This paper presents studies of the numerical prediction of the behaviour of polyurethane (PU) foam filled hat section tubes. Experimental results of the foam-filled single-hat and double-hat components tested in an impact testing machine are described. Consistent experimental load displacement curves were generated. FE analyses using LS-DYNA of the impact behaviours predicted are shown to agree favourably with experimental results.

1. International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Issue 04, Volume 4 (April 2017) (SPECIAL ISSUE) www.ijirae.com
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IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2016): 3.916 | PIF: 2.469 | Jour Info: 4.085 |
ISRAJIF (2016): 3.715 | Indexcopernicus: (ICV 2015): 47.91
IJIRAE © 2014- 17, All Rights Reserved Page -65
Numerical prediction of polyurethane foam filled steel hat
Section tubes under axial loading
B. Haorongbam#1
, A. Deb*2
, T.Y. Reddy$3
#
FOAD, PES University, Bangalore, India
*
CPDM, Indian Institute of Science, Bangalore, India
$
Vemana Institute of Technology, Bangalore, India
Abstract-- This paper presents studies of the numerical prediction of the behaviour of polyurethane (PU) foam filled hat
section tubes. Experimental results of the foam-filled single-hat and double-hat components tested in an impact testing
machine are described. Consistent experimental load displacement curves were generated. FE analyses using LS-DYNA
of the impact behaviours predicted are shown to agree favourably with experimental results.
Keywords—PU-foam, hat section, impact, simulation, LS-DYNA
INTRODUCTION
Tubular structures of single and double hat sections made of steel are frequently used as automotive body structural
components such as front rails and rockers of unitized-body cars. An example is shown in Figure 1. These components
absorb significant amounts of impact energy during front collisions and thus are indispensable countermeasures in ensuring
vehicle crashworthiness and occupant safety. With the need for higher fuel economy and stringent emission norms, auto
manufacturers are looking for means to reduce the vehicle’s weight either by employing lighter materials like fiber-
reinforced plastics or by decreasing the thickness (gauge) of the vehicle structures or a combination of both. Reducing the
gauge leads to structural instability due to early inelastic buckling. This phenomenon of instability evokes the proposition
of filling the thin walled tube like structural members with light, crushable fillers. Such members filled with PU-foam (and
such other fillers) have increased resistance to local buckling mechanisms and higher strengths as well as energy absorbing
capabilities. There has been a continued interest in the study of the axial crush behaviour of thin-walled structural
components with box and hat sections through experimental, semi-analytical, empirical, and numerical means. Mahmood
and Paluszny [1] presented semi-empirical relations for the prediction of average load-carrying capacities of closed
rectangular box sections subjected to progressive local buckling under quasi-static axial compressive loads. Comparisons
with experimental results were also given for steel columns with geometric aspect ratios relevant to automotive body
applications such as front rails. Simplified theoretical and empirical procedures for predicting the performances of hollow-
hat sections were reported in [2 - 4]. White and Jones [5] carried experimental studies on quasi-static axial crushing of steel
tubes of single and double hat-sections. A detailed experimental study on progressive collapse behaviour of thin-walled
closed-section structural components made from high-strength steels under quasi-static and impact axial loads was reported
by Schneider and Jones [6], who also made a comparison with theoretical formulas which had been used successfully for
predicting the behaviour of mild steel thin-walled structures.
Figure 1A typical body-in-white of a unitized body car [11]

2. International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Issue 04, Volume 4 (April 2017) (SPECIAL ISSUE) www.ijirae.com
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IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2016): 3.916 | PIF: 2.469 | Jour Info: 4.085 |
ISRAJIF (2016): 3.715 | Indexcopernicus: (ICV 2015): 47.91
IJIRAE © 2014- 17, All Rights Reserved Page -66
References [7-10] discussed experimental and numerical studies on the behaviour of hollow hat section components. Jamil
et al. [12] studied PU-foam filled single hat sections under quasi-static axial crushing and bending load conditions and the
same study was carried out using LS-DYNA 3D,an explicit finite element code. Axial crushing of empty and polyurethane
foam-filled square and rectangular tubular sections under quasi-static and dynamic loading conditions was studied in [13].
The authors considered the tube walls to behave as plate on foam foundation. They also explained the filler-shell
interaction and the mechanics underlying the increase in the mean loads and reduction of stroke resulting from filling the
tubes with foam.
It appears that very limited studies have been carried out on the behaviour of PU-foam filled hat section tubes under impact
loading. In this study both single and double hat sectioned tubes were subjected to impact loading. With an eye on design
application for which CAE is an indispensable analysis tool, numerical models were developed for an accurate prediction
of the behaviour of foam filled hat sections using the explicit non-linear finite element analysis code, LS-DYNA. These
are described below.
EXPERIMENTS
The schematic views and cross-sectional dimensions these tubes were as shown in Figure 2 and Table 1, respectively. It
needs to be mentioned here that the length of the hat section tubes are 250 mm. A mixture of polyol and iso-cyanide
(making the PU foam) in the required proportions was used to obtain the required density was poured into the tubes and the
ends were sealed to avoid the expanding foam from following out. A foam density of around 0.145 g/cc was maintained in
as higher density foam leads to the bulging of the tube faces. The tubes so prepared were subjected to axial impact loading
using a drop mass facility. The impact or mass was 134 kg and the pre-impact velocity was 4.74 m/s. The dynamic
response was obtained from the load cell supporting the specimen.
TABLE 1DETAILS OF SINGLE-HAT AND DOUBLE-HAT SECTIONS
TEST SPECIMEN TYPE SECTION DETAILS: A(MM), B (MM),
F(MM) AND T (MM)
SPOT-WELD PITCH
(MM)
SINGLE-HAT 60, 60, 25, 1 45
DOUBLE-HAT 60, 60, 25, 1 45
Figure 2 Schematic views of (a) single-hat and (b) double-hat sections
Results for drop tests in the form of load-time histories are presented in Figure 3 for two foam-filled single-hat section tube
specimens and in Figure 4 for two foam-filled double-hat section specimens respectively. It is seen from these figures that
the responses for a given type of specimen are similar. Moreover it is evident from Tables 2and 3. Thus, a high degree of
confidence can be placed on the experimentally-obtained impact loading responses.
TABLE 2COMPARISON OF IMPACT TEST RESULTS OF FOAM-FILLED SINGLE-HAT SECTION TUBES
CASE PEAK LOAD (KN) MEAN LOAD (KN) CRUSH LENGTH (MM)
SHIFF3 51.63 21.39 68
SHIFF4 54.15 22.65 72
TABLE 3 COMPARISON OF IMPACT TEST RESULTS OF PU-FOAM FILLED DOUBLE-HAT SECTION COMPONENTS
CASE PEAK LOAD (KN) MEAN LOAD (KN) CRUSH LENGTH (MM)
DHIFF3 64.12 32.38 49
DHIFF4 63.11 32.57 49

3. International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Issue 04, Volume 4 (April 2017) (SPECIAL ISSUE) www.ijirae.com
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IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2016): 3.916 | PIF: 2.469 | Jour Info: 4.085 |
ISRAJIF (2016): 3.715 | Indexcopernicus: (ICV 2015): 47.91
IJIRAE © 2014- 17, All Rights Reserved Page -67
Figure 3 Load time histories of two foam-filled single-hat section components under axial impact loading
Figure 4 Load time histories of two foam-filled double-hat section components under axial impact loading
MATERIAL PROPERTIES OF PU-FOAM
PU-foam cubes of 50 mm side were made and loaded in a universal testing machine (UTM) to obtain their stress-strain
characteristics. The cubes were crushed at cross-head speed of 1mm/min. From the stress-strain characteristics shown in
Figure 5, it was observed that it first behaved elastically. Then upon reaching the yield stress, the flow stress increased
gradually over a strain range before the material began to stiffen significantly at a particular strain ε1.
Figure 5Quasi-static stress-strain behaviour of PU-foam billet
NUMERICAL PREDICTIONS
The finite element modelling procedure adopted for the impact loading of empty hat section discussed [9] was also
employed here. The PU-foam, however, is modelled with 8 noded solid hexa-element, and using Mat63 as the material
model. The stress-strain curve shown in Figure 5was employed for the foam.

4. International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Issue 04, Volume 4 (April 2017) (SPECIAL ISSUE) www.ijirae.com
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IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2016): 3.916 | PIF: 2.469 | Jour Info: 4.085 |
ISRAJIF (2016): 3.715 | Indexcopernicus: (ICV 2015): 47.91
IJIRAE © 2014- 17, All Rights Reserved Page -68
Figure 6Finite element model of DWITT impact or and foam-filled double-hat component before start of analysis
Additional contact in the form contact interior that takes care of self contact in foam structure was introduced. A finite
element model of DWITT impact or and foam-filled double hat component before the analysis is shown in Figure 6.A
comparison of test and simulated load-time histories are presented in Figures7 and 8 for foam-filled single and double hat
section components respectively. It is noted that a sampling rate of 10 kHz was used in saving the analysis-based responses
being reported in the current study followed with filtering using the SAE J211 (600Hz) filter recommended for structural
components. The simulated responses are seen to correlate well with the test behaviours. Tables4 and 5 show the
comparison of simulation and test behaviour in terms of crash performance parameters for foam-filled single and double
hat section components. A 90 % GCI [14] was achieved for foam-filled single hat section while a higher GCI of 95 % was
able to achieve for double hat section. A comparison of deformed shape of tested and simulated foam-filled double hat
section is shown in Figure 9 wherein the simulated structure is able to predict the exact number of folds (three) occurred in
the tested structure.
TABLE 4 COMPARISONS OF PERFORMANCE PARAMETERS FOR FOAM-FILLED SINGLE HAT TUBE: TEST AND SIMULATION
CASE PEAK LOAD (KN) MEAN LOAD (KN) CRUSH LENGTH (MM) GCI
TEST 54.15 22.14 68 1
SIMULATION 48.64 23.16 65 0.90
TABLE 5 COMPARISONS OF PERFORMANCE PARAMETERS FOR FOAM-FILLED DOUBLE HAT TUBE: TEST AND SIMULATION
CASE PEAK LOAD (KN) MEAN LOAD (KN) CRUSH LENGTH (MM) GCI
TEST 64.12 33.45 45 1
SIMULATION 62.63 31.36 48 0.95
Figure 7 Comparison of load time curves for foam-filled single hat section component: Test and Simulation
Figure 8 Comparison of load time curves for double hat section component: Test and Simulation

5. International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Issue 04, Volume 4 (April 2017) (SPECIAL ISSUE) www.ijirae.com
___________________________________________________________________________________________________
IJIRAE: Impact Factor Value – SJIF: Innospace, Morocco (2016): 3.916 | PIF: 2.469 | Jour Info: 4.085 |
ISRAJIF (2016): 3.715 | Indexcopernicus: (ICV 2015): 47.91
IJIRAE © 2014- 17, All Rights Reserved Page -69
Figure 9Comparison of deformed double hat section component: (a)Test (b) Simulation
CONCLUSIONS
The efficacy of foam-filled structures is demonstrated here. Fairly repeatable impact responses were seen both for foam-
filled single and double hat section tubes. Good numerical prediction of the impact behaviour was achieved. GCIs of 90 %
and 95 % were achieved for foam-filled single and double hat section tubes under axial impact loading.
REFERENCES
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