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April 2006

Fracture Control of pipelines using LINKpipe. From rule based design to direct calculations

by

Christian Thaulow1, Bjørn Skallerud, Kjell Holthe, Espen Berg

NTNU, Norwegian University of Science and technology

Erling Østby, Bård Nyhus, Jack Ødegård 1SINTEF Materials and chemistry, Norway

Introduction Surface cracks pose major challenges for the structural integrity of pipelines. In fracture assessment programs the use of constraint parameters, such as the T-stress, along with K, J or CTOD are important to account for the limitations of single-parameter fracture mechanics. However, the three-dimensional nature of surface cracks precludes detailed 3-D finite element modeling for routine calculations. Here line-spring/shell-element models are demonstrated to be an efficient and reasonably accurate tool even under large deformation levels when general yielding prevails in the pipe. Envisaging the potential use of this procedure in fracture analysis of pipelines, a new software, LINKpipe, has been developed. The start-up company LINKftr AS, was founded in august 2001, as cooperation between The Norwegian University of Science and Technology (NTNU) and SINTEF. LINKpipe is a state-of-the-art software-tool for analysis of the criticality of cracks and defects in pipelines and piping systems. The program simulates external and internal surface cracks in pipelines under tensile, bending and internal/external pressure. LINKpipe combines structural- and local defect analysis and is merging the competence of materials- and structural engineering in a user-friendly way. The first product, LINKpipe Ver1.1 was launched in April 2004. And a new version, LINKpipe Ver2.0, where ductile crack growth is included was presented in April 2006. The software has been developed in close cooperation with the joint industry-project "Fracture Control Offshore Pipelines". The project organized a special session during OMAE 2005 (11). The LINKpipe license has been sold to 6 companies, and is now applied in 3-4 pipeline projects. References from the development work of the program, and recent applications, can be found in the list of references:

1 christian.thaulow@ntnu.no, +47 93059460

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• Paper 1, 2 ,4 and 5 are mainly related to the development of the shell- and

linespring elements, • Paper 6 presents the philosophy of direct calculations • Paper 3, 7, 8, 9, 10, 11 and 12 are related to the verification and application of

LINKpipe Shell- and linespring elements In LINKpipe the geometry of an elliptical surface crack is represented by so-called linespring elements. These elements are introduced in a shell FE model of a structure at critical locations (areas with low toughness or high stresses/strains), (1, 2, 4 and 5). The part through surface crack is a 3D problem. Now, this problem can be formulated within 2D plate- or shell theory with the part through surface crack represented with linesprings, Figure 1.

Figure 1 Representation of a 3D crack by linesprings in a FE model

The plastic deformation and the fracture mechanics parameters, including the T-stress (9), are quite accurately calculated from the shell- and linespring analyses. In LINKpipe the linespring is implemented in a co-rotated kinematical finite element formulation, i.e. accounting for large displacements and rotations. The program also accounts for plastic necking of the ligament and non-proportional loading. The linespring calculations have been verified by 3D FE calculations and full scale testing of pipes, with and without internal pressure. The verifications include the following range of parameters:

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LINKpipe Ver2.0 (April 2006) INPUT

• geometry: plate, SENB, SENT, pipe • loading: tensile, bending, internal/external pressure • crack size: a/2c from 4 to 30% of the circumference of the pipe, a/t from 0.1 to

0.5 • hardening exponent: n=0.05-0.1 • point wise stress-strain curves • ductile tearing resistance curve, CTOD-∆a • cracks positioned outside/inside the pipe • reeling operations (deformation cycles, back tension) • misalignment/difference in wall thickness • yield strength and hardening mismatch between weld and base material • separate the shell elements in “patches”, with specific material properties • “cut back”, automatic step back to obtain convergence

RESULTS • Global: load, displacement • Shell: equivalent strain, mises stress, strain E11, E22, E33 • Linespring: CTOD, J-integral, K-stress intensity, T-stress, ductile tearing

Further developments Axial oriented cracks, ductile crack growth in the circumferential direction, bi-material (split-linespring), kinematic hardening, embedded defects, LINKfatigue, LINKcorr, LINKleak…

In Figure 2 we compare the result of the linespring/shell-elements with 3D large strain FE calculations for a pipe performed with Abaqus. The results are very similar, except for the time of calculation: LINKpipe is 600 times faster. Similar results are obtained for other geometries and hardening exponents.

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Figure 2 CTOD vs. strain for a pipe with an elliptical surface crack. The pipe dimensions are OD=400mm, WT=20mm. The crack is halfway through the thickness. The computation times for the 3D and linespring calculations are indicated.

LINKpipe also calculates the T-stress for cracks in pipes, (3, 7, 8 and 9). One example is shown in Figure 3.

Figure 3 Distribution of T-stress along the crack front for an elliptical surface crack in a pipe. 3D and linespring results, (9).

0 0.2 0.4 0.6 0.8 1s / c

-0.8

-0.6

-0.4

-0.2

0

β =

T (π

a)1/

2 / K

3-DLink

Pipe - Tensiona / t = 0.2

Mid-section Surface

Calculation time 3D 60.000 sec (cpu) LINKpipe 100 sec (cpu)

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Ductile tearing Recently, also ductile tearing has been introduced in LINKpipe (10, 11 and 12), and this option has been included in LINKpipe Ver2.0. See Figure 4. A ductile crack growth model using line-spring finite element was proposed by Lee and Parks (13) for fully plastic, quasi-static through-thickness crack growth in surface cracked shell structures. They employed a plane-strain sliding-off and cracking model to obtain the instantaneous crack tip opening angle in terms of the material parameters and the instantaneous slip-line angle and stress triaxiality at the crack tip. A more simplistic approach to propagate the crack in line-spring model is to use the traditional material crack growth resistance curve. This is in accordance with the established use of the resistance curves to account for ductile tearing. Further, the constraint correction of the resistance curve Nyhus et al., (14) can be easily included in the simulations since the T-stress is readily available from the line-spring element. The local responses displayed in Figure 4 show that for any given strain level, the CTOD increases with increase in crack depth. Hence, the crack growth initiates at lower levels of deformation as crack depth increases. Thus, while the ductile tearing in the shallowest crack (a/t = 0.1) starts at about 4% strain, the same for the deepest crack (a/t = 0.5) begins at strain levels below the yield strain. Further, as the crack depth increases, the stable crack growth regime gets shortened and unstable tearing starts at lower levels of deformation. Thus, the unstable ductile tearing in the deepest cracked pipe occurs almost just after the initiation, and no stable crack growth is observed in this case

Figure 4 The effect of crack depth and ductile tearing on CTOD vs. strain, (11). Surface cracked pipes loaded in tension. 0.2-ST and 0.3-ST refers to static analysis without ductile tearing.

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Internal pressure Shown in Figure 5 are the results obtained from the tensile loading of a surface cracked pipe with additional internal pressure. The magnitude of pressure is marked as the ratio of hoop stress caused by the internal pressure to the initial yield stress. The pressure load was applied first, and then the end displacements were applied gradually, since this loading sequence corresponds to realistic situations. The CTOD responses displayed in Figure 5 show that with increase in magnitude of hoop stress, the CTOD at any given strain level increases significantly. For stationary cracks, Jayadevan et al. (10) have verified from the 3D finite element analyses of surface cracked pipes that the biaxial loading strongly enhance the ligament localisation. As the magnitude of internal pressure increases, the unstable tearing begins at lower values of deformation level. In other words, the deformation capacity of the cracked pipe is significantly reduced under biaxial loading.

Figure 5 The effect of internal pressure, combined with ductile tearing, on the applied CTOD vs. global strain. Surface cracked pipe under tension load. The LINKpipe calculations have been verified by full scale testing of pipes under bending, with and without internal pressure (introduced by water). A paper describing the tests is under preparation, (15). One example is shown in Figure 6. The LINKpipe calculations follow the test results with good accuracy, and capture both the physics (the calculation follows the curvatures of the test) and the final failure.

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Figure 6 Large scale testing of pipe with surface crack loaded with internal pressure and bending, (15). Engineering Critical Assessment To demonstrate the potential for direct calculations with linespring, the crack driving force for Engineering Critical Assessments has been calculated for a pipe loaded in tension. CTOD vs. applied strain was calculated according to LINKpipe, 3-D ABAQUS (with simulation of ductile crack growth with the Gurson model) and BS7910 (with the software CrackWise), Figure 7. All parameters were kept constant except for the crack length (2c), varying from 64 to 377 mm. For all cases, LINKpipe is very close to the 3-D calculations. BS7910 is very conservative with respect to the prediction of plastic collapse. Before plastic collapse occurs, the BS7910 solutions are varying compared with 3D. The best result is obtained for a crack length of 126 mm, representing about 10% of the circumference of the pipe. But the result is unconservative for the short crack and very conservative for the long crack. Mismatch in material properties Normal practice in pipeline technology is to require a certain degree of weld metal overmatch with respect to tensile properties compared with the base material. The purpose is to protect the weld and avoid high deformations in the “weakest link”. The

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a) Plastic collapse in CrackWise according to the rules in BS7910

b) Plastic collapse in CrackWise according to the rules in “strain based design”, OS F-101 Figure 7 Applied CTOD vs. strain for pipe loaded in tension with ductile tearing. LINKpipe, 3D (with simulation of ductile crack growth with the Gurson model) and BS7910/CrackWise are compared. OD=400mm, a/t=0.2, yield stress 460MPa and hardening exponent 0.07 so-called mismatch effect has been a subject for research over the last 20 years, and a range of proposals and equations have been published. The complexity of the topic stems from the interdependence between ranges of parameters, such as: crack size, crack location in the weldment, brittle or ductile behavior, bending or tensile loading, specimen size and geometry, and hardening. It is thus very appealing to introduce the

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0Strain [%]

CTO

D [m

m]

LINK, 2c=64mm

LINK, 2c=126mm

LINK, 2c=377mm

3D, 2c=64mm

3D, 2c=126mm

3D, 2c=377mm

BS 7910, 2c=64mm

BS 7910, 2c=126mm

BS 7910, 2c=377mm

Limit for the valid area for LINK,due to significantly ductile crack growth in the crack length (limitation for cracks with short length compared to depth)

Plastic collapseOS F-101Strain based design

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0Strain [%]

CTO

D [m

m]

LINK, 2c=64mm

LINK, 2c=126mm

LINK, 2c=377mm

3D, 2c=64mm

3D, 2c=126mm

3D, 2c=377mm

BS 7910, 2c=64mm

BS 7910, 2c=126mm

BS 7910, 2c=377mm

Limit for the valid area for LINK,due to significantly ductile crack growth in the crack length (limitation for cracks with short length compared to depth)

Plastic collapseBS 7910

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mismatch topic in the direct calculations in LINKpipe, since most of above parameters are automatically accounted for by the FE model. The mismatch effect due to a crack located in the middle of the weld is accounted for by introducing the “rule of mixture”. The principle is illustrated in Figure 8. According to slip-line theory, yielding will take place under an angle of 45 degree at the crack tip. Initially only the weld material yields, but the yielding soon spreads to the base material and results in net section plasticity. This occurs at low global strain levels, and subsequent loading will result in plastic deformation in both the weld metal and base material. The distribution between the two materials will depend on the crack size, the ligament height and the width of the weld metal, Figure 8.

a= crack depth W= wall thickness L= crack ligament height H= weld metal width a) Specimen with crack positioned in the middle of the weld metal .

b) The "rule of mixture" gives the contributions from the weld metal and the base material

c) The “equivalent” homogenous case with the effective ligament height Figure 8 Correction for mismatch by application of “The rule of mixture” principle, (16).

LH

W BMWM

a

10

The total yield load is calculated by weighting the contribution from the different material zones. For a case with the crack in the middle of the of the weld metal the ideal plastic limit load is:

))H/(m(LσL L

HσL

HσP ,B.,B.,W.L,m 212

12 202020 −+=⎟

⎠

⎞⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+=

where H is the width of the weld metal, L is the physical crack ligament height, m=σ0.2,W/σ0.2,B is the yield stress mismatch ratio between the weld and pipe materials. By making the assumption that the ration between PL,m and PL equals the ratio between the effective crack ligament height, Leff, and the physical ligament height, L, we get the following expression:

With knowledge of the effective ligament height, the mismatch can now be accounted for by the linespring by adjusting the crack depth or the yield stress. This simplified procedure have been developed on the basis of detailed 3D calculations. For more details, reference is made to (16). Two examples will be presented. Yield stress over- and undermatch. Varying width of weld metal The first example is a pipe loaded in tension, with yield stress overmatch and undermatch (15% in both cases). The steel quality is X65, OD=400mm, a=4mm, 2c= .., t=20mm. Young's modulus and Poisson's ratio are taken as 200 GPa and 0.3. Two cases of weld metal width have been considered, H=t and H=0.4t. The correction of the linespring yield stress because of mismatch and the width of the weld, are shown on the legend on Figure 9. Figure 9 compares the LINKpipe results with the 3D calculations. Good correspondence is obtained, except for undermatch with the largest width of the weld metal. The reason for the deviation will be further explored by also adjusting the properties of the shell elements to model the weld metal properties. However, the large undermatch represents a very special case.

2/)1()2/)1((

,2,0

,2.0, HmLLL

HmLL

PP

LB

B

L

mLeff −+=

−+==

σσ

11

pipe_tension_effective yield stress

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

1.60E+00

1.80E+00

2.00E+00

0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02

Strain E11 (mm/mm)

CTO

D (m

m)

OM_H=t_503OM_H=0.4t_477UM_H=0.4t_443UM_H=t_417HOM_4603D_HOM_4603D_OM_H=t3D_OM_H=0.4t3D_UM_H=0.4t3D_UM_H=t

Figure 9 Applied CTOD vs. strain for pipe loaded in tension. The yield stress of the linespring has been corrected according to "rule of mixture". Yield stress overmatch and hardening undermatch The most demanding situation is to take into account both yield stress- and hardening mismatch, Figure 10. The uniaxial plastic behaviour follows the isotropic power law hardening in the following form:

npy

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

00

1εε

σσ

where 0σ and E0

0σε = denote the initial yield stress and strain, respectively.

Further, n is the hardening exponent. The behaviour is elastic for 0σσ <y . The hardening property of the weld metal is obtained by adjusting the whole plastic stress-strain curve according to "the rule of mixture".

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Figure 10 Schematic both yield stress- and hardening mismatch. One example is presented, Figure 11 and 12, with yield stress overmatch and two levels of hardening undermatch (weld metal n=0.05 and 0.07, compared with base material n=0.09). In this case the “rule of mixture” was applied for the whole stress-strain curve.

WM BM

Yield stress mismatch:∆σ0.2

Hardening mismatch:∆(σ0.2/σTS)

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Yield stress overmatch (m=1.15) Hardening undermatch

0

100

200

300

400

500

600

700

800

900

0 1 2 3

Strain (mm/mm)

Stre

ss (M

Pa)

BM_n=0.09WM_n=0.07WM_n=0.05

Figure 11. Tensile properties. Yield stress overmatch, 15%. Hardening undermatch, with hardening exponents: base material 0.09, weld metal 0.07 and 0.05.

Yield stress overmatch (m=1.15) Hardening undermatch

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02

Strain E11 (mm/mm)

CTO

D (m

m)

3D_n=0.073D_n=0.05ls_n=0.05ls_n=0.07

Figure 12 Applied CTOD vs. strain for pipe loaded in tension. The yield stress of the linespring has been calculated according to "rule of mixture".

Tensile properties

Pipes are subjected to deformations during manufacturing, fabrication, laying and operation. Cycles of bending and tension exerts a strong influence upon the mechanical properties of the pipe, and results in varying tensile stress-strain behaviour around the circumference. In order to evaluate the risk of failure the local material properties must be accounted for. In LINKpipe, the tensile properties are either defined according to a power law hardening relationship, with a characteristic hardening exponent, or the input to the calculations can be a point-wise stress-strain curve.

One example is shown in Figure 13.The stress-strain curves are obtained from a pipe after bending and subsequent straightening. 12o’clock represents the tensile location and 6 o’clock the compression. The change of tensile properties has a dramatic effect on the applied CTOD. The results underline the importance of including the so-called history effect in defect assessments.

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Figure 13. Effect of stress-strain curves on the applied CTOD vs. strain. Stress-strain curves after bending and subsequent straightening of pipe (upper), effect on applied CTOD (lower).

Misalignment Two cases with misalignment between two pipes have been analysed.

The first case is a simulation of a sharp transition between the two pipes. The geometry applied in the 3D Abaqus model is schematically shown in Figure 14.

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Figure 14 Sketch of the 3D model with sharp transition between the two pipes.

LINKpipe simulates the sharp transition by introducing a modified crack depth, equal to the average value of 4 mm in the present case. The LINKpipe result is in very good agreement with the 3D calculations, Figure 15.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.01 0.02 0.03 0.04 0.05 0.06

Strain [mm/mm]

CTO

D [m

m]

LINKpipe 2.03D

Figure 15 Effect of a 2 mm misalignment with a sharp transition between the two joints.

In the other case the transition is represented by a continuous change of the diameter, Figure 16.

5 mm3 mm

20 mm 20 mm

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Figure 16 Misalignment between two pipes. The transition is represented by a continuous change of the diameter. The position of the linespring is identified with a darker colour. The crack depth used by the linespring in the present analysis, Figure 17, is 4 mm.

For this case no 3D have been available, so only two LINKpipe results with slope 1:5 and 1:20, are plotted in Figure 17. The effect of the slope is minor up to a strain of about 0.02 (mm/mm). At higher strains, the 1:20 case approaches the previous case, while 1:5 gives lower CTOD's.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Strain [mm/mm]

CTO

D [m

m]

slope 1:5slope 1:20

Figure 17 Effect of 2 mm misalignment with a continuous transition between the two joints.

E11

400

20

404

2 s=2

a

[mm 119 118

400

F

slope=1/1

20

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Conclusions

The use of an efficient and accurate linespring model for fracture assessment of pipelines is presented in this work. Detailed 3-D analysis and large scale testing has been carried out for the verification of the linespring method.

Following are the main conclusions:

-Fracture parameters estimated from the linespring model for surface cracked pipes are in good agreement with those from 3-D simulations

-The linespring model is an efficient and accurate tool for constraint estimation in surface cracked pipes.

-The applied CTOD calculated from analytical solutions (BS7910) can be conservative and unconservative, depending on the crack dimensions. LINKpipe capture both the physics of the CTOD as a function of strain, and the final failure behaviour.

-Ductile tearing strongly influences the CTOD-strain relationships in surface cracked pipes. A significant reduction in deformation capacity from the stationary case is noticed when ductile tearing is considered. As crack size increases, the effect of ductile tearing becomes more important.

- Under biaxial loading, a pronounced effect of ductile tearing on the crack driving force relationships is noticed. With increase in magnitude of internal pressure, the deformation capacity is reduced significantly. The LINKpipe calculations were verified by large scale testing with pipes subjected to bending and internal pressure (water)

-Material mismatch, with the crack positioned in the middle of the weld metal, can be included in the linespring formulation according to “the rule of mixture”

-The importance of including the “history” effect is demonstrated by an example

-Misalignment is simulated by the linespring by introducing an average crack depth. Both sharp and continuous transitions between the two pipes have been considered, but only one case has been validated by 3D calculations, so far.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the support from the Joint Industry Project ”Fracture Control Offshore Pipelines”.

References

(1) Skallerud B (1999) Numerical analysis of cracked inelastic shells with large displacements or mixed mode loading”. Int. J. Solids Structures, 36, 2259-2283.

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(2) Skallerud B and Haugen B (1999). “Collapse of thin shell structures– stress resultant plasticity modelling within a co-rotated andes finite element formulation”. Int. J. Numer. Meth. Engng., 46, 1961-1986.

(3) Chiesa, M., Nyhus, B., Skallerud, B. and Thaulow, C (2001). "Efficient Fracture Assessment of Pipelines. A Constraint Corrected SENT Specimen Approach". Engineering Fracture Mechanics, 68, 527-547.

(4) Chiesa M, Skallerud B and Gross D (2002). “Closed form line spring yield surfaces for deep and shallow cracks: formulation and numerical performance”. Computers and Structures, 80, 533-545.

(5) Skallerud B, Holthe K and Haugen B., (2005). “Thin shell and surface crack finite elements for simulation of combined failure modes”. Comput. Methods Appl. Mech. Engng. 194, 2619-2640

(6) Thaulow C, Østby E, Nyhus B, Zhang Z L and Skallerud B (2004). “Constraint correction of high strength steel: Selection of test specimens and application of direct calculations”. Engineering Fracture Mechanics, 71, 2417-2433

(7) Thaulow C, Jayadevan K R, Skallerud B, Holthe K, Berg B, Østby B and Nyhus B., (2004). “Advances in computational procedures for the structural integrity of pipelines”. Proc. of Int. Conf. on Advances in Structural Integrity, July 14-17, Indian Institute of Science, Bangalore, India.

(8) Skallerud B, Berg E, and Jayadevan KR (2006), “Two-parameter fracture assessment of surface cracked cylindrical shells during collapse”, Engineering Fracture Mechanics 73, 264-282

(9) Jayadevan, K.R., Thaulow, C., Østby, E., Berg, E., Skallerud, B., Holthe, K., Nyhus, B., (2005). “Structural Integrity of Pipelines: T-stress by line-spring”. Fatigue Fract Engng Mater Struct, 28, 467-488.

(10) Jayadevan K R, Berg E, Thaulow C. ,Østby E. and Skallerud B. (2006) “Numerical investigation of ductile tearing in surface cracked pipes using line-spring”. Int. J. Solids and Structures, 43, 2378-2397

(11) Thaulow C, Skallerud B, Jayadevan K R and Berg E. (2005), “Fracture Control Offshore Pipelines – Advantages of using direct calculations in fracture assessments of pipelines”. OMAE Conference, June 12-16, Halkidiki, Greece

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(12) Skallerud B and Berg E (2005), “An integrated approach to analysis of surface cracked shells subject to instabilities”, ECCOMAS conference Marine 2005, 27-29 June, Oslo, Norway.

(13) Lee, H. and Parks, D. M. (1998). “Line-spring finite element for fully plastic crack growth-I. Formulation and one-dimensional results”. Int. J. Solids Structures, 35, 5115-5138.

(14) Nyhus, B., Zhang, Z.L., Thaulow, C., (2002). “Normalisation of material crack resistance curves by the T-stress”. In: Proceedings of 14th European Conference on Fracture, 8-13 Sept, 2002, Cracow, Poland.

(15) Østby E, paper under preparation

(16) Østby E , Thaulow C, Nyhus B and Ødegård J (2006) “A strain-based approach to fracture assessment of pipelines”. Proceedings Int seminar on Application of High Strength Line Pipe and Integrity Assessment of Pipeline 2006. June 15-16, Xi’an, China.