comparison of experimental results with fem for impact

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ISSN 0386-1678

Report of the Research Institute of Industrial Technology, Nihon UniversityNumber 90, 2007

* Part-Time Lecturer, Department of Mechanical Engineering, College of Industrial Technology, Nihon University** Professor, Department of Mechanical Engineering, College of Industrial Technology, Nihon University*** Master’s Course, Mechanical Engineering, Graduate School of Industrial Technology, Nihon University

Comparison of Experimental Results with FEM for Impact Response Behavior of CFRP Tubes and CFRP/Al Hybrid Beams for Absorbing

Impact Energy in Full-lap and Side Collisions of Automobiles

Hyoung-Soo KIM*, Goichi BEN** and Nao SUGIMOTO***

( Received March 30, 2007 )

Abstract

Carbon fiber reinforced plastic (CFRP) laminates are used in various industrial fields because they have excellent properties of a specific strength and a specific stiffness. The CFRP has a potential of weight reduction in the automotive structure which can contribute to the improvement of mileage as well as the reduction of carbon dioxide. On the other hand, the safety issue in case of collision should be also clarified when employing the CFRP as automotive structures. In the automotive industry, try and error systems are adopted to design automobiles. This system is disadvantageous concerning cost and time. Therefore, the reliable simulation technology has been required. The objective of this study is to establish the simulation technology for impact response behavior of rectangular CFRP tubes and Al guarder beams reinforced with the CFRP under full-lap and side collisions. We adopted drop weight impact tests to investigate impact response behavior and impact energy absorption characteristics. Impact tests were carried out by dropping the impactor from the height of 12 m. Impact speed was approximately 55 km/h just before the impact. A finite element (FE) model was also developed by using a nonlinear, explicit dynamic code LS-DYNA and PAM-CRASH to simulate the impact response behavior of the rectangular CFRP tubes and Al guarder beams reinforced with the CFRP under impact load. In case of the rectangular CFRP tubes, the comparison of experimental results with that of FEM for the load-displacement curves was favorable. The maximum load, absorbed energy and final displacement calculated by FEM model were in good agreement with the average values of the impact test results. Furthermore, the experimental relations of impact load to the displacement for the CFRP/Al hybrid members with different thicknesses of CFRP showed good agreement with those of numerical results. These results show that the numerical method developed here is useful for estimating the impact response behavior of CFRP/Al hybrid beams.

Keywords: Impact response, Rectangular CFRP tube, CFRP/Al hybrid beam, Collision experiment, FEM analysis

Hyoung-Soo KIM, Goichi BEN and Nao SUGIMOTO

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1. Introduction

It is well known that CO2 emitted from passenger vehicles is one of major causes of global warming. The most effective method to reduce CO2 is to manufacture fuel efficient automobiles. Improvement of the auto-mobile fuel efficiency can be realized by reducing the automobile weight using lightweight materials such as composite materials. Carbon fiber reinforced plastics (CFRPs) have been widely used in aerospace industries, industrial goods and other application fields because of their high specific strength and high specific modulus compared with conventional metals. This means that the CFRP can contribute to reduce the weight of auto-mobiles significantly.

Besides reducing the weight, the safety of auto-mobiles is also a very important issue which needs to be investigated along with the reduction of weight. Collision safety of the automobile was evaluated by full-lap frontal crash, offset frontal crash and side impact tests. In the frontal crash test, it is possible to absorb energy by large deformation of the front and the rear parts of automobiles. With increasing interests in reduc-ing the automobile weight and securing the safety of passengers, extensive research was performed in the recent years for front and rear collision impact1) ~ 6). However, in the case of the side impact test, it is hard to absorb energy in the same way as the frontal crash, because the survival space of passengers is very narrow. Present door guarder beams made of steel are used inside the door for absorbing impact energy and their deformation is limited to about 150 mm.

In this study, we developed rectangular CFRP tubes with two ribs and CFRP-Al hybrid beams as impact en-ergy absorption members for full-lap and side collisions. Drop weight impact tests were carried out to investigate impact response behavior and impact energy absorp-tion characteristics of the rectangular CFRP tubes and CFRP-Al hybrid beams. A finite element (FE) model was also developed by using the nonlinear, explicit dynamic code LS-DYNA and PAM-CRASH to simulate the impact response behavior and absorbed energy of the rectangular CFRP tubes with two ribs and CFRP-Al hybrid beams under impact loading.

Initial imperfection

300mm

5mm

115mm50mm

Rib : r =5mm

Long

itudi

nal d

irect

ion

Initial imperfection

300mm

5mm

115mm50mm

Rib : r =5mm

Long

itudi

nal d

irect

ion

Fig. 1 Configuration of the rectangular CFRP tube with two ribs

2. Impact Response Behavior of Rectangular CFRP Tubes for Front Side Members

2.1 Experiment

Rectangular CFRP tubes with two ribs were manu-factured from unidirectional prepregs (P3052s-20, Toray Industries, Inc.) by using the sheet winding method. Configuration of the rectangular CFRP tube is shown in Fig. 1. Stacking sequences of the main and rib parts in the rectangular CFRP tubes were [(0/90)6/0]S and [0], respectively. An initial imperfection with an exter-nal bevel type was introduced in order to get a stable progressive failure behavior.

We adopted drop weight impact tests to investigate impact response behavior and impact energy absorp-tion characteristics of the rectangular CFRP tubes. The impact tests were carried out by dropping the impac-tor from height of 12 m (Fig. 2(a)). The mass of the impactor was 105 kg. Also, the impactor speed was approximately 55 km/h just before the impact. The impact load was measured from a load cell under the specimen which was mounted on metallic base (see Fig. 2(b)). In order to investigate the progressive failure mechanism of the rectangular CFRP tubes, a high speed camera was employed.

Comparison of Experimental Results with FEM for Impact Response Behavior of CFRP Tubes and CFRP/Al Hybrid Beams for Absorbing Impact Energy in Full-lap and Side Collisions of Automobiles

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Fig. 2 Tower drop impact test setup (a) impactor (b) mounted specimen

Added mass

Impactor

Added mass

Impactor

Load cell

Specimen

Load cell

Specimen

(a)

(b)

x

z

Long

itudi

nal d

irect

ion

300 mm

Only axial displacement permitted

Perfect clamped

Drop speed : 55 km/h

Mass of impactor : 105 kg

[(0/90)6/0]S

x

y

x y

z

5 mm

Rib part : 3.9 mm Stacking sequence: [0]

Fig. 3 Details of the finite element model of 1-layer model (Model 2)

(a) Model 2 (b) Model 3

Fig. 4 Details of its top part in Model 2 and Model 3

2.2 Finite element modeling

2.2.1 Details of FEM model

In our previous study7), to simulate the progressive failure behavior and absorbed energy of the rectangular CFRP tubes with two ribs under impact loading, a finite element (FE) model was developed by using the nonlin-ear, explicit dynamic code LS-DYNA. In our previous FEM model (designated as Model 1), the rectangular CFRP tube with two ribs was modeled by 24 and 44 layers, respectively. Stacking sequences of the main and rib parts were [(0/90)6/0]S and [010/(0/90)6/0]S, respectively. There were 8,125 elements and 8,316 nodes in the Model 1.

In this study, in order to actually model the rectangu-lar CFRP tube with ribs, a T-shape rib part is modeled as shown in Fig. 3 (designated as Model 2). Furthermore, the FEM model improved the Model 2 is revised as shown in Fig. 4 (designated as Model 3). The stacking


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sequences of the main and rib parts in the Model 2 and Model 3 were [(0/90)6/0]S and [0], respectively. The elements and nodes of the Model 2 and Model 3 were 9,656 and 9,784, respectively. The impactor and rectangular CFRP tube with two ribs were modeled by solid and shell elements, respectively.

In the all FEM models, the imperfection part was introduced to reduce a peak load and to get the stable progressive failure behavior from the top edge of the FEM model to a length of 10 mm below (see Fig. 5). The FEM models with and without the imperfection parts, were designated as thickness-changed and thick-ness-constant models, respectively.

The comparison between thickness-constant and thickness-changed models is shown in Fig. 6. The model without an imperfection part may produce a high initial maximum load. After that, the impact load drops rapidly. The initial maximum load of the thickness-constant model is approximately two times higher than that of the thickness-changed model. On the other hand, impact load in the propagation region is seen that the thickness-changed model is higher than that of the thickness-con-stant model. Therefore, the thickness-changed method in the imperfection part is chosen. As a result, the tendency of the impact response behavior in the FEM analysis is in good agreement with the impact tests.

Fig. 5 Details of the (a) thickness-constant and (b) thickness-changed models

5 mm

Reduce a thickness

5 mm

Reduce a thickness

5 mm 5 mm

10 mm

Fig. 6 Comparison of the thickness-constant and thickness-changed models for the load-displacement curve

0 50 100 1500

100

200

300

400

Load

[kN

]

Displacement [mm]

thickness-changed model thickness-constant model

2.2.2 Boundary and contact conditions and failure criterion

The mass and initial velocity of the impactor modeled as a rigid body were 105 kg and 15.27 m/s (55 km/h), respectively. For the boundary conditions of impactor, the displacements along the global axes x and y, and the rotations for the three global axes were constrained in the FE analysis. The displacement of impactor along the z axis downwards was only permitted. On the other hand, in the case of the rectangular CFRP tube with two ribs, the bottom side of the model was perfectly fixed.

In this FE analysis, the rectangular CFRP tube was modeled by using a shell element (MAT_54, mat_en-hanced_composite_damage) and the Chang-Chang failure criterion8), 9) was used to determine the failure of element.

The mechanical properties used for MAT_54 in LS-DYNA are listed in Table 1. Also, we adopted a removing element method base on a time-step failure parameter (Tfail). These analyses were conducted with Tfail parameter equal to 0.3. Two different contact al-gorithms were used throughout FE analysis. The “con-tact_automatic_surface_to_surface” contact interface type was used for the boundary between the impactor and the top part of rectangular CFRP tube. In case of the CFRP tube, the “contact_automatic_single_surface”


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contact interface type was adopted.

2.3 Results and discussion

2.3.1 Impact test results

Fig. 7 shows the load-displacement curves of the rectangular CFRP tube with ribs under impact loading. It is seen that the same tendency of the impact response behavior was obtained in the all test specimens. In Table 2,

Table 1 Material properties of rectangular CFRP tube used in the FE analysis

※

Material property Symbol Values

EaEbνba

ab) Gabbc) Gbc

XTXCYTYCTransverse compressiv

Longitudinal Young’s modulus

Transverse Young’s modulus

Minor Poisson’s ratio

Shear Modulus in plane (

Shear Modulus in plane (

Longitudinal tensile strength

Longitudinal compressive strength

Transverse tensile strength

e strengthShear strength in plane (ab) SC

140.0 GPa

9.0 GPa

0.0219

4.0 GPa

2.0 GPa

2.6 GPa

1.5 GPa

0.07 GPa

0.05 GPa0.09 GPa

These values were provided by Toray Industries, Inc.

0 50 100 150Displacement [mm]

0

50

100

150

200

Load

[kN

]

No. 2 No. 3

No. 4 No. 5

No. 1

Fig. 7 Load-displacement curves for all test specimens

No. 1 No. 2 No. 3 No. 4 No. 5 Ave.

Max. load [kN] 179.0 173.1 170.9 160.8 180.3 172.8

Absorbedenergy [kJ] 11.7 13.7 12.7 13.1 12.9 12.8

displacement [mm] 128.0 142.6 138.3 146.8 134.6 138.1Maximum

Table 2 Summary of the experimental results

Fig. 8 Photographs of impact tested rectangular CFRP tube with two ribs

the maximum load, the maximum displacement and the absorbed energy obtained from the experimental tests are listed. Here, the absorbed energy was obtained from load-displacement curves.

Fig. 8 shows the photographs of failed CFRP tube with ribs after impact test. It is seen that the crush zone spread out towards inside and outside of the rectan-gular CFRP tube wall. Tearing failure mode was also seen in all of the rectangular CFRP tubes at the corners. Photographs recorded with a high speed camera system


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(a) t = 0 msec (b) t = 2.08 msec (c) t = 2.92 msec

(d) t = 6.25 msec (e) t = 8.33 msec (f) t = 10.42 msec

Fig. 9 Photographs recorded with a high speed camera system (specimen No. 2)

Fig. 10 Load-displacement curves obtained from the FEM analysis

0 50 100 1500

50

100

150

200

250

Load

[kN

]

Displacement [mm]

Model 2 Model 3

Model 1

0 50 100 1500

50

100

150

200

Load

[kN

]

Displacement [mm]

FEM EXP(Model 3)

Fig. 11 Comparison of experimental and FEM (Model 3) load-displacement curves

during impact tests are shown in Fig. 9. From the results, the stable progressive failure behavior was observed.

2.3.2 Comparison between impact test results and FEM results

Fig. 10 shows the impact load-displacement curves

of FEM results, for Model 1, Model 2 and Model 3. It is seen that their tendency of the impact response behavior was relatively the same in the all FEM models.

Fig. 11 shows the comparison of experimental results with that of Model 3 for the load-displacement curves. It is seen that the comparison of the impact response behavior was favorable.


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Model 1 Model 2 Model 3 Exp.(ave. values)

196.0

11.8

146.0

215.0

11.9

136.0

174.0

12.1

140.0

172.8

12.8

138.1

Max. load [kN]

Absorbedenergy [kJ]

displacement [mm]Maximum

Table 3 Comparison between the experimental and FEM results of the rectangular CFRP tube

In Table 3, the maximum load, the absorbed energy and the maximum displacement obtained by the FE analyses and the average values of the experimental results are listed. The results of the Model 3 were in good agreement with the average values of the impact test results.

Fig. 12 Door guard beam and hybrid door guard beam

Door guarder beamSection: a-a

CFRP tape

AluminumAdhesive

Car outside

a

a

Car outside

On the tension side of the Al beam, a unidirectional CFRP laminate was pasted by using adhesive as shown in Fig. 13. The unidirectional CFRP was composed of T700 and epoxy resin and its thickness was changed from 0.5 mm to 2.5 mm with an increment of 0.5 mm. The 1,000 mm length of hybrid guarder beam was sup-ported by two supporters having a head radius of 15 mm and the span between the two supporters was 800 mm.

In order to evaluate the capacity of crash energy absorption and to show the micro and macro fracture behavior of the door guarder beam, a large size of drop tower facility for the impact test was constructed. The beam received an impact load generated by a free drop weight of 60 kg at an impact speed of 55 km/h. The shape of impactor was a half cylinder having a 100 mm radius and a 200 mm width and the hybrid beam was fixed by the belts to prevent from scattering (Fig. 14). The impact load and the displacement of the impac-tor were measured by the load cells attached to both supporters and by a high-speed camera, respectively. Fig. 15 shows the relationship between the load and the displacement of the specimens for the Al beam alone and the hybrid beams with the CFRP of 1 mm.

1000mm

0.5~2.5mm

CFRP

30mm

3.0mm

Aluminum

Fig. 13 Hybrid door guard specimen with square section of Aluminum

3. Impact Response Behavior of CFRP/Al hybrid beams under side collision

We developed CFRP-Al hybrid beams as impact en-ergy absorption members for side collision as shown in Fig.12. Such members have the advantages of plastic de-formation of aluminum alloy combined with high strength and lightweight of CFRP. By using a hybrid structure of aluminum alloy and CFRP, excellent energy absorption is expected within the limited deformation of 150 mm. The goal of this study is to develop simulation technology for the impact behavior of such hybrid beams.

3.1 Experiment

The square section of Al guarder beam was 30 mm x 30 mm and its wall thickness was 3.0 mm. The type of aluminum alloy was A7N01S-T5 and its yield stress, tensile strength, tensile modulus and elongation were 373 MPa, 416 MPa, 70 GPa, and 16.7 %, respectively.


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Fig. 14 Hybrid door guard beam and fixtures in experiment

Fiber break

0

5

1015

20

25

0 50 100 150 200Displacement (mm)

Load

(kN

) Fiber break CFRP-1mm

CFRP-2.5mm

0

5

10

15

20

25

Load

(kN

)

0 50 100 150 200 250Displacement (mm)

Fiber break

0

5

10

15

20

25

Load

(kN

)

0 50 100 150 200 250 300Displacement (mm)

CFRP-1.5mm

300

0

510

1520

25

50 100 150 250Displacement (mm)

Load

(kN

) Aluminum

200

300250

0

Fig. 15 Impact load to displacement curves for hybrid beam with square section of Al

Support LengthR15

R 100

200

800

Supporter

Impactor

Mass=60kgf

Head radius=15mm


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1.5 mm, 2 mm and 2.5 mm. For the case of Al beam alone, after the impact load reached the maximum, it then instantly dropped to almost zero. Within 50 ms, the impact load was recovered to 12.5 kN and became zero when the displacement was about 200 mm. For the CFRP of 1 mm, the recovered impact load after the maximum was faster and higher than that of the Al beam alone and the higher impact loads continued until the break of CFRP. For the hybrid beams with the CFRP of 1.5 mm and 2.5 mm, larger displacement and higher impact load were observed compared with those of the CFRP of 1.0 mm.

Fig. 16 shows the observed fracture modes of CFRP

and the fracture types of each specimen. In the experi-ment, the fracture mode was classified into the following three types, 1) fiber breakage over the entire width and partial delamination of CFRP [Type A], 2) non fiber breakage and larger delamination of CFRP [Type B] and 3) partial fiber breakage in the width direction and the middle delamination [Type C]. The fracture modes for all the specimens are listed in Table 4. When the CFRP was thin, it broke as the Type A, and gradually changed from Type B to Type C according to the thickness of CFRP. The impact absorbing energy was calculated from the area of the load-displacement curve. When the thickness of CFRP increased, the impact energy

Table 4 Classification of fracture modes for all specimens

[A] fiber breakage in the entire width and partial delamination of CFRP

[B] non fiber breakage and larger delamination of CFRP

[C] partial fiber breakage in the width direction and the middle delamination

Fig. 16 Fracture mode of CFRP after impact test

Thickness of CFRP2.5mm2.0mm1.5mm 1.0mm0.5mm

4-24-3

4-15

CBC

6-86-116-156-17

CCCC

2-82-92-102-112-122-13

AAAAAA

3-83-93-103-113-133-14

BABAAA

5-25-35-115-155-165-17

CCCCCC


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also increased as shown in Fig. 17. The 2.5 mm CFRP absorbed 25 % larger impact energy than that of the Al beam alone.

Table 5 Material constants of hybrid beam with square section of Al alloy

CFRP AL Belt JigE1 (GPa) 135 72 0.133 207E2 (GPa) 8.5 --- --- ---G12 (GPa) 3.17 --- --- ---G23 (GPa) 3.04 --- --- ---

ν12 0.34 0.3 0.3 0.3ν23 0.4 ---

Density (kg/mm3) 1.60E-06 2.79E-06 7.93E-03 7.90E-06FL (GPa) 2.55 --- --- ---

εL 0.017 --- --- ---

0

500

1000

1500

2000

Al 0.5mm 1.0mm 1.5mm 2.0mm 2.5mm

Abs

orbe

d en

ergy

(J)

thickness of the CFRP (mm)

Until Fiber breakUntil displacement of 200mm

Until displacement of 100mm

Fig. 17 Relation of impact absorbing energy to CFRP thickness

with the square section and others.

3.3 Comparison of both results and discussion

Fig. 18 shows the comparison of the experimental and numerical results of the impact load to the dis-placement for the Al beam alone. In the experiment, two results were shown due to the scattering of the experiment values. The numerical result showed the good agreement with the experimental results. For the maximum load and displacement, the numerical result was found between the two experiment values. The value of absorbed energy was also close to the experi-mental ones. The results for the experimental failure mode was almost the same as the numerical one as shown in Fig. 19.

The experimental results for Al guarder beams with the CFRP thickness of 0.5 mm agreed well with those of the numerical results as shown in Fig. 20. The fracture mode of fiber breakage in the middle part of the beam and the partial delamination (Fig. 21) was observed in both results. The numerical and experimental results for other hybrid beam with different thickness of CFRP also agreed well one another.

4. Conclusions

1. It was proven that the rectangular CFRP tubes with two ribs were effective as an impact absorption mem-ber under full-lap collision.

2. The comparisons of experimental results with FEM ones for the load-displacement curves were favor-able. Especially, the maximum load, the absorbed energy and the maximum displacement calculated by

3.2 FEM analysis

In the numerical analysis, the dynamic explicit FEM solver (PAM-CRASH, 2004) was employed and the elastic-plastic 4 nodes shell element for the Al part and the laminated shell element for the CFRP were used, respectively. The total node number was 64,863 and the total element number was 56,456. The contact element between the impactor and the upper surface of hybrid guarder beam and between the supporter and the lower surface of hybrid guarder beam was Contact Type 33 with the friction and penalty coefficients of 0.5 and of 0.1, respectively. For the interface of Al guarder beam and the CFRP layer, Contact type 32 was used for modeling adhesion of interface. Table 5 shows the material properties of CFRP (T700), Al guarder beam


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Model 3 were in good agreement with the average values of the impact test results.

3. The CFRP Al hybrid door guarder beam showed the same performance of impact absorbing energy as that of the steel one and its maximum displacement after the impact was smaller than that of steel.

4. The CFRP-Al hybrid member with the thicker CFRP showed the larger impact failure displacement be-cause its fracture was extended by the thicker CFRP and then it absorbed more impact energy.

5. Changing the design parameters of the hybrid door guarder beam may result in larger impact absorbing energy.

6. From the comparison of FEM results with the experi-mental ones for both specimens of CFRP Al hybrid guarder beam with square section of Al, the proposed numerical method was found to be very useful for analyzing the hybrid door guarder beams.

Acknowledgment

This study was conducted as part of the Grant-in-Aid for Scientific Research (C) (No. 15560081) by JSPS (the Japan Society for the Promotion of Science) from April 2003 to March 2005 and the authors acknowledge the assistance of Toray Industries, Inc. who supplied the materials for these test specimens.

Fig. 20 Impact absorbing energy and fracture aspect s after impact for Al beam only

Fig. 21 Impact absorbing energy and fracture mode of hybrid beam with square section of Al and CFRP of 0.5 mm square section

Fig. 18 Comparison of impact load to displacement for Al beam only

0

10

20

30


Load

(kN

) FEM

Experiment

Fig. 19 Comparison of impact load to displacement for hybrid beam with square section of Al and CFRP of 0.5 mm


0

10

20

30

Load

(kN

) FEM

Experiment


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References

1) P.K. Mallick and L.J. Broutman, J. Testing and Evaluation, 5, pp. 190, 1977

2) S.S. Cheon, T.S. Lim and D.G. Lee, Composite Structures, 46, pp. 267-278, 1999

3) D.G Lee, T.S. Lim and S.S. Cheon, Composite Structures, 50, pp. 381-390, 2000

4) G. Ben, T. Uzawa, H.S. Kim, Y. Aoki, H. Mitsuishi and A. Kitano, Transaction of JSME Series A, 70 (694), pp. 824-829, 2004 (in Japanese)

5) A. G. Caliska, Proceedings of IME2002, ASME, Internatinal Mechanical Engineering Congress &

Exposition (2002)6) H.S. Kim, G. Ben and Y. Iizuka, Proceedings of

11th Japan -US Conference of Composite Materials (2004)

7) H.S. Kim, G. Ben, Y. Aoki and A. Shikada, 5th Japan-Korea Joint Symposium on Composite Materials, pp. 95-96, 2005

8) F.K. Chang and K.Y. Chang, Journal of Composite Materials, 21, pp. 809-833, 1987

9) H.S. Kim, G. Ben and Y. Aoki, Proceedings of the 12th US-Japan Conference on Composites Materials, pp. 367-378, 2006

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自動車の前面および側面衝突における衝撃エネルギー吸収用CFRP角柱とCFRP/Al ハイブリッド材の衝撃応答挙動における実験と解析の比較

金　炯秀，邉　吾一，杉本　直

概　　要

カーボン繊維強化複合材料積層板（CFRP）は比強度・比剛性が優れているので様々な分野で使用されている。自動車産業では，自動車の軽量化による燃費の改善や CO2 ガスの減少に CFRPの使用が期待されている。一方，自動車の構造に CFRPを使用する際，衝突安全性を検討しなければならない。一般的に自動車メーカでは自動車の設計にトライ・アンド・エラー方式を採用している。このような方式だと時間およびコストがかかるため，トライ・アンド・エラー方式を代替できるような信頼性のある自動車の衝突解析技術が要求されている。本研究の目的は，自動車の前面および側面衝突時に衝撃エネルギー吸収用 CFRP角柱と CFRP/Alハイブリッド材の衝撃応答挙動を明らかにする解析技術を確立することにある。衝撃応答挙動および衝撃エネルギー吸収特性を調べるために自由落下衝撃試験が行われたが，落錘子を高さ 12mから落下させ，その際の衝突速度はおよそ 55km/hであった。また，有限要素ソルバー LS-DYNAおよび Pam-Crashを用いて CFRP角柱と CFRP/Alハイブリッド材の衝撃応答解析を行い，落錘衝撃試験結果との比較検討も行った。CFRP角柱の衝撃試験および解析結果の比較では，衝撃荷重 -変位線図でよい一致が得られた。特に，初期衝撃荷重，衝撃吸収エネルギー量および最大変位において試験結果と解析結果のよい一致が得られた。さらに，CFRP層の厚さを変化させた CFRP/Alハイブリッド材の衝撃試験および解析結果の比較においても，衝撃荷重 -変位線図でよい一致が得られた。また，この研究で開発した解析手法は CFRP/Alハイブリッド材の衝撃応答挙動を予測するのに有用であることを示した。

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Biographical Sketches of the Authors

Hyoung-Soo Kim is a part-time lecturer of College of Industrial Technology, Nihon University. He was born in Mokpo, Korea on March 10, 1968. He received his Dr. of Eng. from the Kyushu University in 2000. He is now a member of the Japan Society for Composite Materials, Japan Society of Mechanical Engineers and The Japanese Society for Strength and Fracture of Materials.

Nao Sugimoto was born in February 10, 1984 in Tokyo, Japan. He received his B.S. from Nihon University, Japan in 2006. He is a master course student of department of mechanical engineering, graduate school of industrial technology, Nihon University.

Goichi Ben is a professor of College of Industrial Technology, Nihon University. He was born in Akita, Japan on November 29, 1945. He received his B.S. from Nihon University, Japan in 1969, M.S. from the University of Tokyo, Japan in 1971 and Ph.D. in Engineering from the University of Tokyo in 1974. He joined College of Industrial Technology, Nihon University in 1974. He has been engaged in the study of strength and optimum design of light weight structures. The present research is focused on composite engineering, namely mechanics and strengths of composites, evaluation of mechanical properties in composites, optimal design of composite structures, fabrica-tions of composites and so on. Dr. Ben had stayed each one year at the University of Delaware from 1988 to 1989 and at the University of Colorado from 1996 to 1997 in the U.S.A. as a visiting associate and full professor, respectively. He is now a president of the Japan Society for Composite Materials. He is a member of board director of the Association of Reinforced Plastics in Japan. He is a member of council of the Japan Society for Computational Engineering and Science and a member of the Japan Society of Mechanical Engineers, the Japan Society for Aeronautical and Space Sciences, the Society of Material Science, Japan, Dr. Ben is also a member of AIAA in the U.S.A. and American Society for Composite Materials.

comparison of experimental results with fem for impact

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