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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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2 Copyright 2014 by AS
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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3 Copyright 2014 by AS
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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4 Copyright 2014 by AS
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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5 Copyright 2014 by AS
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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7 Copyright 2014 by AS
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.
REFERENCES[1] Selvadurai, A. P. S., and Shinde, S. B., 1993, Frost heave
induced mechanics of buried pipelines, Journal of
geotechnical engineering, Vol. 119(12), pp. 1929-1951.
[2] Mohr, W., 2003, Strain-Based Design of Pipelines, EWI
Report Project 45892GTH., Columbus, OH.
[3] Tyson, W. R., 2009, Fracture Control for Northern
Pipelines Damage and Fracture Mechanics, T.
Boukharouba, M. Elboujdaini, and G. Pluvinage, eds.,
Springer Netherlands, pp. 237-244.
[4] Fairchild, D. P., Kibey, S. A., Tang, H., Krishnan, V. R.,
Wang, X., Macia, M. L., and Cheng, W., 2012, Continued
advancements regarding capacity prediction of strain-based
pipelines, Proceedings of 9th International Pipeline
Conference (IPC2012), Calgary, Alberta, Canada,
September 2428.[5] ASTM, 2011, ASTM E1820-11: Standard Test Method for
Measurement of Fracture Toughness, America Society for
Testing and Materials International, West Conshohocken,
PA.
[6] BSI, 1991, BS 7448-1: Fracture mechanics toughness tests
Method for determination of KIc, critical CTOD and critical
J values of metallic materials, British Standard Institution,
London.
[7] Chiesa, M., Nyhus, B., Skallerud, B., and Thaulow, C.,
2001, Efficient fracture assessment of pipelines. A
constraint-corrected SENT specimen approach,
Engineering Fracture Mechanics, Vol. 68(5), pp. 527-547.
[8] Shen, G., and Tyson, W. R., 2009, Evaluation of CTODfrom J-integral for SE(T) specimens, Pipeline Technology
Conference 2009 Ostend, Belgium.
[9] DNV, 2010, Offshore Standard DNV-OS-F101:
Submarine Pipeline Systems," Det Norske Veritas.
[10] Ruggieri, C., 2012, Further results in J and CTOD
estimation procedures for SE (T) fracture specimensPart I:
Homogeneous materials, Engineering Fracture Mechanics,
Vol. 79, pp. 245-265.
[11] Moreira, F. and Donato, G., 2010, Estimation proced
for J and CTOD fracture parameters experime
evaluation using homogeneous and mismatched clam
SE(T) specimens, Proceedings ASME 2010 Pres
Vessels and Piping Conference, PVP2010, Belle
Washington, USA, July 18-22.
[12] Donato, G. H. B. and Ruggieri, C., 2006, Estima
procedure for J and CTOD fracture parameters using th
point bend specimens, Proceedings of 6th Internati
Pipeline Conference (IPC2006), Calgary, Alberta, Can
September 25-29, Paper Number: IPC2006- 10165.
[13]Cravero, S. and Ruggieri, C., 2007, Estimation procedof J resistance curves for SE (T) fracture specimens u
unloading compliance, Engineering Fracture Mechan
Vol. 74(17), pp. 2735-2757.
[14] Deng, Z., Chang, C., and Wang, T., 1980, Measuring
calculating CTOD and the J-integral with a double
gauge, Strain, Vol. 16(2), pp. 63-67.
[15] Willoughby, A. A. and Garwood, S. J., 1983, On
Unloading Compliance Method of Deriving Sin
Specimen R-Curves in Three-Point Bending, ElaPlastic Fracture Second Symposium, Volume II: Frac
Curves and Engineering Applications, ASTM STP 803,
II-372-II-397.
[16] DNV, 2000, Offshore Standard DNV-OS-F
Submarine Pipeline Systems, Det Norske Ve
(superseded).
[17] Tang, H., Macia, M., Minnaar, K., Gioielli, P., Kibey
and Fairchild, D., 2010, Development of the SENT
for Strain-Based Design of Welded Pipelines, Proceed
of 8th International Pipeline Conference (IPC20
Calgary, Alberta, Canada, September 27October 1.
[18] Shih, C. F., 1981, Relationships between the J-inte
and the crack opening displacement for stationary extending cracks, Journal of the Mechanics and Physic
Solids, Vol. 29(4), pp. 305-326.
[19] Moore, P. L., Pisarski, H. G., 2012, Validation of meth
to determine CTOD from SENT specimens, Internati
offshore and polar engineering conference, Rhodes, Gre
pp. 577-82.
[20] Verstraete, M. A., Denys, R. M., Van Minnebruggen,
Hertel, S., and De Waele, W., 2013, Determination
CTOD resistance curves in side-grooved Single-E
Notched Tensile specimens using full field deforma
measurements, Engineering Fracture Mechanics, Vol.
pp. 12-22.
[21] ADINA,2012, Theory and Modeling Guide, ADIN& D Inc., Watertown, MA.
[22] Lubliner, J., 2008, Plasticity Theory, Courier Do
Publications, Mineola, NY.
[23] Shen, G., Bouchard, R., Gianetto, J. A., and Tyson, W
2008, Fracture toughness evaluationof high strength s
pipe, Proceedings of PVP 2008, ASME Pressure Ve
and Piping Division Conference, Chicago, Illinois, U
July 27-31.
-
5/25/2018 Accuracy of the Double-clip on Gauge Method for Evaluating CTOD of SE(T) Specimens
8/8
8 Copyright 2014 by AS
[24] DNV, 2006, Recommended Practice DNV-RP-F108:
Fracture Control for Pipeline Installation Methods
Introducing Cyclic Plastic Strain, Det Norske Veritas.
[25] Dodds, R. H., 2009 WARP3D: Notes on Solution &
Convergence Parameters for a Shallow-Notch SE(B)
Model,University of Illinois at Urbana-Champaign.
[26] Qian, X., Dodds, R. H., 2006, WARP3D: Effect of Mesh
Refinement on the Crack-tip Stress Field for SSY Models,
University of Illinois at Urbana-Champaign.
[27] Graba, M., Galkiewicz, J., 2007, Influence of The Crack
Tip Model on Results of The Finite Element Method,
Journal of Theoretical and Applied Mechanics, Vol. 45, pp.
225-237.
[28] Shen, G., Gianetto, J. A., and Tyson, W. R., 2009,
Measurement of J-R Curves Using Single-Specimen
Technique on Clamped SE(T) Specimens, Proceedings of
Nineteenth International Offshore and Polar Engineering
Conference, The International Society of Offshore and
Polar Engineers (ISOPE), Osaka, Japan, pp. 92-99.
[29] Wang, E., Zhou, W., Shen, G. and Duan. D., 2012, An
Experimental Study on J(CTOD)-R Curves of Single EdgeTension Specimens for X80 Steel, Proceedings of 9th
International Pipeline Conference (IPC2012), Calgary,
Alberta, Canada, September 2428, Paper Number:
IPC2012-90323.
[30] Soboyejo, W. O., 2003, Mechanical Properties of
Engineered Materials, Marcel Dekker, Inc., New York.
[31] Tracey, D. M., 1976, Finite Element Solutions for Crack-
Tip Behavior in Small-Scale Yielding, Journal of
Engineering Materials and Technology, Vol. 98(2), pp. 146-
151.