Nuclear Power Control, Reliability and Human Factors Part 8 docx

Evaluation of Dynamic J-R Curve for Leak Before Break Design of Nuclear Reactor Coolant Piping System 199 conventional fitting method for tearing modulus curve. However, analytical approach has uncertainty basically by fitting. In this paper, to evaluate reliable T mat curve at long crack extension region experimentally, we have researched the method for measurement of dynamic J-R curve with crack extension as long as possible. Fig. 9. Graphical illustration of J/T method Fig. 10. The illustration diagram for estimation of crack instability point for J/T method 3.2 Dynamic J-R curve testing for long crack extension To obtain the effective J-R curve under the condition of long crack extension, two specimens were used where one is for short crack extension and the other is for long crack extension. By using two test data, the dynamic J-R curve was evaluated over the crack extension length range according to ASTM code. Table 1 shows test matrix for reactor coolant piping base metal for Shin-Wolsung. Nuclear Power – Control, Reliability and Human Factors 200 Item Material Pipe size (Inner Dia.) Number of test Short crack extension Long crack extension Main Loop Piping Hot Leg SA508 Gr. 1a 42 in. 1 1 Cold Leg SA508 Gr. 1a 30 in. 1 1 Elbow SA516 Gr. 70 1 1 Table 4. Dynamic J-R test conditions for short and long crack extension conditions The load - displacement curve for each piping material is shown in Fig 11. In the dynamic J- R curves obtained by normalization method, for hot leg pipe and elbow materials, dynamic J-R curves were similar regardless of crack extension length; whereas for cold leg piping material, J-R curve for short crack extension length was lower than that for long crack extension length as shown in Fig.12. To analyze the reason for the difference between short and long crack extension for cold leg pipe, normalized load-displacement curve is described in Fig. 13. Normalized load-displacement curve, P N - ν’ pl curve shows different shape between two tests with different crack extension length. In general, normalized load – displacement curve should maintain a constant shape regardless of crack extension size. Therefore, optimal normalized P N - ν’ pl curve should be calculated by considering both P Ni - ν’ pli data pair for short and long crack extension. 0246810 0 10 20 30 40 50 60 Load (kN) Load Line Displacement (mm) Short Crack Extension Long Crack Extension Hot Leg Pipe 0246810 0 10 20 30 40 50 60 Load (kN) Load Line Displacement (mm) Cold Leg Pipe Short Crack Extension Long Crack Extension (a) Hot leg pipe b) Cold leg pipe 0246810 0 10 20 30 40 50 60 Load (kN) Load Line Displacement (mm) Elbow Short Crack Extension Long Crack Extension (c) Elbow Fig. 11. The load versus load line displacement curves for each material Evaluation of Dynamic J-R Curve for Leak Before Break Design of Nuclear Reactor Coolant Piping System 201 0246810 0 500 1000 1500 2000 Hot Leg Pipe Short Crack Extension Long Crack Extension J-Integral (kJ/m 2 ) Crack Extension Length (mm) 024681012 0 500 1000 1500 J-Integral (kJ/m 2 ) Crack Extension Length (mm) Cold Leg Pipe Short Crack Extension Long Crack Extension (a) Hot leg pipe (b) Cold leg pipe 0246810 0 500 1000 1500 J-Integral (kJ/m 2 ) Crack Extension Length (mm) Elbow Short Crack Extension Long Crack Extension (c) Elbow Fig. 12. The comparison of dynamic J-R curve by normalization method between the tests for short and long crack extension 0.00 0.05 0.10 0.15 0.20 100 150 200 250 300 350 Long Crack Extension Normalized Load, P N (MPa) Normalized Displacement, V pl /W Short Crack Extension Fig. 13. Normalized load, displacement data pair and its each fitting curve for short and long crack extension of cold leg piping material Nuclear Power – Control, Reliability and Human Factors 202 3.3 Combined analysis Based on this concept, combined analysis is proposed as the evaluation method of J-R curve to long crack extension using the test results with two different crack extensions. The procedure is as follows; At first, the P Ni - ν’ pli data pair is obtained by using load – load line displacement curve for long crack extension length in accordance with Eqs.(9) and (10), and final P Ni - ν’ pli data pair is obtained for two specimens respectively, where final P Ni - ν’ pli values are pl f Ni f P Final P Wa WB W          (9) fff pli vPC Final v' W   (10) A line is drawn from the final P Ni - ν’ pli data pair of short crack extension tangent to the P N - ν’ pl curve of long crack extension. The right side data to the tangent point and data with ν’ pli <0.001 are excluded from effective P Ni - ν’ pli data pair. The coefficients of the fitting function of Eq.(11) instead of Eq.(6) are calculated for two final P Ni - ν’ pli values and the effective P Ni - ν’ pli data pair. 23 pl pl pl N pl abv' cv' d' P ev'     (11) The following least square method is used for curve fitting of the function of Eq.(11).     2 23 Npl plplpl zPev'abv'cv'd' min.  (12) The coefficient values, a, b, c, d, e can be calculated directly by Eq.(13). 23 pl pl pl N pl 23 4 pl pl pl pl pl N 23 4 5 2 pl pl pl pl pl N 34 5 6 3 pl pl pl pl pl N 23 2 NplNplNplN N nv'v' v' P v' a v' v' v' v' v' P b c v' v' v' v' v' P d v' v' v' v' v' P e Pv'Pv'Pv'P P                                             N 2 pl N 3 pl N 4 pl N 2 pl N P v' P v' P v' P v' P                           (13) Figure 14 shows normalized load - displacement curve best-fit by Eq.(11) for two final points of short and long crack extension cases and the effective P Ni - ν’ pli data pair. Next, the crack length a i coinciding with P Ni in Eq.(4) and with P N in Eq.(11) is calculated for each ν’ pli by checking with slightly increasing crack lengths from initial crack length a 0 , where load - displacement curve for long crack extension length is used. However, J-R curve obtained using combined analysis was deviated from individual J-R curve for short and long crack extension respectively in the case of hot leg pipe material as shown in Fig. 14. This reason is Evaluation of Dynamic J-R Curve for Leak Before Break Design of Nuclear Reactor Coolant Piping System 203 that load - displacement curve between short and long crack extension have slightly different shape as shown in Fig. 11. Therefore, it is needed to adjust the position of middle point by reflecting the characteristics of J-R curves for short and long crack extension. To do so, the coincidence level is evaluated by comparing the J-R curves between normalization analysis by only short crack extension and combined analysis. As a method of evaluation for coincidence, best fit curve of Eq.(14) for the J-R curve of short crack extension is used.  m JCa (14) 0.00 0.05 0.10 0.15 0.20 100 150 200 250 300 Normalized Load, P N (MPa) Normalized Displacement, V pl ' Final Point for Long Crack Extension Final Point for Short Crack Extension Fig. 14. The best fit curve by Equation (11) on effective data pair for combined analysis 0246810 0 500 1000 1500 2000 Hot Leg Pipe Short Crack Extension Long Crack Extension Initial Combined Analysis J-Integral (kJ/m 2 ) Crack Extension Length (mm) Fig. 15. Dynamic J-R curve for hot leg pipe material prior to adjustment of middle point on normalized load versus displacement curve in combined analysis Next, the standard deviation σ of Eq.(15) is calculated from J value by combined analysis and J value obtained by J-R curve of Eq.(14). Such that, the data of combined analysis to short crack extension are used in calculating σ  2 fit combined JJ n1     (15) Nuclear Power – Control, Reliability and Human Factors 204 where J fit is J value obtained by fitting function of Eq.(14) J combined is J value obtained by combined analysis and n is the number of effective J-R data to short crack extension. Optimal middle point on the normalized load-displacement relationship is determined as a point when standard deviation σ value of Eq.(15) is reached to minimize by adjusting P N value at ν’ pl value at final point of short crack extension. Using the optimal middle point, final P Ni - ν’ pli data pair of long crack extension and effective P Ni - ν’ pli data pairs, J-R curve can be estimated. Figure 9 shows the comparison of dynamic J-R curve among the combined method and normalization method of short and long crack extension. For all three kinds of piping, dynamic J-R curve by combined analysis is well described with the behavior of that for two different crack extensions. From this combined analysis, we could obtain reasonable dynamic J-R curve until long crack extension for nuclear piping materials. In combined analysis, one J-R curve is obtained using two specimens. Therefore, the scatter of material properties with the position of taking specimen is required not to be large. In LBB analysis, the lowest material property is used among three test results for material property scatter. In this approach, the J-R curve tends to be estimated as an average J-R data for two test results. Further investigation is therefore needed for low bound curve of J-R curve with long crack extension effectively based on the statistical concept. 0246810 0 500 1000 1500 2000 Crack Extension Length (mm) Hot Leg Pipe Short Crack Extension Long Crack Extension Combined Analysis J-Integral (kJ/m 2 ) 024681012 0 500 1000 1500 Crack Extension Length (mm) J-Integral (kJ/m 2 ) Cold Leg Pipe Short Crack Extension Long Crack Extension Combined Analysis (a) Hot leg pipe (b) Cold leg pipe 0246810 0 500 1000 1500 J-Integral (kJ/m 2 ) Crack Extension Length (mm) Elbow Short Crack Extension Long Crack Extension Combined Analysis (c) Elbow Fig. 16. The dynamic J-R curve by combined analysis for each material Evaluation of Dynamic J-R Curve for Leak Before Break Design of Nuclear Reactor Coolant Piping System 205 4. Conclusion From the comparison test results between DCPD and normalization method as a dynamic J- R curve testing method, short crack extension, dynamic J-R curves were similar but, for long crack extension, J-R curve estimated by normalization was higher by 10~30% at the initial loading stage than that by DCPD. For reliable J/T analysis for LBB design of nuclear piping, material J-R curve for long crack extension is needed. However, normalization method is applicable for only short crack extension. To overcome this problem, combined analysis based on normalized method was proposed. In combined analysis, dynamic J-R curve with long crack extension is estimated by two dynamic J-R curve tests with different crack extension length. The dynamic J-R curve beyond the crack extension length range designated by ASTM code could be estimated using the combined analysis. 5. References ASTM (2009). ASTM E1820-09e1 Standard Test Method for Measurement of Fracture Toughness, In: Annual Book of ASTM Standard, Vol. 03.01, ASTM International, West Conshohocken, Pennsylvania, USA Ernst, H.A., Paris, P.C., Rowssow, M. & Hutchinson, J.W. (1979). Analysis of Load Displacement Relationship to Determine J-R Curve and Tearing Instability Material Properties. In: ASTM STP 677 Fracture Mechanics, Smith, C.W. (Ed.), pp. 581-599, ASTM International, ISBN EB 978-0-8031-4746-1, West Conshohocken, Pennsylvania, USA Ernst, H.A., Paris, P.C. & Landes, J.D. (1981). Estimations on J-integral and Tearing Modulus T from a Single Specimen Test Record. In: ASTM STP 743 Fracture Mechanics, Roberts, R. (Ed.), pp. 476-502, ASTM International, ISBN EB 978-0-8031-4809-3, West Conshohocken, Pennsylvania, USA Hackett, E.M., Kirk, M.T. & Hays, R.A. (1986). NUREG/CR-4550 : An Evaluation of J-R Curve Testing of Nuclear Piping Materials Using the Direct Current Potential Drop Technique , U.S. Nuclear Regulatory Commission Johnson, H.H. (1965). Calibrating the Electric Potential Method for Studying Slow Crack Growth. Materials Research and Standards, (September 1965), Vol.5, No.9, pp. 442- 445, ISSN 0025-5394 Joyce, J.A. (1996). Manual on Elastic-Plastic Fracture Laboratory Test Procedures, ASTM International, ISBN 0-8031-2069-9, West Conshohocken, Pennsylvania, USA Kim, J.W. & Kim, I.S. (1997). Investigation of Dynamic Strain Aging on SA106-Gr.C Piping Steel. Nuclear Engineering and Design, Vol. 172, No. 1-2, (July 1997), pp. 49-59, ISSN 0029-5493 Scott, P.M., Olson, R.J. & Wilkowski, G.M. (2002). NUREG/CR-6765: Development of Technical Basis for Leak-Before-Break Evaluation Procedures, U.S. Nuclear Regulatory Commission Landow, M.P. & Marschall, C.W. (1991). Experience in Using Direct Current Electric Potential to Monitor Crack Growth in Ductile Metals, In: ASTM STP 1114 Elastic- Plastic Fracture Test Methods , Joyce, J.A. (Ed.), pp. 163-177, ASTM International, ISBN-EB 978-0-8031-5172-7, West Conshohocken, Pennsylvania, USA Nuclear Power – Control, Reliability and Human Factors 206 Landes, J.D., Zhou, Z., Lee, K. & Herrera.,R. (1991). Normalization Method for Developing J- R Curve with the LMN Function. Journal of Testing and Evaluation, Vol. 19, No. 4, (July 1991), pp. 305-311, ISSN 0090-3973 Lee, B.S., Yoon, J.H., Oh, Y.J., Kuk, I.H. & Hong, J.H. (1999). Static and Dynamic J-R Fracture Characteristics of Ferritic Steels for RCS Piping, 15th International Conference on Structural Mechanics in Reactor Technology , Vol. V, pp. 297-302, ISBN 89-88819-05-5 94500, Seoul, Korea, August 1999 Lee, J.B. & Choi, Y.H. (1999). Application of LBB to High Energy Pipings of a Pressurized Water Reactor in Korea, Nuclear Engineering and Design, Vol.190, No.1-2, (June 1999), pp.191~195, ISSN 0029-5493 Nakamura, T., Shih, C.F. & Freund, L.B. (1986). Analysis of a Dynamically Loaded Three- Point-Bend Ductile Fracture Specimen, Engineering Fracture Mechanics, Vol. 25, No. 3, pp. 323-339, ISSN 0013-7944 Oh, Y.J, Kim, J.H. & Hwang, I.S. (2002). Dynamic Loading Fracture Tests of Ferritic Steel Using Direct Current Potential Drop Method. Journal of Testing and Evaluation, Vol. 30, No. 3, (May 2002), pp. 221-227, ISSN 0090-3973 Sharobeam, M.H. & Landes, J.D. (1991). The Separation Criterion and Methodology in Ductile Fracture Mechanics. International Journal of Fracture, Vol. 47, No.2, (January 1991), pp. 81-104, ISSN 0376-9429 Wallen, K. (2009). Extrapolation of Tearing Resistance Curves. 2009 Proceeding of the ASME Pressure Vessel and Piping Conference , Vol.3, pp. 281-286, ISBN 978-0-7918-4366-6, Prague, Czech Republic, July 2009 11 Feed Water Line Cracking in Pressurized Water Reactor Plants Somnath Chattopadhyay Georgia Southern University, Statesboro, Georgia, USA 1. Introduction As early as 1979, a through wall crack was detected in a pressurized water reactor (PWR) plant. This crack initiated at the counter bore region of the pipe, adjacent to the weld joint attaching the pipe to the steam generator feed water nozzle. Subsequent inspection of the remaining feed water piping revealed cracking in the same vicinity but these were limited to partial wall penetration. As a result of this incident, the US Nuclear Regulatory Commission issued a directive to all operating plants requiring them to perform inspection of their feed water lines. The cracks were subsequently detected in the immediate vicinity of the steam generator nozzles in a number of plants. An exhaustive investigation was undertaken subsequently and this revealed that the primary cause of cracking was due to a fatigue loading mechanism induced by thermal stratification and high cycle thermal oscillations (striping) during low flow conditions. Thermal stratification phenomenon results from a temperature differential across the pipe cross section with the top fluid stream hot and bottom stream relatively cold. During normal plant operations at low flow conditions, when the feed water nozzle is not completely full, hot water from the steam generator remains in the nozzle to fill up the rest of the volume. The difference in buoyancy between the hot and cold fluids inhibits their mixing so that the feed water becomes and remains thermally stratified. Separation of these two flow regions is due to the density difference in the hot and cold streams. The stratified temperature conditions can produce very high stresses, and can occur may times during normal low power operations; therefore this has the potential to initiate cracks in a relatively short period of time. Thermal striping is a local phenomenon that occurs at the interface between hot and cold flowing fluids. The interface level oscillates with periods ranging from 0.1 to 10 seconds. The oscillating fluid temperature gives rise to fluctuating stresses. The magnitudes of the striping stresses are not as high as those due to stratification itself, but the number of cycles is so large that they contribute significantly to fatigue crack initiation. During normal plant operation, a series of temperature measurements has been taken around the pipe circumference at the vicinity of the of the feed water nozzle/pipe weld. Analysis of the data indicates that the stratified temperature distributions may be grouped into a handful of basic profiles corresponding to different levels of the interface between the hot and cold fluids. For analysis purposes these profiles could be assumed to be at steady state conditions because of their long duration observed during the tests. Nuclear piping systems (Class 1) are designed according to the rules of NB 3600 of the ASME Boiler and Nuclear Power – Control, Reliability and Human Factors 208 Pressure Vessel Code, Section III. The loads producing the stresses originate from the internal pressure, mechanical loads due to deadweight, seismic and thermal expansion and the operating thermal transients. Normally piping systems are not designed for circumferential temperature variation. The effect of the thermal stratification on the state of stress in the pipe is manifested in two ways: (a) the difference in temperature between the top and bottom of the pipe causes greater thermal expansion at the top tending to bow the pipe. When such bowing is restrained global bending stresses result; (b) the interface between the two fluid layers causes a local stress in the pipe due to thermal discontinuity across the pipe section. The fatigue damage produced by thermal stratification and the associated thermal striping are a good indication of the contribution of these phenomena to the observed feed water line cracking. A detailed finite element stress analysis has been carried out using a three dimensional model that includes the steam generator shell, the feed water nozzle, and the elbow/pipe. The shell nozzle/elbow model contains three distinct regions with different heat transfer characteristics between the metal and the adjacent fluid. Each of the stratification profiles produces a complex state of stress throughout the nozzle and the elbow (pipe). Different levels of interface produce peak stresses at different locations around the circumference. Since the interface level varies during low flow operating conditions, each point in the counter bore area is subjected to a state of varying stresses of large magnitudes. A maximum range of stress intensity analysis was carried out prior to fatigue evaluation to determine whether the simplified elastic plastic analysis procedure would be required, and if so, to calculate the plastic intensification factor K e by which the peak alternating stresses would be multiplied. The analysis predicted crack locations that that correlated well with the observed cracking. The major cause of growth of the cracks is due to the thermal stratification cycles, which occur during low flows, primarily at hot standby. The thermal striping phenomenon or the oscillations occurring at the interface between hot and cold fluids has some influence on the crack growth, but it certainly impacts the crack initiation predictions. Thermal stratification causes a stress distribution in a pipe that is similar to what happens in a bimetallic strip. In the hot upper region compressive stresses develop as a result of constrained expansion, with the tensile stresses occurring in the lower region. This has been demonstrated using a simplified 2-dimensional finite element model. These are essentially the membrane stresses in the axial direction. Since the piping is flexible, the thermal moment gives rise to a bending stress that is added to the membrane stresses to obtain the total stresses. It is suggested that the equations for obtaining stresses in piping systems as outlined in the ASME Code contain a term addressing circumferential temperature gradients in the pipe. A number of remedial measures have been implemented or suggested in operating power plants to minimize the stress amplitudes and frequency of load cycling during the stratification events. In recent years, thermal stratification phenomenon has been observed to exist on several piping systems in pressurized water reactors. Damages have been observed in the main feed water lines, pressurizer spray lines, unisolable branch piping connected to reactor coolant piping, and pressurizer surge lines, with evidence linked to thermal stratification. The stratification phenomenon results from a temperature differential across the pipe cross- section with the top fluid stream hot and the bottom stream relatively cold. This condition occurs under relatively low flow conditions by cold feed injection into a stagnant hot pipe region or vice versa. Separation of two fluid flow areas is due to density differences in the [...]... levels of the interface between the hot and cold fluids and are shown in Figure 4 212 Fig 4 Stratified Temperature Profiles [3] Nuclear Power – Control, Reliability and Human Factors Feed Water Line Cracking in Pressurized Water Reactor Plants 213 A finite element model has been prepared that includes a part of the steam generator shell, the feed water nozzle and the connecting elbow The model uses... temperature and, on the other hand, it shows an important scatter Figure 3 shows an example of a vessel steel neutron irradiation embrittlement In this figure, Charpy impact test results (absorbed energy vs temperature) from unirradiated and irradiated material, respectively, are represented As can be seen, the most remarkable effects are a shift 2 18 Nuclear Power – Control, Reliability and Human Factors. .. programme design along with the rules for the interpretation of the results of such programmes are 224 Nuclear Power – Control, Reliability and Human Factors regulated in several ASTM standards (ASTM E 185 , 2002; ASTM E 2215, 2002; ASTM E 85 3, 2001) Next, the minimum requirements considered in these standards for the design of a surveillance programme for monitoring the radiation-induced changes in the... location 214 Nuclear Power – Control, Reliability and Human Factors Fig 5 Calculated Temperature input to the Approximate Numerical Model [4] Fig 6 Stress Distribution across Pipe Diameter for Profiles 1 through 6[4] 7 References [1] Enrietto, J.F., Bamford, W H., and White, D H (1 981 ), “Preliminary Investigation of PWR Feed water Line Cracking, International Journal of Pressure Vessels and Piping,... and interstitials eventually migrate and annihilate at sinks long distances from the cascade region Thus long-range diffusion results in additional nanostructural evolution As a consequence of the above mentioned mechanisms three broad categories of nanofeatures can be distinguished: Copper rich or manganese-nickel rich precipitates (CRPs/MNPs)  2 28 Nuclear Power – Control, Reliability and Human Factors. .. these neutrons are referred to as fast neutrons Typical design end of life (EOL) neutron 216 Nuclear Power – Control, Reliability and Human Factors fluences (E>1 MeV) for BWRs are in the order of 10 18 n/cm2, whereas for PWRs this number is about 1019 n/cm2 In Section 2 of this chapter, the embrittlement of nuclear vessel steels is described from a purely phenomenological perspective as well as from... may have resulted the cracking; both high and low cycle fatigue were involved, with high cycle initiating the fatigue and the low cycle propagating it The fracture appearances were studied at high magnification by electron microscopy Striations were found (Figure 2) substantiating the evidence that crack growth 210 Nuclear Power – Control, Reliability and Human Factors was taking place by fatigue, although... by the Nuclear Regulatory Commission, NRC) is especially noteworthy This regulation is contained in the ASME (American Society of Mechanical Engineers) Code The ASME International Boiler and Pressure Vessel Code (ASME Code) establishes rules of safety governing the design, fabrication and inspection of boilers and pressure vessels, and nuclear power plant components during construction This standard... Stratification,” Nuclear Engineering and Design, 239, pp 2236-2241 [5] ASME Boiler and Pressure Vessel Code, 2010, Section III, Nuclear Power Components, American Society of Mechanical Engineers, New York 12 Degradation Due to Neutron Embrittlement of Nuclear Vessel Steels: A Critical Review about the Current Experimental and Analytical Techniques to Characterise the Material, with Particular Emphasis... SIF (and consequently the toughness KIc) are usually expressed in MPa·m1/2 Toughness KIc is determined following the rules of the ASTM E 399 standard (ASTM E 399, 2009) or some other equivalent procedure Thanks to the works of A.A Griffith (Griffith, 1920), C.E Inglis (Inglis, 1913), G.R Irwin (Irwin, 1956, 1957) or H.M Westergaard (Westergaard, 1939) 1 220 Nuclear Power – Control, Reliability and Human . 163-177, ASTM International, ISBN-EB 9 78- 0 -80 31-5172-7, West Conshohocken, Pennsylvania, USA Nuclear Power – Control, Reliability and Human Factors 206 Landes, J.D., Zhou, Z., Lee, K. &. during the tests. Nuclear piping systems (Class 1) are designed according to the rules of NB 3600 of the ASME Boiler and Nuclear Power – Control, Reliability and Human Factors 2 08 Pressure Vessel. load, displacement data pair and its each fitting curve for short and long crack extension of cold leg piping material Nuclear Power – Control, Reliability and Human Factors 202 3.3 Combined