Research ArticleFracture Characteristics Analysis of Pressured Pipeline withCrack Using Boundary Element Method

Han-Sung Huang

Graduate Institute of Engineering Science and Technology National Kaohsiung First University of Science and TechnologyKaohsiung City 824 Taiwan

Correspondence should be addressed to Han-Sung Huang hansunghgmailcom

Received 18 September 2014 Revised 10 March 2015 Accepted 16 March 2015

Academic Editor Peter Majewski

Copyright copy 2015 Han-Sung Huang This 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

Metal materials can inevitably show deteriorated properties by the factors of stress temperature and environmental erosion indistinct operating environments Without proper protection the service life would be shortened or even deadly danger wouldbe caused This study aims to apply Finite Element Method and Boundary Element Method to analyzing the effects of corrodedpetrochemical pipes on the fatigue life and the fracture form The research results of nondestructive testing and software analysesshow that cracked oil pipes with uniform corrosion bear larger stress mainly internal pressure on the longitudinal direction thanthe circumferential direction As a result the maximal fatigue loading cycle of a circumferential crack is higher than that of alongitudinal one From the growing length and depth of a crack the final aspect ratio of crack growth appears in 242ndash337 and271ndash342 on the circumferential and longitudinal direction respectively Meanwhile the ratios of loading cycles of circumferentialand longitudinal crack are 2623 on uncorroded and 2054 on general metal loss oil pipe The complete crack growth and thecorrespondent fatigue loading cycle could be acquired to determine the service life of the oil pipe being operated as well as thesuccessive recovery time

1 Introduction

Steel and other metal materials have been widely applied tocommodity industry building equipment means of trans-portation and nuclear power Nevertheless metal materi-als are likely to affect the deterioration of properties bystress temperature and environmental erosion in differentoperating environments They would gradually reduce thedesigned effectiveness shorten the service life and evenresult in deadly danger without being properly protectedCorrosion and fracture reveal higher proportion in theapplication process of materials According to the statisticsof American National Standards Institute the economic lossof one hundred billion US dollars about 42 of grossnational product in the USA is caused by material fractureone-third of the loss could be protected and avoided byknown technologies and one-fourth of it could be reducedby research and development

Consequently it is an important research directionto reduce the resource waste resulting from corrosion

Corrosion could be defined as material fracture caused bychemical electrochemical or metallurgical functions in theenvironment which usually occurs slowly but still remainsthe property Corrosion is regarded as an electrochemicalreaction causing some parts or the entire part of metal tobe ionized It requires electric current passing the electrolyticsolution which could be ordinary water salted water or acid-base solution with any concentration on some regions of themetal surface The factors in material corrosion are classifiedas follows

(1) chemical corrosion(2) electrochemical corrosion

Chemical corrosion also called direct dissolution refersto materials being placed in the environment with dissolublesolution till thematerials are completely corroded or the solu-tion achieves the saturation point Other conditions like hightemperature and humidity could accelerate the oxygenationof materials to result in corrosion Electrochemical corrosion

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 508630 13 pageshttpdxdoiorg1011552015508630

2 Advances in Materials Science and Engineering

generally refers to two types of heterogeneous metal or metalbeing able to construct both poles with potential differenceand forming anode metal which is constantly deionized intometal ions and corroded in the environment connectingwith electrolytes Electrochemical corrosion presents betterimportance on such two types of corrosion but is more easilyignored

Disastrous fracture failure of general engineering struc-tures is caused by cracks beyond safety All structural cracksno matter they are production defects or resulted fromoperational local damage could to some extent cause crackgrowth through fatigue stress corrosion or creep Crackpropagation could result in decreasing structural intensityso that fracture would appear when the residual strengthcannot continuously bear load Such a mechanism occurswhen a cyclic loading fatigue crack which slowly developsin normal conditions grows and rapidly results in disastrousevents Determination of damage tolerance is a process whichcould continuously estimate the service life of a structurewithcracks As a result any fracture control plans are based on thedetermination of damage tolerance that the fracture controlinformation is composed of the following points

(1) The maximal allowance size is evaluated with theresidual intensity of a crack structure

(2) The service time for the maximal allowance cracksize is deducted with the time function of crackpropagation and the secure operation life for definingstructures

(3) Linear elastic fracture mechanics damage toleranceanalysis is applied to describing crack behaviorsLinear elastic fracture mechanics assumes that crackbehaviors are determined merely by the loading andStress Intensity Factor of the function of the geometricshape of a structure Stress Intensity Factor plays acritical role in the application of linear elastic fracturemechanics

(4) The crack growth is achieved by simulating the crackpropagation increment analysis The crack propaga-tion of each increment is proceeded by stress analysisand Stress Intensity Factor evaluation The crackpropagation path is based on the predicted incre-ment calculated by the Stress Intensity Factor definedin the growth standard to acquire the propagationdirection

Generally a crack with complicated geometric shapesand continuous growth and changing path in an engineeringstructure is evaluated by the Stress Intensity Factor withnumerical calculation Finite Element Method has beenapplied to fracturemechanics for a long period of time whichcould be referred to in the relevant research of Gallagher [1]and Rice and Tracey [2] and is recently widely applied to theresearch on crack growth The method can also be used tosolve many engineering problems for example the plasticity[3 4] and acoustic propagation [5]

Boundary Element Method has been a complete numer-ical technique in fracture mechanics analysis Brebbia andDominguez [6] successfully utilized Boundary Element

120576

XΓ

Γ120576

Γlowast120576

Figure 1 Source point on the boundary rounded by a semicircle

116

35

114

32

112

3

110

28

108

25

106

23

104

2

102

18

100

16

981

3

MNMX

Z X

Y

Figure 2 Stress distribution of an uncorroded oil pipe with internalpressure

Method in the displacement boundary integral equation forthe problems of geometric linear elasticity mechanics withdeterioration Such deterioration could be defined as mathe-matical cracks where the displacement field is discontinuousincluding the internal or marginal surface without area andvolume boundary In terms of symmetric cracks merely onesurface requires modeling cracks and Boundary ElementMethod with a single region could also be used for theanalysis Nonetheless solving general crack problems withBoundary Element Method could not be directly applied to asingle field analysis For this reason some special techniqueshave been applied to overcome such a difficulty includingcrack Greenrsquos function proposed by Snyder and Cruse [7]displacement discontinuity proposed by Crouch [8] andsubregions proposed by Blandford et al [9] A full historyof the Dual Boundary Element Methods with emphasis onhypersingular integrals and divergent series can be found inthis review article [10]

Bueckner [11] first utilized dual integral equation forsolving crack problems Watson [12] on the other hand firstdeveloped dual integral equation from Boundary ElementMethod by forming the expression with displacement equa-tion and the normal differentiation The theory of such anexpression was based on Hong and Chen [13] combiningdisplacement and external force integral equation Whendisplacement and traction boundary integral equation could

Advances in Materials Science and Engineering 3

Time base Trigger C1 DC

C1

LeCroy

500nsdiv500mVdiv Stop 30mv100 ks 20GSs Edge Positive

minus235120583s

minus10mV offset

C1 AC1M

(a)

905854504642

135

180

225

270

315

0

45

(b)

Figure 3 Ultrasonic testing echo and the longitudinal thickness distribution of the tested oil pipe with metal loss

be simultaneously implemented on the crack boundarygeneral crack problems in a single region could be solvedwith Dual Boundary Element Method Although there werestill some problems of crack boundary coincide after inte-grating the path individual boundary integral equation wasdistinct Dual integral equation could be applied to solvingvarious 3D problems including 3D potential problem ([14]Gray) and 3D elasticity mechanics problem ([15] Gray etal) Such two equations were analyzed by hypersingularintegral surrounding the plane element Such an approachrequired the nonstandard boundary interpolating functionset surrounding a node and restricted the analysis beingmerely used for plane elements Moreover such an approachcould not be applied to the propagation problem of marginalcracks Dual integral equation was also applied to solving2D elasticity mechanics problems and proposed to be merelyused for embedded cracks [12]

RecentlyWen et al [16] used theDual Boundary ElementMethod to calculate dynamic Stress Intensity Factors forthree-dimensional cracked structures in Laplace domaindellrsquoErba and Aliabadi [17] developed a decomposition tech-nique for mixed-mode Stress Intensity Factors to solve thethree-dimensional thermoelasticity problem using a Bound-ary Element Method Lu and Wu [18] introduced the step-by-step time integration technique into dual reciprocityBoundary Element Method to analyze the two-dimensionaldynamic crack problems Consequently the singularity ofalgebraic equations was overcome by the sub-region Bound-ary Element Method Keppas and Anifantis [19] developeda subdomain boundary element procedure to predict thefatigue life of elastic media with cyclic transient thermalloads Several cases of pure opening or mixed fracturemode were studied Guz et al [20] reviewed the research inthe dynamic fracture mechanics of materials with interfacecracks in three-dimensional problems Based on boundaryintegral equation and Boundary Element Method a methodfor solving three-dimensional linear dynamic problems forpiecewise-homogeneous materials is presented

Aiming at fracture mechanics characteristics caused bythe crack on an oil pipe bearing repeated pressure and crackgrowth two cases are discussed in this study

(1) an initially installed oil pipe not being corroded andfractured but merely presenting cracks resulting fromthe production

(2) an oil pipe corroded by general metal loss with thecrack locating on the maximal thinning area

The crack direction is divided into circumferential direc-tion and longitudinal direction With the two cases fouranalysis results are presented ANSYS is first applied toanalyze the stress caused by an oil pipe with internal pressurefor the maximal stress area The file format is then convertedinto the format of BEASY for calculating Stress IntensityFactor of the crack Following the crack growth rules to stepby step calculate the crack size in different loading cycles tillthe crack goes through the oil pipe wall

2 Research Principle

21 Fracture Mechanics In the fracture process of researchmaterials or components remote loading and residual stressare normally used for predicting the stress state close tothe crack tip The quantitative indicator is Stress IntensityFactor (SIF) and thematerial is assumed to be homogeneouslinear elastic properties and can be applied to brittlematerialswith fracture standards It is also an important technique indamage tolerance analysis The value of119870 is generally relatedto the geometric shape of samples and the crack size andlocation and the load on the material and the distributionmodel are correlated

Three linear independent crack models Modes I II andIII are utilized in fracture mechanics Among the threemodes Mode I is an opening or tensile mode where the cracksurface would be directly separated Mode II is a sliding orin-plane shear mode where the two surfaces of the crackwould move toward each other along the tip and Mode III

4 Advances in Materials Science and Engineering6

233

101

22

140

11

217

89

256

78

295

67

334

56

373

45

412

34

179

MNMX

ZX

Y

Figure 4 Stress distribution of an oil pipe bearing general metalloss

Load the required BEASY model

Edit the crack simulation data

Define loading on crack faces

Define the crack growth law

Define the fatigue load cycles

Configure the crack growth analysis

Examine and check the results

Figure 5 Simulation processes for the crack growth analysis

is a tearing or antiplane shear mode where the crack surfacewould move vertically towards both sides along the crackfront Generally Stress Intensity Factor of Mode I is shown as119870I and those of Modes II and III are shown as 119870II and 119870IIIThe mathematical equations are presented as follows

119870I = lim119903rarr0

radic2120587119903120590119910119910(119903 0)

119870II = lim119903rarr0

radic2120587119903120590119910119909(119903 0)

119870III = lim119903rarr0

radic2120587119903120590119910119911(119903 0)

(1)

where 120590119894119895is predicted stress distribution close to the crack tip

Stress Intensity Factor 119870 is a parameter determined bystress and geometric parameter 119884 is also included The stressintensity under any models presents direct proportion to the

Principal stress (max-alg)

132010e + 001

127789e + 001

123567e + 001

119345e + 001

115124e + 001

110902e + 001

102459e + 001

106681e + 001

982375e + 000

940159e + 000

897949e + 000

855727e + 000

Min = 85099

Max = 13248

Figure 6 Crack setting location of an uncorroded oil pipe but withcracks resulting from the production

359750e + 001

328771e + 001

297791e + 001

266811e + 001

235831e + 001

204852e + 001

142892e + 001

173872e + 001

111912e + 001

809325e + 000

499572e + 000

189730e + 000

Principal stress (max-alg)

Min = 15496Max = 36323

Figure 7 Crack setting location of an oil pipe with general metalloss corrosion and the crack appearing on the maximal thinning

load on the material When a sharp crack is produced onthe material the minimum 119870I could be determined throughexperiments which is also the critical stress intensity alongthe crack Under plane strainMode I load the critical value iscritical fracture toughness (KIC) of the material The unit forKIC is the square root of the product of stress and distanceshowing the fracture stress of the material would graduallyachieve KIC through the crack propagation Critical StressIntensity Factor KIC in Mode I is generally used for thedesign parameter in fracture mechanics For the designs ofbridges buildings and airplanes the relevant design damagetolerance needs to be understood Polishing could not helpdetect cracks Generally speaking a visible crack would beclose to the critical stress state predicted by Stress IntensityFactor

Advances in Materials Science and Engineering 5

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 8 Growing shape and size of circumferential crack

100020003000400050006000700080009000

10000

06 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Num

ber o

f cyc

les

Crack size

times106

Figure 9 Relationship between loading cycle and crack size

22 Dual Boundary Element Method Dual Boundary Ele-ment Method allows analyzing general crack problems in asingle-region boundary element Using dual integral in DualBoundary ElementMethod is the boundary integral equationof displacement and traction which could be describedas the equation with Cartesian tensor notation Withoutconsidering the effects of body force boundary integral couldbe presented with displacement (119906

119894) and the location of an

inner point (1199091015840) as

119906119894(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(2)

where 119879119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) are the traction displacementrespectively at 1199091015840 of an object The distance between thesource point and the current point is defined as 119903 which isalso presented as |119909 minus 1199091015840| When the source point approachesthe boundary 119903 rarr 0 (2) is presented as a limit transitionThe semicircular area around the boundary shown in Figure 1could be applied to converting the expression to the boundarywith the source point so that the entire boundary is dividedinto two parts where G is the original boundary and Ge theboundary of the source point with a semicircular radius 119890 (2)Consider

119906119894(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(3)

In (3) a weakly singular integrand of order ln(1119903)is included on the right of the integral expression Whenimproper integral is limited in order ln(1119903) and presentsexchangeable properties it is integrable On the other handwhen a strongly singular integrand of order is included onthe left it could be regularized with the first Taylor series ofdisplacements in which the source point could be presentedas

lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓlowast

119879119894119895(1199091015840

119909) [119906119895(119909) minus 119906

119895(1199091015840

)] 119889Γ (119909)

+ 119906119895(1199091015840

) lim120576rarr0

intΓ120576

119879119894119895(1199091015840

119909) 119889Γ (119909)

+ lim120576rarr0

intΓ+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(4)

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

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NanoparticlesJournal of

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Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

generally refers to two types of heterogeneous metal or metalbeing able to construct both poles with potential differenceand forming anode metal which is constantly deionized intometal ions and corroded in the environment connectingwith electrolytes Electrochemical corrosion presents betterimportance on such two types of corrosion but is more easilyignored

Disastrous fracture failure of general engineering struc-tures is caused by cracks beyond safety All structural cracksno matter they are production defects or resulted fromoperational local damage could to some extent cause crackgrowth through fatigue stress corrosion or creep Crackpropagation could result in decreasing structural intensityso that fracture would appear when the residual strengthcannot continuously bear load Such a mechanism occurswhen a cyclic loading fatigue crack which slowly developsin normal conditions grows and rapidly results in disastrousevents Determination of damage tolerance is a process whichcould continuously estimate the service life of a structurewithcracks As a result any fracture control plans are based on thedetermination of damage tolerance that the fracture controlinformation is composed of the following points

(1) The maximal allowance size is evaluated with theresidual intensity of a crack structure

(2) The service time for the maximal allowance cracksize is deducted with the time function of crackpropagation and the secure operation life for definingstructures

(3) Linear elastic fracture mechanics damage toleranceanalysis is applied to describing crack behaviorsLinear elastic fracture mechanics assumes that crackbehaviors are determined merely by the loading andStress Intensity Factor of the function of the geometricshape of a structure Stress Intensity Factor plays acritical role in the application of linear elastic fracturemechanics

(4) The crack growth is achieved by simulating the crackpropagation increment analysis The crack propaga-tion of each increment is proceeded by stress analysisand Stress Intensity Factor evaluation The crackpropagation path is based on the predicted incre-ment calculated by the Stress Intensity Factor definedin the growth standard to acquire the propagationdirection

Generally a crack with complicated geometric shapesand continuous growth and changing path in an engineeringstructure is evaluated by the Stress Intensity Factor withnumerical calculation Finite Element Method has beenapplied to fracturemechanics for a long period of time whichcould be referred to in the relevant research of Gallagher [1]and Rice and Tracey [2] and is recently widely applied to theresearch on crack growth The method can also be used tosolve many engineering problems for example the plasticity[3 4] and acoustic propagation [5]

Boundary Element Method has been a complete numer-ical technique in fracture mechanics analysis Brebbia andDominguez [6] successfully utilized Boundary Element

120576

XΓ

Γ120576

Γlowast120576

Figure 1 Source point on the boundary rounded by a semicircle

116

35

114

32

112

3

110

28

108

25

106

23

104

2

102

18

100

16

981

3

MNMX

Z X

Y

Figure 2 Stress distribution of an uncorroded oil pipe with internalpressure

Method in the displacement boundary integral equation forthe problems of geometric linear elasticity mechanics withdeterioration Such deterioration could be defined as mathe-matical cracks where the displacement field is discontinuousincluding the internal or marginal surface without area andvolume boundary In terms of symmetric cracks merely onesurface requires modeling cracks and Boundary ElementMethod with a single region could also be used for theanalysis Nonetheless solving general crack problems withBoundary Element Method could not be directly applied to asingle field analysis For this reason some special techniqueshave been applied to overcome such a difficulty includingcrack Greenrsquos function proposed by Snyder and Cruse [7]displacement discontinuity proposed by Crouch [8] andsubregions proposed by Blandford et al [9] A full historyof the Dual Boundary Element Methods with emphasis onhypersingular integrals and divergent series can be found inthis review article [10]

Bueckner [11] first utilized dual integral equation forsolving crack problems Watson [12] on the other hand firstdeveloped dual integral equation from Boundary ElementMethod by forming the expression with displacement equa-tion and the normal differentiation The theory of such anexpression was based on Hong and Chen [13] combiningdisplacement and external force integral equation Whendisplacement and traction boundary integral equation could

Advances in Materials Science and Engineering 3

Time base Trigger C1 DC

C1

LeCroy

500nsdiv500mVdiv Stop 30mv100 ks 20GSs Edge Positive

minus235120583s

minus10mV offset

C1 AC1M

(a)

905854504642

135

180

225

270

315

0

45

(b)

Figure 3 Ultrasonic testing echo and the longitudinal thickness distribution of the tested oil pipe with metal loss

be simultaneously implemented on the crack boundarygeneral crack problems in a single region could be solvedwith Dual Boundary Element Method Although there werestill some problems of crack boundary coincide after inte-grating the path individual boundary integral equation wasdistinct Dual integral equation could be applied to solvingvarious 3D problems including 3D potential problem ([14]Gray) and 3D elasticity mechanics problem ([15] Gray etal) Such two equations were analyzed by hypersingularintegral surrounding the plane element Such an approachrequired the nonstandard boundary interpolating functionset surrounding a node and restricted the analysis beingmerely used for plane elements Moreover such an approachcould not be applied to the propagation problem of marginalcracks Dual integral equation was also applied to solving2D elasticity mechanics problems and proposed to be merelyused for embedded cracks [12]

RecentlyWen et al [16] used theDual Boundary ElementMethod to calculate dynamic Stress Intensity Factors forthree-dimensional cracked structures in Laplace domaindellrsquoErba and Aliabadi [17] developed a decomposition tech-nique for mixed-mode Stress Intensity Factors to solve thethree-dimensional thermoelasticity problem using a Bound-ary Element Method Lu and Wu [18] introduced the step-by-step time integration technique into dual reciprocityBoundary Element Method to analyze the two-dimensionaldynamic crack problems Consequently the singularity ofalgebraic equations was overcome by the sub-region Bound-ary Element Method Keppas and Anifantis [19] developeda subdomain boundary element procedure to predict thefatigue life of elastic media with cyclic transient thermalloads Several cases of pure opening or mixed fracturemode were studied Guz et al [20] reviewed the research inthe dynamic fracture mechanics of materials with interfacecracks in three-dimensional problems Based on boundaryintegral equation and Boundary Element Method a methodfor solving three-dimensional linear dynamic problems forpiecewise-homogeneous materials is presented

Aiming at fracture mechanics characteristics caused bythe crack on an oil pipe bearing repeated pressure and crackgrowth two cases are discussed in this study

(1) an initially installed oil pipe not being corroded andfractured but merely presenting cracks resulting fromthe production

(2) an oil pipe corroded by general metal loss with thecrack locating on the maximal thinning area

The crack direction is divided into circumferential direc-tion and longitudinal direction With the two cases fouranalysis results are presented ANSYS is first applied toanalyze the stress caused by an oil pipe with internal pressurefor the maximal stress area The file format is then convertedinto the format of BEASY for calculating Stress IntensityFactor of the crack Following the crack growth rules to stepby step calculate the crack size in different loading cycles tillthe crack goes through the oil pipe wall

2 Research Principle

21 Fracture Mechanics In the fracture process of researchmaterials or components remote loading and residual stressare normally used for predicting the stress state close tothe crack tip The quantitative indicator is Stress IntensityFactor (SIF) and thematerial is assumed to be homogeneouslinear elastic properties and can be applied to brittlematerialswith fracture standards It is also an important technique indamage tolerance analysis The value of119870 is generally relatedto the geometric shape of samples and the crack size andlocation and the load on the material and the distributionmodel are correlated

Three linear independent crack models Modes I II andIII are utilized in fracture mechanics Among the threemodes Mode I is an opening or tensile mode where the cracksurface would be directly separated Mode II is a sliding orin-plane shear mode where the two surfaces of the crackwould move toward each other along the tip and Mode III

4 Advances in Materials Science and Engineering6

233

101

22

140

11

217

89

256

78

295

67

334

56

373

45

412

34

179

MNMX

ZX

Y

Figure 4 Stress distribution of an oil pipe bearing general metalloss

Load the required BEASY model

Edit the crack simulation data

Define loading on crack faces

Define the crack growth law

Define the fatigue load cycles

Configure the crack growth analysis

Examine and check the results

Figure 5 Simulation processes for the crack growth analysis

is a tearing or antiplane shear mode where the crack surfacewould move vertically towards both sides along the crackfront Generally Stress Intensity Factor of Mode I is shown as119870I and those of Modes II and III are shown as 119870II and 119870IIIThe mathematical equations are presented as follows

119870I = lim119903rarr0

radic2120587119903120590119910119910(119903 0)

119870II = lim119903rarr0

radic2120587119903120590119910119909(119903 0)

119870III = lim119903rarr0

radic2120587119903120590119910119911(119903 0)

(1)

where 120590119894119895is predicted stress distribution close to the crack tip

Stress Intensity Factor 119870 is a parameter determined bystress and geometric parameter 119884 is also included The stressintensity under any models presents direct proportion to the

Principal stress (max-alg)

132010e + 001

127789e + 001

123567e + 001

119345e + 001

115124e + 001

110902e + 001

102459e + 001

106681e + 001

982375e + 000

940159e + 000

897949e + 000

855727e + 000

Min = 85099

Max = 13248

Figure 6 Crack setting location of an uncorroded oil pipe but withcracks resulting from the production

359750e + 001

328771e + 001

297791e + 001

266811e + 001

235831e + 001

204852e + 001

142892e + 001

173872e + 001

111912e + 001

809325e + 000

499572e + 000

189730e + 000

Principal stress (max-alg)

Min = 15496Max = 36323

Figure 7 Crack setting location of an oil pipe with general metalloss corrosion and the crack appearing on the maximal thinning

load on the material When a sharp crack is produced onthe material the minimum 119870I could be determined throughexperiments which is also the critical stress intensity alongthe crack Under plane strainMode I load the critical value iscritical fracture toughness (KIC) of the material The unit forKIC is the square root of the product of stress and distanceshowing the fracture stress of the material would graduallyachieve KIC through the crack propagation Critical StressIntensity Factor KIC in Mode I is generally used for thedesign parameter in fracture mechanics For the designs ofbridges buildings and airplanes the relevant design damagetolerance needs to be understood Polishing could not helpdetect cracks Generally speaking a visible crack would beclose to the critical stress state predicted by Stress IntensityFactor

Advances in Materials Science and Engineering 5

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 8 Growing shape and size of circumferential crack

100020003000400050006000700080009000

10000

06 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Num

ber o

f cyc

les

Crack size

times106

Figure 9 Relationship between loading cycle and crack size

22 Dual Boundary Element Method Dual Boundary Ele-ment Method allows analyzing general crack problems in asingle-region boundary element Using dual integral in DualBoundary ElementMethod is the boundary integral equationof displacement and traction which could be describedas the equation with Cartesian tensor notation Withoutconsidering the effects of body force boundary integral couldbe presented with displacement (119906

119894) and the location of an

inner point (1199091015840) as

119906119894(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(2)

where 119879119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) are the traction displacementrespectively at 1199091015840 of an object The distance between thesource point and the current point is defined as 119903 which isalso presented as |119909 minus 1199091015840| When the source point approachesthe boundary 119903 rarr 0 (2) is presented as a limit transitionThe semicircular area around the boundary shown in Figure 1could be applied to converting the expression to the boundarywith the source point so that the entire boundary is dividedinto two parts where G is the original boundary and Ge theboundary of the source point with a semicircular radius 119890 (2)Consider

119906119894(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(3)

In (3) a weakly singular integrand of order ln(1119903)is included on the right of the integral expression Whenimproper integral is limited in order ln(1119903) and presentsexchangeable properties it is integrable On the other handwhen a strongly singular integrand of order is included onthe left it could be regularized with the first Taylor series ofdisplacements in which the source point could be presentedas

lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓlowast

119879119894119895(1199091015840

119909) [119906119895(119909) minus 119906

119895(1199091015840

)] 119889Γ (119909)

+ 119906119895(1199091015840

) lim120576rarr0

intΓ120576

119879119894119895(1199091015840

119909) 119889Γ (119909)

+ lim120576rarr0

intΓ+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(4)

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

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Journal ofNanomaterials

Advances in Materials Science and Engineering 3

Time base Trigger C1 DC

C1

LeCroy

500nsdiv500mVdiv Stop 30mv100 ks 20GSs Edge Positive

minus235120583s

minus10mV offset

C1 AC1M

(a)

905854504642

135

180

225

270

315

0

45

(b)

Figure 3 Ultrasonic testing echo and the longitudinal thickness distribution of the tested oil pipe with metal loss

be simultaneously implemented on the crack boundarygeneral crack problems in a single region could be solvedwith Dual Boundary Element Method Although there werestill some problems of crack boundary coincide after inte-grating the path individual boundary integral equation wasdistinct Dual integral equation could be applied to solvingvarious 3D problems including 3D potential problem ([14]Gray) and 3D elasticity mechanics problem ([15] Gray etal) Such two equations were analyzed by hypersingularintegral surrounding the plane element Such an approachrequired the nonstandard boundary interpolating functionset surrounding a node and restricted the analysis beingmerely used for plane elements Moreover such an approachcould not be applied to the propagation problem of marginalcracks Dual integral equation was also applied to solving2D elasticity mechanics problems and proposed to be merelyused for embedded cracks [12]

RecentlyWen et al [16] used theDual Boundary ElementMethod to calculate dynamic Stress Intensity Factors forthree-dimensional cracked structures in Laplace domaindellrsquoErba and Aliabadi [17] developed a decomposition tech-nique for mixed-mode Stress Intensity Factors to solve thethree-dimensional thermoelasticity problem using a Bound-ary Element Method Lu and Wu [18] introduced the step-by-step time integration technique into dual reciprocityBoundary Element Method to analyze the two-dimensionaldynamic crack problems Consequently the singularity ofalgebraic equations was overcome by the sub-region Bound-ary Element Method Keppas and Anifantis [19] developeda subdomain boundary element procedure to predict thefatigue life of elastic media with cyclic transient thermalloads Several cases of pure opening or mixed fracturemode were studied Guz et al [20] reviewed the research inthe dynamic fracture mechanics of materials with interfacecracks in three-dimensional problems Based on boundaryintegral equation and Boundary Element Method a methodfor solving three-dimensional linear dynamic problems forpiecewise-homogeneous materials is presented

Aiming at fracture mechanics characteristics caused bythe crack on an oil pipe bearing repeated pressure and crackgrowth two cases are discussed in this study

(1) an initially installed oil pipe not being corroded andfractured but merely presenting cracks resulting fromthe production

(2) an oil pipe corroded by general metal loss with thecrack locating on the maximal thinning area

The crack direction is divided into circumferential direc-tion and longitudinal direction With the two cases fouranalysis results are presented ANSYS is first applied toanalyze the stress caused by an oil pipe with internal pressurefor the maximal stress area The file format is then convertedinto the format of BEASY for calculating Stress IntensityFactor of the crack Following the crack growth rules to stepby step calculate the crack size in different loading cycles tillthe crack goes through the oil pipe wall

2 Research Principle

21 Fracture Mechanics In the fracture process of researchmaterials or components remote loading and residual stressare normally used for predicting the stress state close tothe crack tip The quantitative indicator is Stress IntensityFactor (SIF) and thematerial is assumed to be homogeneouslinear elastic properties and can be applied to brittlematerialswith fracture standards It is also an important technique indamage tolerance analysis The value of119870 is generally relatedto the geometric shape of samples and the crack size andlocation and the load on the material and the distributionmodel are correlated

Three linear independent crack models Modes I II andIII are utilized in fracture mechanics Among the threemodes Mode I is an opening or tensile mode where the cracksurface would be directly separated Mode II is a sliding orin-plane shear mode where the two surfaces of the crackwould move toward each other along the tip and Mode III

4 Advances in Materials Science and Engineering6

233

101

22

140

11

217

89

256

78

295

67

334

56

373

45

412

34

179

MNMX

ZX

Y

Figure 4 Stress distribution of an oil pipe bearing general metalloss

Load the required BEASY model

Edit the crack simulation data

Define loading on crack faces

Define the crack growth law

Define the fatigue load cycles

Configure the crack growth analysis

Examine and check the results

Figure 5 Simulation processes for the crack growth analysis

is a tearing or antiplane shear mode where the crack surfacewould move vertically towards both sides along the crackfront Generally Stress Intensity Factor of Mode I is shown as119870I and those of Modes II and III are shown as 119870II and 119870IIIThe mathematical equations are presented as follows

119870I = lim119903rarr0

radic2120587119903120590119910119910(119903 0)

119870II = lim119903rarr0

radic2120587119903120590119910119909(119903 0)

119870III = lim119903rarr0

radic2120587119903120590119910119911(119903 0)

(1)

where 120590119894119895is predicted stress distribution close to the crack tip

Stress Intensity Factor 119870 is a parameter determined bystress and geometric parameter 119884 is also included The stressintensity under any models presents direct proportion to the

Principal stress (max-alg)

132010e + 001

127789e + 001

123567e + 001

119345e + 001

115124e + 001

110902e + 001

102459e + 001

106681e + 001

982375e + 000

940159e + 000

897949e + 000

855727e + 000

Min = 85099

Max = 13248

Figure 6 Crack setting location of an uncorroded oil pipe but withcracks resulting from the production

359750e + 001

328771e + 001

297791e + 001

266811e + 001

235831e + 001

204852e + 001

142892e + 001

173872e + 001

111912e + 001

809325e + 000

499572e + 000

189730e + 000

Principal stress (max-alg)

Min = 15496Max = 36323

Figure 7 Crack setting location of an oil pipe with general metalloss corrosion and the crack appearing on the maximal thinning

load on the material When a sharp crack is produced onthe material the minimum 119870I could be determined throughexperiments which is also the critical stress intensity alongthe crack Under plane strainMode I load the critical value iscritical fracture toughness (KIC) of the material The unit forKIC is the square root of the product of stress and distanceshowing the fracture stress of the material would graduallyachieve KIC through the crack propagation Critical StressIntensity Factor KIC in Mode I is generally used for thedesign parameter in fracture mechanics For the designs ofbridges buildings and airplanes the relevant design damagetolerance needs to be understood Polishing could not helpdetect cracks Generally speaking a visible crack would beclose to the critical stress state predicted by Stress IntensityFactor

Advances in Materials Science and Engineering 5

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 8 Growing shape and size of circumferential crack

100020003000400050006000700080009000

10000

06 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Num

ber o

f cyc

les

Crack size

times106

Figure 9 Relationship between loading cycle and crack size

22 Dual Boundary Element Method Dual Boundary Ele-ment Method allows analyzing general crack problems in asingle-region boundary element Using dual integral in DualBoundary ElementMethod is the boundary integral equationof displacement and traction which could be describedas the equation with Cartesian tensor notation Withoutconsidering the effects of body force boundary integral couldbe presented with displacement (119906

119894) and the location of an

inner point (1199091015840) as

119906119894(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(2)

where 119879119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) are the traction displacementrespectively at 1199091015840 of an object The distance between thesource point and the current point is defined as 119903 which isalso presented as |119909 minus 1199091015840| When the source point approachesthe boundary 119903 rarr 0 (2) is presented as a limit transitionThe semicircular area around the boundary shown in Figure 1could be applied to converting the expression to the boundarywith the source point so that the entire boundary is dividedinto two parts where G is the original boundary and Ge theboundary of the source point with a semicircular radius 119890 (2)Consider

119906119894(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(3)

In (3) a weakly singular integrand of order ln(1119903)is included on the right of the integral expression Whenimproper integral is limited in order ln(1119903) and presentsexchangeable properties it is integrable On the other handwhen a strongly singular integrand of order is included onthe left it could be regularized with the first Taylor series ofdisplacements in which the source point could be presentedas

lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓlowast

119879119894119895(1199091015840

119909) [119906119895(119909) minus 119906

119895(1199091015840

)] 119889Γ (119909)

+ 119906119895(1199091015840

) lim120576rarr0

intΓ120576

119879119894119895(1199091015840

119909) 119889Γ (119909)

+ lim120576rarr0

intΓ+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(4)

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

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Nano

materials

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Journal ofNanomaterials

4 Advances in Materials Science and Engineering6

233

101

22

140

11

217

89

256

78

295

67

334

56

373

45

412

34

179

MNMX

ZX

Y

Figure 4 Stress distribution of an oil pipe bearing general metalloss

Load the required BEASY model

Edit the crack simulation data

Define loading on crack faces

Define the crack growth law

Define the fatigue load cycles

Configure the crack growth analysis

Examine and check the results

Figure 5 Simulation processes for the crack growth analysis

is a tearing or antiplane shear mode where the crack surfacewould move vertically towards both sides along the crackfront Generally Stress Intensity Factor of Mode I is shown as119870I and those of Modes II and III are shown as 119870II and 119870IIIThe mathematical equations are presented as follows

119870I = lim119903rarr0

radic2120587119903120590119910119910(119903 0)

119870II = lim119903rarr0

radic2120587119903120590119910119909(119903 0)

119870III = lim119903rarr0

radic2120587119903120590119910119911(119903 0)

(1)

where 120590119894119895is predicted stress distribution close to the crack tip

Stress Intensity Factor 119870 is a parameter determined bystress and geometric parameter 119884 is also included The stressintensity under any models presents direct proportion to the

Principal stress (max-alg)

132010e + 001

127789e + 001

123567e + 001

119345e + 001

115124e + 001

110902e + 001

102459e + 001

106681e + 001

982375e + 000

940159e + 000

897949e + 000

855727e + 000

Min = 85099

Max = 13248

Figure 6 Crack setting location of an uncorroded oil pipe but withcracks resulting from the production

359750e + 001

328771e + 001

297791e + 001

266811e + 001

235831e + 001

204852e + 001

142892e + 001

173872e + 001

111912e + 001

809325e + 000

499572e + 000

189730e + 000

Principal stress (max-alg)

Min = 15496Max = 36323

Figure 7 Crack setting location of an oil pipe with general metalloss corrosion and the crack appearing on the maximal thinning

load on the material When a sharp crack is produced onthe material the minimum 119870I could be determined throughexperiments which is also the critical stress intensity alongthe crack Under plane strainMode I load the critical value iscritical fracture toughness (KIC) of the material The unit forKIC is the square root of the product of stress and distanceshowing the fracture stress of the material would graduallyachieve KIC through the crack propagation Critical StressIntensity Factor KIC in Mode I is generally used for thedesign parameter in fracture mechanics For the designs ofbridges buildings and airplanes the relevant design damagetolerance needs to be understood Polishing could not helpdetect cracks Generally speaking a visible crack would beclose to the critical stress state predicted by Stress IntensityFactor

Advances in Materials Science and Engineering 5

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 8 Growing shape and size of circumferential crack

100020003000400050006000700080009000

10000

06 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Num

ber o

f cyc

les

Crack size

times106

Figure 9 Relationship between loading cycle and crack size

22 Dual Boundary Element Method Dual Boundary Ele-ment Method allows analyzing general crack problems in asingle-region boundary element Using dual integral in DualBoundary ElementMethod is the boundary integral equationof displacement and traction which could be describedas the equation with Cartesian tensor notation Withoutconsidering the effects of body force boundary integral couldbe presented with displacement (119906

119894) and the location of an

inner point (1199091015840) as

119906119894(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(2)

where 119879119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) are the traction displacementrespectively at 1199091015840 of an object The distance between thesource point and the current point is defined as 119903 which isalso presented as |119909 minus 1199091015840| When the source point approachesthe boundary 119903 rarr 0 (2) is presented as a limit transitionThe semicircular area around the boundary shown in Figure 1could be applied to converting the expression to the boundarywith the source point so that the entire boundary is dividedinto two parts where G is the original boundary and Ge theboundary of the source point with a semicircular radius 119890 (2)Consider

119906119894(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(3)

In (3) a weakly singular integrand of order ln(1119903)is included on the right of the integral expression Whenimproper integral is limited in order ln(1119903) and presentsexchangeable properties it is integrable On the other handwhen a strongly singular integrand of order is included onthe left it could be regularized with the first Taylor series ofdisplacements in which the source point could be presentedas

lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓlowast

119879119894119895(1199091015840

119909) [119906119895(119909) minus 119906

119895(1199091015840

)] 119889Γ (119909)

+ 119906119895(1199091015840

) lim120576rarr0

intΓ120576

119879119894119895(1199091015840

119909) 119889Γ (119909)

+ lim120576rarr0

intΓ+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(4)

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 8 Growing shape and size of circumferential crack

100020003000400050006000700080009000

10000

06 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Num

ber o

f cyc

les

Crack size

times106

Figure 9 Relationship between loading cycle and crack size

22 Dual Boundary Element Method Dual Boundary Ele-ment Method allows analyzing general crack problems in asingle-region boundary element Using dual integral in DualBoundary ElementMethod is the boundary integral equationof displacement and traction which could be describedas the equation with Cartesian tensor notation Withoutconsidering the effects of body force boundary integral couldbe presented with displacement (119906

119894) and the location of an

inner point (1199091015840) as

119906119894(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(2)

where 119879119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) are the traction displacementrespectively at 1199091015840 of an object The distance between thesource point and the current point is defined as 119903 which isalso presented as |119909 minus 1199091015840| When the source point approachesthe boundary 119903 rarr 0 (2) is presented as a limit transitionThe semicircular area around the boundary shown in Figure 1could be applied to converting the expression to the boundarywith the source point so that the entire boundary is dividedinto two parts where G is the original boundary and Ge theboundary of the source point with a semicircular radius 119890 (2)Consider

119906119894(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

(3)

In (3) a weakly singular integrand of order ln(1119903)is included on the right of the integral expression Whenimproper integral is limited in order ln(1119903) and presentsexchangeable properties it is integrable On the other handwhen a strongly singular integrand of order is included onthe left it could be regularized with the first Taylor series ofdisplacements in which the source point could be presentedas

lim120576rarr0

intΓminusΓ120576+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

= lim120576rarr0

intΓlowast

119879119894119895(1199091015840

119909) [119906119895(119909) minus 119906

119895(1199091015840

)] 119889Γ (119909)

+ 119906119895(1199091015840

) lim120576rarr0

intΓ120576

119879119894119895(1199091015840

119909) 119889Γ (119909)

+ lim120576rarr0

intΓ+Γlowast

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(4)

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and EngineeringSI

F

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 5Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 6

Raw K1 inc 10Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

2000

1000

0000

minus1000

minus2000

minus3000

minus4000

minus5000

minus6000

minus7000

Raw K3 inc 0

Raw K3 inc 5Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 6

Raw K3 inc 10Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7

Comparison of K3 SIF values

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

4000

5000

6000

7000

2000

1000

0000

minus1000

minus2000

Raw K2 inc 0

Raw K2 inc 5Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 6

Raw K2 inc 10Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7

Comparison of K2 SIF values

(c)

SIF

30000

25000

20000

15000

10000

5000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 5Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 6

Raw Keff inc 10Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7

(d)

Figure 10 Stress concentration factors of cracks in various crack growing stages

and the right expression is presented as

intΓ

119880119894119895(1199091015840

119909) 119905119895(119909) 119889Γ (119909)

= 119888119894119895(1199091015840

) 119906119895(1199091015840

) + intΓ

119879119894119895(1199091015840

119909) 119906119895(119909) 119889Γ (119909)

(5)

IntroducingGeneralizedHookersquos Law in elasticitymechanics(3) could be converted into

120590119894119895(1199091015840

) + lim120576rarr0

intΓminusΓ120576+Γlowast

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= lim120576rarr0

intΓminusΓ120576+Γlowast

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(6)

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

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MaterialsJournal of

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Nano

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Journal ofNanomaterials

Advances in Materials Science and Engineering 7

a = 3mm a = 35mm a = 45mma = 40mm

a = 55mma = 50mm a = 65mma = 60mm

a = 75mma = 70mm a = 80mm

Figure 11 Growing shape and size of a longitudinal crack

where 119878119894119895119896(1199091015840

119909) and 119863119894119895119896(1199091015840

119909) are the differential expres-sions of 119879

119894119895(1199091015840

119909) and 119880119894119895(1199091015840

119909) respectively Combining (5)and (6) the following could be deducted with mathematicalalgorithm

1

2119905119895(1199091015840

) + 119899119895(1199091015840

) + intΓ

119878119894119895119896(1199091015840

119909) 119906119896(119909) 119889Γ (119909)

= 119899119894(1199091015840

)intΓ

119863119894119895119896(1199091015840

119909) 119905119896(119909) 119889Γ (119909)

(7)

where 119899119894is defined as the 119894th component of unit normal vector

on the source point boundary Equations (5) and (7) composethe basicmathematical expression ofDual Boundary ElementMethod which could be substituted with proper interpola-tion function to acquire the physical properties around thesingular point

3 Research Process

The entire research process is explained in the previouschapter Aiming at the introduced software the practice stepsare interpreted in this chapter The analysis steps are dividedinto FEM analysis of stress of the material under static stressand BEM analysis of Stress Intensity Factor and the crackgrowth processThe detailed explanation is shown as follows

31 Static Analysis of Material with ANSYS The structuralanalysis with FEM is popular that the principles and stepsare no longer repeated but merely the geometric shape ofa pipe the material property and the boundary conditionare explained Simplified hypotheses of plane strain are

6 7 8 9 10 11 12 13 14

375350325300275250225200175150125100

755025

0

Num

ber o

f cyc

les

Crack size

times106

Figure 12 Relationship of loading cycle and crack size of alongitudinal crack

utilized for analyzing a long strait oil pipe Neverthelessin consideration of components presenting horizontal andlongitudinal cracks the 3D geometric shape is analyzed andthe analysis conditions are listed in Table 1 The longitudinaldisplacement of the cut-off plane on both ends of the oil pipeis 0

Aiming at the initial conditions of an uncorroded oilpipe the stress distribution is shown in Figure 2 fromwhich the stress distribution is not correlated with thelongitudinal position and the stress presents concentric zoneIt conforms to the theoretical analysis results showing thehigh accuracy of the analysis results Besides the von Mises

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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BioMed Research International

MaterialsJournal of

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and EngineeringSI

F

60000

50000

40000

30000

20000

10000

00000000 0200 0600 0800 1000 12000400

Position

Comparison of K1 SIF values

Raw K1 inc 0

Raw K1 inc 4Raw K1 inc 3Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 5

Raw K1 inc 9Raw K1 inc 8Raw K1 inc 7Raw K1 inc 6

(a)

SIF

0000 0200 0600 0800 1000 12000400Position

1500

1000

0500

0000

minus0500

minus1000

Comparison of K3 SIF values

Raw K3 inc 0

Raw K3 inc 4Raw K3 inc 3Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 5

Raw K3 inc 9Raw K3 inc 8Raw K3 inc 7Raw K3 inc 6

(b)

SIF

0000 0200 0600 0800 1000 12000400Position

3000

2000

1000

0000

minus1000

minus2000

minus3000

Comparison of K2 SIF values

Raw K2 inc 0

Raw K2 inc 4Raw K2 inc 3Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 5

Raw K2 inc 9Raw K2 inc 8Raw K2 inc 7Raw K2 inc 6

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

60000

50000

40000

30000

20000

10000

0000

Comparison of Keff SIF values

Raw Keff inc 0

Raw Keff inc 4Raw Keff inc 3Raw Keff inc 2Raw Keff inc 1

Raw Keff inc 5

Raw Keff inc 9Raw Keff inc 8Raw Keff inc 7Raw Keff inc 6

(d)

Figure 13 Stress concentration factors of cracks at different growing stages

stress appears in 9813ndash11635MPa and the maximal vonMises stress 11635MPa occurs in the inner wall of the oilpipe

With 10MHz ultrasonic testing an oil pipe with uniformcorrosion acquired the real thinning value of the pipe wallcaused by uniform corrosion the echo situation and thethinning situation Figure 3 where the longitudinal thicknessappears in 344ndash432mm ANSYS is applied to establishing

the model and analyzing the pipe wall thickness at variouspoints The acquired stress distribution is shown in Figure 4in which the stress changes with metal thinning and the vonMises stress appears in 6233ndash41234MPa Although the oilpipe is thinned from 6mm to 344mm which increases thestress the thinning thickness on the circle is distinct thatstress concentration is caused and successive fracture andcrack propagation are further caused

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 9

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 14 Growing shape and size of a circumferential crack on an oil pipe with general metal loss

Table 1 Analysis parameter and material

Outer radius 75mmInner radius 69mmTube length 50mmFluid pressure 1Nmm2

Material property Modulus of elasticity 2051198903Nmm2Poissonrsquos ratio 029

32 Fracture Analysis with BEASY The analysis model andthe results with ANSYS are acquired in the previous chapterFor further fracture mechanics analysis the crack locationand size need to be defined A conversion program is usedfor converting the file to the format of BEASY so as tosimplify the analysis procedure The calculation process isshown in Figure 5 Having defined the fatigue cyclic loadingproperties the parameters related to fatigue loading analysisare constructed where the type of analysis element shouldbe set In the analysis linear element is directly utilized foraccelerating the calculation Two cases are analyzed in thisstudy and the selected node and the propagation direction ofa crack are described as follows

(a) Initially installed oil pipe not being corroded andfractured but merely presenting cracks resulted fromthe production The crack setting location is shownin Figure 6 in which node 557 is the crack node 964is the circumferential crack propagation directionand node 558 is the longitudinal crack propagationdirection

(b) An oil pipe is with general metal loss corrosionand crack appearing on the maximal thinning areaThe crack setting location is shown in Figure 7where node 1756 is the location of crack node 1775is the circumferential crack propagation directionand node 1755 is the longitudinal crack propagationdirection

50100150200250300350400450

575

600

650

850

625

825

675

700

800

950

925

900

750

725

775

875

0

Num

ber o

f cyc

les

Crack size

times106

Figure 15 Relationship between loading cycle and crack size

4 Analysis and Discussion

According to the above analysis process two conditions areacquired to make four analysis results which are elaboratelydescribed in the following chapter

41 Initially Installed Oil Pipe Not Being Corroded but MerelyPresenting Cracks Resulting from the Production With theanalysis of BEASY a crack would constantly grow afterbearing cyclic loading Aiming at circumferential crack thecrack shape and size at each stage are calculated Figure 8The initial crack presents the length (119886) 30mm and thedepth (119888) 10mm From the figure the crack depth increaseswith the crack propagation length When 119886 = 80mmthe crack depth reaches 60mm which is just the crackpropagating to the inner pipe wall In this case the analysiswould be automatically stopped The relationship betweenloading cycle and crack size is shown in Figure 9The analysisresults of crack size (2119886) and loading cycle are shown in thefigure When the crack size achieves 205mm the crack haspropagated to the inner pipe wall that the oil pipe can no

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

Raw K1 inc 0

Raw K1 inc 2Raw K1 inc 1

Raw K1 inc 3Raw K1 inc 4

SIF

30000

25000

20000

15000

10000

5000

0000

Position0000 0200 0600 0800 1000 12000400

Comparison of K1 SIF values

(a)SI

F

PositionPosPositiitiononPosit on

5000

4000

3000

2000

1000

minus3000

0000

minus1000

minus2000

0000 0200 0400 0600 0800 1000 1200

Raw K3 inc 0

Raw K3 inc 2Raw K3 inc 1

Raw K3 inc 3Raw K3 inc 4

Comparison of K3 SIF values

(b)

SIF

Position0000 0200 0400 0600 0800 1000 1200

12000

10000

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

Raw K2 inc 0

Raw K2 inc 2Raw K2 inc 1

Raw K2 inc 3Raw K2 inc 4

Comparison of K2 SIF values

(c)

SIF

Position0000 0200 0400 0600 0800 1000 1200

35000

30000

25000

20000

15000

10000

5000

0000

Comparison of Keff SIF values

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

(d)

Figure 16 Stress concentration factor of cracks at different growing stages

longer be used Meanwhile the loading cycles are achieved102 billion times which has exceeded the normally designedlife of the material It implies that an uncorroded oil pipewould not fracture the components by circumferential crackcaused in the production The SIF change at each stage couldbe further calculated with BEASY Figure 10 The figure isdivided into four parts of 119870

1 1198702 1198703 and 119870eff the value of

1198701is 4-5 times higher than that of 119870

2and 119870

3that the 119870eff

value is largely affected by 1198701 From the analysis of the 119870eff

change at various steps merely SIF under the initial crackshows large change with the crack location The value wouldbecome stable with the crack growth showing that the crack

growth would gradually correct the SIF of the crack tip andthe absorbed energy is distributed to the surrounding elasticregions

Aiming at a longitudinal crack the crack shape and sizeat each stage are calculated Figure 11 The initial crack showsthe length (119886) 30mm and the depth (119888) 10mm From thefigure the crack depth increases with the crack propagationlength When 119886 = 80mm the crack depth reaches 60mmwhich is just the crack propagating to the inner pipe wallTheanalysis process therefore would be automatically stoppedMoreover the element distribution at each stage is distinctespecially the individual grid at the crack tip is even finer

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

a = 45mm

a = 35mma = 30mm

a = 55mm

a = 40mm

a = 50mm

Figure 17 Growing shape and size of a longitudinal crack

The relationship between loading cycle and crack size isshown in Figure 12 From the analysis results of crack size(2119886) and loading cycle the number of loading cycles isachieved 0385 billion times when the crack size is 145mmIt has far exceeded the normally designed life of material Itimplies that an uncorroded oil pipe would hardly fracturethe components by a longitudinal crack The SIF change ateach stage is further calculated with BEASY Figure 13 Thefigure is divided into four parts of 119870

1 1198702 1198703 and 119870eff The

value of 1198701is 2ndash30 times higher than that of 119870

2and 119870

3that

the 119870eff value is largely affected by 1198701 From the analysis of

119870eff change in each step SIF in the initial crack state and theconstant propagation does not reveal large change with thecrack locationThe enlarging value presents the growth crackenhancing the SIF

42 Oil Pipe with General Metal Loss Corrosion and the CrackAppearing on the Maximal Thinning Area With the analysisof BEASY an oil pipe with general metal loss corrosionis analyzed The crack would constantly grow after bearingcyclic loading Aiming at circumferential crack the crackshape and size at each stage are calculated Figure 14 Theinitial crack reveals the length (119886) of 30mm and the depth(119888) of 10mmThe crack depth would increase with the crackpropagation length When 119886 = 55mm the crack depthachieves 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Furthermore the element distribution at each stageis distinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack size isshown in Figure 15 From the analysis results of crack size(2119886) and loading cycle the initial crack length-depth ratio isso large that the crack length is reduced in the initial stageWhen the crack depth reaches 125mm the crack wouldrelease the blocking state and start to show linear openingproperties When the crack size achieves 975mm the crackhas propagated to the inner pipe wall that the oil pipecan no longer be used Meanwhile the number of loadingcycles is achieved 0475 billion times which has exceededthe normally designed life of material It also implies thata corroded oil pipe would not fracture the components bycircumferential cracks even when there is thinning The

1151101051009590858075706560

Num

ber o

f cyc

les

225

20

175

15

125

10

75

25

5

0

Crack size

times106

Figure 18 Relationship between loading cycle and crack size of alongitudinal crack

SIF change at each stage is further calculated with BEASYFigure 16 The figure is divided into 119870

1 1198702 1198703 and 119870eff The

value of 1198701is larger than that of 119870

2and 119870

3 When analyzing

the 119870eff change at each step merely the SIF of crack at initialstate would change the trend with crack locations which isdifferent from the situations at other stages With the crackgrowth the119870eff value at the second stage becomes stable andthe upward concave shows the increasing119870eff value

Aiming at a longitudinal crack the crack shape andsize at each stage are calculated Figure 17 The initial crackshows the length (119886) of 30mm and the depth (119888) of 10mmFrom the figure the crack depth increases with the crackpropagation length When 119886 = 55mm the crack depthreaches 35mm which is just the crack propagating to theinner pipe wall The analysis process is then automaticallystopped Moreover the element distribution at each stage isdistinct especially the individual grid is finer at the cracktip The relationship between loading cycle and crack sizeis shown in Figure 18 From the analysis results of cracksize (2119886) and loading cycles the loading cyclic presents 23million times when the crack size reaches 118mm showingthe designed life of material should be taken into account

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 Advances in Materials Science and EngineeringSI

F

100000

90000

80000

70000

60000

50000

0000

Position0000 0200 0600 0800 1000 12000400

40000

30000

20000

10000

Comparison of K1 SIF values

Raw K1 inc 0Raw K1 inc 4Raw K1 inc 3

Raw K1 inc 2Raw K1 inc 1

(a)SI

F

3000

2000

1000

0000

Position0000 0200 0600 0800 1000 12000400

minus1000

minus2000

minus3000

minus4000

minus5000

Comparison of K3 SIF values

Raw K3 inc 0Raw K3 inc 4Raw K3 inc 3

Raw K3 inc 2Raw K3 inc 1

(b)

SIF

Position

8000

6000

4000

2000

0000

minus2000

minus4000

minus6000

minus8000

minus10000

0000 0200 0600 0800 1000 12000400

Raw K2 inc 0Raw K2 inc 4Raw K2 inc 3

Raw K2 inc 2Raw K2 inc 1

Comparison of K2 SIF values

(c)

0000 0200 0600 0800 1000 12000400Position

SIF

100000

90000

80000

70000

60000

50000

0000

40000

30000

20000

10000

Raw Keff inc 0Raw Keff inc 4Raw Keff inc 3

Raw Keff inc 2Raw Keff inc 1

Comparison of Keff SIF values

(d)

Figure 19 Stress concentration factor of cracks at various growing stages

It also implies that a corroded oil pipe would fracture thecomponents by a longitudinal crack The SIF change at eachstage could be further calculated with BEASY Figure 19The figure is divided into 119870

1 1198702 1198703 and 119870eff The value of

1198701is 10ndash40 times higher than that of 119870

2and 119870

3that the

119870eff value is largely affected by 1198701 From the analysis of 119870eff

change at each step the SIF in the initial crack state and theconstant propagation does not show large change with cracklocations The increasing value presents the growing crackthat SIF would be constantly enhanced Based on the fourcases with fracture mechanics analysis the final statisticaldata are organized in Table 2

5 Conclusion

According to the above research process and the case analysesof two types of oil pipe crack the following results areconcluded

(a) The crack growth resulting in fracture in the actualloading process of an uncorroded oil pipe can beignored as the calculated fatigue loading cycle isextremely high However when there is corrosionon the oil pipe the fatigue loading cycle decreasesrapidly showing that corrosion could easily result infatigue fracture on a metal oil pipe

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 13

Table 2 Crack growth property on the oil pipe with different corrosion conditions

Pipe type Uncorroded oil pipe Oil pipe with general metal lossCrack direction Circumferential direction Longitudinal direction Circumferential direction Longitudinal directionFinal crack length (mm) 203678 146009 97177 117790Final crack depth (mm) 66421 65192 30931 33278Fatigue loading cycle (times) 10245885974 390583049 483412414 23537533Maximal effective SIF in crackgrowing process (MPasdotm12) 22128 49908 30379 86650

(b) From the research results the longitudinal stress ofan oil pipe which bears internal pressure is largerthan the circumferential one that the maximal fatigueloading cycle of a circumferential crack is higher thanthat of a longitudinal one

(c) From the growing length and depth of a crack thefinal aspect ratio of crack size appears in 242ndash337and 271ndash342 on the circumferential and longitudinaldirection respectively The difference is not largepresenting the isotropic material property of metal

(d) The crack growth and the correspondent fatigueloading cycle are determined The ratios of loadingcycles of circumferential and longitudinal crack are2623 and 2054 for uncorroded and generalmetal lossoil pipe respectively It shows the stress level is thedominant factor for the crack growth

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] R H Gallagher ldquoA review of finite element techniques infracture mechanicsrdquo in Proceedings of the 1st Conference onNumerical Methods in Fracture Mechanics A R Luxmoore andD R J Owen Eds pp 1ndash25 University College of Swansea1978

[2] J R Rice and D M Tracey ldquoComputational fracture mechan-icsrdquo in Methods in Structural Mechanics Academic Press NewYork NY USA 1973

[3] S-Y Hsia ldquoOptimization of microextrusion preforming usingtaguchi methodrdquo Mathematical Problems in Engineering vol2013 Article ID 305797 9 pages 2013

[4] S-Y Hsia and P-Y Shih ldquoWear analysis of forging die for longhex flange nutsrdquo Advances in Materials Science and EngineeringIn press

[5] Y-T Chou and S-Y Hsia ldquoNumerical analysis of indoor soundquality evaluation using finite element methodrdquo MathematicalProblems in Engineering vol 2013 Article ID 420316 8 pages2013

[6] C A Brebbia and J Dominguez Boundary ElementsmdashAn Intro-ductory Course Southampton UK Computational Mechanics1989

[7] M D Snyder and T A Cruse ldquoBoundary-integral equationanalysis of cracked anisotropic platesrdquo International Journal ofFracture vol 11 no 2 pp 315ndash328 1975

[8] S L Crouch ldquoSolution of plane elasticity problems by thedisplacement discontinuity method I Infinite body solutionrdquoInternational Journal for Numerical Methods in Engineering vol10 no 2 pp 301ndash318 1976

[9] G E Blandford A R Ingraffea and J A Liggett ldquoTwo-dimensional stress intensity factor computations using theboundary elementmethodrdquo International Journal for NumericalMethods in Engineering vol 17 no 3 pp 387ndash404 1981

[10] J T Chen and H-K Hong ldquoReview of dual boundary elementmethods with emphasis on hypersingular integrals and diver-gent seriesrdquo Applied Mechanics Reviews vol 52 no 1 pp 17ndash321999

[11] H F Bueckner ldquoField singularities and related integral rep-resentationsrdquo in Methods of Analysis and Solutions of CrackProblems G C Sih Ed vol 1 ofMechanics of Fracture pp 239ndash314 Springer Dordrecht The Netherlands 1973

[12] J O Watson ldquoHermitian cubic boundary elements for theanalysis of cracks of arbitrary geometryrdquo inAdvanced BoundaryElement Methods T A Cruse Ed International Union ofTheoretical and Applied Mechanics pp 465ndash474 SpringerBerlin Germany 1988

[13] H Hong and J Chen ldquoDerivations of integral equations ofelasticityrdquo Journal of Engineering Mechanics vol 114 no 6 pp1028ndash1044 1988

[14] L J GrayBoundary ElementMethod for Regions withThin Inter-nal Cavities IBM Bergen Scientific Centre Bergen Norway1987

[15] L J Gray L F Martha and A R Ingraffea ldquoHypersingularintegrals in boundary element fracture analysisrdquo InternationalJournal for Numerical Methods in Engineering vol 29 no 6 pp1135ndash1158 1990

[16] P H Wen M H Aliabadi and D P Rooke ldquoCracks inthree dimensions a dynamic dual boundary element analysisrdquoComputer Methods in Applied Mechanics and Engineering vol167 no 1-2 pp 139ndash151 1998

[17] D N dellrsquoErba and M H Aliabadi ldquoBEM analysis of frac-ture problems in three-dimensional thermoelasticity using J-integralrdquo International Journal of Solids and Structures vol 38no 26-27 pp 4609ndash4630 2001

[18] X Lu and W-L Wu ldquoA subregion DRBEM formulation forthe dynamic analysis of two-dimensional cracksrdquoMathematicaland Computer Modelling vol 43 no 1-2 pp 76ndash88 2006

[19] L K Keppas and N K Anifantis ldquoFatigue life prediction undercyclic thermal loads using the boundary elements method fortwo-dimensional problemsrdquo Computers amp Structures vol 89no 7-8 pp 590ndash598 2011

[20] A N Guz I A Guz A V MenrsquoShikov and V A MenrsquoShikovldquoThree-dimensional problems in the dynamic fracturemechan-ics of materials with interface cracks (review)rdquo InternationalApplied Mechanics vol 49 no 1 pp 1ndash61 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials