boundary element analysis of fatigue crack growth for cfrp … paper 9... · 2015. 5. 15. ·...

Boundary Element Analysis of Fatigue Crack Growthfor CFRP-Strengthened Steel Plates with Longitudinal

Weld AttachmentsQian-Qian Yu1; Tao Chen2; Xiang-Lin Gu3; Xiao-Ling Zhao, F.ASCE4; and Zhi-Gang Xiao5

Abstract: In this paper, steel plates with longitudinal weld attachments strengthened by carbon fiber reinforced polymer (CFRP) laminateson one side were analyzed based on the boundary element method and compared with test data from the literature. Good agreement with thedata indicated that the numerical analysis was reliable for estimation of the fatigue crack propagation of CFRP-bonded steel plates withlongitudinal weld attachments. The effects of double-sided strengthening, double-sided weld attachment and CFRP stiffness on the fatiguebehavior of retrofitted welded joints were also investigated. The results showed that double-sided strengthening was much more efficient thansingle-sided application. It was observed that the crack propagation of steel plates with weld attachments on both sides was acceleratedcompared with those with attachments on only one side. In comparison with steel plates without a weld attachment, the retrofitting efficiency,in terms of the fatigue life extension ratio, was significantly lowered in welded plates with single-sided repair, whereas only a slight differencewas observed in those with double-sided strengthening. The effect of an increased modulus of the composite materials could result in betterfatigue performance, especially with double-sided application. DOI: 10.1061/(ASCE)CC.1943-5614.0000505. © 2014 American Society ofCivil Engineers.

Author keywords: Boundary element method; Carbon fiber; Reinforced polymer (CFRP) laminate; Crack propagation; Fatigue;Welded joint.

Introduction

Steel structures are susceptible to fatigue damage. Fatigue cracksmay emanate and propagate in areas of stress concentration undercyclic loading of traffic volume. Structural investigation reportshave revealed that fatigue fracture is one of the most commoncauses of significant failure behavior for steel structures (Fisheret al. 2001; Xiao et al. 2006).

Structural retrofitting provides an economical and environmen-tally friendly way to improve the load carrying capacity or extendthe service life of structurally deficient members. Recently, the bondrepair technique using carbon fiber reinforced polymer (CFRP)materials has been considered as an innovative way to handlefatigue crack repair of steel structures, avoiding the drawbacksof standard strengthening techniques, such as drilling a hole at acrack front or attaching steel plates to damaged elements.

Extensive research on the fatigue behavior of CFRP-strengthenedsteel plates has been conducted to investigate the strengthening

efficiency of CFRP, and results have shown that composite materi-als have great potential in retarding crack propagation and extend-ing fatigue lives of cracked steel plates (Colombi et al. 2003; Jonesand Civjan 2003; Zhao et al. 2007; Täljsten et al. 2009; Liu et al.2009a; Ye et al. 2010; Wu et al. 2012; Yu et al. 2013).However, studies on welded joints strengthened by compositematerials have been reported less frequently (Fam et al. 2006;Nadauld and Pantelides 2007; Nakamura et al. 2009; Xiao andZhao 2012; Xiao et al. 2012; Chen et al. 2012a, b; Wu et al. 2013).

Fam et al. (2006) proposed a series of fatigue experiments onaluminum truss joints wrapped with fiber-reinforced polymer(FRP) materials. A 90% loss of weld was simulated by grindingthe welded perimeter at the intersection between the diagonalsand the main chord. The test results showed that it was possibleto restore the full strength of the welded joints with CFRP sheets,although the effectiveness was comparatively weak when usingglass fiber reinforced polymer (GFRP) layers. Nadauld and Pante-lides (2007) conducted similar research on aluminum overheadsign structures strengthened with GFRP materials.

Thin-walled cross-beam connections repaired by CFRP sheetswere tested under in-plane fatigue loading by Xiao and Zhao(2012) and Xiao et al. (2012). Circumferential or transverserestraining CFRP patches were successfully applied in the cornerregion to prevent early debonding and led to marked increases infatigue lives.

Chen et al. (2012a) presented an experimental and numericalstudy on the fatigue behavior of strengthened nonload carryingcruciform welded joints. Increased fatigue life was observed basedon limited experimental results and finite element simulations. Theparametric analysis revealed that the weld toe radius and thenumber of CFRP layers had pronounced effects on the strengthen-ing efficiency.

Nakamura et al. (2009) investigated the fatigue behavior ofCFRP retrofitted steel plates with longitudinal weld attachments.

1Ph.D. Candidate, Dept. of Structural Engineering, Tongji Univ.,Shanghai 200092, China; and Dept. of Civil Engineering, Monash Univ.,Melbourne, VIC 3800, Australia.

2Associate Professor, Dept. of Structural Engineering, Tongji Univ.,Shanghai 200092, China.

3Professor, Dept. of Structural Engineering, Tongji Univ., Shanghai200092, China (corresponding author). E-mail: [email protected]

4Professor, Dept. of Civil Engineering, Monash Univ., Melbourne, VIC3800, Australia.

5Lecturer, School of Applied Sciences and Engineering, Monash Univ.,Melbourne, VIC 3842, Australia.

Note. This manuscript was submitted on January 16, 2014; approved onJune 23, 2014; published online on August 5, 2014. Discussion period openuntil January 5, 2015; separate discussions must be submitted for individualpapers. This paper is part of the Journal of Composites for Construction,© ASCE, ISSN 1090-0268/04014044(12)/$25.00.

© ASCE 04014044-1 J. Compos. Constr.

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http://dx.doi.org/10.1061/(ASCE)CC.1943-5614.0000505http://dx.doi.org/10.1061/(ASCE)CC.1943-5614.0000505http://dx.doi.org/10.1061/(ASCE)CC.1943-5614.0000505http://dx.doi.org/10.1061/(ASCE)CC.1943-5614.0000505

They studied CFRP application in combination with drill-holes andincluded the effect of repair on the bonded strength and fatigue per-formance. It was found that fatigue life after repair was signifi-cantly improved.

Chen et al. (2012b) tested 21 out-of-plane gusset welded jointsunder tensile fatigue loading, and the results showed that the fatiguelife was prolonged to some extent after retrofitted with CFRPmaterials. Wu et al. (2013) carried out a series of fatigue tensiontests on steel plates with longitudinal weld attachments with a pri-mary emphasis on the application of ultra-high modulus CFRPlaminates (460 GPa). Test results showed that the fatigue life ofthe welded joints bonded by ultra-high modulus CFRP laminateson a single side could be increased up to 141% of that of un-strengthened ones.

To the best knowledge of the authors, there have been limitedattempts to perform a crack propagation analysis using numericalsimulation on steel plates with longitudinal weld attachmentsstrengthened with composite materials. The boundary elementmethod was employed in this paper to study the fatigue crackpropagation of steel plates with longitudinal weld attachmentsstrengthened with CFRP laminates. The fatigue life was calculatedwith the NASGRO law and compared with test data reported byWu et al. (2013). It was demonstrated that the boundary elementmethod could accurately estimate the fatigue behavior of CFRP-bonded steel plates with longitudinal weld attachments.

The effects of the strengthening configuration, weld attachment,and composite modulus on the fatigue life were then further exam-ined. This study extends the understanding of CFRP-repaired steelplates with longitudinal weld attachments and provides some usefulsuggestions for the strengthening method.

Experimental Study from the Literature

Specimen Geometry and Materials

Wu et al. (2013) conducted fatigue tests on steel plates with lon-gitudinal weld attachments strengthened with ultra-high modulusCFRP laminates. The specimens were made of a base plate witha longitudinal attachment fillet welded on one side. To excludethe scatter effect of the weld attributable to various initial defects,such as bubbles and slags, a crack starter was positioned at the endof the weld attachment, which was also located at the center of thesteel plate. The initial notch consisted of a 5 mm hole and two ini-tial cracks that were 1 mm long and 0.3 mm wide at the center. Thedetailed geometry of the specimen and dimensions are givenin Fig. 1.

Ultra-high modulus CFRP laminates were positioned bystructural adhesive on either side of the steel plate. The material

properties of the steel plates, adhesive, and CFRP laminates arelisted in Table 1 (Wu et al. 2013).

Specimen Configuration

Five retrofitting configurations, as illustrated in Fig. 2, wereadopted to investigate the effects of the bond length, bond width,and bond location on the strengthening efficiency. Configurationsa, b, and c indicate the specimens strengthened with CFRPlaminates with the areas enclosed by ‘a1 − a2 − a3 − a4’, ‘b1 −b2 − b3 − b4’ and ‘c1 − c2 − c3 − c4’, respectively. The geom-etries were designed to study the effects of the bond’s width andlength. Configurations d and e had the same bond width and lengthas configuration b, but different application positions were used toinvestigate the effect of the CFRP bond location on the fatigue per-formance of the welded joints. The CFRP laminate was split intohalves and placed at the edge of the plate and near the weld.

A total of eight different specimen types, as listed in Table 2,were designed in the test program. Referring to the specimennomenclature, F indicates that the composite material was attachedon the flat side of the specimen without the weld attachment,whereas W refers to the specimens with CFRP laminates bondedon the weld side. The bond’s length and width are defined as thelength and width of the attached CFRP laminate. Five cases (con-figurations a-e) were repaired on the flat side, whereas only twocases (configurations d and e) were repaired on the weld side re-sulting from the geometric limitations.

Fatigue Loading

All the specimens were loaded under tensile cyclic loading, whichranged from 13.5 to 135 kN with a frequency of 10 Hz and a stressratio R (minimum load/maximum load) of 0.1. The crack propaga-tion with fatigue cycles was monitored using the beach markingtechnique (Wu et al. 2013).

Fatigue Crack Propagation Prediction with BEM

BEASY, a commercial software package, was employed in thisstudy to analyze crack propagation and predict fatigue life usingthe dual boundary element method technique. Three-dimensionalboundary element models were built based on the configurationsof the test specimens. Only half of the welded joint was adoptedbecause of the symmetric model geometry and boundary condi-tions. The welding was excluded during the modeling processfor the following reasons: (1) the weld size was not recorded duringthe test program; (2) the measured weld size of the remaining spec-imens appeared scattered; and (3) the literature review indicatedthat cracks usually initiate from the weld toe at the end of the weld

300

90

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50

Attachment

Steel plate

Welding1

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R2.5

1

Attachment plate

1

Welding

Fig. 1. Geometric configurations of welded joints (unit: mm, not to scale)


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attachment in this type of welded joints with attachments welded allaround to the base plates (Nakamura et al. 2009; Chen et al. 2012b).In this test, the fillet weld was not applied along the thickness di-rection of the weld attachment: only two longitudinal fillet weldswere applied, as shown in Fig. 1. An artificial defect was intro-duced to initiate the fatigue crack and guide the propagationthrough the weld.

In test specimens F-e and W-e, the CFRP laminates were at-tached beside the welding in the test program and were, therefore,

assumed to be positioned 6 mm away from the attachment in theboundary element model. The surfaces of the steel plates and theCFRP laminates were modeled using quadrilateral-shaped, reducedquadratic order elements. An experimental study at Monash Uni-versity (Liu et al. 2010) showed that the fatigue loading has verylimited influence on the bond strength between steel and CFRP.Based on the findings in Liu et al. (2010), the influence of thedebonding could be ignored for the level of loading and the numberof fatigue cycles applied in the current program. Fernando et al.(2009) revealed that the uniaxial tensile stress-strain behavior ofAraldite 420 adhesive has a nonlinear part after the linear elasticstage. However, the materials in this work (steel, CFRP, and adhe-sives) were all considered under the linear elastic stage for thefatigue loading applied in the current program. The nonlinear partof the material behavior was not relevant. The Araldite 420 adhe-sive was, therefore, modeled as a linear spring element, as shown inFig. 3. The spring stiffness values, defined in terms of normal and

Table 1. Material Properties of Steel, CFRP, and Adhesive

Material property Steel Araldite 420 CFRP laminate

Tensile strength (MPa) 345.7 28.6 1,602.4Yield strength (MPa) 223.8 — —Tensile modulus (GPa) 191.8 1.9 477.5Laminate thickness (mm) 10 — 1.4

(a)

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100

100

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d2d4

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Fig. 2. Specimen configurations (unit: mm, not to scale): (a) configurations a, b and c; (b) configuration d; (c) configuration e


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tangential directions in a local coordinate system, were derivedusing the elastic properties of the structural adhesive and the mea-sured adhesive thickness (Liu et al. 2009b).

The shear spring stiffness Kt and Ku and axial spring stiffnessKn could be evaluated with Eqs. (1) and (2), respectively

Kt ¼ Ku ¼Gata

ð1Þ

Kn ¼Eata

ð2Þ

Ga ¼Ea

2ð1þ νÞ ð3Þ

where Ga and Ea represent the shear modulus and Young’s modu-lus of the adhesive, respectively; ta is the measured adhesive thick-ness of the test specimen; and ν is Poisson’s ratio of the adhesive.

A relatively fine mesh was adopted in the area around the centerhole in consideration of high stress concentration. The element sizewas less than one fourth of that in areas far away from the center.The models were split into zones numbered from nine to 16,because of the aspect ratio limitation and computational efficiency.A uniform tensile loading of 135 MPa was applied on each end

surface, and weak springs were used over the middle elementsto provide a rigid body restraint for this BEASY problem. A typicalboundary element model (W-d) is presented in Fig. 4.

An edge through crack was embedded to simulate the initial slotalong the center hole in BEASY’s Crack Growth Wizard. In thisstudy, the stress intensity factor was determined with the J-integralapproach, and the crack propagation life was integrated using theNASGRO 3 law expressed by Eq. (4)

dadN

¼ C · ð1 − fÞn · ΔKn ·

�1 − ΔKthΔK

�p

ð1 − RÞn · �1 − ΔKð1−RÞKc�q ð4Þ

where N = number of applied fatigue cycles; a = crack length; R =stress ratio; ΔK = stress intensity factor range; C, n, p and q =empirically derived constants that are contained in the NASGROfatigue database; f = crack opening function; ΔKth = thresholdstress intensity factor range; and Kc = critical stress intensity factor.

In this work, the material constants C and n were takenas 6.77 × 10−13 and 2.88 (da=dN in mm=cycle and ΔKin MPa •mm1=2), as recommended by the British StandardsInstitution (BSI 2005; Mashiri et al. 2000; Chen et al. 2013).Exponents p and q both had values equal to 0.5; and, values of148.6 MPa •mm1=2 and 6,950 MPa •mm1=2 were adopted forΔKth and Kc, respectively, as given in the BEASY database file.

Results and Comparison

Comparison of Fatigue Life

Table 3 presents a summary of the fatigue test date and the pre-dicted results. The thickness of the adhesive layer was used tocalculate the spring stiffness in the fatigue analysis. The data ofspecimens W-d-1, W-d-2, W-e-1, and W-e-2 were not recordedin the test program and were, therefore, assumed to be 0.5 mm.A dual specimen was designed in the test program for eachstrengthening configuration considering the scattering nature of

Table 2. Reference Test Specimens

Specimen Bond regionBond length

(mm)Bond width

(mm)Repairside

Bare plate N/A N/A N/A N/AF-a a1 − a2 − a3 − a4 250 90 Flat sideF-b b1 − b2 − b3 − b4 250 50 Flat sideF-c c1 − c2 − c3 − c4 100 50 Flat sideF-d d3; d4 250 25 × 2 Flat sideF-e e3; e4 250 25 × 2 Flat sideW-d d1; d2 250 25 × 2 Weld sideW-e e1; e2 250 25 × 2 Weld side

Kt Ku

CFRP laminate Steel plate

CFRP laminate

Steel plate Kn

Crack

Fig. 3. Illustration of internal spring boundary condition

Fig. 4. Typical boundary element model for specimen W-d


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fatigue experiments, whereas the numerical simulation analyzedonly one model for each strengthening configuration based onthe average thickness of the bond layer, which were then comparedwith the average fatigue life of the test specimens.

Table 3 shows that the ratio of the predicted fatigue cycles to thetested fatigue life ranged between 1.01 and 1.14; and, the meanvalue and the coefficient of variation were calculated as 1.08and 0.045, respectively. The numerical fatigue lives were within14% of their experimental results, indicating that the boundaryelement method could be used to estimate the fatigue life ofCFRP-repaired steel plates with longitudinal weld attachmentswith reasonable accuracy. The boundary element analysis slightlyoverestimated the fatigue behavior of the specimens, which can beattributed to the negative effect introduced by the weld.

Comparison of Fatigue Crack Propagation

The analytical results showed that the fatigue crack propagationwas symmetric with the plate width but uneven throughout the platethickness. For unstrengthened specimens and those with compositematerials attached on the flat side, the cracks propagated faster onthe weld side than on the flat side. For those specimens retrofitted

on the weld side, the crack growth on the flat side appeared tospread relatively quickly.

Fig. 5 presents the crack length variation from one side to theother of specimens F-d and W-d. The coordinates chosen were thehalf crack length ‘a’ measured from the center of the specimen andthe fatigue cycle numbers. This phenomenon is primarily associ-ated with the stress concentration attributable to the weld attach-ment, the shift of the neutral axis caused by the overlay patch,and the constraint effect of the composite materials on thecrack opening displacement. As the crack grew, the differencein the crack front between the weld and flat sides occurred gradu-ally; and, the numerical analysis terminated when the maximumgrowth distance was more than 50 times the minimum growth dis-tance, owing to limitations of the used software. It is believed that atthat time, the crack propagation was quite fast, and the correspond-ing number of fatigue cycles was negligible.

The rough trend of the crack shapes of different specimens wasobserved to be consistent with the test results (Wu et al. 2013).Because only the crack size on the flat side was recorded duringthe test program, the crack propagation with fatigue cycles ofthe numerical results on the flat side is displayed and comparedwith the test data in Fig. 6.

Fig. 6(a) demonstrates that the numerical model could predictthe crack propagation of unstrengthened welded joint accurately.The final crack length was overestimated because of the stoppingcriteria in the numerical simulation. The analysis ended when thestress intensity factor exceeded the fracture toughness (Kc) valuegiven in the fatigue properties. In the test program, the residualcross section of the steel plate at the late stage of crack propagationcould not carry the maximum load applied in each cycle; therefore,the specimen ruptured suddenly. The curve at the late stage ap-peared to be vertical, which also indicates that the crack propagatedvery quickly at the final stage of crack propagation, and that thecorresponding fatigue cycles were negligible.

For the specimens strengthened with composite materials, the si-mulated crack propagation of the strengthened plates agreed well withthe experimental results, particularly in the early stage of fatigue life.The differences primarily occurred at the late stage of crack propa-gation, when a distinct turning point appeared in the test curve.

It should be noted the beach marking technique was utilized in thisstudy to capture the fatigue crack growth. The disadvantage of thismethod is the difficulty in capturing many points towards the end ofthe fatigue life when the fatigue crack growth rate quickly increases.This is most likely the reason for the discrepancy between the mea-sured and predicted values. More research is needed to explore othermeans to capture sufficient points on the fatigue crack growth curve,such as the use of fatigue crack propagation gauges (Yu et al. 2014a).

Table 3. Comparison between Predicted Results and Test Data

Specimens

Bondthickness(mm)

Testedfatiguecycles

Averagedfatigue

cycles (Ne)

Predictedfatigue

cycles (Np) Np=Ne

B1 — 270,970 275,701 287,532 1.04B2 — 266,820B3 — 289,312F-a-1 0.49 320,252 337,219 346,116 1.03F-a-2 0.37 354,186F-b-1 1.16 313,333 299,040 340,434 1.14F-b-2 0.31 284,746F-c-1 0.31 303,365 282,933 320,838 1.13F-c-2 0.43 262,500F-d-1 0.37 336,101 306,048 338,543 1.11F-d-2 0.44 275,995F-e-1 0.46 363,221 337,811 342,599 1.01F-e-2 0.34 312,401W-d-1 0.50a 386,025 372,291 399,349 1.07W-d-2 0.50a 358,557W-e-1 0.50a 388,938 372,854 409,854 1.10W-e-2 0.50a 356,770Mean 1.08Coefficient of variation 0.045aAssumed adhesive thickness.

Fatigue cycles (million)

0.00 0.09 0.18 0.27 0.36 0.45

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Weld sideFlat side

Fig. 5. Comparison of crack propagation between weld side and flat side: (a) specimen F-d; (b) specimen W-d


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Fig. 6. Comparison of N − a curves between BEASY results and test data: (a) bare plate; (b) specimen F-a; (c) specimen F-b; (d) specimen F-c;(e) specimen F-d; (f) specimen F-e; (g) specimen W-d; (h) specimen W-e


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This study also revealed that the simulated final crack lengths ofspecimens F-a, F-b and F-c were comparatively small, because theCFRP laminate was applied on the flat side and close to the crackinitiation in these three specimens. The existence of secondarybending had a considerable effect on the crack propagation andmade the variation of the crack propagation from one side tothe other more severe, thereby resulting in an early terminationof the fatigue crack propagation analysis.

Effect of Retrofitting Configuration

In the test program of Wu et al. (2013), all specimens were repairedwith CFRP laminates on a single side. Because the fatigue crackpropagation of the strengthened steel plates with longitudinal weldattachments could be estimated with reasonable accuracy by theboundary element model, a double-sided strengthening configura-tion was adopted in our work to investigate the influence ofthe retrofitting scheme on fatigue behavior. Only configurationsd and e were suitable for double-sided strengthening attributableto geometric limitations, as presented in Table 4, where D indicatesthat the composite materials were attached on both sides of a speci-men. The bond region is shown in Fig. 2, and the thickness of theadhesive layer was set as a constant at 0.5 mm.

Fatigue Life Analysis

The fracture analysis was performed based on BEASY’s FractureAnalysis Wizard. Fig. 7 illustrates the relationship between therepair scheme and the improvement in fatigue life. In this figure,Np−CFRP is the fatigue crack propagation life of a specimenstrengthened with CFRP, whereas Np−plate is the fatigue crackpropagation life of a bare steel specimen. The specimens strength-ened with configuration e always performed better than thosestrengthened with configuration d, which was consistent withthe test results.

Moreover, the effect of bond location appeared to be moreevident in the double-sided repair cases compared with that insingle-sided retrofitted specimens. Therefore, it is concluded thatit is better to position the composite materials as close to the crackinitiation as possible, particularly for double-sided strengthenedspecimens.

It should be noted that single-sided strengthening, especiallywhen applied on the flat side, only led to very limited improvement;however, a considerable extension of the fatigue life was achievedwith double-sided strengthening. The fatigue life of the configura-tion d bonded specimen was extended by 3.2 times through double-sided repair, whereas the single-sided repair on the flat side onlyprolonged the fatigue life by 1.2 times.

Specimen F-a results lead to the conclusion that, when narrowCFRP strips are applied on both sides far away from the initial slot,the strengthening effect is much more pronounced compared withthat of a specimen where the whole surface of the flat side iscovered.

Wu et al. (2013) also conducted a series of fatigue tests onnonwelded steel plates strengthened by ultra-high modulus CFRPlaminates on a single side to compare the fatigue life extensionratios of both welded and nonwelded specimens. The geometry anddimensions of the steel plates (without a weld attachment), fatigueloading, and test setup were all the same as those of the weldedconnections.

The fatigue crack propagation processes of nonwelded steelplates were correspondingly analyzed using the boundary elementmethod, which is similar to the fatigue life prediction reported in Yuet al. (2014b), where more details can be obtained. The calculatedfatigue life extension ratios of specimens with configurations d ande are compared in Fig. 8, which indicates that the fatigue life ex-tension ratio of a single-sided strengthened welded specimen wassignificantly lower than that of a nonwelded specimen with thesame strengthening configuration. However, the difference wasconsiderably less between welded and nonwelded specimens usingthe double-sided strengthening system.

Taking repaired configuration e specimens as an example, thefatigue extension ratio of the single-sided strengthened weldedplate (F-e) was lowered by 121% of that of the nonwelded speci-men with the same strengthening configuration. However, for thedouble-sided strengthened cases, the difference between the weldedand nonwelded specimens was only 38%. It is also worth noting

Table 4. Double-Sided Strengthened Specimens

Specimen Bond regionBond length

(mm)Bond width

(mm) Repair side

D-d d1; d2; d3; d4 250 25 × 2 Double sidesD-e e1; e2; e3; e4 250 25 × 2 Double sides

Repair scheme

Np-

CF

RP/N

p-pl

ate

0

1

2

3

4

5

Configuration a, b, cConfiguration dConfiguration e

Flat side Weld side Double sides

F-a

F

-b

F-c

Fig. 7. Fatigue propagation life improvement versus repair scheme

Repair scheme

Np-

CF

RP/N

p-pl

ate

0

1

2

3

4

5

Non-welded plateWelded plate

S-eS-d D-d D-e

F-d

W-d

F-e

W-e

Fig. 8. Comparison of the fatigue life extension ratios with double-sided strengthened specimens


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that the extension ratios of the welded joints were always less thanthose of the nonwelded plates. This may be attributed to the neg-ative effect of the attached gusset plate. Further studies are requiredto determine the effect of the gusset plate.

Fatigue Crack Propagation Analysis

Fig. 9 shows the beach marks on the fracture surfaces extractedfrom the numerical data of configuration d strengthened specimens.Only half of the cross section is displayed, because of the symmetrywith the width direction. The horizontal axis represents the platewidth from the center to the edge, and the vertical axis representsthe plate thickness. The first vertical line indicates the artificial slot.

The general trend of the crack propagation was found to be con-sistent with the beach marks recorded during the test program. Inthe plain welded plate without strengthening, the crack on the weldside propagated slightly faster than on the flat side because of thestress concentration resulted from the weld attachment. After retro-fitting the flat side, the difference in crack propagation between theweld and flat sides appeared much more considerable, as shown inFig. 9(b). The application of the CFRP laminate moved the neutralaxis of the specimen, thus accelerating the crack growth on theweld side.

Moreover, the composite materials supplied a bridge effect onthe crack surface, which restrained the crack propagation of the flatside. Although the attached composite materials helped to share thefar field loading, the positive effect was partly counteracted by theexistence of secondary bending. This also explains why only verylimited improvement was achieved by attaching the CFRP laminateon the flat side. However, specimen W-d with overlay on the weldside appeared to have the crack on the flat side propagate faster thanthe crack on the weld side. It should be noted that the crack frontson both sides in specimen D-d were more likely to grow synchro-nously, and very little difference was observed at the early stage.The arrest phenomenon was attributed to the constraint effect of theCFRP laminates.

Fig. 10 compares crack lengths on both the flat and weld sides ofspecimens with different repair schemes versus the fatigue cycles.This figure indicates that crack propagation on both the flat andweld sides was significantly slowed for the double-sided strength-ened specimen in comparison with that of the single-sided repair.Therefore, this study recommends the adoption of double-sidedstrengthening whenever possible.

This study’s conclusion on the superiority of double-sidedstrengthening does not agree with the results of Chen et al. (2014).Their examination of nonload carrying welded joints showed

Plate width-weld side (mm)

0 5 10 15 20 25 30 35 40 45

Thi

ckne

ss (

mm

)

0

5

10

Plate width-flat side (mm)0 5 10 15 20 25 30 35 40 45

Plate width-weld side (mm)

0 5 10 15 20 25 30 35 40 45

Thi

ckne

ss (

mm

)

0

5

10


Plate width-weld side (mm)0 5 10 15 20 25 30 35 40 45

Thi

ckne

ss (

mm

)

0

5

10


Plate width-weld side (mm)0 5 10 15 20 25 30 35 40 45

Pla

te th

ickn

ess

(mm

)

0

5

10


Fig. 9. Beach marks on the fracture surfaces from the numerical simulation: (a) bare specimen; (b) specimen F-d; (c) specimenW-d; (d) specimen D-d


0.0 0.2 0.4 0.6 0.8 1.0

Hal

f cra

ck le

ngth

'a' (

mm

)

0

(a) (b)

5

10

15

20

25

30

35

40

45

F-dW-dD-d


0.0 0.2 0.4 0.6 0.8 1.0

Hal

f cra

ck le

ngth

'a' (

mm

)

0

5

10

15

20

25

30

35

40

45

F-dW-dD-d

Fig. 10. Comparison of N − a curves of specimens with different repair schemes: (a) flat side; (b) weld side


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single-sided repairs on cracked surfaces to be more effective thandouble-sided retrofitting. This may be attributed to different cracktypes and crack propagation directions.

Effect of Longitudinal Weld Attachment

In comparison with nonwelded steel plates, the weld attachment ina single-sided welded joint resulted in stress concentration on theweld side, thus leading to unsymmetrical crack shapes. To furtherexamine the effect of weld attachments, steel plates with longitu-dinal welded attachments on both sides were analyzed, and the de-tails are listed in Table 5. Similar to the cases with double-sidedrepairs, only configurations d and e were considered because ofgeometric limitations. Considering the symmetry of the specimenwith attachments on both sides, S was used to indicate that thecomposite material was attached on a single side of the specimen.The bond region is shown in Fig. 11.

Fatigue Life Analysis

The fatigue cycle numbers of single-sided welded specimens com-pared with double-sided welded specimens with different repairschemes are shown in Fig. 12. This figure shows that the double-sided welded joints resulted in shorter fatigue lives than those ofsingle-sided welded joints.

A comparison of the fatigue life extension ratios was also con-ducted for double-sided welded plates. Fig. 13 shows the ratio ofNp−CFRP to Np−plate against the repair scheme. The general trend of

(a)

(b)

e1e3

e2e4

25

250

25

25

25

250

25

d1d3

d2d4

25

25

25

Fig. 11. Configuration of double-sided welded specimens (unit: mm, not to scale): (a) configuration d; (b) configuration e

Table 5. Double-Sided Welded Specimens

SpecimenBondregion

Bondlength(mm)

Bondwidth(mm) Repair side

Bare plate(double-side welded)

N/A N/A N/A N/A

S-d (double-side welded) d1; d2 250 25 × 2 Single sideS-e (double-side welded) e1; e2 250 25 × 2 Single sideD-d (double-side welded) d1; d2; d3; d4 250 25 × 2 Double sidesD-e (double-side welded) e1; e2; e3; e4 250 25 × 2 Double sides

Repair scheme

Fat

igue

cyc

les

(mill

ion)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Single-sided welded plateDouble-sided welded plate

Non S-d S-e D-d D-e

F-d

W-d

F-e

W-e

Fig. 12. Fatigue cycles of single- and double-sided welded specimens


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the double-sided welded plates appeared consistent with the single-sided welded plates. In comparison with the nonwelded steel plate,the difference in the fatigue life extension ratios between theapplications of single- and double-sided repairs was especially sig-nificant. Single-sided strengthening for double-sided welded jointshad only reached a very limited strengthening effect; however, itwas possible to extend their fatigue lives by 3.3 and 4.4 times withdouble-sided strengthening of configurations d and e, respectively.The extension ratio was approximately that of the nonwelded plate.

The slight reduction of the corresponding data for the single-sidedwelded plate was considered to be associated with the unsymmet-rical specimen geometry.

Fatigue Crack Propagation Analysis

Crack propagation with fatigue cycles of specimens with single- ordouble-sided weld attachments is presented in Fig. 14. For simplic-ity, the vertical axial in Fig. 14 represents half of the crack length onthe centerline of the plates. The results of the bare plate withoutstrengthening, single-sided repair on the flat side, single-sided re-pair on the weld side and double-sided strengthening are illustrated.It is noted that there was only one case of a single-sided repair forspecimens with double weld attachments. It is clearly shown fromthe figure that the crack propagation in the double-sided weldedspecimen was faster than that of the single-sided welded specimen,resulting in a shorter fatigue life and indicating that the existence ofthe additional gusset plate accelerated the crack propagation.

Effect of CFRP Modulus

In Wu et al. (2013), ultra-high modulus CFRP laminates with anelastic modulus of 460 GPa were utilized in the test program.Although high modulus composite materials are considered tobe more effective in most applications, these materials are still notwidely employed in practice. Therefore, normal modulus CFRPlaminates with a modulus of 210 GPa were considered in this studyto evaluate the effect of the CFRP stiffness.

Fig. 15 shows the ratio of the specimen’s fatigue life with ultra-high modulus CFRP laminate to that of the specimen with normal

Repair scheme

Np-

CF

RP/N

p-pl

ate

0

1

2

3

4

5

Non-welded plateDouble-sided welded plateSingle-sided welded plate

S-d S-d D-d D-e

F-d

W-d

F-e

W-e

Fig. 13. Comparison of the fatigue life extension ratios with double-sided welded specimens


0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Hal

f cra

ck le

ngth

'a'

0

(a) (b)

(c) (d)

5

10

15

20

25

30

35

40

45

Single-sided weldedDouble-sided welded


0.0 0.1 0.2 0.3 0.4 0.5

Hal

f cra

ck le

ngth

'a' (

mm

)

0

5

10

15

20

25

30

35

40

45

Double-sided weldedSingle-sided welded


0.0 0.1 0.2 0.3 0.4 0.5

Hal

f cra

ck le

ngth

'a' (

mm

)

0

5

10

15

20

25

30

35

40

45



0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Hal

f cra

ck le

ngth

'a' (

mm

)

0

5

10

15

20

25

30

35

40

45


Fig. 14. Comparison of N − a curves between single- and double-sided welded specimens: (a) bare plate without strengthening; (b) single-sidedstrengthening (flat side, F-e); (c) single-sided strengthening (weld side, W-e); (d) double-sided strengthening (D-e)


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modulus CFRP laminate. In this case, Np−CFRP;H was the fatiguecrack propagation life of a specimen strengthened with ultra-highmodulus CFRP laminates, whereas Np−plate;N was the fatigue crackpropagation life of a specimen strengthened with normal modulusCFRP laminates. Both the single- and double-sided welded plateswere discussed.

Fig. 15 shows that only limited improvement was achieved byusing ultra-high modulus CFRP laminates for single-sided repair,whereas the fatigue life was extended by 174–186% for the double-sided strengthened specimens when the CFRP modulus increasedfrom 210 to 460 GPa. It is noteworthy that the fatigue life of speci-men F-a was even longer with lower modulus CFRP laminate. Thisis related to the fact that higher modulus CFRP laminate leads tomore severe secondary bending, especially for specimen F-a, whichhad the largest cross section of CFRP laminate. Therefore, it isrecommended, that if double-sided strengthening is available, itis better to utilize high modulus CFRP laminate to improve thestrengthening effect. However, for single-sided repair, the improve-ment of CFRP stiffness is not considered to be of great significance.

Conclusions

In this paper, the boundary element method was employed to in-vestigate the fatigue crack propagation of steel plates with longi-tudinal weld attachments strengthened with CFRP laminates undertension. Three-dimensional boundary element models were estab-lished based on the configurations of the reference test specimens.The method was validated with good agreement between thenumerical results and the experimental data. The influence ofdouble-sided strengthening, double-sided weld attachment andCFRP laminate modulus on the fatigue behavior of strengthenedwelded joints was then examined. The following conclusions havebeen drawn:• The boundary element method is well suited for simulating the

fatigue behavior of CFRP-bonded steel plates with longitudinalweld attachments. The crack propagation variation from oneside to the other was also revealed.

• Double-sided repair was more efficient. The single-sidedwelded plate with a composite patch of limited width appliedfar away from the initial crack on both sides performed muchbetter than single-sided repair with the composite materials cov-ering the whole surface of the flat side. Moreover, double-sided

application was shown to effectively provide a constraint effectto the crack propagation.

• In double-sided welded joints, the additional weld attachmentaccelerated the crack propagation and led to a shorter fatiguelife compared with the single-sided welded joints.

• In terms of the fatigue life extension ratio, the retrofitting effi-ciency was significantly lower in welded joints repaired on asingle side compared with steel plates without a weld attach-ment; whereas only a slight difference was observed for double-sided repaired welded joints. Moreover, the effect of the bondlocation on the fatigue behavior of strengthened specimenappeared more evident in cases of double-sided strengthening.

• The modulus of the CFRP laminate had a considerable influenceon the specimens with composite materials attached on bothsides. For the single-sided strengthened specimens, the im-provement of the fatigue behavior by using ultra-high modulusCFRP laminates was limited.

• This study extends the understanding of CFRP-repaired steelplates with longitudinal weld attachments and provides someuseful suggestions for the strengthening method. More experi-mental study is planned for the future to validate the extendednumerical analysis and investigate the negative effect of theweld.

Acknowledgments

This project was supported by the National Natural ScienceFoundation of China (50808139), the Fundamental Research Fundsfor the Central Universities and Kwang-Hua Fund for College ofCivil Engineering, Tongji University, ARC Discovery Grant(DP120101708) and National Key Basic Research Program ofChina (973 Program, 2012CB026200). Thanks are extended toDr. Sharon Mellings from Computational Mechanics BEASYLtd. for her help with the numerical modeling and Dr. Chao WufromMonash University for providing the test data. The first authorwishes to thank the China Scholarship Council and MonashUniversity for sponsoring her research at Monash University.

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Np-

CF

RP

, H/N

p-C

FR

P, N

0.0

0.5

1.0

1.5

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Single-sided welded plateDouble-sided welded plate

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boundary element analysis of fatigue crack growth for cfrp … paper 9... · 2015. 5. 15. ·...

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