THERMOGRAPHIC DEPTH PROFILING OF DELAMINATIONS IN
COMPOSITES
William P. Winfree1 and Joseph N. Zalameda2
iJVIS 231, NASA Langley Research Center, Hampton, VA 23681,US A
2
US Army Research Laboratory VTD,
MS231, NASA Langley Research Center Hampton, VA 23681,US A
ABSTRACT. A method for determining the depth of delaminations in composite specimens is presented.
The method is based on a one-dimensional model for a composite with a delamination that is represented as
a contact resistance between the upper and lower regions of the specimen. To estimate the depth and contact
resistance of a delamination in an efficient method, a method is used that makes use of a eigenvector representation of the measured and theoretical data. The technique is shown to give estimates of manufactured
delamination depths that are in good agreement with the specified depths.
INTRODUCTION
Composite materials are finding significant use in both commercial and military aircraft.
In particular, there has been a substantial increase in the use of graphite fiber reinforce polymer matrix composites due to their high stiffness and strength to weight ratio. With the
increased usage, the development of a rapid large area inspection technique has become
increasingly important. Of particular interest is the detection of delaminations that can appreciably reduce the compressive strength of a composite.
Thermography has been shown to have great potential for detection of delaminations in
composites[l-2]. Efforts have included a variety of heating and data reduction techniques
to improve the detectability and assessment of the size and depth of delaminations. Typically the quantification of the characteristics of the delamination is calibrated by performing
measurements on composites specimens with machined flat-bottom holes. This assumes that
delaminations totally block the heat flow from the region above a delamination to the region
below the delamination.
Real delaminations in composites are an air gap between two layers in the composite. It
is well known that the elevation in temperature over a delamination decays with time. The
typical explanation for this effect is that lateral heat flow around the delamination diffuses
the heat to the backside of the specimen. However if the thickness of the air gap is such
that the heat flow across the gap is much larger than the heat flow around the delamination,
the gap's thermal resistance dominates the time response of the delamination. If the thermal
resistance of the delamination is sufficiently small, the time response at the front surface may
be significantly different than a flat-bottom hole response.
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
2003 American Institute of Physics 0-7354-0117-9
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Flash Lamp
Shutter #1
Flash Head
Imager Shutter
Sample
CPU
Adapter
F
Shutter #2
FIGURE 1. Single sided thermographic measurement system with shutters to remove the direct interaction of
flash lamps and IR imager.
Previous analytic modeling efforts have focused on assuming a condition analogous to
the calibration specimen flat-bottom hole. A one-dimensional model is assumed with a delamination at a given depth modeled as a single layer with a thickness equivalent to the depth
of the delamination. A more accurate one-dimension model is possible by assuming a twolayered structure with the air gap modeled as a contact resistance between the two layers.
For long times this model gives considerably different results than the single layer model.
This paper considers the applicability of a two-layered model for accurate representation
of the temporal thermal response of a delamination in a composite. An analytic expression
for the Laplace transform of the impulse response is given. The Laplace transform is inverted
numerically to give the temporal response for instantaneous flash heating of the surface of the
composite. The parameters of this analytic expression are varied to minimize the squared difference between the model response and measured responses on composite specimens with
known delaminations. If the thermal diffusivity and conductivity of the composite is known
these parameters give the depth of the delamination and the size of the air gap. Determining
the parameters that minimize the square difference between the model and experimental data
is achieve by comparing the coefficients of an eigenvector representation of the experimental data and the model. The technique is shown to give an accurate value for the depth of
delaminations in a composite specimen with fabricated delaminations at known depths.
EXPERIMENTAL SETUP
The measurements on the composites were performed with a thermographic measurement system that has been discuss previously[3]. For accurate measurements of the depth
of delaminations, a measurement of the thermal impulse response was desired. The impulse
response of the composite is obtain by exciting the composite with flash lamp heating. The
flash duration has been measured to be approximately 0.008 second. Since the thermal time
constants of the composites of interest are a least one second, this is a good estimate of the
impulse excitation. The thermal response was measured with a focal plane array infrared imager detector size is 256x256 operating in the 3-5 micrometer wavelength band. The imager
output frame rate was 60 hertz and was connected to a real time digital image processor for
image storage, averaging, and analysis.
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A system composed of three shutters was used to improve the accuracy of the measurement of the thermal response. A schematic of the measurement system is shown in Fig. 1.
The first shutter is positioned in front of the infrared imager. The other two shutters are
mounted on the two flash lamp heads using adapters. The opening and closing of the shutters
and the data acquisition are synchronized electronically. Before firing the flash lamps, the
imager shutter is opened to acquire an image of the ambient temperature of the specimen.
During flash heating, the imager shutter is closed to prevent saturating the infrared imager.
Immediately after the flash, the imager shutter is opened to measure the surface temperature.
This is synchronized to the start of the acquisition of the next imager data frame by adjusting
a delay in the shutter electronics. To remove the residual effect of the flash lamps radiating
heat after firing, shutters on the flash heads are shut to block the infrared heat radiating from
the flash head as it cools. The flash lamp shutters are synchronized electronically with the
imager shutter to open when the imager shutter closes. The shutters are solenoid controlled,
powered by 12 volts and are calibrated up to 60 hertz.
FRONT SURFACE RESPONSE OF TWO LAYERED STRUCTURE TO IMPULSE
HEATING
A simple analytic solution does not exist for the one-dimensional heat flow in multilayered material. A solution does however exist in Laplace space for two layers of thickness l\
and 1% coupled by an intermediate contact resistance(R). Since the configuration of interest
is a composite with a delamination, the first and second layers are assumed to have the same
thermal conductivity (K) and diffusivity (ft). For the surface with the incident heating, the
Laplacian of the temperature response is given by
f(P)
/ (sinh(Zi q) sinhfe q) + cosh(/i q) (coshfe q) + Kg R sinh(Z2 <?)))
Kq (cosh(Z 2 <?) sirih(liq) + (cosli(liq) + KqR8inh(liq)) sinh(Z 2 <?))'
where q is yp/K, p is the coordinate in Laplace space and / is the energy per area of the
flash. A solution for the surface opposite the incident heating is given by
/ (cosh(Zi q)2 - sinh(/i q)2} (cosh(/2 q)2 - sinh(Z2
K q (cosh(/2 q} sinh(Zi q) + (cosh(/i q} + KqR sinh(/i q)) sinh(/2 q))'
T,(r)}
6w = —————— -______________ ' ^______________ -____
^ '
Both equations reduce the appropriate one-dimensional solution for a single layer with a
thickness of Zi + Z2 or /, the thickness of the plate with no delamination. Note equation (2) is
symmetric for depths of delaminations about the center of the specimen, i.e. a delamination
with li — x and / 2 = I ~ % has the identical thermal response as Zi = I — x and Z2 = #•
Therefore estimating the depth of the delamination from two-sided measurement requires
assuming the delamination is in one of the two halves of the specimen.
ESTIMATION OF CONTACT RESISTANCE AND DELAMINATION DEPTH FROM
THERMAL RESPONSES
The parameter on interest in this study is the depth of a delamination. The depth of a
delamination as measured from the front surface is Zi in equations (1) and (2). Since the
depth always appears with diffusivity in the specimen, it is not possible to determine the
absolute value of the depth from the thermal response without an independent measurement
of diffusivity. It is however possible to determine the relative depth of a delamination, if
there is a clear region of the composite where no delamination exists. Representing the
relative depth of the delamination as r ft. = rl and Z2 = (1 — r) Z, equation (1) can be
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rewritten as
2 cosh^) + J*RK
+
sinh(^) - sinh(
- 2
(cosh^ ) -
^
' ''
where a is / <\/K/K, RK is RK //, /^ is the diffusivity of the specimen divided by the full
thickness squared and is estimated from a fit of the region of the specimen where there is no
delamination. The two-sided measurement (equation(2)) as well can be written as,
—————— (
(cosh(^) - co8h(^ - 2
(4)
This parameterization of the equation is used to find the relative depth of a delamination.
Before finding the depth of a delamination, the characteristic KI is determined from a front
surface diffusivity fit for the whole specimen[4]. This enables both an estimate for KI and a
good image for identification of delaminations. The characteristic KI is estimated by taking
the median of the values for KI
A common technique for estimating the thickness from the thermal response is to perform
a nonlinear least squares fit of the data, using the appropriate model as expressed by either
equation (3) or (4), varying r, RK and a to minimize the sum of the squared differences
between appropriate model and the measured thermal response. Since the measured response
is in the time domain and equations (3) and (4) are expressed as the Laplacian of the time
domain response, a direct comparison is not possible. To perform the comparison requires
numerically inverting these equations for each guess of r or RK. This is a very computer
intensive process, making an impractical technique for application to the large volume of
data obtained on a specimen.
A new technique that has found successful application for estimation of flaw characteristics in electromagnetics is a proper orthogonal decomposition technique [5]. A set of
eigenvectors is created from a set of responses of flaws with known characteristics. Using
the eigenvector representations to interpolate between known solutions, good estimates of the
unknown flaw characteristics were found using a least squares fitting algorithm. Recently,
others have shown the applicability of a eigenvector technique that uses thermal data to create a set of eigenvectors that are subsequently used for compression of thermal time response
data and flaw identification [6].
For this case, a set of eigenvectors is calculated from the theoretical response calculated
from the appropriate equation (either equation (3) or (4)). To create the eigenvectors, 625
solutions were found that evenly span the expected domain of the characteristics of delaminations. The delaminations were assumed to be at least one ply deep into the specimen. The
range of RK was set assuming the gap of the delamination is air with a thickness that is no
greater than one fifth ply thickness, a value that gives good fits of the data obtained from
measurements on specimens. The first five eigenvectors, ranked based on their eigenvalues,
are found to accurately represent the thermal responses.
To estimate the relative depth and RKy 10,000 evenly spaced thermal responses were
calculated that span the domain of expected values. After subtracting the mean of each
response, each response is normalized by forcing the sum of the square of the values to be
equal to one. The first five coefficients of the eigenvector representation are calculated and
saved. Some typical thermal responses and their eigenvector representations are shown in
Fig. 2. As can be seen from the figure, the eigenvector representation is indistinguishable
from the theoretical thermal responses in the set. Also notable is the significant variations in
the thermal response for changes in contact resistance.
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r=Q.l,RK/l=l
.2, RK/l=2
r=0.2,RK/l=l
3 -
2 -
1.5
FIGURE 2. Comparison of theoretical thermal response of two-layered system coupled by contact resistance
and eio(*nv(*f*tnr r^nr^cpntfltmnc
Q •
a •
E! Ill 03
a•H
;
• 00
a
A
B
C
D
Delaminations
between
plies
A: 1-2 (10%)
B: 2-3 (20%)
C: 3-4 (30%)
D: 4-5 (40%)
E: 5-6 (50%)
E
FIGURE 3. Specimen with delaminations. The delaminations were fabricated by making the impression shown
in the prepreg before laying-up the composite.
MEASUREMENTS ON COMPOSITE SPECIMENS WITH DELAMINATIONS
The specimen used for testing the viability of the measurement technique was a composite specimen with delaminations at specified depths. The delaminations were intentionally
incorporated in the specimen during manufacturing by deforming the tape lay-up before curing with a rectangular stamp to form an air gap. The 10 ply quasi-isotropic composite panel
with a lay-up of [0, 457,90, -45, 0/,45,90,-45/,0,90/] was 30.5 x 30.5 centimeters and 0.19
centimeters thick. The delamination defect areas were square with sizes of 14.5, 6.54, 3.6,
and 1.6 square centimeters. The defects were buried at depths of 10, 20, 30, 40, and 50
percent of the total thickness. A schematic of the defect layout is shown in Fig. 3.
An estimation of the depth and RK is obtained by finding the first five coefficients of
the eigenvector representation of the measured thermal responses. The sum of squared differences between the coefficients of the measured data and each of the stored coefficients is
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(b)
(c)
FIGURE 4. Comparison of reduced images obtained from single-sided measurement, (a) "effective diffusivity", (b) delamination depth and (c) RK-
calculated. The parameters corresponding to the smallest summed squared differences are
used as the estimate of the depth and RK. This technique enables reduction of a data set
with 256 by 256 signals with 300 time steps in less than 10 seconds on most desktop computer systems. The fits fall well within the noise of the data. The results obtained from this
technique are equivalent to the estimates obtained from the simulated annealing algorithm.
The reduced images of "effective" diffusivity[6], delamination depth and RK that were
obtained from the single sided measurements are shown in Fig. 4. As can be seen from this
figure, the "effective" diffusivity image gives the clearest indication of the location and the
shapes of the delaminations. It is difficult to identify the delaminations from either the depth
or RK images. This is an artifact of the reduction technique used to obtain these images. The
reduction process assumes a delamination exists in the specimen. If no delamination exist
in the region being analyzed, estimation parameters that correspond to the "best" fit tend to
fall between two extremes. The first is the delamination is at the back of the composite.
A variation of contact resistance of the delamination at this location does not significantly
change the thermal response of the layer, since the heat flow is blocked at the back surface
of the specimen. The second extreme is characterized by a near zero value on contact resistance, for which case the thermal response is insensitive to variations in delamination depth.
Therefore, the depth and contact resistance values obtained in regions with no delamination
are meaningless and therefore obscures the visualization of the delaminations.
In regions where the delaminations exist, the estimated values for depth and contact resistance are consistent. By using the "effective" diffusivity image to define the region of the
delaminations, it is possible to estimate the depth of the delamination. The depths determined
from this process are shown in Fig. 5. The straight line in the graph represent perfect agreement between the estimated depths and schematic depths. The errors are calculated from the
variations in the depth measurements in each region designated as a delamination. As can be
seen from the figure, there is good agreement between the estimated values for the depth and
the depths cited in the schematics.
The reduced images of "effective" diffusivity, delamination depth and RK that were obtained from the two-sided measurements are shown in Fig. 6. As can be seen from this
figure, the "effective" diffusivity image still gives the clearest indication of the location and
the shapes of the delaminations, however, the delaminations are also clearly evident in the
RK image. It is difficult to identify the delaminations from the depth image. This again is an
artifact of the assumption of the reduction process that a delamination exists in specimen. If
no delamination exist in the region being analyzed, estimation parameters tend to correctly
identify the region as having a small contact resistance. If the contact resistance is small, the
thermal response is still insensitive to variations in delamination depth. Therefore, the depth
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0.12
1 0.10
^
U 0.08
Delamination Widths
D
3.8 cm
A
2.5 cm
O
O
1.9cm
1.3cm
1 0.06
CO
'« 0.04
0.02
0.0'
3.00
0.02 0.04 0.06 0.08
0.10
Specification Depth (cm)
FIGURE 5. Comparison of estimated depths of delaminations determined from one-sided measurement to
depths in fabrication specifications.
(b)
(c)
FIGURE 6. Comparison of reduced images obtained from two-sided measurement, (a) "effective diffusivity",
(b) delamination depth and (c) RK-
values obtained in regions with no delamination are meaningless and therefore obscures the
visualization of the delaminations.
In regions with delaminations, the estimated values for depth are consistent. Using the
"effective" diffusivity image to define a delaminated region, a delamination depth is estimated. Since from equation(2), the thermal response with depth given by r is equivalent to a
depth of 1 - r, an assumption (totally arbitrary in the absence of other data) is made that the
delamination is within the first half of the composite (r < 0.5). The depths determined from
this process are shown in Fig. 7. The straight line in the graph represents perfect agreement
between the estimated depths and schematic depths. The errors are calculated from the variations in the depth measurements for each designated region. As can be seen from the figure,
there is good agreement between the estimated values for the depth and the depths cited in
the schematics within the first 30% of the composite depth(r < 0.3). As the delamination
approaches the center of the layer, the agreement becomes considerably poorer. This is possibly a combination of two factors, the assumption that the depth is limited to r < 0.5 and a
lack of sensitivity to depth as the delamination approaches the center of the specimen.
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0.10
Delamination Widths
3.8cm
D
2.5cm
A
0.08
1.9cm
1.3cm
0.12
o
o
0,6
0.02
£
0.02
J
0.06 0.08
0.04
0.10
Specification Depth (cm)
FIGURE 7. Depths of delaminations estimated from two-sided measurement compared to depths in fabrication
specifications.
CONCLUSIONS
A thermographic technique has been developed that enables determination of depth of
a delamination from a thermographic measurement. A one-dimensional model for a two
layered system connected by a contact resistance is shown to accurately predict the thermal
response of a composite with delaminations. Good agreement is found between the estimated
depths of the delaminations and schematic values for single-sided measurement.
REFERENCES
1. D.R Almond, P. Delpech, M.H. Beheshtey, and P. Wen,"Quantitative Determination of
Impact Damage and Other Defects in Carbon Fiber Composites by Transient Thermography" in Nondestructive Evaluation of Materials and Composites, Proc. SPIE 2944,
pp. 256-264, SPIE, Bellingham, 1996.
2. Plotnikov, Y.A. and Winfree, W.P, "Temporal Treatment of a Thermal Response for
Defect Depth Estimation" in Review of Progress in Quantitative NDE, Vol 19, edited by
D. O. Thompson and D. E. Chimenti, Plenum Press, New York, 2000, pp. 587-594.
3. ZalamedaJ.N., "Synchronized Electronic Shutter System for Thermal Nondestructive
Evaluation", in Thermosense XXIII,edited by A.E. Rozlosnik and R.B. Dinwiddie, SPIE
Proc. Series Vol. 4360, Bellingham, WA, 2001 pp 616 - 623.
4. Winfree, W. P., and Zalameda, J.N., "Single Sided Thermal Diffusivity Imaging in Composites With a Shuttered Thermographic Inspection System", edited by X.R Maldague
and A.E. Rozlosnik, SPIE Proc. Series Vol. 4710 , 2002 pp 536-544
5. Banks, H.T., Joyner, M.L., Wincheski, B. and Winfree, W. P., "Real time computational algorithms for eddy-current-based damage detection", Inverse Problems,18,795823(2002)
6. Rajic, N., "Principal Component Thermography", Australian Department of Defence
DSTO-TR-1298, April 2002, Aeronautical and Maritime Research Laboratory.
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