ML22271A808
| ML22271A808 | |
| Person / Time | |
|---|---|
| Site: | Orano USA |
| Issue date: | 08/03/2022 |
| From: | Boyle R, Shaw D TN International |
| To: | Division of Fuel Management |
| Garcia-Santos N | |
| Shared Package | |
| ML22271A128 | List:
|
| References | |
| A33010, L-2022-DOT-0007 | |
| Download: ML22271A808 (44) | |
Text
AREVA TN AREVA UNRESTRICTED DISTRIBUTION NUCLEAR LOGISTICS OPERATIONS APPENDIX 2.1-12 A SAFETY FCC PACKAGING ROD BOXES - PROOF OF THE AREVA Form: PM04-4-MO-6 Rev. 00 ANALYSIS MECHANICAL STRENGTH OF BOX EQUIPMENT.
REPORT Prepared by Identification FCC3 - FCC4 DOS-13-00081778-112-NPV Rev. 01 Page 1 / 44 TN International Table of Contents Revisions history 2
- 1. Purpose 3
- 2. Basic Data 3
- 3. Criteria to be respected 9
- 4. Analytical calculations 9
- 5. 3D finite element numerical calculations 15
- 6. Conclusions 21
- 7. References 21 List of figures 22 List of appendices 43 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 2 of 44 Revisions history Rev. Date Purpose and record of changes Prepared by / Checked by 00 04/2012 First issue Rewrite of the document from the former reference AREVA NP FFDC 01074 Revision C See first 01 Integration of the proof of the mechanical strength of the axial and radial spacers in the page EPRTM rod box Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 3 of 44
- 1. Purpose The purpose of this document is to study the mechanical behaviour of spacers in the rod boxes transported in FCC packagings under accident drop conditions.
The study focuses on:
the radial spacers filling the radial space between the rod bundle and the minimum section of the cavity (),
The support plates between the radial spacer and the rod bundle, the compensation spacers filling the space between the radial spacers and the minimum section of the cavity, the axial spacers filling the longitudinal space between the rod bundle and the box length if the fuel rods are shorter than this length.
the end support plates for the fuel rods on the axial spacer side.
The aim is to demonstrate that their geometrical properties are not affected by stresses on the packaging due to accidents.
The assembly drawings and part drawings are available in appendix 1.3-2.
- 2. Basic Data 2.1. Geometrical data The dimensions of the parts to be justified are shown in the drawings in appendix 1.3-2.
2.2. Materials Steel parts are manufactured in type stainless steel.
For demonstrations based on analytical calculations, the conservative assumption used for the mechanical properties of type stainless steel at 100°C is considered in accordance with chapter 1.3-1. These properties are as follows:
Symbol Value Unit Young's modulus E MPa Yield strength Rp0.2 MPa Tensile strength Rm min MPa Allowable stress Sm MPa Criterion
- MPa Min (2.4.Sm; 0.7 Rm)
For demonstrations based on 3D numerical calculations, the assumption used for the mechanical properties of type stainless steel at 100°C is considered (see table in section 5.3). The assumptions adopted are conservative as, according to appendix 2.2-1, the maximum temperature of packaging components in normal conditions of transport is °C.
Aluminium parts are produced in grade aluminium alloy as per chapter 1.3-1. The yield strength Re at 150°C is equal to MPa as per <3>.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 4 of 44 2.3. Load 2.3.1. Radial load Radial spacers (see drawing 47-0-01-99-01-09 in appendix 1.3-2)
The load adopted corresponds to a vertical load distributed over the surface of the lower plate of the radial spacer. In accident conditions, the load is defined based on the application of an acceleration of g to the mass of all of the rods and the support plates. The value of g corresponds to the maximum value observed over a duration of 3 ms during the 9 m flat drop test with whiplash action (according to appendix 2.1-10). Considering a permanent static load of g is therefore conservative.
The table below shows the pressure values for each configuration. In the worst-case configuration (222 rods, 14 x 14 - 8 ft, in a FCC4 packaging), the pressure p on the bearing surface of the spacer is the highest value and equal to 12.0 MPa.
10 222
-2 10 12,0 FCC4.
17x17. 17x17. 16x16. 18x18. 17x17. 15x15. 14x14. 14x14.
14 ft 14-foot 14-foot 14-foot 12 ft 12 ft 10 ft 8 ft EPRTM Maximum number of transportable rods (as per 185 185 148 205 185 148 167 222 chapter 1.3)
Rod mass at maximum tolerances (kg) (as per chapter 1.3)
Radial pressure (MPa) 7.8 8.0 7.5 8.1 7.9 8.0 9.0 12.0 FCC3.
17x17. 15x15. 14x14. 14x14.
12 ft 12 ft 10 ft 8 ft Maximum number of transportable rods (as per 185 148 167 204 chapter 1.3)
Rod mass at maximum tolerances (kg) (as per chapter 1.3)
Radial pressure (MPa) 7.9 8.0 9.0 11.1 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 5 of 44 Support plate (see drawing 47-0-01-99-01-06 in appendix 1.3-2)
The load adopted corresponds to a vertical load distributed over the surface of the support plate. In accident conditions, the load is defined based on the application of an acceleration of g to the mass of all of the fuel rods.
In the worst-case configuration (222 rods, 14 x 14 - 8 ft), the pressure p on the bearing surface of the plate is the highest value and equal to 9.4 MPa.
10 222 10 9,4 2.3.2. Axial load Axial spacer (see drawings 47-0-01-99-01 non-EPRTM / PLA-16-00179264-201 - specific to EPRTM in appendix 1.3-2)
The load adopted corresponds to a distributed load applied to the end plate of the axial spacer (shown on the following figure - item 2). In accident conditions, all of the rods and the box equipment apply a force proportional to the mass of the rod bundle (acceleration considered as based on the results of the drop tests for prototype 1 included in appendix 2.1-9) to the axial spacer. The forces applied by the following elements are added to the rod bundle load:
support plates (figure shown below - item 5),
the radial spacers with their compensation spacers (figure shown below - items 8 and 13),
the fixed end support plates for the rods on the axial spacers side (figure shown below -
item 16).
the axial spacer opposite the spacer considered.
FCC4 packaging - 17x17 and 15x15, 12 ft rods Several configurations exist (number of compensation spacers, length of the axial spacers, etc.) depending on the types of rods loaded. All of the configurations for an FCC4 packaging are defined in appendix 1.3-1.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 6 of 44 For the analytical calculations, the worst-case configuration is selected for the axial spacer based on the following criteria.
The table below shows the loads calculated for each configuration. The worst-case configuration is the load of 148 rods, 15x15 - 12 ft, in an FCC4 packaging. The phases of calculations incorporating the conservative assumptions adopted in the following table are detailed for the worst-case scenario, to give an example.
For a load in an FCC4 packaging, with the maximum number of 148 rods from 15x15, 12 ft arrays, justification of the number N of mm thick compensation spacers is as follows:
. / 2 The value of N =16 compensation spacers is selected to guarantee that the cavity height of mm is not exceeded.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 7 of 44 The force on the bearing surface of the spacer opposite the bundle is equal to 2,161, N.
1111 10 148 10 2 161 680 Data used to calculate the maximum force:
Maximum number of transportable rods in an FCC4 configuration, with 15 x 15 - 12 ft: 148 (as per appendix 1.3-1),
Maximum weight of a 15x15 rod: kg (as per appendix 1.3-1),
4 support plates with a length of mm (unit mass: kg),
2 compensation spacers with a length of mm and a thickness of mm (unit mass:
kg),
N = compensation spacers with a length of mm and a thickness of mm (unit mass: kg),
2 radial spacers with a length of mm (unit mass: kg),
2 rod end plates on the axial spacer side (unit mass: kg),
1 axial spacer with a length of mm (unit mass: kg).
The table below shows the axial spacer load for each configuration:
Configuration Packaging Load 14x14 - 8 ft 1,821,540 N FCC3.
14x14 - 10 ft 1,932,750 N 14x14 - 8 ft 2,012,220 N 14x14 - 10 ft 2,031,150 N 15x15 foot FCC4. 2,161,680 N 17x17 foot 2,136,150 N 17x17 - 14 ft, EPRTM 2,291,100 N For all axial spacers, with the exception of EPRTM spacers, the worst-case load corresponds to the 15x15 - 12 ft configuration in an FCC4 packaging. This worst-case scenario is assessed using a 3D digital model for an axial drop of the axial spacer and the fixed end plate. This evaluation is described in section 5.
For the EPRTM axial spacer, which is based on a specific concept, a detailed 3D digital model of the axial spacer and the fixed end plate is used to assess its mechanical strength in the event of an axial drop in the 17x17 - 14 ft EPRTM configuration in an FCC4 packaging. This evaluation is described in section 5.
Fixed end support plate for the rods on the axial spacer side (see drawings 47-0-01-99 16- non-EPRTM / PLA-16-00179264-202 - specific to EPRTM in appendix 1.3-2)
The load adopted corresponds to a distributed load applied to the fixed end support plate. In accident conditions, all of the rods apply a pressure proportional to the mass of the rod bundle (with acceleration considered as g) to the axial spacer.
The table below shows the load values calculated for each configuration. The two worst-case scenarios are as follows:
the load of 148 rods, in a 15x15 - 12 ft configuration, in an FCC4 packaging. The pressure on the bearing surface of the spacer opposite the bundle is equal to 91. MPa. In this configuration, the height of the rod bundle is mm (for a rod diameter of 10.75 mm).
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 8 of 44 number of rods mass per rod 10 148 10 91,2 The load of 185 rods, in a 17x17 - 14 ft EPRTMconfiguration, in an FCC4 packaging. The pressure on the bearing surface of the spacer opposite the bundle is equal to 105.7 MPa.
In this configuration, the height of the rod bundle is mm (for a rod diameter of 9.5 mm).
10 185 10 105,7 Rod Mass / Max. Bundle Pressure Configuration Packaging diameter rods number height (MPa)
(mm) (kg) of rods (mm) 14x14 - 8 ft 10.75 204 61.5 FCC3.
14x14 - 10 ft 10.75 167 76.9 14x14 - 8 ft 10.75 222 61.6 14x14 - 10 ft 10.75 167 76.9 15x15 foot FCC4. 10.75 148 91.2 17x17 foot 9.5 185 90.8 17x17 - 14 ft, EPRTM 9.5 185 105.7 For all fixed end support plates, with the exception of EPRTM fixed end support plates, the worst-case load corresponds to the 15x15 - 12 ft configuration in an FCC4 packaging. This worst-case scenario is assessed using a 3D digital model for an axial drop of the axial spacer and the fixed end plate. This evaluation is described in section 5.
For the EPRTM fixed end support plate, which is based on a specific axial spacer concept, a detailed 3D digital model of the axial spacer and the fixed end plate is used to assess its mechanical strength in the event of an axial drop in the 17x17 - 14 ft EPRTM configuration in an FCC4 packaging. This evaluation is described in section 5.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 9 of 44
- 3. Criteria to be respected 3.1. Stress limitation For type austenitic steel, checks are carried out as part of an exceptional accident situation, therefore the criteria defined in document <1> in appendix ZF are considered: Rules associated with level D criteria:
Shearing: 0,75. min 2,4. ; 0,7. ,
min 2,4. ; 0,7.
1,5 min 2,4. ; 0,7.
For the aluminium alloy, the yield strength Re is the applicable criterion.
3.2. Buckling Elastic or elastoplastic instability is defined if:
Euler's critical force: Fc F (load).
- 4. Analytical calculations 4.1. Calculation methodology Part design is checked by calculating the strength of the materials in the sections subjected to the highest stresses according to the reference formulas <2>.
4.2. Support plate (see drawing 47-0-01-99-01-06 in appendix 1.3-2)
With a distributed radial load of 9.4 MPa, the plate is subjected to the bending of the plates and shear forces.
The radial spacer reinforcements represent supports, which define the bending areas of the plate. On a conservative basis, we ignore the contribution of the lower plate of the radial spacer and consider that all of the forces are absorbed by the support plate only.
The plate is analysed based on three types of assumptions (shown in annexe 1):
Case 1: plate fixed on 1 side corresponding to the plate not facing the radial spacer (length depending on the support plate in question, bounding width mm, thickness mm) -
calculations are completed, Case 2: plate fixed on 4 sides corresponding to the plate between the axial spacer reinforcements (minimum width of mm, thickness mm) - calculations are completed using the maximum length ( mm),
Case 3: Plate fixed on 3 sides and unfixed on the 4th side, corresponding to the plate outside of the reinforcements (length mm, width mm, thickness mm).
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 10 of 44 Case 1:
According to <2> table 8.1 case 2a. for a beam with the ends fixed - unfixed.
0 Where:
The beam section defined by and .
The maximum bending stress is:
. /2 Where (for a = 0 and wa = wl):
. 2 2 . ,
2 2 4 ,
. 12 12 Giving:
. , 176 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
The maximum shear stress is as follows:
Where:
N Thus, 24 This value is less than the criterion of 176 0,75 min 2,4. ; 0,7. .
The equivalent stress is equal to:
. . 3 181 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 11 of 44 Case 2:
According to <2> table 11.4 case 8a. for a rectangular plate with the 4 sides fixed.
X Where:
plate length of mm, plate width of mm, plate thickness = mm.
The maximum bending stress is:
Where:
= 0.5 according to <2> table 11.4 case 8a.,
= distributed load of MPa, Giving,
. 206 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
The maximum shear stress is as follows:
Where:
. . N Thus, 26 This value is less than the criterion of 176 0,75 min 2,4. ; 0,7. .
The equivalent stress is equal to:
. . 3 211 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 12 of 44 Case 3:
According to <2> table 11.4 case 10a. for a rectangular plate with 3 sides fixed and 1 side unfixed.
z Free Where:
plate length of mm, plate width of mm, plate thickness = mm.
The maximum bending stress is:
Where:
= 1.337 according to <2> table 11.4 case 10a.,
= distributed load of MPa, Giving,
. 177 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
The maximum shear stress is as follows:
Where:
. . N Thus, 11 This value is less than the criterion of 176 0,75 min 2,4. ; 0,7. .
The equivalent stress is equal to:
. . 3 178 This value is less than the criterion of 353 1,5 min 2,4. ; 0,7. .
The dimensions of the support plate are therefore enough to guarantee its mechanical strength.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 13 of 44 4.3. Radial spacer with a radial load (see drawing 47-0-01-99-01-09 in appendix 1.3-2)
The distributed radial load is applied to the lower horizontal plate of the radial spacer.
4.3.1 . Sides and reinforcements The sides and reinforcements of the radial spacer are subjected to compression forces.
For the worst-case configuration assessed in section 2.3.1 (222 rods, 14 x 14 - 8 ft, in a FCC4 packaging), the maximum stress obtained on the sides and reinforcements of the radial spacer is equal to 145 MPa.
10 222 2,12 10
. 145 The maximum compression stress is less than the criterion of 200 MPa.
As the sides and reinforcements are relatively slender (low thickness of mm compared with the height of mm), they are likely to subjected to buckling. The ends are considered to be fixed as they are welded to the upper and lower plates. The free length of the buckling is therefore half of the height of the parts.
The buckling stress for a beam at the fixed ends is:
. E. I L .S Where:
E = 175,000 MPa at 315 °C, L = mm /2 = mm, the height of the flat parts for a fixed beam, S = x = mm2 (conservatively considering a depth of 1 mm for the reinforcement and side),
I = (b x h3)/12 = = mm4 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 14 of 44 So, 1028 The critical buckling stress is greater than the maximum compression stress (with a ratio
/ . 7), therefore no risk of buckling exists and the radial spacer will retain its height.
4.3.2. Lower horizontal plate of the radial spacer The lower plate of the radial spacer, which was not taken into consideration when calculating the bearing plate, is subjected to less stresses than the bearing plate. As the lower plate is made of the same material as the bearing plate, and therefore has the same characteristics, no justification is necessary. This plate can only improve margins with respect the actual stresses applied to the bearing plate assessed in section 4.2.
4.4. compensation spacers with a thickness of mm (see drawings 47-0-01-99-01 non-EPRTM / PLA-16-00179264-203 - specific to EPRTM)
Compensation spacers with a thickness of mm made of aluminium alloy subjected to a radial load are mainly subjected to compression under the loads from the rods combined with those of the bearing plates and the radial spacers.
On a conservative basis, the analysis is carried out considering that one single compensation spacer is subjected to forces. Furthermore, all of the forces transmitted by the radial spacer are distributed uniformly over the bearing surface of the sides and the reinforcements of the radial spacer on the compensation spacer.
For all compensation spacers, with the exception of EPRTM spacers, the worst-case load corresponds to the 14x14 - 8 ft, 222 rod configuration in an FCC4 packaging. The maximum stress obtained for the compensation spacer is 156 MPa.
/ . 10 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 15 of 44 222 2,12 10
. 156 The maximum compression stress is less than the criterion of 205 MPa.
For the EPRTM compensation spacer, which is based on a specific concept, the maximum stress obtained is 113 MPa (17x17 - 14 ft EPRTM, 185 rod configuration in an FCC4 packaging):
/ . 10 185 2,9 10
. 113 The maximum compression stress is less than the criterion of 205 MPa.
- 5. 3D finite element numerical calculations The aim is to determine the stress and strains of the axial spacer and the fixed end support plate in the event of a regulatory axial drop in accident conditions of transport with consideration of the deferred impact of the internal fittings of the FCC4 packaging.
In order to maximise the strains and stresses in the axial spacer, the balsa shock absorber facing the internal fittings (or shell absorber) is not considered in numerical calculations. This assumption offers substantial margins. The consideration of the balsa with a thickness of mm for the FCC4 and the minimum static crush stress of MPa for the balsa would absorb a significant proportion of the drop energy.
The finite element calculations shown below prove the continued integrity of the spacer during the stresses due to an accident involving the packaging, considering maximum accelerations and maximum stresses in the axial spacer and the fixed end support plate. According to section 2.3.2, two conservative configurations are applied for this justification:
15x15 - 12 ft fuel rods in an FCC4 packaging, 17x17 - 14 ft EPRTM fuel rods in an FCC4 packaging.
5.1. Computer software LS-DYNA R6.1.1 <4> are used for calculations and post-processing 5.2. Modelling The geometry of the axial spacer and fixed end support plate models is based on the following drawings:
15x15 - 12 ft configuration: , drawings 47-0-01-99-01-02 and 47-0-01-99-01-16 in appendix 1.3-2 17x17 - 14 ft EPRTM configuration, drawings PLA-16-00179264-201 and PLA-16-00179264-202 in appendix 1.3-2.
Model geometries with dimensions are available in figure 1 and in figure 2.
The meshes of the models are available in figure 3 and in figure 4.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 16 of 44 The model integrates the following detailed assumptions:
a complete model of the spacer is created to avoid preventing the appearance of any asymmetric buckling mode. Furthermore, the axial spacer is not contained laterally (the chassis-door assembly representing the cavity is not modelled) to maximise the risk of buckling; the axial spacer plate with a thickness of mm is not modelled, as its buckling strength is insignificant; the longitudinal welds in the axial spacer are modelled as 3D finite elements, Only the welds connecting the lower plate with a thickness of mm to the end plates are welded using bonding contacts. Details of the modelling process are given below, with the spacer corresponding to the 17x17 - 14 ft EPRTM configuration as an example:
END PLATE - ROD SIDE:
BONDING CONTACT ON THE REAR BASE PLATE END PLATE - TARGET SIDE:
BONDING CONTACT ON THE REAR BASE PLATE A gap of mm is left near to the longitudinal welds between the internal plates and the external plates (see figure below with the spacer corresponding to the 15x15 - 12 ft rod configuration as an example), which maximises the risk of buckling.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 17 of 44 On the surface of the fixed end support plate on the fuel rod side, two rectangular areas are meshed as surface finite elements with a material of null stiffness. The density of these surfaces is adjusted to distribute the mass of the unmodelled rod box components.
Theoretical masses are distributed as follows:
5.3. Materials In accordance with appendix 1.3-1, the properties of the type stainless steel are used in the calculation models. The minimum values at 100°C are given in the following table:
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 18 of 44 Temperature T (°C)
Young's modulus E (GPa)
Minimum yield strength Re (MPa)
Ultimate tensile strength Rm (MPa)
Elongation at rupture A (%)
Poisson's ratio = 0.3 and density = 7850 kg/m3.
The LS-DYNA behavioural law used is an elastoplastic law no. 24
- MAT_PIECEWISE_LINEAR_PLASTICITY. In the domain (true plastic strain p; Von Mises VM equivalent stress), the strain-hardening law is linear between the points (0; Re) and (true A%; true Rm), and extended by a power function beyond A%, with a class C1 continuity to the connection point p = "true A%" (continuous function and continuous derivative).
The conventional characteristics are converted into true characteristics. The yield strength is unchanged. The ultimate tensile strength and rupture elongation are corrected as follows:
1 % .
% ln 1 % 1 % /
The corrected values are presented in the following table:
True ultimate tensile strength Rm true (MPa)
True rupture elongation A (%) true Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 19 of 44 5.4. Masses The distribution of masses for each of the configurations is shown in the following table:
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 20 of 44 5.5. Boundary conditions and contacts On a conservative basis, the axial spacer is placed on a flat non-deformable target and the damping of the drop energy by the packaging shell shock absorber, facing the internal fittings, is not modeled.
The sliding contacts between the parts and the target are defined with a friction coefficient of 0.1.
5.6. Initial conditions All of the parts are driven by an initial speed which corresponds to free-fall from a height of 9.25 m, i.e.: 2 2 9,81 9,25 13,472 /
5.7. Load Gravitational acceleration is applied in the vertical direction (9.81 m/s2).
5.8. Results The results of the calculations are archived in <5>.
Model deformation shapes are is shown in figure 5. The deformation shape in the fixed end support plate demonstrates, for both of the configurations studied, that the gaps between this fixed end plate and the structure of the rod box are filled, which guarantees that the rods are secured in the rod box.
Plastic strain is shown in figure 6. Maximum plastic strains are shown in the table below:
Maximum plastic strains Rupture Component 15x15. 17x17. elongation 12 ft 14 ft EPRTM End plates % % (2)
Axial spacer Longitudinal plates and their
% (1) % (3) %
longitudinal welds Fixed end support plate % %
(1) Value for the upper edges of the longitudinal plates. True rupture elongation of the material (%)
is overshot (by a factor of 1.74). However, the analysis of the main stresses in figure 7 demonstrates that the elements overshooting true criterion A% work as compression. There is therefore no risk of failure.
(2) Elements in the end plate on the rod side of the axial spacer overshoot the ultimate tensile strength.
The true rupture elongation of the material () is overshot (by a factor of 1.36), however, the analysis of the main stresses in figure 8 demonstrates that the elements overshooting true criterion A% work as compression. There is therefore no risk of failure.
(3) Value for the upper edges of the longitudinal plates. True rupture elongation of the material () is overshot (by a factor of 1.3). However, the analysis of the main stresses in figure 8 demonstrates that the elements overshooting true criterion A% work as compression. There is therefore no risk of failure.
Plastic strain, outside of the compression zone, observed in the axial spacer and in the fixed end plate, for both of the configurations studied, is less than the specified rupture elongation.
The strength is therefore guaranteed for an axial drop.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 21 of 44
- 6. Conclusions The strength of the rod box is guaranteed in accident drop conditions.
- 7. References
<1> Construction code for mechanical equipment in PWS nuclear islands (RCC-M).
<2> ROARKS Formulas for Stress & Strain, seventh edition, Warren C. Young - Richard G.
Budynas.
<3> Properties of Aluminum Alloys - Edited by J. Gilbert Kaufman FASM - 1999.
<4> LS-DYNA software, smp d R6.1.1 version 78769 developed by LSTC.
<5> Archiving.
Archiving of the drop calculations for the rod box in the 17x17 - 14 ft EPRTM rod configuration:
08S.CDE3080446.01-SAR / Dynamic / CAL-16-00171218-103-01 Archiving of the drop calculations for the rod box in the 15x15 - 12 ft rod configuration:
08S.CDE3080446.01-SAR / Dynamic / CAL-16-00171218-002-01 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 22 of 44 List of figures Figure Title Number of pages 1 Model geometry with dimensions (mm) - 15x15 - 12 ft configuration 2 2 Model geometry with dimensions (mm) - 17x17 - 14 ft EPRTM configuration 2 3 Model mesh - 15x15 - 12 ft configuration 1 4 Model mesh - 17x17 - 14 ft EPRTM configuration 4 5 Model deformation shape 4 6 Plastic strain at the final instant 8 TOTAL 21 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 23 of 44 FIGURE 1 MODEL GEOMETRY WITH DIMENSIONS (MM) - 15X15 - 12 FT CONFIGURATION (1/1)
FRONT VIEW WITH DIMENSIONS
<<SCALE0702016-01-25_175648_TRIMMED.png>>
RIGHT VIEW WITH DIMENSIONS
<<SCALE0652016-01-25_175709_TRIMMED.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 24 of 44 FIGURE 2 MODEL GEOMETRY WITH DIMENSIONS (MM) - 17X17 - 14 FT EPRTM CONFIGURATION (1/2)
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 25 of 44 FIGURE 2 MODEL GEOMETRY WITH DIMENSIONS (MM)
- 17X17 - 14 FT EPRTM CONFIGURATION (2/2)
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 26 of 44 FIGURE 3 MODEL MESH - 15X15 - 12 FT CONFIGURATION PERSPECTIVE VIEW
<<SCALE0652016-01-25_181820_TRIMMED.png>>
RIGHT VIEW - LONGITUDINAL PLATES AND THEIR WELDS Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 27 of 44 FIGURE 4 MODEL MESH - 17X17 - 14 FT EPRTM CONFIGURATION PERSPECTIVE VIEW
<<SCALE0652016-01-25_181820_TRIMMED.png>>
RIGHT VIEW Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 28 of 44 FIGURE 5 MODEL DEFORMATION SHAPE (1/4)
FRONT VIEW - 15X15 - 12 FT CONFIGURATION TOP VIEW - 15X15 - 12 FT CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 29 of 44 FIGURE 5 MODEL DEFORMATION SHAPE (2/4)
RIGHT VIEW - 15X15 - 12 FT CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 30 of 44 FIGURE 5 MODEL DEFORMATION SHAPE (3/4)
FRONT VIEW - 17X17 - 14 FT EPRTM CONFIGURATION TOP VIEW - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE065cas4\06_d3plot_deformed_2.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 31 of 44 FIGURE 5 MODEL DEFORMATION SHAPE (4/4)
RIGHT VIEW - 17X17 - 14 FT EPRTM CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 32 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (1/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
GENERAL VIEW - 15X15 - 12 FT CONFIGURATION GENERAL VIEW - 15X15 - 12 FT CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 33 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (2/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
END PLATES - 15X15 - 12 FT CONFIGURATION END PLATES - 15X15 - 12 FT CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 34 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (3/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
FIXED END SUPPORT PLATE - CONFIGURATION 15X15 - 12 FT FIXED END SUPPORT PLATE - CONFIGURATION 15X15 - 12 FT Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 35 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (4/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
LONGITUDINAL PLATES AND THEIR WELDS - 15X15 - 12 FT CONFIGURATION LONGITUDINAL PLATES AND THEIR WELDS - 15X15 - 12 FT CONFIGURATION LONGITUDINAL PLATES AND THEIR WELDS - 15X15 - 12 FT CONFIGURATION Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 36 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (5/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
GENERAL VIEW - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE060cas4\06_d3plot_epsp_parts_view1.png>>
GENERAL VIEW - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE060cas4\06_d3plot_epsp_parts_view2.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 37 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (6/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
END PLATES - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE060cas4\06_d3plot_epsp_parts1_2_view1.png>>
END PLATES - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE060cas4\06_d3plot_epsp_parts1_2_view2.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 38 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (7/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
FIXED END SUPPORT PLATE - CONFIGURATION 17X17 - 14 FT EPRTM
<<SCALE060cas4\06_d3plot_epsp_part6_view1.png>>
FIXED END SUPPORT PLATE - CONFIGURATION 17X17 - 14 FT EPRTM
<<SCALE060cas4\06_d3plot_epsp_part6_view2.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 39 of 44 FIGURE 6 PLASTIC STRAIN AT THE FINAL INSTANT (8/8)
N.B. : the scale maximum is blocked at true A%; the elements above this point are shown in black.
LONGITUDINAL PLATES AND THEIR WELDS - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE040cas4\06_d3plot_epsp_parts3_4_5_view1.png>>
LONGITUDINAL PLATES AND THEIR WELDS - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE040cas4\06_d3plot_epsp_parts3_4_5_view2.png>>
LONGITUDINAL PLATES AND THEIR WELDS - 17X17 - 14 FT EPRTM CONFIGURATION
<<SCALE060cas4\06_d3plot_epsp_parts3_4_5_view4.png>>
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 40 of 44 FIGURE 7 MAIN STRESSES (PA) AT MAXIMUM CRUSHING
- 15X15 - 12 FT CONFIGURATION (1/1)
N.B. : the 3 main stresses are shown as vectors superposing the iso values for plastic strain on the most deformed edge (the colour scale on the right correspond to the stresses in Pa).
Post-processing time (4 ms), where the 3rd main stress is the most negative value, is almost the instant (3.36 ms) where spacer crushing is maximum.
The main stress vectors are only displayed for elements overshooting true A% at the final instant.
LONGITUDINAL PLATES AND THEIR WELDS - 15X15 - 12 FT CONFIGURATION This figure shows significantly deformed elements on the edge subjected to compression:
- the largest main stress in absolute values is negative (blue arrows almost parallel to the drop X axis);
- the two other main stresses are also negative (green arrows almost crossing the X axis; cause:
Poisson's ratio).
spacer strength is unaffected.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 41 of 44 FIGURE 8 MAIN STRESSES (PA) AT MAXIMUM CRUSHING
- 17X17 - 14 FT EPRTM CONFIGURATION (1/2)
N.B. : the 3 main stresses are shown as vectors superposing the iso values for plastic strain on the most deformed edge (the colour scale on the right correspond to the stresses in Pa).
Post-processing time (2.5 ms), is almost the instant (2.25 ms) where spacer crushing is maximum.
The main stress vectors are only displayed for elements overshooting true A% at the final instant.
LONGITUDINAL PLATES AND THEIR WELDS - 17X17 - 14 FT EPRTM CONFIGURATION This figure shows significantly deformed elements on the edge subjected to compression:
- the largest main stress in absolute values is negative (blue arrows almost parallel to the drop X axis);
- the two other main stresses are also negative (green arrows almost crossing the X axis; cause:
Poisson's ratio).
spacer strength is unaffected.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 42 of 44 FIGURE 8 MAIN STRESSES (PA) AT MAXIMUM CRUSHING
- 17X17 14 FT EPRTM CONFIGURATION (2/2)
N.B. : the 3 main stresses are shown as vectors superposing the iso values for plastic strain on the most deformed edge (the colour scale on the right correspond to the stresses in Pa).
Post-processing time (2.5 ms), is almost the instant (2.25 ms) where spacer crushing is maximum.
The main stress vectors are only displayed for elements overshooting true A% at the final instant.
UPPER END PLATE (ROD SIDE)
- 17X17 14 FT EPRTM CONFIGURATION This figure shows significantly deformed elements on the edge subjected to compression:
- the largest main stress in absolute values is negative (blue arrows almost parallel to the drop X axis);
- the two other main stresses are also negative (green arrows almost crossing the X axis; cause:
Poisson's ratio).
spacer strength is unaffected.
Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112-NPV Rev.: 01 Page 43 of 44 List of appendices Appendix Title Number of pages 1 Location of contact zones on the support plate. 1 TOTAL 1 Non-proprietary version
AREVA UNRESTRICTED DISTRIBUTION AREVA TN Form: PM04-4-MO-6 Rev. 00 NUCLEAR LOGISTICS OPERATIONS Identification: DOS-13-00081778-112 Rev.: 01 Page 44 of 44 LOCATION OF CONTACT ZONES ON THE SUPPORT PLATE Zone A: plate fixed on 1 side corresponding to the plate not facing the radial spacer (length depending on the spacer, bounding width mm, thickness mm).
Zone B: plate fixed on 4 sides corresponding to the plate between the radial spacer reinforcements (length depending on the spacer, minimum width of mm, thickness mm) - calculations are completed using the maximum length ( mm).
Zone C: plate fixed on 3 sides and unfixed on the 4th side, corresponding to the plate outside of the radial spacer reinforcements(length mm, width mm, thickness mm).
Non-proprietary version