ML22277A751
| ML22277A751 | |
| Person / Time | |
|---|---|
| Site: | 07103097 |
| Issue date: | 01/01/2009 |
| From: | Boyle R, Shaw D AREVA, TN Americas LLC |
| To: | Division of Fuel Management |
| Garcia-Santos N | |
| Shared Package | |
| ML22277A716 | List:
|
| References | |
| A33010, E-61285, EPID L-2022-DOT-0008 | |
| Download: ML22277A751 (18) | |
Text
TN International ANALYSIS OF THE FATIGUE STRENGTH OF THE FCC3/FCC4 CONTAINERS BLA-IG Names Signatures Date Preparation Check Ref.
NTC 00135891E-NPV Rev 01 E
Form : PM04-3-MO-3 rev. 2 Page 1/17 Non-proprietary version CONTENTS
SUMMARY
............................................................................................................................... 3
- 1. INTRODUCTION............................................................................................................. 3
- 2. HYPOTHESES.................................................................................................................. 3
- 3. FATIGUE STRENGTH OF THE FCC 3 CONTAINER.............................................. 5
- 4. FATIGUE STRENGTH OF THE FCC 4 CONTAINER............................................ 10
- 5. BOUNDING NATURE OF ROAD TRANSPORT...................................................... 15
- 6. CONCLUSION................................................................................................................ 15
- 7. REFERENCES................................................................................................................ 15 LIST OF FIGURES............................................................................................................... 17 A
AREVA I
I I
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 2 / 17 Non-proprietary version REVISION STATUS Revision Date Modifications Prepared by /
Checked by 0
12/08 First issue 1
01/09
- Details added
- Modification in the number of handling operations per loading
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 3 / 17 Non-proprietary version
SUMMARY
This document concerns the fatigue analysis of the FCC 3 and FCC 4 containers. The study is based on the hypotheses of road transports per year for the FCC 3 container and road transports per year for the FCC 4 container. These hypotheses are justified by the bounding nature of road transport with respect to maritime and railway transport.
Account is taken of the fatigue cycles caused by handling and stacking. The cumulative alternating stress is calculated on the basis of the MINER law. The maximum lifetimes of the containers are calculated for 3 lashing cases and are recapped in the following table:
Lashing case 1 Lashing case 2 Lashing case 4 Lifetime (FCC 3)
> 40years 37 ans
> 40 years Lifetime (FCC 4)
> 40 years 10 years 37 years
- 1. INTRODUCTION This document presents the fatigue analysis of the FCC 3 and FCC 4 containers in road, maritime and railway transport configuration, taking into account the cycles due to stacking and handling.
- 2. HYPOTHESES The transport hypotheses are as follows:
FCC3 container: transports / year
- road: 1 outward and return road transport = 1200 km
- railway: 1 outward and return railway transport = 1200 km:
- maritime : 1 outward transport: 30.5 d FCC4 container: transports / year
- road: 1 outward and return road transport = 1200 km
- railway: 1 outward and return railway transport = 1200 km:
- maritime : 1 outward transport: 15 d Based on note <1>, it appears that the vertical and horizontal acceleration spectra undergone by a container during railway transport are less penalizing than those obtained during a road transport. As a result, railway transport will be considered as a road transport.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 4 / 17 Non-proprietary version Likewise for the FCC3 container, maritime transport will be considered as a road transport and neglected for the FCC4 container. The justification of these hypotheses will be given in chapter 4. road transports per year are therefore considered for the FCC 3 container and road transports per year for the FCC 4 container.
The stresses considered are the maximum stresses encountered during transport, (based on note <2> and <3>). On the MINER cumulative damage law, the cumulative alternating stresses are calculated and compared with the fatigue limits taken from the curve in figure 1 <6>.
The following table recaps the numbers of cycles to be considered for each direction for an outward and return transport of 1200 km. The number of cycles corresponding to an acceleration level is calculated from <1> proportionally to the number of kilometers travelled Number of cycles ni Level of the accelerations (+/-
g)
Vertical transport (Z)
Transverse transport (Y)
Longitudinal transport (X) 0,4 382212 26575 9303 0,6 29351 2675 3750 0,8 2924 912 1590 1
440 268 631
,2 121 83 203
,4 38 27 52
,6 20 9
15 1,8 11 2
5 2
7 0
0 2,2 5
0 0
The maximum authorized number of cycles Ni is derived from the curve shown in figure
- 1. Ni is obtained according to the value of the maximum variation of stress Sa. The various values Ni are interpolated from two known points on the curve.
For each container, various lashing cases are considered, corresponding to maximum stresses in the three directions.
Stacking and handling are taken into account at a rate of handling operations and stacking operations per transport.
The number of stress cycles per transport due to handling Nm is calculated by the following equation:
Nm = M. Zm. km
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 5 / 17 Non-proprietary version where:
km Max number of stress cycles resulting from a handling operation Zm Number of handling operations per loading M
Max number of handling operations per transport This gives:
Nm = cycles per transport The number of stress cycles per transport due to stacking is calculated by the following equation:
Ng = G. Zg. kg where:
kg Number of stress cycles resulting from a stacking operation 1 (static stress)
Zg Number of stacking operations per loading G
Max number of stacking operations per transport This gives:
Ng = cycles per transport
- 3. FATIGUE STRENGTH OF THE FCC 3 CONTAINER 3.1 Sustained stresses During transport, the stresses in the 3 axes differ for each lashing case. The following table groups together the maximum stresses considered in the 3 directions:
Lashing case type 1 Lashing case type 2 Lashing case type 4 Vertical transport (MPa)
Transversal transport (MPa)
Longitudinal transport (MPa)
These transport loadings must be combined with the handling and stacking loadings.
During a handling operation, the maximum equivalent stress is MPa (at an acceleration of 1.15 g). Although it is not located at the same place as the stress I
I I
l,_______I ____
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 6 / 17 Non-proprietary version generated during the transport, it is conservatively directly combined with that of the transport.
A handling cycle breaks down as follows (as per <4>, by adjusting the peak measured at 1.15 g):
A distinction is made between:
- The main loading cycle described between the values 0 / 1,15 g / 0, or a variation of +/- 0,575 g about the average value of the range,
- Intermediate cycles about the average value of 1 g due to the oscillations before stabilisation. These variations are sufficiently small not to cause fatigue damage.
This means that the fatigue analysis is conducted on the basis of the stress cycle +/-
MPa.
During stacking, the maximum equivalent stress is MPa (envelope value for all the directions and stacking modes) for an acceleration of 1 g. Although it is not located at the same place as the stress generated during the transport, it is conservatively directly combined with that of the transport.
Stacking is considered as a static operation. The loading cycle varies between the values 0 / 1 g / 0, or a variation of +/- 0,5 g about the average value of the range which is /2= MPa. Thus, the equivalent stress for fatigue dimensioning will beMpa.
3.2 Total fatigue damage Knowing:
- The total number of cycles ni corresponding to an acceleration level,
- The maximum authorized number of cycles Ni, depending on the stress value Sa, it is possible to calculate the fatigue damage for an acceleration level by means of the following equation:
i i
i N
n d
1 g 0. g 1,15 g
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 7 / 17 Non-proprietary version The following tables recap the results obtained for the various lashing cases:
Lashing case 1 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.108 5.106 3.106 1,5.106 Vertical damage di =
i N
n i 3,8.10-6 2,9.10-7 2,9.10-8 4,4.10-9 1,2.10-9 3,8.10-10 2.10-7 2,1.10-6 2,3.10-6 3,5.10-6 Transverse comparison stress Sa Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Transverse damage di =
i N
n i 2,6.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,6.10-10 9.10-11 2,3.10-11 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 1,29.10-5 Nb of possible transports 77788 Lifetime 7779 years Lashing case 1 is validated for a lifetime well above 40 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 8 / 17 Non-proprietary version Lashing case 2 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 1.1011 3.106 1.106 4.105 1,5.105 1.105 7.104 4.104 3.104 Vertical damage di =
i N
n i 3,8.10-6 2,9.10-7 9,7.10-4 4,4.10-4 3.10-4 2,5.10-4 2.10-4 1,5.10-4 1,7.10-4 1,8.10-4 Transverse comparison stress Sa Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Transverse damage di =
i N
n i 2,6.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,6.10-10 9.10-11 2,3.10-11 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 2,67.10-3 Nb of possible transports 373 Lifetime 37 years Lashing case 2 is validated for a maximum lifetime of 37 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 9 / 17 Non-proprietary version Lashing case 4 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 1.1011 1.1011 1.107 3.106 1.106 4.105 3.105 2.105 1,5.105 Vertical damage di =
i N
n i 3,8.10-6 2,9.10-7 2,9.10-8 4,4.10-5 4.10-5 3,8.10-5 5,1.10-5 3,5.10-5 3,4.10-5 3,5.10-5 Transverse comparison stress Sa
² Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.109 0
0 Transverse damage di =
i N
n i 2,7.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,7.10-10 9,1.10-11 1,1.10-7 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 2,83.10-4 Nb of possible transports 3535 Lifetime 353 years Lashing case 4 is validated for a lifetime well above 40 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 10 / 17 Non-proprietary version
- 4. FATIGUE STRENGTH OF THE FCC 4 CONTAINER 4.1 Sustained stresses During transport, the stresses in the 3 axes differ for each lashing case. The following table groups together the maximum stresses considered in the 3 directions:
Lashing case type 1 Lashing case type 2 Lashing case type 4 Vertical transport (MPa)
Transversal transport (MPa)
Longitudinal transport (MPa)
These transport loadings must be combined with the handling and stacking loadings.
During a handling operation, the maximum equivalent stress is MPa (at an acceleration of 1.15 g). Although it is not located at the same place as the stress generated during the transport, it is conservatively directly combined with that of the transport.
A handling cycle breaks down as follows (as per <4>, by adjusting the peak measured at 1.15 g):
A distinction is made between:
- The main loading cycle described between the values 0 / 1,15 g / 0, or a variation of +/- 0,575 g about the average value of the range,
- Intermediate cycles about the average value of 1 g due to the oscillations before stabilisation. These variations are sufficiently small not to cause fatigue damage.
This means that the fatigue analysis is conducted on the basis of the stress cycle +/-
MPa.
1. g 0. g 1,15 g
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 11 / 17 Non-proprietary version During stacking, the maximum equivalent stress is MPa (envelope value for all the directions and stacking modes) for an acceleration of 1 g. Although it is not located at the same place as the stress generated during the transport, it is conservatively directly combined with that of the transport.
Stacking is considered as a static operation. The loading cycle varies between the values 0 / 1 g / 0, or a variation of +/- 0,5 g about the average value of the range which is /2=MPa. Thus, the equivalent stress for fatigue dimensioning will beMpa.
4.2 Total fatigue damage Knowing:
- The total number of cycles ni corresponding to an acceleration level,
- The maximum authorized number of cycles Ni, depending on the stress value Sa, it is possible to calculate the fatigue damage for an acceleration level by means of the following equation:
i i
i N
n d
The following tables recap the results obtained for the various lashing cases:
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 12 / 17 Non-proprietary version Lashing case 1 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 5.107 5.106 3.106 Vertical damage di =
i N
n i 3,8.10-6 2,9.10-7 2,9.10-8 4,4.10-9 1,2.10-9 3,8.10-10 2.10-10 2,1.10-7 1,4.10-6 1,8.10-6 Transverse comparison stress Sa Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Transverse damage di =
i N
n i 2,6.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,6.10-10 9.10-11 2,3.10-11 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 7,95.10-6 Nb of possible transports 125658 Lifetime 8321 years Lashing case 1 is validated for a lifetime well above 40 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 13 / 17 Non-proprietary version Lashing case 2 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 3.107 1,5.106 4.105 2.105 1.105 7.104 4.104 3.104 2.104 Vertical damage di =
i N
n i 3,8.10-6 9,8.10-4 1,9.10-3 1,1.10-3 6,1.10-4 3,8.10-4 2,9.10-4 2,7.10-4 2,3.10-4 2,7.10-4 Transverse comparison stress Sa Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Transverse damage di =
i N
n i 2,6.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,6.10-10 9.10-11 2,3.10-11 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 6,1.10-3 Nb of possible transports 164 Lifetime 10 years Lashing case 2 is validated for a maximum lifetime of 10 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 14 / 17 Non-proprietary version Lashing case 4 Acceleration 0,4 g 0,6 g 0,8 g 1,0 g 1,2 g 1,4 g 1,6 g 1,8 g 2,0 g 2,2 g Vertical comparison stress Sa Number of cycles ni 382212 29351 2924 440 121 38 20 11 7
5 Number of cycles Ni 1.1011 1.1011 5.106 1,5.106 4.105 3.105 1,5.105 1.105 7.104 4.104 Vertical damage di =
i N
n i 3,8.10-6 2,9.10-7 5,8.10-4 2,9.10-4 3.10-4 1,3.10-4 1,4.10-4 1,1.10-4 9,7.10-5 1,3.10-4 Transverse comparison stress Sa Number of cycles ni 26575 2675 912 268 83 27 9
2 0
0 Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Transverse damage di =
i N
n i 2,6.10-7 2,7.10-8 9,1.10-9 2,7.10-9 8,3.10-10 2,6.10-10 9.10-11 2,3.10-11 0
0 Longitudinal comparison stress Sa Number of cycles ni 9303 3750 1590 631 203 52 15 5
0 0
Number of cycles Ni 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 1.1011 0
0 Longitudinal damage di =
i N
n i 9,3.10-8 3,7.10-8 1,6.10-8 6,3.10-9 2.10-9 5,2.10-10 1,5.10-10 4,5.10-11 0
0 Handling damage 4,8.10-9 Stacking damage 2.10-10 Total damage 1,78.10-3 Nb of possible transports 560 Lifetime 37 years Lashing case 4 is validated for a maximum lifetime of 37 years.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 15 / 17 Non-proprietary version
- 5. BOUNDING NATURE OF ROAD TRANSPORT The appendix of letter <5> defines the maximum accelerations undergone by the container depending on the sea conditions, together with the associated number of cycles.
They are calculated by taking into account the following accelerations and frequencies
- +/- 0,4 g with a period of 6 seconds throughout the transport, which corresponds to the everyday conditions (sea conditions force 6 on average)
- +/- 0,6 g with a period of 9.2 seconds during 6 % of the transport time, which corresponds to severe conditions (sea conditions up to force 11)
The following table groups together the numbers of associated cycles for each container (1 transport of 30.5 days for the FCC 3 container and 1 transport of 15 days for the FCC 4 container).
Everyday conditions
(+/- 0,4 g)
Severe conditions
(+/- 0,6 g)
Number of cycles ni (FCC 3) 439200 17264 Number of cycles ni (FCC 4) 216000 8490 The number of cycles corresponding to an acceleration of +/- 0.6 g is less than for road transport. For an acceleration of +/- 0.4 g, the number of cycles is of the same order of magnitude as for road transport and the total damage is covered by the inclusion of higher acceleration levels in the case of road transport. The replacement of maritime transport by road transport in the total fatigue damage calculation is therefore fully justified.
- 6. CONCLUSION The following table recaps the maximum lifetimes for lashing cases 1, 2 and 4 on the basis of 10 road transports per year for the FCC 3 container and 15.1 road transports per year for the FCC 4 container.
Lashing case 1 Lashing case 2 Lashing case 4 Lifetime (FCC 3)
> 40 years 37 years
> 40 years Lifetime (FCC 4)
> 40 years 10 years 37 years
- 7. REFERENCES
<1>
D. PUJET, Nuclear Transport Limited Paris et P. MALESYS, Transnucléaire Paris << Measurement of the acceleration undergone by the trunnions of irradiated fuel transport flasks during normal use >> - PATRAM 89, 11-16 juin 1989, WASHINGTON DC, USA.
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 16 / 17 Non-proprietary version
<2>
Containers pour assemblages de combustible neufs FCC3, Données pour l'analyse de la tenue en fatigue des botes de levage et de la coquille supérieure (FCC3 containers for fresh fuel assemblies, data for analysis of the fatigue strength of the lifting boxes and upper shell), ref. NEEL-F 2008 DC 117/B
<3>
Containers pour assemblages de combustible neufs FCC4, Données pour l'analyse de la tenue en fatigue des botes de levage et de la coquille supérieure (FCC4 containers for fresh fuel assemblies, data for analysis of the fatigue strength of the lifting boxes and upper shell), ref. NEEL-F 2008 DC 118/A
<4>
KTA standard 3201.2 - << Safety Standards of the Nuclear Safety Standards Commission - Components of the Reactor Coolant Pressure Boundary of Light Water Reactors / Part 2 : Design and Analysis >> - Edition 06/96
<5>
Courrier COGEMA LOGISTICS S/03-045 du 28 mai 2003 - << Transport de matires radioactives - Sujets génériques - Tenue des arrimages en transport maritime >> (Letter from COGEMA LOGISTICS S/03-045 dated May 28th 2003 - << Transport of radioactive materials - Generic issues - Strength of lashing in maritime transport)
<6>
Courbe de fatigue grand nombre de cycles spécifique pour les aciers au carbone, réf. NEEL-F 09.0011 (Fatigue curve with large number of specific cycles for carbon steels, ref NEEL-F 09.0011)
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Page 17 / 17 Non-proprietary version LIST OF FIGURES Number Rev Title Number of pages 1
A Stress fatigue curve - Carbon steel for large cycle numbers 1
Total 1
TN International Ref. NTC-08-00135891 E-NPV Rev. 01E Index A FIGURE 1 STRESS FATIGUE CURVE - CARBON STEEL FOR LARGE CYCLE NUMBERS (DERIVED FROM <6>)
1,E+00 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 1,E+06 1,E+07 1,E+08 1,E+09 1,E+10 1,E+11 1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 S a (MPa)
Nu m
be r
of cy cle s
J.
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