This content has been downloaded from IOPscience. Please scroll down to see the full text. Download details: IP Address: 128.153.5.49 This content was downloaded on 10/10/2013 at 17:31 Please note that terms and conditions apply. Through-the-thickness identification of impact damage in composite laminates through pulsed phase thermography View the table of contents for this issue, or go to the journal homepage for more 2013 Meas. Sci. Technol. 24 115601 (http://iopscience.iop.org/0957-0233/24/11/115601) Home Search Collections Journals About Contact us My IOPscience
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Please note that terms and conditions apply.
Through-the-thickness identification of impact damage in composite laminates through pulsed
phase thermography
View the table of contents for this issue, or go to the journal homepage for more
Received 6 March 2013, in final form 6 September 2013Published 9 October 2013Online at stacks.iop.org/MST/24/115601
AbstractIn this paper we demonstrate through-the-thickness imaging of barely visible impact damagein a two-dimensional woven, carbon fiber epoxy laminate using pulsed phase thermography(PPT). Specifically we calibrate the defect depth with blind frequency for the particularmaterial system using a specimen with simulated defects in the form of polymer foaminclusions. The calibrated depth versus blind frequency relation is then applied to specimenswith barely visible impact damage due to low-velocity impacts. The polymer foam reproducesthe irregular boundaries and thin nature of the delaminations, but does not reproducethrough-the-thickness variations. The extent of delamination at different depths wasreconstructed as a function of depth for varying levels of impact energy. The extent of damageimaged using PPT corresponded well with visual observations and microscopy images.
(Some figures may appear in colour only in the online journal)
1. Introduction
Non-destructive evaluation (NDE) of laminated compositematerials presents significant challenges as the laminates canfail in a variety of damage modes, which are both distributedand interacting in nature [1, 2]. Non-destructive imagingof these materials is further complicated by the materialanisotropy, leading to a directional dependence in wave speedsthat is exacerbated for high frequency waves. Additionally,the difference in properties of the individual constituents(for example thermal conductivity, electrical conductivity,stiffness and thermal expansion coefficients) further increasesthe difficulty of damage detection and quantification [2].
Despite these challenges, imaging techniques have beenshown to be powerful methods for NDE of thin-walled aircraftcomposite structures. As propagating waves are diffusive innature, the shallow depth of these structures permits imaging
1 Author to whom any correspondence should be addressed.
through the depth of the material. Penetration through thedepth is critical since visible access to the back surface(opposite to the impacted surface) is often not available duringinspection. Recently, infrared (IR) thermography has shownsignificant promise due to the fact that a large section of thestructure can be imaged simultaneously without the need fora specialized environment, drastically reducing the requiredimaging time [3, 4]. As the average airline spends 12–20% ofits total operating expenses on maintenance and inspection, thisreduction in required imaging time can have a major financialimpact on the industry [5].
Active IR imaging methods can be divided intopulse thermography, lock-in thermography, pulsed phasethermography (PPT) and other frequency modulatedthermography techniques [6–8]. In pulse thermography, thematerial to be inspected is heated with a thermal pulse andthen allowed to cool so that the heat pulse diffuses through thematerial. If the material has a localized defect, the defectivearea will reduce the diffusion rate as compared to that of
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
the non-defective material area, creating heat entrapment atthe location of the defect [9]. This reduction in diffusion rateappears as a hot spot in the thermal image reflected from thestructure surface collected during the cooling transient [10].While pulse thermography has been shown to be sensitive tothe defects in composite laminates, it is also sensitive to surfacevariations on the structure, non-uniform heating of the surface,non-planar surface geometries and environmental noise [11].For these reasons, it is difficult to obtain a high quality imagewithout moving the structure to a specialized environment.
In lock-in thermography, the material is instead probedwith a thermal wave modulated at a fixed frequency [12].Through signal processing the phase and amplitude of thethermal reflected wave at the material surface are calculated.The phase image is much less sensitive to the surfacegeometries and environmental noise and can resolve damageat approximately twice the depth of the amplitude information.Lock-in thermography can also be applied to estimate thedepth of a particular defect by tuning the modulation frequencyof the thermal excitation wave. However, the structure to betested must reach an equilibrium temperature in between theapplication of the different modulation frequencies, whichagain can significantly increase the required imaging time.
Most recently, the development of PPT combines thehigh signal to noise ratio and depth resolution of lock-inthermography with the imaging speed of pulse thermography[13]. In PPT, the material is heated with a single, squarethermal pulse and the reflected thermal wave is measuredas a function of time during the cooling transient. Thesquare thermal pulse contains a range of input modulationfrequencies, from which the information at each frequency isextracted through signal processing of the measured thermalwave. Therefore only a single imaging measurement mustbe performed and the imaging time is relatively short.Previous researchers have demonstrated the detection ofartificial defects, impact-induced damage, and debonds atskin-stiffener interfaces applying PPT to composite laminates[3, 14, 15]. In each case the performance of the PPT for damagedetection was comparable with the other NDE techniquesstudied. Further extensions to active thermography have alsobeen demonstrated with different time-amplitude distributions(other than a square wave) to optimize the energy available toresolve information at certain frequencies [6–8].
In this paper, we investigate the quality of through-the-thickness defect resolution using PPT for impact-induceddamage in composite laminated plates. In particular, we choosePPT due to its rapid data acquisition time, although similarresults could be obtained with other active thermographymethods. Previous researchers have successfully demonstratedboth the detection and the measurement of the total areaof impact damage in composites using active thermography[16–22] and have correlated the resulting damage area toimpact energy [16]. Impact damage is characterized by itsirregular boundaries, thickness variations, propagation acrossat several different interlamina interfaces and negligiblethicknesses. These irregular boundaries and thicknessvariations produce complex heat propagation effects transverseto the thickness direction and can cause thermography
techniques to over- or under-predict the damaged area,although the imaging results are highly repeatable [18]. Wewill consider the ability of post-processed PPT data to measurethrough-the-thickness profile of delamination (the most visibledamage mode), rather than simply the total damage area. Thethrough-the-thickness information is important to understandthe interaction of failure modes and to predict the remaininglifetime of the composite structure.
Transferring PPT results based on calibration specimenswith simulated defects in the form of Teflon insertsor flat-bottomed holes, with clearly delineated boundariesparallel to the propagation direction, is problematic foraccurately imaging the extent of impact-induced damage[23]. We therefore apply polymer foam inserts, which theresin impregnates during fabrication of the laminate, forthe calibration specimens. We generate composite laminatespecimens with foam inserts at different depths to calibrate thedepth resolution of the PPT system, based on the determinationof the blind frequency [24]. We then apply this depthcalculation to laminates with varying levels of impact-induceddamage to reconstruct the through-the-thickness extent ofdelamination. The reconstructed damage region is comparedto visual inspection of a sectioned laminate for evaluation ofthe calibration procedure.
2. Background: pulsed phase thermography
As mentioned in the previous section, PPT is a mathematicallink between pulsed thermography and lock-in thermography.We will first review the principles of PPT in this section. Thematerial to be inspected is heated with a square wave thermalpulse. The thermal wave reflected from the surface of thematerial specimen during the cooling transient is measuredwith a thermal camera and saved as two-dimensional pixelarrays of temperature at discrete time intervals (�t), as shownin figure 1. The parameter �t is the sampling interval. A totalof N thermograms are collected over the truncation window.
The frequency content of the excitation pulse with aamplitude A and width τ , centered at t = 0, can be givenas [12]
f (n) = Aτ sin(πnt)
πnt, (1)
where n is the frequency variable. Thus a transformationalgorithm such as the Fourier transform (or in the case ofdiscrete data the discrete Fourier transform, DFT) can be usedto extract specific frequency thermal waves from the measuredreflected thermal wave (at each pixel in the captured in thethermogram) [13]:
F(n) = 1
N
N−1∑k=0
T (k�t) exp
(−2π ink�t
N
)= Re(n) + i Im(n),
(2)
where k is the image index, T(k�t) is the temporal evolutionfor each pixel, and Re and Im are the real and imaginary partsof the Fourier transform, respectively [12]. The frequenciesthat can be extracted from the data range from 0 to 1/(2�t) inorder to satisfy the Nyquist frequency condition.
2
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
defective
non-defective
Δt
N imagesr p
ixe
ls
p pixels
........
thermograms
input thermal wave
reflected thermal wave
defectivenon-defective
(a)
defective
non-defective
(c )
(b)
Figure 1. Schematic process of PPT: (a) specimen excited with input thermal wave and resulting reflected thermal wave (measured withthermal camera). Surface locations of defective and non-defective regions shown; (b) thermograms obtained at discrete time intervals; and(c) phase image calculated from thermograms showing phase difference between pixels representing defective and non-defective regions.
The amplitude and phase of the reflected wave at eachpixel are calculated from the imaginary, and real, parts of theDFT as [12]
A(n) =√
Re2(n) + Im2(n)
φ(n) = arctan
[Im(n)
Re(n)
]. (3)
As the phase information calculated from reflectedthermal wave is not as influenced by noise sources such asnon-uniform heating, surface variations and environmentalconditions, only the phase information will be considered inthis study. It will be seen later that choosing the frequencywindow over which to perform the DFT selects the depth rangethat will affect the phase image. Therefore we will calculateand present the phase information from the DFT for a rangeof frequencies fk with
fk = k
N�t= k
T, (4)
where T is the truncation window length (the truncationwindow always starts at t = 0 in this work) and the maximumfk = 1/(2�t).
The depth at which a particular defect occurs can bedetermined from the thermal transient through the diffusionlength of the thermal wave at different frequencies. For a largerange of frequencies, the depth of the defect, z, is linearlyproportional to the following expression [24]:
z ∝ C√
α
π fb= Cμ, (5)
where α is the diffusivity of the material (in the non-defectivearea), fb is the blind frequency (i.e. the minimum frequency atwhich the defect is not visible due to frequency-dependentattenuation of the thermal wave)2 and μ is the diffusionlength. The diffusion length is the maximum depth at whicha subsurface feature affects the surface temperature at a givenfrequency. The coefficient C depends upon the specimenconfiguration and the defect type. Practically, aliasing of thedata can occur due to the choice of sampling and truncationparameters, therefore C is typically calibrated through a linearregression fit of z to μ for a given specimen type in termsof the apparent blind frequency [24]. By thus defining theapparent blind frequency for a particular defect based on amathematical representation of the phase contrast betweenthe non-defective and defective regions, the defect depth canbe estimated without the need for user interpretation of thethermal images [24].
3. Experimental methods
3.1. Sample preparation
Two different types of laminated, 2 × 2 twill woven carbonfiber epoxy composite plates were fabricated. The first type(specimen type 1) included Rohacell foam inserts introducedbetween different pre-preg layers to simulate manufacturingdefects. This specimen was first used to find the sensitivity
2 Note that the definition of blind frequency applied in PPT is different thanthat commonly applied in lock-in thermography.
3
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
A
A
12
5
125
Section A-A
2.6
Rohacell
inserts
25 25 25
15105
51015
All dimensions are in mm.
Figure 2. Dimensions of specimen type 1 with simulated Rohacelldefects at different depths (drawing not to scale). All inserts aresquare.
of the pulsed phase IR thermography setup for the carbonfiber laminates to be tested and thus to calibrate the minimumdefect size to a depth ratio that could be detected. Secondlythis specimen was used to calibrate the depth resolutionof defects based on the blind frequency. The second type(specimen type 2) was used to investigate the sensitivity ofthe pulsed phase IR thermography to barely visible impactdamage (BVID) and its ability to reconstruct depth informationof delamination for this loading case.
All specimens were prepared from 12 layers of 2 × 2 twillweave carbon fiber epoxy pre-preg with a thermoset matrix(Advanced Composites LTM22/CF0300). The dimensions ofthe specimens of type 1 were 125 mm × 125 mm and type2 were 115 mm × 115 mm. All specimens were assembledand vacuum bagged prior to curing in a hot-press. A single2 mil thickness Mylar release film and four separate pieces ofpolyester peel-ply fabric were used to prevent adhesion of thesample to the vacuum bag. All samples were cured following astepped temperature profile of 15 min at 50 ◦C, 15 min at 65 ◦Cand 180 min at 80 ◦C, followed by 30 min without heating.A constant pressure of 690 kPa was maintained throughoutthe temperature cycle. Afterwards, the assembly was removedfrom the hot-press and allowed to cool to room temperature.
A specimen of type 1 was used to test the IR imagingresponse to inclusions and was thus prepared with controlledRohacell polymer foam inclusions embedded during thelaminate layup process, prior to vacuum bagging. As discussedin the introduction, the motivation for using the polymer foaminserts in this work was to replicate the thermal propagationeffects of BVID as closely as possible while controlling thedamage boundaries. Previous researchers have applied Tefloninserts, nylon bagging film, Rohacell inserts, Kapton inserts,
support ring
impactor support
impactor
specimen
guide rail
clamp
Figure 3. Instrumented drop tower impactor.
flat-bottomed holes and aluminum shims to simulate internaldefects [25–28].
The Rohacell foam sheets (of thickness 3.0 mm) werecut into squares of 1.5 cm × 1.5 cm, 1.0 cm × 1.0 cm and0.5 cm × 0.5 cm and inserted at various locations and depthsin the laminate, following ASTM standard E2582-07 (withthe exception that the largest size defects were not spacedsufficiently far apart from one another). One sheet of each sizewas embedded between the 1st and 2nd layers, one betweenthe 2nd and 3rd layers, one between the 3rd and 4th layers,one between the 4th and 5th layers, one between the 5th and6th layers and one between the 6th and 7th layers (i.e. at themidplane), as shown in figure 2. The assembled laminate wasthen placed under pressure and heated as described above. Thetotal thickness of the samples was 2.60 mm, 0.25 mm greaterthan samples without the foam inserts. The individual foamsheets were therefore partially crushed during the laminatefabrication and the surrounding laminate layers deformedaround them. The thickness of the inserts was not varied,although the thickness is also an important factor in thedefect contrast [29]. Once cured, the sample of type 1 wasspray painted with black Rustoleum Flat Protective Enamel toincrease the emissivity of samples for more accurate thermalimaging.
Four specimens of type 2 were also fabricated as describedabove (without foam inserts). These laminates were used to testthe sensitivity of PPT to impact-induced damage at differentimpact energies. The resulting laminate thickness for thesespecimens was 2.35 mm.
3.2. Low-velocity impact loading
The specimens of type 2 were subjected to a single low-velocity impact using the instrumented drop tower impactorshown in figure 3. The impactor consists of a 19 mm diameter,hemispherical steel impacting probe. The entire crossheadand impactor mass was 5.5 kg. The specimens were mountedbetween two 76 mm diameter steel clamping rings with a layer
4
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
function generator
IR camera
specimen
Halogen lamps
IR power controller
Power
ModuleFunction
Generator
Halogen
lamps
IR Camera
Acquisition
System
Specimen
0.5
m
1 m
(a)
(b)
Figure 4. (a) Schematic and (b) photograph of the experimental setup for pulsed phase IR thermography.
of 1.5 mm neoprene film on each side to distribute the clampingpressure evenly over the clamped area. The crosshead wasmanually arrested during the rebound to prevent secondarystrikes. The impact energy was manually adjusted by changingthe release height of the crosshead. The precise impact energyfor each strike was determined from a magneto-restrictiveposition sensor mounted to the crosshead. The change in theposition versus time was averaged over the 100 data pointsprior to impact to calculate the impact velocity. The impacttime was determined from an accelerometer mounted to thecross-head. The impact energy was then calculated as thekinetic energy of the impactor.
3.3. Pulsed phase infrared thermography
The experimental setup for the pulsed phase IR thermography(measured in reflection) of the specimens is shown in figure 4.All specimens used in this study were laminated flat plates;therefore a specimen mounting system was designed using
machined aluminum rails. The mounting system allows adjust-ment of the IR camera perpendicular to the specimen plane andmovement of the specimen within its own plane. The specimenwas held in place in the frame by a polymer foam grip to reduceheat transfer from the specimen to the aluminum rails. The IRimages were captured with a Cedip Titanium 560 MWIR fo-cal plane array camera, which operates in the mid-wavelengthspectral range (1.5–5.1 μm). This camera has a InSb detectorarray producing images with a resolution of 640 × 512 pixelsand a thermal sensitivity of less than 20 mK at 25 ◦C. Thermalimages were acquired at a frame rate of 60 Hz.
Good imaging results have been demonstrated for lowconductivity (i.e. slow thermal response) materials, such asCFRP, using modest power halogen lamps in a long pulse mode[26]. For the current experiments, the specimens were heatedby two halogen lamps, each of 1700 W maximum capacity, for7 s and then allowed to cool. A function generator (TektronixAFG3021B) sent a square wave pulse to the IR power module(IR Power control 330 US) to activate the heat lamps. The
5
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
0
10
20
30
40
50
0 10 20 30 40 50 60
Heating
Cooling transient
Defective area(1)
Non-defective area(2)
Tem
pe
ratu
re (
°C)
Time (sec)
Observation
time
28
29
30
31
32
33
34
35
36
1.
. 2
Tem
pe
ratu
re (
°C)
(a)
(b)
Figure 5. (a) Single pulse thermography image of specimen of type2 showing defective and non-defective areas. (b) Thermal responseof pixels 1 and 2 from (a) and truncation window selection.
pulse had an amplitude of 5 V, corresponding to a halogenlamp output of 850 W. The lamps were placed at an angleof 30◦ and a distance of 0.5 m to minimize non-uniformitiesin the applied heating. The specimens were imaged from thefront of specimen and images were captured during coolingtransient from the IR camera using a computer and ALTAIRsoftware. The image data files were then saved and importedinto Matlab for further processing. The data from the coolingperiod was processed using the open access Matlab based IRVIEW [30] to calculate the phase and amplitude images.
4. Results and discussion
4.1. Thermal response of composite laminate
Typical pulse durations in pulse thermography vary from a fewmilliseconds to several seconds depending upon the thermo-physical properties of the material being inspected and theproperties of the defect. In general the pulse duration is chosento balance the two competing requirements of maximizingthermal energy to maximize the thermal response of the
material (while remaining below thermal material damage)and minimizing the thermal pulse duration to maximize thetemperature contrast between defective and non-defectionareas [12]. For the 2D woven carbon composite specimen usedin this study, the pulse duration was varied between severaltrials, from which 7 s was selected to produce the best defectimage. This pulse duration was then used for all experimentsdescribed in this paper.
The measured thermal response of two pixels from animpacted specimen of type 2 when heated with a squarepulse of 7 s is shown in figure 5. The thermal response wasmeasured after impact damage was created in the specimen.As carbon fiber epoxy is a low conductivity material, thespecimen required a long time to reach the room temperature,approximately 15 min, and the full measurement time is notplotted in figure 5(b). From figure 5(b), we observe that theobservation time, tobs, defined as the time from the beginningof cooling transient until there is no thermal contrast betweena non-defective and defective area, was approximately 12 s.We compare this observation time to the predicted time, tp, fora thermal wave to propagate from the depth z of a subsurfacedefect [13]:
tp = z2
α. (6)
Using the laminate thickness of 2.35 mm and anapproximate value of α = 0.42 mm2 s−1 for carbon fiber epoxy[3] yields tp = 13.1 s, close to that measured experimentally. Inlater experiments, the full thermal data acquisition time was setto 60 s, including a portion of the heating time. The truncationwindow length, T, was then extracted from the thermal imagesduring post-processing to fall within this observation time.
4.2. Simulated defect detection
As discussed earlier, the specimen of type 1 was used toevaluate the ability of the PPT setup to image defects intwo-dimensional carbon fiber epoxy woven laminates andto calibrate the depth-to-blind frequency relation for thismaterial. The sensitivity (also known as aspect ratio) ofthermography systems is defined as the defect diameter-to-depth ratio required for a given defect to be detectable. In thiswork we define the defect diameter as the length of one of thesides of the square defects.
The composite laminate of specimen type 1 was firstimaged such that the inclusions were embedded in betweenlayers 1–7 with respect to the front of the surface. A measuredthermogram and temperature decay curve for a pixel in adefective and non-defective area of the specimen are shownin figure 6. The absolute contrast, defined as the temperaturedifference between the pixel in the non-defective and defectiveareas, is also plotted in figure 6(b). The pulse thermographyimage with the maximum absolute thermal contrast wascaptured 1 s after the beginning of the cooling transient andis shown in figure 6(a). The available observation time forthis specimen was approximately 10 s (up to point ‘a’ infigure 6(b)). Not all defects are clearly visible in figure 6(a); inparticular the defects between layers 5 and 6 and those between6 and 7 are difficult to distinguish. Additionally, non-uniform
6
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
Time (sec)
Tem
pe
ratu
re (
°C)
Ab
solu
te c
on
tra
st (
°C)
0
0.5
1
1.5
2
2.5
0
10
20
30
40
50
0 2 4 6 8 10 12 14
Defective area (1)
Non-defective area (2)
Absolute contrast
abc
(a)
(b)
27
28
29
30
31
32
33
Tem
pe
ratu
re (
°C)
12
Figure 6. (a) Pulse thermography image of specimen type 1 atmaximum absolute thermal contrast. Defects increase in depth frombottom to top of image; (b) temperature decay for pixels in defectiveand non-defective areas of (a) and absolute thermal contrast. Timebegins at the start of the cooling transient.
heating of the specimen from the left to the right of the imageis also apparent.
For PPT processing, we selected a maximum truncationwindow of 7.4 s, i.e. the time at which the absolute contrast wasnegligible, shown as point ‘b’ in figure 6(b). The acquisitionframe rate was 60 Hz, from which 1 out of every 10 imageswas subsampled, producing �t = 0.166 s, reducing the totalnumber of available images to 45. The minimum frequencyavailable for this truncation window was 0.133 Hz. The phaseimage calculated using this frequency range is shown infigure 7, where all defects are clearly visible. Contrastingfigure 7 and figure 6(a) shows the imaging improvementobtained by the use of phase information. The deepest defects(those in the top row) are not visible in the maximum contrastpulse thermography image of figure 6(a), but they are clearlyvisible in the phase image.
We next demonstrate the importance of the selectedfrequency window on the imaging quality of defects atdifferent depths. Keeping the sampling interval constant,we varied the minimum frequency available by varying thetruncation window length (or N). The resulting phase images
0.65
0.7
0.75
0.8
0.85
Ph
ase
(ra
d)
Figure 7. Phase image of specimen type 1 showing simulateddefects at different depths in layers 1–7.
for four different truncation windows are shown in figure 8.As the minimum frequency decreased the depth of the defectsthat can be imaged also increased. There is also a windowingbehavior, as the defects with the maximum phase shift alsopropagated further into the laminate as the minimum frequencyis decreased. The phase images of figure 8 show that thereis an optimum choice of sampling parameters (i.e. �t, T)for each inspection depth. However, caution should be takenin using these phase images to determine the depth of aparticular defect. The minimum frequency at which a defect is‘visible’ in the phase images (the blind frequency) is influencedby the method of data presentation and user interpretation.A quantitative calibration of the blind frequency will beperformed in the following section.
The specimen was then reversed in the mounting fixturesuch that the inclusions were embedded in between layers7–12. In this manner, all inclusion depths could be studiedwith the same specimen. The best pulse thermography imageobtained at the maximum thermal contrast is shown infigure 9. For PPT processing, the camera rate was reducedto 10 Hz to allow a longer truncation window for thesedepths. Sufficient absolute contrast was obtained over T =8 s. Further subsampling of 1 out of 2 images, reduced thetotal number of images to 41, with a sampling rate of �t =0.2 s. Thus the minimum frequency available for phase imageswas 0.125 Hz. The phase image obtained using this minimumfrequency is shown in figure 10, where all defects of area 225and 100 mm2 size were visible. The deepest defect of area25 mm2 was not visible. Most of the defects are also visiblein the pulse thermography image of figure 9; however thepresence of non-uniform heating created significant noise inthe image. For the deeper defects, the defect detection wasnot above the noise level in figure 9. Finally, the detectablediameter-to-depth ratio for the PPT measurements can beestimated based on the deepest defect of area 25 mm2 thatwas detected at a depth of 2.38 mm. The sensitivity of the PPTsetup for these laminates is therefore approximately equal to5 mm/2.38 mm = 2.1, comparable with other PPT systemsreported in the literature.
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Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
(d)
Pixel Number
Ph
ase
(ra
d)
Pixel Number
(c)
Pixel Number
Ph
ase
(ra
d)
Pixel Number
(b)
Pixel Number
Ph
ase
(ra
d)
Pixel Number
(a)
Pixel Number
Ph
ase
(ra
d)
Pixel Number
Figure 8. Phase image from specimen type 1 for minimum frequency of (a) 0.6 Hz (N = 10, T = 1.66 s); (b) 0.4 Hz (N = 15, T = 2.49 s);(c) 0.3 Hz (N = 20, T = 3.32 s); (d) 0.17 Hz (N = 35, T = 5.81 s).
25
25.5
26
26.5
27
27.5
Tem
pe
ratu
re (
°C)
Figure 9. Pulse thermography image of specimen of type 1 imagedfrom back side to detect inclusions in layers 7–12.
4.3. Depth resolution of simulated defects
The final step, prior to imaging impact damage, is to calibratethe apparent blind frequency as a function of defect depth forthe given specimens and experimental setup. Since α for the
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Ph
ase
(ra
d)
Figure 10. Phase image of specimen type 1 showing simulateddefects at different depths in layers 7–12.
material systems is not known exactly, we write (since α is thesame for all specimens)
z = C1μ′ + C2 = C1
√1
π fb+ C2, (7)
where μ′ is the modified diffusion length, μ′ = μα−1/2.
8
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
(a) (b)
(c)
0 1 2 3 4 5 6−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
Frequency (Hz)
Pha
se (
rad)
Defective areaNon−defective area
fb=3.68 Hz
0 1 2 3 4 5 6−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
Frequency (Hz)
Pha
se (
rad)
Defective areaNon−defective area
fb = 2.32Hz
0 1 2 3 4 5 6−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
Frequency (Hz)
Pha
se (
rad)
Defective areaNon−defective area
Figure 11. Estimation of apparent blind frequency fb by using phase profiles of defects of size 225 mm2 at depths of (a) 0.2 mm,(b) 0.68 mm and (c) 1.4 mm.
Following the procedure of Ibarra-Castanedo et al [24],the apparent blind frequency for a given defect can beestimated by plotting the phase shift versus frequency curve fora pixel in the defective area and a pixel outside the defectivearea. This physical definition is shown in figure 11 for someof the 225 mm2 size defects (when imaged from the front ofthe specimen as in figure 7). To estimate the blind frequencyfor each of the defects, the phase contrast between the pixelin the defective and non-defective regions was plotted. Thefrequency at which these two curves were considered to mergewas obtained by setting a threshold of approximately 0.15 rad.For the deepest defects, this calibration procedure did not workwell as there was not sufficient phase contrast, as shown infigure 11(c). Therefore, only five defects of each area wereused for the calibration.
For each defect, a pixel at the center of the defect was usedfor the calculation of apparent blind frequency. As the phasecontrast is not uniform over the defective area, the choice ofpixel can alter the calculation slightly. Pixels further from the
center of the defective region are influenced by the boundaryvalues near the defect. Gonzalez et al [31] therefore used anaverage phase shift over the defective region. Our goal is tocalibrate the apparent blind frequency as a function of depthfor later, through-the-thickness imaging of impact damage,which does not present a clearly defined boundary. Therefore,the use of a single pixel at the center of the defect to definethe phase contrast was used in this work. Future work willinvestigate methods to better select appropriate phase valueswhen clearly defined boundaries are not present.
The modified diffusion length, μ′, was then calculatedfor each defect from the apparent blind frequency. Theknown defect depth is plotted against the calculated modifieddiffusion length for each defect in figure 12. We observe thatthe relationship is approximately linear. A linear fit to thedata for each defect diameter is also plotted in figure 12.There is an effect of the defect diameter on the slope ofthe curve, consistent with previous observations of thermalimaging of flat bottom holes in steel plates [32]. Gonzalez
9
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90
0.2
0.4
0.6
0.8
1
1.2
1.4
Dep
th (
mm
)
15 mm 10 mm 5 mm
z = 6.19 mm s−1/2 μ′ − 1.59 mm, R = 0.99
z = 5.94 mm s−1/2 μ′ − 1.53 mm, R = 0.99
z = 5.26 mm s−1/2 μ′ − 1.35 mm, R = 0.99
μ′ (s1/2 )
Figure 12. Linear calibration of depth z versus modified diffusionlength μ′ for three different defect sizes.
et al [31] normalized the parameters based on the thermaldiffusivities in the through-the-thickness and the transversedirections to adjust the calculated depth as a function ofapparent blind frequency. As the damage diameter will notbe known a priori for the impact damage, we cannot applya similar normalization to these results. However, as thelargest defect area in figure 12 is nine times larger than thesmallest defect area, this dependence on defect diameter isnot strong (the slope increased by 17.7% between the smallestand largest defects). We therefore neglected the size influencein the calibration, as other noise factors produced higheruncertainties.
We calibrated the depth as a function of modifieddiffusion length for all defect diameters using a linear least-squares regression. Figure 13 shows the resulting calibration,along with the 95% prediction and confidence intervals. Thecorrelation coefficient for this linear fit over all data was R =0.981. The resulting calibration curve was
z = 5.624 (mm/s1/2) μ′ − 1.43 mm. (8)
As mentioned earlier, the constant term in equation (8) is dueto under-sampling of the data and the truncation parameters[24].
4.4. Detection of barely visible impact damage
Two major challenges distinguish imaging through-the-thickness of laminates subjected to impact-induced damageas compared to imaging of inclusions or holes. The first isthat shadowing of damage occurs due to the conical shape ofthe damage region (from the front to rear surface). This sameshadowing is a common problem for imaging applications;however, as we want to measure the extent of damage throughthe thickness of the composite, this is not a serious issue forimaging of BVID. The second challenge is that the thermalcontrast between the defective and non-defective regions dueto BVID is much lower than that of the inclusions used instandardized ASTM testing (even in the phase information),as discussed earlier. For example, Brown et al [28] measureda thermal contrast for impact damage of only 10% that
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.25 0.3 0.35 0.4 0.45 0.5
Dept
h (m
m)
Fi�ed data95% Predic�on Interval
95% Confidence Interval
R=0.98
μ′ (s1/2 )
z = 5.62 mm s−1/2 μ′ − 1.43 mm
Figure 13. Linear calibration of depth z versus modified diffusionlength μ′ for complete data set.
of flat-bottomed holes in the same specimen and lock-inthermography configuration. For this study, we specificallychose to calibrate the PPT configuration with polymer foaminserts to reduce the large thermal property difference; howeverthe effectiveness of the calibration will be determined from theimaging results.
We now compare the PPT imaging results with those fromoptical microscopy of the specimens. Four specimens of type2 were impacted at impact velocities of 1.75, 1.40, 1.10 and0.9 m s−1, respectively. These impact velocities correspond toimpact energies of 8.4, 5.4, 3.3 and 2.2 J. Each specimen wasthen imaged from the same side as the impact event, as this istypically the surface that is available in practical applications.
Figure 14 shows the specimen impacted at the highestvelocity, 1.75 m s−1. The thermal image at maximum contrastis shown in figure 14(a), while the PPT image using themaximum frequency range (T = 5.6 s, N = 35, �t = 0.16 s)is shown in figure 14(b). The minimum frequency availablein this window was 0.17 Hz. Both methods clearly detect thepresence of impact damage. Figures 14(c) and (e) show thefront and back surfaces of the specimen, with the domainof visible damage delineated with a white line. Closer viewsof these surfaces are shown in figures 10(d) and ( f ). Thevisible damage on the front and rear surfaces is typical oflow-velocity impacts in laminated composites [28]. The frontsurface shows localized indentation at the location of theimpact. The front surface damage is not symmetric due tothe orthotropic properties of the material system. The rearsurface shows a more extensive damage region, with cracksparallel to the two principal material directions. During impact,bending of the laminate creates high tensile stress on therear surface, which leads to cracking, followed by extensivedelamination. The resulting damage area has the rhombusshape observed in figure 14(e). Internally in the laminate,the damage region within a lamina (or in-between laminae)is expected to decrease in size from the rear to the frontsurface [33].
Similar images for each of the other three specimensof type 2 are shown in figures 15–17. We observe that thepulse thermography was not able to detect the impact damagefor the specimens impacted at either 1.10 m s−1 (3.3 J) or
10
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
(a) (b)
(c) (d )
(e) (f )
(a) (b)
Figure 14. Post-impact images of specimen impacted at 1.75 m s−1:(a) pulse thermography image at highest contrast; (b) PPT phaseimage over full frequency range; (c) photograph of impacted surface;(d) local view of damage region on impacted surface; (e) photographof rear surface; ( f ) local view of damage region on rear surface.
0.9 m s−1 (2.2 J). PPT was not able to detect damage for thespecimen impacted at 0.9 m s−1. Therefore, we demonstrateddamage detection in the 2D woven material system for aminimum impact energy of 3.3 J using PPT. The extent ofdamage is directly related to impact energy in low-velocityimpact testing of composite laminates [34].
4.5. Depth resolution of impact damage
For through-the-thickness imaging, we will consider the firstspecimen (impacted at 1.75 m s−1) since the damage regionis the largest. The area enclosed by the rhombus regionin figure 10(e) and the circular area in figure 10(c) areapproximately 175 and 64 mm2, respectively. For comparison,the rear surface damage area calculated from the PPT image(the region with sufficient visible phase contrast) is 180 mm2,very close to that estimated from the photograph of therear surface. Therefore PPT imaging provides an excellentmeasurement of the extent of low-velocity impact damage inthis composite laminate material system. In contrast, the pulsethermography image underestimated the extent of damage.
(c) (d )
(e ) (f )
(a)
(b)
Figure 15. Post-impact images of specimen impacted at 1.40 m s−1:(a) pulse thermography image at highest contrast; (b) PPT phaseimage over full frequency range; (c) photograph of impacted surface;(d) local view of damage region on impacted surface; (e) photographof rear surface; ( f ) local view of damage region on rear surface.
This is primarily due to the lower thermal contrast between thedamaged and undamaged regions in the amplitude informationas compared to the phase information.
We next consider the extent of damage at different depthsthrough the laminate. Figure 18 shows the obtained phaseimage for this specimen for different frequency ranges. Thedetected damage in each frequency range is the damage regionspresent between the front surface of the specimen and thediffusion depth associated with each minimum frequency. Toconfirm the assumption that the impact damage increases fromthe front to the rear surface of the specimen, the extent ofdamage does increase as the minimum frequency is reducedin the phase images of figure 18. The damage regions offigure 18 can therefore be considered as the damage region atthe diffusion depth associated with each minimum frequency.
A second important observation is that the phase contrastacross the specimen (i.e. the maximum phase contrastbetween damaged and undamaged regions) in figure 18( f )is approximately 0.18 rad. The maximum phase contrastin the imaged polymer foam inserts (from figure 7) was0.25 rad. Therefore the impact damage phase contrast was
11
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
(b)
(c) (d )
(e) (f )
(a)
Figure 16. Post-impact images of specimen impacted at 1.10 m s−1:(a) pulse thermography image at highest contrast; (b) PPT phaseimage over full frequency range; (c) photograph of impacted surface;(d) local view of damage region on impacted surface; (e) photographof rear surface; ( f ) local view of damage region on rear surface.
72% of the calibration specimen. This is much higher than the10% reported previously for flat-bottom holes [31] and givesconfidence in the validity of the previous calibration data whenapplied to BVID.
The next step is to calculate the blind frequency at differentpixels in order to calculate the depths of each phase image.We did not calculate the blind frequency at all pixels due tothe computational effort involved. Figure 19 shows a selectedportion of the phase image of figure 18( f ) (with the maximumfrequency range) which was used for this calculation. Theblind frequencies at the five points labeled in figure 19 werecalculated following the same procedure as for the calibrationspecimen. Figure 20 plots the phase and phase contrast (ascompared to a pixel in a non-defective region) for these fivepoints, as a function of minimum frequency, obtained from thephase images. We observe a higher level of noise in these plotsat higher frequencies. This noise is typical of experimental PPTdata and can be reduced by curve fitting of the phase versusfrequency plots [24]. From these plots, the blind frequencywas estimated to be 3.8, 2.7, 1.8, 1.2 and 0.8 Hz at points 1,2, 3, 4 and 5, respectively. From these blind frequency values,
(a)
(c ) (d )
(e) (f )
(a) (b)
Figure 17. Post-impact images of specimen impacted at 0.9 m s−1:(a) pulse thermography image at highest contrast; (b) PPT phaseimage over full frequency range; (c) photograph of impacted surface;(d) local view of damage region on impacted surface; (e) photographof rear surface; ( f ) local view of damage region on rear surface.
the modified diffusion length and the predicted depth werecalculated using equation (8).
In order to apply this depth prediction to other pixels in thedamage region, a linear fit of the phase value (from figure 19)to the predicted depth for each of the five points was calculated.There is not a physical justification for a linear fit between thetwo parameters, but this linear fit had a correlation coefficientof R2 = 0.985 for this data set, therefore it was considerablea reasonable method to fit data. Unlike the depth calibrationof equation (8), however, this fit is specific for this image anddoes not necessarily transfer to data from other specimens.Using this linear fit, the depth at each pixel within the damageregion was calculated for the image of figure 19. A contourplot of the calculated damage region as a function of depthis shown in figure 21(a). The plotted contours were chosento be at each interlaminar boundary. The minimum depth inthe damage region calculated was 0.32 mm, located withinthe second lamina from the front surface. We observe that thedamage envelope has the predicted conical form.
To compare the minimum depth calculated with the PPTimages, the specimen was sectioned with a wet saw through
12
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
0.76
0.765
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0.775
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Pha
se (
rad)
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se (
rad)
Pha
se (
rad)
Pha
se (
rad)
Pha
se (
rad)
Pha
se (
rad)
(a) (b)
(c) (d )
(e) (f )
Figure 18. PPT phase images for specimen impacted at 1.75 m s−1 with minimum frequencies of (a) 1.2 Hz, (b) 0.6 Hz, (c) 0.4 Hz,(d) 0.3 Hz, (e) 0.2 Hz and ( f ) 0.17 Hz.
the center of the specimen. Figure 21(b) shows the sectionedspecimen, imaged through a microscope with magnification50x. The width of this image is 5.75 mm (equivalent toapproximately 19 pixels in figure 21(a)), therefore the imagelies in the region of minimum damage depth. Visible types ofdamage are highlighted on the image, including fiber ruptureand tow splitting near the rear surface and delamination,occurring at many locations through the thickness. It isthe presence of delamination which we expect the imagingto detect, due to the large aspect ratio perpendicular tothe direction of the thermal wave propagation. In contrast,
the optical cross-sectional imaging also highlights damagesoccurring in the through-the-thickness (sectioned) plane [35].Additionally, the minimum defect depth of 0.32 mm predictedfrom the PPT imaging is also marked by the dashed line infigure 21(b). We observe that this predicted depth correspondswell the visually observed delamination in the microscopyimage.
A few other challenges in through-the-thickness imagingof the specimen for BVID can be drawn from the microscopyimage. First, localized bending of individual laminae, such asdue to the peeling of the rear surface after fracture of the
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Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
160 180 200 220 240
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5
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el N
um
be
r
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ase
(ra
d)
Figure 19. Subregion including detected damage from PPT phaseimage for specimen impacted at 1.75 m s−1 using full frequencyrange (one pixel corresponds to approximately 0.2 × 0.2 mm2).
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
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se C
ontr
ast (
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se (
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Figure 20. Phase and phase contrast plots calculated for five pixelshighlighted in figure 19.
rear lamina, was not compensated for in the defect depthcalculation. This bending, as well as global curvature ofthe lamina after impact, can create a significant error in thedepth measurement. Secondly, the minimum measured depthof 0.32 mm, or any specific depth, does not correspond toan individual lamina or inter-lamina boundary due to thewoven geometry of the laminate, clearly visible in figure 21(b).This non-planar geometry is especially evident in the surface
(a)
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6080
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th (
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Figure 21. (a) 3 D impact damage progression using PPT (one pixelcorresponds to approximately 0.2 × 0.2 mm2) and (b) microscopicimage of cross section of an impacted specimen.
profile of the specimen (the surface visible here was in thecontact region of the impactor). Care should therefore be takenwhen interpreting the PPT through-the-thickness profiling,specifically when correlating the measured damage regionsto detailed numerical models of the composite behavior.Again, this non-planar geometry highlights the deficiencyof the assumed one-dimensional thermal wave propagation;however, good quality estimates of the extent of damage wereobtained using this assumption.
5. Conclusions
In this work, we demonstrated a calibration method forBVID in polymer-matrix composite laminates. We appliedthe method to two-dimensional woven, carbon fiber epoxylaminates with low-velocity impacts in the range of 2.2 to8.4 J. Both the extent of delamination and the minimumdepth of delamination were well predicted by applying theprevious calibration to the PPT phase images of the impactedspecimen. The minimum detectable damage was measured atan impact energy of 3.3 J. While the exact level of transversethermal wave propagation and its contribution to the phase
14
Meas. Sci. Technol. 24 (2013) 115601 S S Pawar and K Peters
measurements near the damage region are not known, theuse of polymer foam inserts as the simulated damage inthe calibration specimen was effective because it produceda thermal contrast in the PPT phase image similar to that ofthe imaged damage in the impacted specimens.
While the role of defect size has been incorporated intoprevious depth calibration procedures, the application of sizecorrection factors to imaging of BVID is not clear. The sizeof the defect is not known a priori, and is in fact one ofthe parameters to be determined, therefore some fitting of thevarious parameters would be required to include the defectsize. It is not clear if such a fitting process would present aunique solution. However, as demonstrated by these results, theone-dimensional wave propagation assumption and neglect ofthe role of the defect size produce reasonable measures of thedamage size and depth and is therefore a good starting pointfor damage identification. Further detailed analysis of the roleof both of these items on the thermal wave propagation in thelaminate could be performed through detailed finite elementmodels for improvement of the imaging results. One challengewould be that these models would need to be generated for eachspecific material system considered.
Acknowledgment
The authors would like to acknowledge the partial support ofthis work by the National Science Foundation through grantCMMI 0825709.
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