ML20155F196

Engineering Rept for Evaluation of BWR CR Drive Mounting Flange Cap Screw

ML20155F196
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Site:	Grand Gulf
Issue date:	09/01/1998
From:	Brihmadesam J ENTERGY OPERATIONS, INC.
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ML20155F094	List: ML20155F090 ML20155F196
References
EP-98-003-01, EP-98-3-1, NUDOCS 9811050345
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{{#Wiki_filter:.... l l l l Engineering Report No.: EP-98-003-01 Page 1 of 43 l ENTERGY OPERATIONS Engineering Report For The Evaluation of BWR Control Rod Drive Mounting Flange Cap Screw APPLICABLE SITES ANO Unit 1: O GGNS: X W.3: O ANO Unit 2: O RDS: X ECH;O Safety Related: X Yes No Prepared by: f. 8. hh.M. S. Brihmadesam dfIf f[ Date: F Respons l Engineer Prepared by: MC. Gray Date: Responsible Eng[cer Reviewed by: K. R. Rao Date: N Revicwer __,/eg)jg Reviewed by: L. R. Ilowell Date: ( Reviewef g h *IU-Reviewed by: J. R. flamilton Date:,0-23-78 / / Manager, Engmeering Programs if Ceritral De ign Engineering Approved by: 64 J. R. Hamilton Date: I"k // //usponsible CDE Manager '/ (for multiple site reports only) 9811050345 981029 T' . gDR ADOCK 05000416 1-PDR i !e J

ia Engineering Report: EP-98-003-01 Page 2 of 43 l Blank Page f. l. i I' 4 i i

Engineering Report: EP-98-003-01 Page 3 of 43 l i Table of Contents - Section Ijjjls Pane No. List of Figures 3 List of Appendices 4 1 Introduction 5

2 Background

6 3 Evaluation Scope 7 4 Details ofEvaluation 8 5 Discussion 24 6 Conclusions 30 i 7 References 31 List of Firures Fleure No. Fleure Cantion Pane No. 1 Temperature Shift vs. Yield Strength for Steels 33 2 Finite Element Model of CRD Cap Screw 34 3 Linearization of Stress Profile 35 4 Stereo Microscope Photographs of Flaws in CRD Cap 36 Screw 5 Applied Stress Intensity Results for Head-to-Shank 37 Transition 6 . Applied Stress Intensity Results for Shank Region 38 7 Applied Stress Intensity Results for Thread Root Region 39

Engineering Report: EP-98-003-01 Page 4 of 43 l List of Annendices . Annendix No. Annendix Title No. of Pares 1 Stress Analysis 39 '2 Fracture Mechanics Evaluation of Flaws in Bolts 56 3 Bolted Joint Calculations: CRD Cap Screw 7 Evaluation 4 ~ Mechanical Testing and Evaluation of 22 Circumferentially Notched CRD Capscrew Material Record of Revision Revision Number Reason for Revision 01 Added Appendix 4, & modified report to incorporate results from Appendix 4 I-. n

~ Engineering Report EP-98-003-01 Page 5 of 43 l I-

1.0 INTRODUCTION

L Nondestructive examination (NDE), metallurgical and analytical evaluation of control rod drive (CRD) mounting flange cap screws were initiated -in response to the requirements of references 1 and 2. Past evaluations of the CRD cap screws for Grand Gulf Nuclear Station (GGNS) and River Bend Nuclear Station (RBS) are documented as follows: GGNS :- References 3,4 and 21 t l RBS:- References 16 and 17 In reference 3 stress analysis and fracture mechanics evaluations were used to L ' develop an inspection scope expansion criterion. This criterion was based on metallurgical evaluation of flaws found in the CRD cap screws at GGNS. In reference 15 the CRD cap screws from RBS were examined by metallurgical techniques and l the findings' were found to be in agreement with those in reference 3. l The purpose of this engineering report is to evaluate the scope expansion ll criterion with respect to the relevant engineering requirements provided in the applicable sections of the ASME Boiler and Pressure Vessel Code, Section XI. These requirements are obtained from reference 5 for GGNS and reference 6 for RBS. l The scope of the evaluation performed in preparation of this engineering report encompassed the following:

1) Determination of appropriate material property to establish a conservative lower bound toughness value.

2) Stress analysis to defme a conservative upper bound stress distribution for the head-to-shank fillet region of the CRD cap screw based on preload.

3) Structural evaluation to establish a maximum full circumference flaw depth without exceeding the allowable ASME stress limits. (3 x S.).

lb-4)' Evaluation of the bolted joint' connection to establish a maximum full circumference flaw depth that would preclude joint separation under postulated internal pressure load.

5) Fracture mechanics evaluation to conservatively determine the flaw depth that would meet the lower bound threshold toughness for the material in u

l ' the environment for the CRD cap screw. L 6): To compare the flaw depth determined above, (items 3,4 & 5), with the inspection Ll scope expansion criterion presented in reference 3. l iC y . m

Engineering Report: EP-98-003-01 Page 6 of 43 l

2.0 BACKGROUND

l CRD cap screws have been inspected at GGNS and RBS in accordance with the requirements contained in references 1 and 2. Cap screws that were found to show any degradation were replaced following the recommendations in references I and 2. The inspections at GGNS and RBS have shown that the degradation was predominantly located at the head-to-shank fillet region and occasionally in the shank region removed from the fillet region. In all the inspections conducted to date there has not been a single indication of a flaw in the thread root region. Metallurgical evaluations of the degradation show that the flaw to have a pit type morphology (references 3,4 &l7). The indications on the cap screws at GGNS, that were found during the Spring 1992 inspection, were metallurgically evaluated (reference 3). The fmdings from the metallurgical evaluation and the guidance provided in reference 2 led to the development of an inspection scope expansion criterion. This criterion was presented as a recommendation in reference 3. The basis for the criterion was developed by determining the stress distribution in the head-to shank fillet region using finite element analysis (FEA) and the use of fracture mechanics model for a circumferentially notched bar under tensile stress. The limiting flaw depth was based on the applied stress intensity factor (Kupp.) for a given flaw depth to be less than the threshold toughness. A conservative upper bound Kupp., (by virtue of the circumferentially notched model with high surface stress used for the tensile stress), and a lower value for threshold toughness ensured that the criterion based on flaw depth was conservative. In order to implement the scope expansion criterion, in a time etlicient manner, an Eddy Current test technique was developed and qualified (reference 7). This technique was utilized in the Fall 1996 CRD cap screw inspection at GGNS. The Eddy Current based sizing of the flaws was compared to the metallographicclly determined depths for selected CRD cap screws. Results of the evaluation (reference 4) showed that the Eddy Current based sizing was conservative ( Depth aay. > Depth t). At RBS the inspection of CRD cap screws conducted in January 1996 showed pitting in the head-to-shank fillet region on some cap screws. The depth of the pits were found to be lower than the depth provided in reference 2 and were in the range of the GGNS results documented in references 3 and 4.

Engineering Report: EP-98-003-01 ~ Page 7 of 43 l 3.0 EVALUATION SCOPE The scope of this engineering report, based on the documented findings and the need to establish compliance with the established engineering requirements of references 1,2,5 and 6, are as follows: 1

1) Establishment oflower bound material property, for use in fracture mechanics analysis in accordance with the requirements of section XI of the applicable ASME code (references 5 & 6), based on cap screw mechanical propenies and established correlation available in published literature.

2) Detailed stress analysis to establish an upper bound stress distribution and proper Linearization of the stress profile in the head-to-shank fillet region. The resulting stress components and linearized profiles are for use in the fracture mechanics evaluation.

3) Review of bolted joint connection to ascenain prevailing (residual) preload.

4) Determination of a limiting full circumference flaw / notch depth which would result in bolt stress within ASME allowable limit of 3 x S.,.

5) An evaluation of the bolted connection, using botting structural formulations, to determine potential forjoint separation under postulated internal pressure load.

6) Review and evaluation of postulated flaws by various fracture mechanics solutions available in published literature.

7) Comparisons with the results from metallurgical evaluations from references 3 and 4 as applicable.

8) Comparison of the results from the present evaluation with the inspection scope expansion criterion provided in reference 3.

9) Mechanical testing and notch analysis of CRD Capscrew material to verify the results obtained from analytical evaluation.

1

i Engineering Report: EP-98-003-01 l Page 8 of 43 l 4.0 Details of Evaluation: ASME Code Reauirements and Material Properties: In order to ensure that the damage found in the cap screws were dispositioned in an appropriate manner, guidance provided in paragraph IWB-3600 of Section XI from references 5 and 6 were considered. A review of this paragraph in both referenced editions and addenda showed the contents to be similar. The requirements that need to be satisfied are: a) Acceptability of flaw size based on fracture mechanics analyses; and, b) Meeting the primary stress limits of NB-3000 assuming a local area reduction of the primary pressure retaining member Based on the evaluations performed to satisfy the above requirements an acceptable flaw size, which is the lower of the flaw sizes developed by the analyses in accordance with "a" or "b' above. Primary stress determination is based on assuming a full circumference flaw located in the shank of the CRD cap screw. When evaluating flaws in bolts it must be recognized that it is not technically correct to calculate, much less address, net section average stresses. Because the very presence of the flaw causes the re-distribution of stresses, there by creating a combined tension plus bending load. This aspect has been appropriately articulated in reference 28. The discussion states in part, the following: " Paragraph NB-3230 includes methodsfor establishing design conditions, determining the average stress, maximum stress or maximum stress intensity, and the methodfor designing to avoidfatiguefailure. The number and cross-sectional area of boltsfor a given application are determined using Appendix E ofSection HI of the ASME Code. Appendix E describes in detail the methodfor determining the minimum number and cross-sectional area of boltsfor gasketedjoints based on the design of the gasketedjoint, the system operatingpressure and temperature, and the characteristics of the gasket material. Appendix E also allows the use of the methods given in Appendix A-6000, " Discontinuity Stresses ", if the methods given in Appendix E are inadequate. The stresses calctdated using Appendix E or A must satisfy the requirementsfor maximum stress or maximum stress intensity andfatigue stress in Sections NB-3230. Paragraph NB-3232 states that the service stresses in bolts may be higher than the stresses in Table 1-1.3. The maximum average cross-sectionalstress may be as much as twice the stress given in Table 1-1.3. The maximum stress at the periphery of the bolt may be as much as three times the stress given in Table 1-1.3 as long as the l fatigue stresses are not exceeded. These stresses arisefrom the direct tension and bending, neglecting st-ess concentrations. " l l

i Engineering Report: EP-98-003-01 Page 9 of 43 l 4.0 Details of Evaluation (Continued) Therefore, the criterion to evaluate the stress limits, at the location of the flaw, are the combined tension plus bending stresses limits. This criterion, simply stated, will ensure that the bolt will not fail by an over-load condition, which is also the primary intent ofIWB-3610 (b). Attempting to postulaN the flaw as reduction of the bolt shank's cross-section over l its entire length will undoubtedly increase average stresses, but as is shown later it will reduce the bolt stiffness which in turn will result in the joint having to sustain additional stresses. Since the primary interest ofIWB-3610 (b) is to preclude failure by primary stress overload, l the appropriate criterion is the maximum stresses due to direct tension and bending. This l location ofinterest is where groove type pitting was observed (reference 3). The prevailing stresses at the flaw location are based on the results of the finite element analysis performed for the head-to-shank transition region. Applying this stress in the shank region is conservative. In reference 8 it was shown that the prevailing preload on the bolt was always lower than the initial preload at installation. Data from references 8 and 9 showing the l . reduction in magnitude owing to various causes, as follows: j Immediate relaxation after final installation: - 5% to 10% reduction (Ref. 8) Elastic Interaction (embedment etc.) relaxation: - 12% to 18% reduction (Ref. 8) Gasketed joint relaxation (depends on gasket material): - 10% to 50% (Ref. 8) l Long term (1000 hr.) stress relaxation at 550 F: - 20% (Ref. 9) A total reduction factor of 0.632 was computed by taking the average values l stated in reference 8 and ignoring the relaxation due to gaskets, (formulation used in computing the reduction factor is provided in Appendix 3). Thus the prevailing preload and hence the stress in the bolt would be 63.2% of the initially installed value. Ignoring the reduction for gasketed joints and using the average values for the other reduction factors provides a lower bound estimate of reduction factor. Using the reduction factor and the installation preload of 30.0 kip (reference 3) results in a prevailing preload of 18.97 kip. The e material allowable stress intensity at 550 F was obtained from reference 13 as 29.5 ksi. The primary stress limit for bolting provided in NB-3232.2 from the same year and addenda as in i references 5 and 6 is stated as follows : L P.+ P6 s 3 x S. L . Kun for the postulated flaw such that the inequality criteria are satisfied. The criteria The approach presented in IWB-3612 is to determine an acceptable l . provided in IWB-3612 are as follows: (

1) Ka, < Ku /410 for Normal and Upset conditions;

and, t-

2) Ku, < Ku /42 for Faulted and Emergency conditions.

i iu

l L Engineering Report: EP-98-003-01 Page 10 of 43 l j 4.0 Details of Evaluation (Continued) l where Ku is defined as the available fracture toughness based on crack arrest. f and, Ku is defined as the avai'able fracture toughness based on fracture initiation. l The first criterion, based on arrest toughness, is derived from dynamic fracture j mechanics principles (reference 10). The arrest toughness is the lower bound toughness l at the point of arrest of a rapidly propagating crack. The fracture arrest toughness in structural (carbon and low alloy) steels is an inherent manifestation of the effect of imposed loading rate on the materials flow strength property (reference 10). In high l l strength alloy steels, such as the cap screw material, the strain rate sensitivity of fracture toughness is very low (reference 11). The effect of strain rate (loading rate) (reference.ll) l on fracture toughness, is quantified by an absolute temperature shift between the static and dynamic toughness values for the ductile to brittle transition temperature. The measured temperature shift for various steels, from medium to very high strength, as a l function of strength is shown in figure 4.53 of reference 11. Data from this figure was used to reconstruct figure 1 in this report. Typical reactor pressure vessel steels that have yield strength in the range from 60 to 70 ksi show a temperature shift of 110 F to 130 F. CRD cap screw material, which belongs to the low alloy quenched and tempered (LAQT) classification of steel, posses yield strength in the range from 120 to 130 ksi. For this class of steels the temperature shift is in the range from 20 F to 35 F. The larger temperature shift is indicative of significant sensitivity of fracture toughness to loading l rate. Conversely smaller temperature shifts indicate insensitivity of fracture toughness to loading rate. The effect of higher loading rate on rate sensitive materials is manifested by a measurable drop in fracture toughness. Threfore for a material which is not rate j sensitive, like the cap screw material, the fracture toughness is not affected by the loading rate. CRD cap screw material,(LAQT steel), at GGNS possessed an yield strength of 120 ksi (reference 3) and at RBS 110 ksi(reference 16 & 17). At these levels of yield strengths the effect ofloading rate on fracture toughness is expected to be very small to negligible. In addition, from reference 10 (page 15) for bolting material, the following statement is made: l "The applicable toughnessproperty vahtefor bolts shordd be the static L fracture toughness vahte Ku. Dynamic loading would not be expected to occur in bolting. Also, these higher strength steelsgenerally exhibit very l little influence ofloading rate onfracture toughness. " Therefore the toughness property applicable to the CRD cap screw material is Ku, hence for the evaluation of flaws the second criterion ofIWB-3612 is applicable. The degradation of CRD cap screws was found to be corrosion induced pitting (references 3,4,16 & 17). Thus the fracture toughness parameter to account for the F corrosion mechanism would be Kw. (stress corrosion cracking). The value for Kwe for the CRD cap screw material, based on the yield strength (references 3,16 & 17), was determined from figure llB-2 of reference 12 as 130 ksi Vin. The evaluation criterion t for the CRD cap screw can be re-written as follows:

~.- . - _ - - ~ Engineering Report: EP-98-003-01 Page 11 of 43 l 4.0 Details of Evaluation (Continued) K%<Kw/V2 (Ku replaced by Kw) value of 130 ksi Vin. the criterion reduces to: With Kw .] Kw < 91.92 ksilm.- j i In addition to using the CRD cap screw material yield strength to determine Kw, the Charpy absorbed energy was used to determine the value for Kw for the material. The Charpy and tensile data obtained from references 3,16 and 17, for the cap' screws, show: Charpy Absorbed Energy (lowest) = 68 ft-lbs. Yield Strength' = 110.0 ksi The Charpy-Ku correlation of reference 11 (equation 6.1) was used along with the values l provided above to estimate the Ku The value was determined to be 185 ksiVin. This value is higher than the value for Kw obtained from reference 12. Thus the lower bound value would provide conservative results (smaller allowable flaw depth). In order to use the guidance provided in article IWB-3612 from references 5 and 6, it is necessary to address the requirements of article IWB-3610-(b). This requirement necessitates satisfying the primary stress limits of the applicable articles in subsection NB-3000. A review of the relevant articles, pertaining to bolts, shows that the stress limit requirements are for bolt regions removed from discontinuities. However, the stress analysis performed for this report, described in the following section, does model the fillet radius. Thus the requirements for the primary stress limits, are discussed in the stress - analysis section. Stress Annivsis: General Considerations: The observed corrosion damage on the CRD cap screws were . found in two distinct regions, namely: head-to-shank fillet and the shank region. In the head-to-shank fillet region the state of stress is expected to be complex owing to the constraint imposed by the cap screw head. Where as in the shank region, removed from the . fillet, the stresses are expected to be uniform. Therefore for the head-to-shank fillet region detailed finite element analysis (FEA) was performed. For the shank region the tensile stress, - due to preload, were obtained from reference 3. Details of the FEA and subsequent stress analysis are provided in Appendix 1 and summarized below. t' J Y

q Engineering Report: EP-98-003-01 Page 12 of 43 l 4.0 Details of Evaluation (Continued) Finite Element Analysis: FEA of the head-to-shank fillet region was performed using a two dimensional axi-symmetric model. Details of the model and the results are presented in Appendix 1. Two models using different fillet radii,0.05 inch and 0.075 inch based on reference 22, were developed. Both models utilized a very fine mesh refinement to model the fillet region. The FEA model is shown in figure 2. A linear elastic analysis was performed. The applied load equal to the tension developed in the shank with an applied preload of 30.0 kip (reference 3) was applied at the shank end. The bolt head was fixed along the bottom edge to prevent movement in any direction. The effect of fillet radii differences in the stress distribution obtained were insignificant. The stress distribution obtained from the FEA analysis showed a sharp gradient in the head-to-shank fillet region. In the shank region, removed from the fillet, the stresses were uniform. In the head-to-shank region the stress distribution (Von Mises stress) had to be linearized so that the effective distribution could be used as input to the fracture mechanics model. Linearization of Stresses: The FEA stress distribution in the fillet region showed high surface stresses (peak) that rapidly decayed within one element width. Since the analysis was linear elastic, the surface stresses were higher than the material's yield stiength. The previous FEA analysis (reference 3) used a coarser mesh thereby precluding the construction of a detailed stress profile in this region. Hence, Linearization of the stresses in this region was not performed. Therefore, unrealistically high stresses were used as input to the fracture mechanics analysis. In this evaluation a stress profile, along a radial-axial plane from the surface towards the center of the cap screw, was developed. This stress profile was input to two Linearization algorithms as follows:

1) Linearization in accordance with Appendix "A" of Section XI; ASME B&PV Code { references 5 & 6) to obtain the components P. and Ps.

2) Linearized profile based on strain energy density.

Details for these algorithms are provided in Appendix 1. Figure 3 shows the FEA stress profile and the linearized profiles obtained from the two algorithms. The Linearization technique, in accordance with Appendix "A" of references 5 and 6, results in decomposition of the applied stresses into tension (membrane) and bending components. These are defined as P. (tension) and P6 (bending). The values for P..md Ps were utilized for fracture mechanics evaluation which is presented in a later section. The Linearization of the applied stress profile, using strain energy density algorithm, was necessitated for fracture mechanics formulations where the stress term did not separately account for tension and bending. Therefore by developing a reasonable stress profile other fracture mechanics solutions, in which only tensile stresses are considered, could be evaluated and compared.

Engineering Report: EP-98-003-01 Page 13 of 43 l 4.0 Details of Evaluation (Continued) Structural Evaluation of Bolted Joint: The values for the component stresses were utilized to demonstrate that the requirements ofIWB-3610-(b) of references 5 and 6 are satisfied both in the as installed and degraded conditions. The requirement for bolting app!ication implies that the maximum stress limits of Section III, article NB-3232.2 (for the same year and addenda as references 5 & 6) are met..However the requirements stated in NB-3232.2 are for maximum stress intensity neglecting stress concentration. For the CRD cap screws, evaluated in this report, the values for P. and P6 account for the stress concentration caused by the fillet. The results presented in Appendix 1 show that the combined (P. + P ) stress value to be 69.78 ksi. 6 This value is compared to the allowable value permitted by NB-3232.2 as follows: (P. + P6) < 3 x S. for static loading. i and (P. + P ) < 2.7 x S. for fatigue loading. 3 The material allowable stress intensity (S.) values were obtained from Section III, Appendix I (same year and addenda as reference 5 & 6) for the CRD cap screw material and were found to be 29.5 ksi at a temperature of 550 F. The calculated value for the combined stresses is found to be less than the more restrictive 2.7 x S.. Thus the requirements ofIWB-3612-(b) are satisfied for the as installed CRD cap screws. Fatigue of bolts in a bolted joint is dependent on the joint configuration, initial preload and the magnitude of the external load experienced by the bolt. Information obtained from reference 8 shows the following:

1) The magnitude of the mean load on the bolt depends on the preload in the bolt.

2) The magnitude of the load excursion (AFa) depends on:

a) The magnitude ofexternal tension load; b) The bolt-to-joint stiffness ratio (Ka/Ks): and, c) Whether or not the external tension load exceeds the criticalload required to separate thejoint. Elsewhere in this section and in the discussion section the bolted joint analysis presented show that the CRD bolted joint based on prevailing preload has a high critical load required to causejoint separation. The prevailing preload is also relatively high and that the stiffness of thejoint is considerably higher than the CRD cap screw. The considerably higher joint stiffness, compared to the CRD cap screw, ensures that only a small fraction of the applied alternating load will be experienced by the cap screw. The relatively high preload and therefore the high value of critical load required to cause joint separation will provide added assurance that the bolt is not subject to alternating loads. Together these aspects and properties, developed for the bolted joint representing the CRD cap screw, provide adequate assurance that fatigue is not a cause for concern for the degraded cap screw within the limits determined in this report.

l l Engineering Report: EP-98-003-01 Page 14 of 43 l 4.0 Details of Evaluation (Continued) For CRD cap screws that have been in service for a number of years, the structural performance required to satisfy the requirements ofIWB 3610-(b) can be stated as follows: a) Demonstrate that the ASME Code allowable stress (3 x S.)is not exceeded for a cap screw having a full circumference flaw of a certain depth and subjected to a combined load of residual preload plus anticipated internal pressure. b) Demonstrate that the residual preload on the cap screw having a full circumference flaw of a certain depth will sustain postulated internal pressure without joint separation. In order to satisfy the requirements stated above a three step process was adopted. a brief description of the process is provided below. The details of the numerical analysis performed to determine the allowable flaw depth based on the structural requirements delineated above is provided in Appendix 3. In the discussion below only the basic formulations are provided since the detailed equations are presented in Appendix 3 as a Mathcad work sheet. The first step to satisfy the requirements of"a" and 'b" above necessitates the determination of an allowable flaw size (depth) subjected to the estimated preload that would preclude tensile failure of the bolt (i.e. exceed 3 x S.). The primary stress used is the residual value of the combined stresses from Appendix 1. The combined stress in the head-to-shank transition was determined to be 69.78 ksi based on an installation preload of 30.0 kip. As i shown earlier the residual preload is expected to be reduced to 63.2% of the installation value over a period of time (operation of 1000 hours). This residual value remains on the bolted connection. The allowable full circumference flaw size, for the residual preload, can be determined by the following relationship: d, = {D4 - [V((69.78 x 0.632)/(3 x S.)) x D4]}/2 where:

d. = depth of flaw (inch)

Da = Diameter of cap screw shank (inch), and S.= Allowable ASME stress (ksi) Substituting the appropriate value the depth of a full circumference flaw is determined to be 0.120 inch. ( In the second step the joint integrity based on a full circumference flaw which is 0.120 inch deep was determined and the details of the calculation are provided in Appendix

3. This evaluation uses the bolted joint analysis scheme presented in reference 8. Three CRD cap screw geometry's and one joint configuration were used in the evaluation. Thejoint stiffness was computed using the configuration of the assembly from references 26 and 27 and the formulations from reference 8. The joint stiffness from reference 8 is given as:

) Engineering Report: EP-98-003-01 Page 15 of 43 l 4.0 Details of Evaluation (Continued) K, = E x Ac/T where; Ks = Joint Stiffness (kip /in) E = modulus ofElasticity (ksi) 2 Ac = Area of the Equivalent Cylinder comprising the Joint (inch ) and, T = thickness of the Joint or Grip length of Bolt (inch) The stiffness for the CRD cap screw was computed for three different conditions, namely; l) an undegraded nominal cap screw,2) a degraded cap screw with a reduction in the shank diameter by the depth of the full circumferenc" naw over the entire length, and 3) a notch in the middle of the shank with the depth of 0.12; h and width of 0.05 inch. The first degraded condition would provide the lowest bolt stiffness and the second degraded condition would provide the stiffness of the bolt commensurate with the conservatively assumed flaw description. The formulations used in computing the bolt stiffness were obtained from reference 8 and the three geometry's used are presented as case I through 3 in Appendix 3. ) The basic form of the bolt stiffness equation (reference 8) is: Ka = 1/([Li,./(E x As)] + [L /(E x As)]l where: Kn = Stiffness of the cap screw (kip /in) Im = Effective length of Bolt body (inch) 2 Aa = Cross-sectional area of the shank (inch ) L = Effective length ofThreads (inch), and 2 As = Cross-sectional area in the thread region (inch ) In order to determine thejoint separation equation 12.11 of reference 8 was used. The critical external force (load) required for,ioint separation, on a per bolt basis, given a residual preload in thejoint is given as: Lm = Fr x (1 + Ke/Kr) where: Lun = External force required forjoint separation (kip) Fe = Residual preload in the bolt (kip) Thejoint separation force was calculated for the three bolt geometry's described above. The lowest joint separation force was used to determine joint integrity. The imposed external force was calculated using the accident internal pressure in the CRD housing from reference 25. The maximum internal pressure for the CRD housing was given as 5,872 psi. This pressure acts on the CRD cover plate which is connected to the flange by the CRD cap screw. The area of the plate exposed to the pressure was computed from the

Engineering Report: EP-98-003-01 Page 16 of 43 l~ 4.0 Details of Evaluation (Continued) CRD housing internal diameter obtained from reference 27. Thus the total force on the entire bolted joint was determined. The number of CRD cap screws in the connection was eight - (reference 27). Thus the external force per CRD cap screwjoint could be determined. This value of the external force (Lx) was compared with the critical external force required to. cause joint separation (Le). The lowest value of the critical joint separation force was used for this comparison. The details of these computations are provided in Appendix 3 In the third step the computed joint force due to the internal pressure of 5,872 psi was used to calculate the additional bolt load using the relationship from reference 8, which is given as: AFs = (Ks/(Ko + Kr)) x Lx where: AFa = Additionalload on the cap screw (kip) Lx = Extemal force per bolt caused by intemal pressure (kip) The additional bolt load was added to the residual preload and then ratioed to the 4 residual preload. This ratio was used to adjust, upward, the residual combined stress in the bolt. Based on the revised bolt stresses a new allowable flaw depth was computed. Since the bolt stress was revised upward (increased), it was not necessary to recalculate the joint integrity because a lower bolt stiffness used to establishjoint integrity. Fracture Mechanics Analysis: 1 General Considerations: Stress Intensity Factor (SIF) formulat:ons from available literature were reviewed and used in the current evaluation. The fracture mechanics evaluation for the CRD cap screw were divided into three regions, to account for the different stress profiles in these regions, as follows:

1) Thread Root

2) Shank

3) Head-to-Shank Fillet The metallurgical evaluations of the CRD cap screws at GGNS and RBS (references 3,4 & 15) clearly demonstrate that the corrosion induced flaws were predominantly located in the head-to-shank fillet region. There were a few groove type pitting flaws located in the mid-shank region. There were no flaws found in the thread root region of the CRD cap screws. Hence the fracture mechanics evaluation of the thread root tegion was performed and presented here for the sake of completeness.

Engineering Report: EP-98-003-01 Page 17 of 43 l 4.0 Details of Evaluation (Continued) The magnitude and type of stress used in the various fracture mechanics formulations, by the cap screw region of evaluation, were obtained as follows:

1) Thread Root :- Tension stress due to bolt preload from reference 3.

2) Shank :-

Tension stress due to bolt preload from reference 3. L

3) Head-to-Shank Fillet :- FEA and stress linearization presented in previous section.

The nomenclature for the applied SIF, used in this report, is subscripted with the initials of the author (s) of the formulation. In this manner the data files in Appendix 2 could be ised to develop combination plots for comparison. For the applied stress terms the nomenclature is as follows: \\ Stress Type Appendix 2 Literature & Report Uniform Tension So o, ce co Membrane P,,, c. Bending P6 on Peak Surface S.a Used to define the variable stress p Nominal S, profile using the strain energy density In Appendix 2 for each solution the terms utilized in the solution are defined and where the linearized profile was used the linearization scheme has been presented. The solutions described in the following sections follow the solution numbers of Appendix 2. All formulations were solved iteratively, for various flaw depths, using Mathcad 7 professional version. Appendix 2 provides all the Mathcad files and evaluated data. Stress Intensity Factor Formulations (See Accendix 2 for detailst SOLUTION IA through IC: l Formulations provided in reference 18 were based on an evaluation of other available solutions and experimental data The authors of this reference developed an empirical l correlation to fit all the available data in the literature at that time. The final solution was developed to accommodate the differences in the behavior of Ki for two different crack profiles, namely: a circular crack front and a straight crack front. The cases considered were for a single crack in a round bar. The empirical equation developed facilitated a smooth [ transition between the Ki behavior for the two crack profiles. The effect of the thread root was incorporated using an exponential term in the equation for tensile stresses. However for l' the bending stress this effect, the exponential term was not incorporated owing to lack of sufficient experimental data (reference 18). The equation for Ki was: i l

p L Engineering Report EP-98-003-01 Page 18 of 43 l 4.0 Details of Evaluation (Continued) For Tension (membrane) stress: K = eVaa (2.043e-2' +0.6507 +0.5367x + 3.0469x -19.504x' +45.647x*) -(1) 2 i Where; x = a/D,' and a = flaw depth, D = nominal bolt diameter. Likewise for bending stress: 1 K = e64xa (0.6301 + 0.0348Rr - 3.3365x + 13.406x - 6.0421x ) -(2) 2 8 4 i As mentioned earlier, the exponential term is not used in equation 2. In order to utilize equation 1 in the shank region, following the recommendation of reference 18, the exponential term was ignored. In the head-to-shank transition region where bending stret.ses dominate at the surface, equations 1 and 2 are superimposed (added) to obtain the total stress intensity factor, The equations used in the present evaluation for the three regions of the cap j screw were combined as follows: i Thread Root Region

Equation 1 Shank Region

Equation I without the exponential term Head-to-Shank Fillet i,, ion: Equation I w/o exponential term + Equation 2 Details of the solution for the CRD cap screws are provided in Appendix 2 as solution numbers IA through IC.

SOLUTION II This formulation, from reference 19, follows from the solution developed in reference 18. The general form of the stress intensity factor equation retains the same form as in equation 1 but the coefficients were modified based on the author's empirical evaluation of additionai data.' The equation was developed only for tension (membrane) loading and is provided below: Ki = oVua (2.437e*'+ 0.5154 +0.4251x +2.4134x - 15.4491x' + 36.157x' ) - (3) 2 A comparison of equations 3 and 1 shows that the behavior of K with respect i to the normalized crack depth would be similar. In Appendix 2 the solution provided is for the thread root region only since the other regions were evaluated by the solution presented in the preceding section. Details of the solution are provided in Appendix 2 solution II. ll

= - 1 Engineering Report EP-98-003-01 Page 19 of 43 l 4.0 Details of Eval.uation (Continued) SOLUTION III A & IIIB and SOLUTION IV The stress intensity factor solutions were obtained from reference 20. These solutions were for part circumferential circular fronted cracks and were empirically developed based on experimental data and analytical results from finite element analysis. In these solutions the tension and bending loads were explicitly considered. The stress intensity factor j solution provided (reference 20) were: i K = 4xa {co Fo (A) + o F (A) }' (4) i n5 with: Fo (A) = g (A) [ 0.752 + 2.02A %.37(1-sin (n)/2)' l - (5) F6 (A) = g (A) [ 0.923 + 0.199(l-sin (xV2)* 1 - (6) g (A) =0.92 (2/n) (V[ tan (xV2)/(xV2)1/ cos (nA/2)} (7) where: A = a/D and a= crack depth, D= nominal bolt diameter. In the head-to-shank transition region, the stress profile obtained from ' linearization of the finite element analysis results provided the tension and bending stresses explicitly (Appendix 1). The applied stress intensity factor results for this region is provided in Appendix 2 as solution JIA. For the shanx region, where the uniform tension stress dominates, equation 4 was modified to eliminate the bending term, since the bending stress is negligibly small. The resulting values for the stress intensity factors are provided in Appendix 2, solution IIIB. In order to evaluate the significance of the rapidly decaying surface stresses at the head-to-shank transition region the tensile stress term in equation 4 was defined as a -linear variable dependent on the normalized crack depth. The decaying stress was forced to reach the value of the uniform tension stress at a depth determined from the stress profiles (strain energy density) developed from the finite element analysis. The final formulation used in determining the stress intensity factor and the results for the applied stress intensity factors are provided in Appendix 2 solution IV. SOLUTION VA &VB The formulation used in modeling the crack are a combination of the tension and bending solutions for straight fronted cracks provided in reference 18. The equations utilized (reference 18), are as follows: 2 s K = oi xa (0.926 - 1,77lx + 26.42lx,7g,4g gy + g7,9 g g,4 ), V a6 aa (1.04 - 3.64x + 16.86x - 32.596x' + 28.4lx ) -- (8) V 2 4

._~ 4 Engineering Report: EP-98-003-01 Page 20 of 43 l 4.0 9etails of Evaluation (Continued) In the solution of equation 8, the tension stress (ci) is the nominal membrane stress removed from the discontinuity (S ) where the stress profile attains an asymptotic value. The bending stress (ci,) is dermed as a linearly varying function of crack depth and the stress profile was developed using the strain energy density principle (Appendix 1). The details of adapting the stress profile to determine the bending stress is provided in Appendix 2, solution VA. Solution VA was developed for the head-to-shank transition region and the d:: tails of the applied stress intensity factor determination as a function of crack depth is provided in Appendix 2, solution VA. The straight fronted crack solution of reference 18 was used to develop the applied stress intensity factor in the shank region of the bolt. In this evaluation the tension (membrane) stress used was the tensile stress developed in the shank region due to bolt preloed. The applied stress intensity factor equation is the same as the tension portion of equation 8, and is as follows: K = odna (0.926 - 1.77lx + 26.42lx,73,4g g,3 + 37,9g g,4 ) ,_(9) 2 i The details of the evaluation for this equation as it applies to the CRD cap screw is provided in Appendix 2, solution VB. SOLUTION VIA & B ~ The solutions developed for analysis use the circumferentially natched bar geometry described in reference 21. For this geometry the crack is simulated as a full circumferential crack. The solution provided in reference 21 is for tension loading and hence for the head-to-shank transition region a linearized stress profile, developed using the strain energy density principle (Appendix 1), was used to determine the net section tension stress (o ). The stress intensity factor solution for this geometry, from reference 21, is given as: Ki = c., VnD f(d/D) ---(10) with: o,,,, = o/(d/D)2 ,,,( } } ) where: o = nominal tension stress in bar (ksi) d = reduced diameter at the notch (in) D = nominal diameter of bar (in) f(d/D) = influence function, table 5 of reference 19. In order to utilize the influence function (f(d/D)} in a parametric form, data from table 5 of reference 21 was curve fitted with a ninth order polynomial with (d/D) as an independent variable. This would permit determination of the influence function at various crack depths in a continuous manner. The resulting polynomial was tested against the values

l Engineering Report: EP-98-003-01 Page 21 of 43 ] 4.0 Details of Evaluation (Continued) ? l in table 5 of reference 21 and good agreement was achieved. The polynomial developed is i provided in Appendix 2, solution VIA. (_ The applied stress intensity factor in the head-to-shank transition region was l evaluated using two variations of equation 10 above. In the first formulation the tension l stress was the linearized peak surface stress (strain energy density principle), and the influence function was taken at its maximum value of 0.24 from table 5 of reference 21. This solution is identical to the solution utilized in reference 3. This solution is provided in Appendix 2, as solution VIA-I(constant stress). The second formulation the stress term of equation 11 was defined as a linear variable of crack depth. The linear stress profile was determined from the finite element stress contours and linearized using the strain energy density principle (Appendix 1). Additionally the influence function was defined by the polynomial function described earlier. The applied stress intensity factor determination is provided in Appendix 2 as solution VIA-II. For the shank region the stress term was set equal to the nominal tension stress developed in the shank due to bolt preload, and the influence function was defined by the polynomial function. The applied stress intensity factor determination is provided in Appendix 2 as solution VIB. SOLUTION VII The development of toughness requirements for bolting materials, reference 10, were based on the following findings:

1) The stress intensity factor for notched cylindrical bars when tested in bending showed a rapid rise with increasing crack depth. This was attributed to the assumption that the notched region on the compressive side could not sustain compress'on; i

2) The observation that tight cracks could sustain compressive loads; and,

3) The single edge notched geometry (SEN) was considered to be more applicable for bending loads.

Thus in reference 10, the stress intensity factor determination to support ' fracture toughness requirements were based on superposition of the tension solution from notched cylindrical bar testing and the bending solution from the single edge notched i specimen. Hence the combined (superposition) solution accounted for both the effects; tension plus bending. In a similar manner, the tension solution from reference 21 could be combined with the bending solution of reference 20. In reference 18 a straight crack front profile L solution was used and in reference 20 a solution for a circular crack front profile was i developed, it was demonstrated in reference 18, that the stress intensity factor for a straight ( crack front was always higher than that for a circularcrack front for lower crack depths. At larger crack depths the results for the two crack front profiles converged. This aspect 7 suggests that a bounding solution can be obtained by using the stress intensity factor solution

I Engineering Report: EP-98-003-01 Pege 22 of 43 l- ~ 4.0 Details of Evaluation (Continued for a straight crack front profde for bending loads. Thus in this solution the tension solution - for a circumferentially notched cylindrical bar (reference 21) was superimposed on the straight crack front solution in bending (reference 18). The resulting formulation can be represented in the following equation: K = o./(d/D)2 4xD_ f(d/D)'+ o,Vaa (1.04 - 3.64x + 16.86x - 32.596x) + 28.4lx ) - (12) 2 d The variables in the above equation have been previously defined. This combined solution follows the logic utilized in reference 10, which was the bases document for establishing the fracture toughness requirements presented in Section III of the ASME i Boiler and Pressure Vessel code. The tension stress (oi) was taken as the membrane stress component (P.) determined by the profile linearization (Appendix 1), in accordance with Appendix "A" of references 5 and 6.' The influence function was the polynomial equation described earlier. The bending stress is the bending stress (c.) was taken as the bending stress component (P 'i from the linearization mentioned above. This solution was developed for the head-to-shank transition region only, The details of the evaluation are presented m Appendix 2, as solution VII. SOLUTION VIII This solution is applicable in the head-to-shank transition. The stress intensity factor solutions were obtained from reference 24. The solutions were developed for a full circumference notch in a cylindrical bar subject to bending and tension. The applied stress intensity solutions are as follows: 2 3 4 Km = ot Vxa (0.5 x(l + 0.5x + 0.374x - 0.363x + 0.731x )} (tension) -(13)

and, Ka, = o 4xa (0.375 x-25 (1 + 0.5x + 0.375x + 0.3125x + 0.2734x + 0.537x')} (bending) --(l4) 2 2

4 s - where x = (D-2a)/D; a = flaw depth and D= diameter of shank. The above equations were combined to produce the solution for the head-to-shank transition. Details of the equations and results are presented in Appendix 2, solution Vill. Mechanical Testing: Mechanical testing of CRD capscrew material was performed to:

1) Determine mechanical properties to establish equivalency with the CRD capscrew material.

2) Obtain load-strain trace for applied loads equivalent to the CRD capscrew preload at operating temperature.

3) Evaluate the load-strain traces to determine the effect of notch depth, and to

Engineering Report: EP-98-003-01 Page 23 of 43 l 4.0 Details of Evaluation (Continued) establish the instability load and' strain.

4) Elastic-plastic notch analysis, using Neuber's rule, to determine the limiting load for net section yielding.

i

5) Comparison of results from testing and the notch analysis with the limiting flaw depth determined by analysis.

j The purpose of the testing is to provide experimental verification for the analytically determined flaw limits. The determination of net section yield load and strain would provide the basis for the verification. Appendix 4 provides the details of the mechanical testing and the notch analysis performed. l

Engineering Report: EP-98-003-01 Page 24 of 43 l

5.0 Discussion

Review of Field Inspection Data (GGNS & RBS} A review of the data contained in references 3,4,16,17 and 23 show the - following: Site / Year Number of CRD Can Screws Number Confirmed Max. Depth Insoccted w/ind. (visual) LP Test Other Method (mils) GGNS/1992 176 17 17(10.23 %) 42.0 GGNS/19% 208 78 55(15.4 %) 32' 46.0 RBS/1992 400 53 49(12.25 %) 2 RBS/19% 24 9 3(12.5%) 2 58.0 Notes: 1) Eddy Current Test.

2) Stereo Microscopy (after cleaning).

In summary the information reviewed and the field results presented above show the following:

1) The percentage of cap screws with verified indications were between 10% to 15.5% of the number inspected, considering a large variation in sample size.

2) The maximum measured depth (metallographically determined), show depths between 42 to 58 mils. The measured difference at GGNS between 1992 and 1996, covering two cycles of operation, is 4.0 mils.

3) The morphology of the flaws, determined by metallography, at both GGNS and RBS were similar. Pitting was the predominant flaw type with occasional cracks at prior austenite grain boundary. These grain boundary cracks were limited to a gre.in diameter (reference 3). In all the metallurgical evaluations performed (references 3,4 and 17), no overwhelming evidence of stress corrosion cracking was found.

4) The Eddy Current test method for determining the flaw depth was demonstrated to provide a conservative (upper bound) estimate (reference 4).

In order to provide a perspective of the flaws found on the CRD cap screws at GGNS, one of the cap screws removed in 1992 was photographed with the aid of a stereo microscope.. Figure 4 presents the photographs from the head-to-shank transition region. These photographs were taken at three azimuthal locations. From these photographs it is evident that the flaws in this region are short, basically elongated pits. In some instances there appears to be a linear flawjoining the adjacent pits. The typical flaws observed on CRD cap l screws, in the head-to-shank transition region, are discontinuous elongated pits around the )

i 1 Engineering Report: EP-98-003-01 Page 25 of 43 l 5.0 Discussion (Continuedh i circumference and are confined to the fillet radius. Therefore, a full circumferential notch assumption at this location is conservative. Stress Corrosion Cracking Threshold 1 The ASME Section XI allowable, established for this report, was based on the Kiscc alue obtained from reference 12 at 130 ksiVin. This data was shown to be v representative of the behavior oflow alloy quenched and tempered steels in a water or humid air environment. Two sets of data presented in reference 24 for Kiscc show ; that the water / humid air environment data to be agreement with the data from reference 12 and the data for aqueous chlorides / sea weter show lower Kisce values. In reference 24 the NRC . lower bound curve was also presented for comparison. The NRC lower bound curve appears to be an absolute lower bound to all data. Thus the values for Kisce are significantly lower at the yield strength level ofinterest. It should be emphasized that the environment ofinterest is not as aggressive as the aqueous chlorides and the yield strength levels are well below the levels at which stress corrosion cracking is a cause for concern. Therefore the aqueous chloride data and the NRC lower bound data can be considered as affirmation for the factor of safety provided in the ASME Section XI article IWB-3612. Hence the threshold value for Kiscc, which is applicable to the environment for the CRD cap screws, is 130 ksiVin. Stress Analysis The shape of the stress profiles obtained from the finite element analysis are in agreement with the stress distributions presented in reference 8. The use of alidated stress - profile based linearization technique provides a comprehensive method to evaluate the load carrying capability of the CRD cap screw. Conservative assumption of a full circumference notch to represent the observed pitting damage would provide a lower bound degradation I depth that would preclude tensile failure of the cap screw and precludejoint separation. The structural evaluation of the cap screw (see Appendix 3) using upper bound degradation showed that joint separation is precluded. The calculated external load (Lx), caused by a maximum internal pressure of 5,872 psi, was 13.909 kip. and the joint separation load required for the residual preload (Lxa) was 20.615 kip. Therefore under the worst combination of degradation and maximum internal pressure joint separation will not occur since Lx < Lxa. The evaluation of bolt strength showed that a flaw of 0.107 inch would not cause the bolt to exceed the ASME allowable value of 3S,,, for the combined load of residual preload plus the external load from maximum internal pressure. Therefore for a full circumferential flaw with a depth of 0.107 inch the evaluations presented in Appendix 3 demonstrate:

1) No joint separation, under the maximum internal pressure load, would occur; and,

2) The cap screw will not fail by overload under the combined loads from residual preload and maximum internal pressure.

h Engineering Report: EP-98-003-01 Page 26 of 43 l 5.0 Discussion (Continuedh Fracture Mechanics Evaluation: The fracture mechanics evaluations presented in Appendix 2 were performed to evaluate the assumed flaws in three separate regions. These regions were analyzed separately owing to the distribution of stresses in these regions. The finite element analysis was only performed for the head-to-shank transition region because the steep stress gradients necessitated the decomposition of stress into tension and bending components for use in fracture mechanics formulations. For the shank region where uniform tension prevails, straight forward fracture mechanics formulations were available. In the thread root region, recent empirical formulations had become available which used the nominal tension in the shank as the prevailing stress. The discussion, presented below, provides a synopsis of the application of the fracture mechanics solution as it was applied to the CRD cap screw in the three regions. For each of these regions the depth of degradation (flaw depth) of 0.150 inch was used to compare the applied stress intensity factor with the allowable (ASME Section XI IWB 3612 criterion) stress intensity factor. Head-to-Shank Transition The results of the finite element analysis show the stresses in this region to be highly non-linear. For the fracture mechanics analysis two approaches to accommodate the non-linear stress profile were used. The two approaches, depending on the particular stress intensity factor formulation, have been described earlier in this report. The results from the various fracture mechanics formulations were compared with the allowable ASME limit (Section XI, IWB 3612) of 91.92 ksiVin. This comparison is graphically presented in figure

5. In the previous evaluation (reference 3) a flaw depth limit, based on a full circumferential notch, was set at 0.150 inches (150 mils). The table below provides the pertinent results from the current fracture mechanics evaluations at a flaw depth of 0.150 inches.

• Appendis 2 2

- ? Crack Type & Profik ? Kr C4 0.15" MApplied Stress Form - 1-Solution # > >Typer r Profik b ksiVin ^ IB Single Circular 32.5 P. + Ps IIIA Single Circular 32.5 P. + Ps IV Single Circular 26.88 Profile. Note i VA Single Straight 32.0 Profile. Note i VIA1 Full Notch 85.0 Surface Peak Stress from Circumference linearized profile in note i VIA-Il Full Notch 48.0 Profile. Note ! Circumference Vil Full Circum. Notch 50.0 P. + Ps Single Straight Vill Full Notch 81.64 P. + Ps Circumference Note 1: Lineari:edprofile using strain energy density principle.

Engine. ring Report: EP-98-003-01 Page 27 of 43 l 5.0 Discussion (Continuedh The fracture mechanics results presented above lead to two observations, which are:

1) The single crack model produces a lower applied stress intensity than that for a full circumferential notch; and,

2) For a full circumferential notch, the method of applying the stress profile, whether decomposed values (P,. + P3) or a linearized profile, does not affect the appied stress intensity value in a significant way.

The case for a full circumferential notch subjected to an applied stress equal to the peak stress (solution VIA-I) is not a realistic analogue, rather a very conservativ-upper bound. This case was evaluated because the flaw depth limits for the inspection scope expansion in reference 3 used such a model. As can be seen from figure 5, the applied stress intensity at the depth ofinterest (0.150 inch) is below the allowable value for all cases evaluated. The results from all the fracture mechanics solutions clearly demonstrate that the flaw depth limit for scope expansion, established in reference 3, was rational based on fracture mechanics results. At this flaw depth some margin to the allowable ASME limit of Section XI IWB 3612 (references 5 and 6) exists. Solution VIII which used a full circumference notch subjected to a combined tension plus bending stress yielded high applied stress intensity values. These values were very close to the results from Solution VIA-1. These very high values can be explained by the discussions provided in reference 10, which indicates that the full circumference notch is expected to yield a high stress intensity factor when analytically determined. The reasoning (reference 10) provided, suggests that analytically the notched bar in bending cannot support a compressive load on the opposite side and this leads to the unrealistically high stress intensity. Therefore, in reference 10 a superposition of two flaw models, similar to solution VII was developed to establish fracture toughness requirements for bolting. The rapid decay of stress in this region, as shown by finite element analysis, from a peak at the free surface to below the nominal value in the shank region occurs within 0.03 inch. Thus, in accordance with Appendix "A" of reference 5 and 6 it is appropriate to linearize the stresses in this region. When the results of the linearized stresses, stress components, are used as applied stress in determination of the applied stress intensity, then a realistic but conservative value is obtained. From figure 5 it is observed that for flaw depths below 0.130 inch solution VIA-II provides a more conservative value. At ' law depths above this value solution VII provides a more conservative value. This point is academic, since at the flaw depth ofinterest solution VII provides a conservative value for applied stress intensity. At the flaw depth ofinterest (0.150 inch) the calculated applied stress intensity is shown to be below the allowable ASME limit. Shank Region In the shank region, removed from discontinuities, the stress distribution due to bolt preload is very uniform at an applied stress of 56.5 ksi. For this

Engineering Report: EP-98-003-01 Page 28 of 43 l 5.0 Discussion (Continuedh i region the available stress intensity factor solutions were evaluated using a uniform tensile stress of 56.5 ksi. The crack front profiles evaluated were: straight front crack, circular front i crack, and a full circumference notch. Details of the evaluation are provided in Appendix 2. Figure 6 presents the results for the applied stress intensity factor as a function of flaw depth for this region. The table below presents a summary of applied stress intensity factors at a flaw depth of 0.150 inch, which was the flaw depth recommended for scope expansion criterion in reference 3. e Appendis 2d 9 ' Crack Type & Profile 3 iKa @ 0.15F ? Applied Stress Forna r t 5 Soledon'# n MMType e e aProfile* W ksiVino " " 4M i e *

• IC Single Circular 30.34 Unifonn Tension (56.5 ksi)

IIIB Single Circular 30.19 Unifonn Tension (56.5 ksi) VB Single Straight 42.79 Unifonu Tension (56.5 ksi) VIBE Full Notch 53.77 Unifonn Tension (56.5 ksi) Circumference From figure 5 it is observed that the full circumference notch produced the highest applied stress intensity, followed by the single straight front crack profile. At the crack depth ofinterest (0.150 inch), the above table shows that the highest applied stress intensity is 53.77 ksiVin. This value of applied stress intensity is considerably below the allowable applied stress intensity, in accordance with ASME limits in IWB 3612 (references 5 and 6), of 91.92 ksiVin. Thus the flaw depth prescribed for scope expansion is shown to be conservative with a margin of 1.71 with respect to the allowable value. Thread Root Region In the CRD cap screws inspected to date there has been no evidence of flaws in this region based on detailed visual inspection of about six hundred (600) cap screws. However, for the sake of completeness fracture mechanics analysis for this region was performed. The applied stress was taken as the nominal tension in the shank due to bolt preload and the value was 56.5 ksi. Two applied stress intensity factor solutions were found - in the literature for thread root region (references 18 and 19). Both solutions were evaluated and the details of the analysis are provided in Appendix 2. The results of these evaluations are summarized in figure 7. From figure 7 it is evident that the applied stress intensity at a flaw depth of 0.245 inch is below the applied stress intensity for the other two regions at the limiting flaw depth of 0.150 inch. In this region the flaw depth is considered to be the sum of thread depth plus the flaw depth. For the CRD cap screw the thread depth is approximately 0.09375 inch.. The fracture mechanics presented in Appendix 2 shows that the flaw depth for the scope expansion criterion of 0.15 inch (reference 3) is conservative for this region. This is substantiated by the fact that for a flaw depth of 0.150 inch the additional depth of the thread of 0.09375 would result in a total depth of 0.24375 inch. The applied stress intensity at this total flaw depth is 45.87 ksiVin. This value of applied stress intensity is sufliciently 1 -A.e,, w ,v.-. 7m i% w-yw r

L i Engineering Report: EP-98-003-01 Page 29 of 43 l 5.0 Discussion (Continued): below the allowable value of 91.92 ksiVin. The margin to the allowable value is 2.00. Additionally the specification for the CRD cap screws (reference 22) indicates that the threads were formed by rolling rather than by machining. The threads formed by rolling would have a compressive residual stress at the thread root. Therefore the likelihood of developing stress corrosion cracks in this region is very low given the high threshold stress intensity (Lee) and the existence of compressive stresses at the thread root. Mechanical Testing : The scope, testing details and results from the mechanical testing and notch analysis are provided in Appendix 4. The mechanical testing consisted of ensuring that the materials used for notched tension testing had equivalent material properties and that the shank diameter of the bolts was equivalent to that of the CRD capscrews. The results from the tests to establish material's mechanical properties demonstrate that the procured bolts were equivalent to the material used to manufacture the CRD capscrews. The tension test data was also used to determine the Ramberg-Osgood coefficients. The determined coefficients from the test data compared favorably with data from published literature for similar materials. The Ramberg-Osgood material model enables incorporation of work hardening behavior in the notch analysis. The load-strain behavior of both the un-notched and the notched specimens were very similar. The measured specimen strain (nominal strain) for all specimens tested, (one CRD capscrew removed from service at GGNS, two un notched procured bolts and two specimens for each notch depth of 100,125 and 150 mils), up to a maximum lo,ad of 36.0 kips were nearly the same. Results from a linear regression of the strain and notch depth data, including un-notched data, showed that the notch depth did not affect the nominal strain up to the max load of 36.0 kips and notch depth of 150 mils. The load-strain behavior was linear elastic as indicated by a lirear load-strain trace and clear absence of residual strain upon complete unloading of the specimen. The load where net section yielding occured, discernable by a departure from linearity on the load-strain trace, was well above the maximum expected - preload for the CRD capscrew. - The notch analysis performed showed that at the maximum applied load of 36.0 kips net-section yielding was precluded as the notch strains remained well below the crtitical strain required for net-section yielding. The results presented in Appendix 4 clearly demonstrate that, for the limiting flaw depth and anticipated CRD cap screw loads, net-section yielding does not occur. t M +- go g-y y 4 rw w w m T' -,mq

l l Engineering Report: EP-98-003-01 Page 30 of 43 l 6.0

Conclusions:

j l The results of the analyses presented support the following conclusions:

1) The structural analysis of the CRD cap screws and CRD flanged joint produced a a maximum degradation depth of 0.107 inch, based on a full circumference flaw.

2) The fracture mechanics evaluation showed that at a degradation depth of j

0.150 inch, stress corrosion crack initiation is not likely.

3) The scope expansion criterion of reference 3 was based on fracture mechanics evaluation and did not consider the potential for failure by overload of the net section. Therefore, the scope expansion or screening criterion is revised (lowered) from 0.150 inch (reference 3) to 0.107 inch based on the evaluations presented in this report.

4) The fracture mechanics evaluation also supports the observed flaw morphology, that no evidence of stress corrosion cracking were found. This conclusion is based on the results showing the applied stress intensity at all locations of the CRD cap screw to be significantly below the Ktsec value.

5) The flaw depth measured by Eddy Current testing provides an upper bound value. The upper bound estimate of flaw depth coupled with the conservative threshold depth set for scope expansion criterion provides good assurance against premature failure of CRD cap screws.

6) The measured flaw growth of 4.0 mils over two cycles of operation indicates that there is no evidence of an active stress corrosion cracking mechanism.

A comparison of the results from the metallurgical evaluations of the 1992 and 1996 GGNS reports, provides additional support to the results obtained from the fracture mechanics evaluations.

7) Based on the maximum flaw depth and the observed growth rate for degradation the scope expansion criterion, in terms future operating cycles, can be conservatively defined as:

Present Depth (inch) + 0.008x(number ofcycles to next inspection) 50.107 I

8) Mechanical testing and notch analysis confirm the analytically determined results, for the limiting flaw depth subjected to anticipated loading, that net section yielding is precluded.

~ f l' Engineering Report EP-98-003-01 Page 31 of 43 l 7.0

References:

1) GE RICSIL 483, Revision 1

2) GE RICSIL 483, Revision 2

3) Grand Gulf Nuclear Station Engineering Report, GGNS-92-0033, Revision 0.1992.

4) Entergy Operations Engineering Report, EP-98-001-00,1998

5) ASME Boiler and Pressure Vessel Code, Section XI 1977 Edition including Winter 1979 addenda. {for GGNS}

6) ASME Boiler and Pressure Vessel Code, Section XI 1980 Edition including Winter 1981 addenda. {for RBS}

7) " Eddy Current Feasibility Study for Depth Sizing Flaws in Carbon Steel Type-4140 Cap Screws"; EPRI NDE Center 1996

8) "An Introduction to the Design and Behavior of Bolted Joints"; John H. Bickford; Third Edition, Marcel Dekker Inc.1997.

9) " Specification for Bolting for Flanges and Pressure Containing Purposes"; British Standard 4882-73; BS1, UK

10) "PVRC Recommendations on Toughness Requirements for Ferritic Materials";

WRC Bulletin 175,1972.

11) " Fracture and Fatigue Control in Structures - Application of Fracture Mechanics";

Rolfe and Barsom, Prentice-Hall Inc.1977.

12) " Degradation and Failure of Bolting in Nuclear Power Plants"; Volume 2.

EPRI NP-5769, Electric Power Research Institute,1988.

13) ASME Boiler and Pressure Vessel Code, Section 11 Part D,1992 Edition.

14) NISA II/ DISPLAY III ' Users Manual, Version 6.0

15) Mechanics of Materials; Second Edition, F. P. Beer and E. R. Johnson, Jr.;

McGraw Hill Inc.1992.

16) River Bend Nuclear Station, RBS CR 92-0410

17) River Bend Nuclear Station, RBS CR 96-0310 18)" Review and Synthesis of Stress Intensity Factor Solutions Applicable to Cracks in Bolts"; L. A. James and W. J. Mills; Engineering Fracture Mechanics, Volume 30, Number 5; 1988

19) " Behavior of Fatigue Cracks in a Tension Bolt"; Alan Liu; ASTM STP-1236.

20) " Growth Behavior of Surface Cracks in the Circumferential Plane of Solid and Hollow Cylinders"; R. G. Forman and V. Shivakumar; ASTM STP 905

21) " Stress Analysis of Cracks"; Paul C. Paris and George C. Sih; ASTM STP 381

22) GE Drawing Number ll7C4515 Revision C;" Cap Screws"

23) GGNS CR 1996-0342-00

24) " Requirements and Guidelines for evaluating Component Support Materials under l

Unresolved Safety Issue A-12"; EPRI NP-3528, June 1994; Electric Power Research Institute, Palo alto, CA.

25) GE Report DCA22A4912 Revision 0; Jan. I1,1983.

... ~. Engineering Report: EP-98-003-01 Page 32 of 43 l 7.0 References (continuedh

26) GE Drawing number 149A4291,- Revision 2. - (washer dimensions) -

27) GE Drawing number 922D124, Revision 3.

( CRD Nozzle and Flange)

28) " The Regulatory Approach to Fastner Integrity in the Nuclear Industry"; Davis, J. A.

and Johnson, R. E.; ASTM STP-1236. r I~ L l-j..

Engineering Report: EP-98-003-01 Page 33 of 43 l Effect of Strain Rate on Transition Temp 160 ig I I 155 150 \\ \\ 145 I I 140 w: l\\ l I i35 l j 125 120 tis 110 105 t l\\ l ioa I I I 95 6 !l 90 E.I shit} l\\ l l l o3 I I I 9Sh?nng 80 l '\\ l 75 70 I! 65 A'c 3 60 l\\l 55 \\ 50 A 45 \\ 40 1!l\\ I 33 l !! I I ! I ' i\\ II I I I 3o I I II I I I\\ I 25 Il i l I lI IN I I I [o i >\\ i l i iil i i i i 3 I 10 0.0 ^^ ^ 0 ^ 30 40 50 60 70 80 90 100110120130140 150160170180 190 200 210220 230 240250 260 270 30 270 y),e RBi a Yeild Strength (ksi) 000 Data R-B Equn Figure li Temperature Shift vs. Yield Strength of Steels { Reference 11}

Engineering Report: EP-98-003-01 Page 34 of 43 I 1 bck wve Lies -.+ - Jewa . r ?%o%E (mN vgeeQ egio n % A d e d .om c. LA y-Boundary Conditions , f.e -ph' (.5mte.kgk,g h is.15 not' f'eSed ' heve. ' symmetry. plane saw Ux.= Ug = 0.0 Bolt constrained here (right before the fillet radius) dios" fl\\\\ek adks g3 6A on Cd b u 56,500 psi tension stress, applied . Figure 2: Finite Element Model of CRD Cap Screw { Head-to-Shank Transition)

i Engineering Report: EP-98 003-01 i .. _................ _ _. ~ or.en t.i: sir Prom.in n s.a: e.,ni., sir o Page 35 of 43 iM i.n e l -i i:. tM 3( edi J e.,i' n u t 1 I,,' - N a 3 e'- :_ : : :: i -J. .i. .u .n .n . 3. e.,$ .i Graph 12: Strain En.rgy uneartiation at 0.25 In. from Fillet f; ll i. I i i i i i e in 6 .se., i. 5 m = %(N I s,,'I-i i i ' Y I',, l l I = l 1 u . i, .2 ou .2 u.s Figure 3: Linearization of Stress Profile

l ,3TGh To' . 4% l YJ% Engineering Report: EP 98-003-01 .J..:) v Page 36 of 43 l l N ;.cc Q CcL W,Q 1 l'h lL _w . y ,,. s _ l,'^,,r i ,.a,.n Q < nt A- %ZrAA $ Q M Q +.( t %k'- n'Q;y l '?":g[g{hij y.,

d'*13)

? %',&is ~QQ$;A;hti;bff{ b i iNI 'i- $$gg,ug*" M i j .+ r e yy. i g* v,.. y i '

• f. + [;.y 1 "l9,5 g

~~ /_ g.ysy o, 0

f.,j g,,,

4 'N y l MMC 3(0 -w e: s "A%,~ 'M E, gj l, 61 ' e#" i >w. ) h j , y' 9 -- My[+5 ir p ' * ~d% ~ f 5' fN, ' rd(M.j,5 r . i/ 6 58r/f A i* .s, , % dym g' k j{, - de ; ~ SW p;, N SeyK;,V^ E ~ +v M axw&b2aM&&, 2muidu' o.dn!N l T '> ptse goy Mf:;ve..fu pa m,p, ~- - ,,,3 '*f At. 3 ' j k* , t:l l n a-ms. s %q de, A cm 9 s y ya, pygp , 4, 4W / V ) l a.-

1. g w

w l i Figure & Stereo Microscope Photographs of Flaws in CRD Cap Screw

Engineering Report: EP-98-003-01 Page 37 of 43 l 1 Graphical Comparisor, of Results from "K" solutions for Head to Shank Region l Note : Paris Sih correlation is for a Full Circumferential Crack (360 degrees) whereas the other correlations are for Part-Circumferential Cracks. Comparison Plot for all "K" solutions g, 133 I 130 5 I i i iu I l l ll, i20 110 i 1.r. a g+K m+sf, + 6 i e ggi p i 90 .5 I M' s g3 K gip; l l '( I l g'i e g I I g[ D ) I i i y#~ i -o~ i 60 I f t I s p/y ,%, s,o, 1 I W i C2 I l / __. j ---- *' __j' y,h-h-fh p-f l ** 3W ^ - >I' W e *+0 *'

4.

• 30

^ o' t 0" 4 MA #" ' ~ '^ -- l -- - L l - u n.

o f

15 10 - 3 0 .0 '004 002 003 004 005 006 007 004 009 0.1 0.11 0.12 0.13 0,14 0.15 016 0.17 0.18 0.19 02 b Depth of Flaw (inch) 1 James 4 tills (Soln.1 B) +++ Forman-Shivakumar (Soln. til A) Modified Forman Shivakumar (Soln. IV} +-- Modified Paris Sih (Soln. VI A !!) ~ . ese Paris-Sih (Soln. VI A l) o Cartwright Daoud (Soln. V A) ese Paris Sih & Daoud-Cartwright (Soln. Vil) ASME limit l -+-- EPRI Solution. Soln. VIII Figure 5: Applied Stress Intensity Results for Head-to Shank Transition Region i

- _ =. - Engineering Report: EP-98-003-01 Page 38 of 43 l Note : Pan's Sih correlation is for a Full Circumferential Crack (360 degrees) whereas the other correlations are for Part Circumferential Cracks. I Comparison Plot for all "K" solutions g l l l l l 93 I l-t i I l 90 i 83 80 l r' 7s yn l s'

• K jmsg p f 65 60 K sfy i

Ixxx =Ki I scjmg. l ~ p., so

ig;-

a a> 3.....K asmei "' #~ t 40 y i 7.. < *. #g# f l i as l ... ~ 7 3a I . t ..y*1~ s l.. .a"i LJ f ^ ... ;,.y*- l i [.;.e *;,r 8 l l l l l l t 0 0 0 01 0 02 0 03 0 04 0 0$ 0 06 0.07 0 08 0 09 01 011 0.12 0.13 0.14 0.15 0.I6 0.t? 0.18 019 0 2 l 8 6 Depth of Flaw (inch) i James N! ills (Soln. I C) q xxx Forman Shivakumar (Soln. !!! B) + Straight Crack:. James Niills (Soln. V B) l -+~ Paris Sih (Soln. VI B) i ASNIE limit l g figure 6: Applied Stress Intensity Results for Shank Region i i

l0 Engineering Report: EP-98-003-01 Page39 of 43 l Graphical Comparison of Results from "K" solutions for Thread Root Region e - f Comparison Plot for all "K" solutions ,g, i I l i i i i 90 85 80 73 70 63 C I K jmt l' l 3 i is w, l lK 50 lumi l l g p, 'g R l p# = 40 k. l

1. p l

pg',# 33 '"~ ,/- I p-k \\ 20 _~, _ - l$ 10 s 0 0 001 002 003 004 0.05 006 007 008 0.09 0.1 0.11 012 013 014 0.ls 0.16 Ol? 0.18 019 02 ) h ' Depdi of ftaw (inch) Jarnes-Mills (Soln. I A) - Alan Liu { Soln. II) ASME limit j l Figure 7: Applied Stress Intensity Results for Thread Root Region i s

Engineering Report: EP-98-003-01 Page 40 of 43 l Appendix 1 Finite Element Analysis of CRD Cap Screw t

Engineering Report: EP-98-003-01 Page 41 of 43 l J 1 l Appendix 2 Fracture Mechanics Evaluation of Flaws in Bolts i i i

L j Appendix 1 to Document No. EP-98-003-01 Page 1 of 9 1 Appendix 1: Finite Element Analysis of GGNS CRD Bolt 1.0 Finite Element Model Data

1.1 Geometry

Two CRD bolts were modeled: one with a 0.05" fillet radius (model bo5 ants), which exists on the actual CRD bolt, and one with a 0.075" fillet radius (bo75.n/s) to show the effects of a slightly larger fillet on the through-thickness stress profile. The dimensions on the half cross section of the bolt are given in Figures 1 (for the 0.05" fillet) and 2 (for the 0.075" fillet). The dimensions were taken from hand measurements on an actual CRD bolt. A 2" segment of the bolt shank has been modeled. The lock wire holes and hexagonal head were not modeled, to preserve the simplicity and refinement of the finite element mesh; this wasjustifiable, since the high stress concentrations correspond to regions near the fillet radius and not on the upper head portion of the bolts. 1.2 FEA Model: The CRD Bolt was modeled as a 2-D axisymmetric model(shown in Figures 3 and 4) using the NISA II/ Display III finite element program. The model consists of nodes and elements (NKTP=3, NORDR=1) representing the right-hand side of a 2-D cross section of the bolt. The axisymmetric model interprets the cross section as a full 360' bolt. Axisymmetric elements were used to allow greater refinement of the mesh around the fillet at the shank-to-head region. As mentioned in Section 1.1, the hexagonal bore in the bolt head was modeled as a cylinder in the axisymmetric model for simplicity and because stresses in this portion of the bolt are relatively low. 1.3 Material Properties: The CRD bolt is made of SA-193 Gr. B7 (4140) steel, 6 with a modulus of elasticity of 30 x 10 psi. Poisson's ratio was taken as 0.3. The material yield strength from ASME B&PV Code Section II, Part D,1992 Edition (ref.11), S = 105 ksi and the ultimate strength, So = 125 ksi. The y design stress intensity, Sm = 29.5 ksi (at 550'F). 1.4 Applied Loads: A tension stress of 56,500 psi was applied to the end of the bolt shank (as shown in Figures 2 and 3). This stress represents the preload on the bolt. 1.5 Boundary Conditions: Fixity boundary conditions in both the x-and y-directions (u = u = 0.0) were applied along the bottom of the bolt head, from x y l the edge of the head to just before the onset of the fillet radius. 2.0 Stress Analysis of CRD Bolt from FEA Results The CRD bolt was analyzed for stresses in the fillet region caused by tension due to preload and bending due to the constraint of the bolt head. The membrane (Pm) and l

- - ~ - - _ l l Appendix 1 to Document No. EP-98-003-01 Page 2 of 9 Appendix 1: Finite Element Analysis of GGNS CRD Bolt (cont.) bending (Ps) components of the sectional stress are needed in the fracture rechanics correlations. 2.1 Linearization of Stresses The most critical failure plane for the bolt is a horizontal plane extending from the peak stress location on the surface of the fillet through the thickness of the bolt. This plane is denoted in Attachment 1, Figures 1-3 and 1-4 (bo5 anis) and in Attachment 2, Figures 2-3 and 2-4 (bo75.nis), as Plane A-A. It.is j constructed by drawing a horizontal line from the peak stress node through the bolt cross section. The distance from the reference (peak stress) node to each node (or nodes) along the horizontal plane, closest to the line, is measured. The von Mises stress at these nodes is then plotted against the distance along the plane to give the through-thickness stress profile, as given in Graph 1-1 in (bo5a.nis) and Graph 2-1 in Attachment 2 (bo75.nis). Since the bolt material is a very ductile material, stresses obtained using the von Mises theory of failure most accurately predicts the state of stress along the horizontal Plane A-A. Thus, these stresses are used in the linearization procedure, with minimal loss of accuracy over using all the component stresses. The stress profile begins to go linear as the distance through the bolt increases, an effect of bending (due to constraint of the bolt head) on the applied preload. To resolve the stress profile into separate bending and tension components of stress, the entire profile was linearized using basic principles of mechanics of materials. To determine the average membrane (or tensile) stress, Pm, across Plane A-A, the trapezoidal method of numerical integration was used to calculate the sea under the stress profile using the von Mises stress values at the given points through the thickness. The average stress is determined by ,,- i P,, = S,,,,, = ; [ ;. (S,, + S,,,, ). (x,.i - x,) Eqn. (2-1) t,.i 2 where, Sym.y, is the average (von Mises) stress, t is the thickness to the midplane (for an axisymmetric model), and Sym and x are the n-data points taken from the finite element model for von Mises stress and nodal distance, respectively (whether bo5 anis or bo75.nis).

~ Appendix 1 to Document No. EP-98-003-01 Page 3 of -9 ' Appendix 1:' Finite Element Analysis of GGNS CRD Bolt (cont.) The total membrane plus bending stress, Pm+Po, is found by performing a linear curve fit on the through-thickness stress profile. The y-intercept of the resulting line will fall below the peak stress value of the bolt and represent the total membrane plus bending stress for the bolt along Plane A-A. The bending 1 stress component, Po, is found by subtracting P in Eqn. (2-1) from the total membrane plus bending stress found using the linear regression technique. Attachments 1 (for the 0.05" fillet) and 2 (for the 0.075" fillet) give detailed Mathcad calculations of the Pm and P values, as well as graphically show the b l linearization of the stress profile. 2.2 Use of Membrane and Bending Stresses in Ky Solutions The bending component of stress is caused by the constraint of the CRD bolt head. When performing calculations to determine the stress intensity factors (Ki) for the bolt, several correlations require a separate stress value for both tension and bending. For Plane A-A which extends from the location of peak stress in the fillet radius of the bolt to the mid-plane of the bolt (due to axisymmetry), the membrane stress is less than the applied tensile stress in the shank of the bolt. The membrane plus bending stress, however, is greater than the applied tensile stress. The use of Pm and Pb in K correlations includes the i effects of the stress concentration by the fillet on the sectional properties of the bolt. 2.3 Results of FEA and Stress Analysis The membrane and bending stresses obtained from the finite element analyses and subsequent stress analyses of the CRD bolts with a 0.05" fillet radius and a 0.075" fillet radius, along the Plane A-A, are as follows: FEA Stress Component (units in ksi) Model Membrane, P. Bending, P6 Total, P.+P3 0.05" bolt 34.212 35.564 69.776 0.075" bolt 33.502 36.055 69.557 2.4 Strain Energy Acoroximation to Bolt Stress Profile An additional stress linearization technique w:.s used to determine a piece-wise linear approximation to the stress profile based on a linear regression, followed by a constant loading across the bolt at Plane A-A. This approximation was justified based the stress profile becoming approximately linear at a distance

l l Appendix 1 to Document No. EP-98-003-01 Page 4 of 9 Appendix 1: Finite Element Analysis of GGNS CRD Bolt (cont.) through the bolt (along Plane A-A) of 0.25 inches. Graphs 1-2 (Att.1) and 2-2 (Att. 2) show the point oflinearization, around 0.25 inches. To create an approximation to the stress profile, the concept of equivalent strain energy density was used. With this technique, the area under the stress profile (calculated using numerical integration), divided by the thickness of the bolt at Plane A-A, is equal to the strain energy density (strain energy per unit volume) of the bolt at this location,. The equation for strain energy density, therefore, is a modified form of Eqn.10.4 from ref.13: ,., < 2 (S,,, + S,d "'t Eqn. (2-2) oc = 3 where, acis the strain density per unit volume (units ofin. lbJin ), S, is the von Mises stress, x is the distance along Plane A-A, and Iis the thickness of the bolt at Plane A-A (half the total thickness due to axisymmetry. All other dimensions cancel since the only different dimension terms are the thickness, t, and the distance, x across the horizontal cut plane. Eqn. (2-2) is identical to Eqn. (2-1) for average stress, except that it applies to the strain energy density and is used differently. The strain energy density derived from Eqn. (2-2) is then assumed to be concentrated within the first 0.25 inches along Plane A-A; that is, the entire stress in the bolt head-to-shank region is considered to linearly regress from an initial value to the stress at a distance approximately 0.25 inches from the surface of the fillet. This is due to the behavior of the stress profile at this point. At a distance of approximately 0.25 inches from the surface, the stress profile begins to flatten out and remain linear, with only a very small slope, which is attributed the reduction of bending in this region. For use in fracture mechanics correlations, the stress is then assumed to be constant and equal to the value at 0.25 inches from the surface; however, the strain energy will be considered concentrated only in the first 0.25 inches from the surface. The equation for this formulation is as follows: 1 oc t = -(o, + om)d Eqn. (2-3) 2 where, o, is the y-intercept (reference) stress after linearization, aan is the stress at approximately 0.25 inches into the bolt from the surface of the fillet, and d h the nodal distance of approximately 0.25 inches (slightly larger, since an actual point was taken from the FEA model). All other parameters are the l i

l t Appendix 1 to Document No. EP-98-003-01 Page 5 of 9 Appendix 1: Finite Element Analysis of GGNS CRD Bolt (cont.) same as in Eqn. (2-2). This formula is derived from the equation for the area under a trapezoid; the trapezoid, as shown in Graphs 1-2 (Att.1) and 2-2 (Att.

2) has the two heights as stresses (a and ob.25) and the horizontal width as the i

o distance, d. This method is considered conservative, since an actual linear regression of the stress across the bolt section would reduce the value of the y-intercept stress, o, and allow the strain energy to be released through the entire bolt section and o notjust within a distance of 0.25 inches from the surface. The stress a0.25 is found in the FEA output at a point closest to 0.25 inches from the fillet surface. From the model bo5a.nis, the point on Plane A-A closest to 0.25 inches from the surface of the fillet occurs between nodes 2493 and 2462, with d = 0.252811 in. The stress at this point is o.25 = 23.125 ksi. o From the model bo75.nis, the point on Plane A-A closest to 0.25 inches from the surface of the fillet occurs between nodes 1749 and 1750, with d = 0.24837 in. The stress at this point is ob.25 = 23.408 ksi. Since the strain energy density, the bolt thickness at Plane A-A, and the stress at the predetermined distance of 0.25 inches, ob.25, are known, the only term that is not known is the reference stress, o. Solving for this quantity using o Eqn. (2-3), the reference stress is a = 90.229 ksi(for model bofa.nis) and o = o o 90.636 ksi (for rnodel bo75.nis). Mathcad calculations for the strain-energy approximation are given in Attachments I and 2. The regression line using the strain energy approximation is shown in Attachment 1, Graph 1-2 (for bofa.nis), and Attachment 2, Graph 2-2 (for bo75.nis). The stress values using the strain-energy methods are used in the fracture mechanics correlations in Appendix 2 to solve for K.i

Appendix 1 to Document No. EP-98-003-01 Page 6 of 9 Figure 1: Dimensions of Half Cross-Section of GGNS CRD Bolt with 0.05" Fillet Radius - 0.31" 0.44" = = a a 0.60" 1.00" p a u 1 a L-R0.05" 2.40" 2.00" y u ~ 0.415" = =

l Appsndix 1 to Document No. EP-98-003-01 Page l of 9 Figure 2: Dimensions of Half Cross-Section of GGNS CRD Bolt with 0.075" Fillet Radius ~ 0.31" ~ 0.44" = = - a a 0.60" F 1.00" a 1 u H R0.075" i 2.40" 2.00" y n 0.415" = i

[ GEOM-FEM NISA DYMES VIEW POST MISC ' SET /S FILES I GLOBAL OPTIONS-l g gg Ly ~+ mJe\\eA MISCELLANEOUS f k***cfwd - (mt vegaM) ANNOTATIONS i <evn %Aeled k f(y Boundary Conditions (Smce k%k i %ess 'c not ~ t'esed beve - CURSOR TEXTS symmetry CURSOR LINES plane CURSOR ERASE I.ix=Ug=0.0 TEXT SIZE / COLOR Bolt constrained here (right before the fillet radius) d 05 (I\\\\e_k v% k$ (e h mA ox cd bo u j Appendix 1 to Document No. EP-98-003-01 Page 8 of 9 UND RES RGN CLR WIN PAN f HOT REG UNW COM j KBD ABT EDISPLAVjlLI M MEG? 1 56,500 psi tension stress applied HY ROTX i b Mt- .0 i ROTY 1 { .O ' TITLE => (right before the fillet radius) ROTZ .0 TITLE => symmetry , TITLE => plane bok,w(q l

- - _ _.= ~. -.... -. - ~ -. - i

GEOM FEM

-NISA DYMES VIEW POST MISC SET /S FILES - GLOBAL OPTIONS. Boundzry Conditions f ANNOTATIONS { Q (ock udve b\\es hoY wet j %ker (** Y " y 4 Sivnf c N y \\I (sbce hl h 5 ED CURSOR TEXTS

• • g p<esent beve 1

CURSOR LINES L' i CURSOR ERASE Symmetry - s g = Uy = 0.0 TEXT SIZE / COLOR Plane Bolt constrained here I (right before the fillet radius) l r 0075 fIUtk Mb5 (boer tb% the. I Appendix 1 to Document N No. EP-98-003-01 N\\ CflO ho\\k) ~ i Page 9 of 9 UND RES RGN CLR WIN PAN f HOT ' REG UNW COM KBD ABT I TDISPLAn III464 MEG" f

Ficpft,

!JAN/2729E06i44:54 f sm. _ l k bo75.nis 56,500 psi tension stress applied nY ROTX .0 L ROTY l' E X ,o l TITLE => 56,500 psi tension stress applied ROTZ .0 TITLE => Symmetry TITLE => Plane l l 6

Appendix 1,idtachm;nt 1 to Document No. EP-98-003-01 P ge 1 of 10 2 : Section Stresses on Horizontal Plane A-A through Bolt Using Von Mises Stress (model bo5a.nis) To calculate the average membrane stress across the section of the bolt, the trapezoidal method (from calculus) is used as follows: There are a total of 31 data points (nodes or average of nodes) taken along Plane A-A. ORIGIN := 1 n:=31 i := 1.. n Node No. x-distance (in.) Von Mises Stress (ksi) S node, := x; := vm,

• 2516 0

161.338 2524 0.0163108 92.890 2533.2534 0.0309101 66.892 2543 0 0447637 54.996 2552 0.0590185 50.216 2562 0.0728567 44.067 2572 0.0866949 39.7I I 2582.2504 0.1005885 38.430 2503 0.114478 37.315 2502 0.128311 34.804 2501 0.142144 32.6 % 2500 0.155978 30.883 2499 0.I698II 29.289 2498 0.183644 27.860 2497 0.197478 26.562 2496 0.211311 25.366 2495.2464 0.225144 25.268 2494.2463 0.238978 24.158 2493.2462 0.2528 I I 23.125 2492.2461 0.266644 22.163 2460 0.280478 22.055 2459 0.294311 21.193 2458 0.308144 20.403 2457 0.321978 19.685 2456 0.3358II 19.041 2455 0.349644 18.475 2454-0.363478 17.988 2453 0377311 17.586 2452 0 391144 17.271 2451 0.404978 17.047 2450 0.418811 16.912

Appendix 1, Attachment 1 to Document No. EP-98-003-01 Page 2 of 10 .{ t := x, Section Thickness t = 0.4188 The average Von Mises membrane stress. Svm is n-I '(X + i -X) tS vm. avg ;* I Svm 'S t vm i i 3 i=1-tS vm. avg S vm. avg *~ t Svm. avg = 34.2123 Average stress across the section (membrane stress in ksi) I Linearized Stress Across Section for Curve Fit Stress Profile) x1 := 0,0.005. 0.4205 '3 k := 1 nth order of polynomial 3 B := regress (x,Svm,k) B= 1 69.7762 S(xd) := interp(B,x,Svm,xd) -163.1087 The coefficients for the curve-fit of the stress profile are coe ffs : = submatrix( B,4, length ( B ), !,1 ) T D := coeffs D = [ 69.7762 -163.1087) J := 1.. k + 1 f ::D9 4 ) h := 1.100 .c# O* I)'I' h h The Stress Function now has a range and va!ue of j o( xd)' + c,-( xd)' t c,-(xd)7+ c -(xd)* + c,-(xd)5 c -(xd)# F( xd) := c,, -(xd) tc 7 3 + c { xd)'t c -(xd)2 c -(xd)t e, 4 3 2 F(0) = 69.7762 Stotal:= F(0) l l.

Appena.x 1. Attachment 1 to Document No. EP-98-003-01 PIge 3 of 10 Graph 11: Stress Profile Through the Bolt: Curve Fit of Stress Data 180 Ib - -+1--- 162 ) --t l l 144 126 - 108 - S( xd) _( g S vm, EHi> 72 % $4 %'%g l l

• %'7 I%}%

,2 18 'm%,0OO;pa j, I i I I I 0 0 0 045 0 00 0.14 0.18 0.23 0.27 0 32 0.36 0.41 0 45 xd,xg The function at xd = 0 corresponds (in the linear curve-fit case) to the intercept of the ordinate axis. This value is the membrane + bending (P +Py compenent of stress through the m l thickness of the component. Thus, the individual stress values for membrane and bending (in units of ksi) are Pm *S Pm = 34.2123 vm. avg Pb *Stotal-S P3 = 35.5639 vm. avg Stotal := P tPb Stotal = 69.7762 s tot ' ' 1.7762 m The theoretical stress concentration factor at the horizontal plane of interest due to the notch is 1 Speak "Svm, Peak K := K = 2.3122 t t S tot

. i Appenaix 1, Attachment 1 to Document No. EP-98-003-01 l-Paga 4 of 10 Strain EnernvlEaulvalent Area. The linearized curve and the actual stress profile cross at approximately 0.30 in. through the thickness. However, at a distance of 0.25 in., the stress profile is approximately linear, with a small slope. At this point, the equivalent area under a trapezoidal curve (sloping from a y-intercept to the stress at 0.25 in., then a constant linear value) is calculated. The average Von Mises membrane stress, Svm. is used in determining strain entergy. n-I ). k *i + 1~ b) [ t j,jg **6, 3 **i t il approx. strain energy density calculated \\2) \\ t i=1 from the actual stress profile oc = 34.2123 (in units of kip *in/in3) There are a pair of nodes located at approximately 0.25 in. (the cut plane passes through between nodes 2493 and 2462). The distance here is 0.252811 in, d := 0.252811 in inches The Von Mises stress here is e 0.25 := 23,125 (units in ksi) The area here forms a trapezoid, with the upper (y-intercept) stress as the only unknown if the area of the trapezoid is equated to the total strain energy across the thickness of the bolt, along Plane A-A. The equation is determined by muliplying the strain energy density (from the actual stress profile through the bolt) by the thickness, and equating that with the area under a trapezoid of the stress versus the distance through the bolt at 0.25 in: oc t=1-(oot o,2$) d o 2 Solving for the only unknown, o, o := 2-(as t) - o 0.25 o d l o o = 90.2285 ( f

Appendix 1, AttachmDnt i to Document Mo. EP-98-003-01 Page 5 of 10 Thus, the function for this "new" stress profile is: ,, (" o 0.25) -0 d new(xd) !=i(xd$d,(o - m xd),o 0.25) a o Graph 12: Strain Energy Linearization at 0.25 in. from Fillet I i i 1 160 j 140 120 - L o y xd) 100 - S m. 80 - N g N 60 %g ) N*% i %g% i 40 g%g i I N 20 -t 1 i l l I 0 0-0 05 0.1 0 15 0.2 0.25 0.3 0.35

• *i j

1 i

Appendix 1 Attrchm:nt 1 to Document No. EP-98-003-01 Page 6 of 10 Grseph 1-3: Comparison of the Three Stress Profiles 180 l l l l leo ) 140 120 - i S( xd) i 100 -- neJxd) 8 ( S vmi 80 --- **;.,,. I l es h%g*%*I'..**.*.f 60 i 40 -

• 4 4

g 7,% g 20

• • • • • • • • • • • • • • • b'_.**.

j

• % ** % g l

i 0 0 0 05 0.1 0.15 0.2 0.25 0.3 0.35 04 xd,xd,x, s

[

~ DISPLAY III - GEOMETRY MODELING SYSTEM (6.0.0) PRE / POST MODULE VOH-MISES STRESS I VIEW : 347.1352 f -RANGE: 161337.7-I l (Band

• 1.0E3) l 161.3

_ 149.8 138.3 l h$fk kk_ 126.8 i 115.3 i 103.8 j . - ;s p$!ble$$_ 92.34 l i R .: w _ 80.84 69.34 I _ 57.84 i i 46.34 L f f 34.85 f Appendix 1, Attachment I to l Document No. EP-98-003-01 23.35 10 l Page 7 of' 11.85 l 1 n y. n khilli.3471 l l f EMRC-NISA/ DISPLAY 1 JAN/05/98 07:35:00 { hY ROTX f .0 kx f " 'Y i M %mH .0 f 605a.nis: 0.83" bolt (1.5" head) subject to 56,500 psi tension stress (0.05" R) h i t f f f r

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• 1.0E3) 156.8 Bw 145.6 134.4

_ 123.3 112.1 100.9 hSi9si r&a;&l_ 89.76 l 78.59 67.42 56.25 _ 45.08 33.91 Appendix 1, Attaclunent 2 to 22.74 Document No. EP-98-003-01 i m - 11.57 Page 7 of __ _ _10 $$A$wwiE3_.3974 EMRC-HISA/ DISPLAY DEC/01/97 10:21:23 I nY ROTX .0 Lx "1 L5 G-{ bO75.nis: ROT 2 0.83" bolt (1.5" head) subject to 56.5 ksi tension stress (0.075" R) ,o i i I 8gw(t 1d I

Ih!.}it{ ! it !L! !>!l'!I I!lIl jlll X 0. TYo,Z0 T T 0 Y 1 O O O S A R R R S 34 8 6 4 3 1 9 6 9 2 5 8 1 4 7 4 L 0 E 92 7 P ) 7 5 4 2 0 9 7 5 S 3 R 3 6 5 4 3 2 0 9 T 78 E 5 4 3 2 1 0 9 8 7 6 5 3 2 1 3 D I X 0 S 37 0 1 1 1 1 1 1 8 7 6 5 4 3 2 1 1 06 / S 45 1 A 7 E 11 ~ S 9 S I ,94 / M E d 3- .,s &H I 1 Y ~ ^s $l 0 WG n 5; l e C / 2:% m5 L R M EN a C O I A B E M E . p d# eM E V VR ( ,t 5 s D o1 t 0 2 0 3 1 t 0 kaaN4 .r ne0 t m8f r gsem. ' ) h9 o t u'**,o ' R c aP t E A o. R t 5 7 0 ,Ne 1 0 xt o na ( id eP nm s e u s pc f e po [j.j;m 1 5~ r AD t s n o i s ne E t L U i D s O k M 5 T 5 S ~ O 5 o P / R t E P t ce j ) b 0 us 0 ~ 6 ) d ( a e M h E T S Y 5 S ~ 1 ( 4 GN t I ~ l L o 1. E ~ b D e O M 3 w 8 v Q Y R 0 T E M O s E i G n. 5 I 7 O I b I . s Y _ [s _= A L PS I D l ) II. l ]' 1

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m. i GEOM FEM NISA DYMES VIEW POST MISC SET /S FILES GLOBAL OPTIONS I l l l. I i 4 I KEYIH-IDS j j 4 "W " MULTIPLE PICKS I 4 l BOX-CORNER l s j ~ BORDER l g As. ' ACTIVE l - 3 ,p ALL 4 SET-IDS 8 .re 7 7 ng LAYER-NAME 8 fr 7- ~ 8 7 { 4 6 75 743__ '6 ENTITY-SETS g9 7 Nr I e3 i 55 UND RES l

x RGN CLR WIN PAN H3T REG UNW COM 99 KBD ABT m..

2DISPLAYiII!-32HEG" l 3DEC231/97;!O7:50(11:i l w: E.. uY ROTX .0 ~ ~ ROTY X .0 NODE-ID= 2882 X= .305260 Y= 1.96981 Z= .000000 ROTZ Picked NODE-ID = 2881 X=.30491 Y= 1.95737 Z=.00000 .0 Appendix 1, Attachment 2 to bo76.nis Document No. EP-98-003-01 l Page _ _10 of 10 Rco<t 1~N

Appendix 1, AttachmInt 2 to Documint No. EP-98-003-01 P gs 1 of 10 : Section Stresses on Horizontal Plane A-A through Bolt Using Von Mises Stress (model bo75.nis) To calculate the average membrane stress across the section of the bolt, the trapezoidal method (from calculus)is used as follows: There are a total of 36 data points (nodes or average of nodes) taken along Plane A-A. ORIGIN := 1 n:=36 i := 1.. n Node No. x-distanqq (in.) Von Mises Stress (ksi) S node;:= x, : = vm,

• 2743 0.0 147.009 2754 0.010037I i10.823 2765 0.0199504 85.433 2776 0.0264478 71.364 2788 0.0384018 60.504 2799 0.0482995 55.575 2811 0.0573981 49.506 2822 0.0674182 47.700 2834 0.0769649 43.643 2846 0.0867444 40.306 2857 0.0971337 40.091 2869 0.107367 37.517 2881 0.117833 35.2 %

2893 0.128531 33.354 2905 0.139463 31.640 2917 0.150626 30.105 2929.1217 0.1620685 29.867 1293 0.173740 29.529 1369 0.185597 28.150 1445 0.197687 26.865 1521 0.21009 25.660 1597 0.222564 24.523 1673 0.235351 23.445 1749.1750 0.248370 23.408 1825.1826 0.261622 22.367 1902 0.275107 22.247 1978 0.288824 21.267 2054 0.302774 20.348 2130 0.316956 19.495 2206 0.331370 1l'.711 2282 0.346017 18.003 2358 0.360897 17.378 2434 0.376009 16.845 2510.2511 0.391354 17.260 2586.2587 0.406931 16.913 2662.2663 0.422740 16.683

Appendix 1, Attichment 2 to DocumInt No. EP-98-003-01 Page 2 of 10 t ;= x, Section Thickness . t = 0.4227 The average Von Mises membrane stress, Sym, is n-I vm. avg *

• (S vm,
• 8 tS
• (X

~ *i) vm M i=1 tS vm. avg S vm. avg * ~ S vm. avg = 33.5019 Average stress across the section (membrane stress in ksi) Linearized Stress Across Section for Curve Fit Stress Profile) xd :=0,0,005. 0.4205 k := 1 nth order of polynomial . 3 B := regress (x,S vm,kj 3 S(xd) := interp(B,x,Sym,xd) 69.557 -166.2468 The coefficients for the curve-fit of the stress profile are ~ coeffs := submatrix( B,4, length ( B ), !, I ) T D := coeffs D = ( 69.557 -166.2468) j :: 1.. k t 1 . f := D9 1 h :: 1,.100 Ch 'h'

1 Appendix 1, Attachm:nt 2 to Docum nt No. EP-98-003-01 Pcg3 3 of 10 l The Stress Function now has a range and value of F(xd) := c,,-(xd)' + cio (xd)' + c,-(xd)' + c,-(xd)7+ c -(xd)6 c -(xd)'t e -(xd)4 7 3 s + c -(xd)* + c -(xd)2 c,-(xd) + c 4 3 i F(0) = 69.557 Stotal := F(0) i Graph 21: Stress Profile Through the Bolt: Curve Fit of Stress Data 160 f l i l i t i ) I I44 - ~p- -( l + l l l I i l I ,2, I-l l l l 112 3 i l l 4 96 - l S xd) 7"*i 80 -- r l ( l l l i i i Se I H' - 1 l d--- I' ('* k 64 - ( i 4._ ._i-l- l l I l i l i l i I l *. l l [ ---b ,,'N'%g 32 - h r I [ l i C OC 4-

%Q 16 i

i 1 i I 0 0 0 045 0.09 0 14 0 18 0.23 0 27 0 32 0.36 0 41 0 45 xd,xg The function at xd = 0 corresponds (in the linear curve-fit case) to the intercept of the ordinate axis. This value is the membrane + bending (P +PJ compenent of stress through the m thickness of the component.

Document No. EP-98-003-01 PCge 4 of 10 l l Thus, the individual stress values for membrane and bending (in units of ksi) are l Pm *S Pm = 33.5019 vm. avg Pb *Stotal-S Pb = 36.0551 vm. avg Stotal := Pm+Pb Stotal = 69.557 Stot := 69.557 The theoretical stress concentration factor at the horizontal plane of interest due to the notch is peak S vm, O P K K = 2.1135 t t S tot Strain EneravlEaulvalent Area The linearized curve and the actual stress profile cross at approximately 0.30 in. through the thickness. However, at a distance of 0.25 in., the stress profile is approximately linear, with a small slope. At this point, the equivalent area under a trapezoidal curve (sloping from a y-intercept to the stress at 0.25 in., then a constant linear value) is calculated. The average Von Mises membrane stress, Sym, is used in determining strain entergy. n-I,I, 3 l

• ' _d

.S di vm

• 8 oc :=

approx. strain energy density calculated vm. '+1 t from the ac'ual stress profile i=1 oc = 33.5019 (in units of kip *in/in3) There are a pair of nodes located at approximately 0.25 in. (the cut plane passes through between nodes 1749 and 1750). The distance here is 0.24837 in. d := 0.248370 in inches The Von Mises stress here is o 0.25 :=23.408 (units in ksi) The area here forms a trapezoid, with the upper (y-intercept) stress as the only unknown if the area of the trapezoid is equated to the total strain energy across the thickness of the bolt, along Plane A-A.

Appendix 1, Attachment 2 to Docum:nt No. EP-98-003-01 P g3 5 of 10 The equation is determined by muliplying the strain energy density (from the actual stress profile through the bolt) by the thickness, and equating that with the area under a trapezoid of the stress versus the dictance through the bolt at approximately 0.25 in: -(o o + o 0.25 j d oc t= Solving for the only unknown, o,o o := 2-("* ' } - e 0.25 o d o = 90.6362 o Thus, the function for this "new" stress profile is: {0 - " 0.25 'I o m := ' d new(xd) := if(xd5d,(o - m xd),o 0.25, o o Graph 2 2: Strain Energy Linearization at 0.25 in. from Fillet 160 140 -J h- - f-i 1 j b 1 i l 120 - I I too - l l l I ..s xo s i go -% .1 l I ~~* s ?g% l l j m, ) I N i l j i i l i 60 N,%gt i 2 I I N. I, %'%q 40 [ l*% l l N. -_______I____. 20 ---- = r j --~ l i i i i 0 0.05 0.1 0.1 $ 02 0 25 0.3 0.35 xd,x;

Appendix 1, Attichmint 2 to DocumInt No. EP-98-003-01 Pag 3 6 of 10 Graph 2-3: Comparison of the Three Stress Profiles 160 l l ) l 140 j i I l l f' 120 - i--~ ~ () l i e 6 100 -- +- + t

• *d )

i i i } I 1 I l I I' i j j } i o ggxd) 80 --.,, i -*.4.... i i ~~T i ~ j i i

• • ..,{

l i i i i S ww 4 N !* e., ,I g - _ _ - ~ _ - %,*1 s l I I f l 40 --- f '4 - ~ + - - l l l l -2 gg __. * " w ~.g................,... w ^ w c A+ I I %g i 0 0 0 05 0.1 0 15 0.2 0 25 03 0.35 04 xd,xd,x,

l l L APPENDIX 2 Fracture Mechanics Evaluation of Flaws in Bolts Comparisons of Stress Intensity factors for flaws in bolts: Single Crack Solutions :- James-Atills, Liu, Daoud-Cartwright and Forman Shivakumar. FullClivumferentialCrack: Parls Sih Solution forNotchedBar. l Solutions presented in this appendix are a compilation from various references. The appropriate references are provided for each solution. The nomenclature used in the vanous solutions are provided below. GeneralNomenclature S Nominal Stress in Shank due to Bolt Preload (ksi} 0 P Tension or Membrane Stress (ASME linearized in accordance with m Section XI appendix "A". {ks!} Pg Bendin Stress (ASME linearized in accordance with Section XI appendix. "A". {k S peak Peak Stress at surface linearized by strain energy density method. {ksi} S Nominal stress in the head-shank region interior obtained by linearization nom using strain energy density method. {ksi} a0 Initial Crack Depth. { inch} D Diameter of Bolt in the Shank region. { inch} Notes :-

1) Other variables and constants used in the solutions are defined in the particular solution method.

2) Stresses used in this appendix are obtained from the results presented in appendix 1.

3) Material properties are from references cited in the body of this engineering report.

FP 98-003-01 Appendix 2 1of56

l I I SOLUTION NUMBER l l-A Thread Root Region l l ' James and Mills Correlation: For a Single Curved Crack in the Thread Root Region l (Empincal Equation that considers stress profile in the l Thread Root Region)

REFERENCE:

- James L. A. & Mills W. J. in Engineering Fracture Mechanics, Vol. 30,No. 5,1988. " Review and Synthesis of Stress Intensity Factor Solutions Applicable to Cracks in Bolts". L Ajm := 2.043 E jm := 3.0469 B jm :=- 31.332 Fjm :=- 19.504 C jm := 0.6507 Gjm := 45.647 Djm := 0.5367 Stress Input S o := 56.5 Nominal Tension Stress in Shank due to Preload (ksi} Bolt Geometric data and Initial flaw depth : a := 0.05 initial Flaw Depth { inch} n a ine := 0.005 increment for Flaw Depth (inch} D := 0.822 Diameter of Shank { inch} i := 1. 40 LoopIndex a, := a,_ i + a jne Flaw Growth Simulation I i EP-98-003-01 Appendix 2 2 of 56

4 a Developmunt of Equations for the determination of Applied Stress Intensity Factor as a Function of Flaw Depth a a-x:=f Normalized Flaw Depth 3 Magnification Factor .Yjm,;" Ajm exp(Bjm'X ) t Cjm + Djm x;t Ejm'lX ) + Fjm (x )3 + Gjm'!X )* i i i i Stress Intensity Solution K jmt;::S Yjm,Qn a, l 0 U EP-98-003-0l Appendix 2 3 of 56 ' ~

,,,m---e-- --r p g gypc,-gqy-*yg e famg - y m -w,.p--,.r_pmpw, g---.p---gw,,i g--y -,n gr.y -++-,-4---.-4, ,,w- .%p9 --.m 1eqnteJ gesnl}s ;oJ rewes-n!lis ooJ>eleqou x! g[m' 3 ][mh 0'05S 0'09L E O'6t9 ZzrtL E G9L ilrSL E .Dfj2 ii'E9i 1811 REfi E E QL.f1 77LL8 38L.$ iE OLL QLJQI tE r26 GifI 2E BIL E E G82 ir't95 A E G8.l. tt LEL G IB rS'rt E E QL]2 iS L96 GL.f 29'E 16 GL.f 79 886 .QL]2 2L rL9 GL8 i8 OLL _GS_ C8 96 GBI C6E19 QL85 26 6SE N E agif EO 568 E E E aiff E!riS GifL EI 671 QLQI EE 568 E G02 EE r8S Q_8.lL. EE 685 38.lL Er 969 GII ES ttE M E919E DfI E9 62 E Q_StI EL 969 IStif ES r6Z QLJSL E6 El Q.%21 VD ISE M rI 07E g g M tlifII M rT8SE g g G01 tL.ilif . g g GLt rt 8EE g g M tS 89L g M r9 659 3d-68-00C-0 I yddeup!xi y0159

Graphical Representation :- James-Mills Correlation Magnification Factor "Y" , 93 i I i f p 09 Yjm; l l w .l 0 85 l l 5 i h i 2 08 7--- 0 75 0 0 05 0.1 0 15 ag Depth of Flaw (inch} \\ 50 40 K jmt I i 30 I I I 20 0 05 0.1 0.15 0.2 0 25 8 6 EP-98-003-0 l Appendix 2 5 of 56

) SOLUTION NUMBER :-l-B Head to Shank Region James and Mills Correlatwn For a Single Curved Crack in the Shank-Head Region {Empert al Equation for tension and Bending in the head to shank region)

REFERENCE:

- James L. A. & Mills W. J. in Engineering Fracture Mechanics, Vol. 30,No. 5,1988. " Review and Synthesis of Stress Intensity Factor Solutions Applicable to Cracks in Bolts". C jm := 0.6507 Ejm := 3.0469 Gjm := 45.647 Djm := 0.5367 Fjm :=- I9.504 Ajmb := 0.631 C jmb :=- 3.3365 E jmb :=-6.0021 B jmb := 0.03488 Djmb := 13.406 Stress input Pm := 34.212 Nominal Tension Stress in Shank-Head Region due to Preload (ksi) Pb := 35.564 Bending Stress in the Shank to Head Region due to Preload (ksi} Bolt Geometric data and Initial flaw depth : a := 0.00 initial Flaw Depth (inch} o a ine := 0.005 increment for Flaw Depth (inch) D := 0.822 Diameter of Shank (inch} i := 1. 40 LoopIndex a; := a _ i + a nc Flaw Growth Simulation i EP-98-003-01 Appendix 2 6 of 56

m _.. _ _.. _ -. _..... _. _ _ _.. _ ~ Develo ment of Equations for the determination of Stress Intensity Factor as a Function of Fla Depth a x:=f Normalized Flaw Depth i Magnification Factor Yjm,:= Cjm + Djm'X + Ejm*(X ) + Fjm*(X ) + Gjm'(X )* i i i i 4 Yjmb;:: Ajmbt Bjmb x t Cjmb'(X ) + Djmb'(X ) + Ejmb'(X )4 i i i i Stress Intensity Solution K jm := Pm Yjm 'dn a I 3 3 g K jmb,:=P Yjmb,'dn a, l b K Ihs K jm + K jmb, l I i g EP-98-003-01 - Appendix 2 7 of 56

l Tabular Results for James-Mills Correlation l a y

Yjm, Yjmb, K jm, K jmb, ths; I

K l 3 5 10'3 6.083 10-3 0.654 0.631 2.805 2.813 5.618 0 01 0.012 ppyg E63T TMI-T777-TV63-0 015 0.018 E66T E33T UTI-TT65-9 78 - 0 02 0.024 E66I T&T 3765-TET7-TI IH E62T'- 0.03 gggg ggyg gap-g 33-p gg-0 03 0.036 ygyy Epg 7377-gggy-77g3y l M o.043 gpyg pgg 7ggg-yygg-yygg ) 0 04 0.049 ggg7 ggyg g yyy-7ggg-yg7gg o045 0.055 ggg5 EBII T8T-FIIR-TTTIT 0 05 0.061 E39T EEN VT68-T'19T-TTT57 EU3T-0.067 ggq5 ggy gggg-gggg-TVGET j l TOE-0.073 TT E5H TEJ9T VTg3-T9TF l 0 065 0.079 g757 ggyg 77ggg gyyy-7yggy l 0 07 0.085 gygg EER TIT 71 TFIM TFF75 UT75-" 0.091 D'7TI E3T5 TTITT M TIT 8T 0 08 0.097 UTIT E5TI TTITI TF9If ITI7T l l EUT3-0.103 U75 E5TI TT771 TI TFT ITUIV o 09 0.109 E7T7 EETI TTIN TT36I TT787 0 095 0.I16 D'71T TEF TTE7T TFT57 Tr575 01 0.122 7 776 E3DU TTTTI TITII 76TT6 l 0105 0.128 T7T E657 14 55 TTT56 Tf9T6 \\ 0 ll o.l34 g 7T5 5566 TT78T TI671 2T655 l 0 115 0.14 T7f E665 TrJTI TIVII IT3T5 l 0 12 0.146 UTIT E5UT TF8T7 TTTil 19 TIT l ETIT-0.152 g75g 566J T5IST TTT4T 79'75T l 0 13 0.158 ET6J E6M TETIE 1759-3EJ76 0135 0.164 E76i E6M TTTR TTVI7 TTUTI l 0 14 0.17 y 775 ggUT TT3If TTTRI 3T'7TT l 0145 0.176 E777 E5DT TT9T7 TCTH 3IT77 0 15 0.182 3 787 E60T TIT 1-TT57T 3TUTT l 0 155 0.189 F7E7 E55T TI'191 TTUR T3'7TT O 16 o.195 gyg7 ygg Jy73 TyT7' TTT87 l 0165 ,_b 201 F.79T E3M TOTTI TTTH TITf6 l 0 17 0.207 FIDI E5DI TF077 TT675 T5'7II l 0 175 0.213 gggg gggy 773TI TT9TI 3TTTE l 0 18 0.219 E8TT E6F6 IF15T TET76 ITT3T o I85 0.225 E8H EE57 TFT6I T6T65 3TT5T '019 - 0.231 gg77 gggg TI II7 T6 7J7 3E39T 0195 0.237 EHTT E6TT IT3TT TTMT TUTIT o2 0.243 787T E5TT T2 797 TTIF TETUT l 3 l EP-98-003-01 Appendix 2 8 of 56

Graphical Representation :- James-Mills Correlation Head to Shank Region Magnification Factor "Y" 0.9 l l .k f.Yjm w Yjmbg 'I 0.7 i 1 -_,_T~'----.,~.'-- 06 O 0 05 0.1 0.15 'n Depth of Flaw { inch) l "K" pl t f r James. Mills Correlation 50 40 d_ ./... _.p K jm;' ,..h I 30 ~ l f, .I l K jmb; ' ',..r f K f ....ihq 20 l-m 3 l _,..-r~~~~~~~,,.,, e ~~~~~~,! I IO L __,.s 4 0 0 0 05

0. g o3

• i Depth of Flaw (inch)

Tension / Membrane --- Bending Total EP-98-C%-01 Appendix 2. 9 of 56

-. _. - _. _ - -._ - ~ l l SOLUTION NUMBER :-l-C Shank Region James and Mills Correlation: For a Single Curved Crack in the Shank Region {Empiricalequation modifiedin accordance with the Author's l recommendation forregions removed from the thread root) I

REFERENCE:

- James L. A. & Mills W. '. in Engineering Fracture Mechanics, Vol. 30,No. 5,1988. " Review and Synthesis of Stress Intensity Factor Solutions Applicable to Cracks in Bolts". Cjm := 0.6507 E jm := 3.0469 Djm := 0.5367 F jm :=- 19.504 Gjm := 45.647 Stress input S o := 56.5 Nominal Tension Stress in Shank i. due to Preload {ksi} Bolt Geometric data and initial flaw depth : ? a := 0.00 Initial Flaw Depth { inch} o l a ine := 0.005 Increment for Flaw Depth { inch} l D := 0.822 Diameter of Shank (inch} l r i := 1. 40 Loopindex l a, := a,_ i + a inc Flaw Growth Simulation l l l EP-98-003-01 Appendix 2 10 of 56

t \\ l: Development of Equations for the determination i ' of Apphed Stress intensity Factor as a Function of Flaw Depth i f 1 x:=f Normalized Flaw Depth i t. Magnification Factor Yjm :=Cjm + Djm x,+ Ejm-[x,)2, pjm*(x )3 + Gjm'(X )4 i i i Stress intensity Solution i K jms; *S Yjm,Qn a, I 0 i-l l ' EP-98-003-01 Appendix 2 IIof56

} Tabular Results for James-Mills Correlation a, x;

Yjm, K jms, I

5 10'3 6.083 10'3 0.654 4.632 T5T--- 0.012 U fTg T5tf-FUTF 0.01s F33T TTTT TUT ~ 0.024 ffgy VTIT TUYF 0.03 Eggg TE39[ TUT ~ 0.036 Eg71 ITEI7 FOTF 0.043 E57g TT397 W 0.049 Egg 7 TT6f 1 EUIT-- 0.055 Eggg TT557 W 0.061 EE9T TITT FD33-0.%7 ffg3 T67T 0 06 0.073 V T7T67 i EU33~ 0.079 E754 TT987 TUT ~ 0.Oss E757 TT7T7 F073~ 0.091 E7FI T9T65 TOF 0.097 E7TE 70775 W 0.103 E777 T[~591 1 0 09 0.109 E777 2 TIT W 0.I16 E7JT 72'37N 01 0.122 E7yg ITJU7 TTUI-0.128 T77 T4~527 0 11 0.134 E743 7T74T ETTF 0.14 T7T II437 0 12 0.146 E733 76T5I E173-- 0.152 E75g 76T59 0 13 0.158 E7Ey 7T337 FTJ3~ 0.164 E7Eg K 73T 0 14 0.17 E771 7T937 W 0.176 E777 79 637 0 15 0.182 E7I7 75TJi W 0.159 E757 3T676 0 16 0.195 E7g7 T[737 UT6T-0.201 E79T 72T4T 0 17 0.207 Eggy 73TT6 ET7F 0.213 Eg59 37876 0 18 0.219 EETT TT3DI ETIT-0.225 ERIT T5743 0 19 0.231 Eg27 Tf597 FT9T-- 0.237 E8TJ K837 02 0.243 EI3T 3Y63T 4. 1 EP-98-003-01 Appendix 2 12 of 56 . -. ~

. _.. - _.. _ _ _.. _ _ _ _ _ _ _... _ _ _ _ - - _ _ _. _ _ _ _. _ - _. _ ~. _. l I 4 1 Graphical Representation : James-Mills Correlation Shank Region 0 as . Magnification Factor "Y" 4 i a { 08 l. l-Yjmi l j I 'w l 0 75 i -) a i i 0.7 f l I i 0 65 O O 05 0.1 'O.13 a. 3 Depth of Flaw (inch) I 1 "K" plot for James Mills Correlation I l !~ 30 i .? l s n i .a, I i 1 i i - g h. ms : 20 E l 5 1 l 1 i 10 J i I i 0 0 05 01 0.1$ 8 6 Depth of Flaw (inch) 4 4 9 f .EP-98-0034l Appendix 2 13 of S6 \\

- -.. - ~.- SOLUTION NUMBER. :- ll Thread Root Region Alan F. Liu correlation: Modification to James-Mills Conelation for magnification factors based on Test Data. Single Curved Crack REFERENCE :- ASTM STP 1236 -Behavior of Fatigue Cracks in a Tension Bolt Aal := 2.4371 E al := 2.4134 B at :=- 36.5 Fat :=- 15.4491 C at := 0.5154 Gat := 36.157 Dal := 0.4251 Stress input S o := 56.5 Nominal Tension Stress in Shank due to Preload (ksi} Bolt Geometric data and initial flaw depth : a := 0.05 Initial Flaw Depth (inch) o a ine := 0.005 increment for Flaw Growth { inch} D := 0.822 Diameter of Shank i := 1. 40 Index for Loop ~ a:=ai-t + a inc Flaw Growth Simulation ' EP-98-003-01 Appendix 2 14 of %

'I l i Equations for the determination of the Applied Stress Intensity Factor as a function of Flaw depth, a x,:=f Normalized Flaw Depth i Magnification Factor al'X + Eal-(X ) t Fal'(X )3 + 0al'(X )4 Y, l' Aat exP(B al'X ) + Cal t D al i i i i Stress Intensity factor Solution K g,3 := k Y,'h 0 al 6 (

f3 -

50/(I{ EP-98-003-0l Appendix 2 15of56 ~_

] Tabular Results for Alan Liu Correlation a 3 x, Y K131 al, 0.055 0.067 0.763 17.912 g g N N N N N N W N N N N N N W W N N N N N N W N N N N N V N N N N N W N N N N W N N W N N N g g N M N N N N N N W W N N N N i g g N N N m3T' N N m m N W M N N N N N N N N N N N N N N N N N N N N N N N N N M M N N N N N N N N N N N M N N N N N N N N N N N N N N N N N N N N N EP-98-003-0 l Appendix 2 l6 of 56

l Graphical Representation : Alan Liu Correlation 1 1 Msgnification Factor 0.75 h I Y.i w i j

0. 7

} 0.65 l: 06 0 0.05 0.1 0.15 1 ag Depth of Flaw (inch) "K" Plot Alan Liu Correlation 35 Y .sI I 3o K g lg E ,5 20 .i.- 15 O 0 05 0.1 0.15 'l Depth of Flaw (inch) i EP 98M3-0l Appendix 2 17 of 56

SOLUTION NUMBER :.lll A Head to Shank Region Forman - Shivakumar Correlation, for single Circular Crack in a CylindricalBar. For Constant Bending and Tension Stress. (Use ASME Sect. XI Appendix "A" Linearized stress profile.) REFERENCE :- ASTM STP 905- ~ Growth Behavior of Surface Cracks in the Circumferential Plane of Solid and Hollow Cylinders" Stress and Flaw input data Pm := 34.212 Tension or Membrane Stress {ksi} Pb := 35.564 Bending Stress (ksi} a := 0.0 Initial Flaw Depth { inch} o a inc := 0.005 Flaw Growth Increment { inch} l i i := 1.,40 Index for Loop a, := a,_ i + a ine Flaw Growth Simulation a. A :=f Normalized Flaw Depth i i 3 i 1 i i I I i ' EP-98-003-01 Appendix 2 18 of 56

l - Determination of Applied Stress Intensity Factor as a function of Flaw depth. tan (n - ( 0 5 jx "*i s A, := 0.92 h -

• 5(T)

Magnification factor (Membrane / Tension} F ox :=g A - (0.752) + 2.02 A + 0.37-1-sin (.n A ) g g Magnification factor - (Bending} x A j\\ 1 - sin [; i F b A, : 8 A - 0.923 + 0.199- <) i \\ - Stress intensity Factor Solution K g3r :={(Pm) FoA tP Fbl'h b i EP-98-003-01 Appendix 2 19 of 56

l Tabular Results from Forman-Shivakumar Correlation. (ASME Sect. XI Linearized Pm + Pe} a, A, F ox, F K bA;

isf, 5 10-3 6.083 10"3 0.658 0.653 5.732 0 01 0.012 T6E f639 ITET" EDTT-O.018 BT6T E6T5 ETIRI O 02 0.024 DT61 E6TT TTT97 E5S~

0.03 UT&T EEI7 T272T o03-- 0.036 UT67 E514 TT92T M 0.043 DTfg E6TT TT57T 0 04 0.049 E57T E62T T6T3T 0 045 0.055 E67T E575 TT527 0 05 0.061 E677 EE27 17937 M 0.067 "DTg-T67 1T5T6 TUE-0.073 DTgy E3TT T9Tg7 EUBT"' O.079 ffT7 UT[6 "253T TUT ~' O.085 T5tjr E6TT IT3TT E573~ 0.091 E69T E6TI T2797 0 08 0.097 ffgg TfT '77Tf EDT3-0.103 E7DJ EEUU IT5TI O 09 0.109 ET67 UT5g 7T33T E645~ 0.116 E7TI T655 IT0T7 01 0.122 E7T7 UI55 737f6 0 105 0.128 E727 EgDT 7633T 0 11 0.134 E727 EEUT 77.737 DTT5~ 0.14 E7JJ 765J 1797T 0 12 0.146 E7Jg UT57 2E6T7 M 0.152 E7Ty UT5J 79756 0 13 0.158 E73T E651 TUT 2T ETT5-- O.164 E731 E661 75TTT 0 14 0.17 E75T E65J IT551 0 145 0.176 E77T E65T T2~296 0 15 0.182 E77g UT5T 'TT5T 0155 0.189 E7gg DT5J 7777 0 16 0.195 E79J EE66 TT317 0 165 0.201 ET6[ E357 JT277 0 17 0.207 Tgr UT6g TfDT5 W 0.213 EgTI ~5T59 76T5T 0 18 0.219 EgT7 T5T T7T9T UTIT-0.225 EBT6 E5TI TrJ'8T 0 19 0.231 EgTJ "5'3TT 19T8V 0195 0.237 UT54 E5TI T5'UU'6 02 0.243 Eg3T UIr7 WITE EP-98-003-01 Apoendix 2 20 of 56

-] l Graphical Representation :- Forman-Shivakumar Correlation i . {ASME Sect XI Linearized P + Pn} m 09 ag tca on Factors 1 0 85 / .5I l 4 08 'l F I og / I b4 'O.75 w j - 0.7 I l 0 65 'N % 06 -"~~~~~~~~ 0 0.05 0.1 0.15 "i Depth o(Flaw (inch) Tension Bending "K" Plot Forman Shivakumar 50 45 l '40 P ,8. -35 30 's K g3r, j l j . 25 20 h / -) >[ -l I 10 5 + 4 l 0 i -0 0.02 0.04 0 06 0 08 0.1 0.12 -0.14 0.16

0. I 8 02 a,

Depth of Flaw (inch) 4 EP-96-003-01 Appendix 2 2I of 56

l SOLUTION NUMBER :.lll B Shank Region - Forman - Shivakumar Correlation, for single Circular Crack in a Cylindrical Bar. For Constant Bending and Tension Stress.(Use ASME Sect. XI Appendix 'A' \\ Linearized stress profile.) { REFERENCE :- ASTM STP 905-~~ Growth Behavior of Surface Cracks in the Circumferential Plane of Solid and Ho,' low Cylinders

• i l

Stress and Flaw Input data j S0 := 56.5 Tension or Membrane Stress due to Bolt preload {ksi} l 1 a := 0.0 Initial Flaw Depth (inch} o j a ine := 0.005 Flaw Growth increment { inch} i := 1. 40 Index for Loop a, := a,,,, + a inc Flaw Growth Simulation a A :=f Normalized Flaw Depth i l l [' j l 4 l EP-98-003-0l Appendix 2 22 of 56

j Determination of Applied Stress Intensity Factor as a function of Flaw depth. j I l 0.5 g tan ny/i 6 < n A, T l. g x := 0.92 / - t In A 1 i s i

• 5'Tl l

g l i Magnification factor { Membrane / Tension} 3' / j n.Ai Fox :=g x - (0.752) + 2.02 A + 0.37- (1-sin i i Stress intensity Factor Solution b K gsr3 :=[So Fox,)-[ ~ l. i 4 I ' EP-96-003-01 Appendix 2 23 of 56

~ _. _ . _ = _ _. _ I f l Tabular Results from Forman-Shivakumar (. Correlation. { Shank Region) a, \\ Fog K !sfs g i 5 10-3 6.083 10-3 0.658 4.661 0 01 0.012 Tff T65T' EOTF o.018 E6ET TT07-0 02 0.024 Eggy E51r DW o.03 E6&T TUT 2T o 03 0.036 E6F7 TT.T61 W o.043 K55g TT5H 0 c4 0.049 E6H T3T47 DTJF o.055 E574 TT3TV o 05 0.06i Eg77 TIT 5I EUr 0.067 Tgg-Trg7-0 06 0.073 EggI T576T EUr 0.079 E&g7 T731T W o.085 T5tf TT24T DF o.091 E69T TONI "G 4~ 0.097 Eggi TV,7g7 T5 C o.103 E.757 2E5Ti 0 09 0.109 E757 ~2TTTI E04F o.116 m TF976 01 0.122 E717 TfTUT DT5F o.i28 m IT. TIT 0 11 0.134 E727 TTT6T 0 115 0.14 ETH T4T9T o 12 0.146 E719 Tf6T ETF o.152 E775 7FJ77 0 13 0.158 E73T 27.TT ETT3-0.164 E75g 27%7T 0' 14- O.17 E75T 2 TETE 0145 0.176 E77T Tf3T 0 15 0.152 E773 70 TUT ET5F o.189 E7gg T5'9fI i o 16 0.195 E7gI TDT 5 D.165 0.201 EEUT ~32T' 0 17 0.207 Tgr TT427 ) T175-0.213 EITg TTT&T 0 18 o.219 Egi7 13T27 ETIF o.225 Kgyg JT997 0 19-0.231 EgT5 TfET6 W 0.237 Eg5T IT77i 0.2 0.243 Egg 7 3E6tT6 I EP-98-003-0l Appendix 2 24 of 56

m Graphical Representation : Forman Shivakumar Correlation (Shank Region} Magnification Factors g, 1 0.85 .I ~ I i 4 ,t 08 ~j. t i [- Foq t l 3 i 'd. 0.75 k 1 0.7 + 0 65 0 0.05 0.1 0.15 i o i g Depth of Flaw { inch) 1 Tension .l i ' K" Plot Forman Shivakumar I 36 r g 32

?

E 28 3 ~ 24 4 $I " 15f'i / o 16 3 - 12 lE l 'g ) .+. / 4 0 4 0 0 02 0 04 0.06 0.08 01 0.12 0.14 0.16 0.18 0.2 1 8 6 Depth of Flaw (inch) EP-98-003-01 Appendix 2 25 of 56

. -.. ~.... SOLUTION NUMBER :-IV Forman - Shivakumar Correlation,

REFERENCE:

- ASTM STP 905-Same Reference as l Solution Illa. Bending simss modified to account forlarge surface stress at the fillet radius, from the FEA results for CRD bolt, using strain energy density method to determine a linearized equivalent stress profile. Stress and Flaw Input Data S peak := 90.229 Linearized Peak Stress in Fillet Region {ksi} Snom := 23.125 Linearized Nominal Stress in the head-shank region {ksi} a := 0.0 Initial Flaw Depth { inch} n a 1,y '= 0.005 ' increment for Flaw growth { inch} d b := 0.25 depth at which surface stress decays to nominal [ inch} i := l. 40 Index for Loop a;:=a _ i t a inc Flaw Growth simulation i a g A :=p Normalization of Flaw Depth 3 Modification of Bending Stress term to account for stress distribution at Fillet ' Speak - S nom 3,: (d b-a) b i ,3 b S, *if(Jb 20.0,J, + Snom.S nom) b b g EP-98-003-01 Appendix 2 26 of 56

- ~_ - -- 9 a: Determination of Applied Stress Intensity Factor as a function of Flaw Depth 0.5 tanl X j n A; 81,:=0.92 h\\- \\T/ 2 cos 7 1 Magnification Factor { Membrane / Tension} ix.A 3' F'OA " E A -(0.752) + 2.02 A; t 0.37-1-sin g g Stress Intensity Solution Imsf:(Sb Fox;-[ K i i k EP-98-00381 Appendix 2 27 of 56

Tabular Results from "Forman-Shivakumar" Correlation with modified bending stresses to account for the large stress at the Fillet of the CRD Bolt. a, Fog K Imsf, 5 10'3 0,658 7.333 0 01 ~ T6T TU~27T W E33T TTJ30 0 02 E661 TT596 EUT5'" E65T T3T54 0 03 E637 T3 TIT W EE59 'fT9T 0 04 E67T TT9T9 0 045 EE73 T9T66 0 05 E377 75~3D7 W TfT M T66~ E6g5 1T9g4 E065'~ E5g7 TT5gT 0 07 Tfy' 2 TDT W Eggi IT676 0 08 E39g 176T5 EUF~ E707 ITTIT 0 09 E757 T4T4T EDU5-' E7TI T5377 01 E7T7 75 TIT ETW" E717 2T15T 0 11 E727 YTU3T W E737 13T5T U 12 ' ' E739 763T9 W E775 T6T55 0 13 E73T 75T6I' ETW~ E75g 76T3T TT E75T 76TK7 0 145 E77f T6~75T 0 15 E77E W W E75E 76T63 0 16 E797 26 6 0 165 ENDT 76'3E7 0 17 Tgr 76Tg5 FTC EgTg TsI3T 0 18 Eg27 76T55 ETg3~ EgTE ITgTI O 19 EgT5 IIT6I FTC Eg37 ITI37 02 Eg37 73TJU EP 98-003-0l Appendix 2 28 of 56

. ~. . - ~ _ _. - - - - _. -. _ _., 1. Graphical Representation > modified Forman-Shivakumar Bending Stress Plot {linearized) ,g 86 67 i d 73 33 i E' S-bi t g g .5. l 46.67 j 33.33 l 20 0 0 05 0.1 0.15 I 8: t Depth of Flaw (inch) t. ' 30 I 26.88 l 23.75 20.63 ' I (K / Imsf) 17.5 i w l P 14.38 / li.2s l 8.13 f I i s O 0 05 0.1 0.15

• i Flaw Depth (inch) i s

L i f l i i-l' i EP-98-003-01 Appendix 2 29 of S6 1 a + ,,.. - - - - ~.

l l SOLUTION V A Head to Shank Region SIF for rods in tension and bending with a single edge crack, (Straight Crack Front). Use of James & Mills approximation combined with Daoud & Cartwnght for bending. Stress profile determined by linearization of FEA profile by strain energy density method.(Same profile as in solution IV} ~ Reference : SIF's for Cracks in Bolts: Engr. Fracture Mechanics, Vol. 30; No. 5.1988. Speak := 90.229 Linearized Peak Stress in Fillet region {ksi} S nom := 23.125 Linearized Nominal Stress in head-shank region {ksi} D := 0.822 Diameter of Bolt in Shank region { inch} a := 0.0 Initial Crack depth { inch} o d b := 0.25 Depth at which Surface Stress decays to Nominal (inch} a ine := 0.005 Increment for Crack Growth { inch} i:=1. 40 Index for Loop Simulation For Crack Growth a, := a,_ i + a inc a. x;:=f Normalization of Crack Depth l V EP-98-003-01 Appendix 2 30 of 56

. ~. - -.... l Magnification Factors Tension Magnification Factor :- ~ r i t := 0.926-(1.771 x + (-26.421)-(x,)2- (-78.481)-(x;)3 + (-87.911)-(x )d] F i i f l. . Bending Magnification Factor :- b; ;* (1.04-3.64 x;) t 16.86-(x )2-32.59-(x )3 + 28.41-(x )4 F i 3 i i l Stress Distribution to account for the Fillet region Stress Gradient i 4 l Define the Stress Gradient as Bending Stress as :- i l i Sg-S nom 0 lb (d b-a) g g db o b,:=i{(d b - a,) 20.0,o Ib, 0 0' Applied Stress Intensity Factor as a Function of Crack Depth Icd; *h*(S K Ft + 0 b; Fb;) nom i 1 i i EP-98-003-0l Appendix 2 3I of 56

i Tabular results of Calculations from James-Mills approximation combined with Daoud-Cartwright a, F. F. KIed. t b i i i 5 10-3 0.916 1.018 11.05 C N E99T T5TT N N E979 TT9U o 02 ygg7 ygg gg7y W M E9M TE7T4 0 03 U 591 E92f 'HTR N DE EDTI T43T L 004'- yggg yggg 75 gy F03I N E8T6 T6TI6 0 05 yg-EIN 76T4T N 0 904 N IT46T o 06 gggg 33 7lrgg7 N E9T3 ET47 21r477 i-N N ERIT IKT97 l N E93T N 792T W E919 E!TT 3E6D7 i F083-UT49 E8TT WT99 l 0 09 gyyg ygDI 3UT66 E073- '6N9 E799 T6703 '~ 01 035-E794 3T6T ETU5-E99T T79-3ERTI W T601 UM6 3E9M l 0 115 TUT 4 E787 JIT37 0 12 TH26 M TT17T l ET75-TUTU N 3TJET 0 13 T35T E775 3TT87 ET33-TN4 E771 3T36V 0 14 T67 EMI 3TTI4 0 145 W EDT 1TTEI o 15 TTUI E7H 3T'ITI ET33-TIT 6 E77T 3 I 727 O 16 TTT E7H 3TTH UT6T-' TT4I E77T 3T399 l N TTT6 E772 3TT5T W 0 18 TIKI EU4 3T3TT TTT E77I TT39T UT33-T177 E776 TTATV 0 19 TII-EUR 3T799 l N THI T71F 3TT57 o2 r37 g7sf 7090T l ? I I t-l. EP-98-003-01 Appendix 2 32 of 56 l ... ~

. Graphical Representation :- Daoud-Cartwright & James-Mills i Magnification Factors I I I F, i t H.F bj - 1 A.s. s ~ _. 08 0.6 0 0 05 0.1 0.15

• i i

Flaw Depth (inch) I i Applied Stress intensity Factor 35 30 1 E P .s i 25 f i Kledi w ? 20 i 1 I5 i i i 1 g 0 0 05 0.1

0. I 5 0.2 a;

j Flaw Depth (inch) EP-98-003-01 . Appendix 2 ' 33 of 56

... ~.. H 4 l i-l l-SOLUTION V-8 - Shank Region SIF for rods in tension with a single edge crack, (Straight Crack Front). Use of James & Mills approximation with tension stress caused by bolt preload in the Shank Region. Reference : SIPS for Cracks in Bolts; Engr. Fracture Mechanics, Vol. 30; No. 5.1988. S0 := 56.5 ' Tension Stress in the Shank due to Preload {ksi} D := 0.822 Diameter of Bolt in Shank region (inch} af:= 0.0 Initial Crack depth { inch} d b := 0.25 Depth at which Surface Stress decays to Nominal (inch} a inc := 0.005 Increment for Crack Growth { inch} i := 1. 40 Index for Loop a, ::a _ i + a inc i i a. x.:=f Normalization of Crack Depth i Magnification Factors F, := 0.926- (1.771 x; + (-26.421)-(x,)2_ (,7g,4g;),(x )3 + (- 87.911)-(x;)]. t Applied Stress Intensity Factor as a Function of Crack Depth Iscjm; dx a,-(So F,) l K t 1 l l^ EP-98 003-01 Appendix 2 34 of 56 ll t

Tabular results of Calculations from James-Mills for Straight Crack Front a, F, K t iscjm 3 5 10 O.916 6.488 00I Eg6T TOT 5-0 015 Eg52 TTD37 0 02 Egg 7 TT7T F Egg 7 T4T67 0 03 ' EggI T5Til E6IT-' M TM 0 04 Eggi 'ITW2 W Egq6 FT657 0 05 Tg-T6T4T TGF" EUUT ITIT2 0 06 EgDU N E EgT6 ITIBI W Eg21 T475T F E9Tr 75T27 0 08 EDIg TfgU7 TOIT'- EgTg TT39T 0 09 EgTg Ilf775 I EU9T-Eg3V 17'001 01 ' Egg-TfDT 0105 Eg7T T2TTg 0 11 TUU2 TIITg 0 115 TUTT 34 441 0 12 EUT6 T5T51 0 125 TUIg 75776 0 13 TU3T TT9T DTT E03T 79T37 0 14 E077 TOT 53 0 145 T3g" TIT 6E W TTGI TE737 W IITE TTUTE O 16 TTT T575T 0165 T.T41 T6'47I O 17 T.T53 17T41 ET75'-- TTT T9363 0 18 ITg1 TUTT ETW' T.Tg7 3TTTT 0 19 T2T TTgTE F THJ 3TIDT 02 T.II7 TITgi l EP-98-003-0) Appendix 2 35 Of 56

..~. -.=....-.. - 4 L I. Graphical Representation :- James-Mills for a Straight Crack Front u Magnification Factors .i4 f: w I.2 E ti iw w 0.8 0 0 05 0.1 0.15 "i Flaw Depth (inch) l l ) Applied Stress Intensity Factor g 50 40 .E ? K iscjtng 2 E2 l 20 m 10 / 0 0 0 05 0.1 0.15 0.2 'i Flaw Depth (inch) l EP-98-003-01 Appendix 2 36 of $6 . = -

SOLUTION NUMBER :-VI-A Head to Shank Region Paris-Sih Circumferentially Cracked Barin Tension:

REFERENCE:

ASTM STP 381, " Stress Analysis of Cracks' Paris Equation With Curve titled values for influence Coefficients obtained from ASTM STP 381 Stress input Snom := 23.125 Linearized Nominal Stress in head-shank region {ksi} Speak := 90.229 Linearized Peak Stress in Fillet Region {ksi} Bolt geometric data and initial Flaw depth D := 0.822 Diameter of Shank { inch} a := 0.0 Initial Flaw Depth { inch} o a ine := 0.005 increment for Flaw Growth { inch} l d b := 0.25 Depth at which Surface Stress decays to Nominal { inch} i := 1 40 Index for Loop a; := a,_ i + a inc Flaw Growth Simulation d := D-2.a; Reduced Diameter due to Flaw (inch) i 2 a. x;:=f Flaw Depth Normalization EP-98-003-01 Appendix 2 37 of 56

i Equation for modifying the stress term to account for stress distribution at the fillet in the shank-to-head region of the bolt. [ Speak-S SS; := nom (d b-a) l i l b Stress modified to account for stress distribution from FEA. The fillet stress concentration is represented by a linear fit. S, := if(SS 20.0,SS, t Snom>Snom) 3 Curve Fit equation for influence coefficients from Paris-Sih paper in ASTM STP 381. HT :=[(0.0003 + 7.2879 x - 140.7368-(x )2]+ 1714.21 -(x )3-12801.2885-(x ) i i i i i 1dD,:=HT +((59075.1219-(x )s]-(168504.1995-(x;)# +(288396.4712-(x;)7]-(270720.9370-(x }s F i i g .FdD, := F IdD;+ 106884.1602-(x )' i Applied Stress Intensity Solutions: 1 :- Constant Stress { Tension} on cross-section ('w,j2 (n D)a5 Kg:= 0.24 Peak Stress at fillet Radius considered to i d act across the s ank cross-sectional area II :- Stress distribution at Fillet Radius approximated and actual Stress distribution on the cross-section considered.{S} S K gip := 2 (n D)as pdD, EP-98-003-0l Appendix 2 38 of 56

Tabular Results from Paris.Sih Correlation. d a, f dD, lipi F K N li 5 10'3 0.988 0.071 10.386 35.662 0 01 EU76 ETTI T6TfJ 36.556 0 015 U gf7 ET41 2TT21 37.485 0 02 UV5T ET6T 2TITJ 38.45 0 025 E93V ETT5 Tf6TT 39.453 0 03 EgI7 D'Tg3 78~3Tg 40.495 W EgTI ETVI N'2TI 41.579 0 04 Uy61 EI51 JT77T 42.707 0 045 Eg7T T2T III57 43.882 0 05 UT/g EIT6 ITITF 45.106 M UT(6 UIIT T5THE 46.382 0 06 UT37 E72T T6.756 47.713 0 065 UTTI E72T TT3T6 49.102 T6T~- T8T T2T INT 4T 50.553 W EgIT E23T 3T657 52.068 0 08 UT63 EITI Tf6TI 53.653 E653-~ y'jg1 E2]I TO' TUT 55.312 0 09 D'T8T UTIT T07T 57.048 E695~~ D'[gg E2J5 TIT 76 58.868 01 U'f57 '02T6 T2~667 60.776 0 105 '6, tty E217 TI'67T 62.778 0 11 EyII E2Tg TT35T 64.881 0 Ii5 T77 EIIV 44 03 67.092 0 12 UT6g T27 TTTE7 69.417 0 125 D~6UE EIII 45.3 71.865 TIF E6gT UT4T TITIT 74.446 0 135 UT77 '674T T6TTI 77.167 0 14 E63g T2T Tf777 80.041 0 145 UTT7 T2T TTT65 83.078 0 15 $315 E2T7 T7T57 86.292 0 155 E621 E23T TTUT6 89.696 0 16 E6TT E2Tg TTTET 93.305 0 165 Eggg EI31 TUT 65 97.136 0 17 E3T5 E2Tg TUT 67 101.209 K E57T UT4T T675T 105.543 0 13 '5'T67 5 741 3T767 110.161 0 185 TJ3-UT4T 32 6TT 115.089 F g33g UT4T 3TT6T 120.356 0 195 U376 UT41 3T377 125.992 02 E3TI '6'IJT 3T657 132.034 5p.98 003 01 Appendix 2 39 Of 56

n-- l Graphical Representation : Paris-Sih Correlation i NOTE

1) Solid Curve based on the actual stress distribution from FEA results.

2) Dashed Curve based on assuming the Peak surface stress from FEA to be constant stress acting on the cross-section of the shank.

Full Circumferential Crack {STP 381) 135 130 125 120 / -5 E 105 I / { 100 9$ -j +, 90 / K [ip; y 73 / K g, 70 l 'f,, 65 60 b 55 f.- - 'j --- p . s" g. 3 15 10 0 O O 05 0.1 0.15 02 8 6 Depth of Flaw (inch) Modified Paris Sih Paris-Sih I' l l l i 1 EP-98-003-01 Appendix 2 40 of 56

SOLUTION NUMBER :- VI B Shank Region I Paris-Sih Circumferentially Cracked Barin Tension;

REFERENCE:

- ASTM STP 381, " Stress Analysis of Cracks" Paris Equation %1th Curve fitted values for Influence Coefficients obtained from ASTM STP 381 Stress input S o := 56.5 Tension Stress in Shank Region due to Bolt Preload {ksi} l Bolt Geometric Data and Initial Flaw deptn D := 0.822 Diameter of Shank { inch) a := 0.0 Initial Flaw Depth { inch} n a inc := 0.005 - Increment for Flaw Growth { inch} i:=1. 40 Index for Loop a := a;_ i + a inc Flaw Growth Simulation i d,:= D - 2 a; Reduced Diameter due to Flaw [ inch} 2a x,:=h Flaw Depth Normalization EP-98-003-01 Appendix 2 4 I of 56

Curve Fit equation for influence coefficients from Sih-Paris paper in ASTM STP 381. HT :=((0.0003 + 7.2879 x,- 140.7368-(x )2] t 1714.21 -(x;)3-12801.2885-(x,)4] 3 IdD,:= HT,+((59075.1219-(x j ]-(168504.1995-(x;)6]+(2883%.4712-(x )7]-(270720.9370 ;x s F i i g FdD := F IdD,+ 106884.1602-(x )' i i Applied Stress Intensity Solution: Constant Stress { Tension} on Shank cross-section 4 S o (n D)as,p dD. Kis:= 2-Peak Stress {S} at fillet Radius considered to i 8 act across the ank cross-sectional area i . EP-98-003-0l Appendix 2 42 of56

1 Tabular Results from Paris-Sih Correlation. d. f a FdD K 3 is; 5 10"3 0.988 0.071 6.602 0 01 ggyg gryg 7g ggy N E9T4 ET47 TN N E93T ET6T T6 TOT F E919 EIT5 TN 0 03 E927 ETI6 T9 TOT W E9T5 EIDT ITTII O 04 E907 E2DT IT587 N ET9T T2T ITUDV W M M IT592 N N E22T TsTI7 N ENIT E275 IT979 FU33-N EIII YUT77 N TIT T2T 3FT2T N ERTI E23T ITT37 0 08 gggy pyyy 7733y N E797 E2TI TT687 0 09 N EIT4 T4T6I EDD3-E759 E2T5 T6TT6 01 gyyy gyyg 77775 W E7TI E237 78 TIN 0.11 g777 gyyg Tgygg 01I5 7 77-E7yg T[9UT 0 12 E70T TTT TT5T7 ET2T-M ENT TIT 5T 0 13 E5T.T ENT TEITF ETJ3-E572 E2aT TIT 97 0 14 gg3g Tyr 3EIgy 0145 EiR7 TIT 3TJJ7 0 15 ggy5 gyyg 7777 N E621 E2TI 33T47 0 16 E6TT E2II TTfl1 4 0 165 g3pg gygg 30 ygy 0 17 ETT6 E739 TIT 7T ET73-E37T ENT T6797 l 0 18 gy&2 EITI TF707 ETBT' T5T E174 TT175 0 19 E37I E2TJ 7677T F E526 ENT 79TR 02 E3TJ E2TI TITTI - EP-98-003-01 Appendix 2 43 of 56

Graphical Representation :- Paris-Sih Correlation in Shank Region Full Circumferential Crack {STP 381) g I I 85 80 - + - - 75 70 / l l 65 l i 7 i Ep 55 t 50 --~+ b K; is d' .s i i 40 j-3 i f 35 I l 30 + I 25 .l !4 l I r 20 1 --- is t i t 10 --- l 5 ?- -- W ~~ O O O 05 01 0 15 0.2 1 Depth of Flaw linch) EP 98-003-01 Appendix 2 44 of 56

SOLUTION Vil Head to Shank Region SIF for rods in tension and bending with Paris-Sib formulation for tension and Daoud-Cartwright solution for bending. The tension solution is for full circumferential notched bar and the bending solution is for a single (straight crack front) crack. This superposition method is in accordance with WRC bulletin 175 " Toughness requirements for Bolting" paragraph "B". References : SIF's for Cracks in Bolts: Engr. Fracture Mechanics, Vol. 30; No. 5.1988., ASTM STP 381, & WRC Bulletin 175. _i_nput Dafa-Pm := 34.212 Linearized Membrane Stress in Fillet region {ksi} Pb := 35.564 Linearized Bending Stress in head-shank region {ksi} D := 0.822 Diameter of Bolt in Shank region { inch} a := 0.0 Initial Crack depth { inch} o a inc := 0.005 Increment for Crack Growth { inch} i:=1. 40 index for Loop Simulation For Crack Growth a; := a,_ i + a ine d := D-2 a, i a. x,:=f Normalization of Crack Depth Bending Magnification Factor (Daoud-Cartwright):- l F, "! 1.04-3.64 x;) + 16.86-(x )2-32.59-(x;)3 + 28.41-(x )4 b i i EP-98-003-0l Appendix 2 45 of 56

Curve Fit equation for influence coefficients from Paris-Sih paper in ASTM STP 381. HT, :=((0.0003 + 7.2879 x - 140.7368-(x )2' + 1714.21 -(x;)3-12801.2885-(x )# i i i F IdD, := HT; + '59075.1219-(x;)3)- (168504.1995-(x;)6) + (2883%.4712-(x )7]- (270 g 3 dD, := F IdD;+ 106884.1602-(x,)' F K from Paris-Sih Formulation for Tension Stress i P K M 1p3 := jd D, 2 W K from Daoud-Cartwright for Bending Stress i Ide,:"h*(PFb;) K b i l K combined in the Shank Region i KIpd, := Kips,+ KIde, j i j EP-98-003-0l Appendix 2 46 of 56

. ~. legnleJ wasnl1s ;oJ ocwq!uep deps-s!q y aeonp-oepmp641 3 rds' 3 po 3 ;d ' P f g,, g reg r Sr 9C8Z o oi t_96.l.. E 0 01S E IEII-o ot 2 611-E E 0 075 E E 0 0f E E 0 0f S 12 011 12124 E 0 0r lEl162 11 112 E 0 0rS 11 261 E o os lit 22 LILl M 0 OSS E E 0 09 L166-1fL15 0 095 E O OL E yn y 12EEI LttiJ 10 20I g_ illil LtLtJf EL 42I 0 08S E E 0 06 E 0 065 E IIII5 01 19 414 11.lfI 12.Eth 0 IOS EIEEI o ii LI2E_ 12tIb M O IIS E E o ig 112tl M M O itS E E 01t 12LEL M E qS L16Q.b L16Db tiUUA 01r E E E 01rS E E O IS lllif lIIII E o ISS fIIII E E 0 19 E E 0 195 EIEE1 E O IL E E o ILS SE 661 E O I8 E E 0 185 E E 0 16 ttil.l. ll f.41 .2203 0 165 ' t26QI IG1tJ M l 97 t.6E1tJ II.02I ilfl I 3g.gg.oog.og yddeup!x i 9 01S9

i l 1 80 I I I I I I i i i 75 70 65 60 $5 50 ,/ / 45 / - / K IPSI K ! dei 40 /* 3 S th ,/ 35 / 4 30 / 25 20

• _, _.. ~ = *,,,.... -

l$ s,. s *... *...."**** s sY 10 ,s, ! '.., s,/.,s. .ls!', 5 / I I I I I I l I I 0 O 0 02 0 04 0 06 0.04 O! 0.12 0 14 0 16 0 18 0.2

• h Applied Stress intensity Factor Paris-Sih { tension)

---

Daoud Cartwright (bending}

j Combined EP-98-003-01 Appendix 2 48 of 56

SOLUTION Vill Head to Shank Region SIF for rods in tension and bending with Paris-Sih fonnulation for tension and Besuner solution for bending. Both the tension and bending solutions are fro a notched bar geometry. This superposition method is in accordance with WRC bulletin 175 " Toughness requirements for Bolting", paragraph 'B". l References : Requirements and Guidelines for Component Support Materials Under Unresolved 1 Safety Issue A-12; EPRI NP-3528, & WRC Bulletin 175. i Pm := 34.212 Linearized Membrane Stress in Fillet region {ksi} Pb := 35.564 Linearized Bending Stress in head-shank region {ksi} D := 0.822 Diameter of Bolt in Shank region { inch} D b :=g Outside radius of bolt (inch) a := 0.0 Initial Crack depth { inch} n a ine := 0.005 Increment for Crack Growth (inch} i:=1. 40 Index for Loop Simulation For Crack Growth a ::a _ i + a ine 3 i c; := b - a; c. i x;:=p Normalization of Crack Depth influence Functions mepri :=0.5-(x;)43{l +(0.5 x;t 0.374-(x )2- 0.363-(x,j + 0.731-[x;j'{ 3 F i i bepri; := 0.375-(x ).2.5,1 0.5 x, + 0.375-(x )2 + 0.3125-(x;)3 + 0.2734-(x )4 + 0.537 / x )5' F 3 i i i EP-98-003-01 Appendix 2 49 of 56

a) SIF Solutions for Tension and Bending ] mepri 'h K Itepri; := P F m 3 Ibepri;:= P Fbepri 'h K h g i K lepri; := K Itepri + K 'r:pri, it 3 1 1 1 EP-98-003-01 Appendix 2 50 of 56

I a' K lepri'. J-5 10'3 0.406 9 859 7 FUT-- U r5T 14.00s 7 UTr5-U3gg 17.247 7 TOT-F39T 20.031 7 UM5-Uygg 22.539 7 TUT-F33T 24.s64 7 TJPJ3-U37g 27.06 TOT-U37r 29.167 7 5375-Uygg 31.211 g T03~- U33T 33.212 l g FU55-Uygg 35.iss ) T0F-U33T 37.153 FUKJ-FJzg 391I7 W F33T 4l' 92 F073-U3II l~ TK TUI-- F3IT 43.oss 45.113 i U3g3-U37g 47.176 g T09-- U32T 49.2s6 U393-U3Tg 51.452 TT-- 63TT 53.6s2 UT05-U30g g 55.9 4 TTT-- U30T 5s.36s UTry-Uygg 60.843 N TTT-Uygt 63.4i9 UT25-U3Rg 66.106 TTI-- F3fT 68.917 FTII-U'27g i 71.862 3 TTT-~ FUT 74.955 FTTI-FJ6g 7s.21 Trg-- U36T s1.642 E FT33-Uyyg 85.26s E TTF-U2TT 89.306 - II FT65-U2T6 93 177 TT7-- U21T 97.502 FTyy-Uyyg ) 102.107 E TTI-- 627T 107.019 U Fig 3-Dyyg I12.268 I W D32T J TT7TIF W UTp3-U3rg 123.919 [ T y-- F2TT 130.403 't EP 98-00341 AKmndix 2 31 ef 9A

y i Influence Functions 3 i i i / / / 2.5 / _ / .f p nwpri i u". F epr' ' g b g 2 y _ j.. _1 /,,/ t I.$ I t l g 0 0 03 0.1 'O l$ 0.2 8 6 Flaw Depth (inch) Tension ... Bending SIF Plots 150 1 I I I I i 4 I i 100 K lteprt; K lbeprq k / m K eprt / l i / 50 ,/'/ ... ~c. w ::.. - - ~ ~,....... -,,,. nan. ~ a I I I I I I I I 0 0-0.02 - 0.04 0.06 0 08 0.1 0.12 0.14 0.16 0 18 02 'l Flaw Depth (inch) SIF. Tension SIF. Bending SIF. Combined - EP-98-003-0 l Appendix 2 52 of 56 +

Determination of ASME Section XI Allowable Fracture Toughness Ic I Material Fracture Toughness for initiation (K c} - ksi

• In0 5 l

i ) .K ge := 130.00 Material Stress Corrosion Cracking Threshold Stress Intensity Factor {K sec) - ksi

• in 5

( o i l K i3ce := 130.00 Use the lower of the material toughness value to determine the ASME allowable: j 130 k,!ASME*h t i := 1. 40 Klasme : K 1ASME 3 K IASME = 91.924 EP 98-003 Appendix 2 53 of 56

Plot Number: 1 i i Graphical Comparison of Results from "K" solutions for Head to Shank Region Note : Pan's-Sih correlation is for a Full Circumferential Crack (360 degrees) whereas the othercorrelations are for Part-Circumferential Cracks. 1 Comparison Plot for all "K" solutions gg 135 I l I l 1 J l 1 -i i 83 ~i i l j i i25 t -+- [ ] r 1 I i I I I i l20 -+-. ---4-- l i 115 -t i 110 L' K I

lhs, 103 b

100 -4 K15fi [ l l l l 1 l l I 9' l~ ~' i f i ~"-h-I i i i -t j g ++ 9 Imsfg 90 - ] l hI 1' -- f, _-_h, (, -[ I + f' ~~ 85 i i ---l.-- $...I'Pi' 30 ( [ f I i 75 l~ f i i I K p' t'~~ l - -- - b- + l l' i j 70 ~! .,s, tee 7 f i i i f.d 65 ---+ -y + -l b o 'i 60 -- 4 1- -- U --- yg'M 33 i i yQee __T l \\ j-tf i T i. r-- - lasmeg 50 y b ~- as -+- - s-- y -- - d-45 l -f *'"y- - -' {J K gegig _-p -L --- 1 \\ -+-- 35 f.p' ~ ++-+ b d A bO i--0 h D D' 30 o40 3,,,,,;,,, A l

- p-jr-f--p-]~~j--d r4-~

25 f 20 f- --*',,,,y 4 ( i q t- --i - r - 15 L-- i A-10 - ? l l 4-- +. 4-b--- r 4 { i i i l I t i i i e -ga 1 y ~ I l I i i l l i j f I f i 0 0 001 002 003 004 005 006 007 008 009 01 011 0.12 0.13 014 0.15 0.16 017 018 0.19 02

• i Depth of Flaw { inch) 1 James-Mills (Soln. I B}

+++ Forman-Shivakumar (Soln. III A) -~~ Modified Forman-Shivakumar (Soln. IV)

---

Modified Paris Sih { Soln. VI A-Il}

ese Paris-Sih (Soln. VI A I} -o-Cartwright Daoud (Soln. V A} ese Faris-Sih & Daoud-Cartwright (Soln. Vil) ASME limit --+-- EPRI Solution. Soln. VIII l l EP-98-003-0l Appendix 2 54 of 56

Plot Number: 2 Graphical Comparison of Results from "K" solutions for Thread Root Region Comparison Plot for all "K" solutions I i j l 95 90 SS 80 m 75 70 E 65 4-- P K Ijmtj' .i

K.l, 1

l 50 -K l J. lasme' 45 f- ,s ' ___.,$ ~ 3n 23 . -h"' i 20 ~, + - - 15 N + l0 f 5 9 l. h -) i i i O O 0.01 0.02 0 03 0 04 0 0$ 0.06 0 07 0 08 0 09 0.1 011 0.12 013 0.14 0.15 0.16 0.17 018 0.19 02 i Depth of Flaw (inch) James Mills { Soln. I A} - Alan Liu { Soln. II) ASMElimit i EP-98-003-01 Appendix 2 55 0f 56 ~~

1 1 I Plot Number: 3 Comparison of Graphical Results from "K" solutions for Shank Region Note : Paris-Sih correlation is for a Full Circumferential Crack (360 degrees) whereas the other correlations are for Part-Circumferential Cracks. Comparison Plot for all "K" solutions 95 L I f i 1 ~ 90 ---4----+ t I \\ 85 y -+ ~ 80 I A 4 l { f I \\ f 75 -t - -/f--- 7- - [ ! 70 l h K jmsi 6$ f l [ '- j x 1,,, 60 - Lt H 1 ~XXX $5 I ,. !I AK iscjm; { I .# #w - - +.. 50 &4' -K isj I g D' l l 4' B 45 .#e

1. .9,#

i i 5....... g lasmei 'l l-4-- t ; h',',! l 1 I x 40 g - +- t- +- A I o*g I. -4, g l ' +F-l i j r,e4;#of!ll E 30 j ./ i .i I i I i 25 f e n .o. .0

4-g',i

+ y p--+- l l l l ,t -4 g i i rl L-15 - + - - - -1 --4 i - ;f-,4 j l l i 10 j t-+! j d' i t i . b l l l Il l-f i 0 0 001 002 003 004 005 006 007 008 009 0.1 011 0.12 013 014 015 016 017 0.18 019 02 a; {. Depth of Flaw (inch) James. Mills (Soln. I C} XXX Forman-Shivakumar { Soln. Ill B) Straight Crack: James-Mills (Soln. V B) - - + - - Paris-Sih (Soln. VI B} ASME limit EP-98-003 0l Appendix 2 36 of 56

Engineering Report: EP-98-003-01 Page 42 of 43 l Appendix 3 Evaluation of Bolted Joint 1 1 l 'l

i i l l Appendix 3 j Bolted Joint Calculations: CRO Cap Screw Evaluation Nomenclature i De = Larger of Bolt Head or Washer Dameter (inch) Lo = Gnp Length of Bolt (inch) T = Height of Bolt Head (inch) { H Li = Length of Threads (inch) Lea Length of Bolt Shank (inch) Lo = Grip Length of Bolt (inch) Den = Demeter of Bolt Shank (inch) TN = Heigth of Nut or Length of Threads for CRD cap Screw (inch) A. = Tensile Area of Threads (inch 2) Aa = Crossechonal Area of Bolt Shank (inch? ) AN = Crossectional area of Shank at hutch /Falw (inch 2) Lti. = Equivalent length of Bolt Shank (inch) i L., = Equivalent length of Threads (Inch) { LN = Width / length of circumferential Notch / Flaw (inch) 4 dn = Depth of Notch / Flaw (inch) E = Youngs Modulus (p/ inch) ksi) Ke = Stifness of Bolt (ki A = Crossectional Area of the Equivalent Cylinder used ) represent Joint Stffness (kip / inch) l C T = Total Joint Thickness for CRO cap screw taken as b.gth of Shank (inch) DH = Dameter of Bolt Hole (inch) D; = Effective Dameter of Equivalent Cylinder of Joint urder Preload (inch) K; = Stiffness of Joint (inch) j Fp = Prevailing or Residual Preload (kip) l Lx = Extemal Load on Bolt (kip) Lxent = Critical Extemal Load required to cause Joint Separation (kip) AFs = Additional Load on Bolt due to Extemal Load (kip) % = Load Factor (dimensionless) Fe, = Initial Preload at installation (kip) RFp = Reduction Factor for Initial Preload immediately after tightening (%) l RFer, = Reduchon Factor due to Elastic Interactions (%) RFar = Reduction Factor for Long Term Relaxation of Bolt atTemperature (%) Otir = Dameter of Bolt Shank at Location of Notch / Flaw (ALLOWABLE)(Inch) er = Allowable depth of Notch / Flaw to meet requirements (inch) Pece = Maximum Intemal Pressure causing extemal load on Bolt (ksi) Oncu = Dameter of CRD Nonle 0.1ch) j N = Number of Bolts i F, a Total Preload on Bolt ; including extemal load (kip) ei = Total stress in Bolt at initial Preload (ksi) op = Prevailing Stress in Bolt due to Prevading Preload (ksi) ope = Stress in Bolt Due to Prevailing Preload + Extemal Bolt load (ksi) Sm = Allowable ASME Stress at temperature (ksi) See Figure 1 for explanation of Bolt and Joint Nomenclature EP-98-00341 Appendix 3 I of 7

l CALCULATIONS FOR BOLTED JOINT INPUT DATA (Referencesin Parenthesis) DB := 1.8125 -(Ref. 22 & 26) L o := 3.44 (Ref. 3 & 22) input Below from T pg := 1.00 (Ref. 3 & 22) Report. L := 2.06 (Ref. 3 & 22) LN := 0.05 t L B := 3.44 (Ref. 3 & 22) d n := 0.120 Dsh := 0.822 (Ref. 3 & 22) E := 30.10 3 T14 := 2.05 (Ref. 3 & 22) T := 3.44 A s := 0.462 (Ref. 3,6 & 22) o ; := 69.78 S m := 29.5 Dit := 1.0 (Ref. 27) F p; := 30.0 (Ref. i,2 & 3) RF j g := 7.0 (Ref. 8) p RFei := 15.0 (Ref. 8) RF ltr := 20. (Ref. 9) Pace:=5.872 (Ref. 25) DN 2 :=4.912 (Ref. 27) N := 8 (Ref. 27) 4 EP-98-003-01 Appendix 3 2 of 7

Joint Stiffness Calculation Reference : 8 Equation 5.20 pp 152 Calculation for De < Da < 3 De Use DfDs = 2.0 DBT T2 x 2 n ACT'(UB-DH)+y-(l.0)- 5 + tug AC = 2.331 EAC-4 K := 7 K y = 2.033*10 3 Bolt Stiffness Calculations Case i Nominal Bolt TH Lbe

• L B +T Lbe "3 94 TN Lse :: L o-L B +7 Lse = 1.03 xDsh A B1 ::

A B1 = 0.531 4 i KBl

• Lw L se 3

EAB1 +q KB1 = 3.10810 EP-98403-01 Appendix 3 3 of 7

1 4 Bolt Stiffness Calculation Case 2: Bolt Shank completely degraded by 0.120 inch i TH Lbe ;* L B+7 L be " 3 94 TN Lse ;* LG-L B+7 L se = 1.03 n -(Dsh - 2.d ) n AB2 ;* A B2 = 0.266 4 i KB2 ;* g g g, 3 qtg K B2 = 1,761 10 Bolt Stiffness Calculation Case 3: A Full Circumferential Notch in the Middle of the Shank TH' L be ;* L B+T-LN L be " 3 89 TN lse ;* LG-L B +T l se = 1.03 n-(Dsh-2d ) n 'AN ;* 4 4 AN = 0.266 i nDsh A B3 ;* AB3 = 0.531 4 l 1 ) .K B3; L W L LN se 3 q+qtq KB3 = 3.078 10 EP-98-003-01 Appendix 3 4 of 7 l J

Calculation of Prevailing Preload & and Stress in Bolt M ipl. Mell' M itt Fp:=FpjIl 7 !! g 'l-F p = 18.972 M ip Mcli M itr p:=oi fI g li.1 g ;:1 y a p 44.129 e Calculation of Loads required for Joint Separation Case 1 { Nominal Bolt} K B1i L Xcrit! := F p ' I + L Xcrit! = 21.872 i Case 2 { Fully Degraded Bolt Shank} K B2! L Xerit2 := F p ; I + LXcrit2 = 20.615 Case 3 ( Bolt Shank with a circumferential Notch in the middle} K L Xcrit3 := F p-l 1 + B3 l. LXerit3 = 21.844 Calculation of Load Factor using Bolt Stiffness from Case 3 K B3 k"K B3 + KJ

• k = 0.131

[ I l l l 1 Calculation of Bolt Extemal Load due to Accident Pressure i Fore:= Forc = 111.274 Fore X;* N L x = 13.909 AFB ;"l X'* k AF B =1.829 Fcp := F p + AF B Fip = 20,801 F sp M := 7 P M =1.096 The External Load on the Bolted Joint Smaller than the due to Accident Ataximum Pressure is smaller than the critical externalload to cause Joint Sopration; That is: Lx (13.909 kip) < Lx,,,,(20.615 kip) Therefore Joint Separation is Precluded. Calculation of Allowable Notch / Flaw Depth to sustain Total Bolt Load M pe := o p o, = 48.383 a p ' " pe Dbf;" qD sh o bf = 0.608 i l Dsh-D r h a r:: a r = 0.107 1 The allowable NotclJFlaw depth for a full circumferential Notch is 107 mils l l l EP-98-003-01 Appendix 3 6 of 7

Figure 1 : General Bolt Dimensions L LG l D I ? 4 La Lt LC Figure 2 : Effective Bolt Dimensions for Use in Calculations DJ Ds - r k,3k$E

+ 4 Engineering Report: EP-98-003-01 J: Page 43 of 43 l 4 Appendix 4 l i ~ l Mechanical testing and Evaluation of Circumferentially Notched CRD Capscrew Material i 1 e l i i l i j __--m,.

APPENDIX 4 Mechanical Testing and Evaluation of Circumferentially Notched CRD Capscrew Material INTRODUCTION : The boltedjoint and fracture mechanics evaluation of CRD capscrews showed that the limiting flaw depths, for a full circumferential flaw subjected to a maximum load, were 107 mils and 150 mils respectively. Based on these evaluations a limiting flaw depth of 107 mils was used to establish the inspection criteria. The purpose of the mechanical testing was to ensure that the limiting flaw depth determined by analysis is conservative and provides assurance against premature failure of the capscrew. The CRD capscrew material ofinterest is ASME SA 193 Gr. B7. Additional bolts with the same specification and of similar dimensions were procured for mechanical testing. The details of the testing performed and an evaluation of the test results are presented in the following sections. DETAILS of TESTING : A comparison of the procured bolts and the CRD capscrew is shown below. Attribute CRD Capscrew Procured Bolts Material Specification ASME SA 193 Gr. B7 ASME SA 193 Gr. B7 Overall Length (in) 6.5 8.5 Thread Length (in) 2.0 2.5 Thread Size 1.0" x 8 UNC 7/8" x 9 UNC Shank Length (in) 3.375 5.25 Shank Diameter (in) 0.823 0.850 The CRD capscrews were custom manufactured for the application, hence the procured bolts were selected such that the shank diameters were reasonably close. The shank length of the procured bolts were longer in order to accommodate a clip-on extensometer having a one inch (1.00") gauge length. Two bolts from the procured set were subjected to tension testing in accordance with the Standard ASTM E-8 method. The results from the tension testing are as follows: Property Specimen 1 Specimen 2 Average Yield Strength (ksi) 121.9 122.9 i22.4 Tensile Strength (ksi) 135.4 136.6 135.0 Elongation (%) 20.3 20.9 20.6 Reduction in Area (%) 61.0 60.0 60.5 l ~ Report: EP-98-003 01: Appendix 4; Page l of 17

) 1 The tension properties of the CRD capscrew material from references 1 through 3 were compared to the test data above. This comparison is shown below: Property Procured Bolt CRD Capscrew Material Reference 1 Reference 2 & 3 Yield Strength (ksi) 122.4 127.2 120.9 Tensile Strength (ksi) 135.0 144.5 131.4 Elongation (%) 20.6 N/A 21 Reduction in Area (%) 60.5 N/A 60.6 The comparison presented above demonstrates that the mechanical properties of the procured bolts are similar to the material for the CRD capscrews. Therefore mechanical testing of notched bolts would effectively simulate the behavior of notches in the CRD capscrews. Additional tension testing of bolts in the as-is condition, using two procured bolts and one CRD capscrew removed from service at GGNS, were performed to compare the applied load versus strain behavior. An increasing load to a value of 56.0 kips was applied and the strain recorded. Upon reaching the maximum load the specimen was unloaded and the strain recorded. Figure I shows the load strain trace for the two procured bolts and figure 2 shows the load strain trace for the GGNS CRD capscrew. A comparison of the two figures showed that the behavior was similar in that the strain at a load of 50.0 kips was between 0.0029 in/in and 0.0031 in/in. This test along with the tension properties comparison, clearly demonstrates that the behavior of the procured bolt is representative of the CRD capscrew material. Therefore, using the procured bolts to perform notch testing will enable characterization of the CRD capscrew material and, hence, provide the necessary information for verification of flaw depth limits obtained by analytical methods. A "V" groove notch, ( 60* included angle and 10 mil root radius), were machined in the middle of the shank. The notch depths were 100 mils,125 mils and 150 mils. These depths were selected to cover the range of the depths used in the analytical evaluations. The maximum applied load was based on the initial preload of the CRD capscrew, corrected for test temperature with respect to the normal operating temperature. The load correction to account for temperature correction was obtained by taking a ratio of the room temperature yield strength and the at temperature yield strength. The yield strengths used in the ratio were obtained from Section II of the ASME Boiler and l Pressure Vessel Code (reference 4) for the CRD capscrew material. The maximum load was determined as follows: Maximum Load = 30.0 x (105.0/88.5) = 35.59 or 36.0 kips. Report: EP-98-003-01: Appendix 4; Page 2 of 17

i i The gauge length for the extensometer was one (1.0) inch, and the notch was located in the middle of the extensometer. The extensometer was functional for the entire test including both the loading and the unloading sequence. For each notch depth two specimens were tested, for a total of six tests. The load-strain traces from the test are provided in figures 3 through 5. The traces in these figures clearly show that the strain l behavior is linear for both loading and unloading and that upon complete unloading no residual strain is observed. This behavior is characteristic of a linear elastic behavior and indicates that the notch effect is not pronounced. The two specimens with a 150 mit deep notch were used to evaluate the onset of elastic-plastic behavior. These specimens were loaded incrementally in tension until the strain trace showed a clear departure from linearity. At this point th' unloading e sequence commenced with the extensometer functional. Thus the complete load-strain trace for the full cycle wr s obtained. The results of this test sequence is presented in figure 6. Figure 6 shows that the departure from linearity of the strain trace occurs at a nominal strain of 0.0030 in/in and is clearly discernible at a strain value of 0.0032 in/in. The residual strain was approximately 0.00025 in/in. The residual strain is indicative of the onset of plastic deformation in the notch region. At the departure from linearity of the strain trace the applied load was 46.0 kips. EVALUATION : The test results, presented in the previous section were evaluated using nominal stress and strain concepts and by Neuber's rule (reference 5) for notch analysis. The effect of notch depth on measured strain, at the maximum load of 36.0 kips, was obtained from figures 1 through 5 and graphically presented in figure 7. Also presented in figure 7 is a linear regression line with a slope of 9.11 E -05. The extremely small value of the slope is indicative of a near horizontal line, which implies that the notch depth from 0 to 150 mils has insignificant effect on measured strain. Since the applied load was representative of the initia: preload at temperature, this observ'ation demonstrates that a bolt with a 150 mil deep notch will sustain a tensile load of 36.0 kips without an overload failure. The stress at the notch root was computed by dividmg the maximum load - of 36.0 kips by the cross-sectional area at the notch. The results of the notch root stress as a function of notch depth is presented in figure 8. From this figure and the tensile data presented earlier, it appears the notch root stress reaches yield strength level at a depth of 117 mils. This simplistic analysis shows that at the limiting flaw depth of 107 mils, the stresses at the root of the notch will remain below yield strength. The evaluation of stress and strain at notches is most often performed using Neuber's rule. Neuber's rule states (reference 5): "The geometric mean ofthe stress and strain concentrationfactors remain equal to the elastic stress concentrationfactor during plastic deformation. " Report: EP-98-003 01: Appendix 4; Page 3 of 17

) This rule is mathematically defined as: k = V k, x k,

---

( 1 )

m where: k = elastic stress concentration factor m k, = stress concentration factor ; { local stress @ notch / nominal stress} or o/S k, = strain concentration factor; { local strain @ notch / nominal strain} or c/e Neuber's rule applies only in the deformation regime prior to full plastic yielding of the net section. In the notch region subjected to loading there are three deformation stages possible, namely; elastic, elastic-plastic and fully plastic. For the evaluation of the CRD capscrews the stage of full plastic deformation is undesirable and hence to be avoided. Thus the analysis and testing was undertaken to define a safe flaw depth such that the onset of full plastic deformation is precluded. For these reasons the final stage, the full plastic deformation, will not be discussed. The evaluation of the other two deformation mechanisms, described in reference 5, are summarized below :

1) Linear elastic deformation: When no localized yielding has occurred at the notch root, the notch stress (a) is related to the nominal stress "S" by the elastic stress concentration factor k as follows:

m o = km xS

---

(2) similarly the notch strain can be dermed by:

c = [S x k ]/ E

---

(3); where E is the Modulus of Elasticity m

In this regime of deformation both the stress and strain remain below their respective values at yield in a uniaxial tension test.

2) Elastic-Plastic Deformation (Local Yielding): With an increase in the applied load, local yielding at the notch root occurs when the stresses reach the material's yield strength. At this point only a small volume fraction of the material in the notch region has yielded. Eventually, as the load is increased to a substantially higher level, net-section yielding occurs. The applicability of Neuber's rule in the elastic-plastic deformation regime is limited to a state prior to the net section yielding. The deformation in this regime is quantified by (reference 5):

o x e = [kw xS]2/E -- --(4) Report: EP-98-003-01: Appendix 4; Page 4 of 17

For elastic-perfectly plastic material the strains prior to net section yielding can be determined by the formulation in reference 5, which is: x S]2 [c, x E)

---

(5) c, = [km

/y y where: c = notch strain past local yield but prior to net section yield, yn c, = material yield strength. y In the above equation it is important to note that the notch strains will be higher than the uniaxial yield strain; i.e. s,2 c,/E. y y In order to determine the notch stress and strain behavior for the test specimens a Ramberg-Osgood material behavior was used. The Ramberg-Osgood model provides for strain hardening and hence provides for proper characterization of material behavior. The model is defined as (reference 5): c = (c/E) + (c/H)""

---

(6) where : H = strength coefficient n = strain hardening exponent.

The Ramberg-Osgood coefficients (H and n) were determined by using the stress strain data from the tension tests (provided in figure 9) and performing a linear regression using equation 6. The method used is described in reference 5. The Ramberg-Osgood coefficients obtained were as follows: H= 250.41 ksi and n = 0.131. In order to ensure the validity of these coefficients, values for a similar material obtained from reference 6 were compared. The material in reference 6 for which the values were available was SAE 4130 having two different thermo mechanical treatments. However it was essential to ascertain that the coefficients obtained from test data for the present effort was in reasonable agreement with the published values. This comparison is presented below : Material Condition "n" "H" (ksi) SA 193 - B7 Quenched & 0.131 250.41 Tempered SAE 4130 Annealed 0.118 169.4 SAE 4130 Quenched & 0.156 154.5 Temper Rolled Report: EP 98-003-01: Appendix 4; Page 5 of 17

The above comparison shows that the values for the coefficients appear reasonable and the differences are attributable to the differences in the material chemistry and thermo-mechanical treatment. These martensitic l steels are characterized by low strain hardening exponents and high strength coefficients. When the stress-strain relationship described by equation 6 is substituted in equation 4, the resulting stress-strain at the notch with respect to the applied load becomes (reference 5): [k, x S]2, y2 + c x E x (c/H)""

---

(7) i Equations 6 and 7 were numerically evaluated by using Mathcad worksheets which are included as Attachment I to this Appendix.

The elastic stress concentrativa factor (km) for the various notch depths was obtained from reference 7. For the notch geometry and depths tested the value for the elastic stress concentration factor was found to be nearly constant at a value of 4.9. The upper bound for the notch strain, for the test specimens, at an applied load of 36.0 kips can be obtained from equation 5. This strain, considering an elastic-perfectly plastic material, is 0.0266 in/in. Results from the analysis presented in Attachment I to this Appendix shows that for an applied load of 36.0 kips the notch strain is 0.0202 in/in. This value when compared with that from equation 5 suggests, for the notch depths ofinterest ( 100 to 150 mils) at an applied load of 36.0 kips, that any yielding would be very localized and net section yielding is precluded. The nominal strains obtained from the test of the 150 mil notch specimen (figure 6) and the notch strains from Attachment I can be used to determine strain concentration factors at various load levels as shown below : Applied Load Nominal Strain Notch Strain ke (kips) (in/in) (in/in) 36.0 0.0023 0.0202 8.78 43.04 0.0029 0.0273 9.41 47.43 0.0031 0.0322 10.39 The strain concentration factors below net section yield load (46.0 kips) are reasonably close. Once the load is increased past the net-section yielding, the strain concentration factors tends to diverge in accordance with theoretical predictions (reference 5). The notch strain at the estimated Repon: EP 98-003-01: Appendix 4; Page 6 of 17 \\

tt maximum preload value of 36.0 kips is 62.5% of the notch strain at net section yield load of 46.0 kips. This shows that based on a notch analysis, net-section yielding at estimated maximum preload is precluded. Similar analysis for the 100 mil and 125 mil notch specimens show the strain concentration factors at an applied load of 36.0 kips to be 8.18 and 8.43 respectively. These values compare favorably with 8.78 for the 150 mil notch specimen. This comparison shows that the effect of notch depth, in the range tested, is not significant. CONCLUSIONS : Based on the testing results and the evaluations presented in the previous sections the following conclusions are made:

1) The load-strain trace maintain a linear relationship up to the maximum load of 36.0 kips for all notch depths tested.

2) At the maximum load of 36.0 kips the nominal (measured) strains are not affected by the notch depth. The slope of a linear regression line, on the plot for measured strain as a function of notch depth, was extremely small.

3) For an applied load of 36.0 kips the notch stress, based on net section area, j

would reach material yield strength at a notch depth of 117 mils.

4) The elastic stress concentration factor, for the various notch depths investigated, remained constant at a value of 4.9.

i

5) The calculated notch strains for the applied load of 36.0 kips are above the -

strain at yield in a uniaxial test. Therefore, localized yielding at the notch root is expected to occur for notch depths above 117 mils. However, the calculated notch strain is below the limiting value calculated assuming an elastic-perfectly behavior.

6) Notch analysis using the elastic stress concentration factor of 4.9, using Neuber's rule and a Ramberg-Osgood material relationship, shows that for an applied load of 36.0 kips the notch strains remain below the notch strain required for net section yield. Therefore, for the deepest notch depth evaluated, net-section yielding is precluded at the expected bolt preload of 36.0 kips at room temperature which is equivalent to 30.0 kips at the operating temperature.

Report: EP-98-003-01: Appendix 4; Page 7 of 17 _~

l l l

REFERENCES:

1) Grand Gulf Nuclear Station Engineering Report, GGNS-92-0033, Revision 0.

1992.

2) River Bend Nuclear Station, RBS CR 92-410.

3) River Bend Nuclear Station, RBS CR 96-310.

4) ASME Boiler and Pressure Vessel Code, Section Il Part D,1992 Edition.

l

5) " Mechanical Behavior of Materials"; Norman E. Dowling, Prentice Hall, Englewood Cliffs, NJ 07632.1993.

6) " Failure of Materials in Mechanical Design: Analysis, Prediction,' Prevention";

Second Edition, Jack A. Collins; John Wiley & Sons Inc.; New York, NY. 1993.

7) "Peterson's Stress Concentration Factors"; Second Edition _; Walter D. Pilkey, l

John Wiley & Sons Inc.; New York, NY.1997, l l l i l Repon: EP 98-003-01: Appendix 4; Page 8 of 17

No Notch, Sample 1

• 6..i* *ilaa 7."' * '

uns i + mm. 4 . 4.. i suma I I/ saae ,g.. .. L. ~ 9 mus ... i sV me. e;. .. i.. ne lg.;,9

e. -

...i.. ..i.. s /. i 9,6. i sage 7 y/ 1 & acu. i. i a un 4am a at LVele l ita/ Ire No Notch, Samplo 2

• r* Ah,.g f.,P.3, fyt 8. 2 g

ende t r /! gin:4 .../........ f / /a - s w*Y . cut =. 5 // i .4 /... xga ..a.. 5 /. i um ./. = e i p ,/f' ' m,

1. ,9, :

. 9', .V [tula i . i i 8 wt4 ~ & we a 631 a 4 su .v.,. i n.m e Figure 1: Load Strain Trace for Un-notched Procured Bolts in the as-received Condition. Report: EP 98-003-01: Appendix 4; Page 9 of17

6 i Energy Bolt

• =s F fMf e Ce t 9 feet m t

$14FM $4 a 31 ftW1 l 1 .. f.. ..f.. { l i gy3 . [. ..!. [ # .. l. 4/ h f i P l i /*p, i 4W3 y! + 5 i I i l t i ayu ..k... i,<,,/ i i ,,u .t. 3 l , f f' mos .,j. - I x'e ..I. ..i.. i g.m } e* / f .. l'..... j. -l.. ... j.j.... j. y .4.. .,,.3 l .t.

1. ,9 imu :.

l .A' suu i l 4 L.... jf,1.. 4 .j. .g m,2 d I i l

Asu,

.a a i iww Figure 2: Load-Strain Trace for GGNS Un-notched CRD Capscrew removed from Service Report: EP 98-003-01: Appendix 4; Page 10 of 17 .e 4

t 0.100" Notch, Sample 1

• Bc.2 *n ta h*' * '

as

• i 8

.../.. me t ,/ m,. ....,/.. 1 i [ i 1 ....i.. u, ..+.. I a3 2, ] i + ,.p? u, ..i.. .s iau [.j 3... .ff.. us.... ,y i fue e i i i n wns s us - su L1reio I of a/W 0.100" Notch, Sample 2 r, e go,.g..,p,;-t a 2 =4 e ? i u, .. /... y i a .u. ........../ 1 m, ,N.. } ./ /' ./ * [.. ug . }.. ../ i s/ ...,f ..h.. yg ..t..... ..k.. // 1 t /. # i . u.. .,e w.,. i u.<w Figure 3: Load-Strain Trace for Notched Bolt: Notch Depth of 100 mils. Report: EP-98-003-01: Appendix 4: Page 11 of17 4

1 6- ?.125' Notch, Sample 1 8'*

• kbl* *if a 4"'
• 8

= 4 ......../ f ....y.. ..e ... e. -g e / a .. d.. +, =a

• • y*=

gg ,bs n g ..g. ...//.... I I + b b g4 . 9... ....p... . ~.. .7 g , /.- L, g 1 [gg/' # i i. i e Ytute ikWe & nl Mia i dia/W 0.125' Notch, Sampie 2 frme{.%e fant R 2 e 4126 g . 3.. ., j.. .. [... 9.. sh"y b... MU aus l' S g /..... w i / 220 / - ' - ys ..i.. ./ / ' i ggg ...../,,?.. //

• 4...

g3 ....f ..d.. // ,4,-ll/ im:e e aus a us a us w... i <,sw Figure 4: Load Strain Trace for Notched Bolt: Notch Depth of 125 mils. Report: EP 98 003 01: Appendix 4; Page 12 of17 i l

g 6 I 0.150' Notch, Sample 1

• Ric2 *st aIt'* * '

= .j 2 i 3dngg ..7... j m. u, i 3 1 .. p.. t im . 4.. ..e/ ,a, p. ...,i.. 7 + p - . 9.. m... /f... i . 9.. i If i i i to. .m .w,. i asi 0.150" Notch, Samplo 2

• ff,4= *,ti,,4-'
• 2 au t

i i u, L. ..i.. i ./ ma +- d- + 4.</ - + + e s'; 9 un .....9 y i 3 / ua .j.. ...p.. ......4 d 1 ..}.. +//. i im ...#. I. ... i.. / tan... .././ 't m... /; ..e.. /m;. t' t' I I. i t.u a am tw ,,sua s us,.< Figure 5: Load Strain Trace for Notched Bolt: Notch Depth of 150 mils. Report:EP 98-003 01: Appendix 4; Page 13 of17

I 0.150" Notch, Max Lond=58,380lbs

• • ?*iW**faif**

sem e.w /\\ aamn ......../.. / I.. um ...,/..../ 3 ..i.. / t / // aw

. j... 7......

.4 I e / f f 7./.....l I / / ;/....... ..p. . 4.. in. \\ / '/ ,[. -/ 1- $ Vein 8 Or.hl 0.160" Notch, Max Load =58,380lbs " * @d* *stu if * * .a= ,,,/ uw I /l l / as.\\w ..t.. ........ /.. / /, I / [- } ..t.. mw .Y / I /,/ i / / uw ..y...,..../. ,/- ,Y / !/ l i i .. j,./...f...... // I . / ',< 4 !.: 2"

4. L."-"

f 4. tv.n. s v.,u Figure 6: Load-Strain Trace for Notched Bolt Loaded Beyond Yield: Notch Depth 150 mils. I Report: EP 98-003 01: Appendix 4; Page 14 of 17

6 0.26 e 0.25 e 0 24 O.23 e e e 0.22 Strains 0.2246 +9.11E 5xnotch depth e 0.21 O 20 40 60 80 100 120 140 160 Notch Depth (mils} Figure 7: Nominal (measured) Strain as a function of Notch Depth. The linear regression line is also plotted. The small value for the slope indicates that nominal specimen strain is not affected by notch depth I Report: EP-98 003-01: Appendix 4; Page 15 of 17 r 4 y = e ,-e. 4- -.. --i

.-l. t 160 .150 J 140 c. !130 g o ,ttt'd I '120 110 - ) 11 7 100 100 110 120 130 140 150 Notch Depth (mils} l l Figure 8: Notch Stress as a function of Notch Depth. The notch stress is calculated using net cross section area. material yield strength is reached at a notch depth of 117 mils. i Report: EP 98-003 01: Appendix 4; Page 16 of 17 .-7

1'l') 1 ~.... - - - Tension #1 leEW2 tbtN t'3 30. lY I i .t i 'l .t 4 ...,t.. ... i. I l l i I ism .. I.. i I i !t t ,3 e i .t 18192 .i.. . +. + -. ~ ' ..q.... j i f l ! sigm ..!..... /... .,j,, p .9. r, j' l 2 2 I i k exm p . I.. .b h.. ....s. l i i .4...... em I l i 1 1 u 3IM -j. - ,..J... l f" t I g .i. 1 u, t l p.

e. 388.

8 Jf2 e ses

d. s at

3. 3 39

d. s t a 0,31 Str.viti ! Ovlal Tension #2 aam

e.,.

.o2 i e$+f ll'M D dd:IN a f h ...L.. ,i tag W o ..a. I I l 1 i stava . <.L 'T.. t.. ,, i.. ..d. ..a I f /. / 1 l. ' Itaw ./. N

4.,

e / i l i 3 i / i 1 7 ...j+~ ..k. .. j.. l I ga w [f 4 .. f.' / l i 5... 3 gang ..g. /, i / t i / l l t i - [. y ). etw s i/ / /s j / gm I i l 3 E 230.. .I. .e .1

4. Ja2

8. saa

4. 3d4 4 0.J6 61, a ta

6. II Str giti 4 (Wla)

. Figure 9: Stress-Strain Curves from Tension Test of Procured Bolts. Report JP.98-003-01: Appendix 4; Page 17 of 17 1 i 9 .e -a e .,,--n..., y

0 I ATTACHMENT 1 to A.PENDIX 4 (Notch Analysis of CRD Capocrews} d := 0.875 Bolt Shank Diameter (in) k tn := 4.9 From Petersons chart 2.19 @ r/D=0.012 & i d/D between.647 and.765 3 E := 29.710 H := 250.41 Ramberg-Osgood fit to Tension Data n := 0.131 Ramberg-Osgood fit to Tension Data Calculations 0o := 0.0 oinc:=4.0 I:=1 50 1;*0 i + 0 inc 0 6 L (o )'+ o E-i i i k tn 2 LD, := S, x - 1 c:=r+ks\\," o lo s i C,:= o cii pet ::S 100 e i i i i i 1 l EP 98403 Attachment 1 to 1 of 5 ( Appendix 4 '

Graphical Output Applied Nominal Stress vs. Notch Stress ,gg _ w. _.J _4 a-4_.-j_p.-_ y g _4_.;_. i.J_.4 _;-_-;_.w _M__1_L4_.q_a__

90

-- Li-4-Q t' --+ 4 4-- 7--d k4--4,-y-HL py 44 4-d4 d-L 1-+4 180 - --+ - f-H-r4- -- j---y-4 170 -h 7 y ' p-+{ y+ l! t 1-q j 4---- --4 A 4 160 + t ~i, e i . + - i - t i i I 4 ~-+$- e +3 .I-- i < 150 t -Lp. 4 - + - - 140 p-f--

4--

! f--y--. p-0 130 -+-tH -+. t -d -y- --yf{: -y-hp: - - f-I-- 120 110 -~~--*-+-! + - - - + - - - + -. : : - + - - - - + - 4 -. - l- ' +-- + 100 [ f-- { !M- { M--hp hdd--d ki-f i--+- M 90 + 7-+l j h--+p-h --hd-- - '-H.- i r-+- L-f- --+-4 + -. - 80 -h l ' 4-E 7p

l - 7y-; 7-y

- f y-7--p 7-7 7 70 jjpj l 60 - + - - -+---t---*l--'--* t I i t ! i

• i

-,' +-- i 50 --+t

i. i i i

i I i 4--- -.+i -+ + - - -+ 7 - ,? - p-b-j-H-H' 4-- --f-M M +-- l +--+-4--h 4 h. 4 7-+-- j-- - 7 7-- o 1 p 7d-l 7 40 30 g f--+-*,, 7 L+ 7 f-~ j, 7-" 7-+--+---+ 1 M-l- p-y-4 7-7 j 7-+ 7--+- ' l l ; 7 7--+-- 20 1 - 10 +-+-+-+-+-t--+-+-*-+ "-+. i,' i e i t 5 i - t i,e = i w-+-+- +- i 0 \\ 0 $ 1015 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95100105110115120125130135140145150 S; Applied Nominal Stress (ksi) Applied Nominal Stress Vs. Notch Strain g, 0 095 i 1-- d-M 1 d h-i ' !. ! ! dd k-4 Ld I I -- L +-+--- L-1--4 1 ! d d-A LIMM- -!! I l d-l J d - b-hd-- E- ! ! d +-- 0 09 +4-LM-d b--f l [ddd b--- ! ; ! d--I d Ld d 0 075 -- }- 4--h -h I-h d--- J d--h-+-- {l 0 085 -4 dd d-Lh-f-bd---k I l - f-M-- - + - 0 08 I, i i > i t i ' b-. i k k- - 0 07

---

t -t

!+-+++---+-+ t-+%-+--+-t--+---+-+-+ i i i - - + - - r f-0 065 -+-+i----+-+-&-+j-+- 4--+ i--+--+-4-*-!

-+- -+

L-*---+t-- r 4-i~T-E-k ! [i! L-k L-4 M,-4 C !, ! { i, 0 06 -i+- r 0 055 * + +, - + - - * +- 4 4--+- r+--+--w-+ -+ +-+--+-4-+,--F--+-- f. 0 05 + 4 I-+-+- I-1! d iii-L+u-- d 1-d- !-b j 0 045 d k E-- L d I-Id-h j a4 - i- ' -+ f4 d-f b! d-I I I ! 3 0 04 +-4-- - + -+ -a a - -l-+ W -4? i-+ -- S 0 035 AN NMA W 1 A 5 A--Y ' N ---+ LAN-kb-4 1 J--la 0.03 1-- I-- l-k 4-- d Id b - L l-1-4-- U-- *4 J-Id ! ! l ! 4-i i ) i i i. + t ! 1 i j i I t--t--T- +, i

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. i i 0 025 --+---f--+--+! ~ - " i-- pl - - + ~ + m-- L L + 7t--+ -i -+ 7 0 02 -+- j +4-+--+-- l t-- - 0 015 - l;! LH ! i- - { 4 l 1--+-4 a i t-t i --%-4 1U---t L ' - - ! f--h-y-id d-+Jd--f--h, 4j-t i~- 0 01 0 005 -++-M -+d . !. I - M '

• - - + - -

! i ;iiii I ; - r, i 1 ii 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100105110115120125130135140145150 S-i App, lied Nominal Stress {ksi} EP+98-003-01 Attachment I to 2 of 5 Appendix 4

i l Notch Strain Vs. Notch Stress l90 -. 4_L 4-. - {._?-.-..L-l l ._L __.L-_. 1-U--I d - ! I - I - d----.--. i p___;! _p __.__._; __ l80 -+d - d 1-f-1 d b--h i- ! a-- m -- 170 4 1 -- L - -[-- y ---+7--{ - t--p l f 4-M j -{- 160 l50 y --f---- g-j -+ r -+----j d-p---+--- 7 -- 140 -+-+- r--t 1-1 t - +---

- --+ -

120 !-y-l-d 7-d-k d-I h-1 130 + - - - 110 - -- p { 1 l-J b l j i + - - + - ~ +. - - - -+ H. I -r 1 i i J - - + - - 100 -- -- p- -e - [ --- h-p; M-j j 90 7-w j p ;-- l - - +, -+-L---+ 80 - + - - ~ 4-70 f-60 -r -+--% I 1 -. M -+i t 1-t 1 50 l---4 1-- 40 E ! --I-h-}L ! 1---- A 1 -h 1----M L-- L-- --f { L-} l 30 ---h- - -- 20 - +- - t-- ----f-p-7-- j -+-'

-y--p p-10 t-Y ri T i

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i 7-i 0 0 00050010.01500200250030035004004500500550060065007007500800850090095 01 Ei Notch Strain (in/in) Applied Stress Vs. Stress x Strain ,g ! fh f h-4 h d l L--h b-h e-2s 26 b-N 24 I d--, ! l I I = i i l ; I I i-l t i -l j-I y-22 r t-4

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20 -L +--+-+ a-- 4 --+-+-+-4-~~4--~4-+-+- l { l 1 ( m lg - 4 _4 i l l C 16 -- -h-b--A, l a -- j i h- - d ) 14 - - - - - -d -4 -) -- b- -h 1 j i,_- -._I ! _--)j _i - i I l -.g! j e j l2 p.. t t0 --- pf f-{-- ._._. q-. --j -] __ 7 r -p l q-._H 6 - +- +- y--r--t-s- -- --+--t--+-- ,-7----- [_1 ' ! h__.L i. 4 ! _L L _ ! +-.t_ 4 1il 1-I-l b -- [- -,A b----!-- 2 I f ' i i ! i I ! l l l l I ! i i ! 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 S; Applied Nominal Stress (ksi) EP-98-003-01 Attachment I to 3 of 5 Appendix 4

Applied Load Vs. Notch Stress ,,g 170 -f l j l-q - f--- l } L- [ , ---4 4 160 -*l--+l 1--{7-r7-j --.7--+! 1-l t- -- i - - - + - - - - + - 150 - !-j d-t --- l --f- 'f d-140 _. _7_. _ _ j_ { l30 3-- 120 k b l d' 100 1y 110 j, -4 7_._._r-_L d l l ---+ 5 90 ~7 g j 80 -t--- [-- -J 70 p -+- l 7 60 g- } 7 y j -t -(, --- q-j t 50 7 p-40 j y j { 7-j + p-q-30 +- -+ + l 10 - -f -f j l l -+- 20 j j j t j p j 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 ' 75 80 85 90 LDg Applied Load { kip) Applied Load Vs. Notch Strain g, 0 095 l l L b f{: f t-p-{ }j t l/ - l h y[ -h- -. 0 09 [ f; t--- 0 085 0 08 y-f p b-+- p-f--- j l - - + - +- j +--+ y-]!- 0 075 t j H-p q p-- - 0 07 - +---+ +- -+ j h- ---f l T 0 065 --f 1'~ 0 055 L-f, - d 0 06 'v--* E El i /! I i I g 0 05 ---+i +-4' l m 0 045 -- L- -i 4 l l j! l i g 0 04 4- .I ! 4-d-j-p - + - --4 7--d-4 l Z 0 035 ~ k 1-- N ! i l l hb I ^ i r--- 0 03 0 025 ---+-+---4 4 i d-I--- l-I-- d-L d-J --+- k-4 1--4 f ^ 0 02 0 015 U L- ! h- ' 4 L-N ld h I -+ -4 d L 4-k I 0 01 d !d ' d -l 6--h f I d ! 0 005 -- L l 0 0 $ 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 LD Applied Load (kip) Load (kip) Strain (in/in) 36 0.020161 43.04 0.027248 47A26 0.032236 EP-98-003-01 Attachment I to 4 of 5 Appendix 4

i l l Tabular Output 3, 3,,49 i S, o,

• Pct C,

i 0.816 4 0.013 5.387 10 T33T T-3'U27 2.155 10'3 g y g T167 TO D*G3T 4 848'10 TUgr W D 537 8.62 10-3 TI90 TT U3HT o.013 T7TT 70 UJ97 0.019 N TT D'IDT o.026 T.T4r T6~ U.T2T o.034 TTW W UTII o.044 T9IT W UT41 0.054 '91W '4T' UT67 0.065 TU3TT 3T D'TT6 0.07s i146i W TT9-0.091 12 3 36 '6207 0.106 TTT37 3r U2TT o.122 TTU7T W '623T o.14 TT9T6 7T T2r o.159 T3TR TO N o.18 TirHT7 W '52T6 0.203 T7T5T IT '5757 0.229 TIF93T TO TIT o.258 IUT7T VT U.T5l o.291 2TT6F W T3T 0.329 II9T7 TOU U.727 0.374 TT63-TDT N o.427 T672T TUT D377 0.491 75T41 TTI U397 0.569 ITDT6 TT6 U377 0.663 i IIT6i 176 U.76E o.779 T6T44 T2T UT8T o.922 W T2T T7T E627 1.098 TT271 T37 TT9T 1.315 W3TI TT6 T45I 1.582 3TT97 T4U T337 1.91 TETIT TR T.T49 2.314 3T937 T47 IIOT 2.807 7TT76 T37 I72T 3.409 '75T7' TT6 T274 4.142 T6TEI T36 I8T7 5.029 6.1 L i t i 1 EP-98-003-01 Attachment I to 5 of 5 _ _ Apndix 4

Vki,&q v.~f 8 " ff %

• iLa Technical Review Comments Document EP-98-003-01 Rev.

Subject /

Title:

The Evaluation of BWR Control Rod Drive Mounting Flange Cap Number 1 Screw Doonent Type: Engineering Report (by Echelon) Special Notes or Instructions: Comment Page or Comment Response / Resolution Accep Number Section t Initial s 1. overall This is an impressive piece of work! 2.

p. 5 Inset below I st paragraph - references for RBS do not appear to match those listed in kC.

the reference section. Should be references 16 & 17,I assume. Wr j 3.

p. 9 1 st para., 3rd sentence - Seems like " produce" should be " increase" in " undoubtedly CA e-M d*

produce average stresses". Ist sentence, lower para. - The wording "A total reduction 6* g 4, gg kM E y/P factor of 0.632" suggests preload reduced by 63.2% but rather it is reduced to 63.2% of its initial value. Ilowever, I think it's okay; the factors are called " reduction factors" and one can determine correct meamng from the context and calculation. g 4. p.13 Immediately below middle of page - Change " form" to "from". "M j g 'T b 5. p 14 Ist sentence is worded awkwardly. 3rd paragraph, middle of page - It seems that en Oy implicit assumption is that the flaw is not present or does not develop during this 12) gg W ;,, p g -4reda'e M ] gc(,_ hour period. If true, maybe the assumption should be stated. 6CG. 6. p.15 1st complete para., item 2) - Should " shank length" be " shank width? - 4_7 h 7. p.17 2nd para.,1st sentence - Change " subscript" to " subscripted". ~ 8.

p. I 8 Equations (1) & (3)- Correct position of"x" in exponential term. Delete extraneous M cieW l - - I I~

b b header in middle of page. M 'w, t-6 m n 9.

p. 21 last para.,2nd last sentence - Change " foe" to "for" O

N A .A iewed Erwin Zoch Date 7/23/98 Resolved V l Department: l Site Engineering l Ext. 8-558-4810 Date: l 7h7/SK i

ENTERGY ENGINEERING REPORT REVIEW COMMENTS Page l of f g Document Number Rev. Docurnent

Title:

The Evaluation of BWR Control Rod SafetyRelated? YES @ NO g IP-90403 01 Drive Mounting Flange Cap Screw DocumentType: l l Admi.f i..tive Guide U Standard SpecialInstruction orNotes: Please retura cessaneses se l lI ;.A ! Guide U Procedure Brian Gray at Eckelse by Wedway, July 22,1998. R Design Guide O Appendix C ---. cat Page or No. Section %dwm I Accept t Initials N 0 N, q= W tax transmittalmemo E *W* /

• j f.+ a (y t M

$M ~ = = aon.

• * * * &/fV

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• • S3W t

T. E 1 Reviewed By: rws A./asmf @ Date 7-22-77 Print Signature Departrners. ApaM A og Ext.: d# Resolved By: Dese: 7/27[T / AD-P-001, Form No. I, Rev. 2 i

1 ENTERGY RECOMMENDATION FOR APPROVAL Engineering Report No.: EP-98-003-01 I Date: 7-2kS[ Reviews Completed: i Preparer [ Concurrence: N/A Date: Res nsible 4 nager, ANO M!/- h ?// ff Concurrence: Date: Rhs'ponsible fanager, GGNS / Concurrence: N/A Date: Responsible Manager, W3 Concurrence: Date: Responsible Manager, RBS

\\ ENTERGY RECOMMENDATION FOR APPROVAL Engineering Report No.: EP-98-003-01 1 Date: 7-2kN Reviews Completed: Preparer [ Concurrence: N/A Date: Responsible Manager, ANO i Concurrence: Date: Responsible Manager, GGNS Concurrence: N/A Date: Responsible Manager, W3 %)/f/ff Concurrencek 421 o Date: Responsible Manager, RBS '/ l}}