Cushioning Performance and Mathematical Validation of Hot-Welded Multilayered Polymer Foams Kerimcan 1 2
1 Celebi
, Fatih
1 Daricik
, Yilmaz 1 Horpan
2 Erbil
, Serdar
2 Guzel
, M.Safa
Adana Science and Tecnology University, Adana, Turkey, E-mail:
[email protected] Secant Technology Development A.S., Eskisehir, Turkey, E-mail:
[email protected]
Abstract Modelling of mechanical response of polymer foams require two thorough procedures starting with a set of mechanical experiment, which can then be validated by a series of mathematical simulations using computer software. Polyethylene foams of identical thickness and density (30 kg/m^3) are manufactured via a hot-welding method to obtain desirable thicknesses. A series of compression tests are carried out in order to gauge the cushioning and impact load performance of the monolithic foams in axial and transverse directions. Mathematical simulations, hence validation of the foams is then attained and examined using LS-DYNA, Model 57 for low density foams. A comparison and simulation results is made, finding a considerable correlation between the model and the mechanical tests. Keywords: Cushioning Performance, Material Modelling, Polyethylene foam, LS-DYNA Validation
INTRODUCTION Foam material applications usually require high energy absorbing capabilities and sufficient recovery properties with rather widely known low-density necessities of 21st century materials. Polymeric materials, specifically thermoplastics largely due to their ductile nature, not only provide a successful candidate for foam applications, but appear to be the best options compared to other materials especially other material types are concerned. The three-regime behavior of polymeric foams under compression loads has been shown time and time again. However, there are distinct studies that has shed light on main characteristics of these materials. Avalle et al. , examined different polymeric foams including EPP (Expanded Polyproplyene), UR (Rigid Polyurethane) and modified Polyamides. Results indicate that the behavior of these materials shows a similar tendency in terms of impact response, although material properties show a divergence of plastic deformation differences [1]. Furthermore the formulation of viscoelastic properties of elastomeric foams is investigated in 2004 by Yang and Shim in which a mathematical formulation of material properties is presented thoroughly [2]. Another study is carried by Quellet et al., explaining the function of density and strain rate during compressive tests . The response is examined for three different materials including expanded polystyrene (EPS), high density polyethylene (HDPE) and PUR (Rigid Polyurethane) foams. A non-linear relationship above 103 strain rate is observed between stress and strain [3]. A different approach is adopted by Song et al. as to the nature polymer foams, although the material under scope is a thermosetting material, low density epoxy. It is showed that an increase in strain rate leads to an increase in the modulus of elasticity, cell-collapse and plateau stress [4]. A finite element method is developed by Jebur et al., in order to reproduce compressive load response of LDPE closed cell foams [5]. The cell formation of a certain material appears to have significant effect on material properties as shown by Petel et al.. In this study a comparison is drawn between different polyurethane foam types including open-cell polyurethane (PU) foam, micro-porous open-cell polyurethane foam and low density PE foam in terms their blast wave loading and shock tube loading behaviors. It is ascertained that gas filtration to the foams does not necessarily contribute to mechanical properties of the foam [6].
Apostol and Constantinescu (2013) investigated the influence of temperature on the densification and recovery of PU foams subjected compressive loads in a wide range of strain rate. They proposed a temperature and density dependent mathematical model to obtain compressive stress-strain curves of the foams. However, it was seen that the recovery behavior is not temperature and testing speed dependent, in any case of the density [7]. In a previous study, hot welded polyurethane foams are investigated by Daricik et al. in terms of their response to compression tests [8]. The scope of this study is to validate the mechanical test data obtained by the previous study. Slik et al, provided an adequate example of mathematical validation via MAT57 on LS-DYNA platform for crushable foams [9].
METHODS As the study shown here consists two aspects, the examination will be made in reference to our previous study [8]. The mechanical testing data, obtained from the compression tests carried out by Daricik et al., comprises of results for drop weight compression results. Three different products with the dimensions of 50 x 50 mm used in the process. Although there are three different samples used in the mechanical testing stage, only one will be presented in this poster (LD29, Zotefoam) On the other hand, the details of the mathematical validation of these foams are achieved by using Model 57 for LS-DYNA software, which is for crushable polymer foams [10]. The mechanical equation set below is the fundamental equation in the development of Model 57.
CONCLUSIONS Until this point, fundamentals and background of the study is unveiled. The data obtained from mechanical tests and LS-DYNA simulation is presented below for only one material type, Zotefoam LD29. Compression tests are repeated 3 times for the same sample. LS-DYNA Test Data 1 Test Data 2 Test Data 3
1,0
0,8
Stress (MPa)
Çukurova University Congress Center Adana / TURKEY October 26-28, 2016
0,6
0,4
0,2
0,0 0,0
0,5
1,0
Deformation (%)
where gijkl (t-τ) is the relaxation function. Furthermore the mechanical behavior of these foams can be seen in Figure 1.
REFERENCES Figure 1 – Behavior of the low density urethane foam model [10] Another very important parameter for this model, which underlines relaxation function is decay constant β1 which is given in the equation below.
The function given above in different aspects is in its roots acts like a Maxwell consisting of a damper and a spring in series that includes and hence connects different parameters such as Young’s modulus and decay constant. In order to grasp the fundamentals of the testing stage, Figure 2 is given where the testing conditions and the foam material structure can be seen.
Figure 2 – Foam illustration and material compression testing stage
1. Avalle, M., G. Belingardi, and R. Montanini, Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram. International Journal of Impact Engineering, 2001. 25(5): p. 455-472. 2. Yang, L.M. and V.P.W. Shim, A visco-hyperelastic constitutive description of elastomeric foam. International Journal of Impact Engineering, 2004. 30(8–9): p. 1099-1110. 3. Ouellet, S., D. Cronin, and M. Worswick, Compressive response of polymeric foams under quasi-static, medium and high strain rate conditions. Polymer Testing, 2006. 25(6): p. 731-743. 4. Song, B., W. Chen, and W.-Y. Lu, Compressive mechanical response of a low-density epoxy foam at various strain rates. Journal of Materials Science, 2007. 42(17): p. 7502-7507. 5. Jebur, Q.H., et al., Characterisation and modelling of a transversely isotropic melt-extruded low-density polyethylene closed cell foam under uniaxial compression. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011. 6. Petel, O.E., et al., The elastic–plastic behaviour of foam under shock loading. Shock Waves, 2013. 23(1): p. 55-67. 7. Apostol, D.A. and D.M. Constantinescu, Temperature and speed of testing influence on the densification and recovery of polyurethane foams. Mechanics of Time-Dependent Materials, 2013. 17(1): p. 111136. 8. Daricik F., C.K., Erbil Y., Guzel S., Cushioning Performance of Hot Welded Polyethylene Foams in International Material Science and Technology in Cappadocia 2016: Nevsehir, Turkey 9. Slik, G., G. Vogel, and V. Chawda. Material model validation of a high efficient energy absorbing foam. in Proceedings of the 5th LSDYNA Forum. 2006. Citeseer. 10. LS-DYNA Theory Manual, Materials Models, MAT57. 2015, Livermore Software Technology Corporation
1st International Mediterranean Science and Engineering Congress 1. Uluslararası Akdeniz Bilim ve Mühendislik Kongresi Çukurova University, Congress Center Adana / TURKEY Çukurova Üniversitesi, Kongre Merkezi ADANA October 26-28, 2016 26-28 Ekim 2016
