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Recommendations for Ductile andBrittle Failure Design Criteria forDuctile Cast Iron Spent-FuelShipping Containers

This report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the Un ited State s Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied,or assumes any legal liability or responsi-bility for the accuracy, completeness,or usefulness of any information, apparatus, product,orprocess disclosed, or represents that its use would not infringe privately owned rights. Refer-ence herein to any specific commercial product, process, orservice by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.

Manuscript Completed: ~ ~ ~ i l9B4Date Published:

Prepared byM. W. Schwartz

Lawrence Livermore National Laboratory7000 East AvenueLivermore, CA 94550Prepared forDivision of Engineering TechnologyDivision of Nuclear Regulatory ResearchOffice of Nuclear Reactor RegulationU.S.Nuclear Regulatory CommissionWashington, D.C. 20555NRC FIN No. A0374


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DISCLAIMER

This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United StatesGovernment nor any agency Thereof, nor any of their employees,makes any warranty, express or implied, or assumes any legalliability or responsibility for the accuracy, completeness, orusefulness of any information, apparatus, product, or processdisclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product,process, or service by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply its endorsement,recommendation, or favoring by the United States Government or anyagency thereof. The views and opinions of authors expressed hereindo not necessarily state or reflect those of the United StatesGovernment or any agency thereof.


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DISCLAIMER

Portions of this document may be illegible inelectronic image products. Images are producedfrom the best available original document.


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ABSTRACT

This report presents recommendations for establishing design and acceptancecriteria for the ductile cast iron to be used for fabricating spent-fuelshipping casks.ductile failure, and acceptance criteria for preventing brittle fracture,based upon drop testing a flawed prototype cask.

These recommendations address design criteria for preventing

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............. . . . . . . . . . . . . . . . . . . . . . . . . . . . -. .. . . . . . . . . . . . .

CONTENTS

Chapter Pagei i i

LISTOFFIGURES . . vi iLIST OF TABLES . . . . . . . . . . . . . . . . . . V i i iACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . ixEXECUTIVE SUMMARY . . 11. INTRODUCTION . . . . . . . . . . . . . . . . . 22. DUCTILE CAST IRON 33. RECOMMENDATIONS FOR DUCTILE FAILURE DESIGN CRITERIA 53.1 Minimum Material Properties . . . . . . . . . . 53.2 Design Stress Intensities . . . . . . . . . . . 5Primary Membrane and Bending Stresses -Normal Conditions . . . . . . . . . . . . . . 53.4 Fatigue Analysis for Stresses . . . . . . . . . . 53.5 Primary and Secondary Stresses . . . . . . . . . 63.6 Primary Membrane and Bending Stresses -Accident Conditions . . . . . . . . . . . . . 63.7 Total Stress-Intensity Range . . . . . . . . . . 63.8 Stress Concentration Factors . . . . . . . . . . 6

4. RECOMMENDATIONS FOR BRITTLE FRACTURE ACCEPTANCE CRITERIA . 84.1 DropTest . . . . . . . . . . . . . . . . 84.2 Test Conditions . . . . . . . . . . . . . . 84.3 Location of Test Flaws . . . . . . . . . . . . 84.4 Flaw Configuration . . . . . . . . . . . . . 84.5 Acceptance Criteria . . . . . . . . . . . . . 84.6 Maximum Allowable Flaw Size . . . . . . . . . . 95. VALUE IMPACT ASSESSMENT OF DUCTILE FAILURE DESIGN CRITERIA 105.1 Ductile Design Criteria . . . . . . . . . . . . 105.1.1 Minimum Material Properties . . . . . . . . 11

5.1.2 Design Stress Intensity Limit . . . . . . . 125.1.3 Primary Membrane and Bending Stress -Normal Conditions . . . . . . . . . . . 145.1.4 Fatigue Analysis for Stresses . . . . . . . 155.1.5 Fatigue Curves . . . . . . . . . . . . 165.1.6 Allowable Fatigue Cycles . . . . . . . . . 165.1.7 Stress Concentration Factors . . . . . . . . 175.1.8 Primary and Secondary Stress . . . . . . . . 175.1.9 Fatigue Strength Reduction Factors . . . . . . 185.1.10 Primary Membrane and Bending Stresses -Accident Conditions . . . . . . . . . . . 18

ABSTRACT. . . . 9 .

3.3

3.9 ASTM Specification . . . . . . . . . . . . . 7

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Chapter Page5 . 2 B r i t t l e F a i l u r e Ac ce pt an ce C r i t e r i a . . . .

5 . 2 . 1 Drop T e s t . . . . . . . . .5 . 2 . 2 S c a l e . . . . . . . . . . .5 . 2 . 3 T e s t C o n d i t i o n s . . . . . . .5 . 2 . 4 L o c a t i o n of T e s t Flaws . . . . .5 . 2 . 5 Tes t F law Conf igurat ion . . . . .5 . 2 . 6 Acceptance Cr i ter ia . . . . . .5 . 2 . 7 Maximum Allo wa bl e Flaw S i z e . . .

6 . REFERENCES. . . . . . . . . . . . . .APPENDIX A. RADIOLOGICAL RISK OF A CRACK I N A DUCTILEA P P E N D I X B . FRACTURE TOUGHNESS STRESS INTENSITIES FOR

CAST IRO N CASK . . . . . . . . . . . . .BLUNT-TIP CRACKS . . . . . . . . . . . . .

. . . . 19. . . . 19. . . . 21. . . . 2 1 . . . . 22. . . . 23. . . . 23. . . . 25. . . . 27. . . . 28. . . . 37

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LIST OF FIGURESPage

1.A-1.B-1.B-2.B-3.B-4.B-5.B-6.

The microstructure of ductile cast iron . .Simplified cross section of a ductile cast ironcask with a crack . . . . . . . . . .Coordinates of a blunt crack tip . . . . .Stress at a blunt crack prior to yield . .Comparison of the stress distribution between aThe plastic zone at the tip of a sharp crack .A sharp crack's plastic zone at instability . .The blunt crack's plastic zone when the sharpcrack is unstable . . . . . . . . . .sharp crack and a blunt crack . . . . . .

. . . 2 9 . . . 38. . . 3 8 . . . 3 9 . . . 40. . . 41

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LIST OF TABLES

44

1. ASTM A-536 grades of ductile cast iron . . . . . . . .2. DIN-1693 (Federal Republic of Germany) grades3 . DIN-1693 (Federal Republic of Germany) specificationsof ductile cast iron . . . . . . . . . . . . . .

for guaranteed properties of cast-on test specimensfrom ferritic grades of ductile cast iron . . . . . . . 4Major fission product activities and characteristicsat one year post-irradiation: specific power: 35 MW, 30urnup: 25 000 MWD . . . . . . . . . . . . . .a t o n e y e a r . 31(10.16-cm) thicknesses of iron

A-1.

A-2. Source characteristics for a full cask (16 assemblies)A-3. Attenuation results for 16-in. (40.64-cm) and 4-in.. . . . . . . . . . . . . . . .. . . . . . . . . . 34A-4. Relative effect of a crack . . . . . . . . . . . . 35

36-5. Estimated surface dose rate at cracks . . . . . . . .

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ACKNOWLEDGMENTS

This report s u m izes the esult of research conducted to develop designcriteria and fracture toughness acceptance criteria for spent-fuel shippingcontainers made from ferritic ductile cast iron. The work was done atLawrence Livermore National Laboratory, and was funded by the Mechanical/Structural Engineering Branch within the Division of Engineering Technologyof the Nuclear Regulatory Commission.The author wishes t o thank Mr. K. Goldman of the Transnuclear,Corporation forhis assistance in developing the value impact assessment with regard toindustry, and Mr. M. E. Mount of LLNL's Environmental Science Division forhis contribution to the radiological risk assessment of a damaged cask.

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EXECUTIVE SUMMARY

The purpose of this study was to develop recommendations for establishingdesign and acceptance criteria for the ductile cast iron to be used forfabricating spent-fuel shipping casks. Regulatory Guide 7 . 6 is not entirelyapplicable, since it presupposes that the material properties are availablefrom Appendix I of the ASME Boiler and Pressure Code, or from an ASTM Standardspecification. Since standards for ductile cast iron in the thicknesses usedfor spent-fuel shipping casks fo not exist, it is recommended that the licenseapplicant supply the necessary data to support adopted stress intensity limitsfor both static and cycling loading conditions. In establishing stressintensity limits, a factor of four applied to the minimum ultimate tensilestrength is recommended to determine h. The factors of 1.5% and 3%,which establish limits for the primary membrane plus bending stresses, and theprimary plus secondary stresses, respectively, are based upon a minimumductility requirement of 12% elongation. The same holds true for thefactorsthat apply to accident conditions.A drop test is recommended to qualify the ductile cast iron for brittlefracture. The test procedure is to be conducted in accordance with Appendix Bof Regulatory Guide 7 . 8 .flaws introduced at locations of maximum primary and secondary stresses. If aflaw (other than one generated by fatigue cracking) is introduced, its depthshould be at least 6 times that of a sharp-tip flaw, and its aspect ratioshould not be greater than 1/6. Acceptance is to be based upon no significantflaw growth in areas of primary membrane or bending stress, and a maximumpenetration of three-quarters of the thickness in areas of secondarystresses. Under no circumstances is the maximum allowable flaw size to beless than 10 mm.analyzed, and was found to be inconsequential.

A full-sized prototype cask is to be used, with

The effect of a part-through crack on radiological risk was

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RECOMMENDATIONS FOR DUCTILE AND BRITTLE FAILURE DESIGN CRITERIAFOR DUCTILE CAST IRON SPENT-FUEL SHIPPING CONTAINERS

CHAPTER 1. INTRODUCTIONThe U.S. Nuclear Regulatory Commission is developing Regulatory Guides forthe design of, and the qualification for acceptance of, ductile cast ironshipping containers. A research program was conducted in fiscal year 1982(FY82) to determine if Regulatory Guide 7.6 was applicable to ductile castiron, for establishing design limits against ductile failure under bothnormal and accident conditions. This program also investigated variouscriteria for preventing brittle fracture in ship ing containers made fromductile cast iron. The results of this research were deliberatelypublished without specific recommendations, since such recommendations are tobe accompanied by a value impact assessment. Consequently, the presentreport recommends ductile design and brittle fracture acceptance criteria,and also considers the impact of these recommendations on the shippingcontainer industry and on safety. Originally, our recommendations were tohave been based solely upon the data collected during FY82.additional information received since then has also had an influence on theproposed recommendations. Assistance in evaluating the impact of the designcriteria was obtained from the Transnuclear Corporation, which is one of thetwo existing firms having commercial experience with the design andproduction of spent fuel shipping containers made from ductile cast iron.

P

However,

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CHAPTER 2. DUCTILE CAST IRONThe ductility of cast iron can be significantly improved by adding innoculants(such as magnesium) to produce a uniform dispersion of free graphite in theform of spherical particles, called nodules. This eliminates the sharp,crack-like notches that are characteristic of the more brittle gray castirons, in which the graphite is dispersed as thin flakes. Maximum ductilityis achieved when the matrix in which the graphite nodules are embedded isferritic, as illustrated in Fig. 1. A fully ferritic microstructure can,however, be obtained only by heat treatment.iron contains some pearlite. This has the effect of increasing the iron'sstrength and hardness, at the expense of lower ductility.increased hardness and strength are advantageous for some applications, anumber of grades of ductile cast iron are produced, covering a range offerrite/pearlite ratios. In the United States, specifications for ductilecast irons are provided by the American Society for Testing Materials (ASTM)under ASTM A-536, which lists the five grades shown in Table 1. The threenumbers in the grade designation refer to the ultimate tensile strength (UTS),the yield strength (YS), and the percent elongation (e), respectively. Grade60-40-18 is a fully ferritic ductile cast iron.represent microstructures with increasingly larger percentages of pearlite.Grade 120-90-02 is a martensitic type with a very high hardness and strength,which is obtainable only by using a quench-and-temper heat treatment.specification relevant to this study is the Federal Republic of Germany's(FRG's) D1N-1693. Its five grades, shown in Table 2, roughly parallel thoseof ASTM A-536. Grade GGG-40 is the German designation for a ferritic ductilecast iron. The properties shown in Table 2 are based upon tests performed onseparately cast test specimens. The acceptance of castings weighing over2000 kg with wall thicknesses of less than 20-cm may be based upon the minimummechanical properties of cast-on test specimens, as shown in Table 3 for theferritic grades.

As it is cast, the ductile castBecause the

The next three grades

Another

Ferritematrix\ /-raphitenodulesPearlitematrixF e + Fe,C

(a) Ferritic (b ) PearliticFigure 1. The microstructure of ductile cast iron.

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Table 1. ASTM A-536 grades of ductile cast iron.

Ultimate tensile Yield strength Elongationstrength (UTS) (YS) (e)Grade (MPa (MPa ( % I Matrix

60-40-18 41465-45-12 44880-55-06 552100-70-03 68912 -9 -02 827

276310379683621

1812 Ferritic/pearlitic6 Pearlitic/ferritic3 Pear1 t c2 Tempered martensitic

Fe ri ic

Table 2. DIN-1693 (Federal Republic of Germany) grades of ductile cast iron.

Ultimate tensile Yield strength Elongationstrength (UTS) (YS) (e)Grade (MPa (MPa ( % I Matrix

GGG-40 400GGG-40.3 4 0 0GGG-50 500GGG-60 600GGG-70 700GGG-80 800

250250320380440500

15 Fer it c18 Fer it c7 Pearlitic/ferritic3 Pear1 t ic2 Pearlitic2 Tempered martensitic

Table 3. DIN-1693 (Federal Republic of Germany) specifications for guaranteedproperties of cast-on test specimens from ferritic grades of ductile cast iron.

Ultimate tensile Yield strength Elongationstrength (UTS) (YS) (e)Grade (MPa ( m a ) ( % I

GGG-40. 3GGG-40 370370 2402401212

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CHAPTER 3. RECOMMENDATIONS FOR DUCTILE FAILURE DESIGN CRITERIAThe following design criteria are recommended to the NRC staff for assessingthe adequacy of ductile cast iron irradiated-fuel shipping cask designs (i.e.to see if the designs meet the structural requirements in paragraphs 71.35 and71.36 of 10 CFR Part 71). These criteria are limited to ductile cast ironwith a minimum elongation of 12%. All references in the present paper to theASME Boiler and Pressure Vessel Code are to the 1982 edition.3.1 Minimum Material PropertiesASTM material properties should be used, if available, to derive designstress-intensity values. Otherwise, material properties should be reported inaccordance with Article IV-1000 of Revision I11 of the ASME Boiler andPressure Vessel Code, and submitted to the NRC in the Safety Analysis Review(SAR). The values of material properties that should be used in thestructural analysis are those values that correspond to the appropriatetemperatures at loading.3.2 Design Stress IntensitiesThe values for design stress intensities (E$) for ductile cast iron shouldbe less than the lesser of the two values: one-quarter of the minimum ultimatetensile strength, or one-half of the minimum yield strength.3.3 Primary Membrane and Bending Stresses - Normal ConditionsUnder normal conditions, the value of the stress intensity resulting from theprimary membrane stress should be less than the design stress intensity, S,,and the stress intensity resulting from the sum of the primary membranestresses and the primary bending stresses should be less than 1.5%.3.4 Fatigue Analysis for StressesThe fatigue analysis for stresses under normal conditions should be performedas follows:

(1) Determine the value of Salt.point in the normal operating cycle should be considered, so that amaximum range can be determined.)

(The total stress state at each

(2) Design fatigue curves, similar to those in Appendix 1 of Section I11of the ASME Boiler and Pressure Vessel Code, should be used forcyclic loading.E 606-80, entitled "Standard Recommended Practice for Constant-Amplitude Low-Cycle Fatigue Testing".

Fatigue testing should conform to ASTM standard

(3) If only one type of operational cycle is considered, the number ofcycles corresponding to Salt (taken from the design fatigue curvefor ductile cast iron) is the allowable life. If it is consideredthat two or more types of stress cycles produce significantStresses, the rules for cumulative damage given in Article NB-3222.4in Section I11 of the ASME Boiler and Pressure Vessel Code should beapplied.

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( 4 ) Appropriate stress concentration factors for structuraldiscontinuities should be used. In regions where this factor isunknown, a value of four should be used.3.5 Primary and Secondary StressesThe stress intensity, Sn, associated with the range of primary plussecondary stresses, under normal conditions, should be less than 3%. Thestress intensity is calculated in a manner similar to the calculation of2Salt. However, the effects of local stress concentrations, which areconsidered in the fatigue calculations, are not included in this stress range.The 3Sm limit just mentioned may be exceeded, if the following conditionsare met:

(1) The range of stresses under normal conditions (excluding stressesdue to stress concentrations and thermal bending stresses) yields astress intensity, Sn, which is less than 3Sm.

(2) The value Sa, used for entering the design fatigue curver ismultiplied by the factor &, where:Ke = 1.0 , for Sn < 35, ,Ke = 5 , for Sm > 3Sm .-and

(3) The temperature of the ductile cast iron does not exceed 370OC.(4) The ratio of the minimum specified yield strength of the ductilecast iron to the minimum specified ultimate strength is less than

0.8.(These conditions can generally be met only when thermal bending stresses area substantial portion of the total stress.)3.6 Primary Membrane and Bending Stresses - Accident ConditionsIn an accident, the stress intensity resulting from the primary membranestresses should be less than the lesser value of 2.4Sm or 0.5Su. Also,the stress intensity resulting from the sum of the primary membrane stressesand the primary bending stresses, should be less than the lesser value of3.6Sm or 0.75Su.3.7 Total Stress-Intensity RanqeThe extreme total stress-intensity range of the initial state, the fabricationstate, the normal operating conditions, and the conditions in an accidentshould be less than twice the value of Sa at 10 cycles, as given by theappropriate design fatigue curves.3.8 Stress Concentration FactorsThe appropriate stress concentration factors for structural discontinuities

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should be used. A value of four should be used in regions where this factoris unknown.3.9 ASTM SpecificationA key condition of this recommendation is the requirement of Section 3 . 8 thata complete characterization of a new material be submitted in ASTM form.While the ASME Code further requires that the applicant simultaneously submitthe new material specification to the ASTM for adoption as a standard, it isrecognized that such a requirement could seriously delay the review process,OK even discourage a potential applicant from seeking a license. However, itis also recognized that an authoritative American standard for ductile castiron, applicable to spent-fuel shipping containers, would be desirable. Sucha standard would expedite the review process by removing the necessity for adetailed review of material properties for each license application. It wouldalso assure uniformity of practice in setting design criteria, and provideuniform acceptance criteria for the material. Consequently, it is recommendedthat steps be taken to develop an ASTM standard for ductile cast iron, asapplicable to spent fuel shipping containers. It is further recommended thatfuture applicants be constrained to meet the requirements of this standard asa license condition, when it is formally adopted.

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CHAPTER 4. RECOMMENDATIONS FOR BRITTLE FRACTURE ACCEPTANCE CRITERIA4.1 Drop TestThe brittle fracture resistance of a prototype shipping cask made of ductilecast iron should be evaluated on the basis of full-scale drop tests, inaccordance with the procedure outlined herein. Test casks of a size smallerthan full scale are not acceptable.4 . 2 Test ConditionsThe test conditions should be in acccordance with those for the hypotheticalaccident conditions 3a and 3b, as specified in Regulatory Guide 7 . 8 . Theseare repeated here for convenience.

(1) Free Drop: The cask should be evaluated for a free drop through adistance of 30 ft (9m) onto a flat unyielding horizontal surface.It should strike the surface in a position that is expected toinflict maximum damage, and should contain the maximum weight ofcontents.

(2) Puncture: The cask should be evaluated fo r a free drop of 40 in.(1 m) onto a stationary and vertical mild steel bar of 6 in. (15 cm)diameter, with its top edge rounded to a radius of not more than0.25 in. (6.3 mm). The bar should be of such a length as to causemaximum damage to the cask. The cask should contain the maximumweight of contents, and should hit the bar in a position that isexpected to inflict maximum damage.

In addition, the tests shall be performed with the shipping container at atemperature that is not greater than -20F (-29OC).4.3 Location of Test FlawsFlaws should be introduced in the casting at locations where maximum tensilestress levels are expected, and with an orientation that is normal to thedirection of the stress. For each of the two test conditions, at least oneflaw should be introduced at the location of the maximum primary stress andone at the location of the maximum secondary stress.4.4 Flaw ConfigurationThe sizes and shapes of the flaws should be optional, with the applicantbearing in mind that the flaw size adopted will establish the inspectionrequirements. However, the aspect ratio of the flaw should not be greaterthan 1/6.knife-edge sharpening. In the case of the blunt crack, the radius of thecrack tip should be no greater than 0.005 times the depth of the crack.

The crack tip may be blunt as a result of machining and subsequent

4.5 Acceptance CriteriaAfter the drop tests the flaw should not have propagated more thanthree-quarters of the way through the wall o f the shipping container at

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locations of secondary stress gradients.initiated fracturing at primary membrane or bending stress locations. "Noinitiation" should be interpreted as meaning no evidence of ductile tearing ata distance greater than 1/8 in. (3.2 mm) beyond the crack tip.

The flaw should also not have

4.6. Maximum Allowable Flaw SizeThe maximum allowable flaw size for a production ductile cast iron shippingcask should be aJ6 for a blunt tip test flaw, where:

2a = a ( K~~ (mi* ) .C KID(flaw)

In this equation, a, is the minimum quasi-critical flaw size, aT equalsthe size of the test flaw, KID(flaw) equals the fracture toughness of theductile cast iron at the site of the test flaw, and KID(minA equals theminimum fracture toughness of the ductile cast iron (derlve from samplestaken from various locations in the prototype casting).The maximum allowable flaw size should not be less than 10 mm (0.4 in.) deep.

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CHAPTER 5. VALUE IMPACT ASSESSMENT OF DUCTILE FAILURE DESIGNCRITERIAThe recommendations outlined in Chapter 3 of this report are subjected to avalue impact assessment from the point of view of their influence upon safetyand cost. The present chapter recapitulates the specific recommendations andincludes an associated value impact assessment. In general, the value ofthese recommendations to the NRC will be to provide a consistent basis forreviewing license applications for spent-fuel shipping containers manufacturedfrom ductile cast iron. Similarly, these recommendations will be of value tothe industry insofar as they form the basis for a guideline that, if adheredto, will facilitate the review process.5.1 Ductile Design CriteriaDuring FY82, the applicability of Requlatory Guide 7.6 was assessed, usingdata on ferritic ductile cast iron available in the open literature. It wasrecognized that the mechanical properties of very large ductile cast ironshipping containers might be different from these reported data.because they were proprietary, data reflecting the properties of largecastings were unavailable at the time. Since then, we have had access to somedata about thick sections of ductile cast iron. Much is still proprietary,but the information available to us has influenced our assessment of ductilecast iron for use in shipping containers. Consequently, the recommendationsin this report dealing with ductile failure design criteria for ductile castiron have benefited from the information gathered since FY82.

However,

In assessing design criteria for the structural analyses of spent-fuelshipping containers made from ductile cast iron, we were (at first) guided bythe provisions of Regulatory Guide 7.5. During FY82, each of the regulatorypositions in this guide was assessed for its applicability to ferritic ductilecast iron, even though the positions were originally intended to apply tosteel shipping containers.Position 1 in Regulatory Guide 7.6 presents guidelines for establishing thedesign stress intensity limit, (Sm). Since design stress intensities forductile cast iron are not included in Section I11 of the ASME Boiler andPressure Vessel Code, the recommendations discussed in Article 111-2000 wereused instead. The lesser of one-third of the minimum tensile strength, ortwo-thirds of the minimum yield strength, is specified for use as the designstress intensity limit. Since no data base had shown a yield strength forductile cast iron of less than one-half its tensile strength, the tensilestrength was considered the appropriate strength parameter for establishingdesign stress intensity limits. Position 1 further suggests using the ASTMmaterial property values if ASME values are not given. For ferritic ductilecast iron, the minimum tensile strength reported in ASTM-A536 is 60.0 ksi(414 MPa). Thus, 20 ksi (138 MPa) seemed to be a valid stress intensity limitfor this material. An analysis of the strength data in the open literatureappeared to support this minimum tensile strength level, and the degree ofdispersion of the data supports the adequacy of a safety factor of three.However, since the FY82 research results were documented, other informationrelating to the material properties of thick-wall ductile iron castings hadbecome available, which has influenced the recommendations outlined in this

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report.60-40-18, a full ferritizing. nneal is normally required. Large spent-fuelshipping containers made of ductile iron may not be heat treated. Therefore,even though they are described as "ferritic" ductile iron castings, theirmechanical properties may be significantly less than grade 60-40-18. NOexisting specification provides acceptable minima for thick-walled castingsthicker than 8 in. (20 cm), except for the provision that such minima will bemutually agreed upon by the vendor and customer. It is not possible,therefore, to recommend stress intensity limits for cast shipping containersbefore these minimum mechanical properties have been established.Consequently, in the absence of ASME-recommended stress intensity limits andan applicable specification for thick-wall ductile iron castings, much ofRegulatory Guide 7.6 is not applicable to ductile cast iron shippingcontainers.

To achieve the minimum strength and ductility level of grade

5.1.1 Minimum Material Properties5.1.1.1 RecommendationsASTM material properties should be used, if available, to derive designstress-intensity values. Otherwise, material properties should be .furnishedin accordance with Article IV-1000 of Section I11 of the ASME Boiler andPressure Vessel Code.5.1.1.2 Impact on SafetySafety considerations dictate the exclusive use of those materials that arewell characterized with respect to their strength. Consequently, performingmechanical property tests is a fundamental requirement for materials used insafety related components, especially for a new material that lacks auniversally accepted specification of its properties. Normally, only amaterial that has been evaluated and characterized by the ASTM is consideredsuitable for use.iron applicable to shipping containers, safety is assured if the informationprovided by the applicant is of such a nature that it would meet therequirements of the ASTM.

In the absence of such a specification for ductile cast,

Guidance in this regard is provided by Article IV-1000 of Section I11 of theASME Code, which deals with the procedure for obtaining approval of newmaterials. Normally the ASME adopts for inclusion in Section I11 only thosematerials for which there is an applicable ASTM specification. For othermaterials, the ASME recommends that the ASTM be requested to adopt aspecification before presentation to a Code Committee.the ASTM specification, the Code Committee would consider the new material ifit is presented in ASTM specification form, and if it includes all the dataspecified in paragraphs IV-1200 and IV-1300 of Article IV-1000. These datarequirements are oriented toward the use of steels in a nuclear radiationenvironment, and may not be entirely applicable to ductile cast iron shippingcontainers. The provisions of Article IV-1000 that are applicable and shouldbe addressed by the applicant are:

Pending publication of

(1) Provide a complete specification for the ductile cast iron to beused for the shipping container, including composition andmicrostructure.

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(2) Supply adequate mechanical property data, which serve as a basis'fordesign stress-intensity limits. These data should include valuesfor the ultimate tensile strength, yield strength, reduction inarea, elongation, strain fatigue, creep strength, and creep rupturestrength over the range of temperatures to which the ductile castiron will be subjected.( 3 ) Any heat treatment needed to realize the mechanical properties or

microstructure should be fully described.( 4 ) The brittle fracture characteristics of the material should be

provided. The precise method for qualifying the ductile cast ironshipping container for resistance to brittle fracture is describedin Section 5.2 of this report.The specification of minimum mechanical properties of ductile cast iron ismore appropriately treated in fabrication guidelines for this material.5.1.1.3 Impact on CostThe qualification of a new material, or of a conventional material for anapplication beyond its customary limits, mandates the use of a comprehensivetest program. The costs involved are, therefore, not an unusual orunreasonable requirement, nor are they unanticipated by the potentialapplicant.5.1.2 Design Stress Intensity Limit

5.1.2.1 RecommendationThe values for design stress intensities (S,,,) should be less than the lesservalue of either one quarter of the minimum ultimate tensile strength or onehalf of the yield strength of the ductile cast iron, as revealed by testspecimens obtained from a prototype casting.5.1.2.2 Impact on SafetyThe establishment of appropriate safety factors has a long history ofcontroversy. This arises from the large number of uncertainties thatinfluence the reliability of structures. These include uncertaintiesassociated with material properties, mechanical loads and other environmentalconditions, structural modeling, methods of analysis, and possible degradationof properties resulting from fabrication processes. The number and complexityof these uncertainties has made a rational approach to the establishment ofsafety factors difficult. In the absence of a universally acceptabletechnical basis, safety factor issues have generally been resolved byconcensus among the members of code-writing groups.the establishment of design stress-intensity limits in Article 111-1120, asfollows:

The ASME Code addresses

"The (design stress-intensity) values are obtained by applying (safety)factors to the mechanical properties of the materials. Consideration isgiven to the minimum properties specified and the properties at varioustemperatures as determined by tests on specimens of the material."- 12 -


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The code specifies the factors for ferritic steels, and for non-ferrous metalsand alloys, in Article 111-2110. Position 1 of Regulatory Guide 7.6 refersthe applicant to this article, when materials other than those appearing inSection I11 are encountered. Since the factors in Article 111-2110 may notapply to thick-section ductile iron castings, some other basis needs to beestablished for determining safety factors.Although the ASME Code does not include design stress intensities for ductilecast iron in Section 111, it does deal with this material in Part UCD ofSection VIII, Div. I, entitled "Requirements for Pressure Vessels ConstructedOf Cast Ductile Iron." Here the maximum allowable stress is specified as12 ksi. This represents a safety factor of 5 on the minimum ultimate tensilestrength of 60 ksi that is characteristic of ASTM 60-40-18. Although notexplicitly stated, this safety factor is based upon a design by formulaapproach. In addition, a casting quality factor is required for applicationto the design stress-intensity value; Section VIII, Paragraph UG-29(a) (1)specifies a quality factor of 80%, but it assumes that neither impact testsnor non-destructive examinations will be performed. On the other hand, adesign-by-analysis approach is required under Section I11 of the ASME Code.Section VIII, Div. 1 of the Code requires a safety factor of 4 for steelcomponents based on a design-by-formula approach, but in Section 111, Class 1steel components may be designed by analysis, using a safety factor of three.Since shipping containers made of ductile cast iron will be based on adesign-by-analysis approach, it is recommended that a safety factor of four beused for ferritic ductile cast iron.that fracture toughness characterization of ductile iron castings for spent-fuel shipping containers will be pursued, and that intensive NDE tests will beperformed, a quality factor of unity can be applied.

Furthermore, since it is anticipated

A safety factor of four is considered adequate for ensuring the integrity ofthe shipping cask when a design-by-analysis approach is adopted. This islarger than the safety factor of three recommended by Section I11 of the ASMEBoiler and Pressure Vessel Code, but it reflects the conservative philosophyof the code in assigning larger safety factors for ductile cast iron than forsteel. There is as yet insufficient experience with the behavior of thick-wall ductile iron for shipping casks to allow a lesser degree ofconservatism. On the other hand, a safety factor of five (as recommended inSection VI11 of the ASME Code for pressure vessels made of ductile cast iron)is too high, since it is based upon a design-by-formula approach rather thanupon the design-by-analysis approach, as required by Section I11 of the code.The differences in the ap roach which allow a reduction in safety factor fordesign by analysis are: 23

(1) Section I11 uses the maximum shear (Tresca) theory of failure,instead of the maximum stress theory, resulting in more realisticstress intensity levels for biaxial stress conditions.(2) Section I11 requires the detailed calculation and classification ofall stresses, and the application of different stress limits to

different classes of stress, whereas Section VI11 merely givesformulas for the minimum allowable wall thickness.

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( 3 ) Section 111 requires the calculation of thermal stresses andprovides the allowable values for them.( 4 ) Section I11 considers the feasibility of fatigue failure and givesrules for its prevention.(5) Finally, Section I11 requires that protection against non-ductilefracture be provided.

Since a design-by-analysis approach is required for safety related componentsfor shipping casks, a safety factor of four rather than five is adequate.5.1.2.3 Impact on CostWhile a safety factor of four rather than three would imply a cost penalty byrequiring heavier sections under similar loading conditions, the containmentthickness of the ductile cast iron shipping cask is based upon shieldingrequirements, rather than upon strength. Thus, a safety factor of four is notexpected to require a more massive containment structure than would resultfrom using a safety factor of three, so that this recommendation is note x p e c t e d to have an impact on costs.5.1.3 Primary Membrane and Bending Stress - Normal Conditions5.1.3.1 RecommendationUnder normal conditions, the value of the stress intensity resulting fromprimary membrane stress should be less than the design stress intensity, Sm,and the stress intensity resulting from the sum of the primary membranestresses and the primary bending stresses should be less than 1.5 h.Position 2 of Regulatory Guide 7.6 suggests that under normal conditions thevalue of the stress intensity resulting from the primary membrane stressshould be less than the design stress intensity, Sm. This deviates somewhatfrom ASME Section I11 NB-3211 (a), which states that the design shall be suchthat the stress intensities will not exceed the prescribed limits. However,the wording of Regulatory Guide 7.6 is preferred, since it implies that themargin between the computed stress intensity and the design stress intensityshould be judiciously considered. It is conceivable that a reduction indesign stress intensity may be required, if production castings do not quitemeet minimum tensile strength specifications. In this case, a comfortablemargin of safety with respect to S, could facilitate a decision involvingthe acceptance of a production casting.Position 2 of Regulatory Guide 7.6 also suggests that the stress intensityresulting from the sum of the primary membrane stresses and the primarybending stresses should be less than 1.5 S,,,."shape factor" of a beam with a rectangular cross section, where collapseoccurs as a result of the formation of a plastic hinge. For the large safetyfactors used, a stress factor of 1.5 would limit the maximum stress to a levelbelow the yield strength of ductile cast iron. Even if the combined primary

This limitation stems from the

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stresses were so high that a plastic hinge condition was approached, thestrain at the extreme fiber of the beam will be well below the fracturestrain. Consequently, the factor of 1.5 for the sum of the primary membraneand bending stresses under normal conditions is applicable for ductile castiron. This factor of 1.5 only applies to structures in bending, with arectangular cross section. For other cross sections this factor may besignificantly lower. However, for shell structures the factor of 1.5 isapplicable to primary bending stresses along the thickness of the shell.5.1.3.2 Impact on SafetyThis recommendation reiterates position 2 of Requlatory Guide 7.6.guideline is designed for steel structures, adherence to it will ensure theWhile thissafe use of a ductile cast iron, provided that its ductility allows theformation of a plastic hinge in a deformed beam before a condition of ultimatestrain develops at the extreme fiber.5.1.3.3 Impact on CostProviding sufficient ductility in thick-wall ductile iron castings is a majorfabrication problem. Ductility, in terms of percent elongation, has tended tobe low and to display a wide scatter band.special fabricating processes to consistently achieve acceptable levels ofductility.procedures used to achieve the required ductility levels, and will vary fromone manufacturer to the next. Because of the highly proprietary nature of thefabrication processes for shipping containers made of ductile cast iron, ithas not been possible to assess the impact of ductility requirements on costsin a more specific manner.

It may be necessary to resort toThe cost involved will depend upon the specific fabrication

5.1.4 Fatigue Analysis for Stresses5.1.4.1 RecommendationThe fatigue analyses for stresses under normal conditions should be performedby determining the value of salt.the normal operating cycle should be considered, so that a maximum range maybe determined . The total stress state at each point in5.1.4.2 Impact on SafetyThis recommendation reiterates position 3a of Regulatory Guide 7.6.reflects the approach recommended by Section I11 of the ASME code and is,consequently, a prudent and universally recognized procedure for fatigueanalyses in the nuclear industry.

It

5.1.4.3 Impact on CostApplying this recommendation to shipping containers made of ductile cast ironwould have no greater impact on costs than it has on shipping containers madeof steel.

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5.1.5 Fatigue Curves5.1.5.1 RecommendationDesign fatigue curves similar to (and derived in the same manner as) those inAppendix I of Section I11 of the ASME Boiler and Pressure Vessel Code shouldbe used for cyclic loading.The FY82 investigation of the applicability of ASME design fatigue curves toductile cast iron indicated that they were valid in the range of high-cyclefatigue above lo5 cycles to failure. However, the data used to suggest thismay not have represented the fatigue properties of thick-section ductile castiron. Consequently, if fatigue is a design condition that needs to beaddressed, it is recommended that tests be performed to establish fatigueproperties of as-cast ductile iron; just as tests are required to establishdesign stress-intensity limits.involving both high-cycle and low-cycle fatigue.in the material specifications supplied by the applicant, as outlined inSection 5.1. The fatigue data should be presented in the form of curvessimilar to those appearing in Appendix I of Section I11 of the ASME Boiler andPressure Vessel Code, which are based upon uniaxial strain cycling. Sincethese curves will be specific for ductile cast iron, it will not be necessaryto make adjustments for the modulus of elasticity (as described in position 3cof Regulatory Guide 7.6).

This would apply to design conditionsSuch data would be included

5.1.5.2 Impact on SafetySee Section 5.1.2.2.5.1.5.3 Impact on CostSee Section 5.1.2.3.5.1.6 Allowable Fatigue Cycles5.1.6.1 RecommendationIf only one type of operational cycle is considered, the number of cyclescorresponding to Salt (taken from the design fatigue curve for ductile castiron) is the allowable fatigue life. If two or more types of stress cyclesare considered as being capable of producing sigificant stresses, the rulesfor cumulative damage (given in Article NB-3222.4 of Section I11 of the ASMEBoiler and Pressure Vessel Code) should be applied.5.1.6.2 Impact on SafetyThis recommendation reiterates portions of position 3c of Regulatory Guide-.6.applicable to a wide range of materials, including ductile cast iron. Sinceit cites the ASME Code, it can be considered a prudent and universallyrecognized procedure f o r establishing an allowable number of fatigue cycles.

Although this guideline is designed for steel structures, the rule is

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5.1.6.3 Impact on CostApplying this recommendation to shipping containers made of ductile cast ironwould have no greater impact on costs than it has on shipping containers madeof steel.5.1.7 Stress Concentration Factors5.1.7.1 RecommendationAppropriate stress concentration factors for structural discontinuities shouldbe used. A value of four should be used in regions where this factor isunknown.5.1.7.2 Impact on SafetyThis recommendation reiterates position 3d of Regulatory Guide 7.6. Althoughthis guideline is designed for steel structures, the rule is applicable to awide range of materials, including ductile cast iron.5.1.7.3 Impact on CostSee Section 5.1.6.3.5.1.8 Primary and Secondary Stress5.1.8.1 RecommendationThe stress intensity, Sn, associated with the range of primary plussecondary stresses under normal conditions should be less than 3%.calculation of this stress intensity is similar to the calculation of 2S,lt,.However, the effects of local stress concentrations, which are considered Inthe fatigue calculations, are not included in this stress range.

The

5.1.8.2 Impact on SafetyThis recommendation reiterates a portion of position 4 in RegulatoryGuide 7.6. The secondary stresses referred to here are those which are selflimiting. These include general thermal stresses and bending stresses atgross structural discontinuities. Local yielding and minor distortions cansatisfy the conditions that cause the stress to occur, and failure from oneapplication of the stress is not to be expected. Safety is ensured bycreating a condition of "elastic shakedown" whereby, even if the yieldstrength is exceeded slightly, the stress range may be as high as 2aybefore further plastic deformation can occur. For ductile cast iron, when adesign stress intensity based on one-quarter of the ultimate tensile strengthand a ratio of yield to ultimate strength of about two-thirds is used, therange of primary plus secondary stresses can be as high as 5% to maintainthe 2oY elastic range. Therefore a very conservative design criterion forductile cast iron is implied by S m L 3Sm.5.1.8.3 Impact on CostsApplying this recommendation to shipping containers made of ductile cast iron

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would have no greater impact on costs than it has on shipping containers madeof s ee1.5.1.9 Fatigue Strength Reduction Factors5.1.9.1 RecommendationsThe 3% limit for fatigue analysis may be exceeded, if theconditions are met:

(1) If the range of stresses under normal conditionsdue to stress concentrations and thermal bendingstress intensity, Sn, that is less than 3%.

following

(excluding stressesstresses) yields a

( 2 ) If the value of Sa used in the design fatigue curve is multipliedby a factor Kef where:Ke = 1.0 , for Sn < 3Sm ,

orK, = 5.0 , for Sn 3Sm .

(3) If the temperature of the ductile cast iron does not exceed 37OOC.( 4 ) If the ratio of the minimum specified yield strength of the ductilecast iron to the minimum specified ultimate strength is less than

0.8.5.1.9.2 Impact on SafetyThe recommendations reiterate positions 4a to 4d of Regulatory Guide 7.6,except for the fatigue-strength reduction factors.Regulatory Guide 7.6 were taken directly from Section I11 of the ASME Code(NB-3228.5), and are to be computed using the values of m and n that arefurnished for a variety of materials (but not for ductile cast iron). TheASME Code, however, recommends that (except for the case of crack-likedefects) no fatigue reduction factor greater than five need be used. Unlessfatigue reduction factors are determined experimentally in accordance with11-1600 of ASME Code Appendix 11, conservatism dictates that a K, of five beused for fatigue stresses that are greater than 3Sm.

The factors used in

5.1.9.3 Impact on CostIf thermal stresses are a significant component of the fatigue stress, suchthat 3Sm is exceeded and increasing Sa by a factor of five results in anintolerable design condition, then appropriate analytical methods should beused (or experimental tests performed) to justify a lower fatigue-strengthreduction factor.5.1.10 Primary Membrane and Bending Stresses - Accident Conditions5.1.10.1 RecommendationUnder accident conditions, the value of the stress intensity resulting from

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the primary membrane stresses should be less than the lesser value of 2.4Smor 0.5Su; and, the stress intensity resulting from the sum of the primarymembrane stresses and the primary bending stresses should be less than thelesser value of 3.6Sm or 0.75Su.5.1.10.2 Impact on SafetyThis recommendation is similar to that of position 6 of Regulatory Guide 7.6.However, the coefficients associated with Sm are reduced to reflect a safetyfactor of four for ductile cast iron, rather than using the safety factor ofthree for steel. Although Regulatory Guide 7.6 is designed for steelstructures, adhering to it will ensure the safe use of ductile cast iron;provided that the ductility specification allows a plastic hinge in a deformedbeam to form before the ultimate stress develops at the extreme fiber.5.1.10.3 Impact on Cost

See Sections 5.1.1.3 and 5.1.3.3.5.2 Brittle Failure Acceptance Criteria5.2.1 Drop Test5.2.1.1 RecommendationThe resistance of shipping casks made from ductile cast iron to brittlefracture should be evaluated on the basis of a full-scale drop test, inaccordance with the procedure outlined in Chapter 4.In the FY82 study, three approaches were described for qualifying ductile castiron for resistance to brittle fracture. The first was a fracture arrestapproach that examined ductile cast iron's ability to (in effect) displayupper shelf toughness properties at -20F (-29OC). The second was a classicallinear elastic fracture mechanics approach that attempted to define maximumallowable flaw sizes at yield stress levels based upon the available data forductile cast iron's dynamic fracture toughness. The third approach was toperform a full-scale drop test at -20F (-29OC), in an orientation that couldcause the maximum amount of damage, with a flaw introduced at the mostcritically stressed location.Valid nil ductility transition temperature (NDTT) values for ductile cast ironcan not be obtained. In addition, the experimental values of NDTT reported inthe literature are too high to prevent unstable fracture of through-thicknesscracks for the anticipated casting thickness. Consequently, the fracture-arrest approach was eliminated from further consideration. Furthermore, theavailable data on thesdynamic fracture toughness of ductile cast iron was suchthat, at yield stress levels, the ability to resist fracture initiation couldnot be affirmed by analysis, except by specifying maximum allowable flaw sizesthat current practice considers too small to detect.5.2.1.2 Impact on SafetySafety considerations dictate that the integrity of the spent-fuel containment

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not be compromised as a result of catastrophic crack propagation under dynamicloading conditions. Qualification of the cask by analytical methods wouldrequire assuming minimum anticipated fracture mechanics properties, maximumanticipated stress levels, and a limitation on the maximum allowable flawsize. Given the present state of knowledge, a conservative analysis wouldrequire assuming a low level of fracture toughness and a yield strength levelof stress which restricts the maximum allowable flaw sizes to those thatstate-of-the-art NDE would not guarantee as being detectable with anacceptable level of reliability. Thus, an analytical approach cannot, as yet,assure the prevention of brittle fracture under dynamic loading conditions.many uncertainties that an analytical approach is forced to take intoaccount. First, the containment is subjected to dynamic loading conditionsthat (at present) are considered t o be conservatively representative of severeaccident conditions. No assumption, therefore, need be made regarding themaximum stress levels. Secondly, the response of the ductile iron cask to thedynamic loads in simulated accident conditions may be more benign thanconservative analytical models of its behavior would allow.be the possibility that the graphite nodules in the iron inhibit a reductionin fracture toughness by limiting the size of flaws to the distance betweennodules. Another possibility is that the elastic strain energy (due totensile forces) that remains after dissipation by the inelastic deformation ofother cask components, is not sufficient for catastrophic crack propagation.Finally, introducing flaws creates a condition of vulnerability that providesa basis for establishing limits on flaw size (given a successful test) which,with a high degree of reliability, obviates flaw propagation under theconditions simulated by the drop test.

. On the other hand, a drop test performed in accordance with 10 CFR 71 removes

An example would

The principal ingredients for such a test that assure safety against brittlefracture are:

( 3 )( 4 )

(5)

Using a full-scale ductile iron cask for the qualifying test, whichwill most accurately reflect the brittle fracture behavior ofsubsequent production casks.Identifying the most critically stressed areas for placement of thetest flaws.Introducing test flaws at these most critically stressed areas.Comparing the fracture toughness of the material in the vicinity Ofthe flaw with a lower-bound fracture toughness value, representativeof the test cask, to establish the quasi-critical flaw size.Correlating the lower-bound fracture toughness values of the testcask with the corresponding lower-bound values of cast-on orseparately cast test blocks. This correlation will provide thebasis for accepting subsequent production casks whose fracturetoughness properties cannot be directly assessed by destructivetests.Establishing a maximum allowable flaw size for subsequent productioncasks, based upon the safety factor applied to the quasi-criticaltest flaw.

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5.2.1.3 Imp act on C o s tThe dr op - te s t p rogram requi res a con s id e ra b le commitment of funds t o q u a l i f yt h e d u c t i l e c a s t i r o n s h i p p i n g cask f o r r e s i s t a n c e t o b r i t t l e f r ac t u r e .However, t h e costs would not be i n t o l e r a b l y g r e a t e r t h an t h o s e f o r p e rf or mi nga d r o p t e s t t o q u a l i f y t h e cask's r e s i s t a n c e t o general damage mechanisms.T he p r o t o t ype cask used for t h e t e s t s h ou l d b e r e p r e s e n t a t i v e o f s u b se q u en tp r o d u c t i o n casks, so t h a t t h e costs f o r e ng i n e e ri n g , d e s i g n , p r o c e s sd e ve l op m en t , a nd q u a l i t y a s s u r a n c e p r oc e d u r e s are r e c ove r a b l e . T he cos t oft h e c a s t i n g would be n o g r e a t e r t h a n t h a t fo r a c o n v e n t i o n a l d r o p t e s t , e x c e p tfo r t h e a d d i t i o n a l cost o f i n t r o d u c i n g t h e f la w s. S i n c e t h e t e s t cask i ss a c r i f i c i a l , it c a n also f u r n i s h t e s t s pe ci me ns f o r c h a r a c t e r i z i n g t h e d u c t i l ec a s t i r o n ' s as-cast mater ia l propert ies , b o th f o r e s t a b l i s h i n g f a i l u r ec r i t e r i a an d s t a n d a r d s f o r a c c e p ti n g p r o d u c ti o n casks .5.2 .2 Sca le5.2.2.1 RecommendationTh e t e s t cask u se d i n t h e d r op t e s t s h o u l d be a fu l l - sca le pr o t o t y pe m odelt h a t i s r e p r e s e n t a t i v e o f s u b se q u en t p r od u c t i on casks .5.2.2.2 Impact o n S a f e t yI t is sometimes advantageous t o u s e small-scale models fo r de t e r m i n i ngmechanica l responses f o r v a l i d a t i n g s t r u c t u r a l a n a l y s e s . However, w e a rec o nc e rn e d h e r e w i t h t h e l i k l i h o o d of f r a c t u r e , w h ic h i n v o l v e s knowing t h ef a i l u r e c r i t e r i a fo r d u c t i l e c a s t i r o n . I n t h e case of l a r g e d u c t i l e i r o nc a s t i n g s , w e c a nn o t r e l y o n s e p a r a t e l y c a s t samples or cas t -on t e s t pieces t oa c c u r a t e l y r e f l e c t t h e f r ac t u re t ou g hn e ss o f t h e s h ip p i n g c o n t a i n e r , s i n c et h i s mate r ia l p r o p e r t y var i es w i th t h e s i z e o f t h e c a s t i n g and t h e processv a r i a b le s i n i t s pr oduc t i on .a s su r an c e t h a t it i s r e p r e s e n t a t i v e o f t h e f u l l - s i z e c a s t i n g . F ur th er mo re ,t h e f l a w s i z e s a nd l i m i t s o n p r o p ag a t i on c a n b e s p e c i f i e d w i t h f a r l e ssambigui ty fo r a f u l l - s c a l e c a s k t h a n c a n be done fo r a s u b - s c a l e model .Cons e que n t l y , on l y ful l -scale production m o d e l s o f d u c t i l e c a s t i r o n s h i p pi n gc a s k s s h o ul d s e r v e a s a b a s i s fo r q u a l i f y i n g r e s i s t a n c e t o b r i t t l e f r a c t u r e .

Thus , a sub-scale c a s t i n g w i l l n o t g i v e c o m p l e t e

5.2.2.3 Impact o n C o s tSee Sect ion 5.2.1.3.5 .2 .3 T e s t Cond i t i ons

-5.2.3.1 Recommendations(1) F r e e Drop: The cask s hou l d be e v a l u a t e d for a f r e e d r o p t h ro u gh ad i s t a n c e of 30 f t ( 9 m ) o n t o a f l a t , u n y i e l d i n g , h o r i z o n t a ls u r f a c e . I t s hou l d s t r i k e t h i s surface i n a p o s i t io n t h a t i s

e xpe c t e d t o i n f l i c t maximum damage, and it s h o u l d c o n t a i n t h emaximum weight of c o n t e n t s .( 2 ) Puncture: The cask s h ou l d be e v a l u a t e d f o r a f r e e d r o p o f 40 i n .

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(1 m) onto a stationary vertical mild steel bar 6 in. (15 cm) indiameter, with its top edge rounded to a radius of not more than0.25 in. (6.35 mm). The bar should be of such a length as to causemaximum damage to the cask. The cask should contain the maximumweight of contents, and it should hit the bar in a position that isexpected to inflict maximum damage.

In addition, the test shall be performed with the shipping container at atemperature that is not greater than -20F (-29OC).5.2.3.2 Impact on SafetyThese test conditions are in accordance with the hypothetical accidentconditions 3a and 3b specified in Regulatory Guide 7.8, and are currentlyconsidered as being representative of conditions not likely to be exceededunder real accident conditions.5.2.3.3 Impact on CostThe cost of performing a full-scale drop test should not be much greater thanwhat would be incurred by any conventional drop test performed in accordancewith 10 CFR Part 71.5.2.4 Location of Test Flaws5.2.4.1 RecommendationFlaws should be introduced in the casting at locations where maximum stresslevels are expected, and in an orientation normal to the direction of thestress. For each of the two test conditions: at least one flaw should beintroduced at the maximum primary stress location, and at least one other flawshould be introduced at the maximum secondary stress location.5.2.4.2 Impact on SafetyThis recommendation assures that even if flaws are present in productionshipping containers, these locations need be of no concern if the flawedprototype shipping container successfully passes the drop test.5.2.4.3 Impact on CostA detailed stress analysis using a three-dimensional finite-element programmay be needed. However, for the purpose of introducing flaws, only thelocations of the maximum stress levels need be established to satisfy thereviewer. The magnitude of the computed stress may be of concern to theapplicant, since it will influence the size of test flaws that are chosen foruse. Since the test flaw's size is optional on the part of the applicant, itis considered quasi-critical after the successful drop test. The maximumallowable flaw for inspection purposes is arrived at by applying therecommended safety factors to this quasi-critical flaw size. It is thereforenot necessary to provide specific guidelines for the assurance of preciselycomputed stress levels. Thus, whatever validations are offered tosubstantiate the computations need to demonstrate only that the locations are

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.. .......... - - - -

correct, but do not necessarily have to demonstate what the magnitudes of theStresses are at these locations.that need to be resisted by the fracture toughness of the shipping container.

The drop test will provide the stress levels

5.2.5 Test Flaw Configuration5.2.5.1 RecommendationThe size and shape of the flaws should be optional on the part of theapplicants.1/6.edge sharpening.should be no greater than 0.005 times the depth of the crack.

However, the aspect ratio of the flaw should not be greater thanIn the case of the blunt crack, the radius of the crack tipThe crack tip may be blunt as a result of machining and subsequent knife

5.2.5.2 Impact on SafetySafety requires that a lower bound be established for the size of a flaw thatcan be considered critical under the conditions of the drop test, defined bythe loading and fracture toughness properties of the material.and shape of the flaw is an option of the applicant, whatever is chosenestablishes this lower-bound critical size. The factors by which thequasi-critical flaw size is reduced, to arrive at the maximum allowable flawSize, provides a conservative margin of safety against brittle fracture,.

While the size

5.2.5.3 Impact on CostThe introduction of flaws in the drop-test prototype models represents aunique requirement for demonstrating resistance to brittle fracture. Altlloughit would be desirable to introduce sharp-tip flaws, no proven technique existsfor generating sharp-tip flaws with a controlled configuration in a largeductile iron casting. This does not rule out the use of sharp-tip flaws, ifthe applicant can demonstrate an acceptable procedure for assuring that suchflaws were produced.to the chosen depth in a manner that would limit the crack tip radius to aValue no greater than 0.005 times the crack depth.enough ratio of crack length to tip radius to assure crack-like behavior andbe achievable with state-of-the-art fabrication techniques.5.2.6 Acceptance Criteria5.2.6.1 Recommendation

A n acceptable alternative would be to machine the flawsThis would provide a larqe

!

After the drop tests, the flaw should not have propagated more thanthree-quarters of the way through the wall of the shipping container atlocations of secondary stress gradients, nor should a flaw initiate fractureat locations of primary membrane or bending stress.interpreted to mean no evidence of ductile tearing at a distance greater than1/8 in. (3.2 nun) beyond the crack tip.

"No initiation" should be

5.2.6.2 Impact on SafetyThe initiation and arrest of flaws befoi:e full penetration can only occur atlocations having a decreasing stress gradient along the crack path, and where

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propagation of the flaw does not significantly alter the state of stress.Areas of primary membrane tension stress and primary bending stresses do notmeet these criteria and, consequently, fracture initiation in these areas willmost likely lead to catastrophic flaw propagation through the wall.Therefore, limited flaw penetration is only allowable in areas of decreasingstress gradient, while the requirement for no significant flaw penetrationapplies to areas of primary membrane tension and primary bending.This recommendation precludes a condition whereby the radioactive contents ofthe shipping container can be released to the environment. However, theformation of a crack implies a reduction in shielding at the site of thecrack, which must be presumed to occur in the event of an accident.acceptance criteria constitute the only recommendation that involvesgenerating a possible radiological hazard, the impact of this recommendationon radiological risk needs to be addressed.

Since the

An analysis was performed to conservatively estimate the dose rate at thecrack site, in the event such a crack occurs. The assumptions made in thisanalysis were:(1) The shield thickness is 16 in. (40.6 cm).(2) The crack penetrates a distance of 12 in. (30.5 cm) before it is( 3 ) The crack is semi-elliptical, with a depth to length ratio of 1/6.(4) The crack's sides are smooth and planar, with an unimpeded line of(5) The crack's width is not expected to exceed 0.10 in. (2.5 m m ) .(6) The source term is based upon 16 BWR assemblies with 3.36 MTU per

arrested.

sight from the crack's tip to the surface.

cask, a specific power of 35 MW, a 25 000 MWD burnup, and 1 yearpost-irradiation time.Based on the above assumptions, the longitudinal dose rate at the crack isconputed as being 639 mrem/h, compared with a dose rate of 6.5 mrem/h at thesurface of-an intact cask.cDmputations and the assumptions made about the input data.Appendix A provides more detail on

the

Phis estimated dose rate is below the value specified in 10 CFR Part 71,Paragraph 71.36 ( 9 ) , which (in the event of a reduction of shielding) limitsthe dose rate to 1000 mrem/h at 3 ft (91.4 cm) from the package's externalsurface.The estimated dose rate reflects a considerable degree of conservatism. It isbased on a crack width of 0.1 in. (2.5 mm), whereas it is more likely that thecrack will be much narrower. Furthermore, cracks do not usually propagatealong planes but undergo changes in direction, which provide enough bafflingto limit the dose rate to that of the undamaged cask. The dose also reflectsa conservatively estimated 10-fold buildup factor, which more refinedcalculations would undoubtedly show to be much less. Taking all these factorsinto consideration, it can be concluded that the presence of the crack impliedby the acceptance criterion would not have an unacceptable impact on safety.

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5.2.6.3 Impact on CostThe recommendation allowing partial penetration of a crack is necesitated bythe recognition that areas of local peak stress may experience stress levelshigh enough to initiate a crack. Since it is impractical to limit flaw sizesin these areas to one-half the critical flaw size at peak stress levels, crackinitiation can be tolerated as long as through-wall penetration does notoccur. Since stresses drop off rapidly in regions of peak stress, it isexpected that initiated cracks will be arrested. Thus, the recommendationresults in a lower cost than would be incurred if it were to allow no crackPropagation anywhere in the cask, with the concomitant requirement fordetecting extremely small flaws.5 . 2 . 7 Maximum Allowable Flaw Size5.2.7.1 RecommendationThe maximum allowable flaw size for ductile cast iron production castings usedin shipping containers shall be one-sixth the size of a quasi-critical blunt-tip test flaw.less than 10 mm ( 0 . 4 in.) deep.In any event, the maximum allowable flaw size should not be

The goal of the fracture toughness acceptance test is to establish a maximumallowable flaw size consistent with the stress levels experienced by theshipping container under hypothetical accident conditions (using the minimumanticipated fracture toughness of the ductile cast iron). Presumably, if theacceptance criterion is met, the fracture toughness in the vicinity of thetest flaw will be sufficient to prevent a catastrophic fracture of thecontainment. It would therefore be required to maintain this level oftoughness for all production castings. It is further assumed that the testflaw is only slightly smaller than the critical flaw, since the actual marginis not easily ascertained. Consequently, the successful test flaw will beconsidered quasi-critical.flaw may well not be the minimum toughness of the ductile iron casting, inwhich case the size of the quasi-critical flaw should be reduced. Therefore,post-test samples should be taken from various locations throughout theprototype casting, including the area adjacent to the test flaw. Pre-crackedcharpy test specimens should be machined from these samples, and tested, todetermine the minimum fracture toughness, with a 99% probability that thisminimum toughness can be exceeded.the toughness at the site of the test flaw, and the quasi-critical flaw sizeestablished in accordance with the following formula:

However, the toughness in the vicinity of the test

This minimum value should be compared with

where a, is the minimum quasi-critical flaw size, aT is the size of thetest flaw, KID(min) is the minimum fracture toughness (based on samplestaken from the test casting), and KID(flaw) is the fracture toughness in thevicinity of the test flaw. The maximum allowed flaw size in any subsequentproduction casting for a shipping container should be aJ6, for a blunt-tiptest flaw. This reflects a safety factor of two with respect to the minimumquasi-critical flaw size, and a factor of three above the value for a blunt

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crack developing the same fracture toughness stress intensity as a sharp crack(see Appendix B).5.2.7.2 Impact on SafetyThe thrust of this recommendation is to provide an acceptable margin of safetyagainst brittle fracture due to the presence of flaws.flaws is the same as that recommended in Section XI of the ASME Boiler andPressure Vessel Code (Section IWB-3611). For blunt-tip flaws, the fracturetoughness stress intensity developed is at most l/d3 that of a sharp-tipflaw, which translates into a critical flaw size three times that of a sharp-tip flaw under similar conditions of geometry and loading.reduction to one-sixth of the blunt-tip quasi-critical test flaw size assuresa safety margin equivalent to that for a sharp-tip flaw.

The factor of 1/2 for

Consequently, a

The procedure for establishing the quasi-critical flaw size ensures that it isbased upon the minimum fracture toughness of the ductile cast iron likely tobe encountered throughout any one production casting. It also takes intoaccount the probability that the fracture toughness at the test flaw locationis not necessarily the minimum fracture toughness of the ductile iron casting.5.2.7.3 Impact on CostThe impact of this recommendation is ultimately reflected in the establishmentof a maximum allowable flaw size, which will have to be detected byinspection.derived for the fracture toughness stress intensity, much larger Lest flawsmust be introduced to compensate for this difference.fla wqs ize is judiciously chosen, there should be no difference in themaximum allowable flaw specified either by this test or by the use of asharp-tip test flaw. Furthermore, if the variation of fracture toughnessthroughout the cask is small, then the inspection limit will be close to thatanticipated by the test flaw.variation is large, the inspection limit may be too rigorous for conventionalNDE procedures. If the latter condition is expected, it would be prudent forthe applicant to increase the size of the test flaw to preclude inspectiondifficulties.( 0 . 4 in.) assures detection with state-of-the-art methods.

Since a blunt-tip test flaw results in a lower value beingIf the blunt-tip test

On the other hand, if the fracture toughness

Specifying a maximum allowable flaw size of not less than 10 mm

The recommended method for measuring the fracture toughness of ductile castiron in qualifying it for acceptance is the pre-cracked charpy impactthose obtained from standard specimens (as recommended in ASME-399). However,this is not detrimental to the application considered here, since the fracturetoughness values are not intended for design use. They are, rather, used in acomparative sense: either the toughness at the location of a flaw is comparedto the minimum toughness obtained by the same method, or the toughness of acast-on (or separately cast) test block is compared to its associated castingor to test blocks representing other castings. Thus, having a standard valuefor fracture toughness is less important than being able to apply a familiar,consistent, and cost-effective testing method. A further advantage of takingpre-crack charpy test data is that they are translatable into flaw sizes usinglinear elastic fracture-mechanics formulas, so that relative measures of flawsizes can be established.

The values indicated by this test are not as authoritative as

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REFERENCES1. M. W. Schwartz, and Boyce, L., "Ductile and Brittle Failure DesignCriteria for Nodular Cast Iron Spent Fuel Shipping Containers," LawrenceLivermore National Laboratory, Livermore, Calif., UCRL-53046, March 1983.2. Boiler and Pressure Vessel Code, Section 111, NB-3200 "Design ByAnalysis," Am . SOC. of Mech. Engineers, (1980).3. "Pressure Vessel Codes: Their Application to Nuclear Reactor Systems,"Technical Reports Series No. 56, International Atomic Energy Agency,Vienna, 1966.4 . W. L. Server, "Impact Three-Point Testing for Notched and Pre-Cracked

Specimens," Journal of Testinq and Evaluation, 6(1), ASTM, Philadelphia,Penna., 1978.5 . "Proposed Standard Method of Test for Instrumented Impact Testing of

Pre-Cracked Charpy Specimens of Metallic Materials," ASTM E-24.03.03,April 1980.6. M. Creager, and Paris, P. C., "Elastic Field Equations for Blunt Crackswith Reference to Stress Corrosion Cracking."

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APPENDIX ARADIOLOGICAL RISK OF A CRACK IN A DUCTILE CAST IRON CASK

1. INTRODUCTION

This appendix presents a conservative estimate of the effect on the gamma dosethat a crack would have, if it penetrated three-quarters of the way throughthe cask wall.attenuation were assumed. The projected dose will be most intense along theplane of the crack and will drop off rapidly in a direction normal to thisplane, as the effect of the full shield comes into play. The crack cantherefore be modeled as an isotropic line source emitting into the half spaceand the intensity should decrease with distance in accordance with 1/2ar.

Uniformly distributed point sources and line-of-sight

2. CRACK CONFIGURATIONA semi-elliptical configuration is assumed for the crack, in a plane normal tothe cask's axis, as shown in Fig. A-1. The crack's thickness is assumed to beno greater than 0.1 in. (2.5 mm), but the dose rates are also estimated forsmaller widths.3 . ASSUMPTIONS ABOUT THE SOURCE TERM

(1) 16 BWR assemblies, with 3.36 MTU per cask.(2) 35 MW specific power.(3) 25 000 MWD burnup.( 4 ) One year post-irradiation time.(5) Spacific activities.(6) Gamma energies and branching ratios from GAMANAL MLIB and Lederer'sTable of the Isotopes.

Table A-1 summarizes the source-term specific activities in Ci/MTU, along withthe major gamma energies and their associated branching ratios. (Gammas withbranching rrtios of less than 0.05 were not included.) Table A-2 summarizesthe source terms for the full cask in terms of photons/second. Also includedare the linear attenuation coefficients for iron vs the gamma energy.

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Table A-1. Major fission product activities and characteristics at oneyear post-irradiation; specific power: 35 MW, burnup: 25 000 MWD.P _r_cI -

Half-Life Specific Activity Major Gamma Energy (Branching Ratio)Isotope (Days) (Ci/MTU) (KeV)

1761 (0.000006)1761 (0.000006)1205 (0.0022)

444

10526.5 6.24 x 102.67 6.24 x 10

58.8 1.64 x 1065.0 3.51 lo4 724 (0.43), 757 (0.546)35.1 7.42 x 10

366.5 2.10 x 100.00035 2.10 x 100.00028 2.05 104 658 (0.945), 678 (0.105), 687 (0.0641,707 (0.167), 764 (0.223), 818 (0.073),

1384 (0.242), 1505 (0.130)

90s,

91Y9 5 ~ r

95Nb 766 (0.99)55

512 (0.205), 622 (0.098)lO6RU512 (0.205), 622 (0.098)lo Rh

885 (0.726), 937 (0.343)r

134cs 745.0 1.16 105 563 (0.084), 569 (0.154), 605 (0.9761,796 (0.160), 802 (0.087)662 (0.85)662 (0.85)134 (0.11)697 (0.0133)122 (0.00003)

44554

10960.0 8.13 x 100.0018 7.69 x 10

284.0 4.80 x 100.012 4.80 x 10

147- 958.2 8.73 x 10

137cs137Bal4 ~e144Pr

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Table A-2. Source characteristics or a full cask(16 assemblies) at one year.

Iron AttenuationCoefficient , u iGamma Energy, (Ei) Source Strength(keW (Photons/s (cml

122134512563569605622658662678687697707724757764766796802818885937

1205138415051761

1115161515161515161414141415151515151514151412141410

3.26 x 106.56 x 101.07 x 101.21 x 102.22 x 101.41 x 105.12 x 102.41 x 101.67 x 102.68 x 101.63 x 107.94 x 104.26 x 101.88 x 102.38 x 102.55 x 109.13 x 101.23 x 101.25 x 101.86 x 101.85 x 108.74 x 104.49 x 106.17 x 103.31 x 104.65 x 10

2.0521.7950.6550.6250.6220.6040.5960.5790.5780.5710.5670.5630.5590.5530.5410.5390.5380.5320.5260.5210.5020.4870.4290.4000.3830.351

16Total 8.30 x 10* From Howerton

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4. ASSUMPTIONS MADE ABOUT THE SHIELD(1)( 2 )( 3 )( 4 )( 5 )

P o i n t s o u r c e ( l i n e - o f - s i gh t a t t e n u a t i o n ) .The source s t r e n g t h s a re d i s t r i b u t e d un if o rm l y, a nd are p r o p o r t i o n a lt o area.Bui ldup i s based o n t h e s o u r ce - s t r e n g t h w e i gh t ed en e rg y .The crack d e p t h i s uni form t o 12 in . (30 .48 Cm )The a t t e n u a t i o n i n a i r i s n e g l e c t e d .

For a f u l l s h i e l d , f s , w i th t h e s o ur c e term d i s t r i b u t e d u n i fo rm l y a b o u t t h es u r f a c e o f a r i g h t c i r c u l a r c y l i n d e r h a v i n g a 13-in.h e i g h t o f 1 79 .5 i n . (4.56 m ) , we have: (33-cm) ra d iu s and a

and

where:$ f s ( 1 6 ) = t h e p o i n t s o u rc e f l u x a t 1 6 in . (40.64 c m ) f o r t h e f u l l

s h i e l d , i n p ho to ns /cm 2s= t h e t o t a l Source s t r e n g t h f o r t h e i t h gamma-ray e ne rg y, i n= 16 in . (40 .64 c m ) o f i ron, i n c m= 2prh = 14 665 in .2 (94 549 cm2)= p o i n t s o u rc e s t r e n g t h per u n i t area f o r t h e ithg a m a r ay

i p h o t o n s / sSTt16Acy1S i energy, i n photons/cm2s.

For t h e cracked s h i e l d , c s , a u n if o rm l y d i s t r i b u t e d s o u rc e w it h a n area e q u a lt o t h e crack f r o n t a l area , b, s assumed fo r t h e r e d u c e d a t t e n u a t i o ne f f e c t . T h u s , we wr i t e t h e f l u x a s :

(A-3)

$cs(16) = t h e p o i n t s o u r c e f l u x a t 1 6 i n . (40.64 c m ) f o r t h et 4 = 4 in . (10.16 c m ) o f i r o n , i n cm .c r ack ed s h i e l d , i n p ho to ns /cm 2s

S u b s t i t u t i n g fo r si from Eq. ( ~ - 2 ) ~e have:

(A-4)

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Solving for the relative effect of the crack, we have:

The results of the attenuation calculations of Eq. (A-5) are summarized inTable A-3. The summation results are:

= 2 .35 x photons/s ,s e-pit41 Tiand

86 t-" l6 1 . 2 4 x 10 photons/s .

- 3 3 -

(A -5 )

(A-6)

(A-7 )


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Table A-3. A t t e n u a t i o n r e s u l t s f o r 16-in. (40.64-cm) and4-in. (10.16-cm) th ic kn es se s of i r on .

-'iK16S eTiamma Energy,- 'it4S eTi

( k e w (Photons /s ) (Photons /s )

1 2 213451256 3569605622658

678687

662

697707724757764766796a0281 888 5937

1205138415051761

1.98 x1.37 x2.94 x 1 01.13 x 1 02.33 x 1 0

4445556

3.08 x i o1.55 x 1 01.45 x 1 01.05 x 1 02.24 l o 4

4445556

1.60 x 1 09.18 x 1 05.80 x i o3.26 x 1 06.73 x 1 07.82 x i o2.92 x 1 05.01 l o 5

56.50 x 1051.19 x 1 062.55 x 1 0

2.22 x 1 0651.20 x 1 077

5.38 x i o

2.97 l o 75.75 x 1 0

T o t a l a1.24 x 1 0

2.88 x ioL7.88 x lo71.38 x i o 1 3

122.11 x 101 21 3

4.00 x 103.05 x 1 0

1 31.20 x 1 06.72 x 1 0 l 24.708.10 x io11

115.13 x 1 02.60 x 1 0 l 2

1 2121 21 31 3

1.45 x 1 06.82 x i o9.76 x 1 01.07 x 1 03.86 x i o5.53 x 10l25.97 x 10l29.35 x l o l l

1 31.13 x 1 06.20 x 1 0 l 2

1 05.75 x 1 01 31.06 x 101 26.76 x 10

1.31 l o 91 42.35 x 1 0-

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To est imate t h e dose b u i ld u p , t h e T a y lo r e q u a t i o n w a s used by assuming as i n g l e i n c i d e n t p h ot o n e n e r gy , w e ig h te d by t h e s o u r c e s t r e n g t h . u s i n g t h eda ta from Table A-2, it c a n be s hown t h a t t h e w e igh t e d e ne r gy is 625 K eV andt h e l i n e a r a t t e n t u a t i o n c o e f f i c i e n t , p, i s e q u a l t o 0.595 c m - l . Accordingt o T a y l o r , t h e do s e b u il d u p is given by:

I n t h e case of i r o n a n d a n e n e r g y , E, of 625 KeV: A = 9.5, a = 0.0935, andB = 0.019. S u b s t i t u t i n g f o r A , a, and B i n Eq. ( A - 8 ) , w e o b t a i n :

an d

S u b s t i t u t i n g Eqs. (A-6) and (A-7) i n t o Eq. (A-5), and a l l ow i n g f o r t h ees t imate o f d o s e b u il d u p , w e have:1 484cs (16) Ac (2.35 x 1 0 ) (9.07)$ f s ( 16 ) A y1 (1 .24 x 1 0 ) (85.9)= -

S u b s t i t u t i n g f o r t h e area o f t h e c y l i n d e r a nd s o l v i n g , we o b t a i n :

(A-9)( A - 1 0 )

( A - 1 1 )

( A - 1 2 )

F o r t h e crack t h i c k n e s s e s u n d e r c o n s i d e r a t i o n , w e ha ve c a l c u l a t e d t h e v a l u e sshown i n T a b l e A-4.

T a b l e A-4. R e la t iv e e f f e c t of a crack.

C r a c k T h i c k n e s s F r o n t a l A r e ai n . ( c m ) ( c m 2 ) $O(W/c!f , (16)

0.02 (0 .05) 9.290.04 (0 .10) 18.580.06 (0.1 5) 27.870.08 (0.20) 37.160.10 (0.25) 46.45

19.6639.3258.9778.6398.29

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C o ns id e ri ng t h e p r o p o r t i o n a l i t y o f f l u x t o dose , and t he ca lc u l a t ed gammas u r f a c e d o se r a t e a t t h e c a s k ' s s ide (6 .5 mrem/hr ) , w e have:

(A-13)

an d ca n d e r i v e t h e e s t i m a t e d d o s e r a t e a t t h e s u r f a c e a bo ve seve ra l cracks ofva r i ous w i d t h s , as shown i n Table A-5.

Table A-5. Es t ima ted su r f ac edose r a t e a t cracks .

C r ' a c k ' Thickness Dcs(16)i n . ( c m ) (mrem/h)

0.02 (0.05) 1280.04 ( 0 . 1 0 ) 2550.06 (0 .15) 3830.08 ( 0 . 2 0 ) 5110.10 (0.25) 639

I f w e a ss um e t h a t t h e dose bu i l dup i n t h e cracked s h i e l d can be ne g l e c t e d -- ar e a s ona b l e a pp r oa c h , s ince a ny u n c o l l id e d p ho t on t h a t p e n e t r a t e s t h e 4 - i n .(10.2-cm) thick i r o n s h i e l d and i s t h e n s c a t t e r e d o u t of the narrow beam w i l ll i k e l y be l o s t -- t h e r e s u l t s of Table A-4 and A-5 w i l l be reduced by a f a c t o rof 9.07. Thus , the r e l a t i v e e f f e c t o f t h e crack f o r t h e maximum crackt h i c k n e s s w i l l be ~ 1 1i m e s g r e a t e r t h an t h e d os e ra te a t t h e s u r f a c e o f t h ec a s k . I f w? a s s u m e a 6.5 mrem/h gamma dose r a t e a t t h e s u r f a c e , t h e n t h e do sea t t h e crack would be on t h e orde r of 70 mrem/h.

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APPENDIX BFRACTURE TOUGHNESS STRESS INTENSITIES FOR BLUNT-TIP CRACKS

Mathematically, a blunt crack is conveniently represented by an ellipticalcylinder that is void of material and has a small tip radius, compared to thecrack's length. under these circumstances the configuration of the crack tipis nearly parabolic, as shown in Fig. A-1, with the focus at a distance ofp/2 from the crack tip, where p is the crack tip's radius. This geometricidealization makes it possible to develop a set of field equations for thevicinity of the blunt-crack's tip, which are similar to those for a sharpcrack. For the opening mode I, these are:6

The stress-state relations differ from those of the ideal sharp crack only bythe addition of a second term, which is dependent upon the radius of curvatureof the tip. For distances from the crack tip where p/r + 0, the fieldequations revert to those of the ideal sharp crack and they are perturbed formode-I loading only in the immediate vicinity of the blunt-crack's tip.The stresses in the plane of the crack are:

and= o .XY

Furthermore, at the surface of the crack in the crack plane, uX = 0 andr = p/2, so that:

(B-2a)

(B-2b)

(B-2C)

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t

F i g u r e B-1. C o o r d i n a t e s o f a b l u n t crack t i p .

A t t h e s u r f a c e of t h e b l u n t crack, i n t h e crack p l an e , ax = 0, so t h a t :a ( e = o , r = , ) = = ,2KIY

where = 0, r = p/2) i s t h e maximum s t r e s s a t t h e s u r f a c e o f t h eb l u n t crack. T h e q u an t i t y , 0 , decreases w i t h a n in c r e a s e i n r , as showni n Fig . B-2. Y

F i g u r e B-2. S t r e s s a t a b l u n t crack prior to y i e l d .- 38 -


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.. - . . .. ... . . . .... -- .. - - -

-

For a n i d e a l sharp crack , w i t h i t s t i p a t t h e o r i g i n of t h e b l u n t - c r ackcoordinate s ys te m, t h e d i s t r i b u t i o n fo r 0 i s :*Y

PI2 0-

** KIY G '( e = 0) = -

*where symbol izes parameters associated w i t h a n i d e a l sharp crack. I nFig . B-3, t h e s t r e s s d i s t r i b u t i o n f o r ay is shown superimposed on t h eb l u n t - c r a c k ' s s t ress d i s t r i b u t i o n . Note t h a t if :

** *K I = K I , aY = oY/2 a t r = p/2 .

7 Stress at th e surface

F i g u r e B-3. Comparison of t h e s t r e s s d i s t r i b u t i o n b e t w e e na sharp crack and a b l u n t crack.*I f i d e a l e l a s t i c i t y is assumed, very l o w v a l u e s of K I c a n c a u s e a s h a r p

crack to become uns tab le . However, i n t h e case of rea l metals, a p l a s t i c zoneforms a t t h e t i p of t h e s h a r p crack, which t ends t o i n c r e a s e t h e c r i t i c a ls t r e s s i n t e n s i t y , KIc.p l a s t i c - z o n e s i z e , R , e q u a l s ,,/2, as shown i n Fig . 8 - 4 : ay a tt h e n t h e y i e l d s t ress Q s.s t r e s s i n t e n s i t y f o r t h g sharp crack is :

* *Suppose KI i n c r e a s e s t o a p o i n t w h e r e t h e* i s* T h e r e l a t i o n of t h e p l as t ic - z on e ' s s i z e t o t h e

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*where KI Y i s t h e s t r e s s i n t e n s i t y r e q u i r e d t o de ve l op a p l a s t i c zone,R = p/2.y i e l d i n g i s r e l a t e d t o t h e y i e l d s t r e s s by Eq.The s t r e s s i n t e n s i t y r e q ui r ed for t h e b l u n t crack t o s t a r t( B - 3 ) :

2KI Y 9=ys = 3T

S u b s t i t u t i n g E q . ( B - 6 ) i n t o E q . ( B - 5 ) g i v e s :

*KKI YI Y

- = f i .

Ilunt crack1 9 = p / 2F i g u r e B - 4 . T h e ' p l a s t i c zone a t t h e t i p of a s h

criteria osti gov

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