ML19114A314
| ML19114A314 | |
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|---|---|
| Site: | 07103052 |
| Issue date: | 03/05/2019 |
| From: | Paris A TN Americas LLC, Orano USA |
| To: | Division of Spent Fuel Management |
| Shared Package | |
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| References | |
| Download: ML19114A314 (39) | |
Text
TN International CHAPTER 1 - APPENDIX 9-4 TN-MTR Names Signatures Date Prepared by A. PARIS Ref.
DOS-18-011415-019-NPV Rev. 1.0 Form: PM04-3-MO-3 rev. 2 Page 1/39 NON PROPRIETARY VERSION FITTING OF THE LATERAL DROP OF THE MOCKUP OF THE TN-MTR PACKAGE TABLE OF CONTENTS REVISION STATUS
SUMMARY
- 1. INTRODUCTION
- 2. BASIC DATA
- 3. MODELLING
- 4. RESULTS
- 5. CONCLUSIONS
- 6. REFERENCES LIST OF TABLES LIST OF FIGURES LIST OF APPENDICES
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 2/39 NON PROPRIETARY VERSION REVISION STATUS Revision Date Modifications Prepared by /
Reviewed by Old reference: DOS-16-00173678-194 0
N/A Document first issue.
APA / ALC New reference: DOS-18-011415-019 1.0 N/A New reference due to new document management system software.
APA / ALC
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 3/39 NON PROPRIETARY VERSION
SUMMARY
The purpose of this study is to fit the lateral drop of the mockup of the 1/2 scale packaging.
The following drop is studied (drop No. 3 described in Chapter 1-6):
- 9.15 m lateral drop with an angle of 4.9° and the centre line of the trunnions parallel to the drop axis, i.e. along the 270° line.
Iso-model fitting with the oblique drop (see chapter 1-9-1) is made at ambient temperature (20°C).
The fitting of the numerical model of the mockup is based upon:
- accelerometer readings for Drop No. 3 derived from Chapter 1-6;
- crushing of the shock absorbing cover and the shell measured during real drops for drop No.
3 taken from Chapter 1 -6.
The purpose of this fitting is to obtain a numerical model that gives reliable compression and acceleration results. This fitted model is then used for calculations on extrapolation to the package model for the lateral drop at -40°C and at maximum temperature under normal transport conditions (see chapter 1-9-5).
The fitting under iso-model conditions with the oblique drop fitting presented in Chapter 1-9-1 gives satisfactory results.
The duration and shape of the acceleration peaks obtained under simulation are representative of the test for accelerometers, giving maximum accelerations. Therefore the fitting is satisfactory in terms of acceleration.
The crushed heights of the shock absorbing cover and the shell deformations measured in the simulation are higher overall than those measured at the end of the drop test. Therefore the numerical model is conservative in terms of crushing.
The fitted numerical model used is representative of the behaviour of the 1/2 scale mockup of the TN--MTR packaging in lateral drop.
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 4/39 NON PROPRIETARY VERSION
- 1. INTRODUCTION The purpose of this study is to fit the lateral drop of the mockup of the 1/2 scale packaging.
The following drop is studied (drop No. 3 described in Chapter 1-6):
- 9.15 m lateral drop with an angle of 4.9° and the centre line of the trunnions parallel to the drop axis, i.e. along the 270° line.
The fitting of the numerical model of the mockup is based upon:
- accelerometer readings for Drop No. 3 derived from Chapter 1-6;
- crushing of shock absorbing covers measured during actual drops for drop No. 3 taken from Chapter 1 -6).
The purpose of this fitting is to obtain a numerical model that gives reliable compression and acceleration results. This fitted model is then used for calculations on extrapolation to the package model at -40°C and to the maximum temperature under normal transport conditions for lateral drop cases (see Appendix 1-9-5).
The iso-model fitting with the oblique drop (see chapter 1-9-1) is made at ambient temperature (20°C). This fitting results in a numerical model that gives reliable compression and acceleration results.
- 2. BASIC DATA The input data for the fitting are as follows:
- mockup geometry (see Chapter 1-4);
- mechanical characteristics of the mockup presented in section 3.6;
- report on regulatory drop tests (chapter 1-6).
- 3. MODELLING 3.1. Computer codes used The geometry of the model is defined using software <3>.
The calculations are made with<2 > in double precision.
The results presented below were processed with LS-PREPOST.2.2.
3.2. Geometry and meshing The geometry of the model representative of the 1/2 scale mockup of the TN-MTR packaging is shown in figure 1-9-4.1. The fitting is made under iso-model conditions with the oblique drop fitting (see Chapter 1-9-1).
The mesh of the model is shown in figure 1-9-4.2.
The orientation of the wood in the shock absorbing cover is shown in Figure 1-9-4.5.
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 5/39 NON PROPRIETARY VERSION 3.3. Calculation cases The calculation case presented in figure 1-9-4.4 is made to fit the lateral drop of the 1/2 scale mockup (drop No. 3 in Chapter 1-6).
The fitting is made for a drop height of 9.15 m with a drop angle equal to 4.9°, downwards on the shell side. The impact line of the mock-up is at 270°.
3.4. Modelling assumptions For reasons of symmetry, only a half-model is modelled.
3.4.1. Content The mass of the content and the spacer is distributed around a 45° angular sector on the numerical model along the internal wall of the shell. The content is modelled by 8 mm thick shell elements with an elastic material.
3.4.2. Lid The complete lid is modelled with the flange, the lead shielding enclosure, the stiffener shell, the outer shell and the inner disk.
The shells (outer and stiffener) are modelled by 5 mm thick shell elements.
The groove of the lid seal located close to the inside of the cavity is modelled.
Class 8-8 M14 screws (mockup) are considered to fix the lid to the shell.
The preload in each screw is applied using
- MAT_ORTHOTROPIC_THERMAL in which a coefficient of thermal expansion is defined. The screw/shell interface is modelled by a sticking contact.
3.4.3. Shell The shell is divided into two parts: the flange and the shell body; they are both considered to be deformable.
The resin is ignored: the volume that it occupies is filled by the lead shielding for which the density is reevaluated accordingly. The shell outside wall is modelled by shell elements sharing a common node with the lead. The inside wall is modelled by shell elements in contact with volume elements representing the lead.
The trunnions are modelled by cylinders with a constant diameter of 60 mm "stuck" to the shell flange.
MAT_ORTHOTROPIC_THERMA L
Sticking contact
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 6/39 NON PROPRIETARY VERSION 3.4.4. Shock absorbing cover The containment plate around the shock absorbing cover is modelled by shell elements.
Lid screw hole tubes are modelled by shell type elements.
The orifice located at the plywood is not modelled. Therefore the plywood is distributed over a 490 mm diameter.
Gusset plate welds and the shock absorbing cover containment plate are represented to improve fitting. These welds are modelled by beam elements (2 mm diameter tubes) with a *MAT_SPOTWELD (see Appendix 1-9-4.1). An erosion criterion is defined, based upon the maximum tensile force along one direction (centreline of beam) and the maximum shear force along the other two directions (See Appendix 1-9-4.1).
The M20 shock absorbing cover attachment screws are simplified and are modelled by 17.5 mm diameter cylinders. Washers are not represented. The screw/shell interface is modelled by a sticking contact, and the screw/ring interface is modelled with a << surface to surface >> contact at the ring. The preload in each screw is applied using a *MAT_ORTHOTROPIC_THERMAL in which a coefficient of thermal expansion is defined.
3.5. Boundary conditions and loads 3.5.1. Conditions of symmetry Nodes located in the plane of symmetry have their translation degrees of freedom normal to this plane fixed, and their rotation degrees of freedom in this plane are also fixed (see figure 1-9-4.3).
3.5.2. Loads Gravity is taken into account by the application of a downwards field equal to 9.81 m.s-2.
3.5.3. Initial speed The mockup was placed at 9.15 m above the ground. The velocity of the package at the moment of impact is calculated using the following formula:
15
,9 81
,9 2
2 0
h g
V
= 13.4 m.s-1 3.5.4. Coefficient of friction The coefficient of friction used between all parts of the mockup is equal to 0.1.
Sticking contact
<< Surface to surface >> contact MAT_ORTHOTROPIC_THERMAL
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 7/39 NON PROPRIETARY VERSION The coefficient of friction used between the mockup and the non-deformable target is equal to 0.1.
3.5.5. Pre-loading of lid screws The maximum preload of M14 screws is taken to be equal to 73.8 kN, this value bounds the maximum preload of mockup lid screws equal to 61.8 kN determined in Chapter 1-5.
3.6. Materials The mechanical properties of the mockup used for the fitting calculations are given in Table 1-9-4.1.
The properties of oak and balsa used for the model of the mockup are given in Appendix 1 4.2.
The properties of plywood used for the model of the mockup are given in Appendix 1-9-4.3.
3.7. Mass balance The mass balance for the numerical model of the mockup is given in the following table:
Component Mockup (see Chapter 1-6) (kg)
Numerical model (kg)
Difference
(%)
Body (shell + bottom + resin
+
outer enclosure + trunnions) 1,920 1,920.2 0.01 Lid 320 319.4 0.2 Shock absorbing cover 180 180.2 0.1 Content 359 359 0
Total 2,780 2,778.8 0.04 The masses of the numerical model used for the fitting are representative of the masses of the mockup.
- 4. RESULTS The results are archived in <1>.
4.1. Energy balance The energy balance of the drop is presented in figure 1-9-4.6. We see that Hourglass energies and sliding energies are very low, which confirms the validity of the calculations.
4.2. Maximum accelerations The position of the accelerometers is shown in figure 1-9-4.7.
The maximum accelerations obtained in simulation are filtered using an 8 order Butterworth filter at a frequency of 1000 Hz. These accelerations and accelerations recorded during the drop tests are shown in figure 1-9-4.8. The curves recorded during the drop tests are taken from chapter 1-6.
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 8/39 NON PROPRIETARY VERSION Two curves have apparently been inverted during the test. Amplitudes from accelerometer 3Ax located on the impact side of the flange are higher than amplitudes from accelerometer 3Bx located on the shell during the shock absorbing cover impact. Physically, the amplitude of the plateau of the accelerometer closest to the shock absorbing cover (3Ax) must be higher, due to the rotation of the mockup that attenuates amplitudes of the signal captured on the shell (3Bx). Therefore these signals were inverted during the comparison between accelerations obtained in the simulation and in the test (figure 1-9-4.8).
Accelerations studied to fit the numerical model are the values obtained for the first impact (first 10 milliseconds of the simulation). Accelerations for the second impact (shell bottom) are not analysed.
The maximum accelerations for the simulation of the mockup drop are shown in the table below:
Acceleromete r (simulation)
Test signal (reference)
Maximum accelerations (t<10 ms) (g)
Differ ence
(%)
Simulations Tests (reference)
Ax 3Bx 17.5 Ay 3Ay 87.4 Bx 3Ax
-8.3 By 3By 21.7 Cx 3Cx
-9.3 Dx 3Dx
-34.3 A large difference is observed on accelerometer Ay when comparing accelerations obtained during the mockup drop and during its simulation. The noise observed on the simulation signal partly explains this difference. Furthermore, since accelerometer Ay is oriented perpendicular to the drop direction, it was not considered useful for studying crushing of the shock absorbing cover.
There are also differences on accelerometers By and Dx that are mainly due to the distance of their positions from the corresponding test accelerometers.
Accelerometers Ax (flange) and Bx (shell), oriented along the drop direction and close to the shock absorbing cover, are the most useful for studying the shock absorbing cover impact.
Differences between these accelerometers and the test are equal to +17.5% and -8.3%.
However, differences in acceleration amplitude are satisfactory and profiles from the different accelerometers are close to profiles from the test. These results are sufficient to validate the numerical model.
4.3. Deformed shape of the top shock absorbing cover after impact:
Figure 1-9-4.9 shows overall deformed shapes for the mockup and figure 1-9-4.10 shows overall deformed shapes for the shock absorbing cover. Fig. 1-9-4.12 shows details of crushing of the wood.
The following table compares measurements of deformed shapes of the shock absorbing cover derived from tests, with the results of the mockup drop simulation (measurement points shown in figure 1-9-4.11).
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 9/39 NON PROPRIETARY VERSION Test results (mm)
Calculated values (mm)
Difference
(%)
Width of dent at bottom 190 193 1.6 Dent position relative to the axis 245 252 2.9 Upper crushing 25 27 8
Lower crushing 55 70 27.3 Crushing values are satisfactory, despite a large difference of 27.3% on the lower crushing measurement. However, it is found that crushing values obtained by numerical calculation are higher than values measured during the tests, which confirms that the numerical model is conservative.
4.4. Shell deformed shape after impact Shell deformations are shown in Figure 1-9-4.13. The following table gives deformed shape measurements for fitting of the mockup drop (measurement points shown in figure 1-9-4.14).
Crushing distance (mm)
Fitting Test results Simulation values Difference Crushing at connecting weld 43 46 7%
Lower crushing 64 66 3.1%
Dent width 350 356 1.7%
The results obtained for the simulation of the mockup drop show that shell deformations are satisfactory with a maximum difference of 7% from test results; crushing values obtained by numerical calculation being slightly higher than crushing values measured during the drops.
Therefore the numerical model is more conservative than the tests.
- 5. CONCLUSIONS This study fitted the 9.15 m lateral drop No. 3 with an angle of 4.9° of the TN-MTR mockup.
The fitting made under iso-model conditions with the fitting of the oblique drop shown in Chapter 1-9-1 gives satisfactory results.
The duration and shape of the acceleration peaks obtained under simulation are representative of the test for accelerometers giving maximum accelerations. Therefore the fitting is satisfactory in terms of acceleration.
The crushed heights of the shock absorbing cover and the shell deformations measured in the simulation are higher overall than those measured during the actual drop test. Therefore the numerical model is conservative in terms of crushing.
The fitted numerical model used is representative of the behaviour of the 1/2 scale mockup of the TN--MTR packaging in lateral drop.
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 10/39 NON PROPRIETARY VERSION
- 6. REFERENCES
<1> File archiving: L\\Archivage\\08S.EMC001171T\\Dynamique\\CAL-10-00016264-003-00
<2> LS-DYNA software v971.7600.1224
<3> NX-IDEAS software m1
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 11/39 NON PROPRIETARY VERSION LIST OF TABLES Table Description Pages 1 x 4.1 Characteristics of materials used in the mockup 1
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 12/39 NON PROPRIETARY VERSION LIST OF FIGURES Figure Description Pages 1-9-4.1 Geometry of the model 1
1-9-4.2 Model meshing 1
1-9-4.3 Conditions of symmetry 1
1-9-4.4 Drop case 1
1-9-4.5 Orientation of the wood 2
1-9-4.6 Energy balance 1
1-9-4.7 Position of accelerometers 2
1-9-4.8 Accelerations 3
1-9-4.9 Overall deformed shapes 1
1-9-4.10 Shock absorbing cover deformed shapes 1
1-9-4.11 Shock absorbing cover strain measurement points 2
1-9-4.12 Crushing of wood 1
1-9-4.13 Shell deformed shapes 1
1-9-4.14 Shell strain measurement points 1
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 13/39 NON PROPRIETARY VERSION LIST OF APPENDICES Appendi x
Description Pages 1-9-4.1 Modelling of welds 1
1-9-4.2 Modelling of the wood in LS-DYNA 4
1-9-4.3 Modelling of the plywood in LS-DYNA 1
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 14/39 NON PROPRIETARY VERSION TABLE 1-9-4.1 CHARACTERISTICS OF MATERIALS USED IN THE MOCKUP Component Re (MPa)
Rm (MPa)
E (GPa)
A (%)
Shell Flange 274 583 210 59.6 Inner bottom 555 728 210 48 Outer bottom 275 565 210 66.9 Inner shell 303 568.5 210 56.5 Outer shell 275 565 210 66.9 Shell body (lead) 19 38.6 42.46
- 50 Lid Shielding enclosure (lead) 19 38.6 42.46
- 50 Flange 577.5 754 210 32 Outer shell 606 785 210 32 Stiffener shell 591.5 799 210 31.75 Inner disk 601 762 210 38 Shock absorbing cover M20 screw hole tubes 273.5 567 210 55.5 Containment plate Ring Gusset plates 277 570.2 210 50.8 Central disks 591 762 210 38 Screws M20 screws 1080 1200 210 8
M14 screws 640 800 210 12
- Numerical data for lead, F. WILMOTTE, Engineering Techniques, Form. M513
TN International Ref.: DOS-06-00032593-194 Rev. 0 Page 15/39 NON PROPRIETARY VERSION FIGURE 1-9-4.1 GEOMETRY OF THE MODEL General overview of model
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 16/39 NON PROPRIETARY VERSION FIGURE 1-9-4.2 MODEL MESH Global view
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 17/39 NON PROPRIETARY VERSION FIGURE 1-9-4.3 CONDITIONS OF SYMMETRY Degrees of freedom fixed for nodes in the plane of symmetry Nodes constrained in the plane of symmetry Dx=free Rx=0 Dy=free Ry=0 Dz=0 Rz=free
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 18/39 NON PROPRIETARY VERSION FIGURE 1-9-4.4 DROP CASE Fitting Drop angle and initial velocity Packaging-target distance 4.9° RIGIDWALL Horizontal Target-packaging distance=26.9mm INITIAL VELOCITY
=13.4 m/s (Normal to the impact plane)
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 19/39 NON PROPRIETARY VERSION FIGURE 1-9-4.5 (1/2)
ORIENTATION OF THE WOOD Orientation of the wood: balsa Orientation of the wood: upper oak
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 20/39 NON PROPRIETARY VERSION FIGURE 1-9-4.5 (2/2)
ORIENTATION OF THE WOOD Orientation of the wood: lower oak and plywood
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 21/39 NON PROPRIETARY VERSION FIGURE 1-9-4.6 ENERGY BALANCE Fitting Overall energy balance
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 22/39 NON PROPRIETARY VERSION FIGURE 1-9-4.7 (1/2)
POSITION OF ACCELEROMETERS Ax Ay Bx By Cx Dx
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 23/39 NON PROPRIETARY VERSION FIGURE 1-9-4.7 (2/2)
POSITION OF ACCELEROMETERS Position of accelerometers A and B Position of accelerometers C and D 446.7 658.5 Ax Ay Bx By (84050)
(14803) 80 157 Packaging centreline Cx Dx (488248)
(494122)
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 24/39 NON PROPRIETARY VERSION FIGURE 1-9-4.8 (1/3)
ACCELERATIONS Fitting Accelerometer Ax (simulation) with signal 3Bx (test reference)
Accelerometer Ay (simulation) with signal 3Ay (test reference)
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 25/39 NON PROPRIETARY VERSION FIGURE 1-9-4.8 (2/3)
ACCELERATIONS Fitting Accelerometer Bx (simulation) with signal 3Ax (test reference)
Accelerometer By (simulation) with signal 3By (test reference)
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 26/39 NON PROPRIETARY VERSION FIGURE 1-9-4.8 (3/3)
ACCELERATIONS Fitting Accelerometer Cx (simulation) with signal 3Cx (test reference)
Accelerometer Dx (simulation) with signal 3Dx (test reference)
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 27/39 NON PROPRIETARY VERSION FIGURE 1-9-4.9 OVERALL DEFORMED SHAPES Fitting Overall deformed shape t = 20 ms Impacted face (270° line). t = 20 ms
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 28/39 NON PROPRIETARY VERSION FIGURE 1-9-4.10 SHOCK ABSORBING COVER DEFORMED SHAPES Fitting Shock absorbing cover deformed shape: side view. t = 20 ms Shock absorbing cover deformed shape: trunnion recess. t = 20 ms
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 29/39 NON PROPRIETARY VERSION FIGURE 1-9-4.11 (1/2)
SHOCK ABSORBING COVER STRAIN MEASUREMENT POINTS Fitting Width of dent at bottom (along the Z direction of the global coordinate system). t = 20 ms Width of dent relative to the axis (along the Z direction of the global coordinate system). t = 20 ms z
y Packaging centreline 253 192+1=193 z
y
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 30/39 NON PROPRIETARY VERSION FIGURE 1-9-4.11 (2/2)
SHOCK ABSORBING COVER STRAIN MEASUREMENT POINTS Fitting Crushing depths (measured along the X direction of the local coordinate system). t = 20 ms 27 70 Local coordinate system (nodes 158980-221003-158978)
X
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 31/39 NON PROPRIETARY VERSION FIGURE 1-9-4.12 CRUSHING OF WOOD Fitting Crushing of wood. t = 20 ms Detail of the most highly loaded wood parts. t = 20 ms
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 32/39 NON PROPRIETARY VERSION FIGURE 1-9-4.13 SHELL DEFORMED SHAPES Fitting Crushing of shell. t = 20 ms Crushing of shell: bottom view. t = 20 ms FIGURE 1-9-4.14
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 33/39 NON PROPRIETARY VERSION SHELL STRAIN MEASUREMENT POINTS Fitting Crushing of the shell (measured along the X direction in the local coordinate system defined in figure 0).. t = 20 ms Width of dent (along the Z direction of the global coordinate system). t = 20 ms At weld At bottom 46 66 178
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 34/39 NON PROPRIETARY VERSION APPENDIX 1-9-4.1 MODELLING OF WELDS The above figure shows modelling of welds.
The rule used to model them is presented below. This rule is based upon *MAT_SPOTWELD:
Description Unit value RO Density kg/m3 The directions R, S and T are defined as described above (No distinction between S & T)
E Young's modulus Pa (1)
PR Poisson's ratio SIGY Yield stress Pa (2)
ET Tangent modulus Pa NRR Maximum tensile force N
(3)
NRS Maximum shearing force following S in the plane perpendicular to R N
(3)
NRT Maximum shearing force following T in the plane perpendicular to R N
(3)
MRR Maximum moment following R N.m MSS Maximum moment following S N.m MTT Maximum moment following T N.m (1) The Young's Modulus in question is that of the steel, divided by 10 in order to avoid adding mass to these extremely short elements (~1mm in length). This assumption has no impact on the results as the material is considered elastic and the size of the element is small. Thus, regardless of the force considered, the stretch will be low in comparison with other elements making up the model.
(2) Values selected to ensure that the element remains elastic.
(3) 3 2
0 0
S rational R
NRS S
al convention R
NRR m
m
where tion element S
sec 0
The other values are the default values.
APPENDIX 1-9-4.2 (1/4)
R T
S
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 35/39 NON PROPRIETARY VERSION MODELLING OF THE WOOD IN LS-DYNA The modelling used to model the behaviour of wood is as follows:
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 36/39 NON PROPRIETARY VERSION APPENDIX 1-9-4.2 (2/4)
MODELLING OF THE WOOD IN LS-DYNA Fitting Scope Parameter Formula LS-Dyna parameter Unit Value for Oak Value for the balsa density RO kg/m3 630.8 130.2 Orthotropic elastic behaviour:
Young's modulus // to fibres L
E E
1,1
//
(1)
EAAU = E //
GPa 16.28 2.35 Young's modulus to fibres
L R
L T
L E
E E
E moy E
E 1,1 (1)
EBBU = ECCU =
E GPa 1.683 0.0355 Shear modulus //
to fibres
L LT L
LR E
G E
G moy E
G
//
//
(1)
GABU = GCAU =
G//
GPa 1.118 0.106 Shear modulus to fibres L
RT E
G E
G
//
(1) or if not available min min
/
/
//
(*)
G G
G G
GBCU = G GPa 0.2674 0.0118 Perfectly plastic orthotropic behaviour (tension +
compression):
Crushing stress // to fibres See the red curve above LCB (see the definition below)
Crushing stress // to fibres at start of plateau See the blue curve above LCC (see the definition below)
Compressd material:
elastic isotropic behaviour -
perfectly plastic Maximum compression ratio cellulose wood c
1
cellulose wood VF
42 20(3)
Young's modulus Ec= 35 GPa for a load //
= 10 GPa for a load (taken from (2))
E = EC GPa 35 35 (radial wood) 10 (axial wood)
Poisson's ratio
= 0.3 (taken from (2))
PR =
0.3 0.3 Yield stress y = 120 MPa for a // load
= 150 MPa for a load (taken from (2))
SIGY = y (MPa) 120 120 (radial wood) 150 (axial wood)
Viscosity
= 0.05 (default value)
MU =
0.05 0.05 (1) Characteristics taken from the Wood Handbook (2) Thesis by C. ADALIAN: "The behaviour of wood during multi-axial dynamic compression - Applications to the simulation of container crashes".
(3) Value defined for the fitting.
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 37/39 NON PROPRIETARY VERSION APPENDIX 1-9-4.2 (3/4)
MODELLING OF THE WOOD IN LS-DYNA Fitting Scope Parameter Formula LS-Dyna parameter Value for Oak Value for the balsa Influence of crushing stress/angle To add a stress figure dependant on angle using the LCA curve.
Here the curve is zero regardless of the angle LCA = "nil" curve Shear rupture Shear rupture max = [200% - 1000%]
Very high values (such rates are far higher than those that the wood could reach)
SSEF = [2 - 10]
10 10 Shear rupture // to fibres
//
Damage defined subsequently LCAB=LCCA (see definition below)
Shear rupture to fibres No damage LCBC (unitary curve)
The LCB curve is defined as follows:
Formula Value for Oak Value for the balsa
(-)
(MPa)
(-)
(MPa)
(-)
(MPa)
Perfectly plastic orthotropic behaviour in tension
-1.00
Vf y
t
)1(
//
-1.00 50.46
-1.00 24 (radial wood) 30 (axial wood)
-1e-4
-1e-4 50.46
-1e-4 24 (radial wood) 30 (axial wood)
Perfectly plastic orthotropic behaviour in compression 0.0
//
1
0.0 53 0.0 12
-ln(1-max //)
+ 0.5 0.53 54 1.43 12.5 For oak:
cellulose wood
ln For balsa:
vf ln y = 120 MPa for a // load
= 150 MPa for a load (taken from (2))
0.87 120 1.61 120 (radial wood) 150 (axial wood)
(1) Characteristics taken from the Wood Handbook (2) Thesis by C. ADALIAN: "The behaviour of wood during multi-axial dynamic compression - Applications to the simulation of container crashes".
//
1
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 38/39 NON PROPRIETARY VERSION APPENDIX 1-9-4.2 (4/4)
MODELLING OF THE WOOD IN LS-DYNA Calibration The LCC curve is defined as follows:
Formula Value for Oak Value for the balsa
(-)
(MPa)
(-)
(MPa)
(-)
(MPa)
Perfectly plastic orthotropic behaviour in tension
-1.00
1
t or
1
t
(*) if not available in (1)
-1.00 5.5
-1.00 1.4
-1e-4
-1e-4 5.5
-1e-4 1.4 Perfectly plastic orthotropic behaviour in compression 0.0
1
0.0 11 0.0 1.4
-ln(1-max )
2
0.42 35 0.76 2.5 For oak:
For balsa:
vf ln y = 120 MPa for a // load
= 150 MPa for a load (taken from (2))
0.87 120 1.61 120 (radial wood) 150 (axial wood)
(1) Characteristics taken from the Wood Handbook (2) Thesis by C. ADALIAN: "The behaviour of wood during multi-axial dynamic compression - Applications to the simulation of container crashes".
The curves LCAB and LCCA are defined uniquely for all types of wood using the following curve:
Deformation in shear
(-)
Stress multiplier
(-)
0.0 1.0 0.05 1.0 0.06 0.99 cellulose wood ln
TN International Ref.: DOS-18-011415-019-NPV Rev. 1.0 Page 39/39 NON PROPRIETARY VERSION APPENDIX 1-9-4.3 MODELLING OF THE PLYWOOD IN LS-DYNA Plywood
- Density (kg/m3)
Young's modulus E of compressed material (MPa)
Poisson's ratio for compressed material Yield stress of compressed material (MPa)
Relative compacted volume VF = Vcompacted/ Vinitial
(%)
Young's modulus E // fibres of the non-compressed material (MPa)
Young's modulus E fibres of the non-compressed material (MPa)
Shear modulus G // fibres (MGPa)
Shear modulus G fibres (MPa)
Behaviour in crushing // fibres Volume deformation Crushing stress (MPa)
Crushing behaviour fibres Volume deformation Crushing stress (MPa)
Reference volume VREF LS-DYNA behavioural rule
- MAT_MODIFIED_HONEYCOMB (2) Values taken from NTC-07-00088449 Rev.0: "Sensitivity analysis on plywood properties in the top shock absorber of TN 81 1/3 scale model"