ExperimentalStudyonHigh-CycleFatigueBehaviorof GFRP

Research ArticleExperimental Study on High-Cycle Fatigue Behavior ofGFRP-Steel Sleeve Composite Cross Arms

Jiantao Wang 1 Ning Tan2 Shiming Zhou1 and Qing Sun 1

1Department of Civil Engineering Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China2School of Aerospace Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China

Correspondence should be addressed to Qing Sun sunqmailxjtueducn

Received 19 March 2018 Revised 5 July 2018 Accepted 16 July 2018 Published 1 August 2018

Academic Editor Flavio Stochino

Copyright copy 2018 JiantaoWang et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To overcome the fatigue safety problem of transmission tower cross arms caused by the wind-induced vibrations an experimentalstudy on the high-cycle fatigue performance of a new type of GFRP-steel sleeve composite cross arms was carried out A total of sixspecimens were subjected to 500 thousand cyclic loadings based on the practical engineering background -e stress state wasmonitored and a variety of load-displacement-time curves the energy dissipation capacity and the dynamic strain were analyzedto examine the effects of fatigue loading After the fatigue test the specimens without significant fatigue failure were evaluated toderive the residual bearing capacity Based on the residual strength theory the cumulative damage was examined and the fatiguelife was predicted under various loading conditions to ensure the reliability of composite cross arms It is shown that the new typefull-scale GFRP-steel sleeve composite cross arms can demonstrate a high level of safety redundancy on antifatigue performanceand can be expected for wide application in power transmission towers

1 Introduction

Glass-fiber-reinforced polymers (GFRPs) have been applied inmanufacturing power transmission engineering widely asa replacement of conventional materials (wood concrete andsteel) because of its unique advantages of high strength-to-weight ratio resistance to corrosion lower transportation andinstallation and maintenance costs [1 2] Adopting GFRPcross arm in transmission tower can improve the reliability ofpower supply through reducing the negative effects of partialdischarge and contamination flashover while it can obtain thesignificant economic benefits by reducing the width of thetransmission line corridor and maintenance costs Howeverthe fatigue load of GFRP cross arms caused by wind-inducedvibrations is a safety problem that cannot be neglected in thedesign period [3 4] Actually fatigue failure is one of the mostimportant failure types of GFRPs during their service Due tothe inhomogeneity and anisotropy the fatigue failuremechanisms of fiber-reinforced composites are vastly differ-ent from their counterparts in homogeneous and isotropicmaterials likemetals [5] Furthermore structural components

are usually subjected to complex fatigue loadings which isone of the main forms of failure in mechanic and structuralcatastrophes -e GFRP cross arms are exposed to complexstress conditions (like wind oscillation) Once the fatiguefailure occurs it can result in major direct and indirectconsequences on the economy and national security-erefore it is of great importance to examine the fatiguebehavior of GFRP cross arms to ensure the safety oftransmission towers

During the past decades many scholars have studied thefatigue problem of composite materials to the differentextent such as fatigue mechanics behavior residualstrength and fatigue life prediction [5ndash26] For instanceHashin and Rotem [5 8] developed a fatigue failure theorybased on the HashinndashRotem static failure criterion whichhas been applied to predict the fatigue failure of angle-plylaminates Yang et al [9] and Shokrieh and Taheri-Behrooz[12] proposedmethods of fatigue life prediction based on themodulus reduction and energy dissipation respectivelyAbo-Elkhier et al [17] investigated the fatigue life of GFRPcomposites using modal testing which indicates that the

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 6346080 12 pageshttpsdoiorg10115520186346080

changes of modal parameters provide a proper method forpredicting the fatigue behavior of composite structuresZhang et al [22] proposed a macrophenomenological fa-tigue model for the off-axis fatigue behavior of GFRPcomposite laminates However the aforementioned re-searches about the fatigue properties of composite mate-rials mainly concentrate on the material level and reducedscale members especially for the cumulative damage as-sessment and fatigue life prediction So far studies onhigh-cycle fatigue behavior of GFRP based on full-scalecomponents are found lacking -erefore it is necessary tocarry out experimental researches on high-cycle fatigueperformance about the full-scale GFRP componentsconsidering the influence of size effect on composite ma-terial defects

In this paper an experimental study on high-cycle fa-tigue properties of a new type of full-scale GFRP-steel sleevecomposite cross arms was conducted A total of six speci-mens were subjected to 500 thousand cyclic loadings -estress state load-displacement-time curve energy dissipa-tion capacity and dynamic strain were analyzed in detail-e ultimate bearing capacity of the specimens was evalu-ated to derive residual bearing capacity Based on themodified residual strength theory the cumulative damagewas assessed to predict the fatigue life of GFRP-steel sleevecomposite cross arms

2 Experiment Condition

21 Specimen Details In this study a total of six standardspecimens were designed and produced by Jiangsu ShemarElectric Co Ltd All the GFRP pipes with steel sleeves (steelgrade Q345) spliced on both ends were manufacturedthrough the filament winding process A total of thirty fiberlayers divided into ten fixed skeleton layers and twentyvariable angle layers were winded in a constant thickness of066mm per layer where the inside-out layout was 90deg2 (S)-60deg2 (S)-30deg8 (V)-90deg2 (S)-30deg8 (V)-90deg2 (S)-30deg4 (V)-60deg2 (S) In the notation adopted to identify the fiber layersaforesaid the first number denoted winding angles betweenthe fiber orientation and axis the second number denotedthe sums of winding fiber layers the letters ldquoSrdquo and ldquoVrdquodenoted the fixed skeleton layer and variable angle layerrespectively -e specimen size and arrangement of mea-suring points are shown in Figure 1 in which the compositecross arm was 2532mm long and the length of steel sleevewas 466mm -e outer diameter and wall thickness of thecomposite pipe were 461mm and 20mm respectivelySixteen stiffening ribs were welded along the perimeter of thesteel sleeve for which the wall thickness and outer diameterwere 16mm and 600mm respectively In order to monitorthe deformation of the specimen during the fatigue test thelocations of the strain gauges in this fatigue test were mainlymounted on the loading ends which were sensitive to fatigueloads Four strain gauges in the first row including twobiaxial strain gauges and two unidirectional strain gaugeswere arranged in an interval of 90deg along the circumferentialdirection Two biaxial strain gauges were mounted by thesymmetrical layout in the other rows

22 Loading Scheme In this paper based on the XimengndashShengli section ultrahigh voltage (UHV) transmissionproject in China the finite element method was firstemployed to carry out the dynamic time-history analysis fordetermining fatigue peak loads of the experiment -e ac-curacy and validity of this finite element method wereverified by Northwest Electric Power Design Institute CoLtd of China Power Engineering Consulting Group -einternal forces of the transmission tower cross arms at thebasic wind speed of 10ms and strong wind speed of 30mswere extracted as the basic and ultimate reference loadingconditions respectively -e practical UHV transmissiontowers located in Xilin Gol League of China were subjectedto the adverse wind-induced vibrations -erefore throughthe statistic of the local climate condition the 500000 timeshigh-cycle fatigue loading was determined to simulate theactual stress state in life cycle at different safety marginsbased on the design requirement namely for the GFRPcomposite cross arms of the UHV transmission towersfatigue failure cannot occur at the basic frequent design windspeed (10ms) and extremely infrequent ultimate windspeed (30ms) respectively Further if there was no evidentfatigue failure occurred during the aforesaid conditions themore adverse loading protocols about the equal amplitudesof tension-compression were determined to examine thedifferent safety margins based on the ultimate referenceloading conditions (30ms) for further reliability -e fa-tigue test was carried out by the MTS24431 hydraulic servoactuation system-e loading scheme based on the dynamicanalysis result is shown in Table 1

As is shown in Table 1 the fatigue cycle load was appliedat 1Hz frequency using the displacement control After thetest ultimate bearing capacity of the specimens withoutsignificant fatigue failure was evaluated to derive residualbearing capacity using the TianshuindashHongshan 20000 kNcomputer-controlled electrohydraulic servo pressure andshear testing machine -e loading device of the high-cyclefatigue test and ultimate bearing capacity test is shown inFigure 2 For comparison three standard composite crossarms from the same batch were tested to obtain the originalno-fatigue compressive bearing capacity before the residualbearing capacity experiment

3 Test Results and Analysis

31 FailureMode After the test the summary of test resultsis shown in Table 2 in which there was no significant fatiguefailure occurred of GFRP-steel composite cross arms duringthe 500 thousand high-cycle fatigue test -en the axialcompression test was carried out to derive the residual ul-timate bearing capacity of the specimens A summary of thefailure modes is shown in Figure 3 from which the severeshear failures appeared in the composite material portionAll the tested specimens demonstrated the similar failuremodes after the residual bearing capacity test Taking thespecimen GZ-5 as an example the last two photos in Figure 3indicate that the ultimate bearing capacity was reached asthe layered fibers broke from the resin accompanied bya huge ldquobangrdquo simultaneously Moreover the specimen test

2 Advances in Civil Engineering

Table 1 Loading scheme

Specimen Loading conditionLoad peak (kN)

Cycles CommentsUpper limit Lower limit

GZ-1 1 9788 4363 500000 Basic windy condition 10msGZ-2 1 9788 4363 500000 Basic windy condition 10msGZ-3 2 17898 minus4096 500000 Ultimate windy condition 30msGZ-4 3 17898 minus17898 500000 Equal amplitudes of tension-compression loadingGZ-5 4 20000 minus20000 500000 11 times of loading condition 3GZ-6 5 23000 minus23000 500000 13 times of loading condition 3Negative sign of the load peak indicates tension loads while positive sign indicates compression loads

Actuator SpecimenCounterforce

frame

(a)

Test area

(b)

Figure 2 Test devices (a) high-cycle fatigue test (b) ultimate bearing capacity test

1ELEMENTSUROTACEL

1081

1101

1103

X

20032002

2000

Biaxial straingauge

Unidirectionalstrain gauge

16001601

2001

16

421

461

irdrow

Secondrow

Firstrow

Loading endFixed end

46625

ϕ600

ϕ545

1266

2532 50 50

Figure 1 -e specimen size and arrangement of measuring points

Advances in Civil Engineering 3

(like the coupon test) was conducted to obtain the originalno-fatigue compressive bearing capacity in which theoriginal average compressive bearing capacity was 6472 kN-e failure modes of the no-fatigue specimen test were similarto those specimens with fatigue loading

32 Load-Displacement-Time Curves A variety of me-chanical properties of GFRP cross arms can be monitored byload-displacement-time curves during the fatigue test Dueto the page limitations the GZ-6 specimen under the mostunfavourable loading condition 5 was taken as an example toillustrate the response of the GFRP-steel sleeve compositecross arms

-e load-displacement-time curve of the GZ-6 specimenis shown in Figure 4 It can be seen that the load peak and

valley of the specimen were stable during the fatigue testwhich was consistent with the preset value of the loadingscheme Compared with the load-displacement-time curvesand test results of the other specimens it indicates that theGFRP cross arm has good workability after 500000 times ofhigh-cycle fatigue load without obvious fatigue failurephenomenon based on the macrophenomenon

33 Energy Dissipation Based on the energy analysis theload-displacement data of five cycles were fitted at theloading times of 100000 200000 300000 400000 and500000 seconds nearby -e energy dissipation of differentmonitoring nodes namely the area of the load-displacementhysteresis loop could be calculated by the numerical in-tegration [27ndash29] and the changes of mechanical properties

Table 2 Summary of test results

Specimen Test phenomenon Failure test Residual ultimate bearing capacity (kN)GZ-1 No significant fatigue failure phenomenon Axial compression 5850GZ-2 No significant fatigue failure phenomenon Axial compression 5825GZ-3 No significant fatigue failure phenomenon Axial compression 5891GZ-4 No significant fatigue failure phenomenon Axial compression 6304GZ-5 No significant fatigue failure phenomenon Axial compression 5617GZ-6 No significant fatigue failure phenomenon Axial compression 5566

GZ-1

(a)

GZ-2

(b)

GZ-3

(c)

GZ-4

(d)

GZ-5

(e)

GZ-6

(f ) (g) (h)

Figure 3 Typical shear failure mode


and development of cumulative damage were investigatedthrough energy dissipation analysis shown in Figure 5

Figure 5 provides the energy dissipation analysis of thecorresponding monitoring points of the specimens -eresults indicated that the energy consumption values of GZ-1 GZ-2 and GZ-4 specimens increased before 300000cycles and values of GZ-3 GZ-5 and GZ-6 increased before200000 cycles-en the energy dissipation values decreasedslowly It is shown that the microcracks grew constantly incomposite materials until the stable state and then thestiffness degenerated gradually with an increase in the cu-mulative damage which could be observed by the variationin energy dissipation Due to the first transcendental damagecaused by the anisotropy of composite and the increase offatigue loads the attenuation of energy dissipation values of

GZ-3 GZ-5 and GZ-6 was advanced Moreover in the laterstage the cumulative damage developed gradually and theenergy dissipation values decreased to a lesser extent

-e typical energy dissipation loop of each specimen isshown in Figure 6 taking the GZ-6 specimen as an examplefrom which a long ldquoneedlerdquo loop could be observed and thedegradation phenomenon of the specimen under high-cyclefatigue loads was not obvious It reflected that the GFRPcross arms still worked in the elastic stage and the cumu-lative residual microplastic deformation was tiny

34 Strain Analysis In this part the dynamic strain duringfatigue loading and the static strain during the ultimatebearing capacity test were monitored to evaluate the negativeeffects caused by fatigue loads on the GFRP cross arms

0 1 2 3 4 5 6ndash4

ndash2

0

2

4

100000 100001 100002 100003 100004 100005 100006

Disp

lace

men

t (m

m)

Time (s)

Displacement (mm)Load (kN)

ndash200

0

200

400

Load

(kN

)

(a)

200000 200001 200002 200003 200004 200005 200006ndash4

ndash2

0

2

4

300000 300001 300002 300003 300004 300005 300006

Disp

lace

men

t (m

m)

Time (s)


Load

(kN

)

ndash200

0

200

400

(b)

400000 400001 400002 400003 400004 400005 400006ndash4

ndash2

0

2

4

499994 499995 499996 499997 499998 499999 500000

Displacement (mm)

Disp

lace

men

t (m

m)

Time (s)

Load (kN)Lo

ad (k

N)

ndash200

0

200

400

(c)

Figure 4 Analysis of the GZ-6 load-displacement-time curve


341 Dynamic Strain In the process of the high-cycle fa-tigue test in order to monitor the deformation and stressstate of the specimens especially the composite materialpart the dynamic strain gauges were employed to monitorthe variety of deformation -e specimen GZ-1 with min-imum fatigue load and the GZ-6 specimen with the maxi-mum fatigue load were taken as examples to analyze thedynamic strain value near the nodes of 500000 cycles where

the numerals 2-1 and 3-1 denote the longitudinal strain atthe first row of the composite material section 2-2 and 3-2denote the circumferential strain at the first row of thecomposite material section -e dynamic strain is shown inFigure 7

Figures 7(a) and 7(b) are the dynamic strain graphs ofthe specimen GZ-1 under condition 1 and the specimen GZ-6 under condition 5 It can be seen that the strain value of the

79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)

Monitoring node (times10000)

(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )

Figure 5 Energy dissipation analysis (a) GZ-1 (b) GZ-2 (c) GZ-3 (d) GZ-4 (e) GZ-5 (f ) GZ-6


GZ-1 specimen was tiny when subjected to high-cycle fa-tigue loading where it had a maximum peak strain of 30 μεin longitudinal compression and 30 με in circumferentialtension respectively Apparently under the most adversecondition 5 the longitudinal and circumferential peak strainof the specimen GZ-6 were about 200 με and 400 με re-spectively while the relative longitudinal amplitude wasabout 600 με which indicated that fatigue loads had slightimpact on the deformation capacity of GFRP cross arms Onthe whole the specimens were basically in the elasticworking state

342 Static Strain During the residual ultimate bearingcapacity test the strain of GZ-6 (taking as an example) wasmonitored as shown in Figure 8 Compared to the dynamicstrain in Figure 7 an unconspicuous nonlinear relationshipcould be observed until the specimens failed and the finalstrain was obviously greater than its dynamic strain -erewere some differences in the static strain because of theanisotropic nature of the composites but the overall vari-ation was consistent -e ultimate strain of longitudinal andcircumferential directions reached up to 12000 με and7000 με respectively After the high-cycle fatigue loads theGFRP composite cross arms could demonstrate favourableantideformation ability

35 Residual Ultimate Bearing Capacity After the fatiguetest the ultimate bearing capacity of specimens was analyzedto examine the adverse impact of fatigue loads Figure 9describes the variety of load-displacement curves after thefatigue test It indicated that the loads had an approximatelylinear increase with the increment in displacement and thena sudden drop occurred as the ultimate bearing capacity wasreached Compared to the original average no-fatiguecompressive bearing capacity of 6472 kN the average re-sidual ultimate bearing capacity after the fatigue test was584217 kN It indicated that the whole GFRP cross armssubjected to 500 thousand cycles fatigue loads had an ob-vious decrease (973) in ultimate bearing capacity -is

could provide basic references for the cumulative damageevaluation and fatigue life prediction based on the macro-scopic phenomenon From GZ-1 to GZ-6 it can be seen thatthe ultimate bearing capacity of GZ-6 decreased at a maxi-mum extent of 1400 and GZ-4 reduced to a minimumdegree of 260 It should be noted that the maximum andminimum cyclic loading levels of GZ-6 and GZ-1 were 36and 15 of the original no-fatigue compressive bearingcapacity respectively-ough the cyclic loading levels in thistest could not be further improved due to the limitation ofthe loading apparatuses the composite cross arms showedthe gradual degradation behavior under fatigue loadingreflecting the fact that the accumulated damage of GFRPcannot be neglected in the design period Moreover due tothe anisotropy of the composite material and discreteproduction process except for the GZ-3 and GZ-4 theultimate bearing capacity of specimens decreased obviouslywith the increase in fatigue loading amplitude

4 Fatigue Life Prediction Based on ResidualStrength Theory

-e fatigue test especially for high-cycle fatigue experimentis time-consuming and costly -ere is no accurate guar-antee for researchers to make every specimen produce thevisual fatigue failure under the preset loading schemes Howto assess the fatigue cumulative damage and to predict thefatigue life of the full-scale components under the finiteloading cycles is a practical problem needed to be solvedurgently

-e residual strength is one of the most importantproperties of composite materials under the fatigue loadingand is the basis of cumulative damage assessment and fatiguelife prediction [8 9] In GFRP fatigue damage initiates andpropagates during cyclic loading where several types ofdamage may exist physically at one time or another which inadditionmay be different during different periods Certainlythese damages will affect the macroscopic mechanicalproperties of the material such as strength or stiffnessConsidering the requirement that the parameters should bemeasured easily it is assumed for the definition of thecumulative damage model that the strength loss can be usedas a metric to evaluate fatigue damage phenomenologicallyIn this part the residual strength theory can be applied toassess the fatigue cumulative damage and to predict thefatigue life under finite loading cycles

41 Residual Strength1eory In the earlier literatures someanalyses and experiments on the residual strength ofpolymeric composite materials have been carried out basedon materials level [8ndash10 26 30ndash33] To evaluate the fatiguedamage it must define the damage extent caused by onesingle loading cycle Commonly the PalmgrenndashMiner rule(P-M rule) defines the damage caused by one single loadingcycle while ΔD 1Nf where Nf is the fatigue life under theapplied loading while the damage accumulates linearly untilthe critical value of 1 is reached -e damage developsunevenly during the cyclic loading so the cumulative

ndash4 ndash2 0 2 4ndash300

ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)

Figure 6 Typical energy dissipation loop


damage should reflect the variety of stress-strain state underdifferent loading history In this part the cumulative fatiguedamage can be defined by the following equation [8 11]

ΔDn A[R(nminus 1)minusR(n)] (1)

where ΔD is the cumulative damage value R(n) is the re-sidual ultimate bearing capacity after the nth fatigue loadingcycle and A is a proportionality coefficient Differentloading cycles lead to different residual ultimate bearingcapacities So there is ΔDi neΔDj(ine j) apparently whichreflects the damage developing unevenly As for A in (1) if

the applied fatigue spectrum is the constant amplitude thespecimen will fall when the cycle number is equal tothe fatigue life Nf and A can be generally derived bythe maximum cumulative damage value Dcr 1 [11] asfollows

Dcr 1113944

Nf

i1A[R(iminus 1)minusR(i)] A R(0)minusR Nf( 11138571113858 1113859

A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)

Figure 7 Dynamic strain of composite material (a) GZ-1 (b) GZ-6

0

1000

2000

3000

4000

5000

6000

ndash12000 ndash10000 ndash8000 ndash6000 ndash4000 ndash2000 0Strain (με)

Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)

Figure 8 Static strain at the first row of the composite material section of GZ-6 (a) longitudinal load-strain curves (b) circumferential load-strain curves


A 1

R(0)minus Sm (3)

where Sm is the peak fatigue loadIn this paper residual ultimate bearing capacity of the

specimens after the fatigue test was obtained in the form ofaxial compressive ultimate bearing capacity and the residualstrength of specimens after nth loading cycle can bemodifiedand expressed in (4) and (5) based on the existing theories[9 30 34 35]

R(n) R(0)minus R(0)minus Sm1113858 1113859fn

Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)

-e variety of residual strength shown in (4) and (5) canbe depicted in Figure 10 it indicates that at the beginning ofthe loading the residual strength decreases rather quicklywhich is mainly related to the abrupt forming of smallcracks then the residual strength decreases moderately andevenly which is mainly due to the slow development of thecumulative damage near the fatigue life Nf there isa sudden ldquosudden deathrdquo behavior which demonstrates thatthe specimen unexpectedly suffers from the complete fatiguefailure [11 34]

-e factor v in (5) is a degradation parameter that can bedetermined by energy dissipation in this paper for which itcan be defined as follows

v Eend

Em (6)

where Eend is the energy dissipation value of the final cycleunder the fatigue load and Em is the maximum value ofenergy dissipation in the fatigue loading history In this paperthe parameter v depicting the degraded behavior under cyclicfatigue loads through the dissipated energy is determined bythe experimental data -e definition about the parameter v

specific in physical meaning is totally different from the otherempirical coefficients gained by parameter fitting and can beprecisely applied to predict fatigue life

42 Cumulative Damage Evaluation In this part the cu-mulative damage values were evaluated based on theaforementioned modified residual strength theory Figure 11shows the cumulative damage assessment for all specimenscompared to the intuitive residual strength method based onthe continuum damage mechanics which can be obviouslydepicted as follows

ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)

where ω is the continuum cumulative damage value -erange is 0leωle 1 while ω 0 demonstrates no damagephenomenon and ω 1 displays complete failure

Figure 11 reveals the fact that the damage assessmentsof two methods agree reasonably well -e cumulativedamage values of the intuitive method are slightly smallerbecause it does not take the different fatigue stress am-plitudes into consideration -e verification shows that themodified model based on the residual strength theory canbe utilized to calculate the cumulative damage values at thecomponent level and also can provide the basic referencesfor the follow-up fatigue life prediction In Figure 11except for the large divergence in the cumulative damagevalue of GZ-4 due to the anisotropy of the compositematerial and discrete production process overall the cu-mulative damage values amplify with the increase in fatigueloads

43 Fatigue Life Prediction Table 3 provides the fatigue lifeprediction results of the specimens based on the macro-scopic residual bearing capacity Meanwhile assuminga specimen GZ-7 by taking the average residual ultimatebearing capacity of 584217 kN into consideration the mostunfavorable loading condition 5 was used to predict themean fatigue life It should be noted that the original no-fatigue compressive bearing capacity and residual bearingcapacity after fatigue loading of the vested specimen cannotbe obtained synchronously thus in this study the fatiguelife prediction was conducted based on the original average

0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

Mean value after fatigue584217 kNMean value6472 kN

Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566

Figure 9 Analysis of ultimate bearing capacity after fatigue

R

R(0)

Sm

0

Sudden death

Nf n

Figure 10 -e residual strength model


compressive bearing capacity of the composite cross armswhere the statistical variation of the composite materials dueto the anisotropy was not considered

-e results in Table 3 show that the fatigue life of theGZ-6 specimen having a cyclic loading level of 36compared to the original average no-fatigue compressivebearing capacity is still more than 35 million cycles underthe most adverse loading condition 5 and because of theanisotropy of the composite material the fatigue life of theGZ-4 specimen with a cyclic loading level of 28 is higherthan other specimens Moreover from GZ-1 to GZ-6 ex-cept for GZ-4 the predicted fatigue lives decrease appar-ently with the increase in fatigue loads -e average fatiguelife (cyclic loading level 36) predicted by the averageresidual ultimate bearing capacity is more than 55 millioncycles indicating that the GFRP composite cross arms canresist the multimillion fatigue loads caused by the wind-induced vibrations of 13 times of the ultimate windycondition (30ms) -e overall prediction result shows thatthe GFRP-steel sleeve composite cross arms can demon-strate high level of safety redundancy on antifatigue per-formance and can be expected for wide application intransmission towers

5 Conclusions

In this paper a total of six GFRP-steel sleeve composite crossarms were subjected to 500 thousand cyclic loads to examinethe fatigue performance After the test the ultimate bearingcapacity of the specimens without significant fatigue failurewas evaluated to derive the residual bearing capacity -econclusions are as follows

(1) -e GFRP-steel sleeve composite cross arms candemonstrate the favourable antifatigue performanceunder practical loading conditions Although theload-displacement-time curve shows that there is noapparent degradation phenomenon the energy dis-sipation analysis reveals the slow cumulative fatiguedamage process

(2) -e dynamic strain of the specimens is tiny andoverall the residual ultimate bearing capacity afterfatigue loading decreases gradually with the increasein fatigue loads All specimens can display the rea-sonable elastic working state before reaching theultimate limit state of bearing capacity

(3) Utilizing the residual ultimate bearing capacitya modified residual strength model based on the

Table 3 Fatigue life prediction

Specimen Loading condition Cycles Parameter v Residual ultimate bearing capacity (kN) Fatigue life predictionGZ-1 1 500000 0880 5850 7037400GZ-2 1 500000 0891 5825 6516700GZ-3 2 500000 0983 5891 5643500GZ-4 3 500000 0932 6304 24397000GZ-5 4 500000 0981 5617 3812200GZ-6 5 500000 0979 5566 3590400GZ-7 5 500000 0941 584217 5721700

GZ-1 GZ-2 GZ-3 GZ-4 GZ-5 GZ-6

002

004

006

008

010

012

014

016

Modified modelIntuitive method

Cum

ulat

ive d

amag

e

Specimen

Figure 11 Cumulative damage evaluation


component level is presented to evaluate the cu-mulative fatigue damage and to predict the fatiguelife After 500 thousand cycles of fatigue loads theGFRP cross arms can still perform ideal fatigue lifeaccompanied by the different cumulative fatiguedamages to some extent

In summary the new type GFRP-steel sleeve compositecross arms can demonstrate the high level of safety re-dundancy on the antifatigue performance and can be ex-pected for the wide application in power transmission towers

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the State Grid Corporation of China (SGTYHT15-JS-197) which is gratefully acknowledged -e authors are alsograteful to everyone who participated in this research for theirassistance during the experimental program

References

[1] K Fujikake S Mindess and H Xu ldquoAnalytical model forconcrete confined with fiber reinforced polymer compositerdquoJournal of Composites for Construction vol 8 no 4pp 341ndash351 2004

[2] B Saboori and S M R Khalili ldquoStatic analysis of tapered FRPtransmission poles using finite element methodrdquo Finite Ele-ments in Analysis and Design vol 47 no 3 pp 247ndash255 2011

[3] Y Momomura H Marukawa T Okamura E Hongo andT Ohkuka ldquoFull-scale measurements of wind-induced vi-bration of a transmission line system in a mountainous areardquoJournal of Wind Engineering and Industrial Aerodynamicsvol 72 pp 241ndash252 1997

[4] P Zhang L Ren H Li Z Jia and T Jiang ldquoControl of wind-induced vibration of transmission tower-line system by usinga spring pendulumrdquo Mathematical Problems in Engineeringvol 2015 Article ID 671632 10 pages 2015

[5] Z Hashin and A Rotem ldquoA fatigue failure criterion for fiberreinforced materialsrdquo Journal of Composite Materials vol 7no 4 pp 448ndash464 1973

[6] R Talreja ldquoFatigue reliability under multiple-amplitudeloadsrdquo Engineering Fracture Mechanics vol 11 no 4pp 839ndash849 1979

[7] R Talreja ldquoFatigue of composite materials damage mecha-nisms and fatigue-life diagramsrdquo Proceedings of the RoyalSociety A Mathematical Physical and Engineering Sciencesvol 378 no 1775 pp 461ndash475 1981

[8] Z Hashin ldquoCumulative damage theory for composite ma-terials residual life and residual strength methodsrdquo Com-posites Science and Technology vol 23 no 1 pp 1ndash19 1985

[9] J N Yang L J Lee and D Y Sheu ldquoModulus reduction andfatigue damage of matrix dominated composite laminatesrdquoComposite Structures vol 21 no 2 pp 91ndash100 1992

[10] S Subramanian K L Reifsnider and W W Stinchcomb ldquoAcumulative damage model to predict the fatigue life ofcomposite laminates including the effect of a fibre-matrixinterphaserdquo International Journal of Fatigue vol 17 no 5pp 343ndash351 1995

[11] W X Yao andN Himmel ldquoA new cumulative fatigue damagemodel for fibre-reinforced plasticsrdquo Composites Science andTechnology vol 60 no 1 pp 59ndash64 2000

[12] M M Shokrieh and F Taheri-Behrooz ldquoA unified fatigue lifemodel based on energy methodrdquo Composite Structuresvol 75 no 1ndash4 pp 444ndash450 2006

[13] A Varvani-Farahani H Haftchenari and M Panbechi ldquoAfatigue damage parameter for life assessment of off-axisunidirectional GRP compositesrdquo Journal of Composite Ma-terials vol 40 no 18 pp 1659ndash1670 2006

[14] E N Eliopoulos and T P Philippidis ldquoA progressive damagesimulation algorithm for GFRP composites under cyclicloading Part I material constitutive modelrdquo CompositesScience and Technology vol 71 no 5 pp 742ndash749 2011

[15] Y H Huh D J Kim and Y S Lee ldquoEffect of stress ratio onfatigue life of GFRP composites for WT bladerdquo Journal ofMechanical Science and Technology vol 26 no 7 pp 2117ndash2120 2012

[16] X S Sun A Haris V B C Tan T E Tay S Narasimalu andC N Della ldquoA multi-axial fatigue model for fiber-reinforcedcomposite laminates based on Puckrsquos criterionrdquo Journal ofComposite Materials vol 46 no 4 pp 449ndash469 2012

[17] M Abo-Elkhier A A Hamada and A B El-Deen ldquoPre-diction of fatigue life of glass fiber reinforced polyestercomposites using modal testingrdquo International Journal ofFatigue vol 69 pp 28ndash35 2014

[18] S Mortazavian and A Fatemi ldquoFatigue behavior and mod-eling of short fiber reinforced polymer composites includinganisotropy and temperature effectsrdquo International Journal ofFatigue vol 77 pp 12ndash27 2015

[19] S Stelzer G Pinter and A J Brunner ldquoComparison of quasi-static and cyclic fatigue delamination resistance of carbonfiber reinforced polymer-matrix laminates under differentmode loadingrdquo Procedia Materials Science vol 3 pp 1087ndash1092 2014

[20] J Brunbauer H Stadler and G Pinter ldquoMechanical prop-erties fatigue damage and microstructure of carbonepoxylaminates depending on fibre volume contentrdquo InternationalJournal of Fatigue vol 70 pp 85ndash92 2015

[21] D Vasiukov S Panier and A Hachemi ldquoDirect method forlife prediction of fiber reinforced polymer composites basedon kinematic of damage potentialrdquo International Journal ofFatigue vol 70 pp 289ndash296 2015

[22] W Zhang Z Zhou B Zhang and S Zhao ldquoA phenome-nological fatigue life prediction model of glass fiber reinforcedpolymer compositesrdquo Materials and Design vol 66 pp 77ndash81 2015

[23] E Belmonte M D Monte C Hoffmann andM QuaresiminldquoDamage mechanisms in a short glass fiber reinforcedpolyamide under fatigue loadingrdquo International Journal ofFatigue vol 94 pp 145ndash157 2017

[24] A J Brunner S Stelzer G Pinter and G P Terrasi ldquoCyclicfatigue delamination of carbon fiber-reinforced polymer-matrix composites data analysis and design consider-ationsrdquo International Journal of Fatigue vol 83 pp 293ndash2992016

[25] Z Liu P Li N Srikanth T Liu and G B Chai ldquoQuanti-fication of flexural fatigue life and 3D damage in carbon fibre


reinforced polymer laminatesrdquo Composites Part A AppliedScience and Manufacturing vol 90 pp 778ndash785 2016

[26] J N Yang and M D Liu ldquoResidual strength degradationmodel and theory of periodic proof tests for graphiteepoxylaminatesrdquo Journal of Composite Materials vol 11 no 2pp 176ndash203 1977

[27] F Y Liao L H Han and Z Tao ldquoBehavior of compositejoints with concrete encased CFST columns under cyclicloading experimentsrdquo Engineering Structures vol 59pp 745ndash764 2014

[28] T Zhou Z Chen and H Liu ldquoSeismic behavior of specialshaped column composed of concrete filled steel tubesrdquoJournal of Constructional Steel Research vol 75 pp 131ndash1412012

[29] S L McCabe andW J Hall ldquoAssessment of seismic structuraldamagerdquo Journal of Structural Engineering vol 115 no 9pp 2166ndash2183 1989

[30] C C Pei and R Croman ldquoResidual strength in fatigue basedon the strength-life equal rank assumptionrdquo Journal ofComposite Materials vol 12 pp 177ndash194 1978

[31] A Haque J Krishnagopalan and S Jeelani ldquoFatigue damagein laminated compositesrdquo Journal of Reinforced Plastics andComposites vol 12 no 10 pp 1058ndash1069 1993

[32] B Liu and L B Lessard ldquoFatique and damage-toleranceanalysis of composite laminates stiffness loss damage-modelling and life predictionrdquo Composites Science andTechnology vol 51 no 1 pp 43ndash51 1994

[33] J R Schaff and B D Davidson ldquoLife prediction methodologyfor composite structures Part Indashconstant amplitude and two-stress level fatiguerdquo Journal of Composite Materials vol 31no 2 pp 128ndash157 1997

[34] L J Broutman and S Sahu ldquoA new theory to predict cu-mulative fatigue damage in fiberglass reinforced plasticsrdquo inProceedings of the Second Conference on Composite MaterialsTesting and Design ASTM STP 497 pp 170ndash188 AnaheimCA USA April 1971

[35] A Charewicz and I M Daniel ldquoDamage mechanisms andaccumulation in graphiteepoxy laminatesrdquo in Proceedings ofthe Composite Materials Fatigue and Fracture ASTM STP 907pp 97ndash274 Dallas TX USA 1986


International Journal of

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Active and Passive Electronic Components

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Shock and Vibration


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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

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Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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wwwhindawicom Volume 2018

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Multimedia

Submit your manuscripts atwwwhindawicom

changes of modal parameters provide a proper method forpredicting the fatigue behavior of composite structuresZhang et al [22] proposed a macrophenomenological fa-tigue model for the off-axis fatigue behavior of GFRPcomposite laminates However the aforementioned re-searches about the fatigue properties of composite mate-rials mainly concentrate on the material level and reducedscale members especially for the cumulative damage as-sessment and fatigue life prediction So far studies onhigh-cycle fatigue behavior of GFRP based on full-scalecomponents are found lacking -erefore it is necessary tocarry out experimental researches on high-cycle fatigueperformance about the full-scale GFRP componentsconsidering the influence of size effect on composite ma-terial defects

In this paper an experimental study on high-cycle fa-tigue properties of a new type of full-scale GFRP-steel sleevecomposite cross arms was conducted A total of six speci-mens were subjected to 500 thousand cyclic loadings -estress state load-displacement-time curve energy dissipa-tion capacity and dynamic strain were analyzed in detail-e ultimate bearing capacity of the specimens was evalu-ated to derive residual bearing capacity Based on themodified residual strength theory the cumulative damagewas assessed to predict the fatigue life of GFRP-steel sleevecomposite cross arms

2 Experiment Condition

21 Specimen Details In this study a total of six standardspecimens were designed and produced by Jiangsu ShemarElectric Co Ltd All the GFRP pipes with steel sleeves (steelgrade Q345) spliced on both ends were manufacturedthrough the filament winding process A total of thirty fiberlayers divided into ten fixed skeleton layers and twentyvariable angle layers were winded in a constant thickness of066mm per layer where the inside-out layout was 90deg2 (S)-60deg2 (S)-30deg8 (V)-90deg2 (S)-30deg8 (V)-90deg2 (S)-30deg4 (V)-60deg2 (S) In the notation adopted to identify the fiber layersaforesaid the first number denoted winding angles betweenthe fiber orientation and axis the second number denotedthe sums of winding fiber layers the letters ldquoSrdquo and ldquoVrdquodenoted the fixed skeleton layer and variable angle layerrespectively -e specimen size and arrangement of mea-suring points are shown in Figure 1 in which the compositecross arm was 2532mm long and the length of steel sleevewas 466mm -e outer diameter and wall thickness of thecomposite pipe were 461mm and 20mm respectivelySixteen stiffening ribs were welded along the perimeter of thesteel sleeve for which the wall thickness and outer diameterwere 16mm and 600mm respectively In order to monitorthe deformation of the specimen during the fatigue test thelocations of the strain gauges in this fatigue test were mainlymounted on the loading ends which were sensitive to fatigueloads Four strain gauges in the first row including twobiaxial strain gauges and two unidirectional strain gaugeswere arranged in an interval of 90deg along the circumferentialdirection Two biaxial strain gauges were mounted by thesymmetrical layout in the other rows

22 Loading Scheme In this paper based on the XimengndashShengli section ultrahigh voltage (UHV) transmissionproject in China the finite element method was firstemployed to carry out the dynamic time-history analysis fordetermining fatigue peak loads of the experiment -e ac-curacy and validity of this finite element method wereverified by Northwest Electric Power Design Institute CoLtd of China Power Engineering Consulting Group -einternal forces of the transmission tower cross arms at thebasic wind speed of 10ms and strong wind speed of 30mswere extracted as the basic and ultimate reference loadingconditions respectively -e practical UHV transmissiontowers located in Xilin Gol League of China were subjectedto the adverse wind-induced vibrations -erefore throughthe statistic of the local climate condition the 500000 timeshigh-cycle fatigue loading was determined to simulate theactual stress state in life cycle at different safety marginsbased on the design requirement namely for the GFRPcomposite cross arms of the UHV transmission towersfatigue failure cannot occur at the basic frequent design windspeed (10ms) and extremely infrequent ultimate windspeed (30ms) respectively Further if there was no evidentfatigue failure occurred during the aforesaid conditions themore adverse loading protocols about the equal amplitudesof tension-compression were determined to examine thedifferent safety margins based on the ultimate referenceloading conditions (30ms) for further reliability -e fa-tigue test was carried out by the MTS24431 hydraulic servoactuation system-e loading scheme based on the dynamicanalysis result is shown in Table 1

As is shown in Table 1 the fatigue cycle load was appliedat 1Hz frequency using the displacement control After thetest ultimate bearing capacity of the specimens withoutsignificant fatigue failure was evaluated to derive residualbearing capacity using the TianshuindashHongshan 20000 kNcomputer-controlled electrohydraulic servo pressure andshear testing machine -e loading device of the high-cyclefatigue test and ultimate bearing capacity test is shown inFigure 2 For comparison three standard composite crossarms from the same batch were tested to obtain the originalno-fatigue compressive bearing capacity before the residualbearing capacity experiment

3 Test Results and Analysis

31 FailureMode After the test the summary of test resultsis shown in Table 2 in which there was no significant fatiguefailure occurred of GFRP-steel composite cross arms duringthe 500 thousand high-cycle fatigue test -en the axialcompression test was carried out to derive the residual ul-timate bearing capacity of the specimens A summary of thefailure modes is shown in Figure 3 from which the severeshear failures appeared in the composite material portionAll the tested specimens demonstrated the similar failuremodes after the residual bearing capacity test Taking thespecimen GZ-5 as an example the last two photos in Figure 3indicate that the ultimate bearing capacity was reached asthe layered fibers broke from the resin accompanied bya huge ldquobangrdquo simultaneously Moreover the specimen test







frame

(a)

Test area

(b)


1ELEMENTSUROTACEL

1081

1101

1103

X

20032002

2000

Biaxial straingauge


16001601

2001

16

421

461

irdrow

Secondrow

Firstrow


46625

ϕ600

ϕ545

1266

2532 50 50










GZ-1

(a)

GZ-2

(b)

GZ-3

(c)

GZ-4

(d)

GZ-5

(e)

GZ-6

(f ) (g) (h)








0 1 2 3 4 5 6ndash4

ndash2

0

2

4

100000 100001 100002 100003 100004 100005 100006

Disp

lace

men

t (m

m)

Time (s)


ndash200

0

200

400

Load

(kN

)

(a)

200000 200001 200002 200003 200004 200005 200006ndash4

ndash2

0

2

4

300000 300001 300002 300003 300004 300005 300006

Disp

lace

men

t (m

m)

Time (s)


Load

(kN

)

ndash200

0

200

400

(b)

400000 400001 400002 400003 400004 400005 400006ndash4

ndash2

0

2

4

499994 499995 499996 499997 499998 499999 500000

Displacement (mm)

Disp

lace

men

t (m

m)

Time (s)

Load (kN)Lo

ad (k

N)

ndash200

0

200

400

(c)






79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)


(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )












ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







frame

(a)

Test area

(b)


1ELEMENTSUROTACEL

1081

1101

1103

X

20032002

2000

Biaxial straingauge


16001601

2001

16

421

461

irdrow

Secondrow

Firstrow


46625

ϕ600

ϕ545

1266

2532 50 50










GZ-1

(a)

GZ-2

(b)

GZ-3

(c)

GZ-4

(d)

GZ-5

(e)

GZ-6

(f ) (g) (h)








0 1 2 3 4 5 6ndash4

ndash2

0

2

4

100000 100001 100002 100003 100004 100005 100006

Disp

lace

men

t (m

m)

Time (s)


ndash200

0

200

400

Load

(kN

)

(a)

200000 200001 200002 200003 200004 200005 200006ndash4

ndash2

0

2

4

300000 300001 300002 300003 300004 300005 300006

Disp

lace

men

t (m

m)

Time (s)


Load

(kN

)

ndash200

0

200

400

(b)

400000 400001 400002 400003 400004 400005 400006ndash4

ndash2

0

2

4

499994 499995 499996 499997 499998 499999 500000

Displacement (mm)

Disp

lace

men

t (m

m)

Time (s)

Load (kN)Lo

ad (k

N)

ndash200

0

200

400

(c)






79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)


(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )












ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









GZ-1

(a)

GZ-2

(b)

GZ-3

(c)

GZ-4

(d)

GZ-5

(e)

GZ-6

(f ) (g) (h)








0 1 2 3 4 5 6ndash4

ndash2

0

2

4

100000 100001 100002 100003 100004 100005 100006

Disp

lace

men

t (m

m)

Time (s)


ndash200

0

200

400

Load

(kN

)

(a)

200000 200001 200002 200003 200004 200005 200006ndash4

ndash2

0

2

4

300000 300001 300002 300003 300004 300005 300006

Disp

lace

men

t (m

m)

Time (s)


Load

(kN

)

ndash200

0

200

400

(b)

400000 400001 400002 400003 400004 400005 400006ndash4

ndash2

0

2

4

499994 499995 499996 499997 499998 499999 500000

Displacement (mm)

Disp

lace

men

t (m

m)

Time (s)

Load (kN)Lo

ad (k

N)

ndash200

0

200

400

(c)






79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)


(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )












ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0 1 2 3 4 5 6ndash4

ndash2

0

2

4

100000 100001 100002 100003 100004 100005 100006

Disp

lace

men

t (m

m)

Time (s)


ndash200

0

200

400

Load

(kN

)

(a)

200000 200001 200002 200003 200004 200005 200006ndash4

ndash2

0

2

4

300000 300001 300002 300003 300004 300005 300006

Disp

lace

men

t (m

m)

Time (s)


Load

(kN

)

ndash200

0

200

400

(b)

400000 400001 400002 400003 400004 400005 400006ndash4

ndash2

0

2

4

499994 499995 499996 499997 499998 499999 500000

Displacement (mm)

Disp

lace

men

t (m

m)

Time (s)

Load (kN)Lo

ad (k

N)

ndash200

0

200

400

(c)






79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)


(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )












ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





79312 80144 82722

7312 72815

10 20 30 40 500

200

400

600

800En

ergy

diss

ipat

ion

(kN

middotmm

)


(a)

78445 79888 8101872219 72217

10 20 30 40 500

200

400

600

800

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(b)

326163 325886 327776 328939 323283

10 20 30 40 502000

3000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(c)

612605

684328 681139 659695637532

10 20 30 40 50

2000

4000

6000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(d)

910278 91028 908583 908041 89254

10 20 30 40 504000

6000

8000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(e)

106701 1046674 1045918 104682 1044248

10 20 30 40 50

6000

8000

10000

Ener

gy d

issip

atio

n (k

Nmiddotm

m)


(f )












ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











ndash200

ndash100

0

100

200

300

Load

(kN

)

Displacement (mm)







Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Dcr 1113944

Nf


A R(0)minus Sm1113858 1113859

(2)

Hence

499996 499998 500000

ndash30

ndash20

ndash10

0

10

20

30St

rain

(με)

Time (s)

2-1 2-23-1 3-2

(a)

Stra

in (μ

ε)

2-1 2-23-1 3-2

499996 499998 500000

ndash400

ndash200

0

200

400

Time (s)

(b)


0

1000

2000

3000

4000

5000

6000


Load

(kN

)

Channel number911

1315

(a)

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000 7000Strain (με)

Load

(kN

)

Channel number1012

1416

(b)



A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


A 1

R(0)minus Sm (3)




Nf1113888 1113889 (4)

fn

Nf1113888 1113889

n

Nf1113888 1113889

v

(5)



v Eend

Em (6)




ω R(0)minusR(n)

R(0) 1minus

R(n)

R(0) (7)




0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000


Load

(kN

)

Displacement (mm)

GZ-15850GZ-25825GZ-35891

GZ-46304GZ-55617GZ-65566


R

R(0)

Sm

0

Sudden death

Nf n





5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




5 Conclusions








002

004

006

008

010

012

014

016


Cum

ulat

ive d

amag

e

Specimen





Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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