DELAMINATION DETECTION OF COMPOSITE … DETECTION OF COMPOSITE LAMINATES USING NATURAL FREQUENCY ... simply supported rectangular orthotropic ... Modal analysis is conducted on non

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Int. J. Mech. Eng. & Rob. Res. 2012 R Sultan et al., 2012

DELAMINATION DETECTION OF COMPOSITELAMINATES USING NATURAL FREQUENCY

VIBRATION METHOD

R Sultan1*, S Guirguis2, M Younes2 and E El-Soaly3

*Corresponding Author: R Sultan,[email protected]

Composite materials are widely used in aeronautical, marine and automotive industries,because of their excellent mechanical properties, low density and ease of manufacture.However, composite laminates are susceptible to delaminations, which may not be visibleexternally, but can substantially affect the performance of the structure. Vibration test, inparticular delamination detection, in the composite structures is an active research area.D’Alembert principle is used to determine the theoretical natural frequency of laminatedorthotropic composite plate. The present free vibration experimental study of simply supportedsquare laminated plates is based on the comparison between natural frequencies of healthyand delaminated composite plates. The test square plates made of hand lay up 8 layers E-glass woven fibre and epoxy resin are used. The present paper discusses the observationsmade on the measured natural frequencies of vibration testing from both the healthy and thedelaminated square simply supported plates. The possibility of the delamination detection byvibration test is also introduced. The effects of delamination area on the natural frequencies ofthe plate are presented. The delamination in composite laminates has considerable effect onthe natural frequencies of the plate.

Keywords: Laminated composite material, Free vibration, Delamination

INTRODUCTIONThe applications of composite materials havebecome common in different industries. Thesematerials have higher stiffness and strength

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Int. J. Mech. Eng. & Rob. Res. 2012

1 Libyan Air Force, Libya.2 Egyptian Armed Forces, Egypt.3 10th of Ramadan Higher Institute of Technology, Egypt.

to weight ratio (Shokrieh and Najafi, 2006).Although composite materials offer manyadvantages in the designing andmanufacturing of structures .The application of

Research Paper

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woven fabric composites in engineeringstructures has been significantly increased dueto attractive characteristics, such as flexibleprocessing options, low fabrication cost, whilealso possessing adequate mechanicalproperties (Hu and Wang, 2009).

The laminated composite plates are basicstructural components used in a variety ofengineering structures. Composite platestructures often operate in complexenvironmental conditions and are frequentlyexposed to a variety of dynamic excitations.Measurement of the natural frequency byvibration testing is a very attractive method ofNon-Destructive Test (NDT). The vibration testwould not require access to the whole surfaceand the time taken to perform the test can bevery small. Thus the vibration response of acomposite plate can be used as an indicatorof damage (Houa and Jeronimidis, 1999).

The presence of delamination may degradeseverely the stiffness and strength ofcomposites and in some cases leads tocatastrophic failure. The presence ofdelamination occurs in composite laminates(Pagano and Pipes, 1973). Delamination mayarise during manufacturing (e.g., incompletewetting, air entrapment) or during service (e.g.,low velocity impact, bird strikes). Delaminationmay not be visible or barely visible on thesurface, since it is embedded within thecomposite structures. The delaminationdetection methods based on modal analysisis that delamination reduces the dynamicstiffness of a structure, causing reduction ofthe natural frequencies which can detected byvibration testing. Zak et al. (1999) and Diazand Soutis (1999) investigated the effect ofdelamination on the natural frequencies of

laminated composite beams. Zhang et al.(2010) developed a vibration monitoringmethod for detecting the delamination incomposite structures based on change innatural frequencies before and after damage.Shiau and Zeng (2010) presented the effectsof delamination length, delamination locationin the thickness wise, span wise directions,and aspect ratio of the plate on the naturalfrequencies.

Delamination can be captured by measurednatural frequencies of the non-defectedmaterial (healthy material) and the defectedmaterial (delaminated material) is highlighteddepending on the natural frequency reduction.Ullah and Sinha (2011) introduced dynamicsbehaviour of the composite plates with andwithout delamination based on theexperimental study at which the test platemade of E-glass fibre and epoxy resins. Thedynamics of the delaminated composite plateswere then compared with a healthy compositeplate when the vibration experiments havebeen conducted.

In the present study, D’Alembert principle(Victor, 2012) is used to determine thetheoretical natural frequency of laminatedorthotropic composite plate. A free vibrationtesting is performed on square simplysupported composite plates where thedelaminations are reproduced inserting a thinsilver foil coated with chemical wax tosimulate the delamination between twolayers. Experimental measured naturalfrequencies are compared for both the healthyand the delaminated simply supported handlay-up square E glass woven fiber compositeplates.

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DETERMINATION OFNATURAL FREQUENCYUSING D'ALEMBERTPRINCIPLED'Alembert principle was used to determinethe natural frequencies of orthotropic laminatedcomposites in another research (Almasryet al., 2011). In the present study, the lateralload is replaced by D'Alembert load

2

2

t

w based on static analysis. Where

is the mass of unit area, is the w lateraldeflection, and t is the time variable.

The basic differential equation has beenobtained in the form:

12121212

11221122

11111111 42 wDwDwD

02

22222

2222

t

wwD ...(1)

The solution of Equation (1) for a four sidedsimply supported rectangular orthotropiclaminate plate, shown in Figure 1, can bewritten as presented in Equation (2).

121222

112222

11114 42 DNMDNMDM

022222

4 DN ...(2)

where

is angular frequency of free vibration

b

nN

a

mM

,

m and n = 1, 2, 3, …

D1111

, D2222

, D1122

, D1212

, are the flexuralrigidities of the orthotropic laminate, which canbe expressed, in terms of material propertiesE

11, E

22, v

12, v

21 and G

12 with the laminate

thickness (h).

2112

113

1111 112 vv

EhD

2112

223

2222 112 vv

EhD

2112

22123

1122 112 vv

EvhD

12

3

1212 12G

hD ...(3)

when,

Figure 1: Simply Supported Orthotropic Plate

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m = 1 and n = 1 leads to the first mode ofvibration,

m = 2 and n = 1 leads to the second modeof vibration,

m = 1 and n = 2 leads to the third mode ofvibration, and

m = 2 and n = 2 leads to the fourth mode ofvibration.

PREPARATION OF THE TESTSPECIMENSThe composite plate specimens used in thisexperiment are made from woven eight plies(0/90) with (= 3.75 kg/m2) composite of Eglass fiber and epoxy matrix with hardener(Epolam, 2017). After the curing process atroom temperature, four test specimens of size(200 200 2.5 )mm3 are cut from a plate of

Figure 2: Test Specimens

(c) Delamination (100 100 mm2) (d) Delamination (150 150 mm2)

200 mm 200 mm

(a) Healthy Plate (No Delamination) (b) Delamination (50 50 mm2)

200 mm 200 mm

20

0 m

m

20

0 m

m

20

0 m

m

20

0 m

m

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8 plies laminate by using cutting machine, withdifferent area of mid plane artif icialdelaminations (50 50, 100 100, 150 150)mm2. All the test specimens are finishedby abrading the edges on a fine sand paperas shown in Figure 2.

TENSILE TESTNine specimens are prepared for tensile testusing material test system machine as relevantto ASTM standard code (D 3039). Themechanical properties of 8-layered wovenfiber glass/epoxy are determined using 3 mmelectrical strain gages. Unidirectional tensiletests are performed on specimens cut inlongitudinal and transverse directions to obtainE

11, E

22 and v

12. A specimens cut at angle 45°

to the longitudinal direction to find the shearmodulus.The measured experimental valuesof the elastic moduli (E

11, E

22, v

12, G

12) are

shown below:

E11

= E22

= 19 GPa

v12

= v21

= 0.256

G12

= 2.8 GPa ...(4)

Considering the above measuredmechanical properties, the flexural rigidities (3)are obtained as:

D1111

= D2222

= 25.14 Nm

D1122

= 2.51 Nm

D1212

= 3.64 Nm ...(5)

The introducing of the flexural rigidities (5)into Equation (2), leads to the values of thetheoretical natural frequencies presented inTable 2.

VIBRATION TESTVibration tests are conducted on 8-layers(0/90) woven E glass fiber/epoxy composite

plates, with and without artif icialdelaminations to detect the effect ofdelamination area on plate naturalfrequencies. Sixteen specimens wereprepared; four square plates of dimension(200 200 2.5)mm3 without delamination(healthy plate), and twelve square plates ofthe same dimension with different area ofdelamination (50 50, 100 100, 150 150)mm2. The natural frequencies aremeasured for all specimens with four edgessimply supported boundary condition. Locallymanufactured, two square frames with sideelement diameter of 5 mm, Figure 3, are usedto simulate four edges simply supportingconditions. An impact hammer was used tohit the plate five times at the marked pointand the data averaged for each test. Tenrepeated tests were conducted for each plate.The force was measured using a forcetransducer with charge amplifier (B&K type2626).This output is captured by oneaccelerometer which mounted at differentplaces to measure dynamic response and isamplified using a conditioning amplifier (B&Ktype 2626) and then read using the highresolution signal analyzer (B&K type 3562A),giving the Frequency Response Function(FRF) as shown in Figure 4.

RESULTS ANDDISCUSSIONSModal analysis is conducted on nondestructive testing (vibration test) to extractnatural frequencies for the healthy plates andthe delaminated plates. Generally, a plate withdelamination will experience reduction innatural frequencies due to the loss of stiffness.The extent of the stiffness loss depends ondelamination characteristics.

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In the present experimental work, we havestudied the effect of increasing delaminationarea on natural frequencies of squarelaminated cross-ply (0/90) woven E glass

plates, which are simply supported around itsfour edges. The experimental measured firstfour modes of vibration for differentdelamination area are given in Table 1.

Figure 4: Vibration Test System

Figure 3: Simply Supported Fixture Apparatus of Square Laminate Specimen

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The experimental measured values ofnatural frequency for healthy plate arecompared with those obtained theoretically,using Alembert principle in Table 2.

First 172.2 Hz 170.3 Hz 169.2 Hz 159.4 Hz

Second 459.5 Hz 420.8 Hz 314.5 Hz 258.2 Hz

Third 466.3 Hz 432.5 Hz 337.4 Hz 271.2 Hz

Fourth 686.4 Hz 637.3 Hz 549.2 Hz 293.3 Hz

Table 1: Experimental Measured Natural Frequencies (Hz) of Square Laminate Plateswith Different Central Mid Plane Delamination Area

Mid Plane Delaminated AreaHealthy PlateMode

(50 50 mm2) (100 100 mm2) (150 150 mm2)

Mode Theoretical Experimental Percentage Error

First 169.44 Hz 172.2 Hz 1.60%

Second 455.86 Hz 459.5 Hz 0.79%

Third 455.86 Hz 466.3 Hz 2.30%

Fourth 677.79 Hz 686.4 Hz 1.25%

Table 2: Comparison Between Theoretical and Experimental Natural Frequency Resultsin Hz for Healthy Plate

Through the next Figure 5, we can clearlyobserve that, the delamination results in thedecrease in natural frequency, morepredominantly for higher modes.

Figue 5: Variation of Natural Frequencies with Normalized Delamination Area for theFirst Four Modes of Vibration

Normalized Delamination Area

0 0.1 0.2 0.3 0.4 0.5 0.6

Nat

ura

l Fre

qu

ency

(Hz)

200

190

180

170

160

150

140

(a) First Mode

293


Figue 5 (Cont.)


0 0.1 0.2 0.3 0.4 0.5 0.6

Nat

ura

l Fre

qu

ency

(Hz)

500

450

400

350

300

250

200

(b) Second Mode


0 0.1 0.2 0.3 0.4 0.5 0.6

Nat

ura

l Fre

qu

ency

(Hz)

500

450

400

350

300

250

200

(c) Third Mode


0 0.1 0.2 0.3 0.4 0.5 0.6

Nat

ura

l Fre

qu

ency

(Hz)

500

450

400

350

300

250

200

(d) Fourth Mode

294


Figue 5 (Cont.)

Normalized Delamination Area0 0.1 0.2 0.3 0.4 0.5 0.6

Nat

ura

l Fre

qu

ency

(Hz)

800

700

600

500

300

200

100

(e) First Four Modes

400

First Natural FrequencySecond Natural FrequencyThird Natural FrequencyFourth Natural Frequency

It can be seen that, as expected, for allmodes the larger delamination area, the moresignificant decrease in natural frequency, also

It can be deduced that different modes havedifferent sensitivities to the delamination areasas shown in Table 3 and Figure 6.

First 1.10 1.74 7.43

Second 8.42 31.55 43.80

Third 7.24 27.64 41.84

Fourth 7.15 19.98 57.26

Table 3: Percentage Reduction of Natural Frequencies Reduction (%) Due to DifferentDelamination Area in First Four Modes of Simply Supported Square Laminated Plate

Mid Plane Delaminated Area

(50 50 mm2) (100 100 mm2) (150 150 mm2)Mode

Figure 6: Percentage Reduction of First Four Natural Frequencies with RelativeDelaminated Area (50 50 mm2)

Relative Delaminated Area

1 3 5 7 9

Pe

rce

nta

ge

Re

du

cti

on

of

Na

tura

l Fre

qu

enc

y (%

)

200

190

180

170

160

150

140

180

First ModeSecond ModeThird ModeFourth Mode

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For instance, the natural frequency of firstmode has small reduction for delaminationarea (100 100)mm2 (1.74%) whereas thereduction of the higher mode is significant(19.98%) relative to healthy plate.

The delamination-induced changes of thefirst natural frequencies are small, whichindicate that, the delamination-inducedfrequency change is insignificant for first modeespecially for small delamination area.Therefore, it is indispensable to analyze thedelamination effects based on higher modesrather than first mode. Hence, it is notreasonable to detect the delamination byvibration test depending, only on first mode ofnatural frequency.

CONCLUSIONFree vibration testing of square compositeplates with different areas of artificialdelamination is studied. The influence of thedelamination area on the measured first fournatural frequency modes is investigated. Basedon obtained theoretical and experimentalresults, the following conclusions can be drawn:

• A good correlation between theoretical andexperimental analysis is observed (errorless than 2.3%).

• Delamination in a laminated plate reducesits natural frequencies and reductionincrease when delamination area increase.

• The effect of the delamination area on firstmode is very small.

• The higher natural frequency modes aresignificantly influenced by the delaminationarea.

• The influence of delamination on naturalfrequency varies with vibration modes, and

this phenomenon may be useful todetermine the area of delamination.However, this is basically impracticable,because, the experimental equipment canhardly extract modes higher than five forcomposite plates.

REFRENCES1. Almasry Z, Younes M and El-Soaly E

(2011), “Determination of NaturalFrequency of Anisotropic Plates Using D'Alembert Priciple”, ASAT 14, ST243, May.

2. Diaz S H and Soutis C (1999),“Delamination Detection in CompositeLaminates from Vibration of their ModalCharacteristics”, Journal of Sound andVibration, Vol. 228, No. 1, pp. 1-9.

3. Houa J P and Jeronimidis G(1999), “Vibration of Delaminated ThinComposite Plates”, Composite Part A:Applied Science and Manufacturing,pp. 989-995.

4. Hu Hand and Wang J (2009), “DamageDetection of a Woven Fabric CompositeLaminate Using a Modal Strain EnergyMethod”, Engineering Structures, Vol. 3,pp. 1042-1055.

5. Pagano N J and Pipes R B (1973), “SomeObservations on Interlaminar Strength ofComposite Laminates”, InternationalJournal of Mechanical Sciences, Vol. 15,No. 8, pp. 679-688.

6. Shiau L-C and Zeng Y (2010), “FreeVibration of Rectangular Plate withDelamination”, Journal of Mechanics,Vol. 26, No. 1, March.

7. Shokrieh M and Najaf i A (2006),“Experimental Evaluation of Dynamic

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Behaviour of Metal l ic PlatesReinforced by Polymer Matr ixComposites”, Composite Structures,Vol. 75, pp. 472-478.

8. Ullah I and Sinha J K (2011),“Experimental Vibration Study on theHealthy and Delaminated CompositePlates”, Journal of Physics: ConferenceSeries, Vol. 305.

9. Victor B (2012), “Solid Mechanics and It’sApplications:Plates Structures”, Vol. 178,p. 149.

10. Zak A,Krawczuk M and Ostachowicz W(1999), “Numerical and ExperimentalInvestigation of Free Vibration ofMultilayer Delaminated CompositeBeams and Plates”, ComputionalMechanics, Vol. 26, No. 3, pp. 309-315.

11. Zhang Z, Shankar K, Tahtali M andMorozov E V (2010), “Vibrat ionModelling of Composite Laminates withDelamination Damage”, Proceedings of20th International Congress onAcoustics, ICA.

Nomenclature

APPENDIX

a, b, h Plate length, width, and thickness

D Flexural rigidities

E Young’s modules

FRF Frequency response function

G Shear modules

M, Nb

n

a

m ,

NDT Non-destructive test

t Time variable

w Plate lateral deflection

, , , = 1, 2 Two dimensional tensorial indices

v Poisson’s ratio

Mass of unit area

Angular frequency of free vibration

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DELAMINATION DETECTION OF COMPOSITE … DETECTION OF COMPOSITE LAMINATES USING NATURAL FREQUENCY ... simply supported rectangular orthotropic ... Modal analysis is conducted on non