structural integrity associates, inc. file no.nozzle sizes for these cases are selected based on the...

Structural Integrity Associates, Inc. File No.: 0900876.304

CALCULATION PACKAGE Project No.: 0900876

Quality Program: N Nuclear D Commercial

PROJECT NAME:

SI PT Curve LTR Revision

CONTRACT NO.:

437044285, Rev. 1; 437044287, Rev. 1

CLIENT: PLANT:

GE Nuclear Energy N/A

CALCULATION TITLE:

Generic Analysis and Methodology for Instrument Nozzle Fracture Mechanics Analysis

Document Affected Project Manager Preparer(s) &Revision Pages Revision Description Approval Checker(s)

Signature & Date Signatures & Date

0 1 - 45 Initial Issue Responsible En2ineerA-i - A-7B-i -B-12

D. V. Sommerville Minghao Qin6/20/2011 6/20/2011

Responsible Verifier

Daniel Sommerville6/20/2011

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Structural Integrity Associates, Inc.

Table of Contents

1.0 IN TR O D U C TIO N ........................................................................................................ 52.0 M ETH O D O LO G Y ...................................................................................................... 5

2.1 Method of Stress Analysis ............................................................................. 62.2 Model Geometry, Materials, and Heat Transfer Coefficients ....................... 62.3 L oad C ases .................................................................................................... 7

2.3.1 Internal Pressure Load Case ......................................................................... 72.3.2 Therm al Transient ........................................................................................ 72.3.3 P ipe R eaction Loads ...................................................................................... 7

2.4 Stress Extraction Paths ................................................................................. 72.5 Boundary Integral / Influence Function (BIE/IF) Solution .......................... 82.6 Finite Element Linear Elastic Fracture Mechanics Model with Crack Tip

E lem ents ...................................................................................................... . . 83.0 A SSU M PTION S ....................................................................................................... 84.0 FINITE ELEMENT MODEL ...................................................................................... 9

4.1 Finite Element Model Development ............................................................. 94.2 Finite Element Model Validation ............................................................... 10

4.2.1 Mesh Density Check for Uncracked Model ................................................ 10

4.2.2 Mesh Density Check for Cracked Model .................................................... 115.0 INSTRUMENT NOZZLE LOAD CASES ............................................................... 11

5.1 Internal Pressure Load Case ........................................................................ 11

5.2 Therm al Transient ....................................................................................... 115.3 Pipe Reaction Load Case ............................................................................. 12

6.0 PRESSURE, THERMAL, AND PIPING LOAD RESULTS ................................... 12

6.1 Internal Pressure Load Case ........................................................................ 126.2 Thermal Transient Load Case ...................................................................... 146.3 Pipe Reaction Load Case ............................................................................. 14

7.0 OBSERVATIONS AND DISCUSSIONS ................................................................. 158.0 GENERIC METHODOLOGY FOR K1 ESTIMATION ........................................... 16

8.1 Stress Intensity Factor Empirical Equation Development ........................... 168.2 Verification of Stress Intensity Factor Empirical Equations ....................... 17

9.0 SU M M A R Y .................................................................................................................... 1810.0 R E FE R E N C E S ............................................................................................................... 19Appendix A VERIFICATION OF FEACTURE MECHANICS FINITE ELEMENT

M E T H O D ................................................................................................. A -1Appendix B SUPPORTING FILES .................................................................................. B-1

File No.: 0900876.304 of 45Revision: 0

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List of Tables

Table 1: Dimensions Used for Instrument Nozzle Parametric Studies ............................ 20Table 2: List of Typical Instrument Nozzle Assembly Materials ...................................... 21Table 3: Material Properties for SA-533, Grade B, Class 1 .............................................. 21Table 4: Material Properties for Type 304 Stainless Steel (18Cr-8Ni) ............................ 21Table 5: Material Properties for Alloy 600 (N06600) ...................................................... 22Table 6: Material Properties for Vessel Pad, Material Assumed Equivalent to Vessel

(T able 3) ........................................................................................................ . . 22

Table 7: Material Properties for SA-182 F304 (18Cr-8Ni) ............................................... 22

Table 8: Material Properties for SA-541 Class 1 ............................................................... 23Table 9: A ir Properties ...................................................................................................... 23Table 10: Therm al Transient Definition ............................................................................. 23

Table 11: Mesh Density Check Results for the Uncracked Models ................................. 24Table 12: Mesh Density Check Results for the Cracked Models ...................................... 24Table 13: Summary of Stress Intensity Factors for 1000 psi Pressure Load Case with

D ifferent N ozzle M aterial .................................................................................. 24

Table 14: Summary of Stress Intensity Factors for Thermal Transient Load Cases withPath Excluding the Clad ................................................................................... 25

Table 15: Comparison of Stress Intensity Factors for the Paths Including/Excluding theClad under Thermal Transient Loads ............................................................... 26

Table 16: Summary of Stress Intensity Factors for the Attached Piping Load Cases ..... 26

Table 17: Summary of FE LEFM and BIE/IF K1 Results ................................................. 26Table 18: Verification of Stress Intensity Factors ............................................................. 27Table 19: Summary of K, Empirical Equations .................................................................. 27


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List of Figures

Figure 1: Stress Path Orientation in Postulated Flaw ........................................................ 28

Figure 2: Generic M odel Dim ensions ............................................................................... 28

Figure 3: Therm al Transients ............................................................................................. 29

Figure 4: BIE/IF Solution for Instrument Nozzle Evaluation .......................................... 30

Figure 5: Quarter Symmetric FEM of Instrument Nozzle and Reactor Pressure Vessel ....... 30

Figure 6: Finite Element Fracture Mechanics Model ........................................................ 31

Figure 7: Structural Boundary Conditions and Internal Pressure Load Applied toU ncracked M odel ............................................................................................. 31

Figure 8: Structural Boundary Conditions and Internal Pressure Load Applied toC racked M odel .................................................................................................. 32

Figure 9: Mesh Density Check Configurations for Uncracked Models ............................ 32

Figure 10: Mesh Density Check Results for Non-Crack Models ...................................... 33

Figure 11: Mesh Density Check Configurations for Cracked Models ............................... 33

Figure 12: Mesh Density Check Results for Cracked Models .......................................... 34

Figure 13: Applied Piping Loads and Boundary Conditions ............................................. 35

Figure 14: Stress Extraction Path ...................................................................................... 35

Figure 15: Circumferential Stress Distributions for the Unit Pressure Load Case ............ 36

Figure 16: Samples of Pressure and Thermal Ramp Load Case Path Stress Distribution ..... 37

Figure 17: An Example of Pressure Load Case Path Stress Distribution for Path throughthe A ir G ap ........................................................................................................ 38

Figure 18: KI Distribution along the Crack Front for Internal Pressure Load Case ....... 39

Figure 19: Path through the Vessel Bore Comer ............................................................... 39

Figure 20: Paths Including and Excluding Clad ............................................................... 40

Figure 21: K, Distribution along Crack Front for Thermal Ramp Transient andComparison to BIE/IF Solution ........................................................................ 40

Figure 22: K, Distribution along Crack Front for Thermal Shock Transient andCom parison to BIE/IF Solution ........................................................................ 41

Figure 23: Summary of Thermal Ramp K, for FE-LEFM and BIE/IF Analysis ............... 42

Figure 24: Summary of Thermal Shock K, for FE-LEFM and BIE/IF Analysis ............... 43

Figure 25: K, Estimation Equation for Pressure Load ...................................................... 44

Figure 26: K, Estimation Equation for Thermal Ramp Load ............................................. 45

Figure 27: K, Estimation Equation for Thermal Shock Load ............................................. 45


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1.0 INTRODUCTION

Nuclear Regulatory Commission (NRC) Generic Letter (GL) 96-03 allows plants to relocate theirpressure-temperature (P-T) curves and numerical values of the other P-T limits (such asheatup/cool-down) from Technical Specifications into a Pressure Temperature Limits Report(PTLR). The Structural Integrity licensing Topical Report (LTR) SIR-05-044-A, which wasreviewed and approved by the NRC in April 2007, can be referenced by any boiling water reactor(BWR) licensee, who supported development of the LTR, in a license amendment request toadopt NRC GL 96-03 requirements for a PTLR.

The LTR SIR-05-044-A addresses forged nozzle configurations in that it provides a BoundaryIntegral Equation / Influence Function (BIE/IF) solution for these nozzle designs and requires thatall such nozzles in the beltline, and extended beltline due to exposure to neutron fluence, beconsidered as a part of P-T curve development. However, a more recent finding associated withreactor pressure vessel (RPV) instrumentation nozzles is not addressed in the LTR. The partialpenetration style nozzle configuration of the RPV instrumentation nozzles is different thantraditional forged nozzle designs. These nozzles have been determined to be located in thebeltline plate material (or have become part of the extended beltline) where fluence exceedsIxI0

17 n/cm 2 in many BWRs. As a result, the NRC has been providing Requests for AdditionalInformation to all applicants developing PTLRs in accordance with the LTR asking for theinstrument nozzles to be addressed.

The purpose of this calculation package is to introduce a BIE/IF solution for the partialpenetration RPV instrumentation nozzles, and to calculate stress intensity factors associated withapplicable pressure and thermal transient loads. A generic approach for addressing the effect ofthe partial penetration RPV instrumentation nozzles in P-T curve development is provided. Thisapproach is benchmarked against results from plant specific calculations.

2.0 METHODOLOGY

A finite element model (FEM) of a generic instrument nozzle is constructed, and hoop stressresults are extracted along a limiting path for various loading conditions. As required by ASMESection XI, Appendix G [1], a V4 thickness postulated flaw at the J-groove weld is assumed asshown in Figure 1. A BIE/IF solution is introduced, and a stress intensity factor is calculated foreach load case considered. The BIE/IF solution is benchmarked against results obtained fromlinear elastic finite element fracture mechanics analyses in which the postulated crack is modeledusing the commonly used method of meshing the crack front with quadratic elements which havehad the midside nodes on the crack face moved to the 1/4 point location in order to simulate thesingularity at the crack tip. A total of thirty-eight FEMs are constructed with four different vesseldiameters, two different instrument nozzle diameters, two different J-groove weld lengths, andthree different nozzle materials. The generic approach presented for addressing RPVinstrumentation nozzles in P-T curve development is based on the results of the parametric studiesdocumented in this calculation package.


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The following topics are described separately below:

" Method of stress analysis

" Model geometry, materials, and heat transfer coefficients

• Load cases

* Stress extraction paths

* Boundary Integral Equation / Influence Function Solution

* Finite element linear elastic fracture mechanics model with crack tip elements

2.1 Method of Stress Analysis

A three dimensional (3-D) linear elastic finite element analysis (FEA) of the instrument nozzle isperformed to obtain the nozzle stress distribution resulting from the applied load cases. TheANSYS FEA software [2] is used for all thermo-elastic stress analyses. Depending on the natureof the applied loading, either a quarter symmetric (900) or a full (3600) model is used for the FEA.The type of model used for each load case is discussed below.

2.2 Model Geometry, Materials, and Heat Transfer Coefficients

The dimensions used for this analysis are based on typical vessel and nozzle sizes. Four typicalvessels, i.e., 251", 238", 218" and 205", and 2 typical instrument nozzles, i.e., 2" and 3" aresimulated in this calculation. Table 1 and Figure 2 show the dimensions selected for this analysis.The dimensions are based on typical instrumental nozzles documented in References 9 through11. The FEM includes a portion of the low alloy steel RPV shell, stainless steel RPV clad, Alloy.600 J-groove weld, Alloy 600 weld butter, nozzle insert (can be Alloy 600, Stainless Steel (SS), orCarbon Steel (CS) per Table 2-1 of Reference [13]), Alloy 600 nozzle-to-safe end weld, andstainless steel safe end. The extents of the RPV shell and safe end are defined such that the FEMboundaries do not introduce non-representative end effects at the location of interest. Table 2 listsa typical component material. Tables 3 to 8 list the corresponding material properties.

The majority of the analyses are performed using an Alloy 600 nozzle insert; however, the effectof nozzle material was specifically considered by adding additional analysis cases in which thenozzle insert was modeled as 304 SS and CS. The nozzle safe end material is the same as thenozzle forging per Table 2-1 of Reference [13]. Since there is no specific material specificationidentified for the CS nozzle inserts from Table 2-1 of Reference [13], SA-541 Class 1 is assumed.Per Table 2-1 of Reference [13], there are three different vessel dimensions for 304 SS nozzleforgings, 218", 238" and 251", and one vessel dimension for CS nozzle forgings, 251". Thenozzle sizes for these cases are selected based on the bounding cases from the Alloy 600 nozzleanalyses. Since the thickness for some plant instrument nozzles has been shown to be 0.7 inches[11], an additional dimension with a 0.7" nozzle thickness for an Alloy 600 and a SS nozzle insertis analyzed. The weld material is always assumed as Alloy 600 for the different nozzle materialcases.


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For the thermal analysis, a typical convection heat transfer coefficient for the inside surface of thevessel and nozzle is assumed as 500 Btu/hr-ft2-°F, at all fluid temperatures, and a typicalconvection heat transfer coefficient for the outside surface of the vessel and nozzle is assumed as0.2 Btu/hr-ft2-°F, at all times, to simulate the insulation. Table 10 lists the heat transfercoefficients applied for two different thermal transients. Note that Figure 1 shows an air gap islocated between the nozzle and the vessel. Air elements are used during the thermal analysis tosimulate heat transfer across the air gap. Table 9 shows the air properties applied in the FEA.The effects of radiation heat transfer are ignored during the thermal analysis.

2.3 Load Cases

The following load cases are considered:

1. Internal pressure

2. Thermal transient

3. Pipe reaction loads

2.3.1 Internal Pressure Load Case

An internal pressure of 1,000 psig is applied to the inside surfaces of the RPV and the instrumentnozzle. Membrane (or cap) loads are applied to the end of the safe end and to the edges of thevessel shell. Since the analysis is linear-elastic, the load case may be treated as a "unit" load andthe resulting stresses can be scaled to obtain a K, for other applied pressures.

2.3.2 Thermal Transient

Both a 100 ° F/hr thermal ramp and a 450 OF thermal shock are evaluated in this analysis. Table10 and Figure 3 show the thermal transient definitions considered for this work.

2.3.3 Pipe Reaction Loads

The stress path between the instrument nozzle and the RPV passes through the J-groove weld,which is at the same location as the postulated flaw required for P-T curve analysis. Therefore,pipe reaction loads are evaluated in order to assess the effect of piping loads on the stress intensityfactor calculated at the instrument nozzle. Both bending moments and an axial force load case areconsidered. Since the analysis is linear-elastic, these load cases can be considered to be "unit"loads and any plant specific results can be inferred by scaling the results using the plant specificpiping loads.

2.4 Stress Extraction Paths

A stress path, with the orientation shown in Figure 1, is chosen for extracting hoop stress resultsfrom the FEA. The path begins from the nozzle inner corner surface at the inside radius of thelow alloy steel RPV. The path extends to the outside surface of the RPV, oriented at a 45' anglewith respect to the nozzle centerline. The orientation of this path is consistent with the necessaryinputs for the BIE/IF solution for the nozzle corner crack in Section 2.5. Since the short J-grooveweld configuration may cause the postulated flaw path to cross the air gap, additional cases, witha longer J-groove weld, are considered in this work. Sixteen (16) FEMs with Alloy 600 nozzle


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material, six (6) FEMs with SS Nozzle material, two (2) FEMs with CS nozzle material, andfourteen (14) FEMs with 0.7" nozzle thickness are evaluated in this calculation.

2.5 Boundary Integral / Influence Function (BIE/IF) Solution

For the instrument nozzle, as a minimum, the stress concentration effect of the nozzle on the platematerial should be addressed as part of P-T curve development. This can be accomplished withthe use of a fracture mechanics model that applies to the partial penetration nozzle design.Calculation of the stress intensity factor, K1, is based on a quarter circular crack in an infinitequarter space [5]. The fracture mechanics model and associated equation used to calculate K1 areshown in Figure 4 [5]. The K, equation is reproduced here:

Kl =vza 0.723A0+0.551A, 2a+0.462A2-aI-+0.408A 3 41)

where:a = ¼ through-wall postulated flaw depth, inA0,Al, = pressure or thermal stress polynomial coefficients, obtained from a curve-fitA2,A3 of the extracted hoop stresses from a FEA

2.6 Finite Element Linear Elastic Fracture Mechanics Model with Crack Tip Elements

A linear elastic finite element fracture mechanics model with crack tip elements is developed inorder to benchmark the BIE/IF solution selected for this work.

3.0 ASSUMPTIONS

The following assumptions are used in the analysis.

1. The heat transfer coefficient of all external surfaces is assumed to be 0.2 Btu/hr-ft2-°F,which is consistent with General Electric standard practice. The ambient temperature isassumed to be 100TF. The assumed temperature does not have a significant effect on theresults of the analysis since the heat transfer coefficient at the internal surfaces (500Btu/hr-ftZ-°F) is more than three orders of magnitude greater than the assumed value of 0.2Btu/hr-ft2 -°F.

2. The external convection coefficient in Assumption 1 is an overall heat transfer coefficientand accounts for the effects of the insulation.

3. Material properties for the weld components listed in Table 2 are assumed based onpractices established in the ASME Boiler and Pressure Vessel (B&PV) Code, Section IX[6]. Weld material properties are based on weld procedure qualifications. Testing is theonly way to verify the properties. In general, the failure location is in the base metalduring material failure tests. Therefore, applying the weaker base metal properties insteadof weld material properties is typically considered conservative.


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4. Material designation for some components is not readily available. The followingassumptions are made:

* Vessel Pad - low alloy steel, similar to the RPV base metal, is assumed. The weldreinforcement at the partial penetration nozzle is typically low alloy steel.

• J-Groove Weld - Alloy 600 is assumed, and is the typical weld filler material.

* Nozzle-to-Safe End Weld - Alloy 600 is assumed. The effect of this assumption isnegligible since it is far from the location of interest.

5. Density and Poisson's ratio are assumed temperature independent for all materials. Inaddition, typical values are assumed for these values.

6. The residual stresses due to the application of austenitic cladding are insignificant at ornear normal operating temperature, for both the cladding and the RPV base metal [7].Therefore, a stress free temperature of 550'F is assumed for all materials in thisevaluation. The choice of stress free temperature will affect the magnitude of thedifferential thermal expansion stresses induced in the nozzle assembly.

4.0 FINITE ELEMENT MODEL

4.1 Finite Element Model Development

Sixteen (16) 3-D FEMs with Alloy 600 nozzle material, six (6) 3-D FEMs with SS Nozzlematerial, two (2) 3-D FEMs with CS nozzle material, and fourteen (14) 3-D FEMs with 0.7"nozzle thickness are constructed in ANSYS [2] using the dimensions shown in Table 1 and Figure2. Appendix B identifies all FEM input files used for this analysis. Three dimensional SOLID45elements are used for structural analyses, and 3-D SOLID70 elements are used for the thermalanalyses. CONTA174 and TARGE 170 contact and target elements are used to model possiblecontact between the instrument nozzle and the RPV bore. Figure 5 illustrates a sample quartersymmetric model.

The stainless, steel RPV clad, Alloy 600 J-groove weld, Alloy 600 butter, Alloy 600, stainlesssteel, or carbon steel instrument nozzle, low alloy steel RPV, low alloy steel vessel pad, Alloy 600nozzle-to-safe end weld, and stainless steel or carbon steel safe end are modeled as separatematerials. The air in the gap between the instrument nozzle and RPV shell is modeled for thethermal analysis only.

A 3-D FEM with crack tip elements is constructed in ANSYS [2] using a SI developed crackmeshing algorithm "Antip." A crack is modeled using quadratic elements (Solid95 elements)with the midside nodes moved to the quarter point location such that the stress singularity at thecrack tip is simulated. Appendix A contains a benchmark of the adequacy of the Antip meshingalgorithm based on a comparison of the stress intensity factor solution obtained using Antip tothat from a commonly accepted fracture mechanics solution in the open literature. Thedimensions for this model are chosen from Table 1 and Figure 2 with a 3" instrument nozzle, 251"vessel diameter, and long J-groove weld with Alloy 600 nozzle material. Three dimensionalSOLID45 elements and SOLID95 elements at the crack tip are used for structural analyses, and


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3-D SOLID70 elements and SOLID90 elements at the crack tip are used for the thermal analyses.Figure 6 illustrates the quarter symmetric fracture mechanics model developed for this study.

4.2 Finite Element Model Validation

Model validation checks are performed using an internal pressure load case. A uniform internalpressure of 1,000 psi is applied on the inside surfaces of the instrument nozzle and RPV wall. Inaddition, membrane or "cap" loads are applied to the end of the safe end and to the RPV shell toaccount for closed-end effects of the attached piping and vessel. The membrane loads arecalculated as follows:

P.R 2 (2)CAP -- 2 2

0 I

where:P = Internal pressure (P = 1,000 psig)Ri = Inner radius of cylindrical section, inR. = Outer radius of cylindrical section, in

This membrane load is applied such that it acts as a tensile load on the instrument nozzle and RPVshell. The nodes on the free end of the safe end are coupled in the nozzle axial direction to ensureequal axial displacement of the end of the nozzle and RPV in response to the membrane load so asto simulate the effects of the attached piping and closed end of the RPV.

Symmetry boundary conditions are applied to both lateral boundaries of the FEM, as well as tothe RPV shell opposite to the applied membrane load. For the model with crack tip elements, thesymmetric boundary conditions are not applied to the crack face. A 1000 psi uniform pressure isapplied on the crack face.

Figures 7 and 8 illustrate the applied loads and boundary conditions for the un-cracked andcracked models, respectively.

The results of the mesh density check are summarized below.

4.2.1 Mesh Density Check for Uncracked Model

Four different meshes are evaluated for this model validation check. Figure 9 shows the originalmesh and the finest mesh density. The 1,000 psi pressure is directly applied on the inside surfacesof the instrument nozzle and RPV wall (including cladding). Figure 10 shows the stress intensityplots for each model after removing the peak stress at the J-groove weld between the nozzle andbutter. Table 11 summarizes the stress intensities obtained from each model. Also shown inTable 11 is the difference in the peak stress intensity for each mesh evaluated. The results of thischeck show that the peak stresses in the nozzle forging have converged to a stationary value. Theoriginal model mesh is considered acceptable. The difference in the stress intensity resultsbetween the coarsest and finest mesh densities evaluated is less than 1%; therefore, the originalmodel mesh is considered acceptable for the analyses documented in this calculation package.


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4.2.2 Mesh Density Check for Cracked Model

Three different mesh densities are evaluated. Figure 11 shows the original mesh and the finestmesh. A uniform internal pressure of 1,000 psig is applied on the inside surfaces of theinstrument nozzle, RPV wall, and crack face. Consistent with the'intent of ASME Code, SectionIII [8], the RPV clad is not considered for the pressure load case. For this load case, the cladelements are removed and internal pressure is applied directly to the low alloy steel RPV shell.Figure 12 shows the stress intensity factor along the crack tip for each model. Table 12summarizes the stress intensity factors obtained from each mesh case evaluated. Also shown inTable 12 is the difference in the stress intensity factor for each mesh. The original model mesh isconsidered acceptable for the fracture mechanics analyses documented in this calculation package.The differences in stress intensity factor associated with the model mesh used are less than 7%and the K, value obtained from the selected mesh gives the most conservative value of the meshdensities considered.

5.0 INSTRUMENT NOZZLE LOAD CASES

The applied loads and boundary conditions for each load case are described below.

5.1 Internal Pressure Load Case

A uniform internal pressure of 1,000 psi is applied on the inside surfaces of the instrument nozzleand RPV wall. Consistent with the intent of ASME Code, Section III [8], the RPV clad is notconsidered for the pressure load case. For this load case, the clad elements are removed and theinternal pressure is applied directly to the low alloy steel RPV shell.

The boundary conditions are the same as detailed in Section 4.2. Figures 7 and 8 illustrate theapplied loads and boundary conditions to one of the un-cracked models and one of the crackedmodels, respectively. The cracked model geometry is taken from Table 1 with a 251" vessel, 3"nozzle, and long J-groove weld with Alloy 600 nozzle material. The ANSYS input files for theinternal pressure analyses are listed in Appendix B.

5.2 Thermal Transient

Per Section 2.3.2, two thermal transients are evaluated on all un-cracked models and one crackedmodel. The transients are defined in Table 10. In the un-cracked models, the SOLID70 elementtype is used for the thermal analysis and the SOLID45 element type is used for the subsequentstress analysis. In the cracked model, the SOLID70 and SOLID 90 element types are used forthermal analysis and the SOLID45 and SOLID95 element types are used for the subsequent stressanalysis. During the thermal analysis, the air elements between the nozzle and the vessel bore areactivated to simulate the conduction heat transfer between the two surfaces. These elements areremoved during the subsequent stress analysis. The RPV clad is considered in both the thermaland stress analyses so that the differential thermal expansion stresses induced by the cladding arecaptured.

The thermal stress analysis is performed in two parts. First, a thermal run is completed usingSOLID70 or SOLID70 and SOLID90 elements. A temperature solution is output from thethermal run. Then the thermal stress run is performed using the temperature solution from the


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thermal run as input. The temperatures are applied to the structural model for each time step, andthermal stresses are calculated using SOLID45 or SOILD 45 and SOLID95 elements. As statedpreviously, symmetric boundary conditions are applied to the symmetry faces of the instrumentnozzle model, and the nodes at the end of the nozzle are coupled in the axial direction to simulatethe effects of the attached piping. For the cracked model, the symmetric boundary conditions arenot applied to the crack face. The cracked model geometry is taken from Table 1 with a 251"vessel, 3" nozzle, and long J-groove weld with Alloy 600 nozzle material.

One additional evaluation is performed for the un-cracked model by applying the thermalboundary conditions directly to the vessel base metal, i.e., the clad is removed from the model.This case is run to investigate the effect of ignoring the clad entirely in the thermal transientanalysis as authorized in the ASME Code when the clad thickness is less than 10% of the wallthickness. The geometry of this model is taken from Table 1 with a 251" vessel, 3" nozzle, andlong J-groove weld with Alloy 600 nozzle material.

The ANSYS input files for the thermal transient analyses are listed in Appendix B.

5.3 Pipe Reaction Load Case

Per Section 2.3.3, three moments and an axial force are applied to an un-cracked model asseparate load cases. The pipe load cases are evaluated using a nozzle geometry taken from Table1 with a 251" vessel, 3" nozzle, and long J-groove weld with Alloy 600 nozzle material.

The unit force (1,000 lbs) and the moment loads (1,000 in-lbs) are applied to a pilot node usingthe CONTA175 and TARGE170 element types. All loads are applied separately. The full modelis used for this load case. Symmetry boundary conditions are applied to the lateral boundaries ofthe FEM. One horizontal boundary is fixed in the vertical direction to prevent rigid body motionof the RPV shell. For this load case, the clad elements are removed. Figure 13 illustrates theapplied axial forces and boundary conditions for this load case.

The ANSYS input files for the piping load analyses are listed in Appendix B.

6.0 PRESSURE, THERMAL, AND PIPING LOAD RESULTS

This section presents the results of each load case, separately.

The stress extraction path for all load cases is chosen starting from the instrument nozzle comer atthe vessel inner diameter in the axial direction along the vessel. This path then travels at a 450angle through the thickness of the vessel base metal. Figure 14 shows this path on the FEM. Thepiping reaction load case contains additional path for stress extraction, which are discussed inSection 6.3.

6.1 Internal Pressure Load Case

Figure 15 illustrates the circumferential stress distribution for one of the un-cracked models forthe pressure load case. The circumferential, or hoop, stresses are used to calculate the stressintensity factor for the postulated nozzle comer crack since this stress is the largest pressure stress(i.e. higher than the axial stress). The contour scale for Figure 15 has been truncated to exclude


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the peak stresses at the nozzle to RPV shell discontinuity. Since the analysis is linear elastic, andthe FEM includes the small gap between the instrument nozzle and RPV with a fine mesh in thisregion, the stress solution exhibits a large elastic pseudo-stress adjacent to the geometricdiscontinuity. This pseudo-stress may be ignored since the real structure would exhibit localyielding which would redistribute the stress; whereas, for the linear-elastic simulation theelastically calculated stress is intensified because of the sharp notch in the FEM. Defining thecontour plot scale such that this local stress is excluded enables a more accurate presentation ofthe stress distribution throughout the remainder of the model, in the region of interest for thepostulated nozzle corner crack.

Figure 16 shows an example of the path hoop stress distribution for the internal pressure load casewith a 3" nozzle, a 251," vessel and a long J-groove weld with Alloy 600 nozzle material.Applying the polynomial coefficients shown in Figure 16, along with the ¼ thickness postulatedcrack length to Equation 1 yields stress intensity factor, K1, due to a unit pressure load. For somemodels, when the path went through the small air gap between the instrument nozzle and theRPV, The hoop stresses extracted along the postulated crack path were lower (See Figure 17)because the path crossed over the modeled air gap. In order to investigate if this introduced asignificant non-conservatism into the path stress curve fit used to calculate the stress intensityfactor, the "long J-groove weld" cases were introduced into the parametric study. For the caseswhere the path defined for stress extraction crosses the air gap, the curve fit is determined withoutincluding the hoop stress distributions immediately adjacent to the air gap which is influenced bythe gap; in other words, the region of the path significantly affected by the air gap are excluded.Figure 17 shows an example of this processing. The stress intensity factors calculated for all 38models are summarized in Table 13. This table reports BIE/IF K, values calculated for each of theparametric runs performed for this study. Parameters changed include nozzle diameter andthickness, j-weld dimension, nozzle insert material, and RPV diameter. These results are used todevelop the bounding solution against which the plant specific results are compared.

Figure 18 displays the KI distribution along the postulated crack front for the internal pressure FELEFM load case. Also shown on Figure 18 are the K, values calculated for the same modeldimensions using the BIE/IF solution. This comparison is provided to illustrate the conservatisminherent in using the BIE/IF approach to calculate the KI for the nozzle corner crack. Since theBIE/IF solution provides a K1 representative of the root mean square (RMS) K, along the crackfront the BIE/IF result is compared to the RMS of the K, distribution along the crack frontobtained from the FE LEFM analysis. The results provided in Figure 18 show that the BIE/IFsolution bounds the RMS value obtained using FE LEFM. An additional BIE/IF comparison,with a path starting from vessel bore rather than the nozzle bore, is shown in Figures 18 and 19.The results obtained from this path also show that the BIE/IF solution provides bounding resultscompared to the RMS value of the FE LEFM results; however, the path defined at the vessel boreexhibits less conservatism.


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6.2 Thermal Transient Load Cases

The hoop stresses obtained from the un-cracked FEM for both thermal transient cases consideredin this evaluation are extracted for all time steps along the paths shown in Figure 20. Figure 16shows an example of the path hoop stress distribution for the thermal ramp load case with a 3"nozzle, a 251" vessel and a long J-groove weld with Alloy 600 nozzle material. Paths are definedfor a case where the RPV clad is excluded in the path definition, and for a case where the pathincludes the RPV clad. Figure 20 shows these two paths. A third order polynomial curve fit isdetermined for the path hoop stresses at each time step in the thermo-elastic analysis. A stressintensity factor for each thermal transient calculated at each time step is then calculated using thepolynomial coefficients and the ¼ thickness postulated crack length with Equation 1. Themaximum K, for each thermal transient case is summarized in Table 14 for each model.

From the thermal transient analyses using the FE LEFM model, the K, distribution along the crackfront obtained for both thermal transients considered are calculated and shown in Figures 21 and22 along with comparisons to the results obtained using the BIE/IF solution. The maximum K,along the crack front and RMS K, taken over the crack front, for the FE LEFM analysis, at eachtime step is calculated and shown in the top of Figures 23 and 24 for the thermal ramp and shock,respectively. A K, distribution along the crack front, at the time for which the maximum K, overthe entire transient and across the entire crack front occurred, and a K, distribution along the crackfront, at the time for which the maximum RMS K, along the crack front occurred, for the FELEFM analysis is also calculated and shown in the bottom of Figures 23 and 24 for the thermalramp and shock, respectively.

A comparison of the stress intensities for the paths including and excluding the clad is listed inTable 15. This comparison is only for illustrating the effect of the clad to the results and not forthe evaluations. As can be seen, the path including clad has a higher K, value for the thermalramp load case because of the differential thermal expansion stresses induced in the clad.

The results of the comparison between the BIE/IF and FE LEFM results show that the BIE/IFresults bound the RMS K1 obtained for each thermal transient.

6.3 Pipe Reaction Load Case

Due to the complexity of the applied load, the location of the postulated crack orientation at whichthe effect of the pipe loads is maximum is not obvious; therefore, path stresses were extractedalong an additional path oriented along a plane rotated 90 degrees from the orientation at whichthe pressure hoop stress is maximum. This additional path is shown in Figure 13.

Table 16 summarizes the maximum stress intensities calculated for each piping load. The resultsof the pipe reaction load cases show that contribution of attached piping loads to the K, calculatedfor the postulated ¼ thickness crack is significantly less than the K, obtained for the internalpressure and thermal load cases. These results show that the pipe reaction loads may be neglectedin the evaluations of water level instrument nozzles for P-T curve development.


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7.0 OBSERVATIONS AND DISCUSSIONS

For the unit pressure load case, the BIE/IF solution is conservative compared to RMS andmaximum values obtained from FE LEFM, as shown in Figure 18. Table 17 shows the summaryof these results. For the cases considered in this study, the BIE/IF solution is observed to beapproximately 39% conservative when compared to the RMS K, obtained from a more detailed3D FE LEFM analysis of the same configuration and load.

For the thermal ramp and thermal shock load cases, as shown in Figures 23 and 24, the maximumK, along crack front over the transient and the maximum value of the RMS KI occur at differenttimes in the transient.

Consideration of the clad in developing the curve fit used with the BIE/IF solution has asignificant effect on the results.

Further, the BIE/IF solution is shown to be conservative when compared to the RMS valuesobtained from the FE LEFM analysis. Table 17 summarizes the results of a comparison betweenthe thermal ramp and thermal shock RMS K, obtained using the BIE/IF solution and from the FELEFM analysis. This comparison shows that the BIE/IF solution is approximately 46% and 51%conservative for the thermal ramp and thermal shock transients, respectively.

The BIE/IF solution is shown to not bound the maximum K, along the crack front obtained fromthe FE LEFM analysis. Although this observation is considered to be important in order tounderstand the nature of the BIE/IF solution, it is not considered to be an indication of aninadequacy of the BIE/IF solution. For P-T curve analysis a conservative ¼/4 thickness flaw isassumed; a real flaw does not exist. Consequently, the inherent conservatism in assuming a ¼thickness flaw is considered sufficient such that requiring use of the maximum K1 along the entirecrack front is considered to be excessively conservative. The RMS KI along the crack front isconsidered a more reasonable indicator of the driving force acting on the crack and moreappropriate for consideration in development of P-T curves.

Tables 13 through 14 summarize the results obtained for the pressure and thermal load cases usingthe BIE/IF method. It can be seen that for the internal pressure load case, the results obtained forthe Alloy 600 nozzle bound the results obtained for the other two nozzle materials. It can be seenthat for the thermal transient load cases, the results obtained for the 304 SS nozzle material boundthe other two nozzle materials. This trend is consistent with expectations since the coefficients ofthermal expansion for stainless steel are significantly larger than for the LAS vessel material;therefore, during a cool-down transient the instrument nozzle will be held in tension by the largerLAS vessel wall which will cause the path stresses calculated along the portion of the nozzle pathin the stainless steel nozzle to be highly tensile. In comparison, the coefficients of thermalexpansion for the Alloy 600 and carbon steel materials used for instrument nozzles are muchcloser to those for the LAS RPV material and the differential expansion stresses induced in thenozzle for these materials are significantly less than for the stainless steel nozzles.


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The results of the present study, shown in Table 16, show that the pipe reaction loads do not havea significant contribution to the stress intensity factor calculated for the postulated nozzle comercrack; therefore, attached piping loads may be neglected for P-T curve analyses performed for thewater level instrument nozzles.

Significant variation in results obtained using the BIE/IF method can be seen based on differencesin analytical practices such as:

" Include clad in thermal and stress run, exclude clad in post-process (shown in Table 14)" Include clad in thermal and stress run, include clad in post-process (shown in Table 15)" Exclude clad in thermal and stress run (shown in red line in Figures 21 and 22)" Orient path at comer of nozzle or comer of RPV bore (shown in Figures 19 and 20)

" Quality of the curve fit of the path stress distribution

Although these trends are not surprising in the sense that analyst judgment and assumptions inconducting an analysis have long been known to affect the results of the analysis, the points aboveare made simply to document the importance of the items on the results obtained using thisapproach.

Overall, the following observations are concluded:

" The BIE/IF method is conservative and thus acceptable." The water level instrument (WLI) nozzle designs with a SS nozzle insert will exhibit

significantly larger KIT results than the other nozzle designs. This observation isreasonable and understandable; thus, the results are not problematic.

" Attached piping loads are not important and can be neglected for WLI nozzles. Thissimplifies the analysis and reduces the burden on the utility.

8.0 GENERIC METHODOLOGY FOR K, ESTIMATION

8.1 Stress Intensity Factor Empirical Equation Development

Table 13 is presented in Figure 25 with a plot of the stress intensity factors obtained for the 1000psi internal pressure load case as a function of R/tv*•1(tv/4+t,). Where R, tv, and tn are the vesselradius, vessel thickness, and instrument nozzle thickness, respectively. A linear equation isgenerated as shown in Figure 25. The best estimate linear equation for the 1000 psi internalpressure load case is:

K1_Pressure 2.9045*[R/tv.ý,(tv/4+t,)] - 4.434 (3)

where R is the vessel nominal radius (in.), tv is vessel thickness (in.), and tn is the nozzle thickness(in). The correlation coefficient for this curve fit, R-squared value, is 0.823.


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Table 14 with maximum K, for the thermal ramp load case is presented in Figure 26 with a plot ofthe 100 0 F/hr thermal ramp stress intensity factors presented as a function of a(tv + tn). A linearequation is generated shown in Figure 26. The best estimate linear equation for the 100 0 F/hrthermal ramp is:

Klramp = 874844[ca(tv + tn)] - 20.715 (4)

where t, is the vessel thickness (in), tn is the nozzle thickness (in), and a is nozzle materialthermal expansion coefficient (in/in/°F) at the highest thermal ramp temperature. The R-squaredvalue is 0.942.

Table 14 with maximum K, for the thermal shock load case is presented in Figure 27 with a plotof the 450 'F thermal shock stress intensity factors presented as a function of ac(tv + t,). A linearequation is generated and shown in Figure 27. The best estimate linear equation for the 450 'Fthermal shock is:

KIshock= 872475[a(tv + tnA)] + 80.290 (5)

where tv is the vessel thickness (in), t, is the nozzle thickness (in), and cc is nozzle materialthermal expansion coefficient (in/ini°F) at the highest thermal shock temperature. The R-squaredvalue is 0.618.

Considering the inherent conservatism of the BIE/IF solution as discussed in Section 7, a best fitcurve is considered acceptable and to effectively bound the K, along the crack front as would bedetermined from a more accurate FE LEFM analysis. Consequently the best estimate curve fit isused rather than an upper bound curve fit. Use of an upper bound curve fit would introduceexcessive conservatism in the results.

8.2 Verification of Stress Intensity Factor Empirical Equations

SI performed three plant specific instrument nozzle analyses in which the BIE/IF solution wasused to obtain a pressure and thermal KI [9, 10, 11]. The objective of these analyses was to obtaina population of plant specific results which could be used to investigate the validity of the genericinstrument nozzle results provided in this calculation package. Adequacy of the generic equationsprovided in this calculation package are considered to be demonstrated if the generic equationssuggested in Section 8.1 above are shown to be close to the results provided in [9, 10, 11] forthree specific BWR instrumental nozzles. The plant specific configurations documented in [9, 10,11] were selected since they provide a sample which spans the range of dimensions and materialspresented in the BWR fleet. Table 18 compares the predicted stress intensity factors for thethermal and pressure load cases using equations above, with the plant specific results obtainedfrom [9, 10, 11]. It can be seen that the predicted results agree well with the results obtained fromthe plant specific analyses. Since the BIE/IF solution has been shown to be conservative byapproximately 40-50% when compared to a more accurate FE LEFM analysis, the results of thebenchmark of the generic pressure and thermal load case equations is considered acceptable.Consequently, Equations 3 and 4 may be used to obtain plant specific K, values for an internal


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pressure and 100 ° F/hr load case. These results can then be used to develop plant specificinstrument nozzle P-T curves for consideration in development of a plant specific beltline P-Tcurve without having to construct a plant specific instrument nozzle FEM.

9.0 SUMMARY

Thirty-eight (38) quarter symmetric instrument nozzle finite element models and one fullinstrument nozzle finite element model were developed and applied to analyze pressure, thermal,and attached piping load cases. Parametric analyses were performed in which critical dimensions,materials, and typical analysis assumptions were investigated. Hoop stresses were extracted fromthe FE analysis results and the stress intensity factors for all parametric cases were calculatedusing a BIE/IF stress intensity factor solution proposed for the instrument nozzle comer crackconfiguration. Further, one finite element linear elastic fracture mechanics model was built andused to benchmark the accuracy of the proposed BIE/IF solution. Unit pressure loads, thermalramp loads, and thermal shock loads were applied to the FE LEFM model and results from the FELEFM model and the BIE/IF solution were compared. The BIE/IF solution is shown to beconservative compared with the more detailed FE LEFM analysis. Pressure and thermal stressintensity factor equations are presented which can be used by any BWR containing a 2" or 3"instrument nozzle, with a configuration consistent with those evaluated in this study, to assess theeffect of the instrument nozzle on the beltline P-T curves. It is important to note that should thebounding values obtained using the methods in this calculation show that the instrument nozzlecontrols a portion of the beltline P-T curve then the utility can attempt to further refine theanalysis by performing a plant specific FEA using the BIE/IF approach or by performing a plantspecific FE LEFM analysis. Table 19 summarizes the Kijpressure, Kliramp, and K1 _shock best fitequations determined for the BWR 2" or 3" water level instrument nozzle.

File No.: 0900876.304Revision: 0

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10.0 REFERENCES

1. ASME Boiler and Pressure Vessel Code, Section XI, "Rules for Inservice Inspection ofNuclear Power Plant Components," Appendix G, "Fracture Toughness Criteria for ProtectionAgainst Failure," 2004 Edition with no Addenda.

2. ANSYS Mechanical and PrepPost, Release 11.0 (w/Service Pack 1), ANSYS, Inc., August2007.

3. ASME Boiler and Pressure Vessel Code, Section II, "Materials," Part D, "Properties(Customary)," 2004 Edition with no Addenda.

4. Warren M. Rohsenow and Harry Y. Choi, "Heat, Mass and Momentum Transfer," Prentice-Hall, Inc. 1961.

5. Delvin, S. A., and P. C. Riccardella, "Fracture Mechanics Analysis of JAERI Model PressureVessel Test," ASME, 78-PVP-91, New York, April 5, 1978 (originally presented at the jointASME/CSME Pressure Vessels and Piping Conference, Montreal, Canada, June 25-30, 1978),SI File No. 1000720.206.

6. ASME Boiler and Pressure Vessel Code, Section IX, "Qualification Standard for Welding andBrazing Procedures, Welders, Brazers, and Welding and Brazing Operators," 2004 Editionwith no Addenda.

7. Ganta, B. R., D. J. Ayres, and P. J. Hijeck, "Cladding Stresses in a Pressurized Water ReactorVessel Following Application of the Stainless Steel Cladding, Heat Treatment and InitialService," Pressure Vessel Integrity - 1991, PVP-Vol. 213 (MPC-Vol. 32), ASME, June 1991,pp. 245-252, SI File No. 0900876.203.

8. ASME Boiler and Pressure Vessel Code, Section III, "Rules for Construction of Nuclear

Facility Components," 2004 Edition with no Addenda.

9. SI Calculation No. 0900876.301, Revision 0 Draft, "Instrument Nozzle Stress Intensity FactorCalculation for Plant Specific 251-Inch BWR."

10. SI Calculation No. 0900876.302, Revision 0 Draft, "Instrument Nozzle Stress Intensity Factor

Calculation for Plant Specific 218-Inch BWR."

11. SI Calculation No. 0900876.303, Revision 0 Draft, "Instrument Nozzle Stress Intensity FactorCalculation for Plant Specific 238-Inch BWR."

12. Newman, J.C., Jr., and Raju, I. S., "Stress-Intensity Factor Equations for Cracks in Three-dimensional Finite Bodies," Fracture Mechanics: Fourteenth Symposium - Volume I: Theoryand Analysis, ASTM STP 791, J.C. Lewis and G. Sins, Eds., American Society for Testingand Materials, 1983, pp 1-238-1-265.

13. "BWRVIP-49-A: BWR Vessel and Internals Project, Instrumental Penetration Inspection andFlaw Evaluation Guidelines", EPRI, Palo Alto, CA: 2002, 1006602, SI File No. BWRVIP-01-249-AP.


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Table 1: Dimensions Used for Instrument Nozzle Parametric Studies.

Nozzle Size 2-inch Nozzle' <' : I 3-inch Nozzle

Vessel Size <~21238 [218>½9 205'~ 251 238 21 205~

ri (in) 126.162 120.000 110.157 103.000 126.162 120.000 110.156 103.000

tc (in) 0.337 0.188 0.2199 0'188 0.339 0.188 0.219. 0.188

Vth (in) 6.102 5.625 5.375 5.438 6.102 5.625 5.375 5.438

rol (in)v 1.203 1.245 1.203.,. 1.245. 1.500 .1.500" 1.500 1.500.

ril (in) 0.969 0.969 0.969 0.969 0.965 0.969 0.969 0.969

ro2 (in). 1.245 1.245 1.245" 1.245 . 1.500 1.500 1.500' 1.500

Hi3 (in) 1.250 1.253 1.250 1.253 1.508 1.508 1.508 1.508

ro4 (in) 7.750 7350 7.750 7.750 7.750 .7.750 7.750 .. .750

ri6 (in) 1.300 1.300 1.250 1.300 1.555 1.555 1.508 1.555

ro6 (in) > 1.295- 1.295 . 1.245 1.295 ,W1.550 1.550 1.500 1.550

I1 (in) 3.000 2.000 3.000 2.000 2.000 2.000 3.000 2.000

13 (in) 4.438~ ' 448~ 4.438 4;438 4. 43818 4,48"4438 " 4.438

14 (in) 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375

15 (in) 14.688. 14.688<. 14.688 • ' ýý14,688 14.688 14.6688 14.688. 1 14.•688"

16 (in) (1) 0.964 0.813 0.844 0.813 0.964 0.813 0.844 0.813

17• (in) 0.7o14 0.563, 0.594 0.563 0.7 , 14 0.563 0.594: 0.563

18 (in) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

td (in) 1.654 1.125 . 1.125 1.125. 1.654Y" 1.1125~~ 1.125 1.125

Is (in) 0.063 0.063 0.0625 0.063 0.063 0.063 0.0625 0.063

d:s (in) 3.500 3.500 2.688, 3.500.> 3.5001> 3.500 2.688 3500,

R1 (in) 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

R2 (i) 05 0.250 0250 0.250 0.2510 0.25> o0250 0.250 0.250

af (0) 14.000 0 14.000 0 0 0 14.000 0

af (•0) 15.000 15.000 15.000 15.000 15.000, 15.000 1 5.00& 15.000.

af2 (0) 45.000 45.000 45.000 45.000 45.000 45.000 45.000 45.000

af3 (0) 15.000 15.000 1i5000 : o 15.000. o15.000 15.000 1500oo0 15.000

Note: 1. For the longer J-groove weld case, 16 and 17 are increased by 0.5 inches.


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Table 2: List of Typical Instrument Nozzle Assembly Materials.

.t6om'ponent Material

RPV Shell SA-533 Gr. B Class 1

RPV Cladding . ' Type 304<Stainless Steel :Alloy 600 (use N06600), Stainless Steel

Instrument Nozzle (use SS 304), or Carbon Steel (use SA-541 Class 1)

Vessel Pa. SA-533 Gr. B Class 1J-Groove Weld Butter Alloy 600 (use N06600)i,-Groove .Weld i~7'• . AIl6yý.600'(use-N`06 1610)Nozzle-to-Safe End Weld Alloy 600 (use N06600)

S a fe End SA-1 82 F304"

Table 3: Material Properties for SA-533, Grade B, Class 1 13].Temperatu re TYoung's Modulus Mean Thermal ExpansionI Thermal CondUctvty e

(OF) { ( psi) :.4 (x10 in/in/OF) 4 fh (.tu/hr.ft.eF.. (t•..u/lb.F)70 29.0 7.0 23.7 0.106

200 . 28.5 7.3 23.5 0.113

300 28.0 7.4 23.4 0.119

400 27.6` 7.6'~ 23.1 0.125500 27.0 7.7 22.7 0.130

600 (p = 26.3,' 7.8at ( 22.2 0.1-35Density (p) 0.283 ibm/in3 , assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (-u) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).

Table 4: Material Properties for Type 304 Stainless Steel (18Cr-8Ni) [3].

Temperature Yo 'sMduu Mean Thermal Expansion Thermal Codc ivt SpcfcHaff) !i (xlOi psi) •i x1i:'• -6: ini/F (Btuhr-f-'F (Bu/Ib-F

70 28.3 8.5 8.6 0.114

200 27.5" 8.9' 9.3 .0.119

300 27.0 9.2 9.8 0.122

400> 26.4 '9.5 10.4 0.126500 25.9 9.7 10.9 0.129

6 0 0 D s ( = 25.3 asue 9.8 i 11.30 A m o0.1305

Density (p)R 0.290 ( i/in 3, assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (i) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).


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Table 5: Material Properties for Alloy 600 (N06600) 13].Temperature Young's Modulus Mean Thermal Expansion J Thermal Conductivty Specific Heat

(OF) j . X106 psi. [ J (x.i66 iniin/nF) (Btu/hr-ft-OF.• j (BtU/ ibm- 0 F)

70 31.0 6.8 8.6 0.108

200 30:3 7.1 ,.9.1 :"0.113300 29.9 7.3 9.6 0.116

400...29.4 7. •510.1 0.118.iv500 29.0 7.6 10.6 0.120

600 28.6< 7.8 11.1 'i 0.122

Density (p) = 0.300 ibm/in-, assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (u) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).

Table 6: Material Properties for Vessel Pad, Material Assumed Equivalent to Vessel(Table 3) [3].

I 6ng's Modulus~ Temlcnductivity SeiicHaT~emperature Y IMean Thermal Expansion Therma SpciioHa

(OF) (X10 6 psi) J (xlO- in/in/F) <i , (Btuhr- ) i, ft-' (Btu/Ibm-FF)

70 29.0 7.0 23.7 0.106

200 28.5 7.3 23.5. 0.113300 28.0 7.4 23.4 0.119

400 27.6..7.6 23.1 . 0.125500 27.0 7.7 22.7 0.130

600 '1 26.3 .7.8 22.2 2 . 0.135

Density (p) = 0.283 ibm/in3 , assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (u) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).

Table 7: Material Properties for SA-182 F304 (18Cr-8Ni) [3].Temperature Young's Modulus Mean Thermal Expansion. Thermal Conductivity Specific Heat

(OF)_____4___ psi)< (X1O, 6 in/in/0F). (Btu[ -f [ (Btu/ lb~, -')

70 28.3 8.5 8.6 0.114__ _ _ __ _ _ __ __ __ __ __ _ 8.9 9.3 0'.119

300 27.0 9.2 9.8 0.122

400 26:4 9.5 10.4. 0.126500 25.9 9.7 10.9 0.129600 25.3, 9.8 113 0.130

Density (p) = 0.290 Ibm/in 3, assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (u) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).


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Table 8: Material Properties for SA-541 Class 1 [3].

TemnperatureA Yo6ung's Modulus% Mean Thermal Expansion TJhermal cConductivity Specific Heat(xO___Psi)(OF) ( •'lO6 psi) i (x1O-6 infin/oF) j J (Btu/hr-ft-0 F) (B•tu/ lb, -F)

70 29.2 6.4 34.9 0.102

200 28.6,- 6:7 33.7, 0113300 28.1 6.9 32.3 0.118400 27.7 7.1. 30.9,, 0.122'

500 27.1 7.3 29.4 0.127600 26.4•- 7.4 28.0 0.132,

Density (p) =0.283 Ibm/in3 , assumed temperature independent (see Section 3.0, Assumption #5).Poisson's Ratio (u) = 0.3, assumed temperature independent (see Section 3.0, Assumption #5).Specific Heat = thermal conductivity / (thermal diffusivity * density).

Table 9: Air Properties [4].

Tepeatre Density Thermal Conductivity~ Specific,'HeA't

70 0.075 0.015 0.240

200 0.060: 0.018 0.242

300 0.054 0.020 0.244

400: 0.048 0.023, 0.246

500 0.041 0.025 0.248

600 0.038 0.027 .0.251

Table 10: Thermal Transient Definition.

•-; <..j -> ,Time Temperature, HeatTransfer Coefficient (Btu/hr-ft2 -•F)•'

.- J• ~ s),. [:j<,A- ).. Vessel. INoizle~l ', . outside ,i

0 550 500 500 0.2

Thermal 6,300 -3.75 500 500 0.2-

Ramp 6,900 330 500 500 0.2(100 °F/hr cooldown) 15,180 100 500o 500 0.2

20,000* 100 500 500 0.2

Thermal 0 550- 500 500 0.2

Shock 1 100 500 500 0.2(450 'F down shock) 20,000* 100 500 500 0.2

* After 20,000 seconds, a steady state condition is applied


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Table 11: Mesh Density Check Results for the Un-cracked Models.

Mesl•Factor 3 Stress intensity (psi) "Difference(%) jj

1.0 69,340 --

1.4 69,442 0.151.8 69,499 0.232.0' 69521 ,: ,. 0.26;1

Mesh Factor is defined as the ratio of model elements with respect to the baseline case (MeshFactor 1.0)

Table 12: Mesh Density Check Results for the Cracked Models.

~K, (ksi-ýin) K ->% Change'Base~ 2x 3x~ 2)(- B~ 3x -2x~

Max!I 60.7 60.5 60.6 -0.2% 0.0%

Min: 52.5. 49.9. 46.7 -4.9%,. -6.5%

RMS' 55.7 55.0 54.6 -1.3% -0.8%

Table 13: Summary of Stress Intensity Factors for 1000 psi Pressure Load Case withDifferent Nozzle Material.

RPV Nozzle Size JGr 1o"ve . .... ... .....

•Diam eter- Nom ial:Diaj X-G - ,...(in.)i Tnhickness(in.) W : Alloy 600 e Al y 600 304 S5 -

205 2 / 0.28 long 62.84 short 68.02 -

218 " 2/0.23 long 66.95 short 71.70 70'40,.

238 2 / 0.28 long 71.35 short 78.09 76.82

2515, ::2 / 0.231- long 72.37 short 78.00 76.76 76.62

205 2 / 0.70 long - short 74.25 - -

218:. 2/0.70 long'.., short 79.69 77.30

238 2 / 0.70 long short 84.45 81.56

251 -_2/0370 long . short .. 85.11. 83.53.. -

205 3 / 0.53 long 66.54 short 71.68 -

218 33,0.53, long-, 71.01 short, 78.46 76.25 -

238 3 / 0.53 long 75.63 short 81.42 81.10

lo2513 / 0.54 .. long: 76.59 short 83.94 81.53"': 82.52

205 3/0.70 long short 77.04

.218. : ' ./ , 0.70 long:. . short 83.35- 80.71 -

238 3 / 0.70 long short 87.65 84.72

251 3 / 0.701"- long .... _ - '._.. short 88.35. 85.48 -


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Table 14: Summary of Stress Intensity Factors for Thermal Transient Load Cases withPath Excluding the Clad.

RPV ... Nozzle Size Max. K, (ksiin~Diameter Nominal.Dia./ Groove Thermal~ Thermal

Material(im);. Thcilcknesst (in.)• JWeld , •Ramp,. Shock

205 Alloy 600 2 / 0.28 long 18.77 120.16218 Alloy 600 2 / 0.23 long 18.44,-,, 116.531,'238 Alloy 600 2/0.28 long 19.80 122.30251 Alloy 600 2 / 0.23 long 22.23: 117.67T'ý

205 Alloy 600 3 / 0.53 long 19.58 124.98218 Alloy 600 3 / 0.53. long 19.22 12i51.'I-238 Alloy 600 3/0.53 long 20.67 127.28251 Alloy 600 3 / 0.54 long. 23.15 22.60:'

205 Alloy 600 2/0.28 short 19.41 123.68218 Alloy 600 2 / 0.23 short 18.83 117.98.238 Alloy 600 2 / 0.28 short 20.79 128.02251 Alloy 600, 2/0.23 . short 22.48 .. 118.43205 Alloy 600 3/0.53 short 18.11 115.36218 Alloy 600 3/0.53 short 18.31- 114.80

238 Alloy 600 3/0.53 short 19.00 116.72251, Alloy 600 " 3/0.54 short ., 21.27,''' 112.35218 304SS 3/0.53 long 28.29 131.13238 304-SS. * 3/0.53 ] long 32.22: Z 'J 138.87251 304SS 3/0.54 long 33.86 134.05

251, CS ! 3/0.54" long:. 22.44. 124.07205 Alloy 600 3 / 0.70 long 19.51 123.78218i, ;AlloyI600, '3/0.70:. long 120.919.2 08238 Alloy 600 3 / 0.70 long 20.56 125.78

L 251, . Alloy600 3/ 0370 long, 22.99 121.62k

218 304SS 3/0.70 long 33.95 134.37238,- 304S" j 3/0.70 long. 353293 '39.48

251 304 SS 3/0.70 long 38.87 136.62


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Table 15: Comparison of Stress Intensity Factors for the Paths Including/Excluding theClad under Thermal Transient Loads.

TP oze J Path Without Clad' Path With Clad~Diameter. Size> .Groove% __.__ -,.._,_____________ .______________

.... in;)'>.(in..) .Weld Max" Kr (ksi;-4in)Jfor Thermal Ramp

205 3 long 19.58 21.67

218' 3 long ' 19.22 21.78238 3 long 20.67 22.81

251 3 long 23.15 27.58

Max. K, (ksi•4in) for Thermal Shock

205 3 long 124.98 139.09 :

218 3 long 121.51 138.07

238'• 3 long 127.28 .. 141.39''

251 3 long 122.60 144.31Note:

1. The maximum K, is the peak K, obtained using the BIE/IF solution throughout the entiretransient solution.

Table 16: Summary of Stress Intensity Factors for the Attached Piping Load Cases.

Piping Load Direction Value 4iax ,..____________ ___________ l .. (ksi-1in)

Fx Axial 1000 lb 0

___......_Mx_ Torsion:- 1000 in-lb 2.'55&-05.

MY Bending 1000 in-lb 1.91E-05

__ .M___,_____ Bendihg, 10001in-lb, 2.28E-05'"

Table 17: Summary of FE LEFM and BIE/IF K, Results.

Load F LEFMRMS K BiE/iF KIkelativie Duff.

_______________ (k'si'-Vin) K~(ksii-in)j N %Pressure 55.00 76.59 39%

Thermal Ramp 15.67 22.9 46%

Thermal Shock 77.791 117.752 51%

1. The maximum RMS K, is taken.2. The BIE/IF K, value is taken at the time corresponding maximum FE LEFM RMS K1.

Note:


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Table 18: Verification of Stress Intensity Factors.: Reference•1[0]J [ Reference [11] [ Reference [12]

Vessel Nominal Diameter (in) 251 218 238Dimensions Vessel Tce(n 6.102:. 5.375 6.000::5

Nozzle Thickness (in.) 0.5315 0.27625 0.7145

Nozzle Material Alloy 600, Alloy 600 . 304SSMaterial : Nozzle Thermal Expansion

____- _ _77 Coefficient (in/in/F).70e-6 7.70e-6 9.75e-6

K1 per Eq. 3 (ksi- 4in) -, , , . 81.24 70.53 81.29

Pressure KI per Reference (ksi-4in) 72.88 71.26 69.40

Error (%)• 11.47%, -1.02% 17.13%,

K, per Eq. 4 (ksi-in) 23.97 17.35 36.56

Thermal Ramps K1-per Reference (ksi4in) 24.5 17.87 38.6

Error (%) -2.16% -2.89% -5.29%

K1 per Eq. 5 (ksi-Nin)''. 1124.85:. 118.26 137.41,

Thermal Shock K, per Reference (ksi4in) -

Error (%) .. ..:._ _ "_ _ _ _ _

Table 19: Summary of K, Empirical Equations.

..;...K, Pressure Load Thermal Ramp Load 'TeralShock Lo.ad......

Kip... = 2.9045*[R/td(tv/4+tn)] -4.434 K1 r,,p= 874844*[ct(t,+t,)] - 20.715 Kl_shock 872475*[t(t,+t,)] + 80.29

Equation.3 . Equation 4. Equations5Where R is the vessel radius (in), tv is the vessel thickness (in), tn is the nozzle thickness (in), and cc is nozzle materialthermal expansion coefficient (in/in/°F).


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Nozde Symef/r Line

Aif elements di-ringthermail cancysys

PostulotedCrock Tip

Ve-sel

Direction

Figure 1: Stress Path Orientation in Postulated Flaw.

ri : 3r61

Figure 2: Generic Model Dimensions.


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Thermal Ramp Transient

C-

600

500 i..

400

300 L7

200.

100

0

5000 10000

Time (sec.)

15000 20000

Thermal Shock Transient

CL

E

600

500

400

300

200

100

0

0 5000 10000

Time (sec.)

15000 20000

Figure 3: Thermal Transients.


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QUARTER-CIRCULAR CRACK IN QUARTER-SPACE2a a423(4a 3K1 :7 0.723Ao + 0.551A, + 0.462A2 + 0.408A3 ]

Figure 4: BIE/IF Solution for Instrument Nozzle Evaluation.

ELEMENTS

HAT NUM

3 i;,.. trument Nozzle with 251 RPV

Figure 5: Quarter Symmetric FEM of Instrument Nozzle and Reactor Pressure Vessel.


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Figure 6: Finite Element Fracture Mechanics Model.

_ _ _ __ _ _ _ - -AN 1I!

R~V

d,~

I I II I I

I I3 inch Ins

Figure 7: Structural Boundary Conditions and Internal Pressure Load Applied toUn-cracked Model.


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E.LEME0NTSAN

<001 -0450 0079 -070? -235,70.5 ''-II"~ I -z-0006 '0404 '70~ 4470 1000 0 U4 Nj 47N

Figure 8: Structural Boundary Conditions and Internal Pressure Load Applied to CrackedModel.

-AL IA 2--

Baseline Mesh (Mesh Factor 1.0) Finest Mesh (Mesh Factor = 2.0)

Figure 9: Mesh Density Check Configurations for Un-cracked Models.


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Mesh Factor = 1.0AN*

Mesh Factor = 1.4

392& 9)WJI t

Mesh Factor = 1.8 Mesh Factor = 2.0

Figure 10: Mesh Density Check Results for Un-Cracked Models.

(Units in psi)

Baseline Mesh (Mesh Factor = 1.0) Finest Mesh (Mesh Factor = 3.0)

Figure 11: Mesh Density Check Configurations for Cracked Models.


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70 ............................................................................I.....................................................................................................................

60

50

40

30

20

10

0

Noz

-BaselineCase -Mesh Factor = 2.0 -Mesh Factor = 3.0

S ..................... .......................... 30..................10 20 300

zle Bore40 50

Angle (Degree)

60 70 80 90

RPV ID

Figure 12: Mesh Density Check Results for Cracked Models.


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FLEMENT5TYPE NU•M

AMNDEC 14 -'01

21. 42:0

Horizontal Path

2 inch Instrument Nossle with 251 P.PV

"Vertical Path

Figure 13: Applied Piping Loads and Boundary Conditions.

Figure 14: Stress Extraction Path.


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NODAL 4OMUTION AN08C 14 20I0

SUB =1SIMZE-1

sy AVG)

SPN -4678

,3xx =69097

Figure 15: Circumferential Stress Distributions for the Unit Pressure Load Case.

(Units in psi)


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Hoop Stress

70,000,

60,000

Pr Pesswne Load Case

..... 1/4 lhkkness Location I

50,000

70,000 r-

I Pressure Load Case-228.14x' + 3717x2 20608x +-57318

K,4 76o.59 ksi-Vin, R' = 0.9594

30,000o i

20,000 -

10,000-

0

-10,000 ---

T]hermal Load Case at Time = 6900 sec;y = 141.64x3 + 2496.2x

2- 14533x,+ 24126

K, = 23.15 ksi-4in, R' = 0•9786

~~A~ AA A A.

0 2 3 4 5 6' 7 8 9

Depth (in)

Figure 16: Samples of Pressure and Thermal Ramp Load Case Path Stress Distribution.


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Pressure Hoop Stress

80,000

70,000

(;f. flfl I -.-.--~-~.-....---.-.-..----"-..---.-.-...

50,000 .- \--,I

\ Excluding the Three LocationsY-='-261,3Wx ý 4324.W - 2418%,+ 64143 1

ýj= 83.94 ksi-'i in, R' ='0.9669

40;000

30,000

20,000 -

10,000,

1ý11....... .... . .. \

-- --------

Exchidiiig Thet~eIThiee Locatiolls

-201.18x'+4 3286.lx2 - 18614x + 550891L , K1 75.24 ksi-4in, R" 0.8334ý

............ ........ ............. ................... ............... .............. ........ ................................... ...............................

0

0 1 3 4 5 6

Depth (in)

8 9

Figure 17: An Example of Pressure Load Case Path Stress Distribution for Path throughthe Air Gap.


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BIE/IF Path at Nozzle............................................... ....5....................K,= 76.59 ksi-Vin -

70 __ BIE/IF Path at Vessel

0

K, = 56.69 ksi-Vin

6 030 -

30 "

20 .....-.-.- -.--. ......__...--.-------

10 .........................................................................................................................................................................................................

A BIE/IFEvaluation'withPathatNozzle -FE LEFM Evaluation 0 BIE/IFEvaluation with Path at Vessel

Nowzle 10 20 30 40 50 60 70 80 90Bore Angle (Degree) -RPV-D .

Figure 18: K, Distribution along the Crack Front for Internal Pressure Load Case.

,J i~n c h i n i .r u m ,e n t ,,o ', l ,¢ t: '

Figure 19: Path through the Vessel Bore Corner.


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NI'

Paths Including and Excluding Clad.

Thermal Ramp

Figure 20:

x10'

X le3.5•

3 -

2.5

---------------------------------------------------------- I

Fa Load-- I

o B 1.5a

t o •• :. . ... J - - -- -- - -- -

205.5

x 100

?dme [n B sN ozzle Bore at 0°

Figure 21: K, Distribution along Crack Front for Thermal Ramp Transient andComparison to BIE/IF Solution.

O


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BIE/IF Solution withThermal Load Applied

on Base Metal

Them-al Shock

1'J

BIE/IF Solution withThermal Load Appliedon Clad

4 1

-L

9080 -- RPV ID at 900

0.570

60

40x i10 2

Angte [deg]

7ime [s] Nozzle Bore at 00

Figure 22: K1 Distribution along Crack Front for Thermal Shock Transient andComparison to BIE/IF Solution.


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35

30

25

20

15

10

0--4-FE-LEFM MAX - FE-LEFM MIN

1 FE-LEF M RMS -- BI/IF -Therma Load Applied on CladBIE/IF -Thermal Load Applied on Base Metal

0 2000 4000 6000 8000 .1,0000 12000 14000 16000 18000 20000

Time, Sec

35

30

25

20

10

1 0 ...................................................................

X BIV/IF Maximum KI -rhermal Load Applied on Clad

BIE/IF Maximum KI -Thermal Load Applied on Base Metal

-- FE-LEFM KI at Maximum Max KI occurred (time = 15190 sec)...................•.FE-ItLEM Kh'ot.Maximum.RM5 l.KO~cur red.(tme•.x.6900.Sec) .....

0 10 20 30 40 50 60 70 80 90

Crack Front Location (0)

Figure 23: Summary of Thermal Ramp K, for FE-LEFM and BIE/IF Analysis.


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1 6 0 . ..... . . . . . . . . . . . . . . . . . . . . . . . .

140

120

100

!-,• 80

60

40

20

0

-#O-FE-LEFM MAXtFE-LEFM RMS

-20. -ýBI/ll ý Ihermal Loa

-41-FE-LEFM MIN--- IBIE/IF -Thermal Load Applied on Clad

d Applied on Base M etal............................................

0 100 1000 10000

Time, Sec

160

140

120

100

- 80 .

60

40

20 iX BIE/IF Maximum KI -Thermal Load Applied on Clad "\ BIE/IF Maximum KI -Thermal Load Applied on Base Metal

i ---- FE-LEFM KI at Maximum Max KI Occurred (time = 169 sec) -*-FE-LEFM KI at Maximum RMS KI Occurred (time= 453 sec)0 L .. . . .. ......... .... ... ..-.. .. . ... ... .. . ......... ..................

0 10 20 30 40 50 60 70 80 90

Crack Front Location (-)

Figure 24: Summary of Thermal Shock K, for FE-LEFM and BIE/IF Analysis.


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.0.

÷,_

•Z

90 ........

80

70

60

'o.

40

30

20 .. . .. . .

t0 o

~ A

Kl,, 2.9M4 51 1/tý (t,14-1)I - 4 .434

* SI.Mo IGL,v Weld M).V 6O0

* Sho0t P-G ve Weld CS

27 28 29 30 31 32

K/tý*'ý(tj4l+tj

22 23 24 25 26

Figure 25: K, Estimation Equation for Pressure Load.


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45 ...

40 .......... .......... . .. .. .. . ... . ... .. .. .. .

874844 1.(t.t,,)j 20,715R- = 0,9419

30

25

44*

1.5

10

10'-,o Woid Aloy COOSI- 4Ofoc-v ,M W Iek G1de4 j)-o4e Woll cO

0 1 .............

4.001C-05 4.M0E-05 5.00C-05 .503E-05 6.00E-05 6.01E-05 7,001-05

Figure 26: K, Estimation Equation for Thermal Ramp Load.

140

120 ......

100

80

40

20

K,,, 872475jaett~j- j +I80,29R'= 0.6183

......... .................~Id A ll y 1 0

........... .......e.....

4aE-05 91,.05 ,.105 7,E.,05 7,.E05

Figure 27: KI Estimation Equation for Thermal Shock Load.


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Appendix A

VERIFICATION OF FRACTURE MECHANICS FINITE ELEMENT METHOD


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A.1 Benchmark of Finite Element Fracture Mechanics Modeling Methodology

Newman and Raju [12] developed a series of equations to calculate the stress intensity factor for cracks inthree-dimensional finite bodies. The model for a comer crack at a hole is selected for the benchmarkingperformed of the FE LEFM methodology used in this analysis. This solution is selected since it closelymatches the configuration of the instrument nozzle considered in this work. Equation 50 [12] is used for thisevaluation. Figure A. 1 shows the comer cracked hole model from [12].

S

2h

-L

Figure A.1: Corner Crack at Hole Model.

The stress intensity factor can be calculated using following equation [A 1, Eq50 to Eq63].

KI.P. =)K , = S IT F h ( C t t ' b ' "

Where

(50)

(2a)Q = 1+ 1.464 ()165 for a/c < 1


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For 0.2 < a/c < 2, a/t < 1.0.5:< R/t:< 1, (R + c)/b < 0.5 and 0 < 4 < 762, The Fch was chosen as:

Fch = [M 1 + M 2 (a)2 + M 3 ( )4] 9192.93fofto (51)

For a/c < 1

M, = 1.13 - 0.09 (a) (52)0.89 (3

M2 = -0.54 + 0.8+a/ (53)

M3 = 0.5- 1.65 +14 1 -- (54)[.65+a/c C)

g, = 1 + 0.1 + 0.35 (a (1 - sin(P)2 (55)

1+0.358)+1.425,, 2 -1.578)3+2.156A 4

92 = 1+0.13a2 (56)

where

AL = 1 (57)1+'ccos(0.850)

9 (1 + 0.04 ) [1 + 0.1(1_- cosk)2] [0.85 + 0.15 (a)] (58)

fc• = [(a)2cos 2 (p + sin' (P]1/2 (10)

f[w S eC (rR sec ( 7w(2R+nc) (47)

Where n = 1 for single crack, n = 2 is for two-symmetric cracks and the hole is located in the center of theplate.

A.2 Dimensions and Parameters

The following dimensions are used for the model:

a=c=2",t=4",R=2",b=h= 10",andn=2.

The tensile load, S, is set as 1000 psi.

File No.: 0900876.304 Page A-3 of A-7Revision: 0

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A.3 Finite Element Model

A quarter symmetric 3-D model is built using the ANSYS finite element analysis program. SOLID45 andSOLID95 elements are used for this analysis. Symmetric boundary conditions are applied on the sectionswhich lie on planes of symmetry. Figure A.2 shows the finite element model created for this benchmark.

AN

ILEFMt ar:n!a x l ti w~ing tn~iffora It-1cý -__________________________

Figure A.2: Finite Element Model Boundary Conditions and Applied Load.

A.4 Crack Tip Meshing

Three crack tunnel meshes are evaluated in this model. The first mesh is obtained using a SI developedcrack tip meshing program shown in Figure A.3, the second is obtained using the ANSYS code with asquare crack tunnel shown in Figure A.4, and the third is obtained using the ANSYS code with asemicircular crack tunnel shown in Figure A.5. Each method is evaluated using four different mesh sizes.Figures A.3 through A.5 show the parameter locations and Table A. 1 shows the parameter values for eachmesh size considered.


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Figure A.3: AnTip Mesh and Parameter Locations.

ELEME4TS

TYPE [UUM

Figure A.4: ANSYS Code Square Crack Tunnel Mesh and Parameter Locations.


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EQ5O

Figure A.5: ANSYS Code Semicircular Crack Tunnel Mesh and Parameter Locations.

Table A.I: Summary of Mesh SizeswSqureArea 4 ANSYS'Half-CircleAnTip Meshing I AeMehn

_____ TsRs - Ts Rs- -' >LTs,Case 1 0.03125 0.004688 0.0625 0.005 0.0625 0.005Case2. 2 0.06250 0.009375 0.0625 0.010 0.0625 0.010.Case 3 0.12500 0.018750 0.1250 0.010 0.1250 0.010Case 4 0.25000 0.023600 0.2500 0.010 0.2500 0.010

Note: Units are in inches.

A.5 Results of AnalysisFigure A.6 shows the finite element calculated stress intensity factor, K1, using the ANSYS code, for allmesh sizes and types, and using Equation 50. The root mean square K1, along the crack front, for each caseis listed in Table A.2. As can be seen, the mesh density does not significantly affect the results; however,the results obtained using the AnTip method for sizing the crack tunnel are closest to the results published inReference [12]. The results obtained using the AnTip crack tunnel sizing methodology are shown to beconservative but within 11% of the published results by Raju and Newman [12].


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euuu •Eq 50-0.0625-0.01 circle ANSYS

-0.125-0.01 circle ANSYS-0.0625-0.005 square ANSYS

7000 r- __7000 ...... 0.25-0.0236 AnTip

6000

5000

- 0.0625-0.01 square ANSYS -0.0625-0.009375 AnTip- 0.0625-0.005 circle ANSYS - 0.25-0.01 circle ANSYS- 0.125-0.01 square ANSYS - 0.25-0.01 square ANSYS

-0.03125-0.004688 AnTip - 0.125-0.0187SAnTip

Olr-.4ý4000

3000

2000

.. . .. . .... ................... ................. ..... .......................................... ..... ... .... ................ .... ..... . ................................ ...... ......... ..............................................

1000

0

10 20 30 40 50 60 70 80 90

Angle (degree)

Figure A.6: Comparison of Stress Intensity Factor.

Table A.2: Summary of RMS K[ for Each Case.

EQ. 50 AnTip

ANSYS•'SqareCrack

'Tunnel

ANSYS,Semicircular:

Tunnel,,,,Case 1 3,563 4,837 3,935Case 2 3215 3,571 4,754 3,946Case 3 [ 3,572 4,910 3,927Case 4 3,616 4,854 3,929

Average K, I - 3,581 4,839 3,934

Relative Errorwith respect to 11% 51% 22%

Eq. 50Note: the unit is psiinch.


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Appendix B

SUPPORTING FILES


Page B-1 of B-12

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r~enric ode Fil IJ DescriptionIN-step.INP ANSYS input file for a generic instrument model.

MATPROPS.INP ANSYS input file for material properties.

M esh Sensitive Files Descriptionr ~ ~ ~ ~

IN-step-SFxx.INP ANSYS input file for a mesh sensitive models, where xx is 1, 1.4,and 1.8 for meshing factors.

INPress.INP ANSYS input file for applying pressure to mesh sensitive models.

MATPROPS_M.INP Mesh sensitive ANSYS input file for material properties.

~Load Sensitive Files (Press~ure Load) JDeritoANSYS geometry input files. Where # is 205, 218, 238, and 251

IN-step-#-@&.INP for vessel diameters, @ is 2 or 3 for nozzle diameters, and & is Lor S for long or short J-groove weld. Total has 16 files.


ANSYS pressure load input files. Where # is 205, 218, 238, andINPRESS-#-@&.INP 251 for vessel diameters, @ is 2 or 3 for nozzle diameters, and &

is L or S for long or short J-groove weld. Total has 16 files.

ANSYS post-processing file for extracting hoop stress underMAPSTRESS-MAX-PiPress_@&.INP pressure loads. Where @ is 2 or 3 for nozzle diameters and & is

L or S for long or short J-groove weld. Total has 4 files.ANSYS output file for hoop stress under pressure loads. Where

lN-STEP-#-@& PRESS P1 MAP.OUT # is 205, 218, 238, and 251 for vessel diameters, @ is 2 or 3 fornozzle diameters, and & is L or S for long or short J-groove weld.Total has 16 files.Calculating polynomial coefficients files. Where # is 205, 218,

IN-STEP-#-@& PRESSP1_MAP.csv 238, and 251 for vessel diameters, @ is 2 or 3 for nozzlediameters, and & is L or S for long or short J-groove weld. Totalhas 16 files.

The modified output file from IN-STEP-#-3SPRESS P1 MAP.OUT with remove the stresses in the nozzle. Where # is 205,218, 238, and 251 for vessel diameters, and @ is 2 or 3 for

nozzle diameters. Total has 8 files.

Calculating polynomial coefficients files. Where # is 205, 218,IN-STEP-#-@SPRESSP1_MAP-MOD.csv 238, and 251 for vessel diameters, and @ is 2 or 3 for nozzle

diameters. Total has 8 files.

MAPSTRESS-MAX-Pi_3LVessel.INP ANSYS post-processing file for extracting hoop stress underpressure loads with path starting at vessel bore corner.

IN-STEP-251-3LPRESSP1_MAPVessel ANSYS output file for hoop stress under pressure loads for path.OUT starting at vessel bore corner.

IN-STEP-251-3LPRESSP1_MAPVessel Calculating polynomial coefficients files for path starting at vessel.csv bore corner.


Page B-2 of B-12

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Load Sensitive ilees (Thermal Ramp Load) Description

ANSYS geometry input files. Where # is 205, 218, 238, and 251IN-step-#-@&.INP for vessel diameters, @ is 2 or 3 for nozzle diameters, and & is L

or S for long or short J-groove weld. Total has 16 files.


IN-htbc.inp ANSYS thermal boundary condition input file.

ANSYS thermal ramp load thermal input files. Where # is 205,IN-RampT-#-@&.INP 218, 238, and 251 for vessel diameters, @ is 2 or 3 for nozzle

diameters, and & is L or S for long or short J-groove weld. Total

has 16 files.

ANSYS monitor input files. Where # is 205, 218, 238, and 251 forIN-RampT-#-@&_mntr.inp vessel diameters, @ is 2 or 3 for nozzle diameters, and & is L or

S for long or short J-groove weld. Total has 16 files.

ANSYS thermal ramp load stress input files. Where # is 205,INRampS-#-@&.INP 218, 238, and 251 for vessel diameters, @ is 2 or 3 for nozzleI_ p-#diameters, and & is L or S for long or short J-groove weld. Total

has 16 files.

ANSYS post-processing file for extracting hoop stress underMAPSTRESS-MAX-PI-ramp_@&.INP thermal ramp loads. Where @ is 2 or 3 for nozzle diameters and

& is L or S for long or short J-groove weld. Total has 4 files.

ANSYS output file for hoop stress under thermal ramp loads.IN-RampS-#-@&_P1 MAP.OUT Where # is 205, 218, 238, and 251 for vessel diameters, @ is 2 or

N-a - -@ -3 for nozzle diameters, and & is L or S for long or short J-grooveweld. Total has 16 files.

Calculating polynomial coefficients files. Where # is 205, 218,

IN-RampS-#-@&_P1_MAP .csv 238, and 251 for vessel diameters, @ is 2 or 3 for nozzlediameters, and & is L or S for long or short J-groove weld. Totalhas 16 files.ANSYS post-processing file for extracting hoop stress under

MAPSTRESS-MAX-PI-ramp_@&_clad.INP thermal ramp loads under the path with clad. Where @ is 2 or 3for nozzle diameters and & is L or S for long or short J-grooveweld. Total has 4 files.ANSYS output file for hoop stress under thermal ramp loadsunder the path with clad. Where # is 205, 218, 238, and 251 forvessel diameters, @ is 2 or 3 for nozzle diameters, and & is L orS for long or short J-groove weld. Total has 16 files.

Calculating polynomial coefficients files under the path with clad.cdP1MAP.csv Where # is 205, 218, 238, and 251 for vessel diameters, @ is 2 or

3 for nozzle diameters, and & is L or S for long or short J-groove

weld. Total has 16 files.

EXCEL File for Summarizing thermal ramp results. Where @ is 2SummaryThemramp-@&.xlsx or 3 for nozzle diameters, and & is long or short for long or short

J-groove weld. Total has 4 files.

EXCEL File for Summarizing thermal ramp results under the pathSummaryThem ramp clad-31ong.xlsx with clad.


Page B-3 of B-12

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Load Sensitive •iles (Thermal Shock Load) Description

ANSYS geometry input files. Where # is 205, 218, 238, and 251IN-step-#-@&.INP for vessel diameters, @ is 2 or 3 for nozzle diameters, and & is L

or S for long or short J-groove weld. Total has 16 files.



ANSYS thermal shock load thermal input files. Where # is 205,IN Shock T-#-@&.INP 218, 238, and 251 for vessel diameters, @ is 2 or 3 for nozzle

IN o-#diameters, and & is L or S for long or short J-groove weld. Total

has 16 files.

ANSYS monitor input files. Where # is 205, 218, 238, and 251 forIN-ShockT-#-@&_mntr.inp vessel diameters, @ is 2 or 3 for nozzle diameters, and & is L or

S for long or short J-groove weld. Total has 16 files.

ANSYS thermal shock load stress input files. Where # is 205,INShockS-#-@&.INP 218, 238, and 251 for vessel diameters, @ is 2 or 3 for nozzle

diameters, and & is L or S for long or short J-groove weld. Total

has 16 files.

ANSYS post-processing file for extracting hoop stress underMAPSTRESS-MAX-P1-shock_@&.INP thermal shock loads. Where @ is 2 or 3 for nozzle diameters

and & is L or S for long or short J-groove weld. Total has 4 files.

ANSYS output file for hoop stress under thermal shock loads.IN-ShockS-#-@&_PI_MAP.OUT Where # is 205, 218, 238, and 251 for vessel diameters, @ is 2 or

3 for nozzle diameters, and & is L or S for long or short J-grooveweld. Total has 16 files.

Calculating polynomial coefficients files. Where # is 205, 218,

IN-Shock S-#-@&_P1_MAP.csv 238, and 251 for vessel diameters, @ is 2 or 3 for nozzlediameters, and & is L or S for long or short J-groove weld. Totalhas 16 files.

ANSYS post-processing file for extracting hoop stress under

MAPSTRESS-MAX-PI-shock @& clad.INP thermal shock loads under the path with clad. Where @ is 2 or 3for nozzle diameters and & is L or S for long or short J-grooveweld. Total has 4 files.ANSYS output file for hoop stress under thermal shock loadsunder the path with clad. Where # is 205, 218, 238, and 251 forvessel diameters, @ is 2 or 3 for nozzle diameters, and & is L orS for long or short J-groove weld. Total has 16 files.

Calculating polynomial coefficients files under the path with clad.

_kcladP1_MAP.csv Where # is 205, 218, 238, and 251 for vessel diameters, @ is 2 or3 for nozzle diameters, and & is L or S for long or short J-grooveweld. Total has 16 files.

EXCEL File for Summarizing thermal shock results. Where @ isSummaryThemShock-@&.xlsx 2 or 3 for nozzle diameters, and & is long or short for long or short

J-groove weld. Total has 4 files.

EXCEL File for Summarizing thermal shock results under the pathSummaryThemShock_clad-31ong .xlsx with clad.


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uescripYion i l

ANSYS geometry input files.IN-step-251-3L.INP


IN-htbc-woclad.inp ANSYS thermal boundary condition input file.

ANSYS thermal load input files. Where # is ramp and shock forthermal ramp and shock loads, respectively. Total has 2 files.

IN-#_T--251-3L-woclad mntr.inp ANSYS monitor input files. Where # is ramp and shock forthermal ramp and shock loads, respectively. Total has 2 files.

ANSYS thermal load input files. Where # is ramp and shock forthermal ramp and shock loads, respectively. Total has 2 files.

MAPSTRESS-MAX-P1-woclad.INP ANSYS post-processing file for extracting hoop stress.

ANSYS output file for hoop stress. Where # is ramp and shock for-- othermal ramp and shock loads, respectively. Total has 2 files.

Calculating polynomial coefficients files. Where # is ramp andIN-#_S-251-3L-wocladP1_MAP.csv shock for thermal ramp and shock loads, respectively. Total has 2

files.

Summary_Them woclad.xlsx EXCEL file for calculating the Ki.!K

IN-step-251-3-Full.INP ANSYS geometry input files.

ANSYS pressure load input files. Where # is Fx, Mx, My, Mz forINPiping-251-3-Full-#.lNP four different loads. Total has 4 files.


[email protected] ANSYS post-processing file for extracting hoop stress. Where @is 1 and 2 for vertical and horizontal paths. Total has 2 files.

ANSYS output file for hoop stress. Where # is Fx, Mx, My, Mz forIN_Piping-251-3-Full-#_P@_MAP.OUT four different loads, and @ is 1 and 2 for vertical and horizontal

paths. Total has 8 files.

Calculating polynomial coefficients files. Where # is Fx, Mx, My,IN_Piping-251-3-Full-#_P@_MAP.csv Mz for four different loads, and @ is 1 and 2 for vertical and

horizontal paths. Total has 8 files.

SummaryPiping.xlsx EXCEL file for calculating the K1.


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IN-step-251-3L#.INPANSYS geometry input files. Where # is 1, 2, and 3 for differentmesh densities. Total has 3 files.


IN-step-251-3L#-Crack.INP ANSYS geometry input files for creating crack surface. Where # is1, 2, and 3 for different mesh densities. Total has 3 files.

ANSYS input files for creating crack tip elements. Where # is 1,M-T2, and 3 for different mesh densities. Total has 3 files.

ANSYS input files for calculating K1. Where # is 1, 2, and 3 forFMN-Tdifferent mesh densities. Total has 3 files.

ANSYS input files for called by FMIN-STEP-251-3L#-FMIN-STEP-251-3L#-CrackKCALC.INP CrackLOAD.INP. Where # is 1, 2, and 3 for different mesh

densities. Total has 3 files.

ANSYS output file for K1. Where # is 1, 2, and 3 for differentF N-SE Lmesh densities. Total has 3 files.

Nodes.inp Input file for Antip program.

AnTip7.mac Antip program file.

FE LEFM Fie (Pressure load) ~ ,Dsription~<KK

IN-step-251-3.INP ANSYS geometry input files.


IN-step-251-3-Crack.INP ANSYS geometry input files for creating crack surface.

FMIN-STEP-251-3-Crack.INP ANSYS input files for creating crack tip elements.

FMIN-STEP-251-3-CrackLOAD.INP ANSYS input files for calculating K1.

ANSYS input files for called by FM IN-STEP-251-3-FMIN-STEP-251 -3-CrackKCALC. INP CakLA.IP- - Crack LOAD.ANP.

FMIN-STEP-251-3-CrackLOADK.CSV ANSYS output file for K1.




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IN-step-251-3-Crack.INP ANSYS geometry input files for creating crack.

FMIN-STEP-251-3-Crack.INP ANSYS input files for creating cracktip elements.

FMIN-STEP-251-3-CrackLOAD T ramp.INP ANSYS input files for thermal run.

FMIN-STEP-251-3-CrackLOAD T rampmntr ANSYS monitor input files for stress run..INP

FMIN-STEP-251-3-CrackLOADS ramp.INP ANSYS input files for calculating K1.

ANSYS input files for called by FMIN-STEP-251-3-FMIN-STEP-251-3-CrackKCALC.INPCrcODSIP- - Crack LOAD S.INP.

FMIN-STEP-251-3- ANSYS output file for K1. Where is 1 to 41 for time steps.CrackLOAD_S_ramp_K_#.CSV Total has 41 files.



FE LEF Files (Themalshock loadDescriptiOn



IN-step-251-3-Crack.INP ANSYS geometry input files for creating crack.

FMIN-STEP-251-3-Crack.INP ANSYS input files for creating crack tip elements.

FMIN-STEP-251-3-CrackLOAD T shock .INP ANSYS input files for thermal run.

FMIN-STEP-251-3-CrackLOADT-shock-mntr ANSYS monitor input files for stress run..INP

FM_IN-STEP-251-3-CrackLOAD S shock.INP ANSYS input files for calculating K1.FM IN-STEP-251-3-Crack KCALC.INP ANSYS input files for called by FM_IN-STEP-251-3-

FMN-S Crack LOAD S.INP.

FMIN-STEP-251-3- ANSYS output file for K,. Where is 1 to 38 for time steps.Crack LOAD S shock K #.CSV Total has 38 files.




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Ltoad Sensitive Files' (Nozzle Forging Mat. Decito_ _ _ I

[email protected] ANSYS geometry input files for 2" nozzle with short J--grooveweld. @ is 2 or 3 for nozzle diameters. Total has 2 files.

MATPROPS-CS.INP ANSYS input file for material properties with carbon steelmaterial.

ANSYS pressure load input files. @ is 2 or 3 for [email protected] diameters. Total has 2 files.

[email protected] ANSYS post-processing file for extracting hoop stress. @ is 2 or

3 for nozzle diameters. Total has 2 files.

IN-STEP-251-@SPRESS-CSP1 MAP ANSYS output file for hoop stress under pressure loads. @ is 2.OUT or 3 for nozzle diameters. Total has 2 files.

IN-STEP-251-@SPRESS-CS P1 MAP.csv Calculating polynomial coefficients files. @ is 2 or 3 for nozzlediameters, Total has 2 files.ANSYS geometry input files for 3" nozzle with long J--groove

IN-step-251-3L-CS.INP weld.

INRampT-251-3L-CS.INP ANSYS thermal ramp load thermal input files.


IN-Ramp_T-251-3L-CSmntr.inp ANSYS monitor input files.

IN_RampS-251-3L-CS.INP ANSYS thermal ramp load stress input files.

ANSYS post-processing file for extracting hoop stress underMAP_STRESS-MAX-PI-ramp_3L-CS.INP thermal ramp loads.

IN-RampS-251-3L-CS P1 MAP.OUT ANSYS output file for hoop stress under thermal ramp loads.

IN-RampS-251-3L-CS P1 MAP.csv Calculating polynomial coefficients files.

INShockT-251-3L-CS.INP ANSYS thermal shock load thermal input files.

IN-shockT-251-3L-CSmntr.inp ANSYS monitor input files.

INshockS-251-3L-CS.INP ANSYS thermal shock load stress input files.

ANSYS post-processing file for extracting hoop stress underMAPSTRESS-MAX-PI-shock_3L-CS.INP temlsoklas- - thermal shock loads.

IN-shock_S-251-3L-CSP1_MAP.OUT ANSYS output file for hoop stress under thermal shock loads.

IN-shockS-251-3L-CS P1 MAP.csv Calculating polynomial coefficients files.


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ANSYS geometry input files for 2" nozzle with short J--groove weld.Where # is 205, 218, 238, and 251 for vessel diameters. @ is 2 or 3for nozzle diameters, Total has 8 files.

IN-step-#[email protected]


ANSYS pressure load input files. Where # is 205, 218, 238, and 251IN-PRESS-#[email protected] for vessel diameters. @ is 2 or 3 for nozzle diameters, Total has 8

files.

MAPSTRESS-MAX-PIPress_2S-07.INP ANSYS post-processing file for extracting hoop stress.

ANSYS output file for hoop stress under pressure loads. Where # isIN-STEP-#-@SPRESS-07_P1 MAP.OUT 205, 218, 238, and 251 for vessel diameters. @ is 2 or 3 for nozzle

diameters, Total has 8 files.

Calculating polynomial coefficients files. Where # is 205, 218, 238,IN-STEP-#-@SPRESS-07_P1 MAP.csv and 251 for vessel diameters. @ is 2 or 3 for nozzle diameters, Total

has 8 files.

ANSYS geometry input files for 3" nozzle with long J--groove weld.IN-step-#-3L-07.INP Where # is 205, 218, 238, and 251 for vessel diameters. Total has 4

files.

IN_RampT-#-3L-07.1NP ANSYS thermal ramp load thermal input files. Where # is 205, 218,238, and 251 for vessel diameters. Total has 4 files.

IN-htbc.inp ANSYS thermal boundary condition input file. Where # is 205, 218,238, and 251 for vessel diameters. Total has 4 files.

ANSYS monitor input files. Where # is 205, 218, 238, and 251 forIN-Ramp_T-#-3L-O7_mntr.inp vessel diameters. Total has 4 files.

IN_Ramp_S-#-3L-07.1NP ANSYS thermal ramp load stress input files. Where # is 205, 218,238, and 251 for vessel diameters. Total has 4 files.

MAPSTRESS-MAX-P 1-ramp_3L-07.INP ANSYS post-processing file for extracting hoop stress under thermalramp loads.

ANSYS output file for hoop stress under thermal ramp loads. Where# is 205, 218, 238, and 251 for vessel diameters. Total has 4 files.

N- _S-#-3L-07P1MAP.csv Calculating polynomial coefficients files. Where # is 205, 218, 238,

IN-Ramp_S and 251 for vessel diameters. Total has 4 files.

INShockT-#-3L-07.INP ANSYS thermal shock load thermal input files. Where # is 205, 218,238, and 251 for vessel diameters. Total has 4 files.

IN-shock_T-#-3L-O7_mntr.inp ANSYS monitor input files. Where # is 205, 218, 238, and 251 forIN-shock____T _mntr________inpvessel diameters. Total has 4 files.

INshockS-#-3L-07.INP ANSYS thermal shock load stress input files. Where # is 205, 218,238, and 251 for vessel diameters. Total has 4 files.ANSYS post-processing file for extracting hoop stress under thermalMAPSTRESS-MAX-PI-shock_3L-07.INP soklas

- - shock loads.

ANSYS output file for hoop stress under thermal shock loads.IN-shockS-#-3L-07_P1_MAP.OUT Where # is 205, 218, 238, and 251 for vessel diameters. Total has 4

files.

IN-shock S-#-3L-07 P1 MAP.csv Calculating polynomial coefficients files. Where # is 205, 218, 238,N -sand 251 for vessel diameters. Total has 4 files.


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Load Sensitive Files (Nozzle Forging MaýT~esripio

ANSYS geometry input files for 2" nozzle with short J--groove weld.IN-step-#[email protected] Where # is 218, 238, and 251 for vessel diameters. @ is 2 or 3 for

nozzle diameters, Total has 6 files.

MATPROPS-SS.INP ANSYS input file for material properties for SS nozzle forging.

IN-PRESS-#[email protected] ANSYS pressure load input files. Where # is 218, 238, and 251 forvessel diameters. @ is 2 or 3 for nozzle diameters, Total has 6 files.

[email protected] ANSYS post-processing file for extracting hoop stress.

ANSYS output file for hoop stress under pressure loads. Where # isIN-STEP-#-@SPRESS-SSP1_MAP.OUT 218, 238, and 251 for vessel diameters. @ is 2 or 3 for nozzle

diameters, Total has 6 files.Calculating polynomial coefficients files. Where # is 218, 238, and

IN-STEP-#-@SPRESS-SS P1 MAP.csv 251 for vessel diameters. @ is 2 or 3 for nozzle diameters, Total has6 files.

IN-step-#-3L-SS.INP ANSYS geometry input files for 3" nozzle with long J--groove weld.Where # is 218, 238, and 251 for vessel diameters. Total has 3 files.

ANSYS thermal ramp load thermal input files. Where # is 218, 238,IN_RampT-#-3L-SS.INP and 251 for vessel diameters. Total has 3 files.

IN-htbc.inp ANSYS thermal boundary condition input file. Where # is 218, 238,and 251 for vessel diameters. Total has 3 files.

ANSYS monitor input files. Where # is 218, 238, and 251 for vesselIN-Ramp_T-#-3L-SS~mntr.inp diameters. Total has 3 files.

ANSYS thermal ramp load stress input files. Where # is 218, 238,IN_RampS-#-3L-SS.INP and 251 for vessel diameters. Total has 3 files.

ANSYS post-processing file for extracting hoop stress under thermalMAPSTRESS-MAX-PI -ramp_3L-SS.INP ramp loads. I

IN-Ramp_ S-#-3L-SSP1_MAP.OUT ANSYS output file for hoop stress under thermal ramp loads. WhereN -# is 218, 238, and 251 for vessel diameters. Total has 3 files.

Calculating polynomial coefficients files. Where # is 218, 238, andIN-Ramp_S-#-3L-SSP1_MAP.csv 251 for vessel diameters. Total has 3 files.

IN_Shock_T-#-3L-SS.INP ANSYS thermal shock load thermal input files. Where # is 218, 238,and 251 for vessel diameters. Total has 3 files.

IN-shock_T-#-3L-SS~mntr.inp ANSYS monitor input files. Where # is 218, 238, and 251 for vesseldiameters. Total has 3 files.

IN shock S-#-3L-SS.INP ANSYS thermal shock load stress input files. Where # is 218, 238,Is _-#and 251 for vessel diameters. Total has 3 files.

ANSYS post-processing file for extracting hoop stress under thermalMAP_STRESS-MAX-PI-shock_3L-SS.IN P shock loads.

IN-shock S-#-3L-SS P1 MAP`.OUT ANSYS output file for hoop stress under thermal shock loads.N -sWhere # is 218, 238, and 251 for vessel diameters. Total has 3 files.

IN-shock S-#-3L-SS P1 MAP.csv Calculating polynomial coefficients files. Where # is 218, 238, and- 251 for vessel diameters. Total has 3 files.

1;I _


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I N-step-#-@S-SS-07. NPANSYS geometry input files for 2" nozzle with short J--groove weld.Where # is 218, 238, and 251 for vessel diameters. @ is 2 or 3 fornozzle diameters, Total has 6 files.

MATPROPS-SS.INP ANSYS input file for material properties for SS nozzle forging.

IN-PRESS-#[email protected] ANSYS pressure load input files. Where # is 218, 238, and 251 forvessel diameters. @ is 2 or 3 for nozzle diameters, Total has 6 files.

MAPSTRESS-MAX-PIPress_@S-SS- ANSYS post-processing file for extracting hoop stress.07.1NPIN-STEP-#-@SPRESS-SS-07 P1 MAP ANSYS output file for hoop stress under pressure loads. Where # is.OUT 218, 238, and 251 for vessel diameters. @ is 2 or 3 for nozzle

diameters, Total has 6 files.IN-STEP-#-@SPRESS-SS-07 P1 MAP Calculating polynomial coefficients files. Where # is 218, 238, andN-STR 251 for vessel diameters. @ is 2 or 3 for nozzle diameters, Total has

.csv 6 files.

IN-step-#-3L-SS-07.1NP ANSYS geometry input files for 3" nozzle with long J--groove weld.Where # is 218, 238, and 251 for vessel diameters. Total has 3 files.

ANSYS thermal ramp load thermal input files. Where # is 218, 238,IN_RampT-#-3L-SS-07.1NP and 251 for vessel diameters. Total has 3 files.

IN-htbc.inp ANSYS thermal boundary condition input file. Where # is 218, 238,and 251 for vessel diameters. Total has 3 files.

ANSYS monitor input files. Where # is 218, 238, and 251 for vesselIN-Ramp_T-#-3L-SS-07_mntr.inp diameters. Total has 3 files.

ANSYS thermal ramp load stress input files. Where # is 218, 238,IN_RampS-#-3L-SS-07.1NP and 251 for vessel diameters. Total has 3 files.

MAPSTRESS-MAX-Pi-ramp_3L-SS-07.INP ANSYS post-processing file for extracting hoop stress under thermalramp loads.

IN-RampS-#-3L-SS-07 P1 MAP.OUT ANSYS output file for hoop stress under thermal ramp loads. WhereN -R S S# is 218, 238, and 251 for vessel diameters. Total has 3 files.

IN-RampS-#-3L-SS-07 P1 MAP.csv Calculating polynomial coefficients files. Where # is 218, 238, and-R 251 for vessel diameters. Total has 3 files.

IN Shock T-#-3L-SS-07.1NP ANSYS thermal shock load thermal input files. Where # is 218, 238,I_ _-#and 251 for vessel diameters. Total has 3 files.

IN-shockT-#-3L-SS-07 mntr.inp ANSYS monitor input files. Where # is 218, 238, and 251 for vesselIN-shdiameters. Total has 3 files.

INshockS-#-3L-SS-07.INP ANSYS thermal shock load stress input files. Where # is 218, 238,and 251 for vessel diameters. Total has 3 files.

MAPSTRESS-MAX-PI-shock_3L-SS-07.NP ANSYS post-processing file for extracting hoop stress under thermalshock loads.

ANSYS output file for hoop stress under thermal shock loads. WhereN -s# is 218, 238, and 251 for vessel diameters. Total has 3 files.

IN-shock S-#-3L-SS-07 P1 MAP.csv Calculating polynomial coefficients files. Where # is 218, 238, andN -s251 for vessel diameters. Total has 3 files.


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Data Summary Files

SummaryCrackThermal_Ramp.xlsx EL file for summarizing FE LEFM thermal ramp load results.

SummaryCrackThermalShock.xlsx EXCEL file for summarizing FE LEFM thermal shock load results.

Summary KI handcalccurve-fit.xls EXCEL file for summarizing all load sensitive results.


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structural integrity associates, inc. file no.nozzle sizes for these cases are selected based on the...

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