THEORETICAL BACKGROUND OF "LEAK-BEFORE-BREAK" AS A CONCEPT IN PRESSURE VESSELS DESIGN. Šárka Pacholková a Howard Taylor b

Transcription

1 METAL , Hrade nad Moravií THEORETICAL BACGROUND OF "LEA-BEFORE-BREA" AS A CONCEPT IN PRESSURE VESSELS DESIGN Šárka Paholková a Howard Taylor b a VÚ- NOVÁ HUŤ, a.s., Vratimovská 689, Ostrava-unčie, CZ, spaholkova@novahut.z b DEPARTMENT OF ENGINEERING AND TECHNOLOGY, Manhester Metropolitan University, Chester Street, Manhester, M1 5GD, U, h.taylor@mmu.a.uk Abstrat In pressure vessels, raks an initiate from regions of high stress onentration or from defets, whih are already present in the vessels, usually in welds. There are generally two possible modes of failure, depending on the load and the toughness of the material. Either the rak grows steadily through the wall by fatigue to form a stable "through-rak", or it beomes unstable before or after it has reahed the rear surfae and spreads rapidly over a large portion of the vessel. In the former ase, whih is alled "leak-before-break", there is a hane for damage to be deteted or for the internal pressure to be relieved before sudden atastrophi failure of the vessel. Therefore, LBB behaviour is an important requirement for the safe design and re-assessment of pressure vessels. This paper reviews the priniples of LBB and disusses the importane of rak shape development and rak leakage rates in the implementation of LBB. The urrent role of LBB as a tool in strutural integrity safety ases and its plae alongside other tehniques suh as NDT is also disussed. 1. INTRODUCTION As a result like fatigue, reep, or stress orrosion, a rak an be initiated and grow in a strutural part under relatively small stresses. In ase of pressure vessels, suh raks are usually formed at one surfae and grow to the other. There are generally two possible modes of failure, depending on the load (pressure) and the toughness of the material. Either the rak grows steadily through the wall to form a stable "through-rak", or it beomes unstable before or after it has reahed the rear surfae and spreads rapidly over a large portion of the vessel. In the former ase, whih is alled "leak-before-break" (LBB), there is a hane for damage to be deteted or for the internal pressure to be relieved before it omes to a sudden atastrophi rupture of vessel. Therefore, LBB behaviour is an important requirement for the safety of pressure-ontaining strutures. LBB design gives suffiient warning before leading to atastrophi failure of strutures.. REVIEW OF WOR RELATED TO LBB In LBB design, an initial rak is assumed to be present at highly probable loation of rak initiation site. The evolution of rak is predited using frature mehanis priniples. LBB design ensures that the rak grows through the thikness leading to detetable leakage and demonstrates that the rak will stable under the maximum loading onditions between the suessive inspetions. Many authors have investigated and experimentally demonstrated LBB [1,=]. Zhukov et al. [1] determined the riteria of leakage ourrene as applied to pressure vessels. The riteria for rupture of the elasti plasti bridge ahead of the part through 1

2 rak were developed in their work. Poussard et al. [] arried out high temperature LBB experimental studies on austeniti stainless steel surfae raked plates. However at high temperatures, deeleration in rak growth with inreasing values of stress intensity fator range was observed. Review of some LBB researh ativities undertaken by various researh organizations throughou the world at different time an be found in [3]. The onept of LBB is applied mainly to the design of nulear power plants. Various ountries suh as the USA, U, Germany, Frane, Italy, Spain, Czeh Republi, Russia and Japan have hanged or are in proess of hanging the regulatory proedures to aommodate LBB for pressure vessels and pipework in nulear design [4-8]. Experimental studies to haraterise rak behaviour in relation to pressure vessels integrity was extremely time onsuming and ostly. With the advent of omputers, the use of finite element modelling has enabled suh haraterisation to be easier and eonomially viable [9]. 3. GENERAL LEA-BEFORE-BREA CRITERION A general leak-before-break riterion an be derived on the basis of aepted frature mehanis priniples [10]. The frature ondition for a surfae flaw is: t p R = 1,1M 1 + πa (1) Θ s in whih t is the frature toughness of the material for rak propagation in the thikness diretion, p is the internal pressure, R is the radius of vessel, s is the wall thikness, M is the obayashiho stress intensity magnifiation fator [11] aounting for the proximity of the front free surfae. The dependene of the M on a shape of defet a is shown in Figure 1. Θ is an elliptial integral of the seond kind, given by Θ = π / a sin ϕ dϕ () where a is the depth and the length of a rak. It is possible to develop a series expansion for Θ: π 1 a 3 a Θ = (3) 4 64 Even for a ratio a/ approahing zero the third term an be negleted, then by taking 3π π a Θ= and using eq (1), the pressure p 1 for unstable propagation of the surfae flaw is:

3 METAL , Hrade nad Moravií Figure 1. obayashi stress intensity magnifiation fator [11]. π a 3 + t 8 p 1 = (4) R 1,1M 1 + πa s The surfae flaw will develop into a through rak of size. The stress intensity fator for a through-the-thikness rak of length is given by: ( λ) σ π = M, (5) F where M F (λ) is the Folias orretion for bulging [1], σ is the hoop stress, σ = pr s, is the frature toughness for rak growth in the axial diretion. Aording to eq (5), the pressure p, ausing unstable propagation of the through rak, given by p = (6) R M F ( λ) π s The rak arrest may our if the pressure to propagate the through rak of length is larger than the pressure for instability of a flaw with depth a. Hene, the leak-before-break riterion follows from p >p 1, or by using eqs (4) and (6): 3

4 t π a 3 + M F 8 > R 1,1M 1 + s ( λ) R S a (7) For thin walled pressure vessels the R/s ratio is large and surfae flaws are usually in the order of a few times the plate thikness. The resulting through rak has the same size, and sine R/s is large, the Folias orretion is still approximately M F 1. Then eq (7) an be simplified to: π a + a > 3 9 M t 1 There is a general agreement in the literature that LBB requires the through-the-thikness rak to remain stable as soon as it is reated from the deep surfae rak. This leads to the ondition that the stress intensity fator of the newly formed through-rak must be smaller than the ritial one [13], whih is usually asertained by means of the orresponding ondition of linear elasti frature mehanis. However, by this simple approah some important aspets are not adequately aounted for, sine the transition proess from a surfae rak to a through-rak, whih is ruial for the LBB behaviour, involves some theoretial diffiulties: the rak is in general loaded beyond the ritial rak driving fore, the ligament is in a state of full plasti yielding, and its geometry is rather omplex and signifiantly hanging with rak growth. 3. OTHER FACTORS INFLUENCING LBB BEHAVIOUR Aording to Smith [14], two generally reognized key elements for LBB ase are: The size of through-wall rak that is unstable under aident onditions. The size of through-wall rak that gives detetable leak under normal operating onditions. One more key element, whih is thought to be important aording to Xie [15] is The density, e.g. rak number per unit length, unit area, or unit volume, of initial raks in omponent vulnerable zone suh as a weld or seam. The signifiane of this element is due to the fat that surfae raks found in strutures or omponents are usually not a single rak but multiple raks. These raks grow by the proedure of initiation, growth and oalesene up to fature and, in many situations, rak oalesene ours quite frequently. Several effets of multiple raks on the LBB ase, as well as the effet of harateristi rak size on the leak-before-break ase of pressure vessels and piping with multiple raks have been investigated by Xie [15, 16] As is shown theoretially and validated by experimental data by Shindler [17], the failure of a pre-raked pressure vessel is often not ontrolled by the initiation of rak growth, but by its tearing stability. This explains several experimental phenomena onerning the frature behaviour of nothed pressure vessels, e.g. why the failure behaviour of ylinders is often found to be almost independent of the sharpness of the noth or rak and why many systems are flow stress rather than toughness dependent. Shindler s analysis of LBB behaviour is based on the onsideration of the tearing stability of a deep surfae rak. If there is tearing stability throughout the omplete wall thikness and onstant loading onditions, the rak is not likely to beome unstable in any phase of rak growth, inluding (8)

5 METAL , Hrade nad Moravií the transition phase from a surfae rak to a through-rak, regardless of whether the onsidered rak was originally formed by a mahined noth or by naturally grown fatigue or stress orrosion rak. For these reasons LBB behaviour is strongly related to the tearing stability of a rak in shell. From a solution for the burst stress, a new LBB riterion ould be derived, where LBB requires the following two onditions to be met [17]: σ appl π σ f 1 (9) and σ COA. E. s,83 + σ f appl M F r ( λ) π (10) where σ appl is the applied or prinipal stress due to sustained load or maximum of a yli load with onstant amplitude, E is Young s modulus, σ f is flow stress, r is fator on I as introdued in the CGEB-R6 proedure. 4. LEA BEFORE BREA PROCEDURE The various stages in the development of a LBB argument may be explained with the aid of the diagram shown in Figure. The diagram has axes of rak depth, a, and length, normalized to the pressure vessel wall thikness, s. An initial part-through rak is represented by a point on the diagram. The rak may grow by fatigue, tearing or any other proess [5, 6, 9, 17-19] until it reahes some ritial height at whih the remaining ligament ahead of the rak may break through the wall. The rak then ontinues growing in surfae length until there is suffiient opening [0, 1] to ause a detetable leak or until the rak beomes unstable. A LBB argument is aimed at demonstrating that leakage of fluid through rak in the wall of a pressure vessel an be deteted prior to the rak attaining onditions of instability at whih rapid rak extension ours. In safety ritial appliations there must also be ample margin between the detetable limit and the ritial rak size. Figure. The leak-before-break diagram [3]. 5

6 The proedure for leak-before-break assessment an be summarised as a series steps below. More detailed guidane on arrying out eah of the steps are given in R6-proedure or BS 7910, respetively [, 3]. 1) Charaterize the flaw To use LBB proedure the defet must be haraterized as a surfae defet. The extended, irregular defets where a narrow ligament exists over only a small fration of the overall defet length the haraterisation may be based on that part of the defet where the narrow ligament exists. Embedded defets must first be re-haraterized as surfae defets. ) Determine limiting length of the through-wall flaw The limiting length at whih a through-wall defet at the position of the initial surfae defet would beome unstable should be determined for the most onerous loading ondition using lower-bound values for materials properties. It may be appropriate to apply relevant fators of safety to the size of ritial through-wall defet. 3) Estimate flaw length at breakthrough To determine the length at breakthrough: a) alulate the flaw length at whih ligament failure is predited to our b) re-haraterize the flaw for whih ligament failure is predited to our as a through-wall flaw The defet length at breakthrough is given by length of the through-wall defet resulting from this reharaterisation. Ligament failure should be assessed under normal operating onditions unless some other loading onditions ould result in a larger defet length at breakthrough. Where sub-ritial defet growth as a result of fatigue or environmentallyassisted raking mehanisms an our prior to breakthrough then this must be allowed for when alulating the failure defet size. 4) Calulate rak-opening area (COA) of flaw The COA of a potential through-wall flaw is required to estimate leakage flow rate. The COA depends primarily on the rak geometry, the omponent geometry, the loading and material properties [3]. In addition, if operating at high temperature, the COA hanges with time owing to reep. 5) Calulate leak rate from flaw Several omputer odes are available to predit leakage rates for single and two-phase flows through a wide range of through-wall raks [4, 5, 6]. An alternative means of estimating the leakage rate would be to use relevant experimental data if these are available. Fators affeting the leakage rate whih need to be onsidered are the path length, the nominal opening and the surfae roughness of the rak flanks. Surfae roughness an be diffiult to estimate and may will require a detailed knowledge of the raking mehanism and typial roughnesses whih are assoiated with the surfaes produed. Experimental verifiation of leakage rates may be the most appropriate method where reliable estimates annot be made. 6) Estimate time to detet leak from flaw The leak detetion system should be seleted with due regard to the nature of the leaking fluid and the alulated leak rate. In order to estimate the time required to detet the leak the sensitivity of the proposed leak detetion system must be ompared with the alulated leak rate from the defet. The time for detetion and the exeution of the subsequently required ations should be less than that required for the rak to grow to the limiting length. Various tehniques may be employed to detet leakage, depending upon the leaking fluid, suh as interspae gas/fluid detetion or pressure hold tests. 7) Calulate time to grow to limiting length

7 METAL , Hrade nad Moravií If the through-wall rak an ontinue to grow in length as a result of fatigue or other mehanisms then the time required for flaw to grow to a limiting length should be alulated by integrating growth law for any appliable sub-ritial growth mehanism. 8) Assess results LBB ase has been made provided that the alulations arried out in the preeding steps show that: a) The defet length at breakthrough is less than the limiting length of a through-wall defet. b) The time to detet the leak is less than the time for the defet to grow to a limiting length. Only if the above two onditions an be satisfied with adequate margins throughout the range of variations likely to our in the input data an a satisfatory leak-before break ase be laimed. It should be noted that an initial failure to demonstrate that the flaw length at breakthrough is less than the limiting length, that the leak will be detetable before the flaw ould grow to a limiting length, or that adequate margins exist, does not neessarily mean a LBB ase annot be made. It may be possible to refine either the margins or the alulations of limiting rak length, flaw length at breakthrough, rak-opening area, leak rate or leak detetion system and as a result make a satisfatory LBB ase. Typially in pressure hold tests the leak detetion an be improved by extending the time over whih a pressure drop is expeted CONCLUSIONS Leak Before Break is widely reognised as a very important methodology for supporting strutural integrity safety ases. Suh ases an be made both for new designs and reassessments of existing pressure vessels and pipework. LBB omplements other methodologies suh as tearing/arrest or NDT based assessments. LBB requires very areful onsideration of all the parameters used in the assessment to ensure onservatism at all times. LBB an potentially be applied to any ase where stable rak growth ours up to break through and measurable leakage. The margin between the smallest detetable rak and the minimum ritial rak size must be adequate to support LBB. Reliable leak detetion methods must be employed to ensure the ultimate suess of the tehnique in preventing atastrophi failure. REFERENCES [1] ZHUOV, V. V. et al. Criteria of leakage ourrene and pressure vessels failure as applied to reators. Trans. ASME, J. Pres. Ves. Tehnology. 199, 114, [] POUSSARD, C. Trans. of The 14 th International Conferene on Strutural Mehanis in Reator Tehnology (SMiRT 14), G13/5, 1997, Lyon, Frane. [3] UADGAONER, V. G., BABU, R. S. Review of work related to leak-before-break assessment. Int. J. Pres. ves. Piping. 1996, 69, [4] ZDARE, J., PECINA, L., ADECA, P. Leak-before-break riterion applied to VVER 440/30 unit. Int. Pres Ves Piping.1995, 3, [5] BERGMAN, M., BRICSTAD, B. A proedure for analysis of leak before break in pipes subjeted to fatigue or IGSCC aounting for omplex rak shapes. Fatigue Frat. Engng. Mater. Strut. 1995, 18, (10), [6] BERGMAN, M., BRICSTAD, B. A proedure for analysis of leak before break in pipes subjeted to fatigue or IGSCC. Welding in the World. 1997, 39, (1),

8 [7] ARZHAEV, A. I., et al. Leak-before-break riteria and strength monitoring implementation impat on in-servie inspetion of RBM primary iruit omponents. Int. J. Pres. Ves. Piping. 1996, 66, [8] BARTHOLOMÉ, G., WELLEIN, R. Leak-before-break behaviour of nulear piping systems. Int. J. Pres. Ves. Piping. 1995, 3, [9] BURANDE, S., SETHURAMAN, R. Computational simulation of fatigue rak growth and demonstration of leak before break riterion. Int. J. Pres. Ves. Piping. 1999, 76, [10] BROE. D. Elementary Engineering Frature Mehanis. 3rd revised edition. Hague: Martinus Nijhoff Publishers, [11] OBAYASHI, A. S., ZIV, M., HALL, L. R. Approximate stress intensity fator for an embedded elliptial rak near two parallel free surfaes. Int. J. Frat. Meh. 1965, 1, [1] FOLIAS, E. S. An axial rak in a pressurized ylindrial shell. Int. J. Frat. Meh. 1965, 1, [13] ROLFE, S: T. and BARSOUM, J. M. Frature and Fatigue Control in Strutures.Prentie- Hall, NJ, [14] SMITH, E. The effet of rak-system ompliane on the leakage area for a irumferentially raked pipe subjeted to ombined axial and bending loading. Int. J.Pres. Ves. Piping. 1997, 7, [15] XIE, L. The effet of multiple rak on the leak-before-break ase of pipe. Int. J. Pres. Ves. Piping. 1998, 75, [16] XIE, L. The effet of harateristi rak size on the leak-before-break ase of pressure vessels and piping with multiple raks. Int. Pres. Ves. Piping. 1999, 76, [17] SCHINDLER, H. J. A CTOA-based approah to burst and leak-before-break behaviour. Int. J. Pres. Ves. & Piping, 1996, 69, [18] NAM,. W., et al. Fatigue life and penetration behaviour of surfae-raked plate under ombined tension and bending. Fatigue Frat. Engng. Mater. Strut. 1994, 17, (8), [19] NAM,. W. Leak-before-break onditions of plates and pipes under high fatigue stresses. Fatigue Frat. Engng. Mater. Strut. 199, 15, (8), [0] WUTHRICH, C. Crak opening areas in pressure vessels and pipes. Engng. Frat. Meh. 1983, 18, (5), [1] NOWLES, J. A., EMP, S. Crak opening areas for longitudinal and part-irumferential through-wall raks in ylinders. Report AEA/RS/4498. Abingdon, Oxon: AEA Tehnology, [] Central Eletriity Generating Board, Assessment of the Integrity of Strutures Containing Defets. CEGB Doument No. R/H/R6-Rev. 3, April [3] BS 7910: Guidane on Methods for Assessing the Aeptability of Flaws in Metalli Strutures. British Standards Institution, U. [4] EWING, D. J. F. Simple Methods for Prediting Gas Leakage Flows Through Craks. Paper C376/047 In: Po. of Int. Conf. on Pipework Engineering and Operation, I. Meh.E., February 1989, London. [5] NORRIS, D. M., CHEXAL, B. PICEP: Pipe Crak Evaluation Program (Revision1). EPRI Report NP-3596-SR, Revision 1 (1987). [6] PAUL, D. D., et al. Evaluation and Refinement of Leak-rate Estimates Models: Topiat Report, NUREG/CR-518 (Draft Report, Marh 1988).