Experimental Investigations on Polymeric Foams

Klar, Oliver and Ehlers, Wolfgang

Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70 569 Stuttgart, Germany,www.mechbau.uni-stuttgart.de/ls2

The knowledge of the material behaviour of polymeric foams and their experimental investigation is the starting point for thestructure of the chosen constitutive equations and for the following identification of the material constants therein. Especiallyfor the parameter identification, it is necessary to make an adequate set of experimental data available.In this regard, it is important that the experiments make the different kinds of material behaviour visible like elastic, plasticor viscous material properties. For this reason, the foam is observed under uniaxial tension and compression and undersimple shear tests combined with different deformation states in axial direction. Unfortunately, due to different reasons, e. g.,the foam must be sticked on the fastener to realize the tests mentioned above, it is very difficult to initialize a homogenousdeformation state in the specimen. Therefore, the experiments are recorded with a standard digital camcorder to get localinformation of the deformation state by tracking single points with algorithms of the digital image processing.

1 Polymeric foams

The various properties of polymeric foams, for instance, the thermal insulation, the cushioning behaviour and the absorbing ofkinetic energy, enable a variety of applications for these materials. Increasingly, their mechanical characteristics are utilizedand they are used, e. g., as impact bumpers and seat cushions in the automotive industry or as packaging for industrial products.Due to the production process, where the polymeric feedstock is foamed by introducing gas bubbles into the liquid polymer, itis obvious that the evolving foam consists of a polymeric solid skeleton with an open and/or closed fluid-filled cell structure.

In Gibson and Ashby [1], the general mechanical behaviour of polymeric foams is discussed under uniaxial compressionand tensile loads. Therein, it is shown that independently from an elastomeric, elastio-plastic and elastic-brittle foam, theresponding force in a displacement driven compression test can be divided into three characteristic areas: a small linear elasticzone that is controlled by cell wall bending followed by a long collapse plateau that is associated with collapse of the cells(elastic buckling, formation of plastic hinges and brittle crushing) and completed with a densification towards a compactionpoint, when opposing cell walls touch each other. For uniaxial tensile tests, a small linear elastic area can also be observed. Incase of elastomeric and elastic-plastic foams, larger strains lead to an alignment of the cell membranes and for this reason toan increase of the stiffness of the structure. In case of elastic-brittle foams, the cell walls break and the specimen fails.

2 Experimental investigation

In the present contribution, experiments were made for an open-cell, flexible polyurethane (PU) foam (bulk density 48 kg/m3

→ porosity 96 %), which is used, e. g., as seat cushions in the automotive industry. For this purpose, cubic PU foam specimensof size 70×70×70mm3 were glued on the aluminium fasteners of a servo-hydraulic load frame and were displacement-drivenloaded and unloaded. Performing uniaxial compression and tensile tests with a maximal compression/strain of 86.7 %/55.3 %,Figure 1 confirms the characterized behaviour mentioned above. Additionally, a rate dependent behaviour becomes visible, ifeither the loading and unloading cycles were incorporated with several holding times (Figure 1, left) or the deformation ratewas varied (Figure 1, right). To find out that the material does not undergo plastic deformations, it has to be ensured that theviscous overstresses relax completely. This can be verified, if the relaxation boughs meet during the loading and the unloadingcycle at the same deformation state. Due to the long relaxation time of the investigated PU foam, the purely viscoelasticbehaviour is only shown at one deformation state, where the final value of the relaxation bough lies in the middle of the twoboughs of experiments with shorter relaxation times (magnification in Figure 1, left).

Similar to the tensile behaviour is the responding force under a simple shear experiment (Figure 2, left). This property isconsistent with the idea that the cell membranes align with the shear angle during the experiment and were therefore pulled.Obviously, the specimens behave stiffer, if they are pre-extended. As a result of the tensile load, damage of the cell structureoccurs by breaking of single cell walls. This can be observed in cyclical tests, where the stress response under tensiondecreases after each load cycle. Unlike, the compression behaviour stays nearly unaffected (Figure 2, right).

Additionally, the pore gas motion through the open-cell foam superposed a time dependent force to the intrinsic vis-coelasticity of the polymeric skeleton. This part of the overall stress increases with higher deformation rates and growingcompression states. In the first case, particles of the pore fluid have not enough time to flow relaxed to the surface of thespecimen. In the second case, the narrowed openings between the cell membranes prohibit a free escape. Especially, due

PAMM · Proc. Appl. Math. Mech. 4, 402–403 (2004) / DOI 10.1002/pamm.200410182

© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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to the interaction between the polymeric solid skeleton and the pore fluid, the investigated PU foam can be described withconstitutive equations based on the well-founded Theory of Porous Media [2,3].

3 Tracking algorithm to determine local deformation

For the identification of the material constants in the chosen constitutive equations, it is necessary to have an adequate set ofexperimental data. Due to the difficulty to initialize a homogenous deformation state in the specimen during the experiments,a contactless, optical measuring method is used to get local information of the deformation state. Therefore, the specimen ismarked with specifiable characteristics at each point that will be tracked and is recorded with a standard digital camcorderwhile the experiment runs. With this digitized picture information in the form of a matrix that displays the luminosity valueof the RGB-colours at every pixel of the CCD-sensor (charged coupled device), it is possible to follow every marked point onthe specimen and therewith to obtain an information about their relative motion. For this purpose, a template is cut from theoriginal picture that includes the marked point, and therewith, the problem reduces to find the best statistical correlation ofthe template with an area of the same size within a trust region of the following picture. The size of the trust region dependson the velocity the tracked points move in the frame rate and displays the most probable region for the location of the markedpoint. The result of the application of this algorithm can be seen in the frame rate of Figure 3.

Fig. 3 Tracking of a single point on the specimen with algorithms of the digital image processing.

References

[1] L.J. Gibson and F. Ashby, Cellular Solids, Structure and Properties, 2nd ed. (University Press, Cambridge 1997).[2] W. Ehlers and B. Markert, On the viscoelastic behaviour of fluid-saturated porous materials, Granular Matter 2, 153-161 (2000).[3] W. Ehlers, B. Markert and O. Klar Biphasic description of viscoelastic foams by use of an extended Ogden-type formulation. In W.

Ehlers, J. Bluhm (eds.): Porous Media: Theory, Experiments and Numerical Applications, 275-294 (Springer, Berlin 2002).

© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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