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{{#Wiki_filter:Structural Integrity Associates, Inc. File No.: 1400669.313Project No.: 1400669CALCULATION PACKAGE Quality Program Type: Z Nuclear E] CommercialPROJECT NAME:Palisades Flaw Readiness Program for 1R24 NDE InspectionCONTRACT NO.:10426669CLIENT: PLANT:Entergy Nuclear Operations, Inc. Palisades Nuclear PlantCALCULATION TITLE:Crack Growth Analysis of the Hot Leg Drain NozzleDocument Affected Project Manager Preparer(s) &Revision Pages Revision Description Approval Checker(s)Signature & Date Signatures & Date0 1 -23 Initial Issue Preparer:A-i -A-3Computer FilesNorman EngNE 5/11/15 Minji FongMF 5/11/15Checkers:Wilson WongWW 5/11/15Gole MukhimGSM 5/11/15Page 1 of 23F0306-01R2 S&NwbiMral lhfe y Associates, IncOTable of Contents1.0 O B JE C TIV E ......................................................................................................... 42.0 D E SIG N IN PU T S .................................................................................................... 42.1 Piping Interface Loads ................................................................................. 42.2 Residual Stresses at Normal Operating Temperature and Pressure .............. 52.3 Mechanical Load Boundary Conditions ...................................................... 52.4 C rack G row th R ate ........................................................................................ 53.0 A SSU M PTIO N S ...................................................................................................... 64.0 DETERMINATION OF STRESS INTENSITY FACTOR ...................................... 64.1 Crack Face Pressure Application .................................................................. 64.2 K Calculation for Circumferential Flaws ..................................................... 74.2.1 Finite Element Model with Circumferential Flaws ..................................... 74.2.2 Stress Intensity Factor Results ....................................................................... 84.3 K Calculation for Axial Flaws ...................................................................... 84.3.1 Finite Element Model with Axial Flaws ........................................................ 84.3.2 Stress Intensity Factor Results ....................................................................... 85.0 CRACK GROWTH CALCULATION .................................................................... 96.0 C O N C LU SIO N S ...................................................................................................... 97.0 R E FE R E N C E S ........................................................................................................ 11APPENDIX A COMPUTER FILES LISTING ............................................................... A-1File No.: 1400669.313 Page 2 of 23Revision: 0F0306-01R2 jSiniuorai lateurify Associates, inc.List of TablesTable 1: Stress Intensity Factors for Circumferential Flaws ............................................ 12Table 2: Stress Intensity Factors for Axial Flaws ............................................................. 12Table 3: Crack Growth Time to 75% Through-Wall ........................................................ 12Table 4: Crack Growth Time to 95% Through-Wall .................................. ............................ 12Table 5: Allowable Detected Flaw Size ............................................................................ 13List of FiguresFigure 1. Base Finite Element M odel M esh ...................................................................... 14Figure 2. Applied Mechanical Load Boundary Conditions ............................................... 15Figure 3. Circumferential Flaw with Crack Tip Elements Inserted ................................... 16Figure 4. Transferred Residual Stress + NOC + Pressure Stress for Circumferential Flaws. 17Figure 5. Stress Intensity Factors as a Function of Depth for Circumferential Flaws ..... 18Figure 6. Axial Flaws with Crack Tip Elements Inserted ................................................. 19Figure 7. Transferred Residual Stress + NOC + Pressure Stress for Axial Flaws ........ 20Figure 8. Stress Intensity Factors as a Function of Depth for Axial Flaws ....................... 21Figure 9. Crack Growth for All Flaw Types with 0.025" Initial Flaw Size ..................... 22Figure 10. Crack Growth for All Flaw Types with 0.1" Initial Flaw Size ........................ 23File No.: 1400669.313Revision: 0Page 3 of 23F0306-01R2 V smnI ur IWihurily Associates, Inc.1.0 OBJECTIVEThe objective of this calculation package is to determine maximum allowable flaw sizes for 18 and 36months of continued operation based on crack growth analyses for a series of postulated flaws in the hotleg drain nozzle boss weld in support of a Primary Water Stress Corrosion Cracking (PWSCC)susceptibility study at the Palisades Nuclear Plant (Palisades). The stresses due to the hot leg pipeinterface loads which are determined in this calculation, and residual stresses extracted from a previousanalysis [1] are used to calculate stress intensity factors (K) which are used to perform crack growthanalyses. The PWSCC crack growth analyses are performed using the pc-CRACK [2] program for bothcircumferential and axial flaws. The allowable detected flaw sizes are determined by back-calculatingthe predicted growth time to a maximum flaw size of 75% through wall thickness per ASME CodeSection XI, IWB-3643.2.0 DESIGN INPUTSThe finite element model shown in Figure 1 was developed in Reference [3] and is used for thedetermination of stress intensity factors.2.1 Piping Interface LoadsReference 4 (PDF file, page 88) indicates that, for the hot leg, the bounding thermal transient stress of1.010 ksi is due to case Thermal 002, the deadweight (DW) stress is 0.096 ksi and the friction stress is1.056 ksi. The hot leg loads are applied as an equivalent bending moment to the axial free end of themodeled hot leg. The equivalent bending moment is based on the combined stress which is assumed tooccur at the outside surface of the hot leg. The maximum combined bending stress is:DW + Friction + Thermal = 0.096 + 1.056 + 1.010 = 2.162 ksiThe moment based on the bending stress is calculated as:M u.I i" (24.81254-20.81254).2.162M=- =-- _= 13099in -/kipsOR 4 24.8125where,M = Moment (in-kips)S = Stress on hot leg pipe free end (ksi)I = Moment of Inertia -(7/4)(OR4 -IR4) (in4)IR = Inside radius of hot leg pipe (in) = 20.8125" [3]OR = Outside radius of hot leg pipe (in) = 24.8125" [3]Since half the hot leg pipe is modeled, the equivalent moment applied to the model is 6549.5 in-kips(= 13099 in-kips /2). The moment is applied to the axial end of the hot leg run piping by means of a pilotFile No.: 1400669.313 Page 4 of 23Revision: 0F0306-01R2 j ruIUcrwl IitMUrly Associates, Inc.node pair to transfer the loading. The pilot node pair is composed of a target node at the center of thepipe (ANSYS TARGE170 element) and a set of surface contact elements on the axial end of the pipe(ANSYS CONTA 174 element). The surface elements are bonded to the pilot node in a slave/mastercoupling relationship, so that the moment load applied to the pilot node is transferred to the end of thepipe. The hot leg drain nozzle piping loads are considered to have negligible effects on the resulting K'sfor the boss weld, and are therefore not considered.2.2 Residual Stresses at Normal Operating Temperature and PressureResidual stresses at the fifth operating condition cycle (at time = 2484 minutes) are taken fromReference 1. These stresses include the effects of normal operating temperature of 583°F and pressure of2085 psig [1].2.3 Mechanical Load Boundary ConditionsThe mechanical load boundary conditions for the stress analysis are symmetric boundary conditions atthe symmetry planes of the model, axial displacement restraint at the end of the nozzle, and axialdisplacement restraint on the pilot node, as shown in Figure 2. In the case where axial flaws are modeledon the symmetry planes, the boundary conditions are released at the nodes where the flaw exists.2.4 Crack Growth RateThe default PWSCC crack growth rate in pc-CRACK [2] is used. This relation is based on expressionsin Reference [5, Section 4.3] and the resulting equation for the crack growth rate is as follows:da Cexp[L Q 1 1 (K-Kh)'3  for K > Kaidt T+460 T,ref +460For times (t) in hours, temperatures (T and Tref) in 'F, crack length (a) in inches and K in ksi-4in, thefollowing reference values are used:Tref = 617°FC = 2.47x10-7 (constant)0 1.6 (constant)Q 28181.8°R (constant)Ka, = 0 (threshold stress intensity factor below which there is no crack growth)T = operating temperature at location of crackFile No.: 1400669.313 Page 5 of 23Revision: 0F0306-01R2 V an" Ibf Assoas, Inc03.0 ASSUMPTIONSThe following assumptions are used in this analyses:" The hot leg drain nozzle piping loads are not considered in calculating stress intensity factorssince loads on the drain nozzle do not produce Mode I crack opening stress intensity factors thatcontribute to crack growth in the boss weld.* The maximum combined stress on the hot leg piping is assumed to occur at the outside surface ofthe hot leg.4.0 DETERMINATION OF STRESS INTENSITY FACTORThe stresses described in this section are used with a modified version of the finite element model(FEM) developed previously in Reference [3] to determine stress intensity factors. The modification ofthe FEM consists of adding crack tip elements as addressed in Section 4.2 and 4.3. The stress intensityfactors (Ks) are calculated using the KCALC feature in ANSYS [6] which is based on linear elasticfracture mechanics (LEFM) principles. For the LEFM evaluations, only the elastic properties are used inthe FEA.4.1 Crack Face Pressure ApplicationIn order to determine the Ks for the circumferential and axial flaws due to residual stresses, the stresseson the boss weld-to-nozzle interface, at the fifth operating condition (at time = 2484 minutes in theresidual stress analysis [1]), are extracted from the residual stress analysis and reapplied on the crackface as surface pressure loading.This approach is based on the load superposition principle [7], which is utilized to transfer the stressesfrom the weld residual stress finite element model onto the fracture mechanics finite element model thatcontains crack tip elements. The superposition technique is based on the principle that, in the linearelastic regime, stress intensity factors of the same mode, which are due to different loads, are additive(similar to stress components in the same direction).The superposition method can be summarized with the following sketches [7, page 66]:PFW PWx PWxPW x P(x)(a) (b) (c) (d)File No.: 1400669.313 Page 6 of 23Revision: 0F0306-01 R2 7 ankinal grlty Associates, Inc?A load p(x) on an uncracked body, Sketch (a), produces a normal stress distribution p(x) on Plane A-B.The superposition principle is illustrated by Sketches (b), (c), and (d) of the same body with a crack atPlane A-B. The stress intensity factors resulting from these loading cases are such that:Ki(b) = Ki(c) + Ki(d)Thus, Ki(d) = 0 because the crack is closed, and:Ki(b) = Ki(c)This means that the stress intensity factor obtained from subjecting the cracked body to a nominal loadp(x) is equal to the stress intensity factor resulting from loading the crack faces with the same stressdistribution p(x) at the same crack location in the uncracked body.4.2 K Calculation for Circumferential Flaws4.2.1 Finite Element Model with Circumferential FlawsThe stress intensity factors for full circumferential flaws in the nozzle boss weld are determined by finiteelement analysis using deterministic linear elastic fracture mechanics (LEFM) principles. As a result,five fracture mechanics finite element models are derived to include "collapsed" crack meshing thatrepresent full (3600) circumferential flaws surrounding the nozzle at various depths within the bossweld.The circumferential flaws align with the interface between the boss weld and the nozzle. The modeledcrack depths are: 0.13", 1.17", 2.05", 3.13", and 3.97" as measured at the 00 axial side of the hot legpipe.The modeling of the flaws, or cracks, involves splitting the crack plane and then inserting "collapsed"mesh around the crack tips followed by concentrated mesh refinements that surround the "collapsed"mesh, and are referred to as "crack tip elements". This step is implemented on a source finite elementmodel without the cracks (the FEM developed in Reference 3) where the crack tip elements are insertedby an in-house developed ANSYS macro.For the fracture mechanics models, 20-node quadratic solid elements (ANSYS SOLID95) are used in thecrack tip region, while 8-node solid elements (ANSYS SOLID 185) are used everywhere else in themodel. The mid-side nodes for the SOLID95 elements around the crack tips are shifted to the "quarterpoint" locations to properly capture the singularities at the crack tips, consistent with ANSYSrecommendations. The finite element model for the 3.97" deep circumferential flaw, with the crack tipmesh, is shown in Figure 3 as an example; the crack tip mesh for the other crack depths follows the samepattern.File No.: 1400669.313 Page 7 of 23Revision: 0F0306-01R2 jsftatbrnI IntegriAy Associates, Inc.The quarter point mid-side nodes combined with the extra layers of concentrated elements around thecrack tips provide sufficient mesh refinement to determine the stress intensity factors for the fracturemechanics analyses.4.2.2 Stress Intensity Factor ResultsThe radial stresses (radial to the nozzle axis) on the weld/nozzle interface are transferred to thecircumferential flaws as crack face pressure per the superposition principle described in Section 4.1.Figure 4 depicts, as an example, the transferred radial stresses as crack face pressure for the 3.97"circumferential flaw depth. During the crack face pressure transfer, the operating pressure of2085 psi [1] is added to the crack face pressure to account for the internal pressure acting on the crackface due to cracking. A far field in-plane bending moment per Section 2.1 is also applied to the free endof the hot leg run piping to account for piping moments in the main loop piping.Each crack model is analyzed as a steady state stress pass at the operating and reference temperature of583°F [1] in order to use the material properties at the operating temperature, but without inducingadditional thermal stresses.At the completion of each analysis, the ANSYS KCALC post-processing is performed to extract the K'sat each crack tip node around the nozzle. The maximum K results are summarized in Table 1 for variouscrack depth ratios "a/t". Since the crack tip location is same in the circumferential flaw, the maximum Kfrom all locations at each crack size is conservatively used for the K vs. a profile. The "K vs. a/t" trendsare then plotted in Figure 5.4.3 K Calculation for Axial Flaws4.3.1 Finite Element Model with Axial FlawsThe stress intensity factors for axial flaws are determined using the same methodology as thecircumferential flaws. However, the mesh of weld nuggets was removed to insert thumbnail shape flawsin the model. Also, the orientation and shape of the flaws allow all crack depths at the 0' and 900 facesof the symmetric hot leg pipe model to be inserted simultaneously. Figure 6 shows the five modeledcrack depths (0.25", 1.06", 1.90", 2.91", and 3.85") on the 0' face (hot leg axial face) and the 90' facewith crack tip elements inserted.The modeling of the axial flaws uses the same crack tip elements as described in Section 4.2.1. Thecrack tip mesh is the same pattern used in the circumferential flaws and is shown in Figure 6 for theaxial flaws at the 0' and 90' faces.4.3.2 Stress Intensity Factor ResultsSimilar to the circumferential flaw analyses, the crack opening residual stresses and additional operatingpressure are transferred to the axial flaws as crack face pressure. Figure 7 depicts, as an example, theFile No.: 1400669.313 Page 8 of 23Revision: 0F0306-01R2 C mumral bItrify Associates, Inc.transferred hoop stresses as crack face pressure for the axial flaws. In addition, a far field in-planebending moment per Section 2.1 is applied to the free end of the hot leg run piping to account for pipingmoments in the main loop piping. The K results at the deepest point of the flaws are summarized inTable 2 for various crack depth ratios "a/t" and plotted in Figure 8. Since the deepest point of thepostulated axial flaws has the smallest remaining wall thickness, the K at the deepest point is used forthe K vs. a profile.5.0 CRACK GROWTH CALCULATIONStress intensity factors (Ks) at four depths for 3600 inside surface connected, part-through-wallcircumferential flaws as well as two axial thumbnail flaws at the 0-and 90-degree azimuthal locations ofthe nozzle, are calculated using finite element analysis (FEA). For the circumferential flaw, themaximum K values around the nozzle circumference for each flaw depth are extracted and used as inputinto pc-CRACK to perform the PWSCC crack growth analyses. For the axial flaws, the K at the deeppoint of the thumbnail shape is used as input for performing the PWSCC crack growth analyses. Sincethe K vs. a profile is used as input, the shape of the component is not relevant.For the crack growth analyses, two initial flaw sizes are chosen. These are based on expectedengineering flaw sizes that could be present for a flaw that would then grow by PWSCC. The final flawsize for these analyses is 75% of the wall thickness. This final depth is chosen as it is the maximumallowable flaw depth per Section XI of the ASME Code for pipe flaw evaluations. Additionally, a finalflaw size of 95% of the wall thickness is also considered in this calculation.The key parameters used in the crack growth calculations included:Two initial crack depths = 0.025" and 0.1" (assumed)Temperature = 583 °F (operating temperature [1])Wall thickness = 4.0" (hot leg pipe thickness [3])The resulting crack depths for the circumferential and axial flaws, as a function of time, as calculated bypc-CRACK are shown in Figure 9 for the 0.025" initial flaw size, and Figure 10 for the 0.1" initial flawsize. The time for a flaw to grow from the initial flaw size to 75% and 95% through-wall is tabulated inTable 3 and Table 4 for both circumferential and axial flaw types, respectively. Table 5 shows themaximum allowable detected flaw sizes for the postulated flaws if continued operation for 18 and 36months is considered.
==6.0 CONCLUSION==
SStress intensity factors were calculated for the 360' circumferential flaws as well as the axial flaws at the0' and 90' locations. The stress intensity factors were calculated using residual stress distributions forresidual stress plus normal operating conditions. In addition, a far field in-plane bending moment isFile No.: 1400669.313 Page 9 of 23Revision: 0F0306-01R2
,shin rai hitegrlfy AssociaMes, Inc.applied to the free end of the hot leg run piping to account for piping moments in the main loop piping.This combined loading is used for the determination of the stress intensity factors for both thecircumferential and axial flaws. Figure 5 and Figure 8, as well as Table 1 and Table 2, show thecalculated stress intensity factors for the circumferential and axial flaws.Crack growth evaluations were performed for circumferential and axial flaw configurations using twodifferent initial flaw sizes. As shown in Figure 9 and Table 3, the shortest time for an initial 0.025" deepflaw to grow to 75% through-wall in all cases is 30.5 years for an axial flaw on the 0' plane. Figure 10and Table 3 show that the shortest time for an initial 0.1" deep flaw to grow to 75% through-wall in allcases is 29.7 years for an axial flaw on the 00 plane. Table 5 shows the maximum allowable detectedflaw sizes for 18 and 36 months continued operation.File No.: 1400669.313Revision: 0Page 10 of 23F0306-01R2 7 whtnorel te grily Associates, Inc.
==7.0 REFERENCES==
: 1. SI Calculation No. 1400669.312, Rev. 0, "Hot Leg Drain Nozzle Weld Residual StressAnalysis."2. pc-CRACK 4.1, Version 4.1 CS, Structural Integrity Associates, December 2013.3. SI Calculation No. 1400669.3 10, Rev. 0, "Finite Element Model for Hot Leg Drain Nozzle."4. Palisades Document, Report No. CENC- 1115, "Analytical Report for Consumers Power Piping,"SI File No. 1300086.204.5. Materials Reliability Program: Crack Growth Rates for Evaluating Primary Water StressCorrosion Cracking (PWSCC) ofAlloy 82, 182 and 132 Welds (MRP-115), EPRI, Palo Alto, CA:2004, 1006696.6. ANSYS Mechanical APDL and PrepPost, Release 14.5 (w/ Service Pack 1), ANSYS, Inc.,September 2012.7. Anderson, T. L., "Fracture Mechanics Fundamentals and Applications," Second Edition, CRCPress, 1995.File No.: 1400669.313Revision: 0Page 11 of 23F0306-01R2 CsfaffreMOMAssocbels, Inc.Table 1: Stress Intensity Factors for Circumferential FlawsCrack Depth a/t Max. K(in) (ksi-in°.5)0.13 0.03 19.611.12 0.28 22.762.04 0.51 14.783.15 0.79 13.033.97 0.99 35.15Table 2: Stress Intensity Factors for Axial FlawsHL Axial Plane 00 HL Circ. Plane 900Crack Depth a/t K at Deep Pt Crack Depth a/t K at Deep Pt(in) (ksi-in°'5) (in) (ksi-in°'5)0.25 0.06 18.50 0.25 0.06 14.161.06 0.26 18.64 1.10 0.27 14.431.90 0.47 17.60 1.96 0.49 14.772.91 0.73 19.34 2.95 0.74 16.983.85 0.96 23.44 3.81 0.95 21.41Table 3: Crack Growth Time to 75% Through-WallInitial Flaw Size Axial Crack Axial Crack Circ. Crack(in) (00 plane) (900 plane) (years)_ (years) (years) (years)0.025 30.5 42.9 33.90.100 29.7 41.7 33.1Table 4: Crack Growth Time to 95% Through-WallInitial Flaw Size Axial Crack Axial Crack Circ. Crack(in) (0' plane) (900 plane) (years)(years) (years) (years)0.025 36.7 50.3 42.10.100 36.0 49.2 41.4File No.: 1400669.313Revision: 0Page 12 of 23F0306-01R2 jSIvrura I~tegrlfy Associatos, Inc.Table 5: Allowable Detected Flaw SizeAllowable Detected Flaw Size (a/t)Hot Leg Thickness, t = 4.00"Months of Axial Flaw Axial Flaw CircumferentialContinued at 0° plane at 900 plane FlawOperation a/t a (in) a/t a (in) a/t a (in)18 0.7070 2.83 0.7165 2.87 0.7260 2.9036 0.6690 2.68 0.6785 2.71 0.6975 2.79File No.: 1400669.313Revision: 0Page 13 of 23F0306-01R2 tj s bwftn Associates, k=6ANSYSR14.5Figure 1. Base Finite Element Model MeshFile No.: 1400669.313Revision: 0Page 14 of 23F0306-01 R2 C an"s~iru lMq*rl Assocates, Inc.0'RFAI, NNflCoupled to pilot nodeIPilot node and axial restraintsAxial displacement restraint//Figure 2. Applied Mechanical Load Boundary ConditionsFile No.: 1400669.313Revision: 0Page 15 of 23F0306-OIR2 5SVOW&W bft wE Assocates, 1=Figure 3. Circumferential Flaw with Crack Tip Elements Inserted(Note: Deepest circumferential flaw shown for example)File No.: 1400669.313Revision: 0Page 16 of 23F0306-01R2 C OW&*~re lWabdY ASSOciats, InWFigure 4. Transferred Residual Stress + NOC + Pressure Stress for Circumferential Flaws(Note: Deepest circumferential flaw shown for example)File No.: 1400669.313Revision: 0Page 17 of 23F0306-01 R2 can&* MW* Assadates, /mein"-71'40353025201510500.0 0.2 0.4 0.6 0.8 1.0Depth (a/t)Figure 5. Stress Intensity Factors as a Function of Depth for Circumferential FlawsFile No.: 1400669.313Revision: 0Page 18 of 23F0306-01R2 Van&* MWW ASWCWOS, kasI00900Figure 6. Axial Flaws with Crack Tip Elements InsertedFile No.: 1400669.313Revision: 0Page 19 of 23F0306-01R2 CSbam"r MOMgr Assocates, #MKCAU~ anal1l-ksi1.96433 6.99' 15.950, 24.9077 33.865iKCgrC a__ 7. ira sfrred cReiu S a+cs s+ Pressure... ............ .. ..... sFigure 7. Transferred Residual Stress + NOC + Pressure Stress for Axial FlawsFile No.: 1400669.313Revision: 0Page 20 of 23F0306-01R2
~jSVOW& ruwl py Associates, ln.2520Tune-,151050.0-0.00.2 OA 0.6 0.81.0Depth (a/t)Figure 8. Stress Intensity Factors as a Function of Depth for Axial FlawsFile No.: 1400669.313Revision: 0Page 21 of 23F0306-01R2 cjanswfGuu MW*f Assocades, hmD.1.00.90.80.7" 0.6m 0.5c' 0.40.30.20.10.0/I-Circ. Crack---Axial Crack_0--Axial Crack_90/ 10 10 20 30 40 50 60Time (years)Figure 9. Crack Growth for All Flaw Types with 0.025" Initial Flaw SizeFile No.: 1400669.313Revision: 0Page 22 of 23F0306-01R2 cjbh.airwI Iabpf AssCIatS, kne.10.90.80.70.60-m 0.40.30.20.10e-Circ. Crack---Axial Crack_0--Axial Crack_900 10 20 30 40 50 60Time (years)Figure 10. Crack Growth for All Flaw Types with 0.1" Initial Flaw SizeFile No.: 1400669.313Revision: 0Page 23 of 23F0306-01R2 SkuowiraI Iiegrlty Associates, Inc.APPENDIX ACOMPUTER FILES LISTINGFile No.: 1400669.313Revision: 0Page A- I of A-3F0306-01R2 Vj asiofrraI Integffly Assocades, hIWOFile Name DescriptionPalisades HL Drain.INP Input file to create base geometry model [3]MPropMISO.INP Elastic-plastic material properties inputs [3]BCNODES.INP Component setting for the boundary conditions.Crack tip node inputs for fracture mechanics model conversion forNODESC##.INP circumferential flaws. ##=03, 30, 50, 75, and 95 with 03 = 0.13", 30 =1.17", 50 = 2.05, 75 = 3.13", 95 = 3.97" of flaw sizeFMHLC##.INP Geometry input files to create circumferential flaw at specified depth.-##=03, 30, 50, 75, and 95FM HL C## COORD.INP Input files to determine circumferential crack face element centroidFMHLC# Ccoordinates. ##=03, 30, 50, 75, and 95_EHLCH##COORDl.txt Circumferential crack face element centroid coordinate outputs.F -##=03, 30, 50, 75, and 95FMHLC##_GETSTR.INP Input files to extract circumferential crack face stresses from residualstress analysis. ##=03, 30, 50, 75, and 95Extracted circumferential crack face stresses from residual stressanalysis. ##=03, 30, 50, 75, and 95Input files to transfer stresses into circumferential crack face pressureFMHLC##_IMPORT.INP (plus operating pressure on crack face and applied pipe moment).##=03, 30, 50, 75, and 95Formatted K result outputs for circumferential flaws. ##=03, 30, 50,FMHLC## IMPORTK.CSV 75ad9.... 75, and 95HLAXIAL.INP Input file to modify base mesh for axial crack tip insertionCrack tip node inputs for fracture mechanics model conversion forA _ saxial flaws. **=00 and 90 with 00 = 00 plane and 90 = 900 planeFM HLAXL**.INP Geometry input files to create axial flaws on the plane. **= 00 and 90FM HL AXL** COORD.INP Input files to determine axial crack face element centroid coordinates.FM _- C**=00, and 90FM HL AXL**_COORDI.txt Axial crack face element centroid coordinate outputs. **=00, and 90FMHLLAXL** GETSTR.INP Input files to extract axial crack face stresses from residual stressanalysis. **=00, and 90Extracted axial crack face stresses from residual stress analysis.STR_FieldOperAXL**1.txt **=00, and 90Input files to transfer stresses into axial crack face pressure (plusFMHLAXL**_IMPORT.INP operating pressure on crack face and applied pipe moment). **=00,and 90FMHLAXL** IMPORT K.CSV Formatted K result outputs for axial flaws. **=00, and 90AnTip8 IKCALC.INP KCALC post-processing input filepc-CRACK PWSCC growth input file for circumferential flaw.CirFlaw_$$$$.pcf $$$$=0.025 and 0.1 with 0.025 = 0.025" and 0.1 = 0.1" initial flawsizeFile No.: 1400669.313Revision: 0Page A-2 of A-3F0306-01R2}}

Revision as of 00:22, 7 June 2018

1400669.313, Rev. 0, Crack Growth Analysis of the Hot Leg Drain Nozzle
ML15190A264
Person / Time
Site: Palisades Entergy icon.png
Issue date: 05/11/2015
From: Fong M
Structural Integrity Associates
To:
Office of Nuclear Reactor Regulation
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ML15190A274 List:
References
10426669, 1400669 1400669.313, Rev. 0
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Structural Integrity Associates, Inc. File No.: 1400669.313Project No.: 1400669CALCULATION PACKAGE Quality Program Type: Z Nuclear E] CommercialPROJECT NAME:Palisades Flaw Readiness Program for 1R24 NDE InspectionCONTRACT NO.:10426669CLIENT: PLANT:Entergy Nuclear Operations, Inc. Palisades Nuclear PlantCALCULATION TITLE:Crack Growth Analysis of the Hot Leg Drain NozzleDocument Affected Project Manager Preparer(s) &Revision Pages Revision Description Approval Checker(s)Signature & Date Signatures & Date0 1 -23 Initial Issue Preparer:A-i -A-3Computer FilesNorman EngNE 5/11/15 Minji FongMF 5/11/15Checkers:Wilson WongWW 5/11/15Gole MukhimGSM 5/11/15Page 1 of 23F0306-01R2 S&NwbiMral lhfe y Associates, IncOTable of Contents1.0 O B JE C TIV E ......................................................................................................... 42.0 D E SIG N IN PU T S .................................................................................................... 42.1 Piping Interface Loads ................................................................................. 42.2 Residual Stresses at Normal Operating Temperature and Pressure .............. 52.3 Mechanical Load Boundary Conditions ...................................................... 52.4 C rack G row th R ate ........................................................................................ 53.0 A SSU M PTIO N S ...................................................................................................... 64.0 DETERMINATION OF STRESS INTENSITY FACTOR ...................................... 64.1 Crack Face Pressure Application .................................................................. 64.2 K Calculation for Circumferential Flaws ..................................................... 74.2.1 Finite Element Model with Circumferential Flaws ..................................... 74.2.2 Stress Intensity Factor Results ....................................................................... 84.3 K Calculation for Axial Flaws ...................................................................... 84.3.1 Finite Element Model with Axial Flaws ........................................................ 84.3.2 Stress Intensity Factor Results ....................................................................... 85.0 CRACK GROWTH CALCULATION .................................................................... 96.0 C O N C LU SIO N S ...................................................................................................... 97.0 R E FE R E N C E S ........................................................................................................ 11APPENDIX A COMPUTER FILES LISTING ............................................................... A-1File No.: 1400669.313 Page 2 of 23Revision: 0F0306-01R2 jSiniuorai lateurify Associates, inc.List of TablesTable 1: Stress Intensity Factors for Circumferential Flaws ............................................ 12Table 2: Stress Intensity Factors for Axial Flaws ............................................................. 12Table 3: Crack Growth Time to 75% Through-Wall ........................................................ 12Table 4: Crack Growth Time to 95% Through-Wall .................................. ............................ 12Table 5: Allowable Detected Flaw Size ............................................................................ 13List of FiguresFigure 1. Base Finite Element M odel M esh ...................................................................... 14Figure 2. Applied Mechanical Load Boundary Conditions ............................................... 15Figure 3. Circumferential Flaw with Crack Tip Elements Inserted ................................... 16Figure 4. Transferred Residual Stress + NOC + Pressure Stress for Circumferential Flaws. 17Figure 5. Stress Intensity Factors as a Function of Depth for Circumferential Flaws ..... 18Figure 6. Axial Flaws with Crack Tip Elements Inserted ................................................. 19Figure 7. Transferred Residual Stress + NOC + Pressure Stress for Axial Flaws ........ 20Figure 8. Stress Intensity Factors as a Function of Depth for Axial Flaws ....................... 21Figure 9. Crack Growth for All Flaw Types with 0.025" Initial Flaw Size ..................... 22Figure 10. Crack Growth for All Flaw Types with 0.1" Initial Flaw Size ........................ 23File No.: 1400669.313Revision: 0Page 3 of 23F0306-01R2 V smnI ur IWihurily Associates, Inc.1.0 OBJECTIVEThe objective of this calculation package is to determine maximum allowable flaw sizes for 18 and 36months of continued operation based on crack growth analyses for a series of postulated flaws in the hotleg drain nozzle boss weld in support of a Primary Water Stress Corrosion Cracking (PWSCC)susceptibility study at the Palisades Nuclear Plant (Palisades). The stresses due to the hot leg pipeinterface loads which are determined in this calculation, and residual stresses extracted from a previousanalysis [1] are used to calculate stress intensity factors (K) which are used to perform crack growthanalyses. The PWSCC crack growth analyses are performed using the pc-CRACK [2] program for bothcircumferential and axial flaws. The allowable detected flaw sizes are determined by back-calculatingthe predicted growth time to a maximum flaw size of 75% through wall thickness per ASME CodeSection XI, IWB-3643.2.0 DESIGN INPUTSThe finite element model shown in Figure 1 was developed in Reference [3] and is used for thedetermination of stress intensity factors.2.1 Piping Interface LoadsReference 4 (PDF file, page 88) indicates that, for the hot leg, the bounding thermal transient stress of1.010 ksi is due to case Thermal 002, the deadweight (DW) stress is 0.096 ksi and the friction stress is1.056 ksi. The hot leg loads are applied as an equivalent bending moment to the axial free end of themodeled hot leg. The equivalent bending moment is based on the combined stress which is assumed tooccur at the outside surface of the hot leg. The maximum combined bending stress is:DW + Friction + Thermal = 0.096 + 1.056 + 1.010 = 2.162 ksiThe moment based on the bending stress is calculated as:M u.I i" (24.81254-20.81254).2.162M=- =-- _= 13099in -/kipsOR 4 24.8125where,M = Moment (in-kips)S = Stress on hot leg pipe free end (ksi)I = Moment of Inertia -(7/4)(OR4 -IR4) (in4)IR = Inside radius of hot leg pipe (in) = 20.8125" [3]OR = Outside radius of hot leg pipe (in) = 24.8125" [3]Since half the hot leg pipe is modeled, the equivalent moment applied to the model is 6549.5 in-kips(= 13099 in-kips /2). The moment is applied to the axial end of the hot leg run piping by means of a pilotFile No.: 1400669.313 Page 4 of 23Revision: 0F0306-01R2 j ruIUcrwl IitMUrly Associates, Inc.node pair to transfer the loading. The pilot node pair is composed of a target node at the center of thepipe (ANSYS TARGE170 element) and a set of surface contact elements on the axial end of the pipe(ANSYS CONTA 174 element). The surface elements are bonded to the pilot node in a slave/mastercoupling relationship, so that the moment load applied to the pilot node is transferred to the end of thepipe. The hot leg drain nozzle piping loads are considered to have negligible effects on the resulting K'sfor the boss weld, and are therefore not considered.2.2 Residual Stresses at Normal Operating Temperature and PressureResidual stresses at the fifth operating condition cycle (at time = 2484 minutes) are taken fromReference 1. These stresses include the effects of normal operating temperature of 583°F and pressure of2085 psig [1].2.3 Mechanical Load Boundary ConditionsThe mechanical load boundary conditions for the stress analysis are symmetric boundary conditions atthe symmetry planes of the model, axial displacement restraint at the end of the nozzle, and axialdisplacement restraint on the pilot node, as shown in Figure 2. In the case where axial flaws are modeledon the symmetry planes, the boundary conditions are released at the nodes where the flaw exists.2.4 Crack Growth RateThe default PWSCC crack growth rate in pc-CRACK [2] is used. This relation is based on expressionsin Reference [5, Section 4.3] and the resulting equation for the crack growth rate is as follows:da Cexp[L Q 1 1 (K-Kh)'3 for K > Kaidt T+460 T,ref +460For times (t) in hours, temperatures (T and Tref) in 'F, crack length (a) in inches and K in ksi-4in, thefollowing reference values are used:Tref = 617°FC = 2.47x10-7 (constant)0 1.6 (constant)Q 28181.8°R (constant)Ka, = 0 (threshold stress intensity factor below which there is no crack growth)T = operating temperature at location of crackFile No.: 1400669.313 Page 5 of 23Revision: 0F0306-01R2 V an" Ibf Assoas, Inc03.0 ASSUMPTIONSThe following assumptions are used in this analyses:" The hot leg drain nozzle piping loads are not considered in calculating stress intensity factorssince loads on the drain nozzle do not produce Mode I crack opening stress intensity factors thatcontribute to crack growth in the boss weld.* The maximum combined stress on the hot leg piping is assumed to occur at the outside surface ofthe hot leg.4.0 DETERMINATION OF STRESS INTENSITY FACTORThe stresses described in this section are used with a modified version of the finite element model(FEM) developed previously in Reference [3] to determine stress intensity factors. The modification ofthe FEM consists of adding crack tip elements as addressed in Section 4.2 and 4.3. The stress intensityfactors (Ks) are calculated using the KCALC feature in ANSYS [6] which is based on linear elasticfracture mechanics (LEFM) principles. For the LEFM evaluations, only the elastic properties are used inthe FEA.4.1 Crack Face Pressure ApplicationIn order to determine the Ks for the circumferential and axial flaws due to residual stresses, the stresseson the boss weld-to-nozzle interface, at the fifth operating condition (at time = 2484 minutes in theresidual stress analysis [1]), are extracted from the residual stress analysis and reapplied on the crackface as surface pressure loading.This approach is based on the load superposition principle [7], which is utilized to transfer the stressesfrom the weld residual stress finite element model onto the fracture mechanics finite element model thatcontains crack tip elements. The superposition technique is based on the principle that, in the linearelastic regime, stress intensity factors of the same mode, which are due to different loads, are additive(similar to stress components in the same direction).The superposition method can be summarized with the following sketches [7, page 66]:PFW PWx PWxPW x P(x)(a) (b) (c) (d)File No.: 1400669.313 Page 6 of 23Revision: 0F0306-01 R2 7 ankinal grlty Associates, Inc?A load p(x) on an uncracked body, Sketch (a), produces a normal stress distribution p(x) on Plane A-B.The superposition principle is illustrated by Sketches (b), (c), and (d) of the same body with a crack atPlane A-B. The stress intensity factors resulting from these loading cases are such that:Ki(b) = Ki(c) + Ki(d)Thus, Ki(d) = 0 because the crack is closed, and:Ki(b) = Ki(c)This means that the stress intensity factor obtained from subjecting the cracked body to a nominal loadp(x) is equal to the stress intensity factor resulting from loading the crack faces with the same stressdistribution p(x) at the same crack location in the uncracked body.4.2 K Calculation for Circumferential Flaws4.2.1 Finite Element Model with Circumferential FlawsThe stress intensity factors for full circumferential flaws in the nozzle boss weld are determined by finiteelement analysis using deterministic linear elastic fracture mechanics (LEFM) principles. As a result,five fracture mechanics finite element models are derived to include "collapsed" crack meshing thatrepresent full (3600) circumferential flaws surrounding the nozzle at various depths within the bossweld.The circumferential flaws align with the interface between the boss weld and the nozzle. The modeledcrack depths are: 0.13", 1.17", 2.05", 3.13", and 3.97" as measured at the 00 axial side of the hot legpipe.The modeling of the flaws, or cracks, involves splitting the crack plane and then inserting "collapsed"mesh around the crack tips followed by concentrated mesh refinements that surround the "collapsed"mesh, and are referred to as "crack tip elements". This step is implemented on a source finite elementmodel without the cracks (the FEM developed in Reference 3) where the crack tip elements are insertedby an in-house developed ANSYS macro.For the fracture mechanics models, 20-node quadratic solid elements (ANSYS SOLID95) are used in thecrack tip region, while 8-node solid elements (ANSYS SOLID 185) are used everywhere else in themodel. The mid-side nodes for the SOLID95 elements around the crack tips are shifted to the "quarterpoint" locations to properly capture the singularities at the crack tips, consistent with ANSYSrecommendations. The finite element model for the 3.97" deep circumferential flaw, with the crack tipmesh, is shown in Figure 3 as an example; the crack tip mesh for the other crack depths follows the samepattern.File No.: 1400669.313 Page 7 of 23Revision: 0F0306-01R2 jsftatbrnI IntegriAy Associates, Inc.The quarter point mid-side nodes combined with the extra layers of concentrated elements around thecrack tips provide sufficient mesh refinement to determine the stress intensity factors for the fracturemechanics analyses.4.2.2 Stress Intensity Factor ResultsThe radial stresses (radial to the nozzle axis) on the weld/nozzle interface are transferred to thecircumferential flaws as crack face pressure per the superposition principle described in Section 4.1.Figure 4 depicts, as an example, the transferred radial stresses as crack face pressure for the 3.97"circumferential flaw depth. During the crack face pressure transfer, the operating pressure of2085 psi [1] is added to the crack face pressure to account for the internal pressure acting on the crackface due to cracking. A far field in-plane bending moment per Section 2.1 is also applied to the free endof the hot leg run piping to account for piping moments in the main loop piping.Each crack model is analyzed as a steady state stress pass at the operating and reference temperature of583°F [1] in order to use the material properties at the operating temperature, but without inducingadditional thermal stresses.At the completion of each analysis, the ANSYS KCALC post-processing is performed to extract the K'sat each crack tip node around the nozzle. The maximum K results are summarized in Table 1 for variouscrack depth ratios "a/t". Since the crack tip location is same in the circumferential flaw, the maximum Kfrom all locations at each crack size is conservatively used for the K vs. a profile. The "K vs. a/t" trendsare then plotted in Figure 5.4.3 K Calculation for Axial Flaws4.3.1 Finite Element Model with Axial FlawsThe stress intensity factors for axial flaws are determined using the same methodology as thecircumferential flaws. However, the mesh of weld nuggets was removed to insert thumbnail shape flawsin the model. Also, the orientation and shape of the flaws allow all crack depths at the 0' and 900 facesof the symmetric hot leg pipe model to be inserted simultaneously. Figure 6 shows the five modeledcrack depths (0.25", 1.06", 1.90", 2.91", and 3.85") on the 0' face (hot leg axial face) and the 90' facewith crack tip elements inserted.The modeling of the axial flaws uses the same crack tip elements as described in Section 4.2.1. Thecrack tip mesh is the same pattern used in the circumferential flaws and is shown in Figure 6 for theaxial flaws at the 0' and 90' faces.4.3.2 Stress Intensity Factor ResultsSimilar to the circumferential flaw analyses, the crack opening residual stresses and additional operatingpressure are transferred to the axial flaws as crack face pressure. Figure 7 depicts, as an example, theFile No.: 1400669.313 Page 8 of 23Revision: 0F0306-01R2 C mumral bItrify Associates, Inc.transferred hoop stresses as crack face pressure for the axial flaws. In addition, a far field in-planebending moment per Section 2.1 is applied to the free end of the hot leg run piping to account for pipingmoments in the main loop piping. The K results at the deepest point of the flaws are summarized inTable 2 for various crack depth ratios "a/t" and plotted in Figure 8. Since the deepest point of thepostulated axial flaws has the smallest remaining wall thickness, the K at the deepest point is used forthe K vs. a profile.5.0 CRACK GROWTH CALCULATIONStress intensity factors (Ks) at four depths for 3600 inside surface connected, part-through-wallcircumferential flaws as well as two axial thumbnail flaws at the 0-and 90-degree azimuthal locations ofthe nozzle, are calculated using finite element analysis (FEA). For the circumferential flaw, themaximum K values around the nozzle circumference for each flaw depth are extracted and used as inputinto pc-CRACK to perform the PWSCC crack growth analyses. For the axial flaws, the K at the deeppoint of the thumbnail shape is used as input for performing the PWSCC crack growth analyses. Sincethe K vs. a profile is used as input, the shape of the component is not relevant.For the crack growth analyses, two initial flaw sizes are chosen. These are based on expectedengineering flaw sizes that could be present for a flaw that would then grow by PWSCC. The final flawsize for these analyses is 75% of the wall thickness. This final depth is chosen as it is the maximumallowable flaw depth per Section XI of the ASME Code for pipe flaw evaluations. Additionally, a finalflaw size of 95% of the wall thickness is also considered in this calculation.The key parameters used in the crack growth calculations included:Two initial crack depths = 0.025" and 0.1" (assumed)Temperature = 583 °F (operating temperature [1])Wall thickness = 4.0" (hot leg pipe thickness [3])The resulting crack depths for the circumferential and axial flaws, as a function of time, as calculated bypc-CRACK are shown in Figure 9 for the 0.025" initial flaw size, and Figure 10 for the 0.1" initial flawsize. The time for a flaw to grow from the initial flaw size to 75% and 95% through-wall is tabulated inTable 3 and Table 4 for both circumferential and axial flaw types, respectively. Table 5 shows themaximum allowable detected flaw sizes for the postulated flaws if continued operation for 18 and 36months is considered.

6.0 CONCLUSION

SStress intensity factors were calculated for the 360' circumferential flaws as well as the axial flaws at the0' and 90' locations. The stress intensity factors were calculated using residual stress distributions forresidual stress plus normal operating conditions. In addition, a far field in-plane bending moment isFile No.: 1400669.313 Page 9 of 23Revision: 0F0306-01R2

,shin rai hitegrlfy AssociaMes, Inc.applied to the free end of the hot leg run piping to account for piping moments in the main loop piping.This combined loading is used for the determination of the stress intensity factors for both thecircumferential and axial flaws. Figure 5 and Figure 8, as well as Table 1 and Table 2, show thecalculated stress intensity factors for the circumferential and axial flaws.Crack growth evaluations were performed for circumferential and axial flaw configurations using twodifferent initial flaw sizes. As shown in Figure 9 and Table 3, the shortest time for an initial 0.025" deepflaw to grow to 75% through-wall in all cases is 30.5 years for an axial flaw on the 0' plane. Figure 10and Table 3 show that the shortest time for an initial 0.1" deep flaw to grow to 75% through-wall in allcases is 29.7 years for an axial flaw on the 00 plane. Table 5 shows the maximum allowable detectedflaw sizes for 18 and 36 months continued operation.File No.: 1400669.313Revision: 0Page 10 of 23F0306-01R2 7 whtnorel te grily Associates, Inc.

7.0 REFERENCES

1. SI Calculation No. 1400669.312, Rev. 0, "Hot Leg Drain Nozzle Weld Residual StressAnalysis."2. pc-CRACK 4.1, Version 4.1 CS, Structural Integrity Associates, December 2013.3. SI Calculation No. 1400669.3 10, Rev. 0, "Finite Element Model for Hot Leg Drain Nozzle."4. Palisades Document, Report No. CENC- 1115, "Analytical Report for Consumers Power Piping,"SI File No. 1300086.204.5. Materials Reliability Program: Crack Growth Rates for Evaluating Primary Water StressCorrosion Cracking (PWSCC) ofAlloy 82, 182 and 132 Welds (MRP-115), EPRI, Palo Alto, CA:2004, 1006696.6. ANSYS Mechanical APDL and PrepPost, Release 14.5 (w/ Service Pack 1), ANSYS, Inc.,September 2012.7. Anderson, T. L., "Fracture Mechanics Fundamentals and Applications," Second Edition, CRCPress, 1995.File No.: 1400669.313Revision: 0Page 11 of 23F0306-01R2 CsfaffreMOMAssocbels, Inc.Table 1: Stress Intensity Factors for Circumferential FlawsCrack Depth a/t Max. K(in) (ksi-in°.5)0.13 0.03 19.611.12 0.28 22.762.04 0.51 14.783.15 0.79 13.033.97 0.99 35.15Table 2: Stress Intensity Factors for Axial FlawsHL Axial Plane 00 HL Circ. Plane 900Crack Depth a/t K at Deep Pt Crack Depth a/t K at Deep Pt(in) (ksi-in°'5) (in) (ksi-in°'5)0.25 0.06 18.50 0.25 0.06 14.161.06 0.26 18.64 1.10 0.27 14.431.90 0.47 17.60 1.96 0.49 14.772.91 0.73 19.34 2.95 0.74 16.983.85 0.96 23.44 3.81 0.95 21.41Table 3: Crack Growth Time to 75% Through-WallInitial Flaw Size Axial Crack Axial Crack Circ. Crack(in) (00 plane) (900 plane) (years)_ (years) (years) (years)0.025 30.5 42.9 33.90.100 29.7 41.7 33.1Table 4: Crack Growth Time to 95% Through-WallInitial Flaw Size Axial Crack Axial Crack Circ. Crack(in) (0' plane) (900 plane) (years)(years) (years) (years)0.025 36.7 50.3 42.10.100 36.0 49.2 41.4File No.: 1400669.313Revision: 0Page 12 of 23F0306-01R2 jSIvrura I~tegrlfy Associatos, Inc.Table 5: Allowable Detected Flaw SizeAllowable Detected Flaw Size (a/t)Hot Leg Thickness, t = 4.00"Months of Axial Flaw Axial Flaw CircumferentialContinued at 0° plane at 900 plane FlawOperation a/t a (in) a/t a (in) a/t a (in)18 0.7070 2.83 0.7165 2.87 0.7260 2.9036 0.6690 2.68 0.6785 2.71 0.6975 2.79File No.: 1400669.313Revision: 0Page 13 of 23F0306-01R2 tj s bwftn Associates, k=6ANSYSR14.5Figure 1. Base Finite Element Model MeshFile No.: 1400669.313Revision: 0Page 14 of 23F0306-01 R2 C an"s~iru lMq*rl Assocates, Inc.0'RFAI, NNflCoupled to pilot nodeIPilot node and axial restraintsAxial displacement restraint//Figure 2. Applied Mechanical Load Boundary ConditionsFile No.: 1400669.313Revision: 0Page 15 of 23F0306-OIR2 5SVOW&W bft wE Assocates, 1=Figure 3. Circumferential Flaw with Crack Tip Elements Inserted(Note: Deepest circumferential flaw shown for example)File No.: 1400669.313Revision: 0Page 16 of 23F0306-01R2 C OW&*~re lWabdY ASSOciats, InWFigure 4. Transferred Residual Stress + NOC + Pressure Stress for Circumferential Flaws(Note: Deepest circumferential flaw shown for example)File No.: 1400669.313Revision: 0Page 17 of 23F0306-01 R2 can&* MW* Assadates, /mein"-71'40353025201510500.0 0.2 0.4 0.6 0.8 1.0Depth (a/t)Figure 5. Stress Intensity Factors as a Function of Depth for Circumferential FlawsFile No.: 1400669.313Revision: 0Page 18 of 23F0306-01R2 Van&* MWW ASWCWOS, kasI00900Figure 6. Axial Flaws with Crack Tip Elements InsertedFile No.: 1400669.313Revision: 0Page 19 of 23F0306-01R2 CSbam"r MOMgr Assocates, #MKCAU~ anal1l-ksi1.96433 6.99' 15.950, 24.9077 33.865iKCgrC a__ 7. ira sfrred cReiu S a+cs s+ Pressure... ............ .. ..... sFigure 7. Transferred Residual Stress + NOC + Pressure Stress for Axial FlawsFile No.: 1400669.313Revision: 0Page 20 of 23F0306-01R2

~jSVOW& ruwl py Associates, ln.2520Tune-,151050.0-0.00.2 OA 0.6 0.81.0Depth (a/t)Figure 8. Stress Intensity Factors as a Function of Depth for Axial FlawsFile No.: 1400669.313Revision: 0Page 21 of 23F0306-01R2 cjanswfGuu MW*f Assocades, hmD.1.00.90.80.7" 0.6m 0.5c' 0.40.30.20.10.0/I-Circ. Crack---Axial Crack_0--Axial Crack_90/ 10 10 20 30 40 50 60Time (years)Figure 9. Crack Growth for All Flaw Types with 0.025" Initial Flaw SizeFile No.: 1400669.313Revision: 0Page 22 of 23F0306-01R2 cjbh.airwI Iabpf AssCIatS, kne.10.90.80.70.60-m 0.40.30.20.10e-Circ. Crack---Axial Crack_0--Axial Crack_900 10 20 30 40 50 60Time (years)Figure 10. Crack Growth for All Flaw Types with 0.1" Initial Flaw SizeFile No.: 1400669.313Revision: 0Page 23 of 23F0306-01R2 SkuowiraI Iiegrlty Associates, Inc.APPENDIX ACOMPUTER FILES LISTINGFile No.: 1400669.313Revision: 0Page A- I of A-3F0306-01R2 Vj asiofrraI Integffly Assocades, hIWOFile Name DescriptionPalisades HL Drain.INP Input file to create base geometry model [3]MPropMISO.INP Elastic-plastic material properties inputs [3]BCNODES.INP Component setting for the boundary conditions.Crack tip node inputs for fracture mechanics model conversion forNODESC##.INP circumferential flaws. ##=03, 30, 50, 75, and 95 with 03 = 0.13", 30 =1.17", 50 = 2.05, 75 = 3.13", 95 = 3.97" of flaw sizeFMHLC##.INP Geometry input files to create circumferential flaw at specified depth.-##=03, 30, 50, 75, and 95FM HL C## COORD.INP Input files to determine circumferential crack face element centroidFMHLC# Ccoordinates. ##=03, 30, 50, 75, and 95_EHLCH##COORDl.txt Circumferential crack face element centroid coordinate outputs.F -##=03, 30, 50, 75, and 95FMHLC##_GETSTR.INP Input files to extract circumferential crack face stresses from residualstress analysis. ##=03, 30, 50, 75, and 95Extracted circumferential crack face stresses from residual stressanalysis. ##=03, 30, 50, 75, and 95Input files to transfer stresses into circumferential crack face pressureFMHLC##_IMPORT.INP (plus operating pressure on crack face and applied pipe moment).##=03, 30, 50, 75, and 95Formatted K result outputs for circumferential flaws. ##=03, 30, 50,FMHLC## IMPORTK.CSV 75ad9.... 75, and 95HLAXIAL.INP Input file to modify base mesh for axial crack tip insertionCrack tip node inputs for fracture mechanics model conversion forA _ saxial flaws. **=00 and 90 with 00 = 00 plane and 90 = 900 planeFM HLAXL**.INP Geometry input files to create axial flaws on the plane. **= 00 and 90FM HL AXL** COORD.INP Input files to determine axial crack face element centroid coordinates.FM _- C**=00, and 90FM HL AXL**_COORDI.txt Axial crack face element centroid coordinate outputs. **=00, and 90FMHLLAXL** GETSTR.INP Input files to extract axial crack face stresses from residual stressanalysis. **=00, and 90Extracted axial crack face stresses from residual stress analysis.STR_FieldOperAXL**1.txt **=00, and 90Input files to transfer stresses into axial crack face pressure (plusFMHLAXL**_IMPORT.INP operating pressure on crack face and applied pipe moment). **=00,and 90FMHLAXL** IMPORT K.CSV Formatted K result outputs for axial flaws. **=00, and 90AnTip8 IKCALC.INP KCALC post-processing input filepc-CRACK PWSCC growth input file for circumferential flaw.CirFlaw_$$$$.pcf $$$$=0.025 and 0.1 with 0.025 = 0.025" and 0.1 = 0.1" initial flawsizeFile No.: 1400669.313Revision: 0Page A-2 of A-3F0306-01R2