Quantitative NDI Integration with Probabilistic Fracture Mechanics for the Assessment of Fracture Risk in Pipelines

Transcription

1 4th Euopean-Ameican Wokshop on Reliability of NDE - F.1.A.3 Quantitative NDI Integation with Pobabilistic Factue Mechanics fo the Assessment of Factue Risk in Pipelines Jochen H. Kuz, Dagos Cioclov, Ged Dobmann, Chistian Bolle Faunhofe Institut fü Zestöungsfeie Püfvefahen (IZFP), Saabücken, Gemany Abstact. In the context of pobabilistic paadigm of factue isk assessment in stuctual components a compute simulation ationale is pesented which has at the base the integation of Quantitative Non-destuctive Inspection and Pobabilistic Factue Mechanics. In this study the static failue unde static loading is assessed in the fomat known as Failue Assessment Diagam (FAD). The key concept in the analysis is the stess intensity facto (SIF) which accounts on the geomety of the component and the size of a pe-existent defect of a cack natue. FAD assessments can be made in deteministic sense, which yields the end esult in dual tems of fail/not-fail. The factue isk is evaluated in pobabilistic tems. The supeposed pobabilistic patten ove the deteministic one (in mean sense) is implemented via Monte-Calo sampling. The pobabilistic factue simulation yields a moe infomative analysis in tems of pobability of failue. An impotant featue of the PVisk softwae is the ability to simulate the influence of the quality and eliability of non-destuctive inspection (NDI). It is achieved by integating, algoithmically, pobabilistic FAD analysis and the Pobability of Detection (POD). The POD infomation can only be applied in a pobabilistic analysis and leads to a efinement of the assessment. By this means, it can be ascetained the decease of pobability of failue (incease of eliability) when POD-chaacteized NDI is applied. Theefoe, this pocedue can be used as a tool fo inspection based life time conceptions. In this pape esults of sensitivity analyses of the factue toughness ae pesented with the aim to outline, in tems of non-failue pobabilities, the benefits of applying NDI, in vaious qualities, in compaison with the situation when NDI is lacking Intoduction 1.1 Failue assessment by factue mechanics methods Nowadays, the non-destuctive evaluation of stuctual components allows the detection of cacks and othe types of flaws with high esolution. When cacks ae involved in mechanical failue events, factue mechanics povides concepts fo lifetime pediction of components when component geomety, mateial chaacteistics and load intensity unde steady state o dynamic loading ae known. Failue isk assessment of load-caying components means analysing the state of the component which is detemined by the conjoint inteaction between defect type and magnitude, mateial micostuctue and the state of stess induced by applied loading. Chaacteizing the defect state means detection of defects, classification of cack-like and non-cack-like and sizing. Obviously, fom the failue potential standpoint, cacks ae the most citical flaws. Nowadays, fo engineeing assessment puposes in metallic stuctues 1

2 unde static loading Failue Assessment Diagam (FAD) epesents a tool which allows, staightfowadly, to evince in a deteministic analysis the event of failue o no failue [16, 18] (Fig. 1). The failue assessment diagam, which epesentation is shown in Fig. 1 in its basic fom fo deteministic analyses, has gained acceptance as a tool fo failue analysis and is pat of seveal standads and ules. Diffeent vesions of this method wee developed [2, 11, 21, 26] unacceptable failue assessment bounday.8 K.6.4 acceptable S Fig. 1: Failue Assessment Diagam (stip yield model) [17, 18]; failue occus when the calculated assessment point (S, K ) eaches the failue assessment bounday. If the assessment point lies within the acceptable aea the component is consideed as safe. FAD appoach to failue is a two-paamete citeion. FAD is expessed in tems of nomalized paametes. One paamete L (o equivalently, S ) is a global measue of the mateial ductility. The othe, K, petains to pue factue mechanics analysis when the mateial is fully bittle. A fomal definition is: K = SIF- the stess intensity fato / K c mateial factue toughness and L = applied load / plasic collapse load. The latte paamete is assessed with the methods of plastic limit state theoy (o by test). The inteaction between K and L (o S ) paametes stem fom Dugdale model of cack tip plasticity in igid-pastic bodies o fom empiical coections to this model (R6-pocedue, SINTAP). In the pesent FAD analysis the basic Dugdale model has been used with the model paametes defined as: K1 K = (1) K1 C σ ef σ y + σ UTS and S = with σ f = (2) σ 2 f In this fomat, the vaiable S is expessed in tems of stess. The efeence stess, σ ef, acting the component containing a cack o flaw is composed of the membane stess σ and bending stess σ. σ y and σ UTS ae the yield stength and tensile stength, m ef b ef espectively. K paamete is the atio of stess intensity facto K 1 to mateial factue toughness K 1c detemined unde standadized test conditions of validity fo oveall elastic behaviou in the defomation pocess peceding factue (e.g. ASME, DIN). It should be emaked that input paametes fo FAD analysis ae both mateial dependent and cack o 2

3 flaw geomety/cack size dependent, in the latte case via the analytical expession of stess intensity facto. The concept of stess intensity facto detemination can be found in textand handbooks (e.g. [1], [2]). 1.2 b) Pobabilistic assessment of failue isk Failue Assessment Diagam was oiginally designed fo deteministic input infomation. Howeve, mateial values ae scatteed and have eo bounds. If the cack o flaw geomety was detemined by non-destuctive testing methods, measuement eos ae also pesent. Theefoe, ealistic assumptions equie the consideation of uncetainties [12]. The esult of such an analysis is a quantitative assessment in tems of pobability of failue. The pobabilistic failue assessment has the capability to take all uncetainties of the input paametes into account. Howeve, the esult is a pobability of failue and not a fail/safe decision which is a matte of a highe level decision which must account on infomation not contained in FAD such as maintenance policy, the opeational isk, human eos included and economic consideations. Though, a ealistic analysis has to conside all souces of uncetainty and vaiability [12]. Within a isk based analysis two aspects play a key ole: the isk fequency and the isk seveity. The isk fequency assessment consists of two components, the statistical infeence on past events (a posteioi analysis) and the pobabilistic pediction (a pioi analysis). The seveity assessment consides the economic, envionmental, social, political etc. aspects. Theefoe, the isk as the esult of a pobabilistic assessment can be, globally, quantified as follows [19]: Consequence Event Consequence Risk = Fequency Seveity (3) UnitTime UnitTime Event One way to educe plants failue pobabilities is to inspect the plant peiodically and epai o eplace the components that show signs of deteioation and damage. Such insevice inspections ae paticulaly common fo pessue vessels, piping and associated welds. In the past, inspection intevals wee based on histoical expeience and engineeing judgement. In ecent yeas, methods have been developed to set inspection locations and intevals on the base of isk. A new engineeing methodology has emeged known as isk based o isk-infomed in-sevice inspection (ISI). Stuctual eliability (SR) and/o pobabilistic factue mechanics (PFM) is used futhe to estimate plants failue pobability and systems isk assessment methodology is used to detemine the effect of the plants failues on the entie isk of the system. These isk estimates ae used to ank o goup the plants components and the plants within the system accoding to thei contibution to the isk. The highe anked components o plants ae inspected moe often and moe thooughly [22]. One method to conside all uncetainties in an analysis and theefoe to quantify the isk of failue is the Monte Calo simulation (MCS). The tem Monte Calo methods descibes a goup of numeical pocedues which all use andom numbes in the numeical analysis o fo the simulation of diffeent pocesses. Monte Calo methods ae used in vey diffeent fields: engineeing, statistical physics, geophysics and economy as most solient examples. Howeve, all appoaches have in common that the a pioi infomation on the model paametes is epesented by a pobability distibution ove the model space [3, 23]. In pinciple, using MCS all uncetainties can be taken into account in fom of statistical distibutions. The pobabilistic factue mechanical appoach followed in this pape is based on the Monte Calo simulation. 3

4 Besides the possibility to take measuement eos and the scatteing of measuement data into account the diect MCS appoach offes also the possibility to conside the influence of the applied non-destuctive testing method. On the one hand this is done by consideing the so called pobability of detection (POD) fo all cacks of a given length which is postulated as the popotion of cacks that will be detected by an NDE technique when applied by qualified opeatos to a population of components in a defined woking envionment. On the othe hand measuement eos can also be consideed in fom of distibutions. POD is an impotant pat of the design and maintenance pocedue based on the damage toleance concept. As a elevant example on this line it is woth mentioning the extended eseach pefomed duing seveal high-tech development pogams such as space shuttle pogam, development of off-shoe stuctual design and maintenance and the development of damage toleance design and philosophy applied to civil aicaft design and health monitoing [1, 14, 23]. The POD has to be detemined individually fo each NDT technique and technical application. So fa, the iegulaities of flaws ae small in size, NDT techniques ae vey nea to the physical limit of detectability, i.e., moe data to evaluate ae in the ange of electical noise hence, less detectability is to be expected [15]. 2. Failue isk sensitivity study in a pipeline 2.1 Mateial chaacteistics and pipe geomety PVisk ationale, adapted fo failue isk assessment in pessue vessels and pipes is based on Monte Calo simulation. Stess intensity factos (SIF) ae calculated accoding to analytical solutions of wide ecognizance. It is possible to implement numeical SIF data esulted fom finite element analysis. The consideed mateial in this study is a high stength low alloy steel (HSLA), API gade X7,.12%C (Nb V), TM-teatment. The deteministic mean values of the mateial stength and toughness chaacteistics, as well as the inne pessue in the pipe ae listed in Tab. 1. Pipe dimensions ae shown in Fig. 2 togethe with the geomety of assumed initial semi-elliptical cack, placed longitudinally on the inne face of the pipe. Fo compaison puposes the same pipe dimension, the cack geomety and cack size as in the analysis epoted by [3, 4] have been consideed. Fig. 2 Sketch of the chosen cack geomety of an intenal semi-elliptical cack in a cylindical pipeline. The geomety values of the specimens ae dawn in the sketch. 4

5 Table 1. Deteministic mateial paametes and inne pessue UTS [MPa] YP [MPa] Kc [MPa m ] Pessue [MPa] Statistical vaiation of mateial chaacteistics Mateial chaacteistics UTS, YP and Kc ae assumed to have statistical vaiations which eflect the nomal pactice in nowadays steel manufactuing pactice. Weibull theepaamete distibution has been chosen since, this extemal distibution is analytically vesatile enabling to fit non-symmetic tends which is meely the ule than an exception encounteed in pocessing expeimental data in defomation and factue of stuctual steel testing. Futhemoe, Weibull distibution has a theoetical backgound stemming fom the weakest-link model. The geneal fom of 3P-Weibull distibution is: ( ) 1 exp b x x P x = (4) x a x with x the infeio theshold, xa the scale paamete and b the shape paamete of the distibution. Statistical paametes of the distibution of mateial chaacteistics used in the sensitivity analysis ae given in Tab. 2. Table 2. 3P Weibull distibution of stength chaacteistics. Statistic paametes. Mateial chaacteistic UTS Ultimate Tensile Stength [MPa] YP Yield Point [MPa] K c - Factue Toughness [MPa m ] Initial cack and its statistics FAD ationale pesupposes the existence of an initial cack. In a pesent analysis the inne longitudinal cack is consideed to penetate the pipe wall as a tansvese cack (b diection) as is illustated in Fig. 2. Fo failue isk analysis of stuctual elements which might contain cacks the poblem of the initial cack is appoached fom the engineeing design standpoint by the concept of equivalent initial flaw (EIF) size. This is a concept of impotance in the design of heavy loaded stuctues in aicaft, off-shoe o metallic stuctues industies [e.g. 13]. In the pesent study FAD analysis have been pefomed unde both deteministic and statistic EIF size. Since it is elatively often the case that measuement eos of cack geometies ae of mino influence on the quantitative NDT esults most of the calculations in this study ae pefomed with deteministic cack geomety values. Stating fom the EIF values the statistic vaiation of cack size is consideed to follow 3P-Weibull distibution with the paametes given in Tab. 3. Table 3. 3P Weibull distibution of cack size. Statistic paametes. Mean - mm Theshold - mm Scale - mm Shape b a = 2b 8.1* ) * ) Dummy value to emulate zeo in compute pocessing. x x a b 5

6 2.4 Pobability of cack detection In ode to exploe the benefit gained in tems of educing the failue isk as esult of applying non-destuctive testing (NDT) on flawed stuctual components, PVisk has a module which simulates the pobability of detection (POD) of flaws as function of thei size, b. The elationship POD(b) esults fom pevious expeiments pefomed unde the vey specific cicumstances encounteed in eal-life opeation of the component. Hence, a POD (b) cuve specifically efes to NDT technique (ultasound, eddy-cuents, magnetic paticles, etc.) as well as the geomety of the component, the NDT opeatos techniques and all othe elevant factos which may influence the non-destuctive inspection. In the pesent study Asymptotic exponential with lowe theshold POD(b) ule have been consideed (e.g. Cioclov 22): ( b a o ) POD ( b) = A 1 exp (5) ( a1 ao ) with A, a and a 1 as empiical fitting paametes. a is the infeio theshold of the cack size unde which the consideed NDT technique has no capacity of detection. a1 is a scale paamete while A is a paamete, close to unity, which is elated with extaneous influences on POD. Fo the pupose of sensitivity analysis, concening the influence of the quality of applied NDT, as eflected, globally, by POD cuves, fou scenaios of NDT have been consideed, labelled in elationship with the type and quality of NDT: MP magnetic paticle testing (MP) technique of cuent pactice and ultasound (US) technique of qualities qualified as: high (H), cuent (C), and poo (P). Tab. 4 gives the statistical paametes fo the POD scenaio unde consideation and Figue 3 shows the coesponding POD cuves in the anking outlined above POD H MP C US I P US II IC US III b [mm] Fig. 3 The fou POD cuves selected fo the calculations. They ae adapted fom [9]. The coesponding NDT methods ae magnetic paticle testing (MP) and thee vaiations of ultasound (US). 6

7 Table 4 gives the paametes of the POD function (5) used in the sensitivity analysis. Table 4. Paametes of POD ule. NDT technique A a - mm a 1 - mm POD I: MP POD II: US I - H POD III: US I - C POD IV: US I - P The esults of the sensitivity study A deteministic analysis is the stating point of the sensitivity analysis. Fig. 4 shows the safety index (based on the FAD) fo inceasing cack depths. A Safety index 1 means safe. A safety index below 1 means failue. In the case unde consideation, opeating with deteministic values, the citical cack depth in this example is at 6.3 mm (FAD paametic analysis in mean cack size). Deteministic analysis of factue occuence is the common pactice in mechanical engineeing design. The end quantitative assessment is expessed in safety factos which quantifies the degee of consevativeness embodied in the design. Howeve, a deteministic analysis does not conside the inheent statistic vaiability of the mateial chaacteistics, cack size and uncetainties elated with the applied nondestuctive testing eflected in the POD cuves. Pobabilistic factue analysis enables a moe efined factue analysis by making explicit a pobability of failue fo evey possible scenaio esulting fom the conjunction of individual ealizations of andom events fomalized by the specific pobability distibutions associated with the govening quantities in the factue pocess. A pobabilistic analysis of factue enables to appoach close the analysis to eal cicumstances. With this scope in mind, the pesent pape epots on a pobabilistic sensitivity analysis of failue isk in a pipeline with geomety and mateial chaacteistics outlined in section Safety Index no failue failue b [mm] Fig. 4 Cack depth vs. safety index of the deteministic analysis. A deteministic analysis does not conside scatteing of the mateial values, measuement eos o the POD of applied NDT inspection methods. Regading design pinciples deteministic assessments equie the use of safety factos. Consideing ealistic input paametes in fom of distibution allows a damage toleant assessment without the need of safety factos. 7

8 Fig. 5 shows the esult of the FAD pobabilistic analysis in which the theshold values of the Weibull distibution have been vaied in ode to assess the failue pobability extending fom extemely pessimistic scenaio of mateial factue toughness (K c =2 MPam 1/2 ) towads though a athe low factue toughness chaacteistic (K c =1 MPa m 1/2 ) of the consideed steel gade. Fo instance, when all othe non-mateial paametes ae at deteministic values and factue toughness has a 3P Weibull statistics vaiability a factue toughness of K c =1 assues a factue pobability of 1-6 when in the pipe subsists a cack of adial depth of appox 7.8 mm. Convesely, if the mateial is highly embittled, K c =2 MPam 1/2, only a cack of appox 1.1 mm is toleated at the same level of pobability of failue. The gey dashed lines indicate the limit value of cack depth below which the pobability of failue would be zeo. 1 K c th 1 K c th K c th 4 K c th 2 log 1 (POF) b [mm] Fig. 5 Cack depth vs. pobability of failue (no POD applied) fo fou diffeent theshold values of the Weibull distibution of the factue toughness. The dashed gey lines indicate the limit values. Fig. 6a and b show the esults of pobabilistic analysis when NDT techniques of vaious quality eflected in the consideed POD cuves (see Sect. 2.3) ae applied. Two levels of theshold factue toughness have been consideed: K c =4 MPam 1/2 and K c =1 MPam 1/2. This analysis evinces the significant ole of the mateial toughness in assuing low pobabilities of failue. On the othe hand, the application of NDT befoe opeation o duing opeation of the stuctue deceases the pobability of failue with moe than two odes of magnitude. Consideing additionally cack size statistics as descibed in section 2.3 instead of deteministic values leads to a significant incease of the POF (Tab. 4). The influence of the applied NDT method inceases simultaneously. The factue toughness theshold was selected as 4 MPa m 1/2. It can be stated that when cack size statistics have to be consideed the application of NDT leads to a moe significant decease of the POF than in the case of deteministic cack sizes values. Table 5. Compaison of POF with and without cack size statistics. No NDT POD II POF cack size statistics POF deteministic cack size

9 1 2 POD I POD II POD III POD IV no POD (a) K c Theshold POD I POD II POD III POD IV no POD (b) K c Theshold log 1 (POF) 5 6 log 1 (POF) b [mm] b [mm] Fig. 6 Compaison of the pobability of failue consideing the diffeent POD cuves and the pobability of failue when no NDT methods ae applied fo two diffeent theshold values of the Weibull distibution of the factue toughness. 4. Conclusion The study develops a methodology fo integating pobabilistic factue mechanics with quantitative NDI fo the pupose of failue isk assessment in load-caying stuctues and machine elements. The uncetainty in ou knowledge and the intinsic stochastic vaiability implied in the physical mechanisms confe a pobabilistic chaacte to the phenomenon of mechanical damage and failue. The estimation of the pobability of failue may be achieved by integating pobabilistic factue mechanics with quantitative NDT. The contibution of quantitative NDT to appoach failue isk estimation is made via the concept of pobability of detection, POD, as function of cack size. A shot outline of PVisk ationale and the associated softwae poduct is pesented togethe with an application petaining to the failue isk in pipelines. A pobabilistic analysis with PVisk consists in: pobabilistic input of mateial chaacteistics such as ultimate tensile stength, yield point, and factue toughness, stess intensity facto computation and the input of the equivalent initial cack size scatte. Finally, fo a epesentative case of pipe geomety and pipe steel, a sensitivity study is pesented in tems of pobabilities. It was evinced the influence of the minimum theshold of the factue toughness, as evaluated with the aid of thee-paamete Weibull distibution, and the influence of the quality of the applied NDT. The significant detimental effect of the low values of mateial factue toughness is met in evidence togethe with benefit of application of NDT of a specific quality eflected in the capacity of cack detection. In the latte case it was shown that the application of NDT of cuent quality fo nowadays pactice deceases the pobability of pipe failue with moe than two-odes of magnitude. Refeences [1] Andeson, T. L.: Factue Mechanics Fundamentals and Applications. 3d Edition, Boca Raton, USA: CRC Pess, 25 [2] Ameican Petoleum Institute: API RP 579: Fitness-Fo-Sevice, 2 [3] Ake Offshoe Patnes (1999): Review of pobabilistic inspection analysis methods. Ake Offshoe Patne A.S., Noway, Rep. 1999/61. [4] Alvaez J. A., Gutieez-Solana F., Ciceo S.: Envionmental Effect on Pipeline Steels: A Fitness fo Sevice Pespective. Open couse wae, Univesity of Cantabia (26). [5] Ayyub, B. M., McCuen, R. H.: Pobability, Statistics and Reliability fo Enginees and Scientists. Boca Raton, USA: CRC Pess, 23 9

10 [9] Benyon J.A., Watson A.S. (21): The use of Monte Calo analysis to incease axle inspection inteval. Poceedings of the 13 th Int. Wheelset Congess, Rome, Italy. [1] Bolle C. (Ed.); Chang F.-K. (Ed.); Fujino Y. (Ed.): Encyclopedia of Stuctual Health Monitoing, Vol.4: Pinciples of SHM-Based Stuctual Monitoing, Design and Maintenance, New Yok, Wiley & Sons, 29. [11] BS 791:25: Guide to methods fo assessing the acceptability of flaws in metallic stuctues. Bitish Standad Institution, 25 [12] Cioclov, D.: Integation of Factue Mechanics and Nondestuctive Testing. A Pobabilistic Appoach. In: Poc. of the South-East Euopean Welding Congess, Timisoaa, Romania, 1, May [13] Cioclov D. (22): Simulation of failue isk by combined pobabilistic factue mechanics and quantitative NDE analysis. 3d Euopean-Ameican Wokshop on Reliability of NDE and Demining, BAM, Belin, Septembe 1 th 13 th.22. [14] Cioclov D.D., Escobedo Medina M.C., and Schmidt H.-J., (23). On the pobabilistic factue mechanics simulation of fatigue life and cack statistics fo the pupose of damage toleance assessment. Poc. 22 nd Symp. Int. Comm. Aeonautical Fatigue. ICAF 23. In: Fatigue of Aeonautical Stuctues as an Engineeing Challenge. Vol. 1, pp EMAS Pub., Sheffield, U.K [15] Dobmann, G., Cioclov, D., Kuz, J. H. (27). The ole of pobabilistic appoaches in NDT defectdetection, -classification, and sizing. Welding in the Wold 51 (27), pp [16] Dowling A. R., Townley C. H. A.: The Effects of Defects on Stuctual Failue: A Two-Citeia Appoach. Intenational Jounal of Pessue Vessels and Piping 3 (1875), pp [17] Dugdale D. S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8 (196), pp [18] Haison R. P., Loosemoe K., Milne, I.: Assessment of the Integity of Stuctues Containing Defects. CEGB Repot R/H/R6. United Kingdom: Cental Electicity Geneation Boad, 1976 [19] Koplan S., Gaick, B. J.: On the quantitative definition of isk, Risk Analysis. In: EPRI Wokshop on Implementation of Risk-Based isi Methods. Chalotte, Noth Caolina, USA: Feb 29 - Mach 1, 1996 [2] Muakami, Y. (Ed.): Stess Intensity Factos Handbook. Vol. 2. Oxfod, UK: Pegamon Books Ltd., 1987 [21] Nichols, R. W. (Ed.): The Revision to the Stuctual Integity Assessment Method CEGB/R6. Intenational Jounal of Pessue Vessels & Piping 32 (1988), pp [22] R6: Assessment of the integity of stuctues containing defects. Appendix 1, Pobabilistic Factue Mechanics Pocedue, Nuclea Electic Pocedue R/H/6 Revision 3, Nuclea Electic, A1.1-24, 1998 [23] Rummel, W. D., Maietta, M., Hady, G. L., Coope, T. D.: Application of NDE Reliability to Systems. In: ASM Handbook: Nondestuctive Evaluation and Quality Contol. 3d Edition, Ohio, USA: ASM Intenational, 17 (1994), pp [24] Sundaamajan: Guide to Reliability Engineeing: Data, Analysis, Applications, Implementation and Management. NY, USA: Van Nostand Reinhold, 1991 [25] Taantola, A.: Invese Poblem Theoy and Methods fo Model Paamete Estimation. Philadelphia, USA: Society fo Industial and Applied Mathematics, 25 [26] Zebst U., Wiesne C., Kocak M., Hodulak L.: SINTAP: Entwuf eine veeinheitlichten euopäischen Fehlebewetungspozedu eine Einfühung. GKSS 99/E/65,