Assessment Of The Length And Depth Of Delamination-Type Defects . - MDPI

Appl. Sci. 2020, 10, 52363 of 19defect position and the composition of the material to the detectability of delamination. Recently,Murat et al. [25,26] analyzed the scattering of A0 mode from delaminations of different sizes which weresituated at different depths. It was observed that the delamination length exerts strong influence onthe scattering directivity, while its depth influences the magnitude of the scattered wave. Despite somepromising results, the abovementioned works in general have discussed the fundamental influence ofthe defect depth on the scattering of guided wave modes. There is still a lack of methods to extract thedepth of the defect without any initial knowledge about its through-thickness location when dispersionis involved.This paper proposes the SHM method to extract the absolute depth and size of asymmetricaldelamination-type defects in plate-like structures with parallel surfaces. The technique proposed inthis study extracts the depth of the damage by analyzing the amplitude variation patterns of directA0 mode at different excitation frequencies. These magnitude variations are caused by the differenceof wave velocities in the upper and lower sub-laminates due to their uneven thicknesses. This leadsto the varying phase differences of the wave-packets at the trailing edge of the defect and resultsin an altering forward scattered amplitude of the direct A0 mode. Hence, in comparison with thepredefined reference dependencies, the absolute values of the delamination depth can be extracted.Such magnitude variation is related to the excitation frequency as the phase velocity of A0 mode isfrequency and thickness dependent. As a result, different magnitude variation patterns at differentexcitation frequencies can be observed. Having such patterns at different frequencies allow to increasethe accuracy of damage depth estimation. This is very important in the presence of strong dispersion,as the rapid changes in velocity of guided wave modes can introduce large errors. Furthermore,the information on the damage depth can be exploited for the assessment of the defect length as theactual depth of the defect determines the phase velocities of A0 and S0 modes in the upper and lowersub-laminates. Then, the delamination size can be evaluated by measuring the ToF between the wavepackets of the converted and direct A0 modes. Hence, the approach proposed in this research canprovide information about the absolute depth and the length of the damage employing a few timetraces measured at a series of different excitation frequencies. The technique proposed in this study isessentially different from the currently existing ones as it uses multiple excitation frequencies, whichleads to different patterns of A0 mode magnitude variation and, subsequently, to better resolution.Most of the available research studies use constant a-priori wave velocities for damage size estimationwhich is not valid in the presence of dispersion. The technique proposed in this paper can be usedeven in the presence of the dispersion of A0 mode as it exploits the dependency of the phase velocityon the thickness of the layers above and below the defect.This paper focuses on the proof of the concept of the proposed delamination depth and lengthestimation method by analyzing a single delamination-type defect. However, in further studies, it isexpected to extend the presented method to extract features of multiple parallel delaminations whichare a common outcome of low velocity impact damage.2. Method for Assessment of Delamination Parameters2.1. Interaction of A0 Mode with Delamination-Type DefectLet us analyze a composite plate with length l and thickness h which is shown in Figure 1. It willbe investigated with the 2D approach, which means that the plate is infinite along the y axis. Let usconsider that the delamination-type defect is present in the structure, which is l1 long and situated atdistances of l0 and l2 from the source (excitation) and monitoring (reception) points, respectively, at adepth of h1 with respect to the top surface. The delamination is parallel to the surface of the sample(Figure 1).

such frequencies, the wavelengths of A0 mode varies from 17.2 mm (at 50 kHz), to 5.6 mm (at 200kHz) at 4mm GFRP plate (Ex 10 GPa, Ez 35.7 GPa; υxz 0.325, υzx 0.091, υyx 0.35; Gxz 2.8 GPa; ρ 1800 kg/m3). This shows that both A0, S0 and higher order A1 and S1 modes can exist at such a constantwavelength (see Figure 2a). However, using a Plexiglas wedge (2700 m/s) as a coupling medium andnormal incidence angles, the fundamental A0 mode is being generated most effectively (see FigureAppl. Sci. 2020, 10, 52364 of 192b), and sophisticated mode isolation techniques were not applied.Appl. Sci. 2020, 10, x FOR PEER REVIEW4 of 19[29,30], in‐phase and out‐of‐phase excitation [31], etc. In this research the fundamental dispersionzone has been selected and the excitation frequencies were limited from 50 kHz up to 200 kHz. Atsuch frequencies, the wavelengths of A0 mode varies from 17.2 mm (at 50 kHz), to 5.6 mm (at 200kHz) at 4mm GFRP plate (Ex 10 GPa, Ez 35.7 GPa; υxz 0.325, υzx 0.091, υyx 0.35; Gxz 2.8 GPa; ρ 1800 kg/m3). This shows that both A0, S0 and higher order A1 and S1 modes can exist at such a constantwavelength (see Figure 2a). However, using a Plexiglas wedge (2700 m/s) as a coupling medium andnormalincidenceangles,the fundamentalA0 modebeing generatedeffectively damage.(see FigureFigure1. Schematicdiagramof considered exampleof isa compositeplate withmostdelamination-typeFigure 1. Schematic diagram of considered example of a composite plate with delamination‐type2b), and sophisticated mode isolation techniques were not applied.damage.Thefundamental A0 mode has been selected in this paper. As multiple guided wave modes arebeing generated simultaneously, different strategies exist to excite isolated modes, such as angle beamexcitation [27], element width selection [28], inter-element spacing or interdigital transducers [29,30],in-phase and out-of-phase excitation [31], etc. In this research the fundamental dispersion zonehas been selected and the excitation frequencies were limited from 50 kHz up to 200 kHz. At suchfrequencies, the wavelengths of A0 mode varies from 17.2 mm (at 50 kHz), to 5.6 mm (at 200 kHz)at 4 mm GFRP plate (Ex 10 GPa, Ez 35.7 GPa; υxz 0.325, υzx 0.091, υyx 0.35; Gxz 2.8 GPa;ρ 1800 kg/m3 ). This shows that both A0 , S0 and higher order A1 and S1 modes can exist at sucha constantwavelength(see Figure2a). However,usingPlexiglasplatewedge(2700m/s) as a couplingFigure 1.Schematic diagramof consideredexampleof aacompositewithdelamination‐typemediumand normal incidence angles, the fundamental A0 mode is being generated most effectivelydamage.(see Figure 2b), and sophisticated mode isolation techniques were not applied.(a)(b)Figure 2. Phase velocity dispersion curves of 4 mm glass fibre reinforced plastic (GFRP) plate (a) andexcitation angle versus frequency using Plexiglas as coupling medium (b).The signal of A0 mode excited at the source point and measured at the monitoring point afterpropagation through the delaminated area will be the subject of all the upcoming investigations.Upon the interaction of A0 mode with the delamination‐type defect, the reflection, transmission andmode conversion occur at each end of the damage. In such a way, at the leading edge of the damage,the incident A0 mode reflects back, and in the forward direction it splits into wave packets whichaccordingly propagate(a)on the sub‐laminates above and below the defect. Moreover,mode conversion(b)occurs at the leading edge; therefore, part of the energy transforms into S0 mode as well (see Figure2.2.Phasedispersionofof4 FRP)(GFRP)plateplate(a)(a)andand3a). FigureSimilarly,at velocitythetrailingedgecurvesof thedamage,A0 and S0 modes are reflecting plingcouplingmediummedium(b).(b).propagating forward and converting to each other (see Figure 3b). This representation does not takeinto accounttheofscatteringof erTheof AA0 vestigations.propagation through the delaminated area will be the subject of all the upcoming fAA0 age.damage.InInsuchsucha edamage,damage,modetheincidentincidentAA0 ccurs at the leadingtherefore, part of the energy transforms into0S0 mode as well (seeFigureSimilarly,at theattrailingedge ofthe damage,both A0 andarereflectingpropagating3a).Similarly,the trailingedgeof the damage,bothS0Amodes0 and S0 modesareback,reflectingback,forward andforwardconvertingeach otherto(seeFigurerepresentationdoes not her3b).(see ThisFigure3b). This achreflected/convertedmode.into account the scattering coefficients of each reflected/converted mode.

Appl.2020,x FOR PEER REVIEWAppl.Sci.Sci.2020,10, 10,5236(a)of 195 of519(b)Figure3. Graphicrepresentationof0 A0 modeinteractionwithdelamination‐typedefectat theleadingFigure3. Graphicrepresentationof Amodeinteractionwithdelamination-typedefectat theleadingtrailingedge(a) (a)andandtrailingedge(b).(b).In thisresearch,onlyonlythe forwardscatteredwave-packetsof A0ofmodewill beconsidered;they areIn thisresearch,the forwardscatteredwave‐packetsA0 modewillbe considered;theysquaredred in FigureMathematically,the spectrumof the signalof Asignal(f ) whichare squaredred in 3b.Figure3b. Mathematically,the spectrumof theofUAIA00 modeUIA0arrives(f) which0 modefirstto thefirstmonitoring(reception)(reception)point can beexpressedarrivesto the monitoringpointcan be as:expressed as: 𝐻 f𝑓,𝑘T01A· H 𝐻f ,𝑓,c 𝑐 , l, 𝑙 · k 𝑘T10SsA ( f𝑓) · H(IAf ) 𝑓 U𝑈sAUIA𝑈, c𝑐p0 A0 , ,l0𝑙 · k T01A· H 𝐻f , 𝑓,cp0𝑐A0 , l2, 𝑙1pST10S0001 𝑓, 𝑐𝑈𝑓 𝐻, 𝑙 𝑘T02A 𝐻 𝑓, 𝑐, 𝑙 𝑘 𝐻 𝑓, 𝑐 , 𝑙( f ) · H f , cp0 A0 , l0 · kT02A UsAsA· H f , cp2 S0 , l1 · kT20ST20S· H f , cp0 A0 , l20 𝑘T01A 𝐻 𝑓, 𝑐, 𝑙 𝑘T10S 𝑈 , 𝐿 𝑙 kT01A · H f , cp1 S0 , l1 · kT10S ,sA 𝑓 𝐻 𝑓, 𝑐 UsA0 ( f ) · H f , cp0 A0 , L l1 · , 𝑙 𝑘T20S ,𝑘T02A 𝐻 𝑓, 𝑐 kT02A· H f , cp2 S0 , l1 · kT20S(1) (1) jl f 𝐻 𝑓, 𝑐 , 𝑙(2)𝑒𝑒p ,H f , cp , l p e α( f )x e cp ( f ) ,(2)where UsA (f) is the frequency spectrum of the excitation signal of A0 mode; H(f,cp,l) is the transferwhere UsA0 (f 0) is the frequency spectrum of the excitation signal of A0 mode; H(f,cp ,l) is the transferfunctionof thewavespropagatingin thecorrespondinglayer;cpA(f0),(f),c cpS0(f(f)) areare thethe phasephase velocitiesvelocities offunction of thewavespropagatingin thecorrespondinglayer;cpA0pS0A0 andS0 modes, respectively; l is the propagation distance (l0, l2–propagation distances in the defect‐of A0 and S0 modes, respectively; l is the propagation distance (l0 , l2 –propagation distances in thefreeareabeforeand afterthe defect,respectively,l1–lengthof theofdefect);L is thebetweendefect-free areabeforeand afterthe defect,respectively,l1 –lengththe defect);L separationis the separationthe sourceand themonitoringpoints points(L l0 (Ll1 ll2); andtheα(ffrequencydependentattenuationbetweenthe sourceandthe monitoringl1 α(f)l2 ); isand) is the frequencydependent0function;kT01A, kT02A, kT10S and kT20S are the transmission coefficients for A0 and S0 modes at the leadingattenuation function; kT01A , kT02A , kT10S and kT20S are the transmission coefficients for A0 and S0 modesandleadingtrailingandedgesof thedelamination,respectively,for the layerandabovebelowthebelowdefect.at thetrailingedgesof the delamination,respectively,for abovethe layerandtheTheestimationof such reflectionand transmissioncoefficientswas outtheofscopeof thisstudy.Theydefect.The estimationof such reflectionand transmissioncoefficientswasofoutthe scopeof delaminationdepth,thematerialpropertiesThey essentially depend on the guided wave mode, the delamination depth, the material escribedbyEquation(1)isA0 mode, which is a superposition of the signalsThe wave packet described by Equation (1) is A0 mode, which is a superposition of the signalstravelingat sfrom0 mode to S0 mode attravelingat rtsfromA0 Amodeto S0 mode attheleadingedgeandbacktoA0 at the trailing edge of the defect. Due to this reason, this wave packetthe leading edge and back to A0 at the trailing edge of the defect. Due to this reason, this wave f Amode0 mode which does not convert withinUIA0(f 0)(f)arrivesearliercomparedto tothethedirecttransmissionof Awhich does not convert within0defectedarea.Thishappensdueto thereasonthatS0 modepossessesa dueto thereasonthatS0 modepossessesa greatergroupvelocityat chawave‐packetshallbereferredtolow frequencies compared to A0 mode. In this research, such a wave-packet shall be referred to as as“first0 arrival”. Consequently, the frequency spectrum of the direct transmission of A0 mode can be“firstA0 Aarrival”.Consequently, the frequency spectrum of the direct transmission of A0 mode can bewrittenas:written as: 𝑓, 𝑐𝑈𝑈𝑓𝑓 𝐻 𝑓, 𝑐, 𝑙 𝑘T01A 𝐻, 𝑙 𝑘T10A 𝐻 𝑓, 𝑐, 𝑙( f ) UsAsA0 ( f ) · H f , cp0 A0 , l0 · kT01AUIIA0 IIA· H f , cp1 A0 , l1 · kT10A· H f , cp0 A0 , l2𝑈sA 𝑓 𝐻 𝑓, 𝑐 , 𝑙 𝑘T02A 𝐻 𝑓, 𝑐 , 𝑙 𝑘T20A 𝐻 𝑓, 𝑐 , 𝑙 UsA0 ( f ) · H f , cp0 A0 , l0 · kT02A · H f , cp2 A0 , l1 · kT20A · H f , cp0 A0 , l2(3)𝑘T01A 𝐻 𝑓, 𝑐 , 𝑙 𝑘T10A (3) 𝑈sA 𝑓 𝐻 𝑓, 𝑐, 𝐿 𝑙 kT01A .· H f , cp1 A0 , l1 · kT10A .𝑓, 𝑐 , 𝑙 𝑘T20A𝑘T02A 𝐻 UsA0 ( f ) · H f , cp0 A0 , L l1 · kT02A · H f , cp2 A0 , l1 · kT20AThe “direct A0 transmission” described by Equation (3) is the wave‐packet which does notconvert to other modes at the leading and trailing edges of delamination.

Appl. Sci. 2020, 10, 52366 of 19The2020,“direct0 transmission”Appl. Sci.10, x AFORPEER REVIEW described by Equation (3) is the wave-packet which does not convert6 of 19to other modes at the leading and trailing edges of delamination.The scatteringscattering ofofthetheincidentincidentAAat thedelamination-typedefectis furtherillustrated0 modeat thedelamination‐typedefectis furtherillustratedwith0 modewithB-scansin Figure4 whichsimulatedby usingthe FiniteElementplane-strainmodelon aB‐scansin Figure4 whichwereweresimulatedby usingthe FiniteElementplane‐strainmodelon a 20002000mm ination-typedefectlocatedmm 4 mm 2D GFRP plate. These B‐scans represent a centered delamination‐type defect located at aata depth1.5 withmm respectwith respecttop surfaceof the sample.waswithexcitedwith adepthof 1.5ofmmto the totopthesurfaceof the sample.A0 modeAwasexciteda Gaussian0 modeGaussianburstcyclesof threeandfrequencya central frequency80 kHz.Thesignalsareenvelope envelopetone bursttoneof threeandcyclesa centralof 80 kHz.ofThesignalswhicharewhichanalyzedanalyzedin thisare asdenoteduIIA0 (t)A(“directA0 transmission”)uIA0A(t)0 arrival”)(“first A0inarrival”)in this paperarepaperdenoteduIIA0(t)as(“direct0 transmission”)and uIA0(t)and(“firstFigurein4. Figure 4.(a)(b)A00 mode interaction with delamination: B‐scanFigure 4. Illustration of AB-scan images of vertical uxx (a) ceof thickness4 mm thicknessGFRPlongitudinalulongitudinal uz (b) component of particle velocity along the top surfaceof 4 mmGFRP sample.sample.2.2. Method to Estimate the Depth of Defect2.2. Methodto EstimatetheEquationDepth of DefectAs it wasshown by(3), the “direct A0 transmission” is a superposition of the which does not convert to other modes,As it was shown by Equation (3),theabove“direct0 transmission” is a superposition of the defect.If thedelaminationtraveling at the sub‐laminates below and above the damage whichdoesnot convertistoasymmetricalother ),thephasevelocitiesatsub-laminatesare12neither at the leading, nor at the trailing edge of the defect. If the delamination is asymmetrical requencyandthicknessofeachsub-laminate.p1 of p2the thicknessthe laminate (h1 h2 in Figure 1), the phase velocities at sub‐laminates are differentBeyonddefect,modesonfromupper andlower sub-laminateseach other,Beyondwhich(cp1 cp2the), andtheythedependthe theexcitationfrequencyand thicknessinterfereof each o0IIA0the defect, the modes from the upper and lower sub‐laminates interfere with each other, which ase,outofphaseorintermediate.Ifthetransducerisin the single forward scattered A0 mode uIIA0(t). The magnitude of this mode is proportional to thedrivenbyinterferencea set of differenta collectionof magnitudepatternscantransducerbe obtainedresult ofwhichfrequencies,can be eitherin phase, outof phase orvariationintermediate.If pleexcitationfrequenciesenablesone todriven by a set of different frequencies, a collection of magnitude variation patterns can be obtainedexploittheforfrequencyphase velocityespecially frequenciesin the case ofthe presence0 mode, excitationand useddamage dependentdepth extraction.The useofofAmultipleenablesone timatethedepthofdamageon theexploit the frequency dependent phase velocity of A0 mode, especially in the case of ntral0IIA0dispersion. Thus, the idea of the proposedmethod to estimatethe depth of damage relies on thefrequencies(f 1 , f 2 , . . . f n ). ofWeshouldthat this techniqueonlysignalsvalid ifwiththe differentdelaminationismagnitude measurements“directA0notetransmission”uIIA0(t) at isburstcentralasymmetrical h1 , h/2 , h2 and cp1 , cp2 . For ideally symmetrical delamination, there will be nofrequencies (f1, f2, fn). We should note that this technique is only valid if the delamination isout-of-phase interference of A0 mode as the velocities at the layer above and below the defect will beasymmetrical h1 h/2 h2 and cp1 cp2. For ideally symmetrical delamination, there will be no out‐of‐very close.phase interference of A0 mode as the velocities at the layer above and below the defect will be veryTo extract the absolute values of the defect depth, a database of reference dependencies is requiredclose.which would represent the collection of magnitude variation patterns at different excitation frequencies,To extract the absolute values of the defect depth, a database of reference dependencies isthe depth and the length of delaminations. Then, the estimated reference dependency can be comparedrequired which would represent the collection of magnitude variation patterns at different excitationto the experimental measurement in order to extract the depth of delamination. It is presumed that thefrequencies, the depth and the length of delaminations. Then, the estimated reference dependencycan be compared to the experimental measurement in order to extract the depth of delamination. Itis presumed that the reference dependency which best matches the experiments is the one that givesthe closest definition of the damage depth in the structure. The step‐by‐step procedure of the damagedepth estimation can be outlined as follows:

Appl. Sci. 2020, 10, 52367 of 19reference dependency which best matches the experiments is the one that gives the closest definition ofthe damage depth in the structure. The step-by-step procedure of the damage depth estimation can beoutlined as follows:1.2.3.4.5.The source of guided waves E is driven by burst with Gaussian envelope of central frequency f 1to introduce A0 mode in the investigated structure.Time trace uA0 (t) is received with sensor Rref , which represents the structure without the damage(the reference signal). Meanwh

Delamination is one of the most common defects found in fiber-reinforced composite laminates due to their weak transverse tensile and inter-laminar shear strengths [1]. . scattering and energy leakage of guided waves for the detection and sizing of delamination-type defects [3-7]. By interaction of guided waves with delamination, waves are .