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Study on Deformation of Rectangular Metal Tube during Dynamic Three-Point

Bending for Modeling of Pole Side Impact of Vehicle

Tadanori ONO1

, Ichiro SHIMIZU2

, Naoya TADA2

and Nobuaki TAKUBO3

1

Okayama Prefectural Police Headquarters, Okayama 700-0816, Japan

2

Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan

3

National Research Institute of Police Science, Kashiwa 277-0882, Japan

(Received 8 January 2013; received in revised form 4 April 2013; accepted 20 April 2013)

Abstract

With the aim of estimating the collision speed of a

vehicle in a pole side impact accident, dynamic lateral

local compression (D-LLC) and dynamic three-point

bending (D-3PB) modeling tests were carried out. These

tests were performed using rectangular metal tube

specimens, and the deformation results were compared to

those of an experiment vehicle during pole side impact.

The results indicated the possibility to estimate vehicle

deformation during pole side impact by D-LLC and D-

3PB testing of rectangular metal tube specimens.

Key words

Traffic Accident Investigation, Dynamic Test, Pole Side

Impact, Experimental Modeling, Absorbed Energy

1. Introduction

Pole side impact is a type of traffic accident that

occurs when the side of a vehicle collides with a narrow,

rigid object such as an electric pole. This collision causes

deformation of the vehicle body. At high speeds, bending

and local collapse of the vehicle can occur. In many

countries, estimates for the energy absorbed during pole

side impact have been proposed by evaluating the collapse

depth and area. In Japan, the energy absorbed from

vehicle body deformation is estimated using energy

absorption diagrams [1]. However, an estimation method

for the energy absorbed from vehicle bending has not yet

been suggested, and the effects of bending deformation on

the estimated collision speed have not been clarified.

Therefore, an energy absorption diagram cannot be

applied simply to estimate the collision speed in the case

where bending deformation occurs.

On the other hand, there have been several studies on

the collapse and bending of metal tubes [2, 3]. If vehicle

deformation during pole side impact can be simulated by

simple modeling using metal tubes, it would be beneficial

to establish an estimation method for the absorbed energy

of a high-speed pole side impact accident. In a previous

study [4], vehicle deformation and the absorbed energy in

an actual vehicle collision at 80 km/h were analyzed to

investigate the possibility of static modeling of the pole

side impact of the vehicle. The results showed that the

deformation behavior and absorbed energy were required

to study static scale models. Next, lateral local

compression (LLC) and three-point bending (3PB) tests

were conducted using rectangular steel tubes. It was found

that the former induced mainly local collapse, while the

latter induced mainly tube bending. The LLC test was

followed sequentially by the 3PB test using the same

rectangular steel tube specimen. The experimental results

using the rectangular steel tubes were compared with

those obtained for a real vehicle. It was found that it was

possible to model the pole side impact of the vehicle by

LLC and 3PB sequential testing of the rectangular steel

tube. However, it is also important to clarify the

possibility of the dynamic modeling of the pole side

impact accident at higher collision speeds [5]. In the

present study, the dynamic lateral local compression (D-

LLC) and dynamic three-point bending (D-3PB) tests

were performed on rectangular metal tubes to compare the

deformations of the metal tube and vehicle during pole

side impact. From these results, the potential to model

vehicle deformation during pole side impact was

discussed.

2. Analysis of Vehicle Experiment Results

The deformation and absorbed energy from an actual

vehicle collision at 80 km/h were analyzed. The experiment

vehicle was a passenger car with a mass of 1152 kg and a

length, width, and wheelbase of 4410, 1695, and 2600 mm,

respectively. The vehicle slid and collided with a 300 mm

diameter, fixed steel pole at 80 km/h. The impact point was

located in the middle of the wheelbase on the right side of

the vehicle near the driver's seat. Fig.1 shows the top view

of the vehicle just after the pole side impact. The width and

depth of the vehicle’s collapsed area were about 860 and

830 mm, respectively. The bending angle between the front

and rear axles was about 50 degrees. The variations in load

Pv, collapse deformation u

v, collapse depth Cd

v, and

bending angle θv—all with respect to time T—after the

Fig.1 Experiment vehicle after a pole side

impact at 80 km/h

Journal of JSEM, Vol.13, Special Issue (2013) s131-s136Copyright Ⓒ 2013 JSEM

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impact are shown in Fig.2. The load Pv was calculated by

multiplying the acceleration of the vehicle’s center of

gravity by its mass. The collapse deformation uv occurs

immediately after the impact. The collapse depth Cdv

rapidly increases for 50 ms after the impact and then its rate

of increase gradually reduces. On the other hand, the

bending angle θv starts to develop about 20 ms after the

impact, and continues to increase until about 120 ms. From

these results, the vehicle deformation during pole side

impact can be divided into three stages, as shown in Fig.2.

Collapse deformation mainly occurs in stage (1) just after

the impact. The overall bending appears in stage (2). Then,

the overall bending becomes dominant and the collapse

deformation scarcely increases in stage (3).

3. Experimental Method

The specimen used was a rectangular, aluminum alloy

tube (JIS A6063-T5). It was annealed at 688 K for 2.5 h

along with furnace cooling. The width and height of the

specimen were w = 20 mm and h = 30 mm, respectively,

and the wall thickness was t = 1.5 mm. These dimensions

were selected based on the vehicle’s characteristics.

Regularly aligned circles with diameters of 5.0 mm were

printed on the side surface of the specimen to observe

deformation.

Two kinds of dynamic tests were conducted: the D-3PB

test and the D-LLC test. Dynamic tests were performed by

dropping a striker up to 2.0 m (Fig.3 (a)).

The mass of the striker was 5 kg, and the striker tip was

a cylindrical tool with a diameter of 5.0 mm (Fig.3 (b), (c)).

The specimen was set up on the lower supports in the D-

3PB test. The lower supports were steel cylinders with 20

mm radii, and the outer span was set to a = 75 and 100 mm.

The dynamic load of the D-3PB test was applied to the

specimen in the middle of the span. The specimen was set

up on the pressure resistance plate in the D-LLC test. The

dynamic load of the D-LLC test was applied to the

specimen in the middle of the specimen’s length. The load

PD of the dynamic test was measured using 50 kN capacity

load cells (A&D LC1205-T005). The load cells were

attached under the lower supports in the D-3PB test and

were attached under the pressure resistance plate in the D-

LLC test. The sampling frequency of the load was 5000

Hz. The deformation of the specimen during the test was

recorded using a digital camera (CASIO FH-20) in the

high-speed mode (1000 fps). The displacement of the

striker uD, collapse depth Cd

D, and bending angle θ

D were

measured using the captured pictures. The energy absorbed

by the specimen's deformation was evaluated by the load-

displacement relationship.

Striker

Specimen

(a) Whole view

Striker

Specimen

Lower

supports

Load cell

(b) Setup of specimen for the D-3PB test

Tip of striker

Specimen

Pressure

resistance

plate

(c) Setup of specimen for the D-LLC test

Fig.3 Drop test apparatus

0 50 100 150 200

0

100

200

300

400

500

0

30

60

90

120

150

Time T (ms)

Load Pv

(kN

)

Pv

uv

Cdv

θv

Displacem

ent uv

, Cdv

(cm

)

Angle θv

(deg)

(1) (2) (3)

Fig.2 Variations in load, displacement, and bending

angle of the experiment vehicle with respect to time

T. ONO, I. SHIMIZU, N. TADA and N. TAKUBO

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4. Results and Discussions

The D-3PB and D-LLC tests on rectangular aluminum

alloy tubes were conducted by dropping the striker from a

height of 2.0 m. Fig.4 shows specimens after testing. Fig.5

shows the progress of specimen deformation in the D-3PB

test at a span distance of a = 75 mm from 0 to 11 ms after

the impact. Until 3 ms after the impact, local collapse

occurred and the sides of the specimen deformed outward

to form a pyramidal shape. After 3 ms, the pyramidal area

folded and overall bending occurred, which increased the

collapse depth. The overall bending continued to increase

until 11 ms after the impact. Fig.6 shows the progress of

specimen deformation in the D-LLC test from 0 to 9 ms

after the impact. Until 2 ms after the impact, local collapse

occurred and the sides of the specimen formed a pyramidal

shape, similar to those in the D-3PB tests. Then, overall

bending occurred and the collapse depth increased.

However, the pyramidal shape was not folded in the D-LLC

test, which is different from that in the D-3PB tests.

(a) D-3PB test a = 100 mm

(b) D-3PB test a = 75 mm

(c) D-LLC test

Fig.4 Specimens after dynamic testing

0 ms

1 ms

2 ms

3 ms

4 ms

5 ms

6 ms

7 ms

8 ms

9 ms

10 ms

11 ms

Fig.5 Deformation of specimen in the D-3PB

test with span length a = 75 mm

Journal of JSEM, Vol.13, Special Issue (2013)

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From these results, it was found that the deformation trend

of the rectangular aluminum alloy tube in the D-3PB test

was somewhat similar to that of the vehicle during pole side

impact.

The variations in load PD, striker displacement u

D,

collapse depth CdD, and bending angle θ

D with respect to

time are shown in Fig.7. In the D-3PB and D-LLC tests, all

loads immediately increased, and peaked at about 2 or 3 ms.

At the peak, overall bending started to appear and the

difference between the striker displacement and collapse

depth became evident. However, in the D-LLC test, the

collapse depth was deeper than that in the D-3PB test for

the same bending angle.

0 5 10 15

0

1

2

3

4

0

20

40

60

80

Time T (ms)

Lo

ad

P (k

N)

PD

uD

CdD

θD

Disp

lacem

ent u

, Cd

(m

m)

An

gle θ

(d

eg

)

(a) D-3PB test a = 100 mm

0 5 10 15

0

1

2

3

4

0

20

40

60

80

Time T (ms)

Load P

(kN

)

PD

uD

CdD

θD

Displacem

ent u

, Cd (m

m)

Angle θ

(deg)

(b) D-3PB test a = 75 mm

0 5 10 15

0

1

2

3

4

0

20

40

60

80

Time T (ms)

Lo

ad

P

(k

N)

PD

uD

CdD

θD

Disp

lacem

en

t u

, Cd

(m

m)

An

gle θ

(d

eg

)

(c) D-LLC test

Fig.7 Variations in load, displacement, and angle

with respect to time in the dynamic tests

0 ms

1 ms

2 ms

3 ms

4 ms

5 ms

6 ms

7 ms

8 ms

9 ms

Fig.6 Deformation of specimen in the D-LLC test

T. ONO, I. SHIMIZU, N. TADA and N. TAKUBO

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0 20 40 60 80

0

20

40

60

80

Collapse depth ratio RCd (%)

Bend

ing

an

gle θ

(d

eg

)

D-3PB test a = 100 mm

D-3PB test a = 75 mm

D-LLC test

Experiment vehicle

(a) Bending angle-collapse depth ratio curves

0 20 40 60 80

0

20

40

60

80

100

0

70

140

210

280

350

Bending angle θ (deg)

Ab

so

rb

ed

energy

o

f specim

en E

(J)

Abso

rbed en

erg

y of vehicle E

v (k

J)

D-3PB test a = 100 mm

D-3PB test a = 75 mm

D-LLC test

Experiment vehicle

(b) Absorbed energy-bending angle curves

0 20 40 60 80

0

20

40

60

80

100

0

70

140

210

280

350

Collapse depth ratio RCd (%)

Ab

so

rb

ed energ

y o

f sp

ecim

en

E

(J)

Ab

so

rb

ed

en

erg

y of veh

icle E

v

(k

J)

D-3PB test a = 100 mm

D-3PB test a = 75 mm

D-LLC test

Experiment vehicle

(c) Absorbed energy-collapse depth ratio curves

Fig.8 Comparison of dynamic test results with those

obtained for the experiment vehicle

Fig.8 (a) shows the relationship between the bending

angle and the collapse depth ratio. The result of the D-3PB

test with a span distance a = 75 mm is similar to that with a

= 100 mm. The variation in the bending angle for the

collapse depth ratio of the specimen in the D-3PB test was

similar to that of the experiment vehicle during pole side

impact. The results from the D-LLC test were similar to

those of the experiment vehicle only in the early stages of

deformation, and as the deformation increased, so did the

dissimilarity.

The variation in the absorbed energy plotted against the

bending angle is shown in Fig.8 (b), and the variation in the

absorbed energy plotted against the collapse depth ratio is

shown in Fig.8 (c). There exists little difference between the

results of the D-3PB test, D-LLC test, and experiment

vehicle under pole side impact.

In Fig.9, the deformation of specimens in the D-3PB

tests is compared with those of the experiment vehicle.

Fig.9 (a) shows the conditions when the collapse

deformation mainly occurred: 3 ms after the impact in the

D-3PB test with a = 75 mm, and 30 ms after the impact for

the experiment vehicle. Fig.9 (b) shows the conditions

when the overall bending appeared: 11 ms after the impact

in the D-3PB test with a = 75 mm, and 120 ms after the

impact for the experiment vehicle. The similarity between

the deformation behavior observed in the D-3PB test and

that for the experiment vehicle suggested the possibility to

model the vehicle’s pole side impact by dynamic testing of

the rectangular metal tubes.

D-3PB

a = 75 mm

T = 3 ms

Experiment

vehicle

T = 30 ms

(a) Collapse of the specimen and the experimental

vehicle

D-3PB

a = 75 mm

T = 11 ms

Experiment

vehicle

T = 120 ms

(b) Overall bending of the specimen and the

experimental vehicle

Fig.9 Comparison of the deformed shapes in the

D-3PB test and the experiment vehicle during

pole side impact

Journal of JSEM, Vol.13, Special Issue (2013)

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5. Summary

To establish an estimation method of vehicle speed for

high-speed pole side impact collisions, the D-3PB and D-

LLC tests were performed using rectangular aluminum

alloy tube specimens. The experiment results were

compared with those obtained for a experiment vehicle. The

bending angle-collapse depth ratio relationship observed in

the test results was found to be similar to that observed in

the experiment vehicle results. Similarity was also found

among the variation in the absorbed energy against the

bending angle and the collapse depth ratio. Therefore, the

deformation of the rectangular aluminum alloy tube

specimen in the D-3PB tests seems to be similar to the

vehicle deformation during pole side impact.

Acknowledgement

Part of this work was supported by the Japan Society

for the Promotion of Science (JSPS) KAKENHI

(23917014).

References

[1] Sukegawa, Y., Kubota, M., Yamazaki, S. and Yamada, K.:

Energy Absorption Characteristics of Passenger Car Side

(in Japanese), J. JARI Research, 29-9 (2007), 471-476.

[2] Gupta, N.K. and Sinha, S.K.: Collapse of a Laterally

Compressed Square Tube Resting on a Flat Base, Int. J.

of Solid Structures, 26-5-6 (1990), 601-605.

[3] Gupta, N.K. and Ray, P.: Simply Supported Empty and

Filled Thin-square-tubular Beams under Central Wedge

Loading, Thin-Walled Structures, 34-4 (1999), 261-278.

[4] Ono, T., Shimizu, I., Tada, N. and Takubo, N.: Absorbed

Energy Evaluation by Lateral Compression of

Rectangular Steel Tube Simulating Pole Side Impact of

Vehicle (in Japanese), DVD-ROM. JSME annual meeting

(2011), G030114.

[5] Drazetic, P., Ravalard, Y., Dacheux, F. and Marguet, B.:

Applying Non-Direct Similitude Technique to the

Dynamic Bending Collapse of Rectangular Section

Tubes, Int. J. Impact Engineering, 15-6(1994), 797-814.

T. ONO, I. SHIMIZU, N. TADA and N. TAKUBO