Proceedings of the ASME 2015 Pressure Vessels and Piping Conference PVP2015 July 19-23, 2015, Boston, Massachusetts, USA PVP2015-45567 UNCERTAINTY CHARACTERIZATION OF THE TWC_FAIL THROUGH-WALL CIRCUMFERENTIAL CRACK STABILITY MODULE FOR XLPR Paul Scott Battelle Memorial Institute 505 King Avenue Columbus, OH, 43201 USA Tel: (614)-571-5520 Email: [email protected] Richard Olson Battelle Memorial Institute 505 King Avenue Columbus, OH, 43201 USA Tel: (614)-424-4539 Email: [email protected] for Leak-Before Break (LBB) relief, the US NRC and EPRI have been jointly funding the development of a fully probabilistic analysis software tool, known as xLPR for eXtremely Low Probability of Rupture, to evaluate the probability of ruptures in Alloy 82/182 dissimilar metal welds [1]. Probabilistic pipe fracture analyses are built upon deterministic models. In xLPR there are models for crack initiation, crack growth, crack coalescence, crack opening displacement (COD), leak rate, and crack stability in order to characterize the crack behavior from when it first appears as a surface crack (SC), to when it may become a leaking throughwall crack (TWC), to when the through-wall crack finally fails. Models embedded into xLPR also include crack inspection, leak detection, and mitigation to deal with the effect on probability of rupture of actions associated with operation and maintenance. Focusing only on crack stability, it is assessed in xLPR for both surface cracks and leaking through-wall cracks. In either case, conditions (crack size and load), at some instant of analysis time, may be large enough to cause an instability (rupture), so xLPR must include an assessment of whether or not the current state is stable at each time step. Generally, such stability assessments are performed using limit-load or elasticplastic fracture mechanics (EPFM) models. Restricting attention to the circumferential crack case, the xLPR module for TWC stability is called TWC_Fail. TWC_Fail evaluates circumferential through-wall crack stability based on the minimum critical crack size of a limit-load solution and an EPFM J-estimation scheme. Although it would be ideal if uncertainty of such a module was only the consequence of the uncertainty of the input parameters, these are, after all, only simplified models of very complex behavior so the model itself has uncertainty. Within ABSTRACT The US NRC/EPRI xLPR (eXtremely Low Probability of Rupture) probabilistic pipe fracture analysis program uses deterministic modules as the foundation for the calculation of the probability of pipe leak or rupture as a consequence of active degradation mechanisms, vibration or seismic loading. The circumferential through-wall crack stability module, TWC_Fail, evaluates through-wall circumferential crack stability based on the minimum crack size from the Net-Section Collapse or an EPFM J-estimation scheme analysis. Beyond the uncertainty of xLPR data inputs, each module has an uncertainty. This paper documents the module uncertainty for TWC_Fail. Using 32 pipe fracture experiments, including: base metal, similar metal weld, and dissimilar metal weld experiments; bend only and pressure and bend loading; pipe diameters from 2-inch nominal diameter to 42-inch diameter, cracks that range from short to long, the uncertainty of the TWC_Fail methodology is characterized. Results show that TWC_Fail predictions are sensitive to the choice of J-R curve input (J-D or J-M from C(T) specimen tests) and the fit of the stress-strain data. Module uncertainty is characterized in terms mean fit and standard deviation between predictions and experimental values. INTRODUCTION Probabilistic fracture analyses use system input parameters such as material strength, material toughness, operating conditions (temperature, pressure, external loads), etc. sampled many times to determine the probability of some undesirable event occurring. For nuclear power plant piping, the events of interest are leaks and ruptures. To address the contemporary issue of primary water stress-corrosion cracking (PWSCC) in nuclear piping systems that the US NRC has already approved 1 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use the complete context of probabilistic pipe fracture analyses, the calculated probability of rupture is really a joint probability involving the uncertainty in the sampled inputs and the uncertainty of the model(s). To be able to isolate the effect of the uncertainty of the xLPR TWC_Fail circumferential crack stability models, a comparison of TWC_Fail predictions with real-world experience must be made. Ideally, such a comparison would be based on operating plant experience. Unfortunately (or fortunately, really), there have not been any TWC pipe ruptures in nuclear power plants. Instead, characterization of the TWC_Fail module uncertainty must rely on data from rather idealized pipe fracture experiments. Using pipe fracture experiments including: base metal, similar metal weld, and dissimilar metal weld experiments; bend only and pressure and bend loading; cracks that range from short to long, the uncertainty of the TWC_Fail methodology is characterized and documented in this paper. The results of this work will be used to condition the calculated rupture probabilities from xLPR and will serve as a benchmark for subsequent work in TWC crack stability. yes (if_flag = 1) or no (if_flag = 0), as well as the ratio of the ). known crack angle ( ) to the critical crack angle ( The TWC_Fail module uses a main subroutine TWC_Fail, for doing the through-wall crack assessment and, presently, two ) prediction methodologies are TWC critical crack size ( implemented: • Idealized through-wall crack Net-Section Collapse (NSC) analysis method [2, 3] and • LBB.ENG2 elastic-plastic fracture mechanics (EPFM) though-wall crack J-estimation scheme [4]. In the current version of TWC_Fail, both the idealized crack NSC and LBB.ENG2 elastic-plastic through-wall crack predictions are made. Upon return to the calling program, the solution that yields the smallest critical crack size is used for the pass/fail assessment and for calculating the ratio of the current crack size to the critical crack size. The critical crack size that TWC_Fail predicts is a function of the pipe geometry, TWC crack size, pipe strength properties, pipe material fracture toughness, and applied load. The reader is directed to References 2-4 for details of the theory. DATA FOR TWC_FAIL UNCERTAINTY ASSESSMENT TWC_Fail methodology uncertainty was characterized by comparing the outputs of the module with existing full-scale experimental pipe fracture data. Over the years, a number of NRC-sponsored research programs have conducted full-scale pipe tests. Those programs include: • The Degraded Piping Program – Phase II [5] • The First and Second International Piping Integrity Research Group (IPIRG) programs [6, 7] • The Short Cracks in Piping and Piping Welds program [8] • The Dissimilar Metal Weld Pipe Fracture program [9]. The test specimens for these experiments were sections of nuclear grade piping of various sizes, materials, loading conditions, and crack geometries. • Pipe sizes – 2 to 42-inch nominal diameter, with wall thicknesses up to 89 mm (3.5 inches). • Materials – carbon steels (including representative weld processes), stainless steels (including representative weld processes), Inconel, and dissimilar metal welds. • Loading conditions – simple quasi-static four-point bending, combined pressure and four-point bending, dynamic, cyclic, and combined dynamic/cyclic pipe system experiments. • Crack geometries – simple through-wall cracked pipe, part-through surface cracked pipe, and complex cracked pipe geometries. However, for this validation exercise, only the simple through-wall cracked pipe experiments were included in the evaluation matrix. In total, there were approximately 140 pipe fracture experiments conducted at Battelle as part of these NRCsponsored research programs [5-9]. In addition, there were a few early experiments conducted at Battelle as part of an Electric Power Research Institute program [10]. Included in the NOMENCLATURE d-c EP direct current electric potential drop DMW dissimilar metal weld EPFM elastic-plastic fracture mechanics EPRI Electric Power Research Institute J-D deformation J J-M modified J J Fracture toughness initiation value of J J , J-R curve fitting coefficients MP percent of the stainless steel strength properties to use in a DMW analysis NSC net-section collapse SC surface crack TWC through-wall crack US NRC United States Nuclear Regulatory Commission ∆ crack extension , Ramberg-Osgood equation coefficients strain Ramberg-Osgood reference strain experimental TWC half angle predicted critical TWC half angle stress Ramberg-Osgood reference stress. TWC_FAIL TECHNICAL BASIS The TWC_Fail module assesses the stability of a circumferential through-wall crack (TWC) in a pipe subjected to combined tension and bending loading. Based on input pipe/crack geometry, pipe material properties and loads, the ) is predicted critical crack size of the through-wall crack ( compared with a known current crack size, . A flag is returned that indicates the result of this comparison: Predicted failure, 2 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use overall matrix of pipe fracture experiments, 57 considered circumferential through-wall cracked pipe subjected to a variety of loading conditions. Of these 57 circumferential through-wall cracked pipe experiments, 25 were missing one or more of the required inputs for the TWC_Fail module so that they were not considered in the uncertainty assessment for TWC_Fail. That left 32 experiments to be used in the evaluation of TWC_Fail. Table A-1 is a summary of the primary characteristics of those 32 experiments. Material strength properties, Ramberg-Osgood parameters, consistent with Equation 1 are needed as inputs for TWC_Fail, as well as fracture toughness (J-R) data consistent with Equation 2. (1) ∆ TWC_Fail as part of the Quality Assurance documents for xLPR. Both deformation J (J-D) and modified J (J-M) formulations [11] were fitted to Equation 2, where the data were available. Typically, data from multiple fracture toughness specimens were available for analysis. Some specimens were side grooved while others were not. For some specimens, the machined notches were fatigue pre-cracked, while for others they were not. For those cases where there were multiple specimens of the same geometry, i.e., same side grooves and same notch acuity, average values of Ji, C, and m for the multiple specimens were used in the analyses. Figure 1 shows typical data for a Ramberg-Osgood fit, while Figure 2 shows a typical J-R curve fit. In both cases, the fits are very good. (2) . For this exercise, the engineering stress-strain data for each of the individual tensile test specimens for a particular experiment were fit over the range of 0.1 percent strain to the strain corresponding to 80-percent of the ultimate strength using a least squares fit. For those materials for which there were multiple tensile specimens available, a composite fit of the ensemble of stress-strain curves was made by minimizing the error, in a least square sense, between every measured stress-strain data point and the single best equation for all of the available tensile specimens. Prior experience has shown that predictions of TWC stability for welds are governed by strength properties of the base metals and toughness of the weld material. For the dissimilar metal weld (DMW) pipe tests where there are two base metals, stainless steel and carbon steel, a combination of the two base metal strength properties was used in the analysis using Equation 3. 100 100 100 Figure 1. Comparison of actual stress-strain data for tensile specimens F26-5 and F26-6 with composite fit to RambergOsgood relationship for both specimens (3) Per the nomenclature, MP is the percent of the stainless steel properties to use in the analysis, i.e., 30-percent for the 30/70 Mixture Percentage used for the case where the crack is located in the butter material. Although “yield” is indicated in Equation 3, the same kind of relationship applies for the ultimate strength, reference stress, Ramberg-Osgood coefficient α, strain hardening exponent n, and elastic modulus E. The strength property mixture equation given in Equation 3 was established through analysis of 13 DMW experiments and finite element results and is documented in the Model Validation Report for Figure 2. Comparison of actual J-R curve data for fracture toughness specimens F49W-3 and F49W-4 with average fits to Equation 2 for both J-D and J-M formulations of J 3 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use The main uncertainty associated with the experimental data is the estimate of the crack size at the maximum moment. In order to obtain this value, it was necessary to estimate the crack growth up to maximum moment from d-c electric potential drop (d-c EP) data. For the record, d-c EP data are never smooth and user interpretation is always needed. Experimental load-displacement data and pipe geometry are never an issue. 1.1.1.24 1.1.1.26 1.2-1 1.2-7 1.2-8 TWC_FAIL UNCERTAINTY ANALYSIS RESULTS Tables 1 and 2 show results from the TWC_Fail analyses of various TWC pipe fracture tests. Looking at these two tables, we can see that TWC_Fail predictions using the J-M fracture toughness does a better job, on average, than predictions using 1.20 compared with J-D toughness curves [ ⁄ ⁄ 1.49] and that the scatter is less using J-M (Std dev = 0.35 versus 0.49) The ⁄ values shown in red font in Table 1 and Table 2 are those values of ⁄ where TWC_Fail predicted a critical crack angle ( ) that was more than a factor of 2 smaller than the crack angle at maximum moment ( ) from the values fall remarkably pipe experiment. (None of the ⁄ below 1.0) As can be seen from Table 1, there are 2 value was experiments (1.1.1.24 and1-8) for which the ⁄ greater than 2.0 for at least one of the JM-R curves used in the analyses. When using J-D, it can be seen in examining Table 2 that the number of “problematic” experiments increases to five (1.1.1.21, 1.1.1.23, and 1-9, in addition to 1.1.1.24 and 1-8). Looking at the two tables, it is apparent that the choice of J-R curve can have a dramatic impact on the results. For is 2.47 when using Experiment 1.1.1.24, the value of ⁄ JM-R curve data from a 20% side-grooved specimen, while it is only 1.38 when using JM-R curve data for a non-side grooved specimen. This improvement in the prediction when using the non-side grooved specimen can be easily explained when looking at the two J-R curves (20% side grooved versus nonside grooved), see Figure 3, for the material evaluated in this experiment (F49W). The J-R curves for the non-side grooved specimens (Fracture Toughness Specimens F49W-5 and F49W6) are almost a factor of 2 higher than the J-R curves for the side grooved specimens (Fracture Toughness Specimens F49W3 and F49W-4). For the other “problematic” results from Table 1 (Experiment 1-8) the failure mode was Net-Section-Collapse (NSC). There does not seem to be any significance to this, particularly because the crack size used for the NSC is the crack size at maximum moment, so any thought that NSC does not consider crack growth is moot. 1.2-11 1.2-12 1-8 1-9 4.2-1 4.3-1 4111-2 4111-3 4111-4 4111-5 4131-1 4131-3 4131-5 4131-7 1.1.1.28 4141-1 4141-3 4141-5 EPRI-6T EPRI-8T WJ-1 (1) Table 1. Results of TWC_Fail uncertainty analysis using J-M fracture toughness data Expt. Number 1.1.1.21 1.1.1.23 J-M Specimen Geometry (1) 20% SG; FC 20% SG; SMN 20% SG; FC 0% SG; FC Failure Mode ENG2 ENG2 ENG2 ENG2 (2) 20% SG; FC ENG2 0% SG; FC NSC 0% SG; FC No Fail 20% SG; SMN NSC 0% SG; SMN NSC 20% SG; SMN ENG2 0% SG; SMN ENG2 20% SG; SMN No Fail 0% SG; SMN No Fail 20% SG; SMN ENG2 0% SG; SMN ENG2 20% SG; SMN ENG2 0% SG; SMN ENG2 20% SG; FC NSC 20% SG; FC (2) NSC 20% SG; FC ENG2 20% SG; FC (2) ENG2 20% SG; FC NSC 20% SG; FC (2) NSC 20% SG; FC NSC 20% SG; FC ENG2 20% SG; SMN ENG2 0% SG; FC ENG2 0% SG; SMN No Fail 3-pt bend; SMN No Fail 20% SG; FC ENG2 20% SG; SMN NSC 0% SG; SMN NSC 20% SG; FC ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 20% SG; SMN ENG2 20% SG; SMN NSC 0% SG; SMN NSC 20% SG; FC ENG2 0% SG; FC No Fail 0% SG; SMN No Fail 20% SG; SMN ENG2 20% SG; FC No Fail 20% SG; SMN No Fail 0% SG; FC ENG2 0% SG; SMN ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 0% SG; SMN ENG2 3-pt bend; SMN NSC 3-pt bend; SMN ENG2 20% SG; FC No Fail 0% SG; FC No Fail Average =1.20, Std dev = 0.35 2.47 1.38 0.98 1.18 1.18 1.04 1.01 0.94 0.92 1.07 1.04 1.06 1.03 2.46 2.46 1.26 1.55 1.30 1.30 1.54 1.07 1.13 1.07 0.85 0.97 1.01 1.06 1.06 1.20 1.08 1.12 1.27 1.38 1.38 1.07 0.95 0.99 1.14 0.94 0.94 1.26 1.25 1.09 1.08 1.09 1.02 1.21 0.93 0.93 SG=side groove; SMN=sharp machine notch; FC=fatigue precracked Dynamically loaded C(T) specimen; all other specimens loaded quasi-statically ⁄ 1.15 1.38 1.37 1.06 4 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 2. Results of TWC_Fail uncertainty analysis using J-D fracture toughness data 1.1.1.21 1.1.1.23 1.1.1.24 1.1.1.26 1.2-1 1-8 1-9 4.2-1 4.3-1 4111-2 4111-3 4111-4 4131-1 4131-3 4131-5 4131-7 1.1.1.28 4141-1 4141-3 4141-5 EPRI-6T EPRI-8T WJ-1 DMW-6 DMW-9 DMW-11 DMW-13 (1) (2) J-M Specimen Geometry (1) 20% SG; FC 20% SG; SMN 20% SG; FC 0% SG; FC 20% SG; FC 0% SG; FC 0% SG; FC 20% SG; SMN 0% SG; SMN 20% SG; FC 20% SG; FC (2) 20% SG; FC 20% SG; FC (2) 20% SG; FC 20% SG; FC (2) 20% SG; FC 20% SG; FC 20% SG; SMN Failure Mode ENG2 ENG2 ENG2 ENG2 ENG2 ENG2 No Fail ENG2 ENG2 ENG2 ENG2 ENG2 ENG2 NSC ENG2 ENG2 ENG2 ENG2 No 0% SG; FC Solution 0% SG; SMN ENG2 3-pt bend; SMN ENG2 20% SG; SMN ENG2 0% SG; SMN ENG2 20% SG; FC ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 20% SG; SMN ENG2 20% SG; SMN ENG2 0% SG; SMN ENG2 20% SG; FC ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 20% SG; SMN ENG2 20% SG; FC No Fail 20% SG; SMN ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 0% SG; FC ENG2 0% SG; SMN ENG2 0% SG; SMN ENG2 3-pt bend; SMN NSC 3-pt bend; SMN ENG2 20% SG; FC No Fail 0% SG; FC No Fail 20% SG, FC ENG2 20% SG, FC No Fail 20% SG, FC ENG2 20% SG, FC No Fail Average =1.49, Std dev = 0.64 ⁄ 1.83 2.41 2.91 2.17 4.15 1.81 0.98 1.27 1.28 2.71 3.02 1.56 2.09 1.30 1.32 1.79 1.22 1.38 Figure 3. Comparison of J-R curves for weld F49W between 0% and 20% side-grooves (F49W is weld material evaluated in Experiment 1.1.1.24) Considering the distribution of the predictions, Figure 4 data from Table 1. Variation shows a plot of all of the ⁄ in ⁄ from using different kinds of fracture toughness specimens are indicated by multiple symbols plotted at the same abscissa. Aside from the two outliers (1.1.1.24 and 1-8), all of the points lie within ± one standard deviation of the mean. Additionally, Figure 4 suggests that it is unlikely that TWC_Fail will yield a severely non-conservative prediction 1). Confidence interval testing with the data from ( ⁄ ⁄ Figure 4 suggests that the value is 1.34 with a 99-percent confidence that the true value is between 1.2 and 1.48. N/A 1.20 1.05 1.14 1.12 1.32 1.20 1.25 1.55 1.50 1.52 1.19 1.07 1.11 1.52 0.99 1.01 1.73 1.57 1.23 1.19 1.19 1.02 1.32 0.96 0.93 1.06 0.97 1.01 0.98 3 2.5 2 θ/θcrit Expt. Number 1.5 1 0.5 0 0 5 10 15 20 25 30 Unique Experiment in Order of Table 1 Table 1 results Figure 4. Distribution of ⁄ (J-M fracture toughness) Realizing that it may not be possible to dictate to the end user which formulation of J (deformation J (J-D) or modified J (J-M)) to use in their analysis and that it may not be possible to specify which fracture toughness specimen geometry to use, TWC_Fail, on average, underpredicts the actual failure crack SG=side groove; SMN=sharp machine notch; FC=fatigue precracked Dynamically loaded C(T) specimen; all other specimens loaded quasi-statically 5 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use =1.34) with a standard deviation of size by 34-percent ( ⁄ 0.53, considering every result in Tables 1 and 2. to Leak-Before-Break and In-Service Flaw Acceptance Criteria, March 1984-January 1989; NUREG/CR-4082, Vol. 8; March 1989. 6. Wilkowski, G. M., et al; “International Piping Integrity Research Group (IPIRG) Program”; Program Final Report; NUREG/CR-6233, Vol. 4; June 1997. 7. Hopper, A., et al; “The Second International Piping Integrity Research Group (IPIRG-2) Program”; Final Report, October 1991-April 1996; NUREG/CR-6452; March 1997. 8. Wilkowski, G. M., et al; “Short Cracks in Piping and Piping Welds - Seventh Program Report, March 1993December 1994”; NUREG/CR-4599, Vol. 4, No. 1; April 1995. 9. Scott, P., et al; “Dissimilar Metal Weld Fracture Program”; NRC Job Code 6958; July 2012. 10. Kanninen, M. F., et al; “Mechanical Fracture Predictions for Sensitized Stainless Steel Piping with Circumferential Cracks”; EPRI Report NP-192; September 1976. 11. Zhu, X-K and Lam, P-S; “Deformation Versus Modified JIntegral Resistance Curves for Ductile Materials”; PVP2012-78729; Proceedings of the ASME 2012 PVP Conference; Toronto; 2012. DISCUSSION The uncertainty of the xLPR TWC_Fail module has been evaluated by comparing the experimental crack angle at maximum moment from pipe tests with the TWC_Fail would predicted critical crack angle. A value of 1.0 for ⁄ indicate that there was perfect agreement between the TWC_Fail prediction and the experiment. Deviations from this value of 1.0 represent uncertainty in either the analysis methodology or the input data, including the uncertainty due to the choice of J-R curve used in the analysis. Considering that it may not be possible to specify to the end user which formulation of J (deformation J (J-D) or modified J (J-M)) to use in their analysis and that it may not be possible to specify which specimen geometry to use, TWC_Fail underpredicts the actual failure crack size on average by 34-percent with a standard deviation of 0.53. Furthermore, it is unlikely that TWC_Fail will give a non-conservative prediction. With respect to the overall xLPR analysis, TWC_Fail predictions of through-wall crack instability will, on average, predict that a crack being evaluated at some pressure, moment, and axial load, will fail before such a failure is actually observed in an experiment or in a plant. The implication for xLPR is that TWC rupture probabilities, from a crack stability perspective, will be conservatively high. ACKNOWLEDGMENTS This work was conducted at Battelle Columbus as part of the NRC’s Piping Integrity Program. The authors would like to thank the NRC’s Office of Research for their support of this program. The authors also wish to thank U.S. NRC and EPRI for their continued development of the xLPR Program. REFERENCES 1. Rudland, D. and Harrington, C.; “xLPR Pilot Study Report”; NUREG-2110; U.S. Nuclear Regulatory Commission; May 2012 [ADAMS ML12145A470]. 2. Rahman, S. and Wilkowski, G.; “Net-Section-Collapse Analysis of Circumferentially Cracked Cylinders - Part I: Arbitrary-Shaped Cracks and Generalized Equations”; Engineering Fracture Mechanics; Vol. 61; 1998; pp. 191211. 3. Rahman, S.; “Net-Section-Collapse Analysis of Circumferentially Cracked Cylinders - Part II: Idealized Cracks and Closed-Form Equations”; Engineering Fracture Mechanics; Vol. 61; 1998; pp. 213-230. 4. Brust, F. W., and Gilles, P.; “Approximate Methods for Fracture Analysis of Tubular Members Subjected to Combined Tensile and Bending Loads”; ASME, Journal of Offshore Mechanics and Arctic Engineering; Vol. 116; November, 1994; pp 221-227. 5. Wilkowski, G. M, et al; “Degraded Piping Program - Phase II”; Summary of Technical Results and Their Significance 6 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use ANNEX A TWC_FAIL UNCERTAINTY CHARACTERIZATION EXPERIMENTAL DATA EVALUATION MATRIX Table A-1. Evaluation Matrix for TWC_Fail Module Loading Conditions Outside Radius, mm Wall Thickness, mm Initial Half Crack Length, radians Half Crack Length at Maximum Moment, radians Experiment Number Program(1) Material / Crack Location 4111-2 DP3-II CS Base 4-Point Bend 355.60 23.62 1.162 1.304 4111-3 DP3-II SS Base 4-Point Bend 533.40 7.11 1.162 1.228 4111-4 DP3-II CS Base 4-Point Bend 533.40 15.88 1.162 1.255 4111-5 DP3-II SS Weld 4-Point Bend 359.79 30.20 1.162 1.316 4131-5 DP3-II SS Base 4-Point Bend 79.43 13.94 1.219 1.417 4131-7 DP3-II CS Base 4-Point Bend 136.53 18.26 1.087 1.172 4141-1 DP3-II SS Weld 4-Point Bend 84.14 14.27 1.166 1.241 4141-3 DP3-II SS Weld 4-Point Bend 206.76 26.19 1.153 1.257 4141-5 DP3-II SS Weld 4-Point Bend 83.88 14.10 1.203 1.270 WJ-1 DP3-II CS Weld 4-Point Bend 84.14 11.05 0.955 0.984 1.2-1 IPIRG-1 SS Base 4-Point Bend 84.49 13.89 1.194 1.325 1.2-7 IPIRG-1 CS Base 4-Point Bend 83.82 13.97 1.131 1.241 1.2-8 IPIRG-1 CS Base 4-Point Bend 83.72 13.69 1.169 1.243 1.2-11 IPIRG-1 CS Base 4-Point Bend 83.55 13.11 1.169 1.311 1.2-12 IPIRG-1 CS Base 4-Point Bend 83.71 13.77 1.172 1.312 4.2-1 IPIRG-2 CS Base 4-Point Bend 84.14 14.50 0.522 0.740 1.1.1.21 Short Cracks CS Base 4-Point Bend 355.60 22.68 0.196 0.407 1.1.1.23 Short Cracks SS Weld 4-Point Bend 355.60 30.23 0.196 0.347 1.1.1.24 Short Cracks CS Weld 4-Point Bend 306.07 31.34 0.248 0.375 1.1.1.26 Short Cracks SS Base 4-Point Bend 53.12 8.31 0.767 0.815 4.3-1 IPIRG-2 CS Base 4-Point Bend 381.76 38.18 0.522 0.764 EPRI-6T EPRI SS Base 4-Point Bend 30.16 6.02 0.719 0.726 EPRI-8T EPRI SS Base 4-Point Bend 206.76 26.19 1.156 1.319 4131-1 DP3-II SS Base Pressure + Bend 83.22 13.41 1.162 1.269 4131-3 DP3-II CS Base Pressure + Bend 137.07 18.69 1.162 1.328 7 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Loading Conditions Outside Radius, mm Wall Thickness, mm Initial Half Crack Length, radians Half Crack Length at Maximum Moment, radians Experiment Number Program(1) Material / Crack Location 1-8 IPIRG-2 CS Base Pressure + Bend 199.64 26.16 0.377 0.740 1-9 IPIRG-2 CS Base Pressure + Bend 84.46 11.18 0.782 0.886 DMW-6 DMW DMW 4-Point Bend 108.45 21.25 0.636 0.740 DMW-9 DMW DMW 4-Point Bend 108.97 21.85 1.170 1.229 DMW-11 DMW DMW 4-Point Bend 108.12 21.2 1.184 1.242 DMW-13 DMW DMW 4-Point Bend 108.8 22.2 1.181 1.267 1.1.1.28 Short Cracks DMW 4-Point Bend 463.55 85.85 1.128 1.223 (1) DP3-II – Degraded Piping Program Phase II; IPIRG – International Piping Integrity Research Group program; DMW – Dissimilar Metal Weld Pipe Fracture program 8 Copyright © 2015 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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