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International Journal of Pressure Vessels and Piping 84 (2007) 487–492

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Prediction of failure strain and burst pressure in high yield-to-tensilestrength ratio linepipe

M. Lawa,�, G. Bowieb

aInstitute of Materials and Engineering Science, Australian Nuclear Science and Technology Organisation (ANSTO), Lucas Heights, NSW, AustraliabBlueScope Steel Ltd., Level 11, 120 Collins St, Melbourne, VICTORIA 3000, Australia

Received 16 February 2006; received in revised form 10 April 2007; accepted 10 April 2007

Abstract

Failure pressures and strains were predicted for a number of burst tests as part of a project to explore failure strain in high yield-to-

tensile strength ratio linepipe. Twenty-three methods for predicting the burst pressure and six methods of predicting the failure strain are

compared with test results. Several methods were identified which gave accurate and reliable estimates of burst pressure. No method of

accurately predicting the failure strain was found, though the best was noted.

Crown Copyright r 2007 Published by Elsevier Ltd. All rights reserved.

Keywords: Pipe; Burst pressure; Failure strain

1. Prediction of failure strain and burst pressure

The failure pressures and strains have been predicted fora number of burst tests as part of an Australian PipelineIndustry Association (APIA) sponsored research projecton the effects of yield–to-tensile strength (Y/T) ratio onfailure strain in high-strength seam welded pipe. Twentyequations (Table 1) and two other methods based onplastic collapse (described later) were used to predict theburst pressure. The pipe tests were all carried out on well-characterised modern thin-walled high-strength linepipe,where the yield strength was measured in a consistent andaccurate manner using ring expansion testing and tangen-tial tensile specimens (TT).

Four equations (see Table 2) and two methods based onplastic collapse (described later) were used to predict thefailure strain (the average hoop strain at failure). Thefailure strain estimate of half the uniform strain is anindustry rule of thumb. The Liessem–Graef equation isbased on curve fitting to published data, and is valid forY/T values from 0.7 to 0.95 based on round bar tests.

e front matter Crown Copyright r 2007 Published by Elsevie

vp.2007.04.002

ing author. Tel.: +612 97179102.

ess: mlx@ansto.gov.au (M. Law).

2. Plastic instability and cylindrical instability stress (CIS)

methods

In a tensile test the rate of strain hardening is greaterthan the increase in stress due to loss of cross-section due tostraining up to the ultimate tensile strength (UTS). At theUTS, plastic instability and necking occurs as furtherstraining reduces the load the specimen can support. Pipefailure is also due to the onset of plastic instability. Thestress increases for two reasons: reduced cross-sectionalarea (as in the tensile test), and increasing inner diameter(which raises the stress via s ¼ PDi/2t). For a pressurevessel the condition of instability is that s ¼ 1/2 ds/de [21].The stress where this occurs is termed as the cylindricalinstability stress (CIS) and is close to the flow stress (theaverage of the yield stress and the UTS) for many pipesteels. In a material that follows power law plasticity, thefailure strain will be half the uniform strain (the uniformstrain is the strain at maximum load).This project offered the opportunity of testing five well-

characterised pipes, each providing stress–strain curves andwall thickness data taken from 14 TT around the pipecircumference. Other methods of deriving material data inthe hoop direction may involve flattening the pipe materialthat strongly affects the measured material properties of

r Ltd. All rights reserved.

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Nomenclature

D, Di, Do, Dave diameter, inner, outer, averaget wall thicknesse 2.718, etc.E Young’s moduluseu uniform straink Ro/Ri

n strain hardening exponent, n ¼ exp(1+eu)]Ro, Ri outer radius, inner radiussYS, sflow, sTS yield, flow, and tensile strengthn Poisson’s rationsecant failure secant Poisson’s ratio ¼ 0.5�(0.5�n)

sTS/(euE)YT yield-to-tensile ratio

Table 1

Equations for predicting burst pressure

ASME [1]Pmax ¼ sTS

k � 1

0:6k þ 0:4

� �Marin [2] Pmax ¼

2ffiffiffi3p

sTSð1þ �uÞ

ln ðkÞ

Barlow OD, ID, or flow, Pmax ¼ sTS2t

Do; sTS

2t

Di; or sflow

2t

Di

Marin (3) [3] Pmax ¼2t

ðffiffiffi3pÞðnþ1Þ

sTSRi

Bailey-Nadai [4]Pmax ¼

sTS2n

1�1

k2n

� �Max. shear stress [5]

Pmax ¼ 2sTSk � 1

k þ 1

� �

Bohm [6]Pmax ¼ sTS

0:25

0:227þ �u

� �e

�u

� ��u 2t

Di1�

t

Di

� �Nadai [7] Pmax ¼

2ffiffiffi3p sTS ln ðkÞ

DNV [8] Pmax ¼ sFlow2t

Dave

Nadai [9]Pmax ¼

sTSffiffiffiffiffi3np 1�

1

k2n

� �

Faupel [10] Pmax ¼2ffiffiffi3p sYSð2� YTÞ lnðkÞ Soderberg [11]

Pmax ¼4ffiffiffi3p sTS

k � 1

k þ 1

� �

Fletcher [12] Pmax ¼2tsflow

Dið1� �u=2ÞSvenson [13]

Pmax ¼ sTS0:25

0:227þ �u

� �e

�u

� ��uln ðkÞ

Margetson [14]Pmax ¼

4t

Di

ffiffiffi3p sYS exp �2�u

ð1þ usecantÞffiffiffi3p

� �Turner [15] Pmax ¼ sTS lnðkÞ

Marin [16] Pmax ¼ 2:31ð0:577ÞntsTSDi

Zhu and Leis [17]Pmax ¼

2þffiffiffi3p

4ffiffiffi3p

� �ð1þ0:239ðð1=YTÞ�1Þ0:596Þ4tsTSDave

Table 2

Equations for predicting hoop failure strain

Half uniform strain �FAILURE ¼�u2

Liessem and Graef (Y/T ¼ 0.7–0.95) [18] �FAILURE ¼ � 2608YT4 þ 8406:8YT3

� 10149:8YT2 þ 5424:9YT � 1075:34

Gaessler and Vogt [19]�FAILURE ¼

�u2�

nffiffiffi3p

3eYT ð1=nÞ Zhu and Leis [20]

�FAILURE ¼ 0:11951

YT� 1

� �0:596

M. Law, G. Bowie / International Journal of Pressure Vessels and Piping 84 (2007) 487–492488

high strength pipe [22]. Analysis was performed with thesedata based on the CIS, taking the wall thickness variationinto account. This method does not assess propertiesvariation along the pipe. The pipes have longitudinal seamwelds made by high-frequency electric resistance welding(HF-ERW); these welds are autogenous (the joint is madeby heating and upsetting the parent metal). These welds are

shown by production testing to be stronger than the pipematerial, they are also locally thicker; for this reason thewelds have not been included in the analysis. In otherproduction methods the weld may require analysis also.The first method used data from all positions around the

pipe wall; this was referred to as the CIS-full method and isdetailed further in the appendix. An empirical curve fitting

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Yeild elevation for pressure vessel

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

0 20 40 60 80 100

D/t

Yie

ld e

levation f

acto

r

Fig. 2. The increase in pressure above that predicted from the use of yield

strength and the hoop stress is described by the yield elevation factor.

Table 3

Pipe properties

X42

ex-mill

X65

aged

X70

aged

X80

ex-mill

X80

aged

OD (mm) 355.65 273.14 457.20 356.90 356.17

Thickness (mm) 6.41 7.10 9.97 6.96 6.91

TS (MPa) 471 662 700 677 684

YS (RE) (MPa) 321 587 637 568 640

Y/T Barlow ID 0.68 0.89 0.91 0.84 0.94

Uniform strain (%) 20.6 8.8 5.8 8.8 6.8

M. Law, G. Bowie / International Journal of Pressure Vessels and Piping 84 (2007) 487–492 489

procedure was used. The engineering stress–strain datawere converted to true stress-true plastic strain data, fittedwith a quadratic curve (Fig. 1) in the area around half theuniform strain, and the CIS stress and failure strain wereestimated from this. The quadratic curve gave a better fit inthe area of interest than the Swift or Holloman equations(Fig. 1). With the quadratic fit, s ¼ 1/2 ds/de can be solveddirectly.

The method of predicting plastic collapse using the CIS-full method relies on a precise knowledge of all variationsin material behaviour and thickness, and as such is not aconvenient predictive method, but adds to an under-standing of the fundamental processes of plastic collapseand failure.

A more convenient method is to use two TT samplestaken from positions likely to capture the maximum andminimum material properties. These are then analysedin a similar way to the CIS-full fit method to estimatethe burst pressure and strain. If the seam weld is taken asbeing at the 12 o’clock position, the weakest positionin the pipe wall is generally at the 3 or 9 o’clock positions,and the strongest is generally at the 6 o’clock position.The positions chosen to represent the weakest andstrongest segments were at 1031 and 2061 (case A), and at1801 and 2831 (case B). These are referred to in the resultsas CIS-A and CIS-B. Further details are given in theappendix.

Each burst test specimen is made by welding endcaps tothe pipe; internal pressure causes an axial stress which isequal to half the hoop stress. The biaxial stress statesuppresses yielding and plasticity, this may be calculated byuse of the von Mises stress. Yielding in a pressure vessel(for a burst test) is predicted to occur at approximately 1.12times higher than would be predicted from the uniaxialtensile test yield strength, depending on the D/t ratio. Thisincrease in pressure for a pressure vessel is given by afactor, which is equivalent to the ratio of the hoop stress tothe von Mises stress [23], where x ¼ Di/t (Fig. 2).

650

660

670

680

690

700

710

720

730

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

True plastic strain

Data

Holloman

Swift

Local quadratic

Tru

e S

tress (

MP

a) UTS

Fig. 1. Data points from TT testing (X65 coated pipe, position 6, 2061),

Holloman and Swift curves, and local quadratic fit to data.

3. Burst pressure

Some average material properties from testing are givenin Table 3. The yield strength is the 0.5% total strain valuederived from ring expansion testing. The predicted andactual burst pressures are given in Table 4. The averagediscrepancy is the average of each predicted value minusthe test result; a positive figure indicates the predictionswere, on average, greater than the actual result and arethus conservative. The standard error of discrepancy is thestandard deviation of the predictions divided by the resultand expressed as a percentage.The equations that are conservative, are within an

average of 5% of the burst pressure, and have a standarderror of discrepancy less than the (arbitrary) value of 6%are (in order) the CIS-full, Fletcher, Bohm, and Bayley–Nadai, Barlow ID, ASME, and maximum shear stressequations.The CIS predictions overestimated the burst pressure.

An explanation is the inevitable variation of strengthalong, and around, a pipe. The weakest point, whereburst occurs, will generally be weaker than the areatested due to the greater volume of material that issampled in a full-scale pressure test as compared to a

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Table 4

Burst pressure results and predictions (MPa)

X42 ex-mill X65 aged X70 aged X80 ex-mill X80 aged Average

discrepancy (%)

Standard error

(%)

Test result 15.75 36.33 30.53 27.44 27.8 — —

ASME 17.23 35.19 31.06 27.38 26.88 0.94 5.2

Barlow OD 16.98 34.45 30.52 26.96 26.46 �0.75 5.3

Barlow ID 17.61 36.35 31.91 28.04 27.53 3.57 5.1

Barlow flow 14.81 34.29 30.48 25.95 26.64 �4.23 2.5

Bayley–Nadai 17.19 35.26 31.14 27.40 26.94 1.04 5.0

Bohm 16.28 36.02 32.72 28.29 28.24 2.92 3.0

CIS-full 16.38 37.76 31.75 29.39 29.53 5.10 1.5

CIS-A 16.45 37.76 32.06 29.92 29.98 6.10 2.2

CIS-B 16.53 38.15 32.14 29.85 29.86 6.33 1.7

DNV 14.54 33.37 29.80 25.44 26.12 �6.28 2.4

Faupel 17.94 40.33 35.74 31.04 31.04 13.40 2.5

Fletcher 16.58 35.87 31.40 27.20 27.59 1.09 2.9

Margetson 14.05 36.06 33.32 27.63 28.23 0.01 7.2

Marin 12.23 34.07 31.29 25.23 27.86 �6.73 9.8

Marin(2) 16.45 37.55 34.04 29.07 29.15 6.07 3.3

Marin(3) 18.62 40.53 35.94 30.85 30.97 14.32 3.5

Max shear 17.29 35.38 31.20 27.49 26.99 1.37 5.2

Nadai 19.97 40.86 36.03 31.74 31.16 17.07 6.0

Nadai(2) 19.85 40.72 35.96 31.63 31.11 16.67 5.8

Soderberg 19.96 40.85 36.03 31.74 31.16 17.05 6.0

Svensson 16.89 37.98 34.20 29.42 29.37 7.38 3.0

Turner 17.29 35.38 31.21 27.49 26.99 1.38 5.2

Zhu–Leis 13.88 33.27 29.92 25.13 26.47 �7.05 3.9

Predictions of burst test results

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

ASM

E

Bar

low O

D

Bar

low ID

Bar

lowflo

w

Bay

ley-

Nad

ai

Boh

m

CIS

TT fit

CIS

TT-A

CIS

TT-B

DNV

Faupe

l

Fletche

r

Mar

getson

Mar

in

Mar

in(2

)

Mar

in(3

)

Max

she

ar

Nad

ai

Nad

ai(2

)

Sod

erbe

rg

Sve

nsso

n

Turne

r

Zhu-L

eis

% V

ari

ati

on

Fig. 3. Averaged predictions and scatter compared to burst test pressures.

M. Law, G. Bowie / International Journal of Pressure Vessels and Piping 84 (2007) 487–492490

single TT specimen. This reflects the reality that the actualmaterial property variation cannot be fully quantified.Despite this, the predictions had the lowest standard error(1.5–2.2%) of all methods, as indicated by the small errorbars (Fig. 3).

4. Failure strain

The failure strains are given in Table 5. All methodsoverestimated the strain by 15–60%, with large standarddeviations. When the results for the X80 aged pipe are

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Table 5

Failure strain results and predictions (%)

X42 X65 aged X70 aged X80 ex mill X80 aged Average

discrepancy (%)

Standard error

(%)

Test result 9.09 3.29 2.53 2.56 1.01 — —

Gaessler–Voght 8.37 3.39 2.39 4.70 2.62 34.7 (18.0) 53.3 (44.0)

Half uniform strain 10.70 4.40 2.93 4.60 3.45 62.2 (36.4) 63.2 (30.1)

Liessem-Graef 6.10 3.49 3.01 4.07 2.27 25.0 (12.6) 43.2 (38.1)

Zhu–Leis 7.59 3.51 3.01 4.24 2.42 32.0 (18.4) 42.9 (34.9)

CIS-full 9.07 2.87 1.98 3.03 2.66 17.4 (-4.4) 51.0 (17.3)

CIS-A 9.87 3.36 2.41 2.77 2.64 23.2 (3.2) 45.0 (5.9)

CIS-B 9.52 2.71 2.00 2.61 2.71 15.1 (�8.3) 53.4 (12.8)

Statistics excluding X80 aged test in brackets.

-50

-25

0

25

50

75

100

125

Gaes

sler-

Voght

Eu/2 Liessem-

Graef

Zhu -

Leis

CIS-full CIS CIS-B

Va

ria

tio

n %

All tests

Excluding X80 aged

Fig. 4. Average variation from strains at maximum pressure, including

and excluding X80 aged pipe.

M. Law, G. Bowie / International Journal of Pressure Vessels and Piping 84 (2007) 487–492 491

ignored all the predictions have better accuracy and lessscatter, particularly in the CIS predictions (Fig. 4). Theweakest position in the X80 aged pipe was relativelyweaker than in the other pipes, this variation in propertieswas not captured by the material testing as it only sampledfrom one ring of the pipe material, and not at the failurearea. The variation in properties along the X80 aged pipewas greater than in the other materials tested. This wascompounded by the shape of the stress–strain curve for theaged X80 material which has low strain hardenabilityimmediately after yield. Removing the X80 aged materialresults made little difference to the pressure predictions.

Another factor reduces the pipe strains at failure (9–1%)to below half the uniform elongations seen in Table 4(21–7%). This is the effect of circumferential propertyvariation; a small portion of the circumference with thelowest strength can reach plastic instability at approxi-mately half the uniform strain while the average strain inthe pipe is still low. This effect is more important in highY/T material.

5. Conclusions

Burst test results showed a rapid reduction in failurestrain with Y/T, as seen in other published work. Despite

the low average hoop strains at failure, all pipes burst athigh pressure (4128% SMYS, 4108% AYS). Thepredicted failure pressures and strains for five burst testshave been calculated based on a number of equations andother methods.The best predictions of failure pressure which were (on

average) conservative and had low scatter were from theCIS-full, Fletcher, Bohm, and Bayley–Nadai, Barlow ID,ASME, and maximum shear stress equations. The CISpredictions uniformly overestimated the burst pressure,indicating that the worst material properties had not beenfully characterised.The best predictions of failure strain came from the CIS

methods, and the best explicit method was the Liessem–Graeff equation. The results were more accurate and thescatter was significantly reduced after one set of results(X80 coated) had been removed from the data. The scatterin failure strain predictions was larger than in theprediction of failure pressure. Failure strains were all lessthan half the uniform elongation, and much less than thetotal elongation. For high Y/T ratio materials, largevariation in failure strain may occur with little scatter infailure pressure.

Acknowledgement

The work reported herein was sponsored by theAustralian Pipeline Industry Association (APIA).

Appendix. Description of methods of CIS analysis

The analysis uses data from the pipe excepting the weldarea, as rapid changes in the metallurgy and wall thickness,and the localisation of the weld, make analysis difficult.

Method 1—CIS-full

The failure strain and stress are calculated from theintersection of the stress–strain curve and half the slope ofthe stress–strain curve (s ¼ 1/2 ds/de). The portion of thecurve fitted is in the region about the strain value of n/2 andsome curve is fit to the data points after they have been

ARTICLE IN PRESSM. Law, G. Bowie / International Journal of Pressure Vessels and Piping 84 (2007) 487–492492

converted to true stress true strain. The choice of curve to fitdepends on the data; a quadratic equation was used here. Inthis case the intersection of the curves can be calculated easilyto give the failure strain and stress. If the predicted failurestrain lies outside the area of the curve fit, the area must beexpanded to include this value. From this is calculated thecorresponding von Mises stress and hoop stress ( ¼ onMises stress�PV factor). The pressure that corresponds tothis hoop stress is calculated, taking into account the currentwall thickness and ID, using total strains.

The lowest failure pressure from any segment is noted asthe global burst pressure. To calculate the strains, the hoopstress at the global burst pressure is found (normalised towall thickness) for each segment. From this the plastic andelastic strains are then calculated and summed for theentire circumference.

Method 2—CIS-A and CIS-B

Data from tangential tensile specimens at approximately3 and 6 o’clock (A) and the 9 and 6 o’clock (B) positionwere converted to true stress–strain data. The method ofthe CIS-full method is used from this point, with the strainsbeing averaged between the two samples (i.e. the weightingfunction is 0.5 in this case).

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