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THEORETICAL BACKGROUND OF "LEAK-BEFORE-BREAK" AS ACONCEPT IN PRESSURE VESSELS DESIGN

Šárka Pacholková aHoward Taylor b

a VÚ- NOVÁ HUŤ, a.s., Vratimovská 689, 707 02 Ostrava-Kunčice, CZ,E-mail: spacholkova@novahut.cz

b DEPARTMENT OF ENGINEERING AND TECHNOLOGY, Manchester MetropolitanUniversity, Chester Street, Manchester, M1 5GD, UK

, E-mail: h.taylor@mmu.ac.uk

AbstractIn pressure vessels, cracks can initiate from regions of high stress concentration or

from defects, which are already present in the vessels, usually in welds. There are generallytwo possible modes of failure, depending on the load and the toughness of the material.Either the crack grows steadily through the wall by fatigue to form a stable "through-crack",or it becomes unstable before or after it has reached the rear surface and spreads rapidly overa large portion of the vessel. In the former case, which is called "leak-before-break", there isa chance for damage to be detected or for the internal pressure to be relieved before suddencatastrophic failure of the vessel. Therefore, LBB behaviour is an important requirement forthe safe design and re-assessment of pressure vessels.

This paper reviews the principles of LBB and discusses the importance of crack shapedevelopment and crack leakage rates in the implementation of LBB. The current role of LBBas a tool in structural integrity safety cases and its place alongside other techniques such asNDT is also discussed.

1. INTRODUCTIONAs a result like fatigue, creep, or stress corrosion, a crack can be initiated and grow in

a structural part under relatively small stresses. In case of pressure vessels, such cracks areusually formed at one surface and grow to the other. There are generally two possible modesof failure, depending on the load (pressure) and the toughness of the material. Either thecrack grows steadily through the wall to form a stable "through-crack", or it becomesunstable before or after it has reached the rear surface and spreads rapidly over a largeportion of the vessel. In the former case, which is called "leak-before-break" (LBB), there is achance for damage to be detected or for the internal pressure to be relieved before it comes toa sudden catastrophic rupture of vessel. Therefore, LBB behaviour is an importantrequirement for the safety of pressure-containing structures. LBB design gives sufficientwarning before leading to catastrophic failure of structures.

2. REVIEW OF WORK RELATED TO LBBIn LBB design, an initial crack is assumed to be present at highly probable location of

crack initiation site. The evolution of crack is predicted using fracture mechanics principles.LBB design ensures that the crack grows through the thickness leading to detectable leakageand demonstrates that the crack will stable under the maximum loading conditions betweenthe successive inspections. Many authors have investigated and experimentally demonstratedLBB [1,=2]. Zhukov et al. [1] determined the criteria of leakage occurrence as applied topressure vessels. The criteria for rupture of the elastic plastic bridge ahead of the part through

crack were developed in their work. Poussard et al. [2] carried out high temperature LBBexperimental studies on austenitic stainless steel surface cracked plates. However at hightemperatures, deceleration in crack growth with increasing values of stress intensity factorrange was observed. Review of some LBB research activities undertaken by various researchorganizations throughou the world at different time can be found in [3].

The concept of LBB is applied mainly to the design of nuclear power plants. Variouscountries such as the USA, UK, Germany, France, Italy, Spain, Czech Republic, Russia andJapan have changed or are in process of changing the regulatory procedures to accommodateLBB for pressure vessels and pipework in nuclear design [4-8].

Experimental studies to characterise crack behaviour in relation to pressure vesselsintegrity was extremely time consuming and costly. With the advent of computers, the use offinite element modelling has enabled such characterisation to be easier and economicallyviable [9].

3. GENERAL LEAK-BEFORE-BREAK CRITERIONA general leak-before-break criterion can be derived on the basis of accepted fracture

mechanics principles [10]. The fracture condition for a surface flaw is:

asRpMK Kct π�

��

� +Θ

= 112,1 (1)

in which Kct is the fracture toughness of the material for crack propagation in the thicknessdirection, p is the internal pressure, R is the radius of vessel, s is the wall thickness, MK is theKobayashiho stress intensity magnification factor [11] accounting for the proximity of the

front free surface. The dependence of the MK on a shape of defect ac2

is shown in Figure 1. Θ

is an elliptical integral of the second kind, given by

ϕϕπ

dc

ac 21

2/

0

22

22

sin1�

��

� −−=Θ (2)

where a is the depth and c the length of a crack. It is possible to develop a series expansionfor Θ:

���

��

���

−���

�

� −−−−=Θ ...643

411

2

2

2

22

2

22

cac

cacπ . (3)

Even for a ratio a/c approaching zero the third term can be neglected, then by taking

Θ = +38 8

2

2

π πac

and using eq (1), the pressure p1 for unstable propagation of the surface flaw

is:

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Figure 1. Kobayashi stress intensity magnification factor [11].

asRM

Kca

pK

ct

π

π

���

� +

���

���

�+

=112,1

38 2

2

1 (4)

The surface flaw will develop into a through crack of size 2c. The stress intensity factor for athrough-the-thickness crack of length 2c is given by:

( ) cMK Fc πσλ= , (5)

where MF(λ) is the Folias correction for bulging [12], σ is the hoop stress, σ = pRs

, Kc is the

fracture toughness for crack growth in the axial direction. According to eq (5), the pressurep2, causing unstable propagation of the through crack, given by

( ) csRM

KpF

c

πλ=2 (6)

The crack arrest may occur if the pressure to propagate the through crack of length 2c islarger than the pressure for instability of a flaw with depth a. Hence, the leak-before-breakcriterion follows from p2>p1, or by using eqs (4) and (6):

( )

ca

sRM

SRM

ca

KK

K

F

ct

c

���

� +

���

���

�+

>112,1

38 2

2

λπ

(7)

For thin walled pressure vessels the R/s ratio is large and surface flaws are usually in theorder of a few times the plate thickness. The resulting through crack has the same size, andsince R/s is large, the Folias correction is still approximately MF ≈ 1. Then eq (7) can besimplified to:

21

2

2

39

−�

��

����

���

�+>

ca

ca

MKK

Kct

c π (8)

There is a general agreement in the literature that LBB requires the through-the-thicknesscrack to remain stable as soon as it is created from the deep surface crack. This leads to thecondition that the stress intensity factor of the newly formed through-crack must be smallerthan the critical one [13], which is usually ascertained by means of the correspondingcondition of linear elastic fracture mechanics. However, by this simple approach someimportant aspects are not adequately accounted for, since the transition process from asurface crack to a through-crack, which is crucial for the LBB behaviour, involves sometheoretical difficulties: the crack is in general loaded beyond the critical crack driving force,the ligament is in a state of full plastic yielding, and its geometry is rather complex andsignificantly changing with crack growth.

3. OTHER FACTORS INFLUENCING LBB BEHAVIOURAccording to Smith [14], two generally recognized key elements for LBB case are:

• The size of through-wall crack that is unstable under accident conditions.• The size of through-wall crack that gives detectable leak under normal operating

conditions.One more key element, which is thought to be important according to Xie [15] is

• The density, e.g. crack number per unit length, unit area, or unit volume, of initialcracks in component vulnerable zone such as a weld or seam.

The significance of this element is due to the fact that surface cracks found in structures orcomponents are usually not a single crack but multiple cracks. These cracks grow by theprocedure of initiation, growth and coalescence up to facture and, in many situations, crackcoalescence occurs quite frequently. Several effects of multiple cracks on the LBB case, aswell as the effect of characteristic crack size on the leak-before-break case of pressure vesselsand piping with multiple cracks have been investigated by Xie [15, 16]

As is shown theoretically and validated by experimental data by Schindler [17], thefailure of a pre-cracked pressure vessel is often not controlled by the initiation of crackgrowth, but by its tearing stability. This explains several experimental phenomenaconcerning the fracture behaviour of notched pressure vessels, e.g. why the failure behaviourof cylinders is often found to be almost independent of the sharpness of the notch or crackand why many systems are flow stress rather than toughness dependent. Schindler’s analysisof LBB behaviour is based on the consideration of the tearing stability of a deep surfacecrack. If there is tearing stability throughout the complete wall thickness and constant loadingconditions, the crack is not likely to become unstable in any phase of crack growth, including

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the transition phase from a surface crack to a through-crack, regardless of whether theconsidered crack was originally formed by a machined notch or by naturally grown fatigue orstress corrosion crack. For these reasons LBB behaviour is strongly related to the tearingstability of a crack in shell. From a solution for the burst stress, a new LBB criterion could bederived, where LBB requires the following two conditions to be met [17]:

�

����

�

�

+−≤

csECOA

f

fappl

σ

πσσ..283,2

21 (9) and σλ πapplr c

F

K KM c

≤( )

(10)

where σappl is the applied or principal stress due to sustained load or maximum of a cyclicload with constant amplitude, E is Young′s modulus, σf is flow stress, Kr is factor on KI asintroduced in the CGEB-R6 procedure.

4. LEAK BEFORE BREAK PROCEDUREThe various stages in the development of a LBB argument may be explained with the

aid of the diagram shown in Figure 2. The diagram has axes of crack depth, a, and length c′,normalized to the pressure vessel wall thickness, s. An initial part-through crack isrepresented by a point on the diagram. The crack may grow by fatigue, tearing or any otherprocess [5, 6, 9, 17-19] until it reaches some critical height at which the remaining ligamentahead of the crack may break through the wall. The crack then continues growing in surfacelength until there is sufficient opening [20, 21] to cause a detectable leak or until the crackbecomes unstable. A LBB argument is aimed at demonstrating that leakage of fluid throughcrack in the wall of a pressure vessel can be detected prior to the crack attaining conditions ofinstability at which rapid crack extension occurs. In safety critical applications there mustalso be ample margin between the detectable limit and the critical crack size.

Figure 2. The leak-before-break diagram [23].

The procedure for leak-before-break assessment can be summarised as a series steps below.More detailed guidance on carrying out each of the steps are given in R6-procedure or BS7910, respectively [22, 23].1) Characterize the flawTo use LBB procedure the defect must be characterized as a surface defect. The extended,irregular defects where a narrow ligament exists over only a small fraction of the overalldefect length the characterisation may be based on that part of the defect where the narrowligament exists. Embedded defects must first be re-characterized as surface defects.2) Determine limiting length of the through-wall flawThe limiting length at which a through-wall defect at the position of the initial surface defectwould become unstable should be determined for the most onerous loading condition usinglower-bound values for materials properties. It may be appropriate to apply relevant factorsof safety to the size of critical through-wall defect.3) Estimate flaw length at breakthroughTo determine the length at breakthrough:

a) calculate the flaw length at which ligament failure is predicted to occurb) re-characterize the flaw for which ligament failure is predicted to occur as a

through-wall flawThe defect length at breakthrough is given by length of the through-wall defect resultingfrom this recharacterisation. Ligament failure should be assessed under normal operatingconditions unless some other loading conditions could result in a larger defect length atbreakthrough. Where sub-critical defect growth as a result of fatigue or environmentally-assisted cracking mechanisms can occur prior to breakthrough then this must be allowed forwhen calculating the failure defect size.4) Calculate crack-opening area (COA) of flawThe COA of a potential through-wall flaw is required to estimate leakage flow rate. TheCOA depends primarily on the crack geometry, the component geometry, the loading andmaterial properties [23]. In addition, if operating at high temperature, the COA changes withtime owing to creep.5) Calculate leak rate from flawSeveral computer codes are available to predict leakage rates for single and two-phase flowsthrough a wide range of through-wall cracks [24, 25, 26]. An alternative means of estimatingthe leakage rate would be to use relevant experimental data if these are available. Factorsaffecting the leakage rate which need to be considered are the path length, the nominalopening and the surface roughness of the crack flanks. Surface roughness can be difficult toestimate and may will require a detailed knowledge of the cracking mechanism and typicalroughnesses which are associated with the surfaces produced. Experimental verification ofleakage rates may be the most appropriate method where reliable estimates cannot be made.6) Estimate time to detect leak from flawThe leak detection system should be selected with due regard to the nature of the leakingfluid and the calculated leak rate. In order to estimate the time required to detect the leak thesensitivity of the proposed leak detection system must be compared with the calculated leakrate from the defect. The time for detection and the execution of the subsequently requiredactions should be less than that required for the crack to grow to the limiting length. Varioustechniques may be employed to detect leakage, depending upon the leaking fluid, such asinterspace gas/fluid detection or pressure hold tests.7) Calculate time to grow to limiting length

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If the through-wall crack can continue to grow in length as a result of fatigue or othermechanisms then the time required for flaw to grow to a limiting length should be calculatedby integrating growth law for any applicable sub-critical growth mechanism.8) Assess resultsLBB case has been made provided that the calculations carried out in the preceding stepsshow that:

a) The defect length at breakthrough is less than the limiting length of a through-wall defect.

b) The time to detect the leak is less than the time for the defect to grow to a limiting length.

Only if the above two conditions can be satisfied with adequate margins throughout the rangeof variations likely to occur in the input data can a satisfactory leak-before break case beclaimed. It should be noted that an initial failure to demonstrate that the flaw length atbreakthrough is less than the limiting length, that the leak will be detectable before the flawcould grow to a limiting length, or that adequate margins exist, does not necessarily mean aLBB case cannot be made. It may be possible to refine either the margins or the calculationsof limiting crack length, flaw length at breakthrough, crack-opening area, leak rate or leakdetection system and as a result make a satisfactory LBB case. Typically in pressure holdtests the leak detection can be improved by extending the time over which a pressure drop isexpected

CONCLUSIONSLeak Before Break is widely recognised as a very important methodology for

supporting structural integrity safety cases. Such cases can be made both for new designs andreassessments of existing pressure vessels and pipework. LBB complements othermethodologies such as tearing/arrest or NDT based assessments. LBB requires very carefulconsideration of all the parameters used in the assessment to ensure conservatism at all times.LBB can potentially be applied to any case where stable crack growth occurs up to breakthrough and measurable leakage. The margin between the smallest detectable crack and theminimum critical crack size must be adequate to support LBB. Reliable leak detectionmethods must be employed to ensure the ultimate success of the technique in preventingcatastrophic failure.

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[23] BS 7910: 1999. Guidance on Methods for Assessing the Acceptability of Flaws in Metallic Structures. British Standards Institution, UK.

[24] EWING, D. J. F. Simple Methods for Predicting Gas Leakage Flows Through Cracks. Paper C376/047 In: Poc. of Int. Conf. on Pipework Engineering and Operation, I. Mech.E., February 1989, London.

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