Proceedings of the ASME 2015 Pressure Vessels and Piping Conference PVP2015 July 19-23, 2015, Boston, Massachusetts, USA PVP2015-45575 VALIDATION OF STRESS INTENSITY FACTOR SOLUTIONS IN XLPR VERSION 2.0 CODE Do-Jun Shim† Engineering Mechanics Corporation of Columbus 3518 Riverside Dr., Suite 202 Columbus, OH 43221, USA Jay Wallace‡ US Nuclear Regulatory Commission Office of Nuclear Regulatory Research Mail Stop: CSB-5CA24 Washington, DC 20555-0001, USA Sureshkumar Kalyanam Engineering Mechanics Corporation of Columbus 3518 Riverside Dr., Suite 202 Columbus, OH 43221, USA Michael Benson‡ US Nuclear Regulatory Commission Office of Nuclear Regulatory Research Mail Stop: CSB-5CA24 Washington, DC 20555-0001, USA ABSTRACT As part of the xLPR (Extremely Low Probability of Rupture) project, the stress intensity factor (SIF) solutions required for crack growth calculations were updated. This involved extension of existing solutions and development of new solutions as well. For surface cracks, the Universal Weight Function Method (UWFM) was implemented to handle complex stress distributions. In addition, a crack transition model was developed to more accurately capture the surface to through-wall crack transition. Finally, solutions for idealized through-wall cracks were extended to various pipe sizes and longer crack lengths. In this paper, the SIF (K) solutions in xLPR Version 2.0 were validated against existing experimental data. The SIF modules in the xLPR code were used to simulate fatigue crack growth of circumferential cracks in pipes under bending up to wall penetration and to through-wall crack transition stage until idealized through-wall cracks were formed. The predicted fatigue crack growth results (mainly crack shape evolution) using the xLPR K-solutions provided good agreement with experimental data. † ‡ INTRODUCTION Stress intensity factor (SIF, K) solutions are used in the xLPR (Extremely Low Probability of Rupture) Code for crack growth (fatigue and stress corrosion cracking) calculations [1]. Recently, in xLPR Version 2.0, the SIF solutions required for crack growth calculations were updated. This involved extension of existing solutions and development of new solutions as well. For surface cracks, the Universal Weight Function Method (UWFM) was implemented to handle complex stress distributions (e.g., weld residual stress) [2,3,4]. Solutions for idealized through-wall cracks were extended to various pipe sizes and longer crack lengths and were provided in closed-form solutions [ 5 , 6 ]. In addition, the crack transition model (based on K-solutions for non-idealized through-wall cracks, i.e., through-wall crack with different crack lengths on the ID and OD surfaces) was developed to more accurately capture the surface to through-wall crack transition [7,8]. In this paper, the SIF solutions in the xLPR Version 2.0 code were validated by comparing the crack growth calculation results with published experimental data from the literature [9,10]. The SIF solutions were used to simulate fatigue crack growth of circumferential cracks in pipes under Corresponding author, djshim@emc-sq.com The views expressed herein are those of the author and do not represent an official position of the USNRC Approved for public release; distribution is unlimited 1 Copyright © 2015 by ASME This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government’s contributions. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use bending up to wall penetration and to through-wall crack transition stage until idealized through-wall cracks were formed. The validation was focused on the crack shape evolution during the crack growth. surface crack size, loading condition, and fatigue life (number of cycles to leak and fracture) are summarized in Table 1. The initial surface crack was inserted in the pipe using electric discharge machining or a saw cut. Fatigue tests were conducted using a four-point bending fixture with outer and inner spans of 1,000 mm and 245 mm, respectively. Fatigue load was applied using a sine wave loading with a stress ratio R=0.1 (frequency 1~5 Hz). All tests were conducted at room temperature. In addition, crack growth measurements were made using a stereomicroscope to track beach mark evolution. Example photographs of fatigue fracture surfaces obtained from the experiments are provided in Figure 2. As shown in this figure, the initial surface crack propagated through the pipe wall and then transitioned into an idealized through-wall crack. Additional details of the fatigue pipe test procedure can be found in Ref. [9] and Ref. [10]. EXPERIMENTAL DATA The experimental data used for the present validation was developed by Yoo et al. [9,10] where fatigue crack growth in circumferentially cracked pipes was investigated. In these experiments, a series of surface cracked pipes was loaded under cyclic bending until the surface crack penetrated the pipe wall and transitioned to an idealized through-wall crack (see Figure 1). The pipe material tested in Ref. [9,10] was a carbon steel (STS370) where the yield and ultimate stresses were 227 MPa and 406 MPa, respectively. The pipe geometry, initial Figure 1 Table 1 Test ID (a) (b) (c) Dimensions of (a) semi-elliptical surface crack, (b) non-idealized through-wall crack, and (c) idealized through-wall crack Pipe geometry, initial surface crack size, loading condition, and fatigue life from experiments conducted by Yoo et al. [10] Pipe geometry Initial surface crack size Loading condition Fatigue life Ro t a ci a/t a/ci max min NL* NF** (mm) (mm) (mm) (mm) - - (MPa) (MPa) (cycle) (cycle) TB-1 51.0 8.1 4.5 22.25 0.556 0.202 200.0 20.0 12,407 21,558 TB-2 51.0 8.1 3.0 6.0 0.370 0.500 210.0 21.0 169,750 197,856 TB-3 51.0 8.1 5.0 5.0 0.618 1.000 325.0 32.5 11,200 17,500 TB-4 51.0 8.1 3.0 18.25 0.370 0.164 200.0 20.0 72,910 862,60 TB-5 51.0 12.7 6.0 6.0 0.236 1.000 220.0 22.2 222,920 245,800 TB-6 51.0 12.7 3.0 6.0 0.236 0.500 261.0 26.1 287,500 301,400 No. * NL, number of cycles to leak (crack incubation time prior to crack initiation not included) ** NF, number of cycles to fracture (definition of fracture is not clearly defined in Ref. [10]) 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 (a) TB-4 Figure 2 (b) TB-5 Example of fatigue fracture surfaces from Ref. [10] (c) TB-6 (a) Cases loaded below yield strength (b) Cases loaded above yield strength Figure 3 Fatigue crack growth rate versus SIF range from Ref. [10] In Ref. [10], the fatigue crack growth rate (FCGR) was determined from the pipe tests. Figure 3 shows the FCGR versus the SIF range (K) from Ref. [10] for samples loaded below the yield strength [Figure 3(a)] and those loaded above the yield strength [Figure 3(b)]. This figure includes the crack growth data measured at the deepest and surface points of the surface crack, and inner and outer surface points of the through-wall crack. The K-solutions used for these figures are provided in Ref. [10], where the Newman-Raju solution (for surface cracked plate) [11] was used for surface cracks and Zahoor solution (for through-wall cracked pipe) [12] was used for idealized through-wall cracks. In addition, Yoo et al. developed a simplified K-solution for non-idealized through- wall cracks by modifying the Zahoor solution. However, due to modeling the pipe geometry as a plate, the accuracy of the K-solutions used for the FCGR determinations in Figure 3 may have some uncertainty embedded in it. Effect of this uncertainty on fatigue life predictions is discussed later in this paper. VALIDATION OF SIF SOLUTIONS In order to validate the SIF (K) solutions used in the xLPR Version 2.0 code, the fatigue crack growth results in Ref. [10] were predicted using the modules in xLPR Version 2.0. These modules include K-solutions for surface cracks [4], K-solutions for non-idealized through-wall cracks [7] in the 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 crack transition module (CTM), and K-solutions for idealized through-wall cracks [5]. The K-solutions for surface crack assume that the shape of the surface crack is semi-elliptical, see Figure 1(a). Once the depth of the surface crack reaches 95% of the wall thickness (a/t=0.95), the CTM initiates the surface to through-wall crack transition and forms a through-wall crack. This initial nonidealized through-wall crack has different crack lengths on the ID and OD surfaces [as illustrated in Figure 1(b)], which are determined by the CTM. The crack front shape (or curvature) of the non-idealized through-wall cracks was determined from cylindrical transformation of a straight crack front in a plate (see Ref. [7] for details). The K-solutions in the CTM are used to grow the non-idealized through-wall crack until an idealized through-wall crack is approximated (i.e., 1/2≤1.05) – see Figure 1(c). At this point, the CTM is turned off and the crack growth is continued using idealized through-wall crack K-solutions. In the present study, the FCGR parameters reported in Ref. [10] were employed. The calculations did not include the time to crack initiation, i.e., crack incubation time prior to start of crack growth. After performing a sensitivity study, the step increment used in the crack growth calculations was fixed to 100 cycles/increment. the through-wall crack shape is represented by the normalized crack angles at the ID and OD surfaces, i.e., 1/ and 2/, where 1 and 2 are shown in Figure 1(b) and Figure 1(c). Note that 1=2 for an idealized through-wall crack. The prediction results in Figure 5 start from the initial non-idealized through-wall crack determined by the CTM. As illustrated in this figure, the ID crack angle (1) remains almost constant during the crack transition, whereas the OD crack angle (2) increases until it becomes approximately equal to 1. Once an idealized through-wall crack is formed (1=2), the through-wall crack maintains that shape as it continues to grow around the circumference. The predicted results provided good agreement with the experimental results throughout the crack transition stage as well as the idealized through-wall crack growth. VALIDATION RESULTS In order to validate the surface crack K-solutions, predictions from the xLPR code were compared against the surface crack growth results obtained from the experiments. Figure 4 provides the change in crack depth (a/t) as well as crack aspect ratio (a/ci) during surface crack growth. As demonstrated in Figure 4, overall results show good agreement between the predicted and experimental results. The agreement is excellent for cases where the initial crack aspect ratio (a/ci) are relatively low, i.e., long surface cracks – TB-1 and TB-4. This indicates that, for these cases, the surface crack maintains a semi-elliptical shape during the crack growth [see Figure 2(a)]. Hence, the crack shape evolution is accurately predicted by the surface crack K-solutions. On the other hand, for initial surface cracks with a/ci=0.5 (TB-2 and TB-6), the two results showed good agreement in the earlier stage of crack growth but then deviated from each other as the crack depth increased. This is due to the surface crack shape deviating from the semi-elliptical shape in the experiment – especially as it gets closer to wall penetration [see Figure 2(c)]. Similar behavior is observed for surface cracks that have initial value of a/ci=1.0 (TB-3 and TB-5) where the surface crack shape in the experiment slightly deviated from a semi-elliptical shape [see Figure 2(b)]. The predicted results are provided up to a/t=0.95, when the surface crack is transitioned to a through-wall crack according to the crack transition module (CTM). Validations of K-solutions for non-idealized and idealized through-wall cracks are provided in Figure 5. In this figure, (a) TB-1, TB-2 and TB-3 Figure 4 4 (b) TB-4, TB-5 and TB-6 Comparison of surface crack growth 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 (a) TB-1 and TB-2 Figure 6 Comparison of predicted and measured crack front shapes during crack growth (at random cycles) (b) TB-5 and TB-6 Figure 5 Comparison of crack transition through-wall crack growth and Figure 7 compares the predicted and experimentally measured number of cycles to wall penetration. Experimental data is provided in Table 1. Note that the predictions are based on the FCGR parameters provided in Ref. [10]. The prediction over-predicted the experimental results by an average of 37%. This may be due to the less accurate K-solutions that were used in Ref. [10] to determine the FCGR (see earlier discussions related to Figure 3 in this paper). To investigate the effect of FCGR on crack shape evolution, optimized FCGR parameters were determined from the experimental data by matching the predicted and measured number of cycles to wall penetration with some approximations, as illustrated in Figure 8. Figure 9 demonstrates that the effect of FCGR constants on crack shape evolution for TB-1 is negligible. Figure 6 compares the overall predicted and measured crack front shapes for two example cases. The comparisons are made at a random number of cycles since the number of cycles between beach marks was not presented in Ref. [10]. The crack shape evolutions for surface crack, transitioning crack, and through-wall crack are well captured by the predictions. The differences in the crack front shape for transitioning cracks are due to the assumption that was made in the development of the non-idealized through-wall crack Ksolutions [7]. However, as demonstrated in Figure 5, the effect of this assumption on the overall crack growth predictions are negligible. Furthermore, only crack angles are used in the actual xLPR code calculations. 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 Figure 7 Comparison of number of cycles to wall penetration using FCGR from Ref. [10] (a) Surface crack (b) Transition and through-wall crack Figure 8 Figure 9 Comparison of number of cycles to wall penetration using optimized FCGR CONCLUSIONS In this paper, the SIF (K) solutions (surface crack, nonidealized and idealized through-wall cracks) in xLPR Version 2.0 were validated against limited experimental data on circumferential fatigue crack growth in pipes. Below are the conclusions from the present study. Predictions from the xLPR Version 2.0 modules provided good agreement with experimental data in terms of crack shape evolution (surface crack, nonidealized, and idealized through-wall cracks). Effect of FCGR on crack growth and crack shape evolution Number of cycles to wall penetration was overpredicted compared to the experimental data, which may be due to the uncertainty in the FCGR determined from the reference. By employing an optimized FCGR, it was demonstrated that the crack shape evolution is not sensitive to FCGR parameters. ACKNOWLEDGMENTS The authors would like to thank the U.S. Nuclear Regulatory Commission for their support of this work. 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 REFERENCES [6] Unpublished work by Working Group on Pipe Flaw Evaluation, ASME BPVC Section XI. [7] Shim, D.J., Kurth, R. and Rudland, D., “Development of Non-Idealized Surface to Through-Wall Crack Transition Model,” PVP2013-97092, Proceedings of the 2013 ASME Pressure Vessels and Piping Conference, July 1418, 2013, Paris, France. [8] Shim, D.J., Rudland, D. and Park, J.S., “Surface to Through-Wall Crack Transition Model for Axial Cracks in Pipes,” PVP2014-28048, Proceedings of the 2014 ASME Pressure Vessels and Piping Conference, July 2024, 2014, Anaheim, California, USA. [9] Yoo, Y.S., Ahn, S.H. and Ando, K., “Fatigue Crack Growth and Penetration Behaviours in Pipes Subjected to Bending Moment” Proceedings of the 1998 ASME Pressure Vessels and Piping Conference, PVP-Vol. 371, High Pressure Technology, pp 63-70, 1998. [10] Yoo, Y.S. and Ando, K., “Circumferential Inner Fatigue Crack Growth and Prediction Behaviour in Pipe Subjected to a Bending Moment,” Fatigue Fract Engng Mater Struct 23, pp. 1-8, 2000. [11] Newman, J.C. and Raju, I.S., “An Empirical Stress Intensity Factor Equation for the Surface Crack,” Engng Fracture Mech. 15, pp. 185-192, 1981. [12] Zahoor, A., Ductile Fracture Handbook, Vol. 3, Novetech Corporation and Electric Power Research Institute, 1989. [1] Rudland, D., Harrington, C. and Dingreville, R., “Development of the Extremely Low Probability of Rupture (xLPR) Version 2.0 Code,” PVP2015-45134, Proceedings of the 2015 ASME Pressure Vessels and Piping Conference, July 19-23, 2015, Boston, Massachusetts, USA. [2] Scarth, D. and Xu, S., “Universal Weight Function Consistent Method to Fit Polynomial Stress Distribution for Calculation of Stress Intensity Factor,” J. Pressure Vessel Technol. 134(6), 061204, 2012. [3] Cipolla, R. and Lee, D., “Stress Intensity Factor Coefficients for Circumferential ID Surface Flaws in Cylinders for Appendix A of ASME Section XI,” PVP2013-97734, Proceedings of the 2013 ASME Pressure Vessels and Piping Conference, July 14-18, 2013, Paris, France. [4] Xu, S., Lee, D., Scarth, D. and Cipolla, R., “Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial ID Surface Flaws in Cylinders for Appendix A of ASME Section XI,” PVP2014-28222, Proceedings of the 2014 ASME Pressure Vessels and Piping Conference, July 20-24, 2014, Anaheim, California, USA. [5] Shim, D.J., Xu, S. and Lee, D., “Closed-Form Stress Intensity Factor Solutions for Circumferential ThroughWall Cracks in Cylinder,” PVP2014-28049, Proceedings of the 2014 ASME Pressure Vessels and Piping Conference, July 20-24, 2014, Anaheim, California, USA. 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

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