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Stress Analysis of Safkeg HS Containment Vessel

Croft Associates Ltd F4 Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB

L20008/1/R1

Rev 0B

27/09/2012

Alex Bond +44 (0)7969 819984


Report No: L20008/1/R1 Revision: 0B

27/09/2012 Page 2 of 95

Document Approval and Revision Record

Project HS Package FEA Study

Document Title Stress Analysis of Safkeg HS Containment Vessel

Client Croft Associates Ltd

Document Number L20008/1/R1

Job Number L20008/1

Rev

Date

Issue

Prepared

Reviewed

Approved

0A 24/11/11 Existing design GD Jones AE Bond AE Bond

0B 21/09/11 Buckling / Fatigue Included

AE Bond Jvd Bergh AE Bond

StreCon

RepoRevis

1.0

2.0

3.0

4.0

ess Analysntainment V

ort No: L20008/1sion: 0B

Cover SReport Table oSumma

Introdu

Struct

2.1 2.2

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4.7.2 Stress Calculations 27 4.7.3 Comparison with Allowable Stresses 27

4.8 NCT 8: Free drop on lid (cold) 28 4.8.1 Summary of Pressures and Temperatures 28 4.8.2 Stress Calculation 28 4.8.3 Comparison with Allowable Stresses 28

4.9 NCT 9: Free drop on corner (hot) 29 4.9.1 Summary of Pressures and Temperatures 29 4.9.2 Stress Calculations 29 4.9.3 Comparison with Allowable Stresses 30

4.10 NCT 10: Free drop on corner (cold) 31 4.10.1 Stress Calculations 31 4.10.2 Comparison with Allowable Stresses 31

4.11 NCT 11: Free drop on side (hot) 32 4.11.1 Summary of Pressures and Temperatures 32 4.11.2 Stress Calculations 33 4.11.3 Comparison with Allowable Stresses 33

4.12 NCT 12: Free drop on side (cold) 34 4.12.1 Summary of Pressures and Temperatures 34 4.12.2 Stress Calculations 34 4.12.3 Comparison with Allowable Stresses 34

5.0 Hypothetical Accident Conditions 36

5.1 HAC 1: Free drop on lid (hot) 36 5.1.1 Summary of Pressures and Temperatures 36 5.1.2 Stress Calculations 36 5.1.3 Comparison with Allowable Stresses 36

5.2 HAC 2: Free drop on lid (cold) 37 5.2.1 Summary of Pressures and Temperatures 37 5.2.2 Stress Calculation 37 5.2.3 Comparison with Allowable Stresses 37

5.3 HAC 3: Free drop on top corner (hot) 38 5.3.1 Summary of Pressures and Temperatures 38 5.3.2 Stress Calculations 38 5.3.3 Comparison with Allowable Stresses 38

5.4 HAC 4: Free drop on corner (cold) 39 5.4.1 Stress Calculation 40 5.4.2 Comparison with Allowable Stresses 40

5.5 HAC 5: Free drop on side (hot) 40 5.5.1 Summary of Pressures and Temperatures 40 5.5.2 Stress Calculations 41 5.5.3 Comparison with Allowable Stresses 41

5.6 HAC 6: Free drop on side (cold) 42 5.6.1 Stress Calculation 42 5.6.2 Comparison with Allowable Stresses 42

6.0 Lid Closure Forces 43

7.0 Conclusions 45

8.0 References 46



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Appendix A – Mesh Sensitivity Study 89 Appendix B – Bolt Preload Calculation 96

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1.0 Introduction

This report describes the stress analysis of the Safkeg HS Containment Vessel when subjected to loads due to Normal Conditions of Transport (NCT) and Hypothetical Accident Conditions (HAC). This report describes the finite element model, the assumptions made, the results, and the assessment of the stresses against the allowable values. The Safkeg HS overpack was not included in this analysis as that will be assessed by testing.



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2.0 Structural Evaluation

2.1 Description of Finite Element Model

Figure 1 shows the finite element model of the containment vessel (CV). The model was originally generated using drawings provided by Croft [Ref. 1-3] but the model was subsequently modified so that the CV would satisfy the requirements of Regulatory Guide 7.6. A half-symmetry model was used as both the geometry and the load cases were all symmetric about a vertical plane through the centre of the vessel. First-order brick elements were used throughout the model. In thin sections of the vessel, at least 8 elements through the thickness were used to capture the stress distribution. A mesh sensitivity study on a similar vessel shows that this gives a reasonable compromise between accuracy and model size (Appendix A). Sliding contact was defined between all the parts with a friction coefficient of 0.1. The bolts were tied to the CV body along the threaded length but the bolt heads were free to slide. A pre-load of 8.12 kN was applied to the bolts at the start of the analyses prior to any other loads being imposed (the calculation is given in Appendix B). This corresponds to an applied torque of 10 N m as specified on the drawing. Abaqus has a standard method for applying pre-loads to bolts. This is described in section 29.5 “Prescribed Assembly Loads” in the Abaqus Analysis User’s Manual [5]. In this method, the bolts are broken at a section defined by the user. In the first step of the analysis, the bolt is shortened until the pre-load defined by the user is achieved. In subsequent steps, the length of the bolt is fixed so that the load in the bolt can vary. The model shown in Figure 1 was used for all of the non-impact cases. The model was modified for the impact load cases by including the cork impact limiter, as shown in Figure 2. The outer faces of the cork were fully constrained. A body force was applied to the vessel, which was equivalent to the measured deceleration in an impact. This pushed the vessel into the cork. The inclusion of the cork in the model spread the loads on the vessel. The cork modulus is between 28 MPa (-29°C) and 1.63 MPa (100 °C). A similar analysis was previously performed [4] using these properties, but it was found that the elements in the cork part of the model distorted severely causing the analysis to terminate prematurely. Re-analysing the impact with an artificially high modulus for the cork (1 GPa) allowed the analyses to complete successfully while adding some conservatism to the model. This is a conservative approach as using a higher cork modulus will concentrate the loads over a smaller area of the containment vessel compared with using the actual cork modulus. The plane of symmetry of the model was the plane Z=0. The boundary conditions applied to this plane were UZ=0 URX=0 URY=0 Where U is the displacement and UR is a rotation. This is standard FEA practice. As both the geometry and loading was symmetric about the plane Z=0, the use of a half-symmetry model has no effect on the results. Again, this is standard FEA practice. For the non-impact cases (NCT1-6), the CV was fixed at a single point at the centre of the bottom of the flask in the X-direction. The outer edge of the bottom of the flask was fixed in the Y-direction. These boundary conditions were to prevent any rigid body movement but do



27/09/2012 Page 9 of 95

not affect the overall behaviour of the model. No stress concentrations were observed at these locations. For impact cases NCT7, NCT8, HAC1 and HAC2 (drop on lid), the X and Y boundary conditions were maintained during the pre-loading steps. During the impact loading step, the Y boundary conditions were removed. Excessive movement in the Y direction and rotation about the Z axis was prevented by contact between the flask and the cork. Rigid body motion of the cork was prevented. For impact cases NCT9, NCT10, HAC3 and HAC4 (drop on side), the X and Y boundary conditions were maintained during the pre-loading steps. During the impact loading step, the X boundary condition was removed. The Y boundary condition was changed so that it just applied to the centre of the bottom of the flask. This prevented rigid body motion in the Y direction but about allowed rotation about the Z axis. Excessive movement in the X direction was prevented by contact between the flask and the cork. Rigid body motion of the cork was prevented. For impact cases NCT11, NCT12, HAC5 and HAC6 (drop on top corner), the X and Y boundary conditions were maintained during the pre-loading steps. During the impact loading step, the X and Y boundary conditions were removed. Excessive movement in the X and Y directions was prevented by contact between the flask and the cork. Rigid body motion of the cork was prevented. All of the analyses were performed as static analyses, i.e. dynamic effects were not included in the impact cases. The commercial finite element code Abaqus/Standard v6.10 [5] was used for the analyses. The models were created using Abaqus/CAE v6.10 [6].

2.2 Design Criteria

2.2.1 Load Combinations

The load combinations used for the structural evaluation of the vessel were developed in accordance with Regulatory Guide 7.8 [8]. The NCT and HAC load combinations are summarized in Table 2-1 and Table 2-2. The left-hand column of these tables gives the load case ID. The hot initial condition has been taken as a uniform temperature of 158°C for NCT cases, and a value of 192°C for HAC cases and the cold initial condition has been taken as a uniform temperature of -29°C. The hot environment load case has been taken as a uniform temperature of 158°C and the cold environment load case has been taken as a uniform temperature of -40°C. In all cases, it was assumed that the fabrication temperature was 21°C. The maximum internal pressure is 8 bar absolute and the minimum pressure is 0 bar absolute. Gauge pressures are applied to the FE model, therefore the maximum pressure applied to the model was 7 bar gauge and the minimum pressure was -1 bar gauge. The vibration load was 10g in a vertical direction.



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The three attitudes chosen for the free drop cases were:

1. Drop on lid. 2. Drop on side 3. Centre of gravity over top corner.

It was considered that a drop on to the base of the vessel would do less damage to the containment vessel than the drop on lid case. The same applies to a drop on the bottom corner. A drop on to the top corner may distort the lid and open the seals whereas this would not occur with a drop on the bottom corner. The accelerations values used in the analysis are given in Table 2-3. These values were taken during tests carried out by Croft Associates. In some of the tests, the accelerometers failed, so the accelerations were estimated based on the other results.

Table 2-1: Load Combinations for Normal Conditions of Transport Load Case

ID

Normal or Accident Condition

Initial Conditions Ambient

Temperature1 Solar

heating Decay Heat Internal

Pressure Fabrication

Stress

38°C -29°C Max. Zero Max. Zero Max. Min. NCT1 Hot

environment2

(38°C ambient temperature)

X X X X

NCT2 Cold environment2

(-40°C ambient temperature

X X X X

NCT3 Reduced external

pressure (24.5 kPa)

X X X X X

NCT4 Increased external

pressure (140 kPa)

X X X X X

NCT5 Vibration (10g vertical)

X X X X X NCT6 X X X X X NCT7 Free drop on

lid (1.2m) X X X X X

NCT8 X X X X X NCT9 Free drop on

corner (1.2m) X X X X X

NCT10 X X X X X NCT11 Free drop on

top(1.2m) X X X X X

NCT12 X X X X X Notes:

1. A thermal analysis of the containment vessel has shown that the combination of an ambient temperature of 38°C plus maximum heating from solar heating and decay heat would generate a uniform temperature of 158°C. The “cold ambient temperature” was a uniform temperature of -29°C.



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Table 2-2: Load Combinations for Hypothetical Accident Conditions Load case

ID

Accident Condition

Initial Conditions Ambient

Temperature1 Solar

heating Decay Heat Internal

Pressure Fabrication

Stress 38°C -29°C Max. Zero Max. Zero Max. Min.

HAC1 Free drop on lid (9m)

X X X X X HAC2 X X X X X HAC3 Free drop

on corner (9m)

X X X X X HAC4 X X X X X

HAC5 Free drop on side

(9m)

X X X X X HAC6 X X X X X

Notes: 1. A thermal analysis of the containment vessel has shown that the combination of an ambient temperature

of 38°C plus maximum heating from solar heating and decay heat would generate a uniform temperature of 192°C and the “cold initial condition” was a uniform temperature of -29°C.

2. The puncture case was not included as only the containment vessel is assessed in this document. The punch would not penetrate the over-pack and hence would not affect the containment vessel.

3. The thermal case has not been included as this will be analysed by another contractor.

Table 2-3 Load cases Case ID Description Internal gauge

pressure (MPa) Temperature (°C)

Acceleration (g)

NCT1 Hot environment 0.7 158 n/a NCT2 Cold environment -0.1 -40 n/a NCT3 Reduced external

pressure 0.7755 158 n/a

NCT4 Increased external pressure

-0.140 -29 n/a

NCT5 Vibration (hot) 0.7 158 10g vertically down

NCT6 Vibration (cold) -0.1 -29 10g vertically down

NCT7 Free drop on lid from 1.2m (hot)

0.7 158 434g axial.

NCT8 Free drop on lid from 1.2m (cold)

-0.1 -29 434g axial

NCT9 Free drop on corner from 1.2m (hot)

0.7 158 376g axial 590g radial

NCT10 Free drop on corner from 1.2m (cold)

-0.1 -29 376g axial 590g radial

NCT11 Free drop on side from 1.2m (hot)

0.7 158 294g radial

NCT12 Free drop on side from 1.2m (cold)

-0.1 -29 294g radial

HAC1 Free drop on lid from 10.2m (hot)

0.7 192 458g axial

HAC2 Free drop on lid from 10.2m (cold)

-0.1 -29 458g axial

HAC3 Free drop on corner from 10.2m (hot)

0.7 192 338g axial 228g radial

HAC4 Free drop on corner from -0.1 -29 338g axial



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Case ID Description Internal gauge pressure (MPa)

Temperature (°C)

Acceleration (g)

10.2m (cold) 228g radial HAC5 Free drop on side from

10.2m (hot) 0.7 192 458g radial

HAC6 Free drop on side from 10.2m (cold)

-0.1 -29 458g radial

HAC7 Maximum pressure 1.0 192 n/a HAC8 Immersion -0.150 4 n/a

2.2.2 Allowable Stresses

The allowable stresses were taken from Regulatory Guide 7.6 [9]. These are based on the 1977 edition of the ASME Boiler and Pressure Vessel Code. This guide only gives allowable stress values for primary membrane stress, primary membrane plus primary bending stress and primary plus secondary stress for both NCT and HAC loading conditions. The allowable values for bearing stress and for the bolts have been taken from ASME Code Section III Div 3 [10] as these are not given in Reg. Guide 7.6. Guidance for classification of stresses was taken from Table WB-3217-1 in ASME Code Section III Div 3 [10]. Stress in the non-containment parts of the vessel were not evaluated as these are not covered by Regulatory Guide 7.6 [9]. To demonstrate conformance with the allowable stress limits, it was necessary to determine the stress intensities at critical cross-sections of the containment vessel. Since the critical cross-section locations are load-condition dependent, several “stress evaluation sections” were defined to ensure that all critical locations were evaluated for every load condition. These stress evaluation sections are illustrated in Figure 5. For evaluation of conditions producing a stress distribution in the vessel that it not axisymmetric, stress evaluations were performed at multiple circumferential locations. The section stresses at each stress evaluation location were obtained using the Abaqus “stress linearization” post-processing feature [6]. The user selects a section where the stress linearization is required, and selects which stress components are required. Abaqus then prints a report with the membrane, bending and peak stresses for each stress component and stress invariant. Arcadis Vectra used the membrane and bending stresses for the Tresca stress invariant (which is equal to the stress intensity as required by NRC Regulatory Guide 7.6). The peak stress was taken by probing the model directly. These values were then put in a spreadsheet to determine the design margin. Only the smallest design margins are reported. The average bearing stress was calculated by extracting the axial force in the bolts and dividing it by the bearing area of the bolt heads. The average stress in the bolts was calculated by extracting the axial force in the bolts and dividing by the cross-sectional area of the bolts. The average shear stress was calculated by determining the shear force between the bolt head and lid and dividing by the contact area.



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Using the critical sections from each load case, minimum design margins are calculated and reported for all bounding load combinations. The design margin (DM) is defined as follows:

1_

_

ValueCalculated

ValueAllowableDM

Therefore a negative design margin indicates that the vessel has failed the assessment.

Table 2-4: Containment System Allowable Design Criteria Stress Type Allowable Stress Limits

NCT HAC Other Than Bolts

Primary Membrane Stress Intensity (Pm)

Sm Lesser of 2.4Sm and 0.7Su

Primary Local Membrane Stress Intensity (PL)

Sm (2) N/A (3)

Primary + Bending Stress Intensity (PL or Pm+Pb)

1.5Sm Lesser of 3.6Sm and Su

Primary + Secondary Stress Intensity (PL or Pm+Q)

3.0Sm N/A

Average Bearing Stress Sy N/A Bolts

Average Shear Stress 0.4Sy Lesser of 0.42Su and 0.6Sy

Average Stress (4) 2Sm Lesser of 3Sm and 0.7Su Maximum Stress (5) 3Sm N/A (6)

Notes: 1. Stress limits applicable for components and systems evaluated using elastic system analysis. 2. ASME B&PV code gives an allowable of 1.5Sm for primary local membrane stress, PL. However, Reg.

Guide 7.6 does not specify an allowable for this stress, so a lower allowable value of Sm has been adopted for this assessment.

3. Evaluation of secondary stress is not required for HAC. 4. The axial stress component averaged across the bolt cross-section and neglecting stress

concentrations. 5. The stress due to internal pressure and gasket seating loads (e.g. bolt torque) shall not exceed one

times Sm. 6. Evaluation of maximum bolt stress not required for HAC.

2.2.3 Buckling

The containment vessel inner shell was evaluated for buckling in accordance with the requirements of ASME Code Case N-284-2 [10]. Capacity reduction factors are calculated in accordance with Section -1511 of ASME Code Case N-284-2 to account for possible reductions in the capacity of the shells due to imperfections and nonlinearity in geometry and boundary conditions. Plasticity reduction factors, which account for nonlinear material properties when the product of the classical buckling stresses and capacity reduction factors exceed the proportional limit, are calculated in accordance with Section -1610 of ASME Code Case N-284-2. The theoretical buckling stresses of the vessel inner shell under uniform stress fields are calculated in accordance with Section -1712.1.1 of ASME Code Case N-284-2. The geometric parameters used in the buckling assessment are given in Table 2-5. The capacity reduction factors, plasticity reduction factors, and theoretical buckling stresses for the vessel inner shell are summarized in Table 2-6.



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The allowable elastic and inelastic buckling stresses for NCT and HAC are calculated in accordance with the formulas given in Section -1713.1.1 and Section -1713.2.1 of ASME Code Case N-284-2. The allowable buckling stresses include factors of safety of 2.0 for NCT and 1.34 for HAC in accordance with Section -1400 of ASME Code Case N-284-2. Table 2-7 provides a summary of the vessel inner shell elastic and inelastic buckling stresses for NCT and HAC. Buckling interaction ratios are calculated for the containment vessel inner shell for all NCT and HAC tests that load the shells in compression. The interaction ratios for elastic buckling and inelastic buckling are calculated using the highest values of compressive stress and shear stress from the finite element analysis solutions in accordance with the formulas given in Section -1713.1.1 and Section -1713.2.1 of ASME Code Case N-284-2. An example of the buckling calculation is given in Appendix A. The stresses used in the calculation were taken from point C5, which is mid-way along the length of the inner shell of the containment vessel. Where one of the stress components is tensile in the FE analysis, it should be given a value of 0 MPa in the buckling calculation. However, to avoid divide by zero errors, it was given a very small positive value in the buckling calculation.

Table 2-5: Containment vessel shell buckling geometric parameters Geometric Parameter Inner Shell

Mean radius, R (mm) 35.25 mm Shell thickness, t (mm) 4.7 mm R/t 7.5 Unsupported axial length, l (mm) 152.4 mm Unsupported circumferential length, l (mm) 236.3 mm

Table 2-6: Buckling reduction factors and theoretical buckling stresses Calculation Parameter Hot ambient temp.

(NCT) (200°C) Cold ambient temp. (-29°C)

Capacity reduction factors (-1511)

L 0.2 0.2

L 0.8 0.8

L 0.8 0.8

Plasticity reduction factors (-1610)

0 0.0

0.1 0.1

0.0 0.0

Theoretical buckling values (-1712.1.1)

eL 14762 MPa 15972 MPa

reLeL 2162 MPa 2339 MPa

heLeL 2056 MPa 2225 MPa

eL 5421 MPa 5866 MPa



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Table 2-7: Shell allowable buckling stresses Buckling Regime

Stress type Allowable Buckling Stress (MPa) Hot ambient temp. Cold ambient temp.

NCT HAC NCT HAC Elastic buckling

Axial compression, xa 1528 2218 1818 1818 Hydrostatic pressure, ha 823 1194 890 890 Hoop compression, ra 865 1256 936 936 In-plane shear, a 2169 3148 2346 2346

Inelastic buckling

Axial compression, xc 60.0 84.3 86.0 86.0 Radial external pressure, rc 60.0 84.3 86.0 86.0 In-plane shear, c 36.0 50.6 51.6 51.6

2.2.4 Fatigue

The fatigue analysis was carried out in accordance with section C.3 in NRC Reg. Guide 7.6 [9]. The fatigue analysis was performed as follows:

1. The alternating stress, Salt, was calculated as one-half the maximum absolute value of S’12, S’23, S’31 for all possible stress states i and j where 1, 2 and 3 are principal stresses and

S’12 = (1i – 1j) – (2i – 2j) S’23 = (2i – 2j) – (3i – 3j) S’31 = (3i – 3j) – (1i – 1j)

State i is after the bolt pre-load has been applied and state j is after all the other loads have been applied. This calculation of Salt is carried out in the post-processor.

2. Salt is multiplied by the ratio of the modulus of elasticity given on the design fatigue curve to the modulus of elasticity used in the analysis to obtain a value of stress to be used with the design fatigue curves.

3. The highest value of Salt determine in step 2 is then compared with the design fatigue curves (Figure I-9.2.2) in Appendix I of ASME B&PV Section III [10].

The number of cycles that the Safkeg HS CV will undergo is approximately 50 cycles/year for 20 years = 1000 cycles. The number of cycles was multiplied by 10 to give 10000 cycles, to give a safety margin.



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3.0 Materials

3.1 Material Properties and Specifications

The material specification for each part in the model is given in Table 3-1. The material properties used in the analysis are given in Table 3-2 to 3-4.

Table 3-1: Material specifications Part Material Containment vessel body Type 304L stainless steel Containment vessel lid Type 304L stainless steel Shielding Depleted Uranium Containment vessel bolts SA-320/A320 Grade L43 Bolting Steel Contents of CV 4% Sb Lead

Table 3-2: Mechanical Properties of Type 304L Stainless Steel

Temp (°C)

Design stress intensity Sm (MPa)(2)

Yield strength, Sy (MPa)(3)

Tensile strength, Su (MPa)(4)

Modulus of Elasticity, E (GPa)(5)

Mean. Coef. Of Thermal Expansion, (m/m/°C x 10-6)(6)

-40 115 172 483 198 14.820 115 172 483 195 15.3

149 115 132 422 186 16.6204 109 121 405 183 17.1232 105 117 401 180 17.3260 102 113 396 178 17.5

Notes: 1. Values for SA-240/A240 product specifications. 2. ASME Code, Section II, Part D [10], Table 2A. 3. ASME Code, Section II, Part D [10], Table Y-1. 4. ASME Code, Section II, Part D [10], Table U. 5. ASME Code, Section II, Part D [10], Table TM-1, Material Group G. 6. ASME Code, Section II, Part D [10], Table TE-1, Group 3, Coefficient B (mean from 70°F) 7. The yield strength and tensile strength were not used in the FE model as a linear-elastic analysis was

performed. These values were used in the stress assessment. 8. A Poisson’s ratio of 0.3 and a density of 8030 kg/m3 were used.



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Table 3-3: Mechanical Properties of SA-320/A320 Grade L43 Bolting Steel

Temp (°C)

Design stress intensity Sm (MPa)(1)

Yield strength, Sy (MPa)(2)

Tensile strength, Su (MPa)(3)

Modulus of Elasticity, E (GPa)(4)

Mean. Coef. Of Thermal Expansion, (m/m/°C x 10-6)(5)

-40 241 723 860 195 10.9 -30 241 723 860 194 11.0 25 241 723 860 191 11.6 40 241 723 860 190 11.7 65 235 704 860 189 11.9 100 226 678 860 187 12.1 120 224 671 860 186 12.2 150 220 660 860 184 12.2 204 211 633 862 183 13.1 260 203 610 862 178 13.1

Notes: 1. ASME Code, Section II, Part D [10], Table 4. 2. In accordance with ASME Code, Section II, Part D [10], Table 4, General Note (a), the yield strength is

equal to 3 times the allowable stress value, Sm. 3. Minimum tensile strength from ASME Code, Section II, Part D [10], Table 4. 4. ASME Code, Section II, Part D [10], Table TM-1, Material Group G. 5. ASME Code, Section II, Part D [10], Table TE-1, Group 1, Coefficient B (mean from 70°F) 6. Values shown in italics are calculated using linear interpolation or linear extrapolation. 7. The yield strength and tensile strength were not used in the FE model as a linear-elastic analysis was

performed. These values were used in the stress assessment. 8. A Poisson’s ratio of 0.3 and a density of 7860 kg/m3 were used.

Table 3-4: Mechanical Properties of DU Alloy

Temp (°C)

Density (kg/m3)

Modulus of Elasticity, E (GPa)

Poisson’s ratio Mean. Coef. Of Thermal Expansion, (m/m/°C x 10-6)

-40 18952 172 0.3 11.5 -29 11.7 21 12.7 38 13.0 93 14.1

Notes: 1. Average tension modulus of DU from [11]. 2. Properties from Figure I-2 of [12].

Table 3-5: Mechanical properties of Lead 4% Sb [13]

Density (kg/m3) Modulus of Elasticity (GPa)

Poisson’s ratio Mean. Coef. Of Thermal Expansion, (m/m/°C x 10-6)

11680 16.1 0.44 29



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4.0 Normal Conditions of Transport

This section presents the structural evaluation of the package in accordance with Reg. Guides 7.6 and 7.8 [9, 8] when subject to the NCT tests specified in Reg. Guide 7.8. The package is evaluated for each NCT test individually based on the most unfavourable initial conditions.

4.1 NCT 1: Hot Environment

4.1.1 Summary of Pressures and Temperatures

In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was a uniform temperature of 158°C. The internal gauge pressure was 700 kPa.

4.1.2 Stress Calculations

The stresses in the containment vessel were calculated using the finite element model described in section 2.1. Figure 6 shows the deformations in the vessel, scaled a by a factor of 20. Some parts appear to be passing through each other but that is not the case because of the high scale factor. There was no significant distortion of either the body or the lid. Figure 7 shows the stress intensity in the vessel for this case. The highest stresses were around the bolts. All of the stresses were well below the allowable values.

4.1.3 Comparison with Allowable Stresses

The stresses in the containment vessel were evaluated at the locations shown in Figure 5 Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-1. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-2. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-3. As all of the stress components were tensile in this case, the design margin is effectively infinite, hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling. The fatigue evaluation is given in Table 4-4. As the value of the maximum alternating stress in the containment vessel was below the fatigue threshold, the design margin is effectively infinite. Hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for fatigue.



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Table 4-1: Hot Environment: Containment Vessel Stress Summary Stress type Maximum

stress intensity (MPa)

Stress location Allowable stress intensity

(MPa)

Minimum design margin

Pm 14.9 C6b 109 6.30 Pm + Pb 44.7 C1 163 2.65

Pm + Pb + Q 38.3 C3 327 7.54 Bearing 116 Under bolts 121 0.04

Table 4-2: Hot Environment: Bolt Stress Summary Stress type Maximum stress

(MPa) Allowable stress intensity (MPa)


Average shear 2.09 244 115 Average stress 163 406 1.49

Max. stress 175 609 2.47

Table 4-3: Hot Environment: Buckling Evaluation Stress component Stress (MPa) Design Margin

Axial compression 0(1) n/a(2)

Hoop compression 0 In-plane shear 0

1. If the calculated stress from the FEA is tensile then it is assumed to be zero for the buckling calculation. 2. As all the stresses were tensile, the design margin is effectively infinite.

Table 4-4: Hot Environment: Fatigue Evaluation

Maximum alternating stress

(MPa)

Required no. of cycles

Cycles to failure Design margin

44.72 10000 > 1011 n/a(1)

1. As the alternating stress was below the fatigue threshold, the design margin is effectively infinite.

4.2 NCT 2: Cold Environment


In this case, the package is subject to an ambient temperature of -40°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa.


The stresses in the containment vessel were calculated using the finite element model described in section 2.1. Figure 8 shows the deformations in the vessel. There was no significant deformation.



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Figure 9 shows the stress intensity in the vessel for this case. The stresses were low for most of the vessel. The highest stresses were under the bolt heads.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-5. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-6. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-13. The design margin was above zero hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling. The fatigue evaluation is given in Table 4-14. As the value of the maximum alternating stress in the containment vessel was below the fatigue threshold, the design margin is effectively infinite. Hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for fatigue.

Table 4-5: Cold Environment: Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 5.21 C10 115 21.1 Pm + Pb 6.39 C1 173 26.0

Pm + Pb + Q 10.2 C11 345 33.0 Bearing 19.5 Under bolts 173 7.82

Table 4-6: Cold Environment: Bolt Stress Summary Stress type Maximum stress



Average shear 0.80 289 358 Average stress 27.3 482 16.7

Max. stress 46.0 723 14.7

Table 4-7: Cold Environment: Buckling Evaluation Stress component Stress (MPa) Design Margin

Axial compression 0.33 125

Hoop compression 0.68 In-plane shear 0



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Table 4-8: Cold Environment: Fatigue Evaluation Maximum

alternating stress (MPa)



10.16 10000 > 1011 n/a(1)


4.3 NCT 3: Reduced External Pressure


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was a uniform temperature of 158°C. This case assumed that the external pressure was reduced to 24.5 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 775.5 kPa.


The stresses in the containment vessel were calculated using the finite element model described in section 2.1. The displacements for this case are similar to those for case NCT1. Figure 10 shows the stress intensity in the vessel for this case. The regions of high stress are similar to those for case NCT1. This is because the stresses are dominated by the thermal stresses rather than those due to the pressure.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-9. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-10. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-11. As all of the stress components were tensile in this case, the design margin is effectively infinite, hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling. The fatigue evaluation is given in Table 4-12. As the value of the maximum alternating stress in the containment vessel was below the fatigue threshold, the design margin is effectively infinite. Hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for fatigue.



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Table 4-9: Reduced External Pressure: Containment Vessel Stress Summary

Stress type Maximum stress intensity

(MPa)


(MPa)


Pm 16.5 C6b 109 5.60 Pm + Pb 49.5 C1 163 2.30


Table 4-10: Reduced External Pressure: Bolt Stress Summary Stress type Maximum stress




Max. stress 176 609 2.46

Table 4-11: Reduced External Pressure: Buckling Evaluation Stress component Stress (MPa) Design Margin




Table 4-12: Reduced External Pressure: Fatigue Evaluation Maximum




49.54 10000 > 1011 n/a(1)


4.4 NCT 4: Increased External Pressure


In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was increased to 140 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -140 kPa.


The stresses in the containment vessel were calculated using the finite element model described in section 2.1.



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The displacements for this case were similar to those for case NCT2. Figure 11 shows the stress intensity in the vessel for this case. The highest stresses were under the bolt heads.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-13. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-14. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-15. The design margin was above zero hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling. The fatigue evaluation is given in Table 4-16. As the value of the maximum alternating stress in the containment vessel was below the fatigue threshold, the design margin is effectively infinite. Hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for fatigue.

Table 4-13: Increased External Pressure: Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 3.66 C10 115 30.4 Pm + Pb 8.94 C1 173 18.3


Table 4-14: Increased External Pressure: Bolt Stress Summary Stress type Maximum stress




Max. stress 108.3 723 5.68

Table 4-15: Increased External Pressure: Buckling Evaluation Stress component Stress (MPa) Design Margin

Axial compression 0.46 88.6




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Table 4-16: Increased External Pressure: Fatigue Evaluation Maximum




28.4 10000 > 1011 n/a(1)


4.5 NCT 5: Vibration (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was a uniform temperature of 158°C. This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to a downward vertical acceleration of 10g. This was assumed to be the load due to vibration.


The stresses in the containment vessel were calculated using the finite element model described in section 2.1. The displacements for this case were similar to those for case NCT1. Figure 12 shows the stress intensity in the vessel for this case. The regions of high stress are similar to those for case NCT1. This is because the stresses are dominated by the thermal stresses rather than those due to the vibration load.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-17. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-18. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-19. As all of the stress components were tensile in this case, the design margin is effectively infinite, hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.



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Table 4-17: Vibration (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 16.5 C6b 109 5.60 Pm + Pb 49.5 C1 163 2.30


Table 4-18: Vibration (hot): Bolt Stress Summary Stress type Maximum stress




Max. stress 179 609 2.46

Table 4-19: Vibration (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin




4.6 NCT 6: Vibration (cold)


In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to a downward vertical acceleration of 10g. This was assumed to be the load due to vibration.


The stresses in the containment vessel were calculated using the finite element model described in section 2.1. The displacements for this case are very similar to those for case NCT2. Figure 13 shows the stress intensity in the vessel for this case. The regions of high stress are similar to those for case NCT2. This is because the stresses are dominated by the thermal stresses rather than those due to the vibration loads.



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The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-20. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-21. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-22. The design margin was above zero hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 4-20: Vibration (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 99.2 C6b 115 0.16 Pm + Pb 59.5 C1 173 1.90


Table 4-21: Vibration (cold): Bolt Stress Summary Stress type Maximum stress




Max. stress 109 723 5.62

Table 4-22: Vibration (cold): Buckling Evaluation Stress component Stress (MPa) Design Margin



4.7 NCT 7: Free drop on lid (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was a uniform temperature of 158°C. This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa.



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A body force was applied to the model which was equivalent to an upward vertical acceleration of 434g. This was the measured load due to an impact on the lid from a height if 1.2 metres. The cork impact limiter was included in this model.


Figure 14 the deformations in the vessel, scaled a by a factor of 30. Compared with case NCT1, there was slightly more distortion of the lid. This bowing was caused by the impact of the contents with the bottom of the lid. Figure 15 shows the stress intensity in the vessel for this case. The stress distribution is similar to that for case NCT1, but with some additional stress in the lid and the upper part of the body.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-23. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-24. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-25. As all of the stress components were tensile in this case, the design margin is effectively infinite, hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 4-23: Drop on lid from 1.2m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 22.3 C10 109 3.89 Pm + Pb 37.9 C1 163 3.31


Table 4-24: Drop on lid from 1.2m (hot): Bolt Stress Summary Stress type Maximum stress



Average shear 14.3 244 16.0 Average stress 153 406 1.65

Max. stress 174 609 2.50



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Table 4-25: Drop on lid from 1.2m (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin


Hoop compression -4.51 In-plane shear 0

4.8 NCT 8: Free drop on lid (cold)


In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an upward vertical acceleration of 434g. This was the measured load due to an impact on the lid from a height of 1.2 metres. The cork impact limiter was included in this model.

4.8.2 Stress Calculation

The displacements for this case were similar to those for case NCT7. Figure 16 shows the stress intensity in the vessel for this case. The highest stresses were in the lid.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5: Stress evaluation locations. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-26. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 4-27. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-28. The design margin was above zero hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.



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Table 4-26: Drop on lid from 1.2m (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 22.1 C10 115 4.20 Pm + Pb 26.3 C16 173 5.55


Table 4-27: Drop on lid from 1.2m (cold): Bolt Stress Summary Stress type Maximum stress



Average shear 7.39 289 38.1 Average stress 75.0 482 5.43

Max. stress 116 723 5.23

Table 4-28: Drop on lid from 1.2m (cold): Buckling Evaluation Stress component Stress (MPa) Design Margin



4.9 NCT 9: Free drop on corner (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was at a uniform temperature of 158°C. This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to an acceleration of 376g axially and 590g radially, giving a resultant acceleration of 700g. This was the measured load due to an impact on the top corner from a height of 1.2 metres. The cork impact limiter was included in this model.


Figure 17 shows the displacements for this case. The inner part of the body has rotated clockwise slightly. However, it does not come in to contact with the DU shielding. Figure 18 shows the stress intensity in the vessel. The upper limit on the contour plot is the allowable value for the membrane stress, which was exceeded in several locations. The high stresses in the outer part of the body are not of concern as this is not part of the pressure containment boundary and is not assessed against the allowable stresses.



27/09/2012 Page 30 of 95


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-29. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 5, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The highlighted values show where the stresses exceeded the allowable stress. The stresses in the bolts are summarised in Table 4-30. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-31. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 4-29: Drop on corner from 1.2m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm

235 C4-180 109

-0.54 196 C6b-180 -0.44 179 C7-180 -0.39 141 C8-180 -0.23 152 C9-180 -0.29

Pm + Pb 52.1 C14-180 163 2.14 Pm + Pb + Q 396 C6b 327

-0.17

363 C7 -0.10 609 C7-180 -0.46 384 C9-180 -0.15

Bearing 121 Under bolts 121 0.0

Table 4-30: Drop on corner from 1.2m (hot): Bolt Stress Summary Stress type Maximum stress




Max. stress 184 609 2.31

Table 4-31: Drop on side from 1.2m (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin

Axial compression 0 2365

Hoop compression 0 In-plane shear 0.74

1. If the calculated stress from the FEA is tensile then it is assumed to be zero for the buckling calculation.



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4.10 NCT 10: Free drop on corner (cold)

In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an acceleration of 376g axially and 590g radially, giving a resultant acceleration of 700g. This was assumed to be the load due to an impact on the side from a height of 1.2 metres. The cork impact limiter was included in this model.


Figure 19 shows the displacements for this case, magnified by a factor of 5. The inner part of the body and the contents have rotated clockwise slightly. Figure 20 shows the stress intensity for this case. The upper limit on the contour plot is the allowable value for the membrane stress, which was exceeded in several locations.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-32. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 5, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The highlighted values show where the stresses exceeded the allowable stress. The stresses in the bolts are summarised in Table 4-33. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 4-34. The design margin was above zero hence the containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.



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Table 4-32: Drop on corner 1.2m (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 116 C6a 115 -0.1 258 C6b -0.56 161 C7 -0.29 129 C9 -0.11 401 C6b-180 -0.71 346 C7-180 -0.67 242 C8-180 -0.53 287 C9-180 -0.60 180 C11-180 -0.36

Pm + Pb 89 C15-180 173 0.93 Pm + Pb + Q 827 C6b 345 -0.58

842 C7 -0.59 459 C8 -0.25 431 C9 -0.20

1022 C6b-180 -0.66 1213 C7-180 -0.72 919 C8-180 -0.62 793 C9-180 -0.57 757 C10-180 -0.54 393 C11-180 -0.12

Bearing 96.7 Under bolts 172 0.78

Table 4-33: Drop on corner from 1.2m (cold): Bolt Stress Summary Stress type Maximum stress




Max. stress 192 723 2.76

Table 4-34: Drop on side from 1.2m (cold): Buckling Evaluation Stress component Stress (MPa) Design Margin



4.11 NCT 11: Free drop on side (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was at a uniform temperature of 158°C.



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This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to an acceleration of 294g. This was the measured load due to an impact on the side from a height of 1.2 metres. The cork impact limiter was included in this model.


Figure 21 shows the stress intensity for this case. The upper limit on the contour plot is the allowable value for the membrane stress, which was exceeded in several locations. The high stresses on the outer part of the body are not of any concern as they do not form part of the containment boundary. The inner part of the body rotates clockwise causing high stresses at the top of this part.



Table 4-35: Drop on side from 1.2m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 113 C6b 109 -0.03 184 C4-180 -0.41 145 C6b-180 -0.25 115 C7-180 -0.05

Pm + Pb 64.0 C1 163 1.55 Pm + Pb + Q 420 C6b 327 -0.22

394 C7 -0.17 467 C7-180 -0.30

Bearing 133 Under bolts 121 -0.09



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Table 4-36: Drop on side from 1.2m (hot): Bolt Stress Summary Stress type Maximum stress




Max. stress 222 609 1.74

Table 4-37: Drop on corner from 1.2m (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin




4.12 NCT 12: Free drop on side (cold)


In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an acceleration of 294g. This was the measured load due to an impact on the side from a height of 1.2 metres. The cork impact limiter was included in this model.


Figure 22 shows the stress intensity for this case. The upper limit on the contour plot is the allowable value for the membrane stress, which was exceeded in several locations.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 4-38. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 5, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The highlighted values show where the stresses exceeded the allowable stress. The stresses in the bolts are summarised in Table 4-39. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero.



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Table 4-38: Drop on side 1.2m (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 160 C6b-180 115 -0.28 Pm + Pb 35.8 C2-180 173 3.81

Pm + Pb + Q 355 C6b-180 345 -0.03 380.7 C7-180 -0.09

Bearing 109 Under bolts 172 0.61

Table 4-39: Drop on side from 1.2m (cold): Bolt Stress Summary Stress type Maximum stress




Max. stress 203 723 2.51

Table 4-40: Drop on corner from 1.2m (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin






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5.0 Hypothetical Accident Conditions

This section presents the structural evaluation of the package in accordance with Reg. Guides 7.6 and 7.8 [9, 8] when subject to the HAC tests specified in Reg. Guide 7.8. The package is evaluated for each HAC test individually based on the most unfavourable initial conditions.

5.1 HAC 1: Free drop on lid (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was at a uniform temperature of 192°C. This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to an upward vertical acceleration of 458g. This was the measured load due to an impact on the lid from a height of 10.2 metres. The cork impact limiter was included in this model.


Figure 23 shows the stress intensity in the vessel for this case. The upper limit on the contour plot is the allowable value for the membrane stress


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 5-1. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 5-2. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 5-3. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 5-1: Drop on lid from 9m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 26.1 C10 245 9.03 Pm + Pb 60.6 C10 367 5.47



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Table 5-2: Drop on lid from 9m (hot): Bolt Stress Summary

Stress type Maximum stress (MPa)

Allowable stress intensity (MPa)



Table 5-3: Drop on lid from 9m (hot): Buckling Evaluation

Stress component Stress (MPa) Design Margin Axial compression 0.88 100 Hoop compression 0 (1) In-plane shear 0.01


5.2 HAC 2: Free drop on lid (cold)


In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an upward vertical acceleration of 458g. This was the measured load due to an impact on the lid from a height of 10.2 metres. The cork impact limiter was included in this model.


Figure 24 shows the stress intensity for this case.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 5-4. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 5-5. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 5-6. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.



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Table 5-4: Drop on lid from 9m (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 25.5 C10 331 9.82 Pm + Pb 53.3 C11 497 6.76

Table 5-5: Drop on lid from 9m (cold): Bolt Stress Summary Stress type Maximum stress




Table 5-6: Drop on lid from 9m (cold): Buckling Evaluation

Stress component Stress (MPa) Design Margin Axial compression 3.52 35

Hoop compression 0.66 In-plane shear 0.0

5.3 HAC 3: Free drop on top corner (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was at a uniform temperature of 192°C. This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to an acceleration of 338g axially and 228g radially, which gives a resultant acceleration of 408g. This was the measured load due to an impact on the top corner from a height of 10.2 metres. The cork impact limiter was included in this model.


Figure 25 shows the stresses for this case. The stress distribution is similar to that for case NCT9, but with a greater magnitude.


The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4.



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A summary of the evaluation is given in Table 5-7. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 5, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The highlighted values show where the stresses exceeded the allowable stress. The stresses in the bolts are summarised in Table 5-8. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 5-9. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 5-7: Drop on top corner from 9m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 175 C4-180 245 0.50 Pm + Pb 444 C17-180 367 -0.12

Table 5-8: Drop on top corner from 9m (hot): Bolt Stress Summary Stress type Maximum stress




Table 5-9: Drop on top corner from 9m (hot): Buckling Evaluation

Stress component Stress (MPa) Design Margin Axial compression 0 (1) 6242

Hoop compression 0 (1) In-plane shear 0.68


5.4 HAC 4: Free drop on corner (cold)

In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an acceleration of 338g axially and 228g radially, which gives a resultant acceleration of 408g. This was the measured load due to an impact on the top corner from a height of 10.2 metres. The cork impact limiter was included in this model.



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The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 5-10. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 5, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 5-11. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 5-12. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling. Table 5-10: Drop on top corner from 9m (cold): Containment Vessel Stress Summary

Stress type Maximum stress intensity

(MPa)


(MPa)


Pm 174 C6b-180 276 0.59 Pm + Pb 376 C6b 414 0.10

Table 5-11: Drop on top corner from 9m (cold): Bolt Stress Summary Stress type Maximum stress




Table 5-12: Drop on top corner from 9m (cold): Buckling Evaluation

Stress component Stress (MPa) Design Margin Axial compression 0 (1) 1.65x104

Hoop compression 0 (1) In-plane shear 0.60


5.5 HAC 5: Free drop on side (hot)


In this case, the package is subject to an ambient temperature of 38°C in still air, with solar heating and with maximum decay heat. A thermal analysis has shown that a bounding condition for the containment vessel was at a uniform temperature of 192°C.



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This case assumed that the external pressure was 100 kPa. The internal pressure was 800 kPa absolute, so the internal gauge pressure applied to the model was 700 kPa. A body force was applied to the model which was equivalent to an acceleration of 458g. This was the measured load due to an impact on the side from a height of 10.2 metres. The cork impact limiter was included in this model.


Figure 27 shows the stresses for this case.



Table 5-13: Drop on side from 9m (hot): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 256 C4-180 245 0.02 Pm + Pb 457 C6b 367 -0.14

Table 5-14: Drop on side from 9m (hot): Bolt Stress Summary Stress type Maximum stress






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Table 5-15: Drop on side from 9m (hot): Buckling Evaluation Stress component Stress (MPa) Design Margin

Axial compression 0 (1) 5131



5.6 HAC 6: Free drop on side (cold)

In this case, the package is subject to an ambient temperature of -29°C in still air, zero solar heating and with zero decay heat. This case assumed that the external pressure was 100 kPa. The internal pressure was 0 kPa absolute, so the internal gauge pressure applied to the model was -100 kPa. A body force was applied to the model which was equivalent to an acceleration of 458g. This was the measured load due to an impact on the side from a height of 10.2 metres. The cork impact limiter was included in this model.




The stresses in the containment vessel were evaluated at the locations shown in Figure 5. Stress linearization at these locations was carried out using a post-processing option in Abaqus. The stresses were then compared with the allowable stresses given in Table 2-4. A summary of the evaluation is given in Table 5-16. Locations with a name ending “-180” are on the opposite side of the vessel to those shown in Figure 6, i.e. they are on the side of the vessel closest to the impact with the cork impact limiter. The containment vessel satisfies the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The stresses in the bolts are summarised in Table 5-17. The bolts satisfy the requirements of Reg. Guide 7.6 as all of the design margins were above zero. The buckling evaluation is summarised in Table 5-18. The containment vessel satisfies the requirements of Reg. Guide 7.6 for buckling.

Table 5-16: Drop on side from 9m (cold): Containment Vessel Stress Summary Stress type Maximum



(MPa)


Pm 189 C6b-180 276 0.46 Pm + Pb 394 C6b 414 0.05



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Table 5-17: Drop on side from 9m (cold): Bolt Stress Summary Stress type Maximum stress




Table 5-18: Drop on side from 9m (cold): Buckling Evaluation

Stress component Stress (MPa) Design Margin Axial compression 0 (1) 1.65x104



6.0 Lid Closure Forces

The force required to maintain compression of the O-rings is 9906 N (source: Croft). The total lid closure force (total axial force on all of the bolts) at the end of each analysis is given in Table 6-1. Therefore there is sufficient force in all cases to maintain compression in the O-rings and maintain the containment boundary. The friction coefficient on the bolts can vary by ±20% from value given in the calculation in Appendix B. This gives lower and upper bound values for the bolt tension of 6.99 kN and 9.68 kN respectively. In NUREG/CR-6007, the mean value of K for bolts lubricated with moly grease is 0.137. This gives a bolt tension of 7.30 kN. Using the upper and lower bound values of K (0.16 and 0.10), gives bolt tensions of 6.25 kN and 10.0 kN. These values are similar to those calculated using the method in Appendix D. The lower bound value of 6.25 kN is 23% less than the value used in the analysis. If all the forces reported in 2-7 were reduced by 23%, there would still be sufficient force to maintain O-ring compression.



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Table 6-1: Total lid closure force Case Total Lid

Closure Force (kN)

NCT1 102 NCT2 17 NCT3 102 NCT4 53 NCT5 102 NCT6 53 NCT7 92 NCT8 44 NCT9 97

NCT10 68 NCT11 106 NCT12 58.6 HAC1 105 HAC2 43.4 HAC3 113 HAC4 48 HAC5 121 HAC6 67



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7.0 Conclusions

The Safkeg HS containment vessel has been evaluated using finite element analysis for 12 Normal Conditions of Transport and 6 Hypothetical Accident Conditions. Assessments of the stresses were made against Regulatory Guide 7.6. The analyses have shown that the stresses in the containment vessel exceed the allowable values in US NRC Regulatory Guide 7.6 for a number of the load cases, specifically cases NCT9, NCT10, NCT11 and NCT12 as well as HAC3 and HAC5. For all load cases assessed, buckling and fatigue loads are below the acceptable limits.



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8.0 References

1. “Containment Vessel HS Body Construction”, Drg. No. 1C-5999 Issue A-P4, Croft Associates Ltd, 2009.

2. “Containment Vessel HS Lid Construction”, Drg. No. 1C-5997 Issue A-P2, Croft Associates Ltd, 2008.

3. “Safkeg HS Construction”, Drg. No. 0C-5949 Issue A-P1, Croft Associates Ltd, 2007.

4. GD Jones, “Stress Analysis of Safkeg HS Containment Vessel”, Report No. ESR/D1000586/001 Issue 1, ESR Technology Ltd, May 2008.

5. “Abaqus/Standard v6.10 User’s Manual”, Dassault Systèmes, 2010.

6. “Abaqus/CAE v6.10 User’s Manual”, Dassault Systèmes, 2010.

7. “Methods for Impact Analysis of Shipping Containers”, NUREG/CR-3966, U.S. Nuclear Regulatory Commission, November 1987.

8. “Regulatory Guide 7.8, Load Combinations for the Structural Analysis of Shipping Casks for Radioactive Material”, Revision 1, U.S. Nuclear Regulatory Commission, March 1989.

9. “Regulatory Guide 7.6, Design Criteria for the Structural Analysis of Shipping Casks for Radioactive Material”, Revision 1, U.S. Nuclear Regulatory Commission, March 1978.

10. “American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code”, 2007.

11. Penton Publications, Materials Engineering Materials Selector 1990, December 1989.

12. Weakly, EA, Fuels Engineering Technical Handbook, UNI-M-61, April 1979.

13. Brandes, E.A., Brook, G.B (eds.), “Smithells Metals Reference Book”, seventh edition, 1992.

SC

RR

Stress AnalysisContainment Ve

Report No: L20008/1/RRevision: 0

s of Safkeg HS essel

R1

DUsh

Lid

Body

U hielding

Figure 11: Finite elemennt model

Co

DUshi

ontents

U ielding

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RR




R1

Figuree 2: Finite elemment model withh cork impact limiters

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R1

Figure 3:: Drawing of HSS Containment Vessel Lid Connstruction

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R1

Figure 4: Drawwing of Safkeg HS Keg Constrruction

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R1

Figure 5: S

C2-

Stress evaluatio

C1 C2 -180 C

C6

C16

C17

on locations

C3

C4

C5

6

C7

C8

C9

C10 C11

C13

C14

C15

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R1

Figurre 6: NCT1 Hot Environment: Displacementss (x20)

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Figgure 7: NCT1 Hot Environmennt: Stress intenssity

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Figuree 8: NCT2 Cold

d Environment: Displacementss (x20)

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Figgure 9: NCT2 Coold Environmennt: Stress intennsity

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R1

Figure 100: NCT3 Increassed External Prressure: Stresss intensity

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Figure 11: NCT4 Reducced External Pressure: Stress Intensity

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Fiigure 12: NCT5 Vibration (hot)): Stress intenssity

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Figgure 13: NCT6 VVibration (cold): Stress intenssity

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Figurre 14: NCT7 Droop on lid (hot): Displacementss (x30)

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Figgure 15: NCT7 DDrop on lid (hott): Stress intensity

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Figure 16: NCT8 DDrop on lid (coldd): Stress intennsity

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Figure 177: NCT9 Drop oon top corner (hhot): Displacemments (x2)

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Figure 18: NCT9 Dropp on top corner (hot): Stress inntensity

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Figure 19: NCT10 Drop oon top corner (ccold): Displacements (x5)

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Figure 220: NCT10 Dropp on top cornerr (cold): Stress intensity

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Figuure 21: NCT11 DDrop on side (hot): Stress inteensity

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Figurre 22: NCT12 DDrop on side (coold): Stress inteensity

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Figgure 23: HAC1 DDrop on lid (hot): Stress intensity

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Figuure 24: HAC2 DDrop on lid (cold): Stress intennsity

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Figure 25: HAC3 Dropp on top cornerr (hot): Stress inntensity

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Figure 226: HAC4 Drop on top corner (cold): Stress iintensity

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Figuure 27: HAC5 DDrop on side (hoot): Stress intennsity

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Figuure 28: HAC6 Drrop on side (coold): Stress inteensity

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Stress AnSafkeg HSVessel

Report No: L20Revision: 0

nalysis of S Containm

0008/1/R1

ment

Mesh Appe

Sensi

endix itivity

A Analy

2Pag

ysis

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A-1 Introduction A mesh sensitivity study has been carried out on a containment vessel similar, but not identical to the Safkeg HS containment vessel. The region circled in Figure A1, at the join between the body and the top flange, was the part of the model where the mesh was refined. The number of elements through the thickness of the body was increased from 4, as used in the original study, to 6, 8, 10, 12, 14 and 16. In all cases, the number of elements along the length of this section was adjusted so that the aspect ratio of the elements (length of one side of an element to the other side of the element) was maintained. All of these cases used first-order elements, as used in the original study. Two additional cases used second-order elements. Both of these cases used 16 elements through the wall thickness, but one used 4 elements around the fillet radius, as used in all the other cases, and one used 8 elements around the radius. The results using second order elements are considered to be closest to the actual stresses, however for reasons of computation power and model size, it is not always possible to use these elements because the contact algorithms, which were required in the main study, are not efficient with second order elements, hence the need, as in this case, for the use of fewer, single-order elements.

A-2 Results Figure A2 shows the stress profile, from the inside to the outside, at the junction between the body and top flange for all the cases. The stress shown is Tresca, which is the same as the stress intensity as required by NRC Regulatory Guide 7.6. The model with 4 elements through the thickness produces a profile which, whilst a fair representation of the actual stress profile, does under predict the peak stresses; however, the results are sufficient to give a good approximation to the deformations of the container. The accuracy of prediction of the peak stresses improves with a greater number of elements through the thickness, as might be expected. As stated above, the results using second order elements should give an accurate profile. The case with 8 elements around the radius had a slightly smaller peak stress and the case with 4 elements around the radius. For the assessment of the containment vessel, membrane, bending and peak stresses were calculated and compared with allowable values. The membrane, bending and peak stresses for this study are given in Table A1 and figures C3-C5. The variation in membrane stress was only 6%, the variation in bending stress was 14% and the variation in peak stress was 92%. If we take the final case, second order elements and mesh refinement around the radius, as being closest to the correct answer, the difference between this and the first case with 8 elements (as used in the main study of the Safkeg HS) was -3%, 2% and 31% for the membrane, bending and peak stress respectively. For the HAC cases, the peak stress is not assessed. For the NCT cases, the peak stress result is more important as it affects the fatigue life. The influence of peak stress vs profile is not straightforward, due to the restraining influence of the lower stressed material within the bulk of the section.



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Table A1: Stress linearization

Mesh

Membrane stress (MPa)

Bending stress (MPa)

Peak stress (MPa)

4 elements 7.4 16.5 17.0 6 elements 7.3 17.0 19.0 8 elements 7.3 17.9 22.0 10 elements 7.3 17.9 23.0 12 elements 7.3 18.1 23.8 14 elements 7.4 18.6 25.5 16 elements 7.5 18.8 27.4 16 elements, 2nd order 7.1 18.4 32.7 16 elements, 2nd order, 8 elements around radius 7.1 18.3 31.7

A-3 Conclusions

1. The mesh used in the original study was adequate for the HAC cases as it produced reasonable estimates of the membrane and bending stresses.

2. The mesh used in the original study was less able to accurately capture peak stresses. A very refined mesh, using second-order elements is required to accurately capture the peak stresses at some locations. However, for reasons of model size and computational capacity, it is not generally practical to use this level of refinement in the main study.

StreHS

RepoRevis

Figu

ess AnalysContainme

ort No: L20008/1sion: 0

ure A1: Fin

sis of Safkeent Vessel

1/R1

nite elemen

eg

nt mesh

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RepoRevis

Figu

ess AnalysContainme


ure A2: Str


1/R1

ress profile

eg

e through wwall

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Figure A3: Membrane stress

Figure A4: Bending stress

Mesh sensitivity - membrane stress

0

1

2

3

4

5

6

7

8

4 elements 6 elements 8 elements 10 elements 12 elements 14 elements 16 elements 16 elements,2nd order

16 elements,2nd order, 8

elements aroundradius

Mesh

Mem

bra

ne

stre

ss (

MP

a)

Mesh sensitiviy - bending stress

0

2

4

6

8

10

12

14

16

18

20



elementsaround radius

Mesh

Ben

din

g s

tres

s (M

Pa)



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Figure A5: Outside peak stress

Mesh sensitivity - peak stress

0

5

10

15

20

25

30

35



elementsaround radius

Mesh

Mis

es s

tres

s

StreHS

RepoRevis

ess AnalysContainme



1/R1

B

eg

Aolt Pre

Appeneload

dix BCalcuulation

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CALCULATION SHEET

Project TitleProject NumberCalculation TitleCalculation RefIssue

Stress analysis of Safkeg Flasks925-327Bolt pre-loadC12

Calc by GD Jones Date 18/08/10

Checked by Date

Appd by Date

BOLT TENSIONIntroduction

This calculation determines the tension in a bolt for a given torque tightening.

Bolt Tensile Load

Bolt nominal diameter d 10 mm

Thread pitch P 1.5 mm

Friction Coefficientbetween screwthreads

s 0.11

w 0.11Friction coefficientbetween bearing surfaces

(From Machinery's p1432, Table 1, value for steel bolts with molybdenum sulphide grease.Assume same value for both friction coefficients)

Nut spot face diameter Sd 8 mm

Applied torque T 10 N m

Effective spot facediameter

Dwd Sd

2

Flank angle atanP

2 d



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Pitch diameter of thread d2 d 0.65 P

Torque coefficient(eq. 13 on p1436)

K1

2 dP

s d2 sec ( ) w Dw

Bolt tension WT

K d W 8.120 kN

Reference

1. "Machinery's Handbook 28th Edition ", Industrial Press Inc. 2008.

StreHS

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ess AnalysContainme



1/R1

eg

ABuckl

Appenling C

dix Calculaation

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CALCULATION SHEET

Project TitleProject NumberCalculation TitleCalculation RefIssue

Stress Analysis of Safkeg HS Containment VesselL20008/1Buckling calculation for case NCT2NCT2-C1A

Calc by GD Jones Date 07/08/11

Checked by Date

Introduction This calculation evaulates the buckling resistance of a cylindrical shell using the procedures givenASME Boiler and Pressurve Vessel Code 2007: Code Case N-284-2

Material Properties

Assessment temperature T 40 °C

Young's modulus E 198 GPa

Yield stress σy 172 MPa

Geomerty

Shell mean radius R 35.25 mm

Shell thickness t 4.7 mm

Distance between lines of support in meridional direction

lϕ 152.4 mm

Cross-sectional area of meridional stiffeners

Aϕ 0 m2

lθ 2 π RDistance between lines of support in circumferentialdirection

Cross-section area of circumferential stiffeners

Aθ 0 m2

StreHS

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ess AnalysContainme



1/R1

eg

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Capacity Reduction FactorsCylindrical shell

(a) Axial compression

L ftR

t

M

l

R t

L 00.207 ft 600if

a1 1.52 0.473 logR

t

a2300 y

E0.033

L 0min a1 a2

ft 600if

L 10.627 M 0.5if

L 10.837 0.14 M M 1.5 M 1.73if

L 1

0.826

M0.6

M 1.73 M 10if

L 10.207 M 10if

max L return

L 0.2

(b) Hoop compression

L 0.8

(c) Shear

L ftR

t

L 0.8 ft 250if

.L 1.323 0.218 log ft otherwise

Lreturn

L 0.8



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Local Buckling

Cylindrical shells - unstiffened

Theoretical elastic instability stresses


eL M

l

R t

C 0.630 M 1.5if

C0.904

M2

0.1013 M2 M 1.5 M 1.73if

C 0.605 M 1.73if

C E t

R

eL 15972 MPa

(b) External pressure

(1) No end pressure (K=0)

reL M

l

R t

Cr 1.161 M 1.5if

Cr2.41

M1.49

0.338 M 1.5 M 3.0if

Cr0.92

M 1.17 M 3.0 M 1.65

R

tif

Cr 0.275t

R

2.1

M4

R

t

3

M 1.65R

tif

Cr E t

R

reL 2339 MPa



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(2) End pressure included (K=0.5)

heL M

l

R t

Cr 0.988 M 1.5if

Cr1.08

M1.07

0.45 M 1.5 M 3.5if

Cr0.92

M 0.636 M 3.5 M 1.65

R

tif

Cr 0.275t

R

2.1

M4

R

t

3

M 1.65R

tif

Cr E t

R

heL 2225 MPa

(c) Shear

eL M

l

R t

C 2.227 M 1.5if

C4.82

M2

1 0.0239 M3 0.5

M 1.5 M 26if

C0.746

M

M 26 8.69R

tif

C 0.253t

R

0.5

M 8.69R

tif

C E t

R

eL 5866 MPa



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Plasticity Reduction Factors


L eL

y

1.0 0.55if

0.45

0.18

0.55 1.6if

1.31

1 1.15 1.6 6.25if

1

6.25if

0.0

(b) Hoop compression

eL max reL heL

L eL

y

1.0 0.67if

2.53

1 2.29 0.67 4.2if

1

4.2if

0.1

(c) Shear

L eL

y

1.0 0.48if

0.43

0.48 1.7if

0.6

1.7if

0.0



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Allowable stresses

Elastic Buckling

Axial compression alone xaL eL

FS xa 1818 MPa

Hydrostatic external pressure haL heL

FS ha 890 MPa

Radial external pressure raL reL

FS ra 936 MPa

In-plane shear alone aL eL

FS a 2346 MPa

Inelastic Buckling

Axial compression alone xc xa xc 86.0 MPa

Radial external pressure rc ra rc 86.0 MPa

In-plane shear alone c a c 51.6 MPa



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Assessment

Elastic buckling of cylindrical shell

design_margine K

t

t

DM ha

1 haif

DM

ra 2 ra

ha1

1

1 otherwise

DMreturn

0 K 0.5if

DM

0.5 hat

t

1 0.5 hat

tif

DM

0.5 hat

t

xa 0.5 hat

t

2

1

1 otherwise

DMreturn

0 K 0.5if

DM

xa

a

2

1

1

DMreturn

0if

DM

ra

a

2

1

1

DMreturn

0if

Ks 1

ra

2

DM ha

1 haif

DM

Ks ra 2 Ks ra

Ks ha1

1

1 otherwise

DMreturn

K 0.5if

DM

0.5 Ks hat

t

1 0.5 Ks hat

tif

DM

0.5 Ks hat

t

Ks xa 0.5 Ks hat

t

2

1

1 otherwise

DMreturn

K 0.5if

design_margine 1307.74



13/09/2011 Page 95 of 95

Inelastic buckling of cylindrical shell

design_marginc

DM1 xc

1

DM2 rc

1

DM min DM1 DM2( )

DMreturn

0if

DM1

xc

c

2

1

1

DM2

rc

c

2

1

1

DM min DM1 DM2( )

DMreturn

otherwise

design_marginc 125.47

Conclusion

Take the minimum of elastic and inelastic design margins

design_margin min design_margine design_marginc

design_margin 125.47

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