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Impact-induced damage characterization of composite plates using neural networks
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2007 Smart Mater. Struct. 16 515
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Smart Mater. Struct. 16 (2007) 515–524 doi:10.1088/0964-1726/16/2/033
Impact-induced damage characterizationof composite plates using neural networksSteve E Watkins1, Farhad Akhavan1, Rohit Dua1,2,K Chandrashekhara3 and Donald C Wunsch2
1 Applied Optics Laboratory, Department of Electrical and Computer Engineering,University of Missouri-Rolla, Rolla, MO 65409-0040, USA2 Applied Computational Intelligence Laboratory, Department of Electrical and ComputerEngineering, University of Missouri-Rolla, Rolla, MO 65409-0040, USA3 Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla,MO 65409-1350, USA
E-mail: [email protected], [email protected], [email protected],[email protected] and [email protected]
Received 14 February 2006, in final form 17 January 2007Published 2 March 2007Online at stacks.iop.org/SMS/16/515
AbstractImpact-induced damage in fiber-reinforced laminated composite plates ischaracterized. An instrumented impact tower was used to carry outlow-velocity impacts on thirteen clamped glass/epoxy composite plates. Arange of impact energies was experimentally investigated by progressivelyvarying impactor masses (holding the impact height constant) and varyingimpact heights (holding the impactor mass constant). The in-plane strainprofiles as measured by polyvinylidene fluoride (PVDF) piezoelectric sensorsare shown to indicate damage initiation and to correlate to impact energy.Plate damage included matrix cracking, fiber breakage, and delamination.Electronic shearography validated the existence of the impact damage anddemonstrated an actual damage area larger than visible indications. Thestrain profiles that are associated with damage were replicated using anin-house finite element code. Using these simulated strain signatures and theshearography results, a backpropagation artificial neural network (ANN) isshown to detect and classify the type and severity of damage.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
Advanced fiber-reinforced polymer composite materials areused extensively in aerospace, civil, and mechanicalengineering applications. They have clear advantages of longlifetime, high strength-to-weight ratio, and flexible design,but suffer from damage mechanisms that are difficult todetect at the early stages. The construction of an optimallydesigned load-carrying structural system is more complicatedthan for traditional materials. There are instances of cracks orstructural damage escaping inspection during regular checkupsof complex systems [1]. Therefore, an integral monitoringsystem with built-in intelligence could assess and/or reactto the environment imitating biological patterns of self-organization. Such smart structures have been made possible
through the merging of materials science, structural mechanics,sensor technology, advanced signal processing techniquesand actuator technology. The growth of structural integritymonitoring techniques for smart structures has receivedincreasing attention in recent years. The objectives areto monitor the structural health and to detect the onset ofabnormalities and hence to forewarn of impending failures.There are many advantages in such a system: less downtime,less frequent maintenance, better utilization of material usage,reliability, economy.
Delamination of laminated composites is an importantfailure mode. Since these defects may cause structural failureat loads below the designed load, their assessment has receivedmuch attention in the research community. Delaminationgrowth and the associated structural behavior have been
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studied under various dynamic and static load conditions andfor many material properties, geometric parameters boundaryconditions, and sensor approaches [2–8]. The understandingand prediction of this failure mode is important to compositeapplication and design. Impact events can cause compositedelamination.
A key parameter of impact-induced damage in compositesis impact force during the time the impactor is in contact withthe composite [8–17]. The contact force history is related tothe type of damage which occurs in the composite specimen(i.e. matrix cracking, delamination, fiber breakage, materialpenetration) and to the strain relationship in the specimen.Determination of contact force history is an alternative tomeasurement of the static indentation. The work by Lagaceet al used static indentation for the reasons of simplicityand ease of standardization [18]. Virtually the same damagemechanisms are created and similar load–displacement curvesare produced. However, at the same value of maximumloading, the extent of damage will differ. Static indentationtests have been shown to predict damage at velocities up to2 m s−1 [19, 20].
The total fracture energy absorbed by the plate during theimpact corresponds to the amount of damage done. A linearrelationship has been shown between impact energy and peakcontact force and the resulting damaging area was a distinctfunction of the peak contact force for a fixed material, lay-upand thickness [21]. Therefore, the peak impact force may beused to grade the damage resistance in composite componentswith a fixed design. Also, the structural strain response of theimpacted composite structure can be similarly related to theamount and type of resulting damage.
A specimen’s (structure) size, curvature, lay-up, andboundary conditions affect the structural impact response andthe resulting damage. It is demonstrated that varying theinterface angle gives a significant change in the damage areafor a fixed impact condition. The size and shape of adelamination within an interface depends on the mismatchof bending stiffness between the plies adjacent to theinterface [22]. Influence of the interface angle is the resultof interlaminar shear stress that initiates the matrix failure.Delamination size and shape in multi-ply laminates are noteasily predictable [23]. (In the following impact-induceddamage experiments these factors are held constants. Theimpacts are done at the center of identical square compositeplates, midway from the clamped boundaries where theeffects of curvatures are neglected. The angle between thefiber orientations of the adjacent plies is also fixed.) Thethickness of a composite laminate affects the impact durationand peak contact force as well as the damage initiationand propagation. For specimens with low bending stiffness,damage will initiate at the back surface where bending stressesare the greatest. For specimens with high bending stiffness, thehigh contact stresses will cause damage to initiate underneaththe impact site. Material properties such as fiber strengthor matrix fracture toughness have significant influence on theinitialization, propagation, and the final state of impact damagewithin a composite.
In recent years, the application of neural networks hadattracted increasing attention due to their capabilities includingpattern recognition, classification, and function approximation
and is well documented in the literature. For large monitoringsystems having numerous built-in sensors (and actuators),real-time operation and monitoring requires higher computingspeeds. Artificial neural networks (ANNs) have parallelcomputing architectures and, when implemented in hardware,can quickly process multiple inputs. ANNs can learn to adaptfrom experimental data. They can learn to process data oneway, and when conditions change, the processing can adapt tonew conditions. ANN applications for delamination detectionin composite structures, including damage assessment andfatigue monitoring, have been extensively studied [24–38].Neural networks have been coupled with advanced sensingtechnologies to predict and generalize unknown parameters inphysical systems. Neural networks can integrate the resultingstrain profiles and numerically interpret this information. Priorresearch has characterized non-damaging impacts from strainsignatures using neural networks.
This work contributes to an understanding of damage-inducing impacts of clamped glass/epoxy composite plates.The information contained in the strain signatures andthe development of intelligent health-monitoring systemsis emphasized. In particular, the effects of low-velocityimpacts and the associated impact contact forces on the strainresponse and structural health are investigated. Experimentalimpacts produced damage for a range of kinetic energies fromvarious combinations of impactor masses and velocities. Apolyvinylidene fluoride (PVDF) piezoelectric sensor networkand an impact force cell were used to detect changesin the transient in-plane strain and contact force behaviorfor a damage event. The type and severity of damagewere determined from inspection of and shearographymeasurements for the composite plates and were correlatedwith the impact energies. An in-house finite element analysisreplicated the strain and contact force profiles for damage.Backpropagation ANNs were implemented and trained forimpact damage assessment using strain signatures.
2. Impact-induced strain experiment
2.1. Composite plates and strain instrumentation
Fiber-reinforced-polymer composite plates were fabricatedin-house from 3M prepreg tapes using hot press tech-niques [8, 26]. The twelve-layer symmetric cross-ply lam-inates had a [0/90/0/90/0/90] glass/epoxy lay-up. The ma-terial properties were E1 = 38.6 GPa, E2 = 8.27 GPa,G12 = G13 = 4.14 GPa, G23 = 3.24 GPa, ν12 = 0.26, andρ = 1800 kg m−3. Each plate size was 25.4 cm by 25.4 cmby 2.92 mm. Thirteen identical plates were used in the damagetests. The plates were instrumented with polyvinylidene fluo-ride (PVDF) strain sensors. These piezoelectric sensors weremanufactured by the AMP Corporation and had dimensions of25 mm by 113 mm by 28 μm. The support instrumentationincluded an HP 54540A digitizing oscilloscope at the highestsample rate of 2 giga-samples/second and 1 M� input.
Four sensors were bonded with epoxy to the opposite-to-impact side of each plate as shown in figure 1. The first andsecond PVDF strain sensors were 2.54 and 5.08 cm away fromthe center point of the plate and both were aligned with the ydirection (the direction normal to the glass fibers of the surface
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Sensor 1 Sensor 2
Sensor 3Sensor 4
2.54cm
εx
εy
Impact point
25.4 cm
25.4 cm
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Figure 1. Schematic of PVDF strain sensor configuration on theglass/epoxy composite plates. The sensor distances from the centerpoint are not to the scale of the plate dimensions.
ply). The third PVDF strain sensor was aligned 45◦ to the xdirection and was 2.54 cm from the center point of the plate.The fourth PVDF strain sensor was 2.54 cm from the centerpoint of the plate and was in the x direction (the directionparallel to the glass fibers of the surface ply). For convenienceall four sensors were mounted in one quadrant.
2.2. Drop-weight impact experiment
An instrumented steel tower was used to provide a controlledimpact event. The impact weight and height can be adjustedand the impactor velocity and contact force measured. Thetower and the high-speed support instrumentation are shownin figure 2. It was designed using IDEAS solid modelingsoftware and tested for vibration stability and static loading.The tower is formed with two tracks made from two sets ofwelded, braced angle beams anchored to a base frame. Theimpactor assembly can mount different weights and can bereleased from different heights. The assembly is held withan electromagnet and is released by switching off the batterypower to the electromagnet. The assembly is guided by wheelswithin the tracks so that the impactor head is normally incidentat the center of the plate. The impactor velocity is measuredat the moment of impact by a velocity instrument using aninfrared LED and two photodiodes. The impactor contactforce is measured by a semi-spherical, shear–strain force cellmounted to the impactor head. The diameter of the impactorhead is 1.27 cm. This Kistler PCB Model-208A24 force cellhas a sensitivity of 4.458 mV N−1 (0.995 mV/lb) and a rangeof 11200 N (2500 lbs). A catch prevents the impactor assemblyfrom striking the plate more than once.
The instrumented composite plates were rigidly clampedalong their edges in the tower for testing. The contact forcehistories, the kinetic energies (from the mass and measuredvelocities), and the plate PVDF strain profiles, and the visualinspection information were recorded for each impact. Mostplates were subjected to multiple impacts. After a prescribednumber of impacts, the plates were removed and photographed.In most cases the plates were reinstalled for further testing.
VelocityMeter
Impact Height Adjustment
Roller
CompositePlate
Impactor Head(Force Cell)
SensorInstrumentation
Computerwith Data
AcquisitionSoftware
Sensor Signals
Impact
Impact Tower MagneticRelease
Height
Figure 2. Impact tower and support instrumentation.
After completion of testing on plates #3, #5, and #7, a detailedanalysis using shearography was performed to determine thefull extent of damage (as opposed to that determined fromvisual inspection). The impact parameters for each plate didnot change over the course of multiple impacts. Figures 3 and 4show typical strain and contact force profiles for non-damagingand damaging single impacts. The peak strain magnitude fordamaging impacts is much larger and the strain profile showsmore structure. The force profile for a non-damaging impacthas a smooth rise to a peak and a short contact time [26]. (Infigures 3 and 4, secondary peaks are observed in the contactforce versus time response. This behavior may be attributedto noise in the measurement system.) By contrast, the forceprofile for damaging impacts rises sharply to an abrupt plateauat the initiation of damage and then rises to a peak with morestructure as the damage propagates. These measured profiles,especially the initial rise characteristic of the force profile,contain information on the time, type, and extent of damage.
2.3. Experimental results
A summary of the impact parameters is given in table 1. Theimpact heights are from 0.36 to 0.81 m and the impact massesare from 0.2 to 1.8 kg. The resulting impact energies rangedfrom 0.42 to 14.60 J. The damage severity was correlatedwith impact energy. The first plate was used to refine theexperimental procedure and data collection. All plates werefound to have damage and the measurements indicated damageafter all initial impacts. Figure 5 shows the strain profiles forthe sixth plate during its initial impact event from which severedamage resulted. Figures 6 and 7 show several contact forceprofiles for a mass of 1.8 kg and a mass of 0.36 kg. The peakforce tends to increase with increasing damage severity.
3. Damage classification using visual inspection andshearography
3.1. Visual inspection and shearography
Damage to the plates was characterized using visual inspectionafter each impact and using shearography for selected plates.Visual inspection consists of examining the upper and lowersurface of the plate at the impact site under bright light.This technique can detect surface cracks and discolorationthat is associated with delamination and matrix cracking of
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(a)
(b)
(c)
Figure 3. Non-damaging impact response from a preliminary low-energy test on a similar glass/epoxy plate (plate not shown in thesubsequent table; impactor mass of 1.8 kg and impactor height of 5.08 cm): (a) PVDF strain sensor response at 5.08 cm from the center of theplate along the y axis, (b) PVDF strain sensor response at 2.54 cm from the center of the plate along the x axis, and (c) contact force responseat the center of the plate.
Table 1. Experimental parameters for damage-inducing low-velocity impact tests on glass/epoxy composite plates.
Plate Number of Inspection Impact Height Measured impact Kinetic impactnumber impacts impact numbers mass (kg) (m) velocity (m s−1) energy (J)
1 Multiple Multiple 1.8 0.81 3.34 10.042 2 1, 2 1.8 0.81 3.34 10.043 2 2 1.8 0.66 2.95 7.834 2 1, 2 1.8 0.91 3.74 12.595 10 5, 10 1.8 0.51 2.56 5.906 4 4 1.8 1.12 4.03 14.607 3 2, 3 1.8 0.97 3.79 12.938 4 1, 4 1.8 0.51 2.59 6.049 6 5, 6 1.8 0.36 2.06 3.82
10 4 2, 4 1.8 0.36 2.06 3.8211 6 5, 6 0.8 0.36 2.06 1.7012 3 2, 3 0.6 0.36 2.06 1.2713 3 2, 3 0.2 0.36 2.06 0.42
the inner plies. The surfaces were photographed for selectedimpact numbers (see table 1). The shearography technique canprecisely detect non-visible damage through induced surfacevariations and the correlation of interferograms.
Electronic shearography [38–45] is a non-contact wide-field technique that compares a live video image with a storedvideo image to produce interference fringes. The target surfaceis illuminated with coherent light the image recorded under
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(a)
(b)
(c)
Figure 4. Damaging impact responses of a glass/epoxy plate (plate #2 with impactor mass of 1.8 kg and impactor height of 0.81 m):(a) PVDF strain sensor response at 5.08 cm from the center of the plate along the y axis, (b) PVDF strain sensor response at 2.54 cm from thecenter of the plate along the x axis, and (c) contact force response at the center of the plate.
different amounts of uniform stresses. Shearography splits thelight forming the image and recombines it to create overlappingand laterally displaced images on a CCD camera which recordsthe resultant interferogram [46]. A second image or successiveimages are compared to this first image by the image processorat the pixel level [39, 47]. The processor calculates thedeformation of the test part by analyzing the interference phaseshift of the laser light for each pixel.
A shearography laser/camera SC-4000 and image proces-sor IP-4200, manufactured by Laser Technology, uses greenlight to detect surface deformations of forty microstrains ormore. The plate surfaces were prepared by applying a water-washable coat of light green, non-gloss, and diffusive paint tooptimize the back-reflection of the green laser light. The plateswere placed on a three-point kinematic support and tilted tominimize back-reflection into the camera. The plate interfer-ograms were recorded before and after heat-induced stresses.The system produced images that clearly defined the area ofdamage.
3.2. Damage characterization
The damage characteristics resulting from impact are describedin table 2. The severity of the visible damage is directly
Table 2. Impact damage characteristics of glass/epoxy compositeplates.
Peak Approximate ApproximateKinetic contact visible visible
Plate impact force delaminated surface crackednumber energy (J) (N) area (cm2) area (cm2)
6 14.6 931.7 2.9 11.57 12.9 870.8 1.3 7.64 12.6 — 1.0 —1 10.0 628.1 0.3 2.82 10.0 669.4 0.3 5.73 7.8 499.9 <0.3 2.58 6.0 532.5 — 0.75 5.9 418.6 <0.3 8.7
10 3.8 537.2 — 4.39 3.8 405.4 <0.3 6.2
11 1.7 783.3 — 5.112 1.3 711.8 — 5.713 0.4 468.1 — 3.9
correlated with the kinetic energy of the impact event. Impactpeak contact forces generally vary with the kinetic impactenergy. The damage consisted of delaminations and surfacecracks. For the least severe impacts, only parallel cracks were
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(d)
(c)
(b)
Figure 5. Strain profiles for plate #6 at: (a) 2.54 cm from the center of the plate along the y-axis, (b) 2.54 cm from the center of the platealong the x-axis, (c) 5.08 cm from the center of the plate along the y-axis, and (d) 2.54 cm from the center of the plate 45◦ from the x-axis.
observed. For more severe impacts, the impact surface showedsevere discoloration and matrix cracks several centimeterslong. Also, the later cases showed a few parallel cracks at theopposite-to-impact side of the plate at the center of the plate.These cracks were spaced about 1 mm from each other andwere less than 5 mm in length.
The shearography results for the selected plates showedthat the actual damage areas were significantly larger than thevisible damage areas. Figure 8 shows the shearography imagesfor plates #5, #3, and #7. The delamination area for plate #5 isabout 1.9 times larger than that measured by visual inspection.The delamination area for plate #3 is about 1.8 times largerthan that measured by visual inspection. The delamination areafor plate #7 was about 2.0 times larger than that measured byvisual inspection.
4. Simulation and neural network analysis
4.1. Finite element simulation and damage classification
The nonlinear impact behavior of a composite plate wasdetermined using an in-house finite element code. The
analysis for this work used the composite structure andmaterial properties of the impact tests. Also, the impactparameters, mass, velocity, and energy were in the samerange as well. Prior research using this code has shownthe relationships among contact force, strain, and impactenergy [48]. It is based on a shear flexible finite element modeldeveloped for nonlinear transient analysis [49]. It incorporatesmodified Hertzian contact stiffness [50] in concert with theloading/unloading contact law of Yang and Sun [51]. Itassumes a third-order displacement field and nonlinear strain–displacement relations based on von Karman assumptions.The details are not repeated here. The formulation uses anisoparametric quadrilateral element with nine modes and totalof 63◦ on freedom. The solution gives in-plane deflections, in-plane strains, and the nonlinear contact force.
Strain profiles and contact force profiles were determined.In particular, the X and Y strain profiles were determinedfor a point 2.54 cm from the impact location to match theexperiment. The X strain is parallel to the surface plydirection and the Y strain is perpendicular to the surface plydirection. These profiles had a step size of 3 μs and duration
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Impact-induced damage characterization of composite plates
#5
#3
#7
#6
1000
800
600
400
200For
ce (
N)
–200
0
0.5
1
1.5 -5
510
Time (ms)Drop Height (m)
0
Figure 6. Contact force profile for plates #5, #3, #7, and #6 (in orderof damage severity). The impactor mass is fixed at 1.8 kg and theimpact height is 0.51, 0.66, 0.97, and 1.12 m, respectively.
#13
#12
#11
800
600
400
200
For
ce (
N)
–200
0
00.5
1-5 5 10 15
0
Drop Mass (kg) Time (ms)
Figure 7. Contact force profile for plates #13, #12, and #11 (in orderof damage severity). The impact height is fixed at 0.36 m and theimpactor mass is 0.2, 0.6 and 0.8 kg, respectively.
of 3.3 ms. The parameters of 141 impact events were usedto cover the range of kinetic energies obtained in the priorimpact experiment. To provide additional confirmation of thesimulation validity, XY shear strain profiles at 2.54 cm fromthe impact point and the associated contact force profiles weresimulated for the impact. The simulation results for all types ofprofiles were consistent with the experimental measurementsin structure and amplitude [27].
These X and Y strain profiles were used to train andtest a neural network approach to classifying the type andextent of damage. The simulation results were needed tohave a sufficiently large data set for the neural networkimplementation, i.e. the experimental data was limited. Theexperimental results were used to check the simulation resultsand to determine the damage classification categories thatspecify the damage associated with kinetic impact energy.Table 3 shows the kinetic energy ranges for each type of
(a)
(b)
(c)
Figure 8. Shearography images for selected plates. The images arefor (a) plate #5 with impact energy of 5.9 J, (b) plate #3 with 7.8 J,and (c) plate #7 with 12.9 J. The damaged areas are within themarked ellipses.
damage as determined by the structure of the measured strainand force profiles and by the experimental inspections. Noobservable damage was apparent for preliminary tests withkinetic impact energies below 0.1 J. Six additional categorieswere created ranging from minute surface scratches to severedelaminations and long matrix cracks. Cracks parallel to plydirection were the first observable damage and the lengthincreased with increasing impact energy and matrix cracksoccurred for extreme impacts. Also, delaminations increasedin size as the impact energy increased. The categories werecoded into binary target vectors using Gray Code as shownin table 3. Hence, the neural network output layer had threeneurons.
4.2. Neural network architecture and neural networktraining [52]
MATLAB ‘Neural Network Toolbox’ was used to performthe neural network analysis. The input and output layerrequirements were determined from the characteristics of thesimulation data and damage classifications. The inputs werethe initial 1005 points in the simulated X and Y strain profiles.These FEA data sets were appended to form a single inputvector of 2010 elements, i.e. the first 1005 elements for theX profile and the second 1005 elements for the Y profile. The
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Figure 9. Performance and mean squared error curves for trainingthe neural network with (a) the one-step secant method, and (b) theconjugate gradient method. Note that the conjugate gradient methodreached the desired mean squared error in fewer epochs (2000) thanthe one-step secant method.
vector values were scaled for a range of 0–1 as a preprocessingstep. To remove the redundancy in the data and to create amore manageable vector size, the input vectors were down-sampled to 503 elements. The output vectors were the GrayCode classifications as shown previously. Of the 141 input andoutput sets, 126 were randomly selected for training and 15 fortesting. Except for the first category (‘no observable damage’),all other categories were present in the test vector set.
A 503,10,3 artificial neural network (ANN) was selectedfor training and stimulating the data. Transfer functions ofboth the 10-neuron hidden layer and 3-neuron output layeris sigmoid. Standard backpropagation using different trainingalgorithms was used to train the neural network. Owing to thelarge size of the input vector (503 elements) and consequentlythe huge memory requirements, the Levenberg Marquardt andNewtons algorithm could not be used. Conjugate gradientmethod is suited for large size input vectors and had the bestperformance as seen in figure 9. Other methods of adjacentgradient descent, resilient backpropagation, and one stepsecant were also tried, but they produced poorer convergence.
Table 3. Damage and code classification.
Kinetic TargetClassification energy range vectorof damage (J) (0.5 mv2) code
No observable KE � 0.1 [0 0 0]damageMinute 0.1 < KE � 0.3 [0 0 1]scratchesMinor parallel 0.3 < KE � 4 [0 1 1]surface cracksSurface discoloration and 4 < KE � 8 [0 1 0]small matrix cracksDiscoloration and 8 < KE � 10 [1 1 0]long matrix cracksModerate discoloration, obvious 10 < KE � 12.5 [1 1 1]delamination, and long matrix cracksSevere discoloration, severe KE > 12.5 [1 0 1]delamination, and long matrix cracks
Table 4. Error and epoch table.
Training Number of Number ofalgorithm errors epochs
Conjugate gradient 1 2000descentAdjacent gradient 1 4000descentResilient 2 4000backpropagationOne step 1 4000secant
4.3. Neural network results and discussion
The network had good performance with regard to the requirednumber of training epochs and the classification accuracy forthe test vectors. The desired mean-square-error performancefor all training algorithms was reached in either 2000 or 4000epochs, cf figure 9. The training target performance errorwas 1 × 10−5. Table 4 shows the number of errors when thetest vector set is applied and the number of epochs needed toreach the target error for all training methods. Table 5 showsthe results for all 15 test vectors of a post-regression analysisbetween the network actual response and the correspondingtarget codes. It shows a perfect fit between the Gray Codeclassifications for the actual outputs and the targets except fora single vector that was classified incorrectly. Of the 15 testvectors, this test vector was incorrectly identified for all ofthe training algorithms. The [0 1 0] (fourth class) case wasincorrectly classified as [0 1 1] (third class). Note that theerror was only in the third binary output. Also, the kineticimpact energy associated with this test vector was close to theboundary between the categories (vector energy = 4.212 J),hence the threshold per ANN had some fuzziness.
The conjugate gradient descent algorithm gave the bestresults. It produced only one error which was also producedby all other algorithms and its training converged in half theepochs of the other algorithms. The basic backpropagationalgorithm adjusts the weights in the steepest descent direction(negative of the gradient). This is the direction in which theperformance function is decreasing rapidly. For this work, thefunction decreases rapidly along the negative of the gradient,
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Table 5. Network output of Gray Code classifications for the ANNpredicted response and target response. Note that only test vector #7was classified incorrectly in the third binary bit.
Predicted TargetTest vectors class code class code
#1 (second class) [0 0 1] [0 0 1]#2 (third class) [0 1 1] [0 1 1]#3 (third class) [0 1 1] [0 1 1]#4 (fifth class) [1 1 0] [1 1 0]#5 (sixth class) [1 1 1] [1 1 1]#6 (sixth class) [1 1 1] [1 1 1]#7 (fourth class) [0 1 0] [0 1 1]#8 (fourth class) [0 1 0] [0 1 0]#9 (second class) [0 0 1] [0 0 1]#10 (seventh class) [1 0 1] [1 0 1]#11 (fourth class) [0 1 0] [0 1 0]#12 (fifth class) [1 1 0] [1 1 0]#13 (fifth class) [1 1 0] [1 1 0]#14 (sixth class) [1 1 1] [1 1 1]#15 (fourth class) [0 1 0] [0 1 0]
but steepest descent does not necessarily produce the fastestconvergence. In the conjugate gradient algorithm, a searchis performed along conjugate directions, which producedgenerally faster convergence than steepest descent direction.
5. Conclusions
The in-plane strain signatures that resulted from impact-induced damage in fiber-reinforced composite plates weredirectly linked to the type and extent of damage. The peakstrain was larger and the strain profile was more structuredfor damaging impacts than for non-damaging impacts. Theassociated contact force profile showed the onset of damageand the propagation of damage in the composite structure. Thedamage severity is directly correlated with the kinetic energyof the impact. The damage began as surface scratches and shortcracks parallel to the laminate ply direction, and progressed tolong matrix cracks, fiber breakage, and delamination. The areaof delamination was generally more extensive than the areaapparent from visual inspection.
Low-velocity impact experiments were conducted onthirteen glass/epoxy laminate plates. The surface strains weresuccessfully measured using PVDF piezoelectric film sensorsand correlated to the measured contact force and kinetic energyof the impact. The strains varied greatly with orientationand location with respect to the impact point. The impactsproduced a range of damage as assessed by visual inspectionand shearography measurements. The measured strain andcontact force signatures were validated with a finite elementanalysis.
The use of neural networks as an intelligent healthmonitoring system for characterizing impact-induced damagein composites was shown. A backpropagation artificial neuralnetwork was able to classify damage based on the kineticenergy of impact using the limited strain signatures as inputs.This result is an extension of prior work that showed that astrain-based neural network could characterize impact energyand contact forces for non-damaging impacts [26]. The neuralnetwork approach offers the advantages of processing speedand multiple-input processing. However, a practical system
would need to know the impact location or have additionalinputs to accommodate for this parameter. A neural networkmonitoring system for impact events can warn of damageinitiation and severity. Such an assessment system would allowfor avoidance of catastrophic failure and for better structuralmanagement.
Acknowledgments
This work was supported by the Office of Naval Researchunder grant no. ONR N00014-94-1200, with Dr Thomas MMcKenna as the technical monitor, and was supplementedby support from the Missouri Department of EconomicDevelopment. Laboratory assistance of Ben Baker is gratefullyacknowledged.
References
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