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Review

Fatigue analysis of corroded pipelines subjected to pressure andtemperature loadings

Divino J.S. Cunha a,*, Adilson C. Benjamin a, Rita C.C. Silva b, Joo N.C. Guerreiro c,Patrcia R.C. Drach c

a PETROBRAS Research and Development Center, Brazilb Federal University of Par e UFPA, Brazilc National Laboratory for Scientic Computation e LNCC, Brazil

a r t i c l e i n f o

Article history:

Received 10 January 2011

Received in revised form

7 October 2013

Accepted 17 October 2013

Keywords:

Multiaxial fatigue

Biaxial fatigue

Strain-life

Out-of-phase cyclic loadingsHeated pipelines

Corroded pipeline fatigue analysis

Corrosion defect SCFs

a b s t r a c t

In this paper a methodology for the fatigue analysis of pipelines containing corrosion defects is proposed.This methodology is based on the nominal stresses from a Global Analysis using a one-dimensional Finite

Element (FE) model of the pipeline together with the application of stress concentration factors (SCFs).As the stresses may exceed the yielding limit in the corrosion defects, the methodology also adopts a

strain-life approach (eNmethod) which is capable of producing less conservative fatigue lives than thestress-based methods. In addition the proposed methodology is applied in the assessment of the fatiguelife of an onshore-hot pipeline containing corrosion pits and patches. Five corrosion pits and ve

corrosion patches with different sizes are considered. The corrosion defects are situated on the externalsurface of the pipeline base material. The SCFs are calculated using solid FE models and the fatigue

analyses are performed for an out-of-phase/non-proportional (NP) biaxial stresses related to the com-bined loading (internal pressure and temperature) variations caused by an intermittent operation with

hot heavy oil (start-up and shut-down). The results show that for buried pipelines subjected to cycliccombined loadings of internal pressure and temperature fatigue may become an important failure mode

when corroded pipeline segments are left in operation without being replaced.2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fatigue is not usually a failure mode that occurs in buriedpipelines subjected only to internal pressure. However, this is notalways the case if other types of loadings act on the pipeline, likethe cyclic combined loadings of internal pressure and temperature

resulting from intermittent operation with hot heavy oil.Furthermore, fatigue may become an important failure mode,

even in buried pipelines subjected only to internal pressure, if any

type of defect (cracks, dents or corrosion) is found in periodicalinspections[1,2].

In the case of hot pipelines designed under the traditional phi-losophy of preventing buckling by burying, fatigue becomes animportant failure mode when corroded pipeline segments are left

in operation without being replaced. This is a worldwide trend

where very conservative corrosion assessment methods have beenreplaced by more accurate methods which are capable of not only

guaranteeing the pipeline structural integrity but also toleratinglarger corrosion defects for longer periods of time.

This paper presents a methodology for the fatigue life assess-ment of hot pipelines with corrosion defects in the base material.

The proposed methodology is based on nominal stresses and stressconcentration factors (SCFs) together with a BrowneMiller (BM)strain-life critical-plane method [3e5]. Although stress-life

methods are more disseminated[6], strain-life methods are moreadequate for pipelines which undergo plastic deformation.

The BM method handles plasticity, which may occur in thecorrosion defect, as well as the multiaxial stresses/strains and theout-of-phase/non-proportional (NP) characteristic of the applied

loadings or the corresponding stresses[3e5,7].The proposed methodology was applied to an onshore corroded

API-X60 pipeline with a 57.7 ratio of the diameter to the wall

thickness. The pipeline operates 3 times a week alternating be-tween hot heavy oil and light products at ambient temperature. Themaximum operating pressure is 8.2 MPa and the maximum oper-ating temperature of the oil is 80 C.

* Corresponding author. Av Horcio Macedo 950, Cidade Universitria, Ilha do

Fundo, 21941-915 Rio de Janeiro, RJ, Brazil. Tel.: 55 21 3865 4743; fax: 55 21

3865 3764.

E-mail addresses: [email protected], [email protected](D.J.

S. Cunha), [email protected] (A.C. Benjamin), [email protected] (R.C.

C. Silva),[email protected](J.N.C. Guerreiro),[email protected] (P.R.C. Drach).

Contents lists available atScienceDirect

International Journal of Pressure Vessels and Piping

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / i j p v p

0308-0161/$ e see front matter 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.ijpvp.2013.10.013

International Journal of Pressure Vessels and Piping 113 (2014) 15e24
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/03080161http://www.elsevier.com/locate/ijpvphttp://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://dx.doi.org/10.1016/j.ijpvp.2013.10.013http://www.elsevier.com/locate/ijpvphttp://www.sciencedirect.com/science/journal/03080161http://crossmark.crossref.org/dialog/?doi=10.1016/j.ijpvp.2013.10.013&domain=pdfmailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]

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2. Methodology of analysis

As shown in Fig. 1, the proposed methodology for the

corroded pipeline fatigue life assessment has three main phases:(1) Stress Global Analysis, (2) Stress components amplication bythe corrosion defect SCFs, with the SCFs obtained from a (20)Local Analysis, and (3) Fatigue Analysis using a multiaxial strain-

life method. The steps (20)e(2) and (3) must be repeated for eachcorrosion defect. These three phases will be described in moredetail later on.

Using SCFs means that the stress analysis is carried out for the

plain pipeline (uncorroded) and a one-dimensional model may be

considered for the pipeline (Global Analysis). This approach differsfrom that[3,4,8,9]where the stress analysis is normally performedwith the structure containing the corrosion defect (Local Analysis).

In such cases, the stresses which result from the analysis arealready amplied in the defect, but the nite element model, beinga solid model, is more complex.

In other words, although the calculations of the SCFs require a

solid model,neither this model northe stresses from it are employedin the fatigue analysis. Only the values of both SCFs are utilized.

The SCFs also imply that the Global Analysis only needs to beperformed once irrespective of the type or the geometry of the

corrosion defects.

Nomenclature

a straight portion of the corrosion defect depth

b Basquins fatigue strength exponent

c CofneManson fatigue ductility exponent

BM BrowneMiller

CM Cof ne

MansonCP critical plane (highest damage plane)C/P Ang FE-SAFE nomenclature for the CP anglefCWP cylindrical wide pitCycle-Ampl FE-SAFE nomenclature for the fatigue parameter

amplitude (e/2)

d corrosion defect depth

dsi(i 1, 2, 3) stressdatasets(FE-SAFE data line with the stresstensor components)

e BM parameter or strain (e h gmax n)e BM-parameter range (ee2e1 DehDgmax Dn)

eL elongation

D total damage (D SDi)

De pipe external diameter

Di damage of a single loading cycle (Di 1/N)DFF design fatigue factor

E elastic (Youngs) modulusEFF environmental fatigue factor

h hardening exponent

H hardening coefcient

hc cyclic hardening exponent

Hc cyclic hardening coefcient

hs soil cover

L corrosion defect length (longitudinal dimension)LP longitudinal patch

n number of loading repeats

N number of strain cycles to failure (obtained from eNcurve)

N loading history life (N 1/D), FE-SAFE output fatiguelife

NP non-proportional

p internal pressure

pd design pressure

poper maximum operating pressure

r pit radius or patch-bottom llet radius

R patch-top llet radiusSCF stress concentration factorSMTS minimum specied ultimate tensile stress

SMYS minimum specied yielding stresst time

t pipe wall thickness

T temperature

Tinst pipeline installation temperature

Toper maximum operating temperaturew pipe weight

w corrosion defect width (circumferential dimension)

x, y, z local cylindrical co-ordinates

X, Y, Z global cylindrical co-ordinatesz distance between the soil surface and the trench

bottom

afat fatigue usage factor

g shear strain (gij i jon the shear planeiej,i,j 1,2, 3,i s j)

i(i1,2,3) principal strains: in-plane (1, 2), out-of-plane/out-

of-surface (3 h z)n normal strain

ijn i j=2 on the shear plane iej,i,

j 1, 2, 3, i s j)

0f

fatigue ductility coefcient

true uniaxial true strain

n Poissons ratio

strue uniaxial true stress

s

0

f Basquin

s fatigue strength coef

cientsh hoop stress (sh pDi/(2t))

si(i 1, 2, 3) principal stresses: in-plane (s1,s2), out-of-plane/out-of-surface (s3 h sz)

sL longitudinal stress

su engineering ultimate tensile stress

sy engineering yield stress

s* reference sample (stress-tensor/dataset, within the

stress history, taken by FE-SAFE to dene theorientation of stress principals and principal/shearplanes)

s*i (i 1, 2, 3) reference principal stresses related todatasets*

f rotating angle of the principal/shear planes round theout-of-surface axis 3 h z(0 f 180), measuredbetween the plane normal nand the stress principals*1, and identied in FE-SAFE output le as C/P Ang

fx angle between the CP normal nand the x-axis(positive from x-axis towards y-axis), identied inFE-SAFE output le as CP/X/Ang

q1 angle betweens1and s*

1 (q1 0 for constant direction

principals)

DT temperature loading (DT T Tinst)(,)h hoop (circumferential)(,)L longitudinal

(,)max maximum(,)nom nominal

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3. Pipeline characteristics

This study was carried out on a buried API-X60 steel pipeline(seeFig. 2) designed according to the ASME B31.4 code [10]. It

was assumed that the pipeline curvature is negligibly small andthat the soil cover is large enough to prevent the pipeline globalbuckling. In this case, as the nominal stresses are uniform in bothlongitudinal and circumferential directions, the fatigue loading of

the pipeline containing one corrosion defect reduces to only onestress history.

The pipeline operates 3 times a week alternating betweenhot heavy oil and light products at ambient temperature. The

maximum operating pressure is 8.2 MPa and the maximum oper-ating temperature of the oil is 80 C.

The main characteristics of the pipeline are shown in Table 1. As

the operating temperature is below 120

C, no derating is appliedon the steel properties[10].

4. Geometry of the corrosion defects

It is supposed that the pipeline has been operating for severalyears and during this time corrosion has occurred on its externalsurface.

Two types of corrosion defects are considered in this study:cylindrical wide pit (CWP) and longitudinal patch (LP). In bothcases ve corrosion defect sizes are evaluated.

The geometry of each pit is described by three key parameters:

the pit depthd, the radius of the pit root rand the length a of thecylindrical portion of the pit. Other geometric parameters are: the

pit length L, which is the pit longitudinal dimension and the pitwidthw, which is its circumferential dimension.

A corrosion pit is sketched inFig. 3. The length a of the cylin-drical part of the pit is equal tor, the pit depthd is equal to 2r, thepit length L is equal to2rand the pitwidth w is approximately equalto 2r. Consequently, the pit length L and the pitwidth w are equal to

the pit depth d. Table 2 presents the dimensions of each pitconsidered.

The corrosion patch geometry is described by the following

parameters: the depth d, the length L, the width w, the llet radius rand R and the straight lengtha of the rectangular part. The shape ofthe corrosion patch is shown inFig. 4and the patch dimensions areinTable 3.

5. Local Analysis

5.1. Solidnite element model

The corrosion defects (pits and patches) inTables 2 and 3weremodeled using solid (3D) Finite Elements (FE) and their corre-sponding SCFs were calculated using these models. Each model wasrepresented by a 2.6 m straight pipe with a single corrosion defect.

A cylindrical coordinate system was used with the followingconvention: X-axis (radial), Y-axis (circumferential) and Z-axis(longitudinal).

The local analyses of all the corroded pipeline models were

performed with the ANSYS program [11]. To take advantage of

Fig. 1. Methodology owchart.

soil

hs

+

Fig. 2. Pipeline burial parameters.

Table 1

Design and operating parameters of the pipeline.

Parameter e

Pipe material API 5L X60

SMYS 413 MPa

SMTS 517 MPa

Elongation eL 0.22

Youngs modulusE 206 GPa

Poissons ration 0.3

Thermal expansion coefcienta 1.17 105 mm/mm/C

Pipe external diameter De 457.2 mm (18 in)Pipe wall thicknesst 7.92 mm (0.312 in)

Soil coverhs 1.0 m

Pipe weightw 2.18 N/mm

Design pressurepd 10.30 MPa

Maximum operating pressurepoper 8.2 MPa

Pipeline installation temperatureTinst 20 C

Pipeline operating temperatureToper 80 C

Design life 40 years

Number of operations per week 3

Number of operations during design life 6240Design fatigue factor DFF 5

Environment fatigue factor EFF 2

Fig. 3. Cylindrical wide pit (CWP): (a) top view, (b) longitudinal view.

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symmetry only a quarter of each model was analyzed. The solid FE

models were constructed using the non-conforming 8-node brickelement SOLID45 available in the ANSYS FE library. Appropriateboundary conditions were applied to the symmetry planes (seeFig. 5). The FE models were extended far enough beyond the

corroded region to prevent the end conditions from affecting theresults.

In the corroded region, 8 elements were used through itsthickness and at some distance outside the corroded region this

number was reduced to 4 elements through the thickness (seeFig. 6). This mesh density was selected after a convergence study inwhich linear analyses were performed using an increasing degreeof mesh renement.

The analysis of the plain pipe (uncorroded) was performed using

a uniform mesh solid FE model with 4 elements through thethickness.

In total, eleven solid FE models were constructed: one for theplain pipe and ten for the pipe with each type of corrosion pits and

patches presented in Tables 2 and 3. For each solid FEmodela linearanalysis was performed. In these analyses, the pipeline was sub-

jected to an internal pressure and a longitudinal tension. In fact, thelongitudinal tension simulates the temperature loading effect.

5.2. Stress concentration factors (SCFs)

For each applied loading (internal pressure and longitudinaltension) and each direction (longitudinal and circumferential orhoop) the SCFs were determined as the ratio between the

maximum stress component in the corroded region and the cor-responding stress in the uncorroded pipeline (nominal stress):

SCFik

sk

i

max

ski

nom

i L; h and k p; DT (1)

In order to simplify the SCFs application, the SCF for longitudinal

stress was taken as the mean value between the two longitudinalSCFs related to the internal pressure and the temperature loading.Therefore, as the temperature (or longitudinal loading) has no in-

uence in the circumferential (hoop) direction, in this work theSCFs are given as:

SCFL SCFL

p SCFLDT

2 ; SCFh SCFh

p (2)

The SCFs curves are shown in Fig. 7 as a function of thenormalized defect depth (d/t). Their numerical values are presentedinTables 4 and 5. The SCFs unitary values corresponding to the

plain pipe (design condition) were included in the rst line of bothtables as new corrosion defects named CWP0 and LP0 respectively.

Table 2

Dimensions of the cylindrical wide pits (CWPs).

Defect d(mm) r(mm) a(mm) L(mm) w(mm) d/t

CWP1 0.792 0.396 0.396 0.792 0.792 0.10

CWP2 1.584 0.792 0.792 1.584 1.584 0.20

CWP3 2.376 1.188 1.188 2.376 2.376 0.30

CWP4 3.168 1.584 1.584 3.168 3.168 0.40

CWP5 3.960 1.980 1.980 3.960 3.960 0.50

Fig. 4. Longitudinal patch (LP): (a) top view, (b) longitudinal view, (c) cross-section.

Table 3

Dimensions of the longitudinal patches (LPs).

Defect d(mm) r(mm) a(mm) L(mm) w(mm) R(mm) d/t

LP1 0.792 0.634 0.158 60 20 1.268 0.10

LP2 1.584 1.267 0.317 90 30 2.534 0.20

LP3 2.376 1.901 0.475 120 40 3.802 0.30

LP4 3.168 2.534 0.634 150 50 5.068 0.40

LP5 3.960 3.168 0.792 180 60 6.336 0.50

Fig. 5. Boundary conditions of the solid FE models.


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6. Global Analysis

6.1. Pipe model

The Global Analysis was carried out using ABAQUS [12] andPATRAN[13]programs. The pipeline was represented by a 1.0 m-long pipe segment. The stress and strain components are refer-

enced to a local coordinate system with the following convention:x-axis (longitudinal), y-axis (circumferential) and z-axis (radial).

A single PIPE21 available in ABAQUS FE library was used tomodel the 1.0 m long pipe segment. This element has two nodes

with 3-d.o.f. per node.

Both extreme nodes were considered clamped. Due to this re-striction on the pipeline movement, and also the pipeline straight

geometry, the soil has no inuence on the stress analysis.As the Global Analysis is elastic, the material behavior is char-

acterized only by the Youngs modulus and Poissons ratio.Furthermore, the analysis is considered to be nonlinear geo-

metric (NLGEOM optional parameter).

6.2. Basic cyclic loadings

The basic loadings are made up of the internal pressure p andtemperature loading DT variations related to the pipeline inter-mittent operation with hot heavy oil.

In the numeric Global Analysis with ABAQUS, the basic loadings

were applied throughout 4 cycles as depicted in Fig. 8. Each cycle

was composed of 4 load-steps[14]in such a way as to representboth thestart-upoperation (internal pressure application followedby the temperature loading application) and the shut-downoper-

ation (internal pressure removal or depressurization of the pipelinefollowed by the temperature loading removal or pipeline cooling).

Within each step, the loading was incremented using an auto-matic time stepping algorithm, (only the initial/nal values and

minimum/maximum increment limits were provided).The internal pressure was applied considering the pipeline in-

ternal diameter as a reference.

Fig. 6. Solid FE models used to calculate the SCFs: (a) plain pipe, (b) pit CWP3, and (c) patch LP2.

1,00

2,00

3,00

4,00

0 0,1 0,2 0,3 0,4 0,5

d/ t

SCF

Patch - (SCF)L

Patch - (SCF)h

Pit - (SCF)L

Pit - (SCF)h

Fig. 7. Stress concentration factors of the corrosion defects.


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6.3. Nominal stresses

In a pressurized, sufciently buried pipeline, the longitudinal

strain is nil because of the soil imposed restriction. Under theseboundary conditions, a hot pipeline develops only membranestresses: one circumferentialsh and other longitudinalsL, the latterresulting from the sum of the longitudinal stresses (sL)

P and (sL)DT

caused by the longitudinal displacement restraint.The pipeline nominal stresses during the rst three cycles are

shown inFigs. 9 and 10. Similarly to the basic loadings, the longi-tudinal and circumferential stress components are out-of-phase

and have constant amplitudes.The pointsB and D in Fig. 10correspond to the operating pres-

sure application (p poper) and removal (p 0) respectively. Thepoints Cand A correspond to the temperature loading application

(DT DTmax Toper Tinst) and removal (DT 0) respectively.Some typical nominal stress values acting on the pipeline during

a cycle are shown inTable 6. They correspond to the vertices of thelozenge in Fig. 10 and/or to the times 1, 2 and 3. Due to thesimplicity of the model, these values could also be obtained

analytically (seeTable 7).As the stresses are elastic and the soil has no effect on their

variations with time, the rst cycle is simply repeated throughoutthe analysis.

7. Fatigue analysis

The fatigue analysis was carried out using FE-SAFE program[8].The fatigue analysis phase is characterized by the following steps:(a) fatigue loading (nominal stresses) reading; (b) stress ampli-

cation by the SCFs; (c) plasticity correction (Neubers rule) using thestatic and cyclic true stressestrain curves and nally (d) the fatiguelife/damage calculation using a multiaxial strain-life methodtogether with a uniaxial eN curve. These steps are described

below.

7.1. Fatigue loading and application of SCFs

In this analysis, the fatigue loading is given by the nominallongitudinal and circumferential stress histories. As the rst stress

cycle repeats itself on all subsequent cycles (seeFig. 9), only onecycle needs to be analyzed, naturally, the rst one (seeFig. 11).

It should be mentioned that the calculated fatigue life is thesame irrespective of whether the complete stress history is input

(as inFig. 11) or only their inection points (stresses at times 0, 1, 2,3 and 4) are provided.

For a corrosion defect, the nominal/elastic stresses are amplied

by the SCFs according to the following expression:

si SCFi,sinom; i L; h (3)

The SCFs of a corrosion defect may be applied either before thefatigue analysis, with the manual calculation of the Eq. (3), or whileentering the fatigue loading (nominal stresses) to the fatigue soft-ware[8]. The second form was adopted in this study due to the

simplicity of considering only one corrosion defect at a time andbecause it allows the application of a different SCF to each stresscomponent. Moreover, by taking different corrosion defects in the

same pipeline, as the nominal stresses are the same, only the SCFsvalues need to be changed in the load denition le (*.ldf) for eachdefect fatigue analysis.

In this way, following the nomenclature shown in Fig. 12, the

nominal stress history is given as two signals, and the corre-sponding stress tensor/datasets dsih [sxx syy szz syz szx], i L,h, are

dened as unit tensor/datasets whose components are nil, exceptthat related to each signal, which is assumed to be equal to 1. Both

signals and unit tensor are provided in two different ASCII les(*.txt).

7.2. Stressestrain curves

7.2.1. Elastic behaviorBefore the plasticity correction, using the multiaxial versions

of the stressestrain relationship for elastic behavior [3,7,15]and

Table 4

Stress concentration factors of the corrosion pits CWPs.

Defect d/t (SCFL)p (SCFL)

DT SCFLa SCFh

CWP0 0.00 1.000 1.000 1.000 1.000

CWP1 0.10 1.707 1.568 1.638 1.601

CWP2 0.20 2.099 1.867 1.983 1.901

CWP3 0.30 2.214 2.094 2.154 2.005

CWP4 0.40 2.284 2.258 2.271 2.086

CWP5 0.50 2.370 2.398 2.384 2.162a TheSCFLmean value (see Eq.(2)) was applied to the longitudinal stresses due to

both basic loadings (internal pressure and temperature loading).

Table 5

Stress concentration factors of the corrosion patches LPs.

Defect d/t (SCFL)p (SCFL)

DT SCFLa SCFh

LP0 0.00 1.000 1.000 1.000 1.000

LP1 0.10 1.719 1.577 1.648 1.769

LP2 0.20 2.152 1.847 2.000 2.445

LP3 0.30 2.520 2.104 2.312 2.902

LP4 0.40 2.988 2.316 2.652 3.465

LP5 0.50 3.484 2.527 3.006 4.046

a TheSCFLmean value (see Eq.(2)) was applied to the longitudinal stresses due to

both basic loadings (internal pressure and temperature loading).

Fig. 8. Basic cyclic loadings (out-of-phase/NP constant-amplitude pressure and tem-

perature variations due to the start-up and shut-down operations).

-200

0

200

400

0 1 2 3 4 5 6 7 8 9 10 11 12

Time

Stress(MPa

)

Mises

(L)nom

(h)nom

Fig. 9. Nominal stress history in the

rst three cycles.


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the amplied nominal principal stresses (seeFigs. 11 and 12), the

corresponding nominal principal strains are calculated (seeFig. 13). Note that the strains are triaxial (3 [v/(1 v)](1 2)) while the stresses are biaxial (s3 sz 0). Both

principal stresses and principal strains in the FE-SAFE output le(*.log) are elastic.

7.2.2. Plasticity correction

In the absence of experimental data, the static stressestraincurve (uniaxial curve) was estimated from the SMYS and SMTSstresses using the RambergeOsgood equation (seeFig. 14):

true strue

E

strueH

1=h(4)

and assuming the engineering ultimate strain to be half of theelongation. According to API Spec 5L[16], for X60 steel, the elon-

gation is 22%. As mentioned inFig. 14, the following values wereobtained for the hardening parameters:H690 MPa andh0.08.

Similarly, the cyclic stressestrain curve was dened as:

true strue

E

strue

Hc

1=hc(5)

Due to the lack of experimental data, in this study, the cycliccurve was taken to be the same as the static material curve, i.e.,

Hc Hand hc h(seeFig. 14). That is, neither a hardening benetnor a detrimental softening was taken into account.

The amplied nominal stress/strain plasticity correction, whichis an integral part of FE-SAFE, is based on a multiaxial approachusing Neubers rule[3e5,8,17,18]. In this process, the cyclic stresse

strain curves are modied to allow for the effect of biaxial stresses[3,15].

7.3. Strain-life method

The uniaxial eNcurve is dened by the CofneManson (CM)

equation:

D

2

s0fE

2Nb 0f2Nc (6)

The fatigue life for a multiaxial strain parameter can be calcu-

lated by modifying the right-hand side of Eq.(6)appropriately[8],

i.e., keeping the same general format and the same material con-stants (E,s0f;

0f,b,c). In this study, the fatigue lives of the corrosion

defects were obtained using the multiaxial BrowneMiller (BM)

algorithm[3e5,8]:

Dgmax2

Dn

2 1:65

s0fE

2Nb 1:750f2Nc (7)

Its worth noting that, under uniaxial conditions (3 2 v1),

the multiaxial BM equation (Eq.(7)) produces the same fatigue lifeas does the uniaxial CM equation (Eq.(6)) itself[8].

The BrowneMiller equation proposes that the maximum fatiguedamage occurs on the plane which experiences the maximum

shear strain amplitude, and the damage is a function of both thisshear straingmaxand the strain nnormal to this plane (seeFig.15).

According to Refs. [3,4], this is an attractive fatigue criterionbecause it uses standard uniaxial material properties and also gives

the most realistic life estimates for ductile metals [3,4].When the principal stresses/strains are out-of-phase/non-

proportional (NP), a critical plane (CP) technique is used. In thebiaxial case, the maximum shear planes are rotated round the 3-

axis, which is normal to the surface, through an angle f(0 f 180) varying typically in 10 increments (see Fig. 15). Theplane with the highest calculated damage is the critical plane, and

0

100

200

300

-200 -150 -100 -50 0 50 100

Longitudinal stress (MPa)

Hoopstress(MPa)

1st cycle

2nd cycle

A (t = 0)

B (t = 1)

D (t = 3)

C (t = 2) B'

Fig. 10. Nominal stresses according to the start-up and shut-downloading sequence.

Table 6

Typical FE nominal stress values acting on the pipeline during a loading cycle (see

Figs. 10 and 11).

Point Time Stress (MPa)

B,B0,C 1-2 Circumferential stressshdue to

the pressurepoper

228.48

B 1 Long itudinal stress (sL)p due to

the pressurepoper

68.54

D 3 Long itudinal stress (sL)DT due to

the temperature loading DT Toper Tinst

144.61

C 2 Total longitudinal stresssL 76.07

C 2 Von Mises equivalent stressseq 274.54

Table 7

Equations of some typical nominal-stress values during a loading cycle in a buried

pipeline (seeFigs. 10 and 11,andTable 6).

Point Longitudinal stress (sL) Hoop stress Von Mises equivalent stress (seq)

A 0 0 0

B vsh sh vsha

B0 0 sh shC EaDT vsh sh EaDT

2 vsh1=2 b

D EaDT 0 EaDTa

v ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffi

1 v v2p

y0:889< 1/seqB0> seqB.b

v EaDT1 2v v2sh > 0/seqC>seqD.

-200

0

200

400

0 1 2 3 4

Time

Stress(MPa

)

(L)nom

(h)nom

Fig. 11. Basic fatigue loading history (nominal stress components of the rst cycle, also

identied in FE-SAFE [8] as the in-plane principal stresses (s1)nom h (sh)nom and

(s

2)nomh

(s

L)nom).


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the calculated damage on this plane determines the fatigue life ofthe structure being analyzed.

Moreover, under the condition of NP loadings the plasticitycorrection is carried out using an incremental Neuber s rule [3e5,8,18] in terms of deviatoric stressestrain combined with amultiaxial cyclic plasticity model, i.e., kinematic hardening model,

together with multiaxial stressestrain relations.

In the absence of experimental data, the uniaxial fatigue pa-rameters were estimated by adjusting the CM equation (Eq.(6)) to

an adequate existing eNcurve. In particular, the fatigue strengthcoefcient was estimated as[19]:

s0f 1:5su (8)

The proposed methodology uses the ASME best-tcurve[20e22] which is, in fact, a strain-life (eN) uniaxial curve [21e23].For the API X-60 steel (su517 MPa) it can be estimated by Eq. (6)

with the following constant values (seeFig. 16):

s0f 775:5 MPa; b 0:14; 0f 0:31; c 0:48

(9)

The endurance limit was assumed to be 1 1015

cycles or2 1015 reversals (half-cycles).

7.4. Fatigue damage

In general, the fatigue damageis supposed to be calculated using

the PalmgreneMiner rule [3,5,8,15]. In this study, as the fatigueloading amplitudes are constant the damage was simply calculatedas:

D nDi n

Niafat (10)

where the fatigue usage factor is given by:

afat 1

DFF,EFF (11)

Alternatively, introducing D0 (afat)1D and N0 afatN with

Nh Ni, the criterion given by Eq.(10)can be rewritten as:

D0 DFF,EFFn

N

n

N0 1 (12)

8. Results

The fatigue life of the pipeline was calculated under the condi-

tions given in Table 1. The geometric characteristics and the SCFs of

the corrosion defects considered in this analysis (ve pits and vepatches) are shown inTables 2e5. Although the metal loss due tocorrosion is a time dependent process, it was assumed that the

corrosion defects exist since the start of the pipeline operation andtheir dimensions did not vary with time.

Fatigue cracks usually initiate from the body surface. In the caseof a pipe, this can be on the outer or on the inner wall surfaces.

However, assuming that the pipe is a thin shell submitted only topressure and temperature loadings, the stresses are the same at anypipe radial surface and so there is not this distinction in terms ofwhich surface cracks initiate.

The absolute value of the elastoplastic BM-parameter amplitudee/2, identied as the left-hand side of Eq. (7), and the corre-sponding fatigue lifeNare shown inFigs. 17 and 18, respectively, as

functions of the angle f related to rotation of principal/shear planesround the principal axis 3(3-axis h z-axis), mentioned in Section

Fig. 12. Amplication of the stresses during the fatigue loading history reading. In

order to apply different SCFs to the stress components, these were given as signals, and

the datasets dsi h [sxx syy szz syz szx], i L , h , dened as unit datasets:

dsL [1 0 0 0 0 0] and dsh [0 1 0 0 0 0].

-2000

-1000

0

1000

2000

0 1 2 3 4

Time

Principalstrain(-stra

in)

(1)nom

(2)nom

(3)nom

Fig. 13. Principal strains of the rst cycle (triaxial strains) for the plain pipe (defect

CWP0 or defect LP0). In this particular case, as the SCF i 1.0, i L, h, these strains

coincide with the nominal principal strains related to the nominal stresses in Fig. 11.

0

200

400

600

800

0 0,02 0,04 0,06 0,08 0,1 0,12

True strain (mm/mm )

Truestress(MPa)

Static (h=0.08, H=690 MPa)

Cyclic (hc=0.08, Hc=690 MPa)

Fig. 14. Estimated uniaxial stressestrain curves (see Eqs. (4) and (5)).

Fig. 15. Browne

Miller (BM) critical plane (CP) method.


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7.3. In fact, the elastic and elastoplastic values of the BM-parameter/strain are available at both extremes of the range/cycle (e1 and e2) infunction of the angle f, so that the user can calculate |e|/2 h je2 e1j/2. According to both these gures, the BM-parameter

is maximum and/or the fatigue life is minimum at f 30 on theplane 1e2.

These results mean that the likely cracks will originate at a plane(critical plane) normal to the pipe surface (case A shown in Fig. 15)

and whose normal vector nmakes a 30 angle with the referenceprincipal axiss*1related to the stress tensors*taken as a reference[8]to dene the surface orientation. In general,s*is dened as thestress tensor, within the stress history, with the largest principal

stress or, if the other two principals at this sample are negligiblysmall, the one with at least two signicant principals[8]. In thisstudy, the stress tensor of time t 1 (the end of the rst load stepwith the internal pressure totally applied), whose rst principal

axis coincides with the pipe circumferential (hoop) direction, was

chosen as a reference.Therefore, the critical plane itself makes a 30 angle with the

pipe longitudinal axis (the reference second principal axis s*2) and/

or, equivalently, its normal makes a 120 angle with the pipe lon-gitudinal axis (x-axis) in accordance with the angle fx.

Moreover, the fatigue loading history (longitudinal andcircumferential stresses shown in Fig. 11) were all classied as

Non-proportional (constant direction principals), that is, q1 0 atany time, and the circumferential stresses/strains were identiedas

the rst principals. The only interval, where the fatigue loadings

were proportional, was the rst load step related to the internal

pressure application, whensL (sL)p

nsh (see Table 7 and Fig.10).In a defect free pipe subjected to internal pressure and an axial

loading or temperature, the stress/strain principal axes are alwaysin the pipe longitudinal (axial) and circumferential (hoop) di-rections regardless of the phase between these loadings[5]. In thisstudy, the fatigue loadings (biaxial stresses) are non-proportional

due to the out-of-phase nature of the basic cyclic loadings.The fatiguelife and fatiguedamage for the corrosion pits and the

corrosion patches are shown inTables 8 and 9, respectively. Thelargest elastoplastic values of the BM-parameter/strain amplitude

e/2 were also included in these tables. For both types of corrosiondefects the larger the defect the higher the fatigue damage. Aspreviously mentioned, the corrosion defects named CWP0 andLP0 are in fact the defect free pipe (design condition).

As shown inTable 8andFig. 19, considering the fatigue damageacceptance criterion D 0.1 from Eqs.(10)and (11), all corrosionpits were accepted for more than 40 years, even the one which hasthe maximum depth (CWP5). However, the same doesnt apply in

the case of patches. As shown in Table 9 and Fig. 19, only thecorrosion patches LP1 and LP2 were accepted for more than 40years. The corrosion patches LP3, LP4 and LP5 violate the fatiguedamage acceptance criterion slightly above 26 years, 13 years and 6years respectively.

9. Conclusions

A methodology for the fatigue life assessment of hot pipelinescontaining corrosion defects in the base material was presented in

this paper. The general procedure includes three main phases:Global Analysis of the pipeline represented by a one-dimensional

0,01

0,1

1

10

100

1000

1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08

2N(half-cycles)

Stra

inamplitude(%)

ASME best-fit curve [2022]

CoffinManson adjusting (Sf'=775.5 MPa, b=0.14, ef'=0.31, c=0.48)

Corresponding BrownMiller equation with parameter e/2 (Eq. (7))

Fig. 16. Uniaxial strain-life curve adopted in the fatigue analysis (CofneManson

adjusting of the ASME best-t curve). The multiaxial BM-curve (Eq.(7)) uses the same

uniaxial constants.

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0 30 60 90 120 150 180

"C/P Ang" or angle (degree)

|Cycle--Ampl|or|e|/2(%)

plane 1-2

plane 1-3

plane 2-3

Fig. 17. BM-parameter amplitude throughout the rotation of the three shear planes

round the 3-axis for the plain pipe (defect CWP0 or defect LP0), after plasticity

correction.

0,E+00

1,E+07

2,E+07

3,E+07

4,E+07

5,E+07

0 30 60 90 120 150 180

"C/P Ang" or angle (degree)

LifeN

(repeats)

plane 1-2

plane 1-3

plane 2-3

Fig. 18. Fatigue life of the loading history throughout the rotation of the three shear

planes round the 3-axis for the plain pipe (defect CWP0 or defect LP0). Lives corre-

spondent to the BM-parameters (|e|/2) shown in Fig. 17.

Table 8

Fatigue damage of the corrosion pits for the pipeline design life (40 years).

Defect d/t e/2 (%)a N (repeats)b D n/Nb,c

CWP0 0.00 0.1202 1.48E06 0.0042

CWP1 0.10 0.1932 2.77E05 0.0225

CWP2 0.20 0.2307 1.58E05 0.0395

CWP3 0.30 0.2450 1.31E05 0.0476

CWP4 0.40 0.2562 1.14E05 0.0547

CWP5 0.50 0.2671 1.00E04 0.0624

a Largest elastoplastic values, critical plane 1e2 withf 30 orfx 120.b N Nh 1/Didue to loading history be consisted of a single cycle.c

n 3 cycles/week 52 weeks/year 40 years 6240 cycles.


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plain pipe model; nominal stress amplication by SCFs obtainedwith solid FE models, and strain-life calculation.

The amplied stresses are elastic and may exceed the yielding

limit. Also, due to the out-of-phase/non-proportional (NP) nature ofthe applied loadings and the pipe cylindrical geometry, the stressesare out-of-phase/NP and their principal directions do not change.Under such conditions, the plasticity correction is performed by

applying a multiaxial approach using Neubers rule, and the fatiguelife is calculated by using an eN method and the critical planetechnique.

The multiaxial BrowneMiller algorithm and the uniaxial eNASMEbest-tcurve were chosen for the fatigue life calculations.

The proposed methodology was applied to an onshore pipelinecontaining corrosion defects on its external surface. Five corrosionpits and ve corrosion patches, with different sizes, were consid-

ered in this analysis. The fatigue results (life and/or damage of allcorrosion defects) showed that all pits and only the two smallerpatches could be accepted for more than 40 years (6240 cycles or

start-up/shut-down operations). The other three corrosion patcheswould be approved up to just over 26, 13 and 6 years respectively.This means that fatigue becomes an important failure mode whencorroded pipeline segments are left in operation without beingreplaced.

It should be noted that despite the complexity related to themultiaxial stress/strain and its out-of-phase/NP characteristics

together with the plasticity, which may occur in the corrosiondefect, the fatigue loading was reduced to only one nominal stress

history, and the fatigue analysis of the various corrosion defectsrequired only the changing of the SCFs values.

Finally, its worth pointing out that this is a purely theoreticalstudy and testing is required to validate the approach.

Acknowledgments

The authors would like to thank PETROBRAS for the permissionto publish this paper.

References

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Table 9

Fatigue damage of the corrosion patches for the pipeline design life (40 years).

Defect d/t e/2 (%)a N (repeats)b D n/Nb,c

LP0 0.00 0.1202 1.48E06 0.0042

LP1 0.10 0.2103 2.11E05 0.0296

LP2 0.20 0.2905 7.86E04 0.0794

LP3 0.30 0.3615 4.23E04 0.1475

LP4 0.40 0.4702 2.08E04 0.3000

LP5 0.50 0.6040 1.08E04 0.5778a Largest elastoplastic values, critical plane: 1e2 withf 30 orfx 120 .b N Nh 1/Didue to loading history be consisted of a single cycle.c n 3 cycles/week 52 weeks/year 40 years 6240 cycles.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0 1 2 3 4 5

Corrosion defect

Damage

Pits

Patches

Fig. 19. Fatigue damage of the corrosion pits and patches for the pipeline design life:

40 years (seeTables 8 and 9).

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