Abstract

In order to enhance the load-carrying and energy-absorbing capacity of the energy-absorbing structure, a new energy-absorbing mode of a metal foam-filled sandwich circular tube (MFSC-Tube) expanded by a conical–cylindrical die under axial compression is designed. An analytical model of expansion of the MFSC-Tube under axial compression is established, considering the bending, stretching, and strain hardening of inner and outer tubes as well as compression of the metal foam core. Subsequently, finite element calculations are performed. Both analytical solutions and deformation modes agree well with the finite element calculation results, which proves the validity of the analytical model. The effects of material and geometrical parameters on the expansion of MFSC-Tubes are considered in detail based on the proposed analytical model. It is found that the load-carrying and energy-absorbing capacity of the expansion of the MFSC-Tube can be enhanced by adjusting such parameters as the ratio of the foam thickness to the wall thickness of the metal circular tube and the semi-angle of the die. Last but not least, the specific energy absorption (SEA) of the MFSC-Tube under expansion is significantly improved compared with that of hollow tubes under expansion.

References

1.
Shakeri
,
M.
,
Salehghaffari
,
S.
, and
Mirzaeifar
,
R.
,
2007
, “
Expansion of Circular Tubes by Rigid Tubes as Impact Energy Absorbers: Experimental and Theoretical Investigation
,”
Int. J. Crashworthiness
,
12
(
5
), pp.
493
501
.
2.
Karrech
,
A.
, and
Seibi
,
A.
,
2010
, “
Analytical Model for the Expansion of Tubes Under Tension
,”
J. Mater. Process. Technol.
,
210
(
2
), pp.
356
362
.
3.
Lu
,
Y. H.
,
2004
, “
Study of Tube Flaring Ratio and Strain Rate in the Tube Flaring Process
,”
Finite Elem. Anal. Des.
,
40
(
3
), pp.
305
318
.
4.
Liu
,
Y. Z.
, and
Qiu
,
X. M.
,
2016
, “
A Theoretical Study of the Expansion Metal Tubes
,”
Int. J. Mech. Sci.
,
114
, pp.
157
165
.
5.
Fischer
,
F. D.
,
Rammerstorfer
,
F. G.
, and
Daxner
,
T.
,
2006
, “
Flaring—An Analytical Approach
,”
Int. J. Mech. Sci.
,
48
(
11
), pp.
1246
1255
.
6.
Almeida
,
B. P. P.
,
Alves
,
M. L.
,
Rosa
,
P. A. R.
,
Brito
,
A. G.
, and
Martins
,
P. A. F.
,
2006
, “
Expansion and Reduction of Thin-Walled Tubes Using a Die: Experimental and Theoretical Investigation
,”
Int. J. Mach. Tools Manuf.
,
46
(
12–13
), pp.
1643
1652
.
7.
Al-Abri
,
O. S.
, and
Pervez
,
T.
,
2013
, “
Structural Behavior of Solid Expandable Tubular Undergoes Radial Expansion Process—Analytical, Numerical, and Experimental Approaches
,”
Int. J. Solids Struct.
,
50
(
19
), pp.
2980
2994
.
8.
Fan
,
X.
, and
Potier-Ferry
,
M.
,
2016
, “
On Axisymmetric/Diamond-Like Mode Transitions in Axially Compressed Core–Shell Cylinders
,”
J. Mech. Phys. Solids
,
94
, pp.
68
87
.
9.
Shi
,
Y.
,
Wu
,
P. D.
,
Lloyd
,
D. J.
, and
Li
,
D. Y.
,
2014
, “
Effect of Rate Sensitivity on Behavior of a Laminated Tube Under Dynamic Loading
,”
ASME J. Appl. Mech.
,
81
(
5
), p.
051010
.
10.
Liu
,
Y. Z.
,
Xiong
,
F.
,
Yang
,
K. J.
, and
Chen
,
Y. L.
,
2020
, “
A Novel Omnidirectional Self-Locked Energy Absorption System Inspired by Windmill
,”
ASME J. Appl. Mech.
,
87
(
8
), p.
085001
.
11.
Niknejad
,
A.
, and
Moeinifard
,
M.
,
2012
, “
Theoretical and Experimental Studies of the External Inversion Process in the Circular Metal Tubes
,”
Mater. Des.
,
40
, pp.
324
330
.
12.
Liu
,
Y. Z.
,
Qiu
,
X. M.
,
Wang
,
W.
, and
Yu
,
T. X.
,
2017
, “
An Improved Two-Arcs Deformational Theoretical Model of the Expansion Tubes
,”
Int. J. Mech. Sci.
,
133
, pp.
240
250
.
13.
Yan
,
J. L.
,
Yao
,
S. G.
,
Xu
,
P.
,
Peng
,
Y.
,
Shao
,
H.
, and
Zhao
,
S. Z.
,
2016
, “
Theoretical Prediction and Numerical Studies of Expanding Circular Tubes as Energy Absorbers
,”
Int. J. Mech. Sci.
,
105
, pp.
206
214
.
14.
Luo
,
M.
,
Yang
,
J. L.
,
Liu
,
H.
,
Lu
,
G. X.
, and
Yu
,
J. L.
,
2019
, “
Energy Absorption of Expansion Tubes Using a Conical-Cylindrical Die: Theoretical Model
,”
Int. J. Mech. Sci.
,
157–158
, pp.
207
220
.
15.
Wu
,
M. Z.
,
Zhang
,
X. W.
, and
Zhang
,
Q. M.
,
2021
, “
A New Model for the Expansion Tube Considering the Stress Coupling: Theory, Experiments and Simulations
,”
Def. Technol.
,
18
(
7
), pp.
1190
1204
.
16.
Daxner
,
T.
,
Rammerstorfer
,
F. G.
, and
Fischer
,
F. D.
,
2005
, “
Instability Phenomena During the Conical Expansion of Circular Cylindrical Shells
,”
Comput. Meth. Appl. Mech. Eng.
,
194
(
21–24
), pp.
2591
2603
.
17.
Seibi
,
A. C.
,
Barsoum
,
I.
, and
Molki
,
A.
,
2011
, “
Experimental and Numerical Study of Expanded Aluminum and Steel Tubes
,”
Procedia Eng.
,
10
, pp.
3049
3055
.
18.
Yang
,
J. L.
,
Luo
,
M.
,
Hua
,
Y. L.
, and
Lu
,
G. X.
,
2010
, “
Energy Absorption of Expansion Tubes Using a Conical–Cylindrical Die: Experiments and Numerical Simulation
,”
Int. J. Mech. Sci.
,
52
(
5
), pp.
716
725
.
19.
Yao
,
S. G.
,
Li
,
Z. X.
,
Yan
,
J. L.
,
Xu
,
P.
, and
Peng
,
Y.
,
2018
, “
Analysis and Parameters Optimization of an Expanding Energy-Absorbing Structure for a Rail Vehicle Coupler
,”
Thin Walled Struct.
,
125
, pp.
129
139
.
20.
Li
,
J.
,
Gao
,
G. J.
,
Dong
,
H. P.
,
Xie
,
S. C.
, and
Guan
,
W. Y.
,
2016
, “
Study on the Energy Absorption of the Expanding–Splitting Circular Tube by Experimental Investigations and Numerical Simulations
,”
Thin Walled Struct.
,
103
, pp.
105
114
.
21.
Chahardoli
,
S.
, and
Nia
,
A. A.
,
2017
, “
Investigation of Mechanical Behavior of Energy Absorbers in Expansion and Folding Modes Under Axial Quasi-Static Loading in Both Experimental and Numerical Methods
,”
Thin Walled Struct.
,
120
, pp.
319
332
.
22.
Moreno
,
C.
,
Beaumont
,
R.
,
Hughes
,
D. J.
,
Williams
,
T.
, and
Dashwood
,
R.
,
2017
, “
Quasi-Static and Dynamic Testing of Splitting, Expansion and Expansion-Splitting Hybrid Tubes Under Oblique Loading
,”
Int. J. Impact Eng.
,
100
, pp.
117
130
.
23.
Moreno
,
C.
,
Williams
,
T.
,
Beaumont
,
R.
,
Hughes
,
D. J.
, and
Dashwood
,
R.
,
2016
, “
Testing, Simulation and Evaluation of a Novel Hybrid Energy Absorber
,”
Int. J. Impact Eng.
,
93
, pp.
11
27
.
24.
Zhang
,
Z. J.
,
Wang
,
Y. J.
,
Huang
,
L.
,
Fu
,
Y.
,
Zhang
,
Z. Q.
,
Wei
,
X.
,
Sui
,
Y. G.
,
Zhang
,
Q. C.
, and
Jin
,
F.
,
2022
, “
Mechanical Behaviors and Failure Modes of Sandwich Cylinders With Square Honeycomb Cores Under Axial Compression
,”
Thin Walled Struct.
,
172
, p.
108868
.
25.
Li
,
Z. B.
,
Chen
,
R.
, and
Lu
,
F. Y.
,
2018
, “
Comparative Analysis of Crashworthiness of Empty and Foam-Filled Thin-Walled Tubes
,”
Thin Walled Struct.
,
124
, pp.
343
349
.
26.
Djamaluddin
,
F.
,
Abdullah
,
S.
,
Ariffin
,
A. K.
, and
Nopiah
,
Z. M.
,
2015
, “
Optimization of Foam-Filled Double Circular Tubes Under Axial and Oblique Impact Loading Conditions
,”
Thin Walled Struct.
,
87
, pp.
1
11
.
27.
Wang
,
Y. J.
,
Zhang
,
Z. J.
,
Xue
,
X. W.
,
Zhou
,
J.
, and
Song
,
Z. X.
,
2021
, “
Axial and Lateral Crushing Performance of Plate-Lattice Filled Square Sandwich Tubes
,”
Compos. Struct.
,
274
, p.
114404
.
28.
Zhang
,
J. X.
,
Ye
,
Y.
,
Zhu
,
Y. Q.
,
Yuan
,
H.
,
Qin
,
Q. H.
, and
Wang
,
T. J.
,
2020
, “
On Axial Splitting and Curling Behaviour of Circular Sandwich Metal Tubes With Metal Foam Core
,”
Int. J. Solids Struct.
,
202
, pp.
111
125
.
29.
Zhang
,
J. X.
,
Guo
,
H. Y.
,
Du
,
J. L.
,
Yuan
,
H.
,
Zhu
,
Y. Q.
, and
Qin
,
Q. H.
,
2021
, “
Splitting and Curling Collapse of Metal Foam Core Square Sandwich Metal Tubes: Experimental and Theoretical Investigations
,”
Thin Walled Struct.
,
169
, p.
108346
.
30.
Haghgoo
,
M.
,
Babaei
,
H.
, and
Mostofi
,
T. M.
,
2022
, “
3D Numerical Investigation of the Detonation Wave Propagation Influence on the Triangular Plate Deformation Using Finite Rate Chemistry Model of LS-DYNA CESE Method
,”
Int. J. Impact Eng.
,
161
, p.
104108
.
31.
Deshpande
,
V. S.
, and
Fleck
,
N. A.
,
2000
, “
Isotropic Constitutive Models for Metallic Foams
,”
J. Mech. Phys. Solids
,
48
(
6–7
), pp.
1253
1283
.
32.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1997
,
Cellular Solids: Structures and Properties
,
Cambridge University Press
,
UK
.
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