Failure Probability Analysis Based on FRI Model for SCC Growth Introducing Stress Intensity Factor Distribution as Function of Crack Depth

Failure Probability of a weld by stress corrosion cracking (SCC) in austenitic stainless steel piping was analyzed by probabilistic fracture mechanics (PFM) approach based on electro-chemical crack growth model (FRI model). In this model, crack growth rate da/dt where a is crack depth is anticipated as the rate of chemical corrosion process defined by electro-chemical Coulomb’s law. The process is also related to the strain rate at the crack tip, taking small scale yielding condition into consideration. Derived transcendental equation is solved numerically by iterative method. Compared to the mechanical crack growth equation like Paris’ law for SCC, FRI model can introduce many electro-chemical parameters such as electric current associated with corrosion of newly born SCC crack surface, the frequency of protective film break and mechanical parameters such as stress intensity factor change with time dK/dt. Stratified Monte-Carlo method was introduced which define the cell of sampling space by the ranges of a/c (c is crack length at surface) and the width of K of sampling space, Kw which has to be defined referring to KSCC below which no SCC is caused. Log-normal distributions were anticipated for a/c distribution and K distribution. Parameter survey performed shows that failure probability which is defined as the ratio of crack number whose depth reached 80% of wall thickness to the total crack number depends on many parameters introduced, especially on yielding stress, electric current decay parameter m, strain hardening index n in Ramberg-Osgood equation and dK/dt. From the requirements of FRI model, two types of threshold value of initial crack depth, cracks having smaller depth than this value can not grow, are proposed. Calculated failure probability does not reach 1 when cracks having smaller initial depth than the threshold value are included in the distribution of analyzing cracks.

This paper describes the validity of successive inspections in a chain of the integrity assessment applying Fitness-For-Service (FFS) Codes to piping with stress corrosion cracks. Integrity assessment of primary recirculation system (PLR) piping with stress corrosion cracks is one of the recent interests in Japanese boiling water reactor (BWR) plants. Girth weld joints with detected stress corrosion cracks are required to secure the integrity during subsequent 5 years operation and to conduct three times of successive inspections for PLR piping. If the safety factor included in FFS Codes works effectively, this, like frequent successive inspections are deemed unnecessary. However, since there is some uncertainty in the measurement of crack size and in crack growth estimation in the integrity assessment of piping with stress corrosion cracks, a possibility of failure cannot be denied when not conducting successive inspections to confirm the validity of the integrity assessment. In this study, piping failure probability when conducting and not conducting successive inspections using a probabilistic fracture mechanics (PFM) code, and the validity of successive inspections were examined quantitatively from the failure probabilities. The effect of crack sizing accuracy, which has great influence on the validity of inspections, was also examined. The validity of successive inspections was examined for 12, 16, and 24 inch pipes which were employed in PLR piping of BWR-5. It became clear that successive inspections were very effective in decreasing failure in 12 and 24 inch pipes, but not as effective in decreasing failure in 16 inch pipes. The reason is suggested that the crack growth rate in a 16 inch pipe is high compared with the other two sized pipes and opportunity of renewal of crack growth estimation at successive inspections is few. When successive inspections are carried out, there are several times of opportunity for improvement of underestimated crack growth behavior unless a crack size is measured smaller than the actual size in all successive inspections. Consequently, the influence of the crack sizing error on failure probability of pipes becomes very small.

Integrity assessment of primary recirculation system (PLR) piping with stress corrosion cracks is one of the recent interests in Japanese BWR plants. Crack detection performance and a sizing error in non-destructive test (NDT) have a great influence on the integrity assessment of piping. This paper presents effects of crack detection performance and sizing accuracy on the reliability of PLR piping with stress corrosion cracks. Failure probability (leak and break) of PLR piping maintained according to the rules in Fitness-For-Service (FFS) Codes of JSME was analyzed using a probabilistic fracture mechanics (PFM) code which could analyze initiation and growth behavior of stress corrosion cracks. For the reliability of PLR piping, reducing oversight of cracks and crack sizing error are effective, and detectable crack size has not much influence on reliability of piping. For the higher reliability, reducing oversight of cracks is more important than the improvement of the detectable crack size in NDT, and the qualified inspectors should be employed for sizing of detected cracks in order to be suitable measurement in NDT.

Failure probability analyses for PWSCC in Ni-based alloy welds

Structural integrity assessments for cracked nuclear components are currently performed on the basis of deterministic fracture mechanics in accordance with the Rules on Fitness-for-Service for Nuclear Power Plant of the Japan Society of Mechanical Engineers. On the other hand, probabilistic fracture mechanics (PFM) is expected as a rational method for a structural integrity assessment because it can account for the uncertainties and scatters of various influencing factors and can evaluate quantitative values such as the failure probabilities of the components as the solutions. In the Japan Atomic Energy Agency (JAEA), a PFM analysis code PASCAL-SP was developed in order to evaluate the failure probability of nuclear pipe by taking into account aging degradation mechanisms such as inter-granular stress corrosion cracking (IGSCC) and fatigue in the boiling water reactor (BWR) environment. Recently, a number of cracks due to primary water stress corrosion cracking (PWSCC) have been detected in nickel-based alloy welds in the primary piping of pressurized water reactors (PWRs). Therefore, the structural integrity assessment for primary piping taking PWSCC into consideration has become important. This paper details the improvement of PASCAL-SP to evaluate the failure probability of primary pipe taking PWSCC into consideration. We introduce several probabilistic evaluation models such as crack initiation, crack growth and crack detection models related to PWSCC into PASCAL-SP. As numerical examples, the failure probabilities for circumferential and axial cracks in nickel-based alloy weld in pipe in the PWR primary water environment are calculated. We also evaluate the influence of non-destructive inspection on failure probabilities. On the basis of the numerical results, we conclude that the improved PASCAL-SP is useful for evaluating the failure probability of primary pipe taking PWSCC into account.

Stress corrosion cracking (SCC) in engineering thermoplastics is commonly observed in the form of a microcrack colony within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. A probabilistic modeling of SCC initiation is briefly discussed. A deterministic modeling of slow stress corrosion (SC) crack growth process is developed using Crack Layer (CL) theory. Numerical solution of SC crack growth equations is discussed. Comparison of the kinetics of cracks driven by SC and by stress only is presented. Conventional plot of SC crack growth rate vs. the stress intensity factor is constructed and analyzed. An algorithm for conservative estimation of lifetime of engineering thermoplastic subject to a combination of mechanical stresses and chemically aggressive environment is discussed.

A modified middle scaled creviced bent beam (CBB) test was conducted in order to investigate stress corrosion cracking (SCC) behavior around fusion boundary between nickel base alloy (Alloy82) and low-alloy steel (LAS) under high stress conditions in light water reactor (LWR) coolant environment.An Alloy182/LAS clad plate specimen was placed between the CBB jigs so that the tensile stress occurs in Alloy182 and the SCC cracks propagate from the Alloy182 surface to the fusion boundary. In pure water, only oxides and cracks propagating along the fusion boundary were observed. Meanwhile in Na2SO4 injected water with electrical conductivity 0.3μS/cm, deep cracks propagated into the LAS. The higher conductivity enhanced the driving force of the SCC cracks.A notched specimen was also tested to investigate SCC propagating behavior in more severe stress conditions than those in a smooth surface specimen. When a notched specimen was used, even in pure water condition, some cracks penetrated the fusion boundary and oxides were observed. In the notched specimen, crack nucleation points are limited in the notch root and the stress relaxation hardly occurs due to multiple crack nucleations. Such severe stress conditions also contribute the cracks to propagate into the LAS.To discuss the crack propagation behavior in the vicinity of the fusion boundary, the cross section was observed with an optical microscope. The observation indicates that the crack propagating depth into the LAS and the diameter of oxides increase with increasing the Alloy182 thickness. Although an effect of applied strain and welding direction of specimen to SCC behavior was investigated, there was no significant difference in the morphology by them.Since 1% strain was applied to CBB specimen surface and much greater strain was observed at a notched specimen, elasto-plasticity should be considered to stress condition of a SCC crack tip. An ‘equivalent stress intensity factor, KJ’ was, therefore, proposed to describe a stress condition in elasto-plastic area. A good relationship was observed between depth of SCC crack in LAS and KJ value. It was found that the proposed parameter KJ was effective to describe the stress state at the crack tip from the elastic region to the plastic region up to approximately 1% strain.Copyright © 2012 by ASME

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 109-119 (2003) No AccessANALYTICAL DETERMINATION OF STRESS INTENSITY FACTOR FOR PLATE BENDING PROBLEMSLALITHA CHATTOPADHYAYLALITHA CHATTOPADHYAYAdvanced Research Group, Structures Division, National Aerospace Laboratories, P.O. Box 1779, Kodhihalli, Bangalore 560 017, India Search for more papers by this author https://doi.org/10.1142/S1465876303000776Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an isotropic elastic plate of constant thickness is examined. The plate containing cracks is infinite and its boundary is subjected to bending moment or twisting moment. Using classical plate theory and integral transform techniques, the general formulae for the bending moment, twisting moment and bending stress distribution in an elastic plate acted upon by moment forces and containing cracks located on a single line are derived. The solution is obtained in detail, for the case in which there is a single crack in an infinite plate and the bending stress intensity factor is determined in a closed form and the results are compared with those obtained from finite element analysis. Close agreements between the analytical solution, numerical solution and reference solution were found in all cases.Keywords:Stress intensity factorplatecrackbendingintegral transform References M. L. Williams, ASME J. Appl. Mech. 28, 78 (1961). Crossref, Google ScholarG. C. Sih, P. C. Paris and F. Erdogan, ASME J. Appl. Mech. 29, 306 (1962). Crossref, Google ScholarJ. K. Knowles and N. M. Wang, J. Math. Phys. 39, 223 (1960). Crossref, Google ScholarR. S. Alwar and K. N. Ramachandran, Eng. Fracture Mech. 17, 323 (1983), DOI: 10.1016/0013-7944(83)90083-8. Crossref, Google ScholarE. Reissner, Quart. Appl. Math. 5, 55 (1947). Crossref, Google ScholarM. J. Vizet al., Int. J. Fracture 72, 21 (1995). Crossref, Google ScholarA. Zucchini, C.-Y. Hui and A. T. Zehnder, Int. J. Fracture 104, 387 (2000), DOI: 10.1023/A:1007699314793. Crossref, Google Scholar S. P. Timoshenko , Theory of Plates and Shells ( McGraw Hill Book Company , Auckland , 1959 ) . Google Scholar I. N. Sneddon , Use of Integral Transforms ( McGraw Hill Book Company , New York , 1972 ) . Google ScholarE. F. Rybicki and M. F. Kanninen, Eng. Fracture Mech. 9, 931 (1977), DOI: 10.1016/0013-7944(77)90013-3. Crossref, Google Scholar Y. Murakami , Stress Intensity Factors Handbook 2 ( Pergamon Press , Oxford , 1987 ) . Google Scholar FiguresReferencesRelatedDetailsCited By 3Two-Dimensional Crack and Contact Problems – Transform MethodArabinda Roy and Rasajit Kumar Bera6 Dec 2019EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENTLALITHA CHATTOPADHYAY, S. SRIDHARA MURTHY and S. VISWANATH20 November 2011 | International Journal of Computational Methods, Vol. 04, No. 02Analytical Solution for an Orthotropic Elastic Plate Containing CracksLalitha Chattopadhyay1 Aug 2005 | International Journal of Fracture, Vol. 134, No. 3-4 Recommended Vol. 04, No. 01 Metrics History Received 28 August 2002 Accepted 24 January 2003 KeywordsStress intensity factorplatecrackbendingintegral transformPDF download

Availability of a pressurized water reactor pressure vessel after a small LOCA

Stress corrosion cracking (SCC) continues to be a safety concern, mainly because it can remain undetected before a major pipeline failure occurs. SCC processes involve complex interactions between metallurgy, stress, external soil environment, and electrolyte chemistry beneath disbonded coatings. For these reasons, assessing SCC failure probability at any given location on a pipeline is difficult. In addition, the uncertainty in data makes the prediction of SCC challenging. The complex interactions that affect SCC failure probability can be modeled using Bayesian network models. The Bayesian network models link events by cause-consequence connections. The strengths of these connections are adjusted using expert knowledge, analytical models, and data from the field. An approach to predicting probability of High pH SCC failure using Bayesian networks was proposed in a previous publication.1 The previous paper discussed the effects of stress only. In this paper, the previously discussed model is extended to the evaluation of other factors that affect high pH SCC. The model can be used to assess the probability of failure due to SCC at different times for different pipeline segments.

Applicability of elasto-plastic parameter for evaluating stress corrosion cracking (SCC) growth rate was examined. Currently linear fracture mechanical approach has been applied for crack evaluation; even though some SCC is found in plastic deformation zone near welding areas where linear elastic fracture mechanics no longer is applicable. Authors have proposed elastic-plastic approach "equivalent stress intensity factor K_j" for evaluating SCC growth rate based on J-integral value, which is valid in both elastic and plastic stress fields. In order to verify the applicability of evaluation by K_j, SCC propagation test in compact tension specimens with varying specimen size and stress conditions were conducted in boiling water reactor environment. As a specimen, sensitized type304 stainless steel was used. When a crack growth rate (CGR) of SCC was evaluated by stress intensity factor K, linear relationship between K and CGR does not exist in the high K value, where CT specimens are out of small scale yielding condition. CGR increases exponentially according to increasing stress intensity factor K to exceed linear relationship. On the other hand when CGR was evaluated by elasto-plastic parameter K_j, linear correlation between K_j and CGR was confirmed regardless specimen size and stress condition. This suggests that by applying elasto-plastic parameter K_j for SCC behavior, CGR at high K value could be estimated easily with using a smaller specimen.

Incubation times of stress corrosion cracking (SCC) for mill annealed and cold rolled type 316L stainless steel (SS) and type 316 SS were examined by the creviced bent beam method in oxygenated high temperature water at 561 K. SCC was observed in type 316L SS after exposure of 1000 h to the test environment, although type 316 SS showed SCC susceptibility after exposure of 500 h. The fracture surface of both type 316L SS and type 316 SS consisted mainly of intergranular SCC with a small fraction of transgranular SCC similar to those observed in the actual components. The maximum SCC crack length [a] on the specimen surface increased in proportion to the logarithm of the exposure time [t] for each SS as ;a=700×ln(t)–4334 : type 316L SS,a=1078×ln(t)–6347 : type 316 SS.The incubation times of 490 h and 360 h were obtained for type 316L SS and type 316 SS, respectively, from the relationship between the crack length and the test time. The SCC incubation times were larger than that of sensitized type 304 SS by >3 times showing higher resistance to SCC of mill annealed, low carbon stainless steels.

Probabilistic ageing and risk analysis tools for nuclear piping

The influence of the strain-rate on the stress corrosion cracking of alloy 600 in high temperature primary water

Environmentally assisted crack (EAC) growth in thermally treated Alloy 690 (Alloy 690TT) cold worked one-dimensionally to the thickness reduction of 25% was investigated by crack growth rate testing in the primary water at low and high temperatures. In water at 50 °C and a dissolved hydrogen (DH) of 2.7–2.9 ppm, the test results suggest that the crack growth rate is lower than 2.2×10−9 mm/s at a stress intensity factor of 35 MPa√m. Stress corrosion cracking (SCC) growth with a rate of <1×10−11 m/s was observed in the alloy in water at temperatures of 320 °C and 340 °C. Over a DH range of 0.37–2.6 ppm, the SCC growth in Alloy 690TT has a similar DH dependence as that in Alloy 600 and its weld metals. The magnitude of the DH dependence, however, is much smaller for Alloy 690TT. In water deaerated by N2 without DH, an extremely low SCC growth rate was observed. Increasing DH in water from 0 ppm to 0.38 ppm caused an active SCC growth, suggesting that hydrogen could promote SCC growth when increasing DH from a very low level. Results of the current work confirmed a general high resistance of 25% cold worked Alloy 690TT to EAC growth in the primary water at both low and high temperatures under moderate stress intensity factors.