Mir Ali GhaffariDepartment of Mechanical and

Industrial Engineering and

Center for Computer-Aided Design,

The University of Iowa,

Iowa City, IA 52242

e-mail: ali-ghaffari@uiowa.edu

Hossein Hosseini-Toudeshky

Professor

Fatigue and Fracture Laboratory,

Amirkabir University of Technology,

Tehran, Iran

e-mail: hosseini@aut.ac.ir

Fatigue Crack PropagationAnalysis of Repaired PipesWith Composite PatchUnder Cyclic PressureThe pipes in offshore and marine structures are mainly made of low-strength structuralsteels such as A537 steel and are subjected to the effects of both corrosive medium andcyclic loading caused by many factors. Reinforcement and repair of components usingcomposite patches can be used for piping to reduce the stress intensity factors at thecrack-front of a corrosion fatigue crack. In this paper 3D finite element analyses in gen-eral mixed-mode fracture condition are performed to study the crack growth behavior ofrepaired pipes subjected to internal cyclic pressure. The required formulations, crackgrowth modeling, and remeshing are automatically handled by developing an ANSYS para-metric design language (APDL) program. For this purpose an offshore pipe made of low-strength steel containing an initial fatigue corrosion crack repaired by glass/epoxy com-posite patch is considered. A parametric study will be performed to find the effects ofpatch thickness on fatigue crack growth life extension and crack-front shape of therepaired pipes. [DOI: 10.1115/1.4023568]

Keywords: cyclic pressure, pipes, fatigue, repair, composite, crack growth

1 Introduction

There are many types of pipes and pressure vessels in differentindustries such as offshore engineering, gas and oil transmission,power plants, and refineries subjected to cyclic loadings such asvariation of internal pressure and/or external loadings. These com-ponents have to be capable of withstanding fatigue damages intheir safe life. Corrosion may also occur on the internal and/orexternal surface of these components due to their environmentalworking conditions. Previous studies mainly focused on the esti-mation of plastic collapse load or creep behavior of pipes contain-ing these kind of corrosion effects, and also fatigue phenomena inpipes with flaws have been examined during recent decades. Afew investigations have been undertaken on internally pressurizedpipes with longitudinal surface cracks [1–4], and research workshave also been performed on circumferential flaws in hollow cyl-inders under tension and bending loading [5,6].

Generally, fatigue crack growth behavior of notched compo-nents depends on the state of stress at the notch front, geometry ofthe component, shape and size of the notch, and loading condi-tions. Standard tests for measurement of fatigue crack growth ratehave been performed significantly using compact tension or threepoint bend specimens following ASTM E647 [7]. The mode-I fa-tigue crack growth under pulsating internal pressure is examinedthrough a theoretical model based on the Paris law, by assuming asemielliptical shape for the crack-front during the propagation pe-riod by Carpinteri et al. [8,9]. They also numerically simulated thefatigue growth of a circumferential external surface flaw in athick-walled round pipe subjected to rotary bending and comparedthe results with those for cyclic bending. Ivankovic and Venizelos[10] performed a finite volume method for modeling of crackpropagation in fluid pressurized plastic pipes. They compared theresults with experiments and realized that results with backfillshowed an increase in critical pressure. External axial surfaceflaws in metallic round thick- and thin-walled pipes have been

examined by Brighenti [11]. In this study, a two-parameter theo-retical model has been employed for the analyses of fatiguegrowth of such longitudinal surface defects under a pulsating in-ternal pressure. Yeon-Sik et al. [12] have also performed fatiguecrack growth studies on full scale piping components. Crackgrowth studies on through-wall cracked pipes in terms of initiationof fracture toughness and the fracture resistance curve (J–R) havebeen studied in Refs. [13,14] for explaining the integrity of pipingcomponents. Singha et al. [15] presented a systematic study todetermine the fatigue crack initiation, fatigue crack growth rate,and fracture resistance behavior of pipes to demonstrate the satis-faction of the leak-before-break (LBB) design criterion. Shahaniand Fasakhodi [16] demonstrated FEM analysis based on theremeshing technique to predict the dynamic crack propagationand crack arrest in a brittle material. In this method, an extremelyrefined mesh near the crack region and a large amount of compu-tational work are required. Ayatollahi and Khoramishad [17,18]compared the stress intensity factors resulting from a two-dimensional analysis of similar cracks in plane strain conditionwith those of the deepest point in the three-dimensional crackmodel. They also calculated the stress intensity factors of externalsemielliptical cracks in a buried pipe. Moreover, they determinedthe mode-I and mode-II stress intensity factors KI and KII for aninternal crack in a pipe buried in the soil. Their results, whichwere presented in nondimensional forms, can be used for evaluat-ing the load bearing capacity of cracked buried pipes.

Composite patches have been used to repair damaged pipelinesfor a long time. The majority of these works involved the repair ofonshore pipelines subjected to corrosion fatigue cracks. Onshorepipelines are typically concerned with circumferential stressesassociated with internal pressure. Repairing the pipes with com-posite patch involves the restoration of hoop strength. Review ofthe open literature demonstrates addressing of this stress state asthe primary focus of research efforts up to now [19–23]. Addition-ally, mechanical damage such as pitting has been repaired bycomposite materials [24,25]. Information available to industry ismainly based on the results of several research programs thatintegrated composite coupon tests, as well as full-scale burstand fatigue testing on pipelines with simulated damage. An

Contributed by the Pressure Vessel and Piping Division of ASME for publicationin the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 21,2012; final manuscript received February 1, 2013; published online May 21, 2013.Assoc. Editor: Saeid Mokhatab.

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experimental and theoretical fatigue crack propagation analysis ofsteel pipes, each with an inclined semielliptical crack, subjectedto tensile stress was performed by Bian et al. [26] and recently theuse of an optical dynamic 3D displacement analysis technique toevaluate the crack propagation in a threaded pipe assembly waspresented by Van Wittenberghe et al. [27] The ASME codes forgas (ASME B31.8) and liquid (ASME B31.4) pipelines addressthe use of composite materials [28,29]. More recently, ASMEdeveloped a document focused on the repair of pressure equip-ment [30].

However, it is well known that during the extrusion of a pipe,numerous local defects and inclusions can be produced. In service,the combination of these factors under loading condition (internalpressure) and the environmental effect (humidity, temperature,and time) tends to reduce significantly the lifetime of these com-ponents. The pipes in offshore and marine structure are mainlymade of low-strength metals such as A537 steel subjected to theeffects of both corrosive medium and cyclic loading caused bymany factors. Therefore, failure of these pipes may occur due tothe corrosion fatigue cracking. Prevention of a catastrophic failureand fatigue life extension of such cracked pipes is possible using aproper repair technique. Reinforcement and repair of componentsusing composite patches is a well-known technique in civil andaerospace engineering. It can be used for piping to reduce thestress intensity factors at the crack-front of a corrosion fatiguecrack. After performing a proper repair by composite patch, themain issue is estimation of fatigue crack growth life of therepaired components. For this purpose it is required to performcrack growth analyses, including both crack trajectory and crackgrowth rate analyses for a 3D medium (repaired pipe). In this pa-per an automatic procedure using the APDL feature of ANSYScode is adapted to handle 3D finite element analyses for bothcrack trajectory and crack growth rate of repaired pipes subjectedto internal cyclic pressure. For this purpose an offshore pipe madeof low-strength steel containing an initial fatigue corrosion crackrepaired by glass/epoxy composite patch is considered. A para-metric study will be also performed to find the effects of patchthickness on fatigue crack growth life extension and crack-frontshape of the repaired pipes.

2 Computational Fracture Analysis

Figure 1 shows a typical geometry and loading of the repairedcracked pipe containing one side through the thickness crack.Having the displacement and stress fields around the crack-front,fracture parameters such as KI, KII, and KIII are calculated, andthen they are used to predict the new fatigue crack-front shape,crack propagation path, and crack growth life of the repaired stiff-ened panels. Linear elastic fracture mechanics (LEFM) assump-tions are used for the analyses. It is also presumed that the crackswill grow in the pipe only and there is no debonding between thepatch and the panel. The computational fracture analyses arebased on the calculation of strain energy release rates (SERRs) by

the aid of the modified virtual crack closure technique (MVCCT)to obtain the local SERR along the crack-front.

The stress intensity factor is calculated from the stress statenear the crack-front. For obtaining the stress intensity factor, it ismore convenient to evaluate that in terms of energy release rateG, with crack extension. By assuming a virtual crack extension(Da) and estimating the variation in strain energy, at any cracklength, strain energy release rate can be obtained. The basic for-mulations for fracture analyses and crack growth of repaired pan-els in general mixed-mode condition are fully explained byHosseini-Toudeshky et al. in [33–36]. The same formulation andprocedure are adapted for repaired pipes here. The calculationprocedure in the virtual crack closure technique (VCCT) is per-formed in two stages. In the first step, the internal nodal forces arecomputed at the crack-tip Fj and in the second step the crack isextended for a value of Da and the analyses are performed to cal-culate the displacements at nodes j and j*, which have been coin-cided before crack growth. For a crack-front modeling using thethree-dimensional eight-node elements (Fig. 2(a)) the energyrelease rates are calculated as follows:

Fig. 1 Typical geometry and loading of a repaired pipes

Fig. 2 (a) Modified crack closer technique for an eight nodessolid element; (b) crack deflection angles u0 and w0 for a gen-eral mixed-mode condition [35]

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GI ¼1

2DAFi

yðujy � uj�

y Þ

GII ¼1

2DAFi

xðujx � uj�

x Þ

GIII ¼1

2DAFi

zðujz � uj�

z Þ

(1)

Considering Fig. 2(a), DA¼ b�Da, b is the element thickness atz direction and GI, GII, and GIII are the energy release rates formodes I, II, and III, respectively. Then the stress intensity factorscan be computed from the following relations:

KI ¼ffiffiffiffiffiffiffiffiffiE0GI

pKII ¼

ffiffiffiffiffiffiffiffiffiffiffiE0GII

pKIII ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi2lGIII

p (2)

where E0 is the modulus of elasticity, and E0 ¼E for plane stresscondition and E0 ¼E/(1��2) for plane strain condition problemsand l and � are the shear modulus of elasticity and Poisson’s ra-tio, respectively.

For three-dimensional general mixed-mode problems the crite-ria of Richard et al. [31] have been used for crack growth analy-ses. Richard’s criteria suggested an equivalent stress intensityfactor that depends on the stress intensity factors in variousmodes. In this generalized fracture criterion, an equivalent stressintensity factor Keq is defined comparable with the equivalentstress, req, for multiaxial stress failure criterion in classical stresstheories, which relates to the stress intensity factors KI, KII, andKIII as follows:

Keq ¼KI

2þ 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK2

I þ 4ða1KIIÞ2 þ 4ða2KIIIÞ2q

(3)

where a1¼KIc/KIIc, a2¼KIc/KIIIc, and KIc, KIIc, and KIIIc are frac-ture toughness in various fracture modes. Deflection angles at anypoint of the crack-front are defined by u0 and w0 as typicallyshown in Fig. 2(b) and they can be calculated by the followingrelations [31].

/0 ¼ 6 AKIIj j

KI þ KIIj j þ KIIIj j þ BKIIj j

KI þ KIIj j þ KIIIj j

� �2" #

(4)

w0 ¼ 6 CKIIIj j

KI þ KIIj j þ KIIIj j þ DKIIIj j

KI þ KIIj j þ KIIIj j

� �2" #

(5)

where the conditions of u0< 0 deg and w0< 0 deg have to be sat-isfied for KII> 0 deg and KIII> 0 deg, respectively. u0> 0 deg forKII< 0 and KI� 0 and also w0> 0 deg for KIII< 0 and KI� 0.Considering the values of A, B, C, and D parameters to be140 deg, �70 deg, 78 deg, and �33 deg, respectively, the resultsof Eqs. 5 and 6 agree well with the crack deflection angles pre-dicted by the Shollman criterion [31]. Another ingredient to calcu-late the fatigue crack growth is definition of a law relating thecrack length to the loading cycles. For this purpose the well-known Paris law is used as follows:

da

dN¼ cðDKÞm (6)

In general mixed-mode condition DK can be substituted by theeffective stress intensity factor range DKeq according to thatexplained in Eq. (3). The values of a1¼ 1.155 and a2¼ 1 are usedin this equation. The values of a1¼ 1.155 and a2¼ 1 are used inthis equation according to the Richard’s study to obtain an excel-lent approximation of the fracture limit curve of the maximumtangential stress criterion [31]. Having the crack growth rate andorientation, the position of each point at the new crack-front in thelocal polar coordinates (Da, u0, w0) is determined. Then the pro-jection of each point of the new crack-front in the local rectangu-lar coordinates is determined to find the components of Da in theX, Y, and Z directions. More details of this procedure can befound in Refs. [33,35].

3 Finite Elements Analysis

The considered repaired pipes as typically shown in Fig. 1 aremade of ASTM A537steel, the patch material is glass/epoxy com-posite, and the adhesive material is FM-73. Material properties ofthe steel pipe, adhesive, and composite patch are given in Table 1.The advantages of glass/epoxy repairs compared to graphite/ep-oxy and boron/epoxy composites are the cost, availability, andmore compatible thermal coefficient with the steel pipe. It wasshown in Hosseini-Toudeshky et al. study [36] that low curingtemperatures with long curing cycles did not have a considerableeffect on fatigue crack-growth life of the repaired panels withglass/epoxy patch and had minor effects for repaired panels withgraphite/epoxy and boron/epoxy composite patches. It was alsoshown that considering the thermal residual stresses, the obtainedFEM fatigue life, and crack-front shapes of the repaired panelsusing glass/epoxy patch are in good agreement with thoseobtained from the experiments. Fatigue crack propagation tests onsteel A537 at room and lower temperatures were partly reportedin a previous study and are presented in Fig. 3 [32]. The stable fa-tigue crack propagation in A537 steel follows the Paris law, butthe Paris exponent m varies with temperature, presenting a muchlarger value at lower temperatures. The material constants in theParis equation were calculated based on the ASTM E-647 methodfor T¼ 273 K and leads to m¼ 2.8578 and C¼ 6� 10�12.

Table 1 Material properties of glass/epoxy patch, ASTM A537 steel, and adhesive

Elasticity modulus (GPa) Shear modulus (GPa) Poisson’s ratio Elasticity modulus (GPa) Poisson’s ratio

Glass/epoxy [35] E11 27.82 G12 2.56 t12 0.31 ASTM A537 steel [38] E 192 t 0.3E22 5.83 G13 2.56 t13 0.31E33 5.83 G23 2.24 t23 0.41 Adhesive FM-73 [35] E 1.83 t 0.33

Fig. 3 Fatigue crack growth rates for A537 steel in various tem-peratures [32]

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In the three-dimensional analysis, an isotropic eight-node-solidelement (SOLID45) was used to model the steel pipe and adhesivelayer. Furthermore, a layered eight-node-solid element (SOLID46)was used to model the composite patch. Figure 4 shows a typicalused FEM mesh of the component. In these analyses a fine meshwas generated near the crack, eight elements along the pipe thick-ness, two elements along the adhesive thickness, and two elementsalong the patch thickness were used. Distribution of elements alongthe thickness are shown in Fig. 4(a) and overall meshing from out-side view of a repaired pipe in the last steps of crack growth analy-ses is shown in Fig. 4(b).

A small debounded area equal to the element size at the crackedges has been considered in the FEM modeling. This is neces-sary for FEM modeling and it is almost compatible with experi-mental evidence [34]. The stress and strain fields of the repairedpipes were obtained using the elastic solution of ANSYS finiteelement program. A macro program using ANSYS parametricdesign language (APDL) was also developed to conduct the auto-matic crack growth modeling process.

In this program, after finite element modeling of the repairedpipe with the initial crack size, a crack propagation procedureusing the recursive method has been developed. At each crackgrowth increment a three stage modeling for the crack-front isrequired [36]. In this procedure, an elastic solution is performedfor the repaired pipe with the existing crack configuration. In addi-tion, the incremental crack length at each point of the crack-frontis calculated based on the obtained three stress intensity factorsand DKeq values, crack growth direction angles, Paris law, and theassumed crack increment size at the unpatched surface of thepipe. For doing this, after calculation and comparing of DKeq forall crack tip nodes through the thickness, the biggest DKeq isselected and then by putting this DKeq to Paris law and consider-

ing assumed 0.8 mm maximum crack increment, the fatigue cyclesamount necessary for 0.8 mm crack growth is obtained. After-ward, having this cycle amount, which is calculated based on maxDKeq, the increments of the other crack tip nodes based on theirown DKeq are calculated. By considering an assumed small crackincrement at the unpatched side of the repaired pipe the corre-sponding required load cycles (DN) can be calculated from theParis law. Having DN and the values of stress intensity factors atthe crack-front nodes, the ratio of crack growth at each node withrespect to the considered increment at the unpatched side and itsdirection are calculated. It is noted that each increment may con-tains the X-, Y-, and Z-coordinate values for each node. Displace-ments of crack tip nodes should be calculated on their own X-Yplane without moving in the Z direction. For doing this, after find-ing the increments of crack tip nodes in X-, Y-, and Z-coordinatethe new positions of the points are calculated by the linear interpo-lation of each of the two nearest points to obtain a three-dimensional new crack-front shape in the second step. The proce-dure is exactly explained in Ref. [36].

To create a new crack-front, the obtained points are rearrangedalong the thickness of the pipe right at the crack-front. In thesecond step, the new positions of the considered points at thecrack-front are calculated by the linear interpolation of each twoneighboring points to obtain a three-dimensional new crack-frontshape. In the third step, new mesh of the repaired pipe is con-structed using the updated crack-front geometry. This procedureis repeated for each crack growth increment. The main steps ofthe developed APDL program to perform the automatic 3D crackpropagation procedure are as follows [33,35]:

(i) geometry and finite element mesh generation ofrepaired pipe

Fig. 4 Typical FEM mesh, (a) distribution of elements along the thickness, (b) overall meshingfrom outside view

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(ii) defining of loading, constraints, and materialproperties

(iii) performing a linear elastic solution(iv) calculation of nodal forces and nodal displacements

at crack-front in three directions(v) calculation of GI, GII, and GIII and then KI, KII and

KIII at crack-front using modified crack closure tech-nique (Eqs. (1) and (2))

(vi) calculation of crack deflection angles uo and wo atvarious points of crack-front

(vii) calculation of Keq at various pints of crack-front usingEq. (3)

(viii) considering 0.8 mm crack increment at unpatched sur-face at each increment and calculating the corre-sponding load cycles (DN) using the Paris law

(ix) having DN and values of KI, KII, and KIII at crack-front nodes the ratio of crack growth at each nodewith respect to the 0.8 mm growth at the unpatchedsurface are calculated and the new crack-front shapeis generated as explained above

(x) construction of new geometry of repaired pipe withnew crack-front shape

(xi) updating the finite element model based on the newcrack length and the crack-front configuration

Fig. 5 (a) Half section of cracked pipe repaired by composite patch lay-up of [90]4that clearly shows crack trajectory and crack front shape; (b) fatigue crack-frontevolution and type of meshing for repaired pipes with patch lay-up of [90]2

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(xii) If Keq�KIc or crack length at the unpatched surfaceis less than a defined value, return to step (iii)

(xiii) process the results and stop the solution.

A sensitivity study on crack increment size was also performed.For the virtual crack closure technique, the energy release ratesare defined as the virtual crack closure integral over a finite crackclosure length. This crack closure length corresponds to thelengths of the elements adjacent to the crack front. This elementlength a must be chosen to be small enough to assure a convergedFE solution but large enough to avoid oscillating results. Theapproach used must be consistent with the definition of the energyrelease rates used for fracture predictions as well as that employedfor material characterization. This does not imply that the materialtests must be evaluated by FE-models, but it should be establishedthat the data reduction scheme is in agreement with the definitionof a finite crack closure length. Consequently, it has been sug-gested to use element lengths at the crack tip in such a mannerthat the computed results are insensitive to the variation of the ele-ment length a at the crack tip as Krueger [37] recommends con-sidering a Da/h value between 0.01 and 0.1 for this purpose. Da isthe element’s length and h is the thickness of the cracked panel.

It was seen that for the increment sizes of larger than 0.8 mm,the obtained crack fronts and crack trajectories were not smoothlypredicted. In the meanwhile we did not see significant differencesbetween the results (crack-front, trajectory, and life) obtained forvalues smaller than 0.8 mm.

Figure 5(a) presents a half section of cracked pipe for clearlyshowing the crack trajectory and crack-front shape after a certaincrack growth of the repaired pipe. In this figure initial crack and

crack trajectory are shown for half of the cracked pipe. It alsoshows the crack-fronts and fine meshing around the crack tips.This figure shows that the crack growth path is almost parallel tothe straight side of the pipe. This is due to the loading conditionand the significant values of circumferential stresses. The crack-front configuration and updated mesh at three different crackincrements for the repaired pipe with the patch lay-up of [90]2 areshown in Fig. 5(b). The half section of the repaired pipe is shownhere to be able to observe the crack-front in the pipe thicknessclearly. As the crack length and crack-front are changed accordingto the described calculation procedure, the mesh distribution isalso changed considering the crack trajectory and new crack-frontshape at each step.

4 Results and Discussions

To verify the developed FEM procedure, the predicted crackgrowth behavior of an unrepaired plain panel without stiffener

Fig. 6 Comparison between the predicted crack growth behav-iors with experimental results of Ref. [34]; (a) unrepaired panel,(b) results at unpatched surface of repaired panel with patchlay-up of [105]4

Fig. 7 Variation of stress intensity factors along the initialcrack-front (Da 5 0) for various patch layers, (a) KI, (b) KII, and(c)KIII

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and containing a 45 deg central inclined crack shown in Ref. [34]is compared with the available experimental results [34] in Fig.6(a). The predicted crack growth behavior is also obtained for thesame panel with a single side composite repair of [105]4 glass/ep-oxy and compared with the experimental results in Fig. 6(b).These figures show a good agreement between the experimentaland the predicted finite element results indicating the verificationof FEM analyses for crack propagation modeling.

Figure 7 shows the variations of stress intensity factors (KI, KII,and KIII) along the initial crack-front for the unrepaired andrepaired pipes with various patch layers before the occurrence of

any crack growth. Figures 7(b) and 7(c) indicate that the values ofKII and KIII stress intensity factors along the crack-front are verysmall and, therefore, mode-I is the dominant fracture mode. Fig-ure 7(a) shows that the mode-I stress intensity factors at thecrack-front of the repaired pipes are considerably reduced. It alsoshows that with increasing the number of patch layers the valuesof KI at each point of the crack-front are decreased. This reductionis more significant near the patched side than the inside of thepipe. It is also observed that the reduction rate of KI is decreasedwith increasing the patch layers.

Figure 8 shows the variation of stress intensity factors for threepoints at the free surface, middle, and patched face along thecrack-front versus the crack length for two typical patch lay-ups.These figures indicate that all stress intensity factors are increasedwith enlarging the crack length; however, as the number of patchlay-ups is increased the difference between the stress intensity fac-tors at the middle point and the patched surface is decreased. Thisbehavior is mainly due to the variation of the crack-front duringthe fatigue crack propagation, as will be shown later in this paper.

Figure 9 exhibits the variation of crack length versus number ofload cycles for unrepaired and repaired pipes with various num-bers of glass/epoxy patch layers. It is worth noting that the majorcomponent of crack growth in both inside and outside of therepaired pipes is in the X-direction, e.g., for crack growth ofDaX¼ 72 mm the Y-component is DaY¼ 0.2 mm only. Therefore,variations of fatigue crack growth lives are presented with respectto the X-coordinate of crack increments in all cases. This figureshows that fatigue crack growth life of repaired pipes is consider-ably extended when compared with the unrepaired pipe results.The crack growth lives of the repaired pipes are also increasedsignificantly with increasing the number of patch layers. But theefficiency of repair is decreased by increasing of the patch layers;e.g. differences of load cycles of repaired pipe with two layers ofpatch and eight layers of patch are much larger than the differen-ces of 12 and 16 layers of patch. It can be also concluded thatusing more than 16 layers of patch may not increase the fatiguelife extension significantly.

Table 2 presents the fatigue crack growth lives of unrepairedand repaired pipes with various patch lay-ups for a small crackgrowth of 0.8 mm (restarting crack growth) and crack extension of63 mm at inside surface of the pipe. This table shows that usingvarious patch layers may lead to the life extension between 65%to 90% for restarting crack growth and 145% to 280% for crackgrowth of 63 mm.

Figures 10(a) and 10(b) show the variations of crack-frontshapes with the patch lay-ups of [90]4, and [90]16 in the X-Zplane at various crack growth steps up to a certain crack growthwith XCtip¼ 68 mm at the unpatched side (inside) of the repairedpipes. Obviously, it is observed that the crack grows nonuniformlyalong the pipe’s thickness for all patch lay-up configurations. Thisbehavior is due to the asymmetry conditions of the repaired pipesthat lead to the change of stress field near the crack-front andalong the pipe thickness. These figures show that the crack-frontshape curvatures of the repaired pipe with the patch lay-up of[90]16 are more bended than those obtained from the patch lay-upof [90]4. The crack-front shape affects the stress intensity factorsat the crack-front especially at the unpatched surface.

Figure 11 shows comparison of the obtained crack-front shapesat Xctip¼ 90 mm for unrepaired and repaired pipes with variouspatch lay-ups in the Z–X plane. This figure shows that theobtained crack-front for unrepaired pipe after a certain value of fa-tigue crack growth is quite different from the repaired pipes. Thecurvatures of the crack-front shapes for the repaired pipes are alsoincreased with increasing the patch thickness. This figure obvi-ously shows that the crack-front shapes obtained for the pipeswith the patch lay-ups of [90]8, [90]12, and [90]16 have almost thesame configuration, indicating that the crack-front shapes are notsignificantly changed for the more than eight patch layers. In factas the number of layers is increased the curvature of crack-tip isslightly increased.

Fig. 8 Variation of KI versus half of the crack length (Xctip), (a)[90]2 patch and (b) [90]16 patch

Fig. 9 Predicted crack growth versus number of cycles forrepaired pipes with various patch thickness

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These crack-front curvatures generated during the fatigue crackpropagation are due to the distribution of stress components nearthe crack front and local bending of the cracked area. Figure 12shows also the local bending in the crack area of the deformedrepaired pipe under internal pressure.

5 Conclusion

In this paper 3D finite element analyses considering a generalmixed-mode fracture condition were performed to obtain thecrack growth behavior of repaired pipes subjected to internalcyclic pressure. For this purpose an offshore pipe made of low-strength steel containing an initial through the thickness crackrepaired by glass/epoxy composite patch was considered. It wasshown that repair of cracked pipes with glass/epoxy compositeleads to significant life extension for both restarting crack growthand crack propagation period; even a repair with two layers ofcomposite leads to a 65% life extension for restarting crackgrowth. It was also shown that the crack-front shape curvatures ofthe repaired pipes are more bended with increasing the patchlayers, but the crack-front shape changes are not significant formore than eight patch layers.

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Table 2 Fatigue lives for initial small growth of 0.8 mm andcrack growth of 63 mm from each side

Fatigue crack growth life(DaMAX¼ 63 mm)

Restarting crack growth-(DaMAX¼ 0.8 mm)

Patch lay-ups Cycles Percentage Cycles Percentage

Unrepaired 2.88e5 0% 15,723 0%[90]2 7.05e5 145% 25,994 65%[90]4 8.09e5 180% 26,660 70%[90]8 9.30e5 223% 27,747 77%[90]12 10.25e5 256% 28,810 83%[90]16 10.94e5 280% 29.913 90%

Fig. 10 Crack-front development for repaired pipes with vari-ous patch lay-ups in X-Z plane; (a) [90]4, (b) [90]16

Fig. 11 Comparison of the obtained crack-front shapes atXCtip 5 90 mm for repaired pipes with various patch thicknessand unrepaired pipe

Fig. 12 Deformed repaired pipe under internal pressure

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