Formula student Racing Team Eindhoven

Crash Safety

MT06.10 Dr. Ir. Witteman M.T.J.Fonteyn March 2006

1

Contents

Chapter Page 1. Minimum requirements 1.1 Reference material 2. 1.2 Dimensions tubing 2. 1.3 Strength in buckling 3. 1.4 Strength in bending 4. 1.5 Strength in tension 5. 1.6 Buckling modulus 5. 1.7 Energy dissipation 5. 1.8 Marc mentat simulation 6. 2. Side impact protection Design 1 2.1 Material and dimensions 7. 2.2 Strength in buckling 8. 2.3 Strength in bending 9. 2.4 Strength in tension 9. 2.5 Buckling modulus 10. 2.6 Energy dissipation 10. Design 2 2.7 Material and dimensions 11. 2.8 Strength in buckling 12. 2.9 Strength in bending 13. 2.10 Strength in tension 13. 2.11 Buckling modulus 14. 2.12 Energy dissipation 14. 3. Front impact protection 3.1 Material impact attenuator 15. 3.2 Design Impact attenuator 16. 4. Material test honeycomb sandwich 4.1 Compression test 19. 4.2 Bending test 20. 5. Appendix A 21. Appendix B 22.

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1. Minimum requirements In this chapter some key values are given and determined for the tubes mentioned as minimum requirements in the rules 2006. With these values a comparison is made between the safety of the FSRTE chassis and the ‘standard’ frame made out of tubes. First the reference material properties and dimensions of the tubes are given. Then the behavior in buckling, bending and tension are investigated. Finally the buckling modulus and energy dissipation are considered. 1.1 Reference material Steel 4130 is used a lot for safety cages, roll bars and many other tube constructions. Many other teams use tubes of steel 4130. So it seems a good choice to compare our construction to tubes of this material. In table 1.1 the material properties of steel 4130 can be found.

Table 1.1 Steel 41301

Yield strength 435 MPa Ultimate strength 670 Mpa Modulus of Elasticity 205 GPa Poisson’s ratio 0.29 Density 7850 kg/m3

1.2 Dimensions tubing The dimensions of the steel tubes are also given in the rules 2006. They are mentioned in table 1.2.

Table 1.2 Dimensions

Outside Diameter Wall Thickness Main & Front Hoops 25.4 mm 2.4 mm Side impact structure, Bulkhead, Roll hoop bracing

25.4 mm 1.65 mm

Front bulkhead support 25.4 mm 1.25 mm The side impact protection of the FSRTE-car will be compared with 3 tubes of a length of 0.52 m because this would be the average length of the upper and lower impact member if the FSRTE car was build out of tubes. (see fig. 1.1) So it is also the average length (distance between the main and front hoop) of the side impact protection of the FSRTE car. This is a safe approximation because the average length of the three impact members is larger as result of the diagonal orientation of the middle impact member. The diagonal member is also the weakest tube of the side impact protection. A length of 0.35 m is chosen, because this is a suitable length to make a comparison with the front bulkhead (See chapter 3). Fig. 1.1 Side impact protection

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. 1.3 Strength in buckling The tube is being considered as a beam that is built in with both ends. The critical buckling force2 is given by:

2

2

el

IEP

⋅⋅= π (eq. 1.1)

With: E = Modulus of Elasticity I = Area moment of inertia le = The effective length. The area moment of inertia should be taken about the axis perpendicular on the axial axis. The area moment of inertia2 can be calculated by using the next equation:

64

)( 440 iDDI−⋅= π (eq. 1.2)

With: Do = Outside diameter Di = Inside diameter The effective length2 is given by:

2

lle = (eq. 1.3)

With: l = Length of the beam Now the critical buckling force is known, it is possible to calculate the critical buckling stress.

A

Pc =σ (eq. 1.4)

2)( ioc RR

P

−⋅=

πσ in case of a tube.

With: A = the cross-sectional area of the Tube. In table 1.3 the results of the calculations, mentioned above, are given.

2 Roger T Fenner, Mechanics of solids

4

Table 1.3 Results buckling

Description Length Value Area moment of inertia - 8.7222e-9 m4

Cross section area - 1.231e-4 m^2 Effective length 0.35 m 0.175 m Effective length 0.52 m 0.260 m Critical buckling force 0.35 m 5.762e5N Critical buckling force 0.52 m 2.610e5 N Critical buckling stress 0.35 m 4.681 GPa Critical buckling stress 0.52 m 2.120 Gpa 1.4 Strength in bending Instead of the case of buckling, for bending the assumption is made that the side impact members are simple supported. The assumptions that the beams are simple supported gives a better approximation for the tube. This is supported with simulations in marc-mentat. (see paragraph 1.7) Also the tube of 0.35 m is best approximated as a simple supported tube. The magnitude of the maximum stress3 in bending is given by:

I

Mc ⋅=maxσ (eq. 1.5)

With: c = The utmost fiber distance M = Bending moment The neutral axis is aligned with the central axis of the tube so utmost fiber distance is given by half of the outside diameter, so c=12.7mm. When the force F is applied on the middle of the beam the bending moment is given by:

2

lFM ⋅= (eq. 1.6)

For maxσ the yield strength 435Mpa is taken to calculate the yield strength in bending. To calculate the ultimate strength in bending 670Mpa is taken for maxσ . The forces for which the yield strength and ultimate strength will be reached are calculated and presented in table 1.4. The results about the strength in bending are presented in table 1.4. Table 1.4 Results bending

Description Length Maximum bending moment

Maximum Force

0.35 m 299 Nm 1707 N Yield strength 435Mpa 0.52 m 299 Nm 1149 N

0.35 m 460 Nm 2629 N Ultimate strength 670Mpa 0.52 m 460 Nm 1770 N

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1.5 Strength in tension When the described tube would be tested during a tensile test the material would start necking when the ultimate strength is reached. The engineering stress can be calculated with the following equation:

0A

Fe =σ (eq. 1.7)

The yield strength will be reached by a force of 53.56 KN. The force for which the ultimate tensile strength will be reached will be 82 KN 1.6 Buckling Modulus It is also required the compare the buckling modulus of the FSRTE design with the tubing frame. The buckling modulus3 is given by:

IEBM ⋅= (eq. 1.8) The buckling modulus of the tube is 1788 Pa.m4. 1.7 Energy dissipation A comparison of the dissipated energy is also required. The calculations are made for elastic deformation because the values of plastic deformation can’t be calculated due to strain hardening and other effects which occur with plastic deformation. During bending the tube dissipates energy. The energy that is being dissipated4:

dFEd ⋅= (eq. 1.9) With: d = Displacement of the beam. The assumption is made that the side impact structure and the bulkhead tubes can be approximated as simple supported beam. (see paragraph 1.7) The displacement of a simple supported beam is given by:

IE

lFxd

⋅⋅⋅=

48)(

3

The displacement of a beam5 that is built in with both ends is given by:

3

33

3

)()(

lIE

xxlFxd

⋅⋅⋅−⋅= (eq. 1.10)

With: x = position on the beam The force F is applied on the middle of the beam because this causes the greatest displacement.

3 Rule 3.3.3.2.1 4 Douglas C. Giancolli, Physics for scientists and engineers 5 Roger T. Fenner, Mechanics of Solids

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For the simple supported tube of 0.52 m this results in a displacement of 1.882466e-3 m when a force of 1149 N is applied. This is the maximum force without causing plastic deformation of the tube. This gives an energy dissipation (in fact storage) of 2.16304 J. For the tube with length 0.35m with both end built in the displacement is 2.13204e-4 m when a force of 1707 N is applied. The displacement is 8.528e-4 m in case of a simple supported beam. This means respectively an energy dissipation of 0.3639J and 1.4559 J. Although these values are very low they give an estimation of which structure will perform better with energy dissipation. 1.8 Marc-mentat simulation. A simulation in Marc Mentat is performed to determine the best approximation of the side impact members. In figure 1.2 the side impact tube frame is shown. The frame used in the simulation is build in approximately the same dimensions as the FSRTE design. It is most likely that in case of a collision more than one side impact member is hit. In this simulation a force on the lowest two members is applied. The forces are so calculated that the displacement of each tube would be the same if they where simple supported. The results of this simulation can be found in table 1.5:

figure 1.2 Marc mentat simulation side impact structure Table 1.5 Force applied on two lower tubes. Part Length Force Hand calculated

displacement: Ends build in

Hand calculated displacement: Simple supported

Displacement calculated with Marc mentat

Middle member

0.649 m 443 N 0.00035 m 0.00140 m 0.00111 m

Lower member

0.450 m 1328 N 0.00035 m 0.00140 m 0.00100 m

It is clear that de displacement in simulation is much higher than in case of a build in tube. When a force is applied on all side impact members the situation is even worse. The force acting on de side impact members results in torsion of the hoops which leads to a higher deformation of the members. It better to assume that the beams are simple supported. Also the tube of 0.35 m is best approximated as a simple supported tube. The results of this approximation are less similar as for the side impact tubing. For the comparison this wouldn’t be a problem because the rear bulkhead of the FSRTE car is similar to bulkhead constructed out of tubes.

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2. Side impact protection In this chapter three steel tubes mentioned in chapter 1 will be compared to two different designs for the side impact structure of the FSRTE car, shown in figures 2.1 and 2.2. This will be done for yield and ultimate strength in bending, for buckling and tension, and also the buckling modulus and the energy dissipation. Design 1 Initially an impact protection on the outside of the car was designed. It is build out of 2 aluminum bars with a honeycomb sandwich (rest material) on it. The advantages are:

- Outside protection doesn’t reduce driver’s space inside of the car. - The structure of the chassis isn’t damaged after a crash on the impact protection. - The structure can be easily fixed and replaced after a crash. - Easy to compare with tube frame, strength can be easily calculated. - The honeycomb structure absorbs impact energy. - Easy to produce.

Disadvantage

- It doesn’t look very nice when the cover of the car is removed. - Honeycomb sandwich is pretty expensive.

2.1 Materials and dimensions

Figure 2.1 Figure 2.2 The side impact protection consists out of two Materials. The sandwich panel is made of aluminum 5005a, the same material as which the car is built of. The skins have a thickness of 0.5 mm; the honeycomb core 9 mm. The I-shaped bars of the impact protection are built of a strong aluminum plate, 7075 T651 with a thickness of 2 mm. The components will be glued and popped together. The construction will be fixed with bolts on the main and front hoops. The total height of the construction is 250 mm, so the ground clearance will be at least 300mm. In table 2.1 and 2.2 the material properties can be found.

sandwich

bar

Bolt

30 mm

3 mm

Main/front-Hoop

Car

8

Table 2.1 Aluminum 5005A, outside. 6

Yield strength 210 Mpa Ultimate strength 225 Mpa Modulus of Elasticity 69.5 Gpa Density 2700 kg/m3 Table 2.2 Aluminum 7075 T651, inside. 7

Yield strength 505 Mpa Ultimate strength 570 Mpa Modulus of Elasticity 72 Gpa Density 2810 kg/m3

A beam with a construction as shown in figure 2.3 will be compared to tree tubes mentioned in chapter 1. The beam and tubes will have a length of 0.52 m.

Figure 2.3

2.2 Strength in buckling The area moment of inertia of the side impact protection can be calculated with eq. 2.1. The area moment of inertia should be calculated about the z-axis, for bending in y-direction, because it is the weakest direction. In case of buckling it will buckle in y direction. This direction represents also the direction of a side impact. The area moment of inertia of the side impact protection can be calculated with:

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3hbI z =

( )2'' zAII zz += (see appendix A) It is possible to calculate the critical buckling force and critical buckling stress with respectively eq 1.1 and eq. 1.4. For safety the assumption is made that the construction is simple supported at both ends. The result of these calculations can be found in table 2.3. For the modulus of elasticity the value of the weakest material, aluminum 5005a is taken, because this delivers the worst result. So it gives a safe comparison.

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Table 2.3 Results Buckling

Description Value FSRTE-car Simple supported Area moment of inertia side impact construction 1.713e-7 m^4

Cross section area 5.140e-4 Effective length 0.520 m Critical buckling force 1.304e6 N Critical buckling stress 2.537 GPa 3 Tubes Tubing frame Both ends built in Critical buckling force 7.830e5 N Critical buckling stress 2.120 Gpa Although the tubes are calculated as build in tubes and the FSRTE-structure is calculated as simple supported, the FSRTE structure performs better. 2.3 Strength in bending Again it is possible to calculate the bending moment and the maximum bending stress with equations 1.5 en 1.6. The results can be found in table 2.4. The load is 4200 N and the utmost fiber distance is 5.5e-3 m. The maximum bending stress in the sandwich material is lower than the maximum bending stress in the tube mentioned in paragraph 1.3. This means the sandwich material can take a higher load before the same stress appears. Table 2.4 Results bending Description Length Maximum bending

moment Maximum Force

Construction FSRTE Yield strength 210 MPa 0.52 m 1456 Nm 5602 N Ultimate strength 225 Mpa 0.52 m 1560 Nm 6002 N 3 Tubes of tubing Frame Yield strength 435 MPa 0.52 m 897 Nm 3447 N Ultimate strength 670 Mpa 0.52 m 1380 Nm 5310 N 2.4 Strength in tension With equation 1.7 the tension force can be calculated. When the assumption is made that the entire construction is made of aluminum 5005a, the yield strength will be reached by a force of 108 KN. The ultimate tensile strength will be reached by a force of 116 KN. For the two I-bars of aluminum 7075 this is respectively 133KN and 150 KN. For 3 tubes this will be respectively 161 and 248 N. So the side impact protection does not satisfy this requirement. This is not necessary because the protection is fixed parallel to the body of the car. The car is made of plates and these will conduct most of the stresses in this direction. 2.5 Buckling modulus The buckling modulus calculated with equation 1.8 is 11905 Pa.m^4. The E-modules of the weakest material is taken. The buckling modulus of 3 tubes as calculated in paragraph 1.5 is 3*1788 =5364 Pa.m^4.The buckling modulus of the sandwich material is better than those of a tube as calculated in paragraph 1.5. 2.6 Energy dissipation The displacement of the beam due to a load can be calculated with equations 1.10 and 1.11 for respectively a beam built in with both ends and a simple supported beam. Also here the modulus of elasticity of aluminum 5005a is taken.. The energy dissipation is calculated using eq. 1.9. The results can be found in table 2.5. Table 2.5 Results energy dissipation

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Description Value FSRTE Structure Displacement, simple supported 1.882e-3 m Force center beam. 7649 N Energy dissipation, simple supported 14.395 J 3 tubes tubing frame Displacement, simple supported 1.882e-3 m Energy dissipation, simple supported 6.489 J The energy dissipation is lower than the energy dissipation in a tube when subjected to the same force. This means that the sandwich material can be subjected to a higher force to reach the same energy dissipation.

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Design 2 The second and definitive design is a protection on the inside on the car. It “looks more professional” but it is pretty much work to make.

2.7 Materials and dimensions

Fig 2.4

Fig 2.5 The side impact protection consists out of two Materials. The outer side of the protection is the aluminum 5005a sandwich material which the car is build of. The skins will have a thickness of 0.5 mm; the honeycomb core 9 mm. The inner side of the impact protection is build of a strong aluminum plate, eg 7075 T651 with a thickness of 1.5 mm. The construction is reinforced with braces as shown in figure 2.1. The components will be glued and popped together. The total height of the construction is 250 mm, so the ground clearance will be at least 300mm. In table 3.1 and 3.2 the material properties can be found. For the calculations the assumption is made that the entire construction is build of aluminum 5005a.

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The calculations are made for a beam with the dimensions showed in the figure below, but in fact it isn’t a beam but a part of the construction.

Fig 2.6 cross section side impact protection Table 2.6 Aluminum 5005A, outside. Yield strength 210 Mpa Ultimate strength 225 Mpa Modulus of Elasticity 69.5 Gpa Density8 2700 kg/m3 Table 2.7 Aluminum 7075 T651, inside. Yield strength 505 Mpa Ultimate strength 570 Mpa Modulus of Elasticity 72 Gpa Density 2810 kg/m3

A beam with a construction as shown in figure 3.2 will be compared to tree tubes mentioned in chapter 1. The beam and tubes will have a length of 0.52 m.

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2.8 Strength in buckling The area moment of inertia of the side impact protection can be calculated with eq. 2.1. The area moment of inertia should be calculated in y-direction, (bending about z-axis) because this is the weakest direction. It represents also the direction of a side impact. (See appendix B) Again, it is possible to calculate the critical buckling force and critical buckling stress with respectively eq 1.1 and eq. 1.4. The assumption is made that de construction is simple supported because thee inner side of the construction is supported by the outer side of the construction, so in fact it is not fixed at the ends. The result of these calculations can be found in table 2.8. For the modulus of elasticity the value of the weakest material, aluminum 5005a is taken, because this delivers the worst care result. So it gives a safe comparison. Table 2.8 Results Buckling

Description Value FSRTE-car Simple supported Area moment of inertia side impact construction 8.86e-7 m^4

Cross section area 8.00e-4 Effective length 0.520 m Critical buckling force 2.248e6 N Critical buckling stress 2.810 GPa 3 Tubes Tubing frame Both ends built in Critical buckling force 7.830e5 N Critical buckling stress 2.120 Gpa Although the tubes are calculated as build in tubes and the FSRTE-structure is calculated as simple supported, the FSRTE structure performs better. 2.9 Strength in bending Again it is possible to calculate the maximum bending moment and force for which the yield strength and ultimate tensile strength are reached.(equations 1.5 en 1.6.) For the utmost fiber distance 63 mm is chosen. That is the distance between neutral axis and the outer side of the construction. The utmost fiber distance at the inner side of the construction is almost infinite because the floor of the car makes part of it. The results of the calculations can be found in table 2.9. The maximum force and bending moment that the construction of the FSRTE-car can withstand is higher than the maximum force and moment of three the tubes of the tubing frame mentioned in paragraph 1.3. This means the construction can withstand an impact with higher velocity. Table 2.9 Results bending Description Length Maximum bending

moment Maximum Force

Construction FSRTE Yield strength 210 MPa 0.52 m 2953 Nm 11359 N Ultimate strength 225 Mpa 0.52 m 3164 Nm 12170 N 3 Tubes of tubing Frame Yield strength 435 MPa 0.52 m 897 Nm 3447 N Ultimate strength 670 Mpa 0.52 m 1380 Nm 5310 N 2.10 Strength in tension With equation 1.7 the tension force can be calculated. The yield strength will be reached by a force of 168 KN. The ultimate tensile strength will be reached by a force of 180 KN. For 3 tubes this will be respectively 161 and 248 N. The FSRTE structure satisfies the requirement. .

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2.11 Buckling modulus The buckling modulus calculated with equation 1.8 is 61577 Pa.m^5. The Lowest E-modulus is taken for a safe approximation. The sum buckling moduli of three tubes from the tubing frame is 5364 Pa m^4. The resistant against buckling of the FSRTE-car side impact protection is higher than the resistant against buckling of the tubing frame. 2.12 Energy dissipation The energy dissipation can be calculated with equations 1.9 and 1.10. The force F is applied on the middle of the beam because this causes the greatest displacement. For the simple supported tube of 0.52 m a displacement of 1.882e-3 meter leads to a energy dissipation of 2.163 w, so three tubes will dissipate 6.489 J. To deform the FSRTE structure 1.883e-3 m a force of 39.569 KN has to be applied. The energy dissipation with this displacement will be 74.484 J. The FSRTE-car structure offers a higher resistant against deformation, so the energy dissipation will be higher with a same deformation. Table 2.10 Results energy dissipation Description Value FSRTE Structure Displacement, simple supported 1.882e-3 m Force on center beam. 39561 N Energy dissipation, simple supported 74.484 J 3 tubes tubing frame Displacement, simple supported 1.882e-3 m Energy dissipation, simple supported 6.489 J The energy dissipation is lower than the energy dissipation in a tube when subjected to the same force. This means that the sandwich material can be subjected to a higher force to reach the same energy dissipation.

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3 Front impact protection The impact attenuator is designed to keep the average deceleration in a crash under a certain level. FS 2006 requires for the impact attenuator to keep the average deceleration under 20 g if it is fixed on a car of 300 kilograms which crashes on a rigid object with a velocity of 7 m/s. The impact attenuator has to be fixed directly on to the front bulkhead. The impact attenuator has to be at least 0.15 meter long, 0.20 meter width and 0.10 meter high and must be able to withstand an off-axis crash. The frontal area of the bulkhead is 0.122 m2 3.1 Material impact attenuator The function of an impact attenuator is to decelerate the car in a safe way and dissipate as much of the crash energy as possible. The average deceleration is has to be kept under a certain level and it is desirable to keep the maximum deceleration low enough to prevent damage on the structure of the car and the driver. It is important to keep the impact attenuator as light and small as possible. The required time to decelerate a car from 7m/s to 0m/s with a constant deceleration of 20 g is 35.7ms. The deformed length during deceleration is 0.125 meter. To keep the impact attenuator short it is important that the material can be compressed as much as possible. When a material can be compressed for 70%, the length of the impact attenuator has to be at least 0.18 meter. Table 3.1 material properties.

Material Density/compressive strength

Max compression

Airex R63 82 85% Delivery time 6 months Herex Airex C70.75 62

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Table 3.2 Properties ROHACELL ROHACELL Compression strength Max compression Density IG31 0.25 MPa 73% 32 Kg/m^3 IG51 1.00 MPa 72% 52 Kg/m^3 IG71 1.50 MPa 72% 75 Kg/m^3 IG110 ±2.7 MPa 70% 110 Kg/m^3 3.2 Design impact attenuator First an impact attenuator with the minimum dimensions was designed. It was just a simple block with the dimensions 0.17x0.20x0.10 meter. It saves space and money, but a pretty heavy construction to fix the block on the bulkhead was needed. So another design with a higher safety/ weight ratio was desirable. To fix the impact attenuator without heavy stiff parts it should cover the entire front bulkhead. It should be designed so that it fits in the cover of the car and a block with the minimum required dimensions just in it. A design was made in unigraphics and is shown in figure 3.1a and 3.1b The shape makes it possible to give an acceptable protection at different impact speeds without making it too large. The higher the impact speed the higher the area of the part that deforms, so the average deceleration will increase with impact speed. The volume is 0.01233 m3. To prevent penetration of the foam by sharp objects an aluminum plate can be fixed in the attenuator.

Fig. 3.2a Impact attenuator Fig. 3.2b Impact attenuator The length in x direction is 0.24 meter. To make it possible to determine a suitable density of the foam and make calculations on the deceleration a function of the cross-section area is calculated.

0 0.05 0.1 0.15 0.2 0.250

0.02

0.04

0.06

0.08

0.1

0.12

0.14Cross-section area impact-attenuator

cross section [m]

Cro

ss s

ectio

n ar

ea [

m2]

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Fig. 3.3 Cross section area impact attenuator The formula for the cross-section area as function the position x is:

xxA 3140.07806.0 2 += (eq 3.1) The area that deforms varies with the deformation x. The force during deformation can be easily calculated with:

)()( xAxF ⋅= σ (eq 3.2) With σ = stress during compression. A= Cross section area of the compressed material. This would be true if the material was compressible for 100%. The material can be compressed up to 72% with a constant stress. When the material will be compressed further the stress will increase. The assumption is made that the material can be compressed at most for 72%. This is a safe approximation because the material can deform further so it will dissipate more energy than is calculated. With this assumption the material will be rigid when a compression rate of 72% is reached, so the attenuator can be compressed for 0.173 meter. The formula of force during deformation has to be scaled to this value. The force during compression can be written as:

+=72.0

3140.0)72.0

(7806.0)( 2xx

xF σ (eq 3.3)

0 0.05 0.1 0.15 0.20

50

100

150

200

Compression [m]

com

pres

sion

for

ce [

KN

]

Compression force impact attenuator

Fig. 3.4 Compression force impact attenuator ROHACELL IG71 In case of Rohacell IG71 is gives:

[ ]xxexF 4361.05058.165.1)( 2 += (eq 3.4)

Integration of this function gives the dissipated kinetic energy during deformation

[ ]23 21805.0519.065.1 xxe +=Ε (eq 3.5)

The energy that has to be dissipated by a crash with 7 m/s is 7350 J

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The deceleration of the car in g can be calculated with:

81.9)(

⋅=

m

xFonDecelerati [g] (eq 3.6)

The maximum deformation at 7m/s can be solved from eq. 3.5 and will be X=0.13 m The average deceleration during deformation from 0 to X in g can be calculated with:

dxm

xF

X

X

∫ ⋅0 81.9)(1

(eq 3.7)

With X the total deformation. The average deceleration in case of a crash with 7 m/s is 19.2 g so it satisfies the requirement of 20 g. The attenuator can dissipate 13.7 KJ, the kinetic energy of the car with velocity of 9.6 m/s. The average deceleration in this case will be about 27g.

0 0.05 0.1 0.150

10

20

30

40

50

60

70

Compression [m]

Dec

eler

atio

n [g

]

Deceleration Car

7 m/s, average deceleration: 19.2 g

9.6 m/s, average deceleration: 27.4 g

Fig. 3.5 Deceleration car.

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4 Material test honeycomb sandwich

To get an idea of the strength of the sandwich material of the FSRTE car a bending test and a compression test is performed. 4.1 Compression test The given properties of the material are not the properties of this material but the properties of a similar material from another manufacturer. Given Measured Compression modulus 634 MPa 108 MPa Compression strength 2.34 MPa 1.46 MPa The measured strength could be lower than the real strength because the sample was relative small to the honeycomb structure. So relatively much of the structure is damaged at the sample boundaries. The difference between measured values and given values are significant.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1000

2000

3000

4000

5000

6000

7000

8000Compression Test Sample 70 x 70 mm

Compression [mm]

Com

pres

sion

for

ce [

N]

20

4.2 Bending test

Calculated Measured Area moment of inertia 8.32e-10 m^4 9.94e-10 m^4

0 0.5 1 1.5 2 2.5 3 3.50

100

200

300

400

500

600

Deflection [mm]

For

ce [

N]

Bending Test sample 242 x 70 mm

Data is measured in linear part of the curve. Calculated results pretty similar to measured results.

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Appendix A

120

( ) ( ) ][10725.3001.0015.0002.0020.0212

002.0020.02

12

026.0002.0 48233

mIzA

−⋅=−⋅⋅⋅+⋅⋅+⋅=

][10971.212

)0095.0010.0(25.0 4933

mIzB

−⋅=−⋅=

( )2'' yAII += 'y = Distance in y direction between neutral axis of particular part en neutral axis of complete

construction.

zz BAZIII '' +=

][10713.1][10490.9)7.2435)(250.0001.0())157.24)(066.0002.0((2 474822 mmIIZAZ

−− ⋅=⋅=−++−⋅+⋅= cross section area 5.140e-4 m^2

22

Appendix B

Figure 1

Figure 2

12

123

3

hbI

bhI

z

y

=

=

For side impact protection only bending in y direction is important. So the area moment of inertia

across the z-axis, zI , is considered. Bending in y direction across the x-axis can be neglected.

( )2'' yAII zz += zI = Area moment of inertia in across z axis and neutral axis the particular part.

A = Cross section area of particular part 'y = Distance in y direction between neutral axis of particular part en neutral axis of complete

construction.

( ) ( ) ][1069.7045.0063.00015.007.012

07.00015.0' 482

3

mIzA

−⋅=−⋅⋅+⋅=

( ) ( ) ][1004.1063.0080.00015.024.012

0015.024.0' 472

3

mIzB

−⋅=−⋅⋅+⋅=

23

( ) ( ) ][1084.1063.0105.0001.008.012

08.0001.0' 472

3

mIzC

−⋅=−⋅⋅+⋅=

"" )502.11sin()502.11cos(' yzD III z ⋅+⋅= (See figure 2)

( ) ( )

][1021.512

255.0001.0)502.11sin(

031.0001.0255.012

)009.001.0(255.0)502.11cos('

473

23

m

IzD

−⋅=

⋅+

⋅⋅+−⋅⋅=

][1086.8''''' 47 mIIIIIzzzz DCBAz

−⋅=+++= To show that this value is realistic we compare it with a tube with simple geometry but with a lower height. A square tube with a height of 50 mm, width off 255 mm, and wall thickness 1.25mm has an I-value of 3.97e-7 m^4. Cross section area 8.00e-4 m^2