Mohammad Malawat, Danardono Agus Sumarsono, Jos Istiyanto, Gatot Prayogo, Felix Dionisius

Corresponding email: m.malawat72@gmail.com

Corresponding email: m.malawat72@gmail.com

**Published at : ** 30 Oct 2019

**IJtech :** IJtech
Vol 10, No 5 (2019)

**DOI :** https://doi.org/10.14716/ijtech.v10i5.2297

Malawat, M., Sumarsono, D.A., Istiyanto, J., Prayogo, G., Dionisius, F., 2019. Theoretical Prediction of Dynamic Axial Crushing on a Square Tube with Eight Holes Used as a Crush Initiator.

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Mohammad Malawat | Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia |

Danardono Agus Sumarsono | Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia |

Jos Istiyanto | Departement of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia |

Gatot Prayogo | Departement of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia |

Felix Dionisius | Department of Mechanical Engineering, Politeknik Negeri Indramayu, Jl. Raya Lohbener Lama No.08, Indramayu 45252, Indonesia |

Abstract

Thin-walled square steel tubes are part of automobile
structures, used as impact energy absorbers on crush boxes. Under axial
crushing, such tubes sometimes produces unpredictable folding forms. There are
three modes of dynamic axial crushing folding forms: the symmetric collapse
mode; the asymmetric mixed collapse mode A; and the asymmetric mixed collapse
mode B. The objective of this paper is to develop a theoretical prediction for
the three modes on a thin-walled square steel tube with eight holes used as
crush initiator. The basic folding mechanism is used to predict the dynamic
axial crushing analysis on the tube. These theoretical analyses can also can be
implemented in different crush initiator positions.

Two types
of cross section (c/h) were used in this study: specimen A (c/h = 60.42) and
specimen B (c/h = 45.69). Thirty-six experimental drop test studies were
conducted on the thin wall square tube. In addition, the results of a previous
drop test were compared to the results of the theoretical prediction. The
results show that the theoretical analysis has good agreement with the
experimental drop test study. This study proposes nine formulas to predict
average force, peak force and energy absorption of the dynamic axial crushing
on the thin-walled square steel tube with eight holes of crush initiator. The
limitation of these formulas, however, is that they are unable to show the
relationship between force and time in a graph.

Crush initiators; Dynamic axial crushing; Square tube

Introduction

Thin-walled tubes have been widely
used in the automotive industry as energy absorber components because of their
excellent energy properties and light weight. Over the years, many researchers
have studied thin-walled tube structures through experiments, numerical
simulations and theoretical analysis, and have attained in-depth understanding
of the characteristics of energy absorption (Hu et al., 2019).

The crashworthiness of thin-walled
structures with di?erent cross-sectional con?gurations, including square (Sun et
al., 2017); circular (Zhang et al., 2018); rectangular (Shena et al., 2017);
star-shaped (Deng et al., 2018); elliptical (Ge et al., 2018; Xiong et al.,
2018); tapered tubes (Tran, 2017); honeycomb (Palomba et al., 2018; Hu et al.,
2019); multi-cell (Xie et al.,

2017; Ding et al., 2018); and hybrid square tubes (Zhang et al.,
2019), have been researched in detail. From these studies, it was
well known that the most severe plastic deformation occurs near sectional
corners of tubes, which could dissipate a great amount of energy due to
membrane and bending deformation along the bending hinge lines (Hu et al., 2019). For example,
Shena et al. (2017) investigated the crashworthiness of rectangular single-,
double- and unequal triple-cell tubes made of aluminium alloy. An analytical
formula for predicting the mean crushing force (MCF) of unequal triple-cell
tubes was first derived. Quasi-static crushing experiments and finite element
analysis (FEA) were then conducted in the axial direction for the three
di?erent tubes. The results from numerical simulations were compared in detail
with data from experimental tests and theoretical predictions. It was found
that the triple-cell tube exhibited the best crash performance, followed by its
double- and single-cell counterparts. A multi-objective optimization design was
employed to investigate the effect of the thickness of each plate and the
arrangements of internal ribs on specific energy absorption (SEA) and MCF. An
experimental study on the crashworthiness of star-shaped tubes under axial
compression was conducted by Deng et al. (2018). A star-shaped tube with twelve
corners produced global buckling in quasi-static compression, while such a tube
with eight corners had a better energy
absorption capacity than tubes with six
and twelve corners. The deformation modes of quasi-static and dynamic impact
were very similar. According to Ge et al. (2018), the elliptical cross-section
becomes narrower compared to the circle one, which is also helpful in
increasing the energy absorption of the thin-walled tube.

To enhance the energy absorption capability and reduce the
initial peak crushing force of thin-walled tubes, the attention of many
researchers has also been drawn to corrugated tubes (Mahbod & Asgari, 2018),
functionally graded thickness (FGT) tubes (Sun et al., 2017), foam-?lled tubes
(Xiong et al., 2018; Googarchin et al., 2019) and metal/composite hybrid tubes
(Zhang et al., 2019). For instance, Mahbod and Asgari (2018) conducted a
theoretical study to investigate the behavior of corrugated composite tubes
under axial and oblique crushing. The corrugated model Cr6n16 improved CFE by
about 343% in comparison to the straight tube, without an sharp reduction in
the SEA in axial crushing. The corrugated tube Cr6n18 increased the SEA by
about 18%, with the same value of CFE as the straight tube in oblique crushing.
Sun et al. (2017) proposed uniform thickness (UT), axial functionally graded
thickness (AFGT) and lateral functionally graded thickness (LFGT) for thin-walled
square structures, and then investigated their crushing characteristics through
theoretical, numerical and experimental approaches under axial crushing loads.
These primary outcomes demonstrate that FGT structures have considerable
potential as energy absorption devices for axial impact. In terms of the methods
for improving energy absorption capacity, a theoretical and numerical
investigation of the energy absorption behavior of foam-?lled tapered
multi-cell tubes was made by Googarchin et al. (2019). Their analysis indicates
that the SEA in the crushing of the foam-?lled tubes with three cell rows in
the cross section and a taper angle equal to 7 degrees would be five times greater
than that in the crushing of the reference tube.

In particular, for the energy absorption structures of
bio-inspired design strategies, natural structural hierarchies were fruitful
learning resources. Based on their results from experimental testing and
numerical modelling, Zhang et al. (2018) concluded that a 2nd-order
hierarchical circular tube (HCT) offers signi?cantly greater energy absorption
than non-hierarchical structures (0th order HCT). Sub-circle diameters and wall
thickness have a signi?cant effect on the crashworthiness indictors of 2nd
order HCT. A bio-inspired bionic honeycomb tubular nested structure (BHTNS) was
proposed and the energy absorption characteristics of this structure under
axial crushing conditions were also investigated by systematic experiments,
numerical simulations, and theoretical analysis (Hu et al., 2019). Finally, a
theoretical model was developed to predict the Pmean of BHTNS. It was observed
that the Pmean of the theoretical model was in good agreement with that from the
numerical simulation.

There are some limitations in conducting experimental drop test
studies. They need a high tower, rig, load cell, high-speed camera, LabVIEW
software, and computer. Meanwhile, numerical analysis requires software such as
ANSYS LS DYNA, LS DYNA, ABAQUS or Pam Crash. Significant costs are involved in
setting up the two methods, which is the main reason why development of
theoretical analysis is needed.

As mentioned above, this study is related to the theoretical
predictions of Zhang et al. (2019), Tran et al. (2017), Ding et al. (2018), Sun
et al. (2017) and Xie et al. (2017). However, the most common theoretical predictions for rectangular tubes
are suggested by Abramowicz and Jones (1984)
and Nguyen et al. (2013). In terms of the number of crush initiators, Nguyen et
al. used one or two, while Abramowicz and Jones did not use any. From the point
of view of the basic folding mechanism, Nguyen et al. employed the symmetric
collapse mode, whereas Abramowicz and Jones used the asymmetric mixed collapse
modes A and B, together with the symmetric collapse mode. Abramowicz and Jones
suggested the prediction of an average force equation, while Nguyen et al.
proposed prediction of average force and peak force equations. Nguyen et al.
also used a coefficient of geometry to peak force equation. This study proposes
a new concept for predicting dynamic axial crushing
performance, including the use of an eight crush initiator, asymmetric
mixed collapse modes A and B and symmetric collapse mode for the basic folding
mechanism, and equations of average force, peak force and energy absorption.
These prediction equations consider the coefficients of peak force and stress
concentration. Finally, the objective of this study
is to develop a theoretical prediction of dynamic axial crushing on a
thin-walled square steel tube with eight holes used as a crush initiator.

Conclusion

This work has presented
a comparison between theoretical and experimental analysis of the behavior of a
thin-walled square tube structure under axial crushing. For the symmetric
collapse mode, the formula for predicting mean dynamic force is shown as
Equation 23; for peak crushing force as Equation 24; and for energy absorption as
Equation 25. For asymmetric mixed collapse mode A, the formula for predicting
mean dynamic force is shown as Equation 35; for peak crushing force as Equation
36; and for energy absorption as Equation 37. For asymmetric mixed collapse
mode B, the formula for predicting mean dynamic force is shown as Equation 47;
for peak crushing force as Equation 48; and for energy absorption as Equation
49. The theoretical analysis shows close agreement with the experimental drop
test study.

Acknowledgement

The authors greatly
appreciate the *Departemen Riset dan Pengabdian Masyarakat* Universitas
Indonesia for the research grant Year 2015 by *Hibah Riset Pascasarjana*
2015.

References

Abramowicz, W., Jones, N., 1984.
Dynamic Axial Crushing of Square Tubes. *International
Journal of Impact Engineering*, Volume 2(2), pp. 179–208

Deng, X., Liu, W., Lin, Z., 2018.
Experimental and Theoretical Study on Crashworthiness of Star-shaped Tubes under
Axial Compression. *Thin-Walled Structures*, Volume 130, pp. 321–331

Ding, X., Zeqi, T., Liu, Y., Liu,
S., 2018. Dynamic Axial Crush Analysis and Design Optimization of a Square
Multi-cell Thin-walled Tube with Lateral Variable Thickness. *International Journal of Mechanical Sciences*, Volume 140, pp. 13–26

Dionisius, F., Istiyanto, J.,
Suliono., Rohmat, Y.R., 2017. *Pengembangan Pengujian Crashworthiness dengan
Simulasi Numerik Menggunakan Impact Transferability* (Development of Crashworthiness Testing with
Numerical Simulation using Impact Transferability). *Jurnal Teknologi Terapan*,
Volume 3(1)*,* pp. 12–17

Ge, C-Q., Gao, Q., Wang, L.,
2018. Theoretical and Numerical Analysis of Crashworthiness of Elliptical
Thin-walled Tube. *International Journal
of Mechanical Sciences*, Volume 148, pp. 467–474

Googarchin, H.S., Pasandidehpoor,
M., Mahmoodi, A., Shojaeefard, M.H., 2019. Energy Absorption Analysis for
Tapered Multi-cell Tubes Improved by Foams: Theoretical Development and
Numerical Simulation. *Composite
Structures*, Volume 207, pp. 213–222

Hu, D., Wanga, Y., Songa, B., Danga,
L., Zhang, Z., 2019. Energy-absorption Characteristics of a Bionic Honeycomb
Tubular Nested Structure Inspired by Bamboo under Axial Crushing. *Composites Part B: Engineering*, Volume
162, pp. 21–32

Mahbod, M., Asgari, M., 2018.
Energy Absorption Analysis of a Novel Foam-?lled Corrugated Composite Tube
under Axial and Oblique Loadings. *Thin-Walled
Structures*, Volume 129, pp. 58–73

Malawat, M., Istiyanto, J.,
Sumarsono, D.A., 2017. Effects of Wall Thickness and Crush Initiators Position
under Experimental Drop Test on Square Tube. *Applied Mechanics and Material*, Volume 865, pp. 612–618

Malawat, M., Sumarsono, D.A.,
2017. Optimization of Impact Energy Absorber Parameters for Automobile Crush
Box using Response Surface Method. *In: *Proceedings
of Quality in Research 2017, Bali, July 24-27^{th}, Volume 15, pp. 333–339

Najafi, A., Rais-Rohani, M.,
2011. Mechanics of Axial Plastic Collapse in Multi-cell, Multi-Corner Crush Tubes.
*Thin-Walled Structures*, Volume 49(1),
pp. 1–12

Nguyen, C.N., Dirgantara, T.,
Gunawan, L., Putra, I.S., Ly, H.A., 2013. Analytical Prediction of Square Crash
Box Structure with Holes Due to Impact Loading. *In:* Regional Conference on Mechanical and Aerospace Technology
2013, Kuala Lumpur, November 25-26^{th}

Palomba, G., Epasto, G., Crupi,
V., Guglielmino, E., 2018. Single and Double-layer Honeycomb Sandwich Panels
under Impact Loading. *International
Journal of Impact Engineering*,
Volume 121, pp. 77–90

Shena, W., Gu, X., Jiang, P., Hu,
J., Lv, X., Qian, L., 2017. Crushing Analysis and Multi Objective Optimization
Design for Rectangular Unequal Triple-cell Tubes Subjected to Axial Loading. *Thin-Walled Structures*, Volume 117, pp.
190–198

Sumarsono, D.A., Istiyanto, J.,
Malawat, M., 2015. *Pengembangan Impact Energy Absorber Dengan Pengaturan
Jarak Crash Initiators* (Development
of Impact Energy Absorber with Distance Management of Crash Initiators).
*In: *Prosiding Seminar Nasional
Tahunan Teknik Mesin XIV 2015, Banjarmasin, Volume 15

Sun, G., Pang, T., Xu, C., Zheng,
G., Song, J., 2017. Energy Absorption Mechanics for Variable Thickness Thin-walled
Structures. *Thin-Walled Structures*, Volume 118, pp. 214–228

Tran, T.N., 2017. Crushing and
Theoretical Analysis of Multi-cell Thin-walled Triangle Tube under Lateral
Loading. *Thin-Walled Structures*, Volume 115, pp. 205–214

Xie, S., Yang, W., Wang, N., Li, H.,
2017. Crashworthiness Analysis of Multi-cell Square Tubes under Axial Loads. *International Journal of Mechanical Sciences*,
Volume 121, pp. 106–118

Xiong, F., Wang, D., Yin, S.,
2018. Optimization Analysis of Novel Foam-?lled Elliptical Columns under
Multiple Oblique Impact Loading. *Materials
and Design*, Volume 156, pp.
198–214

Zhang, J., Lu, B., Zheng, D., Li,
Z., 2019. Axial Crushing Theory of Metal-FRP Hybrid Square Tubes Wrapped with
Antisymmetric Angle-ply. *Thin-Walled
Structures*, Volume 137, pp.
367–376

Zhang, Y., Xu, X., Wang, J.,
Tengteng, C., Wang, C.H., 2018. Crushing Analysis for Novel Bio-inspired
Hierarchical Circular Structures Subjected to Axial Load. *International Journal of Mechanical Sciences*, Volume 140, pp. 407–431