariant. Under adiabatic and plane stress conditions
(surface point on the loaded body) Eq. (1) applies,
where, To is the reference temperature, cσ is the
specific heat coefficient at constant pressure, ρ is the
mass density, α is the linear thermal expansion
coefficient constant, and Δσ is the cyclic change of the
stress invariant [3, 4]. Adiabatic conditions will exist
for the material point under consideration if the heat
conduction rate is negligible in relation to the change
in temperature induced by the thermoelastic effect.
c
TT o .
1... 21 (1)
Eq. (2) is obtained by rewriting Eq. (1) using a
material constant K, defined as K = α/ρ·cσ. The K
values for structural materials are given in Table 1 [2].
This table also gives resolution indications for
determining Δσ values, depending on the ΔT
measurement resolution for the listed materials.
21.. oTKT (2)
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624
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Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
625
applications. Today’s research and equipment are
intended to increase the advantages of TSA while
simultaneously decreasing its disadvantages as much
as possible. Recent literature published on TSA’s
widespread area points to several applications that
attempt to use the method to conduct non-destructive
evaluation tests; correlate the input (load) and output
(temperature) measurements in situations of
quasi-random loading; detect fatigue cracks; quantify
stresses near crack tips; apply the method to
quasi-adiabatic conditions; detect damage in
composite materials; determine vibration modes in
dynamic problems; and to combine TSA and DIC
(digital image correlation) in the investigation of
stresses near crack-tips [2-9]. Recent research
programs have also aimed at developing and using
lower cost equipment for TSA applications [8].
The use of TSA in two laboratory experiments is
described herein. The basic principles used in these
experiments are to be further developed in a research
program in order to consistently apply TSA as an
NDT tool to locate damage, crack-like defects, hot
spots, and to quantify stresses in actual structures
under service conditions.
In the first experiment, a stainless steel T-joint
designed to model a welded structural component was
analysed. The T-joint had a machine-notched crack-like
flaw in the model area that simulates the component’s
weld toe. In the second experiment, a prismatic bar
made from CFRE (carbon-fibre-reinforced-epoxy)
was tested to locate subsurface areas of damage
introduced beforehand into the component.
2. TSA Analysis of a Cracked T-joint Specimen
The objectives of the TSA analysis of a T-joint
specimen were to detect and quantify the highly
stressed areas near the tip of a machine-notched
crack-like defect introduced into the toe of one weld,
and to detect the stress concentration site located at
the opposite weld toe. The experiment was meant to
show that a loaded crack and the stress concentration
existing in a hot spot area can indeed be detected.
Furthermore, the experiment had the purpose of
showing that actuating stresses can be satisfactorily
quantified at any visible point belonging to the image
field, the examined point being located in a hot spot
area or in any nominal location of the structure.
A sketch of the T-joint tested model is presented in
Fig. 2. The model was made from stainless steel
classified as ANSI 316L. The model was machined
from a 4.9 mm thick plate and one notch with length a
equal to 10 mm and nominal width of 0.3 mm was
machined with a milling saw. The notch was
introduced to simulate a crack-like flaw. The observed
surface of the T-joint specimen was painted with two
thin layers of Matt Black RS 496-782 to homogenize
and help with the surface temperature measurements.
A sinusoidal tensile load was imposed on the T-joint
web by means of a servo-hydraulic testing machine
INSTRON 8802. Cyclic sinusoidal loading P was
applied to the test specimen from 1 kN to 3 kN, with a
frequency rate of 5 Hz. The constant load amplitude
was equal to 1 kN. Temperature measurements were
taken with an FLIR 5000 infra-red camera, with a
nominal standard temperature resolution of 10-3 K.
During the experiment, the average reference
temperature of the specimen was 20 °C or 293 K.
Temperature (range) variation measurements were in
the order of 0.5 K at the most stressed points. Image
frames were recorded at 383 Hz (acquisition rate) and
integration time was equal to 1,300 µs. Prior
calibration of the 316L stainless steel used in the
experiment furnished a thermoelastic constant K =
4.04 × 10-12 Pa-1 to be used in Eq. (2).
The data acquired with the infra-red camera and
processed using dedicated developed software are
shown in Figs. 3 and 4. The camera reads the reference
temperature at each observed point as well as the
small temperature variations that occur during the test
acquisition time. Full field images of the reference
temperature distributions and of the temperature
(range) variations are shown in Figs. 3a-3d.
Using T
626
(a
(c) Actua
Fig. 2 Test o
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highlighted
in the figure
Thermoelastic
a) Sketch of the
al T-joint mode
of T-joint mod
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hase measure
assumption t
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he positive o
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Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
627
(a) Test temperature To (b) Test temperature To, colour processed
(c) Full field ΔT map, gray scale (d) Full field ΔT map, colour processed
(e) Full field ΔT Phase map and detail near the crack tip (f) Lines along which data on ΔT and To were requested from the
experiment file. Processed data of ΔT/To from lines 1-4 will furnish (σ1 + σ2) along these lines
Fig. 3 Images and raw data from the T-joint test.
Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
628
Line 3 defines a cross section in the horizontal
element of the T-joint. The cross-section defined by
line 3 was chosen for measuring the bending stresses
caused by the reaction support load ΔP/2. Vertical line
4 coincides with the continuation of the crack-like
notched surface plane and its first acquisition point
was located 1.0 mm in front of the notch root.
Figs. 4a and 4b give the temperature range and the
reference temperature for points on lines 1 to 4, i.e.,
the acquired data in terms of ΔT and To. This
information, processed using Eq. (2), gives the
results for stress invariants (σ1 + σ2) along the
specified lines. Results for (σ1 + σ2) invariants along
lines 1 to 4 are presented in Figs. 5-8.
Line 2 defines a nominal region of the specimen,
where the maximum tensile stress ranges Δσ1 = ΔσN
caused by the normal force is expected to be:
APN / (3)
or 13.6 MP and the minimum stress range Δσ2 is
expected to be zero. In Eq. (3), ΔP is the range of
applied force equal to 2 kN, and A is the cross section
area of the loaded specimen. A plot of the measured
stress invariant of line 2 is given in Fig. 5. It can be
seen that the TSA measurements indicate a strong
presence of bending stresses in this section, superposed
on the stresses N caused by the normal load. The
maximum and minimum bending stresses were equal
to plus and minus 9.5 MPa, respectively. The average
uniaxial stress measured using TSA is equal to 15.6
MPa and this value agrees satisfactorily (13% difference)
with the nominal calculated value of 13.6 MPa.
The measured TSA stresses along line 3 and the
expected bending stresses calculated for this line are
plotted in Fig. 6. The normal stresses were calculated
by using the simple bending equation
3.
..212
Ht
yLP
M
(4)
where, L is the distance from the right support to the
cross section defined by line 3, and H and t are,
respectively, the height and thickness of the cross
section. Coordinate y is the height of a point being
considered with respect to the neutral fibre. It can be
seen in Fig. 6 that the agreement among TSA
experimental and simple bending equation results can
be considered excellent, since both tendency lines (not
plotted) are almost identical.
(a) ΔT data from the experiment file. Data requested from lines 1-4
(b) To data from the experiment file. Data requested from lines 1-4
Fig. 4 Temperature data collected along the chosen lines (1-4) to be analysed.
Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
629
Fig. 5 Plot of TSA measured and calculated stress invariants at points located along line 1. Note the strong influence of bending stresses superposed on stresses caused by normal force.
Fig. 6 Bending stress plot across the section defined by line 3. Plot of TSA measured and calculated stress invariants at points located along line 3.
Stresses calculated in an area near the tip of the
machine-notched simulated crack-like flaw were
experimentally and analytically determined for
comparison purposes. Two sets of data were acquired
from the TSA experiment and are represented by lines
1 and 4. Horizontal line 1 was passed at a distance of
1.5 mm from the crack tip so that the geometry of the
notch root would not influence the theoretical and
experimental stress analysis carried out for comparing
stresses determined by both methods. Vertical line 4
was passed in continuation of the flaw surface.
The stress analysis of the TSA measured data
acquired along lines 1 and 4 passing near the notch
root (or crack tip) can be analysed in two different
ways. The first approach uses measured stress values
for each spatial point location. These stresses and
point locations are then used to determine the stress
intensity values for the machine-notched crack-like
flaw. The second approach, employed in this article,
uses literature equations of stress intensity factors [10]
to determine the stress invariants along lines 1 and 3.
For comparison purposes, these analytically
determined data were plotted in Figs. 7 and 8 together
with the TSA measured invariant stress data.
The analytical equation used to determine the first
stress invariant range as a function of known Mode I
0
5
10
15
20
25
0 10 20 30
Ten
sile
str
ess
(MP
a)
Position along section represented by line 2 -2 (mm)
TSA uniaxial stress measurements
Tensile stress calculations
线性 (TSA uniaxial stress measurements)
-80
-60
-40
-20
0
20
40
60
80
-20 -10 0 10 20Ben
din
g st
ress
(M
Pa)
Position along the height of section 3-3 (mm)
TSA bending stress measurements
Bending stress calculations
Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
630
and Mode II ranges of stress intensity factors ΔKI and
ΔKII, respectively, is [10]:
1 2 I II
2.cos .sin
2 22 .K K
r
(5)
where, r and θ are the coordinates (relative to the
notch root or crack-tip) at each spatial point on lines 1
and 4. From this expression, it can be seen that the
influence of KII is expected to be small for points
along line 1 when they are close to the notch root, due
to the small value of their θ coordinate and,
consequently, of the sine value of θ/2. Values for KI
and KII for similar geometry and loading conditions
were determined (using Photoelasticity) in an earlier
report [11]. In that investigation, the values for KI
were seen to approach standard solutions of cracked
bars under three or four point bending, and the values
for KII were small as 20% of the KI values. For the
present report, the linear elastic analytical equation
used to determine ΔKI represented the standard case of
a bar of isotropic material under four point bending, as
given in Ref. [10]:
4I 3/ 2
.6. . 2 tan( ).2 2. . 0.923 0.199(1 sin( ))
.. 2cos( )2
n
P aLaHK
at H HH
(6)
where, a = 10 mm is the length of the
machine-notched crack-like flaw and Ln = 45 mm is
the distance between the left support of the specimen
and the section containing the notch.
Fig. 7 shows the TSA-measured and the calculated
stress invariant ranges at points located along line 1.
This line passes 1.5 mm below the notch root. The
calculated values employed Eqs. (5) and (6) for the
stress invariant and ΔKI determinations, respectively.
A plot of calculated stresses considering the influence
of ΔKII =0.20ΔKI is also shown, and it can be seen
that the influence of ΔKII is negligible for points along
the line. A satisfactory comparison of the measured
TSA and the analytically calculated results can also be
seen.
The TSA-measured and the calculated stress
invariant ranges at points located along line 4 are
shown in Fig. 8. This line starts 1.0 mm below the
notch root. The calculated values employed Eq. (6) for
calculating stress intensity ΔKI. Points along this line
have coordinate θ = 0 and therefore, the calculations
using Eq. (5) are not influenced by ΔKII. One can also
Fig. 7 Plot of TSA-measured and calculated stress invariant rangesat points located along line 1 passing 1.5 mm below the notch root.
0
50
100
150
200
250
300
350
400
450
500
-20 -10 0 10 20
Str
ess
Inva
rian
t al
ong
lin
e 1-
1 (M
Pa)
Position along line 1-1 (mm)
TSA stress measurements
Near field KI LEFM stress calculations
Near field KI and KII stress calculations
Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
631
Fig. 8 Plots of TSA-measured and calculated stress invariants at points located below the notch root and along line 4.
see a satisfactory comparison of the TSA-measured
and the analytically calculated results for points as
close as 1.0 mm to the notch root and as far as 4 mm
from the notch root.
For the cases of points located along lines 1 and 4,
the validity of analytical equations has to be
considered in terms of the point coordinate locations
having to do with the notch root or crack tip. Eq. (5) is
valid only in the so-called crack tip near field, which
in the present case is bounded by two spatial limits.
One is a very-near-field limit that must consider the
geometric shape of the notch root and its radius of
influence on the stress distribution [12]. The other is
the far field limit. The size of the far field limit
considers the influence of the far field stresses, which
depend on, for example, the size of the remaining
ligament area, the nominal loading, and the proximity
of the crack tip to the horizontal free-boundary of the
bar. To take into account the very-near and far field
influences, stress Eq. (5) would need the insertion of
terms as shown in Refs. [13-15].
The qualitative and quantitative experimental
results presented in this section illustrate how the TSA
method can be thought of as a tool to detect loaded
cracks and hot spots in large structures, and how those
stresses can be quantitatively evaluated. Advanced
research on extending the application of TSA to real
world field structural components, where quasi-cyclic
service loading actuates and adiabatic conditions do
not prevail, is on-going, as discussed in Refs. [6, 8, 9]
for example.
3. Inspection of a Composite Thick Slab with Delamination Defects
The inspection of composite structures is in great
demand due to an exponential increase in the use of
materials in structures that carry high static and
dynamic loads, such as components used in the
aeronautical and automotive fields. Nowadays,
advanced experimental stress analysis and NDT
(non-destructive testing) techniques, which are
appropriate for these materials, are needed in every
phase of their fabrication and in-service life.
Techniques such as Shearography [16] and TSA [4]
were developed as reliable tools some time ago for
this purpose, but today they are being revisited to
extend and enhance their applicability as feasible tools
for inspecting damaged composite panels [5, 17].
The thermoelastic response of composite materials
is not simply proportional to the change of the stress
invariant, but TSA can be an important tool to indicate
damage areas in composite specimens even if these
areas are located beneath the observed surface [2].
The potential for applying the TSA method as an
-200
-150
-100
-50
0
50
100
150
200
250
300
350
-10 0 10 20
Str
ess
Inva
rian
t al
ong
lin
e 4-
4 (M
Pa)
Position along line 4-4 , starting near the crack tip (mm)
TSA stress measurements
Near field LEFM stress calculations
Far field non valid LEFM stress calculations
Using T
632
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ange image. Arrpositions
t to detect in
ponents
e composite
was painted
496-782. A
the specimen
e INSTRON
applied at a
minimum and
espectively.
d images are
e temperature
e temperature
age
rows indicate
nternal lamina
e
d
A
n
N
a
d
e
e
e
a
Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components
633
range image is shown in Fig. 9c. The scale in Fig. 9c
indicates the temperature ranges using DL (digital
level) temperatures, which still have to be processed
and converted to Kelvin degrees. A temperature phase
distribution image is given in Fig. 9d.
Avisual inspection of the images shown in Figs. 9c
and 9d show that the experimental results obtained
with the TSA method can indicate with satisfactory
resolution the positions of the two closest damaged
surface areas of the composite specimen. All three
damaged areas are highlighted by arrows in Figs. 9c
and 9d. The first and second damaged areas are
located at depths of 3.7 mm and 7.1 mm from the
observed surface and can be visually detected,
although noise is present in the images. The third
damaged area, located 9.1 mm from the observed
surface, could not be detected in this experiment.
The overall conclusion from this experiment is that,
although noisier signals are to be expected, careful
examination of CFRE composites will indicate
internal damaged areas, and that these damaged areas
can be as much as 6 mm (a safer distance) from the
observed surface.
4. Conclusions
This paper has shown that TSA can be used as an
advanced tool to detect damaged areas and highly
stressed (hot spot) areas in structural components, and
that stresses in these areas can be suitably quantified.
Two laboratory experiments were presented to
illustrate the quality of the results that can be achieved
using TSA. In the first experiment, a stainless steel
T-joint designed to model a welded structural
component was analysed. The T-joint had a
machine-notched crack-like flaw close to the
component’s weld toe. In the second experiment, a
prismatic bar made of CFRE was tested to locate three
subsurface areas of damage previously introduced into
the component. Two of these inside damaged areas
were detected to be 3.1 mm and 7.1 mm from the
observed surface. The positive results achieved with
the two lab experiments, along with the review of
selected research publications, indicate that TSA
application can be extended to the real-world field of
structural components. Topics to be addressed in this
research field should have to do with components that
work under random or quasi-cyclic service loading,
problems where adiabatic conditions do not prevail,
and reduction of the cost of infra-red cameras.
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