accuracy of the double-clip on gauge method for evaluating ctod of se(t) specimens

5/25/2018 Accuracy of the Double-clip on Gauge Method for Evaluating CTOD of SE(T) Specimens

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1 Copyright 2014 by AS

Proceedings of the 2014 10th International Pipeline ConfereIPC2

September 29 October 3, 2014, Calgary, Alberta, Can

IPC2014-3321

ACCURACY OF THE DOUBLE-CLIP ON GAUGE METHOD FOR EVALUATING

CTOD OF SE(T) SPECIMENS

Zijian Yan, Yifan Huang, Wenxing Zhou1

Department of Civil and Environmental Engineering

The University of Western Ontario

1151 Richmond Street, London, ON, Canada N6A 5B9

KEYWORDSCrack tip opening displacement (CTOD); Double-clip on

gauge; Fracture toughness testing; SE(T) specimen

ABSTRACTThe crack tip opening displacement (CTOD)-based fracture

toughness has been widely used for structural integrity

assessment and strain-based design of oil and gas pipelines.

The double-clip on gauge method has been used to

experimentally determine CTOD. In this study, three-

dimensional (3D) finite element analyses of clamped single-

edge tension (SE(T)) specimens are carried out to investigatethe accuracy of the CTODevaluation equation associated with

the double-clip on gauge method. The analysis considers

SE(T) specimens with ranges of crack lengths (0.3 a/W 0.7)

and specimen thickness (B/W = 0.5, 1 and 2). Based on the

analysis results, a modified CTOD evaluation equation based

on the double-clip on gauge method is developed to improve

the accuracy of the CTOD evaluation. This study will

facilitate the application of the fracture toughness determined

from the SE(T) specimen in the strain-based design of

pipelines.

INTRODUCTION

The strain-based design (SBD) method is considered aviable option to address the demanding loading conditions in

offshore and onshore energy pipeline applications, such as

offshore pipe laying and large ground movements imposed on

onshore pipelines due to, for example, seismic activity,

landslides, frost heave, and thaw settlement [1-3].

1Corresponding author: [email protected]

Tel: 1.519.661.2111 x 87931, Fax: 1.519.661.3779

In the SBD method, the fracture toughness is a key inpu

the evaluation of the tensile strain capacity of the pipeline,

the allowable longitudinal tensile strain in the pipeline g

weld containing circumferential cracks [4]. For du

materials, the fracture toughness is usually characterized by

toughness resistance curve, such as crack-tip open

displacement resistance (CTOD-R) curve, which is typic

obtained from deeply-cracked single-edge bend (SE(B))

compact tension (CT) specimens as standardized in AS

1820-11 [5] and BS7448-1[6]. Due to the similar load

conditions and crack-tip constraint levels between the sin

edge tension (SE(T)) specimen and the full-scale pipe

containing surface cracks under longitudinal tension [7], th

is an increasing interest in using the SE(T) specimen

determine the toughness resistance curve in the pipe

industry over the last decade.

Previous studies [8-10] indicate that CTOD can

determined indirectly from theJ-integral (J) through aJ-CT

relationship that involves a dimensionless constraint parame

m. The value of J can be evaluated from the experiment

measured load-displacement curve through a plastic geom

factor, pl [8-10]. It follows that by adopting this method

accuracy of the determined CTODis largely governed by th

two parameters, i.e. m and pl, both of which are functionthe specimen geometry and material properties [8-11].

Compared with the indirect method, the plastic compon

of CTODcan be determined directly from the measured cr

mouth opening displacement (CMOD) by employing a pla

hinge model assuming two halves of the specimen rotate rig

about a rotational center (i.e. plastic hinge) during tests

specified in BS7448-1[6] for bend specimens. However,

position of the plastic hinge is usually load-, geometry-

material-dependent [12, 13].


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The double-clip on gauge (DCG) method [14, 15] was first

proposed in the 1980s as an alternative to experimentally

determine CTOD. As shown in Fig. 1, a pair of specially-

designed knife edges are used to adapt two clip-on gauges at

different heights above the specimen surface, which can

simultaneously measure two values of CMOD at the two

heights. Based on certain simplifying assumptions, CTODcan

then be related to the two directly measured CMOD values

through a simple geometric relationship. The advantage of the

DCG method is that it is based on the physical deformation of

the crack tip and simple geometric relationship and does not

involve the evaluation of Jor assumption of the location of the

plastic hinge as required in the plastic hinge model. The DCG

method was documented in a version of DNV-OS-F101 [16]

that has since been superseded.

Fig. 1. Schematic illustration of the installation of knife edges

for the double-clip on gauge method

Tang et al. [17] examined the applicability of the DCG

method for SE(T) specimens numerically based on two-

dimensional (2D) plane strain finite element analyses (FEA).

The crack propagation was simulated, and the CTOD was

defined as the opening length of the original crack tip before

blunting, which is different from the commonly used 90

intersect definition of CTOD [18]. These two CTOD

definitions are schematically illustrated in Fig. 2. Tang et al.

reported that the CTODvalues obtained from the DCG method

agree well with the corresponding values directly obtained from

FEA. Moore and Pisarski [19] investigated the accuracy of

the DCG method experimentally by comparing the CTOD

values obtained from DCG with those measured from the

specimen notch replicas. They adopted the same definition of

CTODas that by Tang et al. [17] and reported that the CTOD

values measured using DCG agree well with the physical

measurements taken from the notch replicas with errors being

less than 10% if the relative crack length (a/W) is in the range

of 0.3 to 0.5, where aand Ware the crack length and specimenwidth, respectively. Verstraete et al. [20] employed the Digital

Image Correlation (DIC) technology to obtain the full field

optical deformation measurements of the SE(T) specimen and

concluded that CTOD values obtained through the full field

measurements are in excellent agreement with those obtained

from DCG for a/W = 0.2 and 0.4. In their study, the CTOD

obtained from DCG was defined based on the 90 intersect

method starting from the deformed crack tip [18], as illustrated

in Fig. 2.

In this study, systematic three-dimensional (3D) fi

element analyses of clamped SE(T) specimens are carried

to investigate the accuracy of CTODmeasured from the D

method. The analysis considers SE(T) specimens with ran

of crack lengths and thickness-to-width ratios. The commo

used 90 intersect definition of CTODwas adopted in this st

and is denoted by CTOD90

or 90

. The geometric relation

in the vicinity of the deformed crack tip that is key to the D

method was examined, and the impact of specimen thickn

to-width ratio on the accuracy of the DCG method was

investigated. Based on the analysis results, the exis

equation for evaluating CTODbased on the DCG method

slightly modified to improve the accuracy of the CT

evaluation. This study will facilitate the application of

fracture toughness determined from the SE(T) specimen in

strain-based design of pipelines.

Fig. 2. Schematic illustration of CTODdefinitions

The rest of this paper is organized as follows. A b

illustration of the DCG method for evaluating CTOD9included in Section 2; the 3D FEA models and anal

procedures are described in Section 3; Section 4 shows

analysis results and modification of the existing DCG-ba

equation for evaluating CTOD90, and the summary

concluding remarks are presented in Section 5.

CTOD MEASURED FROM DOUBLE-CLIP ON GAUMETHOD

A detailed geometry near the crack tip regarding

double-clip on gauge method was developed and shownFig. 3, where point O is the deformed crack tip and OB is

45 interception line that used to determine CTOD90.

following equation can be derived from the geome

relationships shown in Fig. 3 to evaluate the CTOD v

considering the similar triangles betweenBEFandFHG:

{= +co()sin =


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where V1 and V2 are the two measured crack mouth opening

displacements corresponding to two different knife edge

heightsz1andz2, respectively; a0is the initial crack length, and

DC90denotes the CTODvalue obtained from the double-clip on

gauge method here. Generally the angle is small such that

Eq. (1) can be simplified as:

= + Equation (2) is the same as that used by Tang et al. [17],

although they adopted a different definition of CTOD.

Fig. 3. Schematic illustration of the geometric relationship for

the evaluation of CTOD

In the 2000 version of DNV-OS-F101 [16], DC90 isseparated into an elastic component and a plastic component as

follows:

= () + where the first term on the right hand side of Eq. (3) is the

elastic component of DC90 and evaluated from the stress

intensity factor KI; v, E and YS are Poisson's ratio, Youngs

modulus and the yield strength of the material, respectively; the

second and third terms on the right hand side of Eq. (3) are the

plastic component of DC90, and Vpl1 and Vpl2 are the plastic

components of the two measured CMOD values. Theaccuracy of both Eqs. (2) and (3) was examined in this study.

FINITE ELEMENT ANALYSESThe commercial software package ADINA 8.7.4 [21] was

used to carry out the 3D FEA. The J2 incremental theory of

plasticity [22] with the finite strain formulation was employed

in the analysis. All the SE(T) specimens considered in this

study are end-clamped, plane-sided, and have the same width

(W= 20mm) and daylight length (H= 10W) [23, 24], but five

different relative crack lengths, i.e. a/W = 0.3 to 0.7 with

increment of 0.1, and three different thickness-to-width ra

i.e.B/W = 0.5, 1 and 2, whereBis the specimen thickness.

Because of symmetry, only a quarter of the specimen

modeled using 8-node 3D isoparametric brick elements w

the 2 2 2 Gaussian integration [21]. The model

divided into 17 layers along the thickness direction with mesh density increasing from the mid-plane to the free sur

to capture the high stress gradients near the free surface.

blunt crack tip with initial radii (0) of 2.5, 5 and 10 m

incorporated in the model to simulate the crack-tip blun

during the loading process and facilitate convergence of

finite strain analysis [25]. The first value of 0is the base

case that applies to all the specimens considered, whereas

latter two values were employed for selected geome

configurations only (i.e. B/W= 1 and a/W= 0.5) to investi

the impact of the initial crack tip radius on the accuracy of

DCG method. The mesh surrounding the crack tip consist

40 concentric semicircles. In the vicinity of the crack tip,

minimum in-plane size of the elements closest to the crackis about 1/10 of the crack-tip radius [26, 27], whereas the

plane size of the elements in the outermost ring (i.e. 40 thrin

about 2,000 times that of the element closest to the crack

[25]. The total number of elements is approximately 32,

for a typical model. The geometric and mesh configurat

for a typical specimen withB/W= 1and a/W= 0.5 are show

Fig. 4 together with the fixation and loading conditi

Stationary cracks were assumed in the present analysis.

The uniaxial stress-strain relationship of the materia

described using an elastic-power law plastic expression:

= { , , > where 0 is the reference stress; 0 is the reference strain,

0/E; n denotes the strain hardening exponent of the mate

In this study 0 = YS= 520 MPa,E= 200 GPa and n= 10 w

selected.

According to the reported test results in the literature

29], all the specimens were loaded by a displacem

controlled load up to the level corresponding to large pla

deformations, i.e.P/Py= 1.3, through about 5,000 steps, wh

P is the applied load, and Py is the reference load define

B(W - a)Y [8]. Note that Y is the effective yield strendefined as Y= (YS+ TS)/2, where TS is the ultimate ten

strength. Applying Consideres necking criterion [30] to

(4), one can derive the following equation to evaluate TS:

= /where e= 2.71828 is the base of the natural logarithm.


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Fig. 4. Geometric and mesh configuration of the finite element model with a blunt crack tip

Convergence studies on mesh density and deformation rate

were conducted and showed good convergence in the elastic-

plastic analyses. As illustrated in Fig. 5, due to symmetry,

CTOD90/2 was evaluated based on the intercept between a

straight line at 45 originating from the crack tip in the

deformed position and the deformed crack flank at the mid-

plane of the specimen. The interception point was captured

using a linear interpolation between two nearest deformednodes on the deformed flank given the corresponding nodal

displacements [8, 10, 31]. The value of CTOD90 obtained

from FEA based on this approach is denoted by FE90 and

considered as the true value of CTODin this study.

Fig. 5. Schematic illustration of the determination of CTOD

in FEA

As shown in Fig. 6, the two measured CMODs, i.e. V1

V2, are calculated from the nodal displacements of the

outermost nodes on the deformed crack flank at the mid-p

of the specimen in FEA, i.e. points M and N, which

corresponding to the two knife edge heights of zero and

Therefore, Eqs. (2) and (3) can be employed to calculate

double-clip on gauge measured DC90 according to the F

results. Several other positions of pointN(shown in Fig. Ni, i= 2, 3, 4, 5) have been analyzed as sensitivity cases, wh

indicates that DC90is insensitive to the position of point N.

Fig. 6. Schematic illustration of the double-clip on gaug

method in FEA


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RESULTS AND DISCUSSIONSLet e1 = (DC90 - FE90)/FE90 denote the error of DC90

evaluated using Eq. (3). The values of e1 are plotted against

P/Py for specimens with the same B/W ratio but different a/W

ratios in Figs. 7(a) through 7(c). The figures suggest that once

P/Py exceeds 0.3, DC90 can markedly overestimate FE90, and

when the applied load reaches around 0.9Py, the error reaches a

peak value of up to 40%. The specimen B/W ratio has a

negligible impact on this error. It is also observed that the

error associated with DC90evaluated using Eq. (2) (i.e. without

separating CTOD into the elastic and plastic components) is

even higher than that associated with DC90evaluated using Eq.

(3), with the peak value reaching as high as 100%. The main

reason attributing to this error is that the idealized geometric

relationship as shown in Fig. 3 does not always hold in real

situations.

(a) B/W= 0.5

(b) B/W= 1

(c) B/W= 2

Fig. 7. Variation of e1against P/Py

Figure 8(a) schematically illustrates the geome

relationship in the vicinity of the blunt crack tip accordin

the FEA results, which indicates that the intersection p

between the 45 line from the crack tip and deformed cr

flank, i.e. point D, is not on the extension of the straight

that connects the two outermost nodes on the deformed cr

flank in FEA, i.e. points M and N. In other words,

assumption that the intersection pointDis collinear with po

Mand Nas involved in the DCG method (see Fig. 3) does

hold in real conditions. Figure 8(a) also clearly shows

relationship between the true CTOD90, FE90, and the CT

value evaluated using the DCG method. The above observa

suggests that although the DCG method is more advantage

than the single clip-on gauge method by avoiding

assumption of the plastic hinge location, the accuracy of

DCG method can be further improved. The relatively la

errors associated with the DCG method as reflected in Fi

are in contrast to the results reported in [19], which indic

that the accuracy of the DCG method is within 10%. Note

the CTOD definitions adopted in this study and in [19]

different; therefore, the difference between the accuracy ofDCG method reported in the two studies suggests that

accuracy is sensitive to the definition of CTOD.

(a)

(b)

Fig. 8. Geometric relationship surrounding the blunt cra

tip

-10%

0%

10%

20%

30%

40%

50%

0 0.2 0.4 0.6 0.8 1 1.2 1.4

a/W = 0.7

a/W = 0.6

a/W = 0.5

a/W = 0.4

a/W = 0.3

P/Py

e1

-10%

0%

10%

20%

30%

40%

50%

0 0.2 0.4 0.6 0.8 1 1.2 1.4

a/W = 0.7

a/W = 0.6

a/W = 0.5

a/W = 0.4

a/W = 0.3

P/Py

e1

-10%

0%

10%

20%

30%

40%

50%

0 0.2 0.4 0.6 0.8 1 1.2 1.4

a/W = 0.7

a/W = 0.6

a/W = 0.5

a/W = 0.4

a/W = 0.3

P/Py

e1


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To improve the accuracy of CTOD measured using the

DCG method, a correction factor, DC, as defined in Fig. 8(b)

by settingMC'=DCa0, is introduced to modify the initial crack

length a0used in Eq. (1). Equation (1) can then be revised as

follows by considering the similar triangles between D'EMand

NFM:

{= +co()sin = where the correction factor DCcan be uniquely determined by

setting DC90= FE90. The values of DC are plotted against

P/Pyfor clamped SE(T) specimens with ranges of B/Wand a/W

ratios in Fig. 9(a). It is observed that DCgenerally decreases

towards unity as P/Py or a/W increases, which means that for

deeply-cracked specimens, i.e. point Din Fig. 8 being far away

from pointsMandN, the required correction factor,DCis close

to unity. For specimens with a/W= 0.5, 0.6 and 0.7, the B/W

ratio has a negligible impact on DC, and for specimens witha/W= 0.3 and 0.4, the maximum difference between DCvalues

corresponding to differentB/Wratios is about 4%. The impact

of the initial blunt crack tip radius in the FEA mesh, 0,on the

proposed correction factor DC was also investigated. Based

on clamped SE(T) specimens with a/W= 0.5 and B/W= 1, the

values ofDCcorresponding to three different0are depicted in

Fig. 9(b), which shows thatDCis insensitive to0.

(a)

(b)

Fig. 9. Variation of DCagainst P/Py

To facilitate the practical application of DC, the follow

expression of DCwas developed based on the results obtai

in this study:

= (/) (/) (/),0.3 / 0.7 where the fitting coefficients q0, q1, q2 andq3are functiona/Wand given as follows:

= 1.1803/ 2.0817= 2.5743/ 1.9859= 4.5977/ 3.1564= 2.3633/ 1.5551

The fitting error of Eq. (7) is generally less than 3%.

error of the DCG method by employing the modified equati

i.e. Eqs. (6) and (7), denoted as e2, is plotted against P/Pyspecimens with B/W = 1 in Fig. 10, which indicates that

modified equations can significantly improve the accuracy

CTODevaluated from the DCG method with e2being generwithin 10%. It should be noted that Eq. (7) is applicable

the stain hardening exponent of n= 10.

Fig. 10. Variation of e2against P/Pyfor specimens with B/W

SUMMARY AND CONCLUDING REMARKSThe double-clip on gauge method used to experiment

measure CTOD for clamped SE(T) specimen was review

and the accuracy of this method was systematically investig

by carrying out three-dimensional finite element analyse

clamped SE(T) specimens with a wide range of specim

dimensions (a/W= 0.3 to 0.7 with an increment of 0.1, and= 0.5, 1 and 2). The commonly-used 90 degree intersec

definition of CTOD was adopted in this study rather than

definition used in [17] and [19].

It is observed that the CTOD values evaluated using

existing equations based on the CMODmeasurements obta

from the double clip-on gauges can involve significant err

This error primarily depends on a/W and loading l

characterized byP/Py, and can be as large as 40 - 100%.

specimen B/W ratio has a negligible impact on the er

Based on the 3D FEA results obtained in this study,

geometric relationship surrounding the blunt crack tip

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4

B/W = 1

B/W = 2

B/W = 0.5

P/Py

D

C

a/W = 0.7

a/W = 0.3

1

1.1

1.21.3

1.4

1.5

1.6

1.7

1.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Initial radius 2.5m

Initial radius 5m

Initial radius 10m

P/Py

DC

-10%

0%

10%

20%

30%

40%

50%

0 0.2 0.4 0.6 0.8 1 1.2

a/W = 0.7

a/W = 0.6

a/W = 0.5

a/W = 0.4

a/W = 0.3

P/Py

e2


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investigated and the existing DCG-based equations were

modified by introducing a correction factor to the original crack

length included in the equation. This correction factor was

then fitted as a polynomial function of a/W and P/Py. The

modified equation can significantly improve the accuracy of the

CTODevaluated from the double clip-on gauges, with the error

being generally within 10%. Further analyses will be carried

out to investigate the impact of the presence of side grooves

and the stain hardening exponent n of the material on the

accuracy of the DCG method and compare the numerical

results with experimental data.

ACKNOWLEDGMENTSThe authors gratefully acknowledge the financial support

provided by the Natural Sciences and Engineering Research

Council (NSERC) of Canada and TransCanada Ltd. through the

Collaborative Research and Development (CRD) program.

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accuracy of the double-clip on gauge method for evaluating ctod of se(t) specimens

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