Volumetric behavior of polymer foamsduring compression and tension

MT 10.24

Bachelor End ProjectAuthor: Stephan Wijnands

November 2010

Supervisors:J.G.F. Wismans L.E.Govaert

Contents

1 Introduction 1

2 Polymer Foams 2

2.1 Deformation mechanisms of foams . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Materials 5

3.1 IMPAXX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 PUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Experimental 7

4.1 Mechanical testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.1 IMPAXX sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.2 PUR sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.2 Photo-acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2.1 Digital Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2.2 Aramis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Results 11

5.1 IMPAXX results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.2 PUR results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Comparison between IMPAXX and PUR . . . . . . . . . . . . . . . . . . . . . . . 17

6 Conclusion 18

1 Introduction

Polymer foams are a group of polymers which have been imbued with a gas, causing them to have alower density and different properties, such as different mechanical, thermal and acoustic behavior.The behavior will partially be determined by the material of which the foam is made and partiallyof the cell structure and the filler gas behavior. These foams are useful for various applications,such as insulation, cushioning or absorbing impacts. The goal of the project is to characterizethe volume effects of two different types of polymer foams (open-celled and closed-celled) undertensile or compression stresses, to gain a better understanding of the mechanical behavior.

In literature there are several models describing the relationship between the material propertiesof the polymer and the cell wand properties [1] but the macroscopic volumetric effects are not de-scribed as such. This project focuses on volumetric behavior under compression and tensile loads.Both materials will undergo a series of tests which are recorded by a camera. Advanced techniquesare used to analyze these images in 2-D, after which the 3-D volume changes are determined. Theexpectation is that the compression and tensile tests will not have the same volumetric behavior,due to different deformations of the microstructure in tension and compression.

This report will start by providing the necessary background about foams to better understandthe mechanical properties and afterwards the foam materials themselves will be clarified. Thenext chapter will describe the mechanical tests for both materials and the method to analyse theimages made by the camera. Afterwards the results will be discussed and a conclusion statedabout the volumetric effects.

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2 Polymer Foams

Foams are used in many different applications. The mechanical properties of foams are relatedto their complex microstructure and to the properties of the material of which the cell walls aremade. Some unique properties of foams are the relative density (R = ρ∗

ρ , in which the ∗ stands

for the foam properties), the degree to which cells are open or closed and the geometric shape ofthe foams.

The most important properties of the solid base material are the polymer density ρs , Young’smodulus Es and yield stress σys. These material parameters can be found in literature or areprovided by the manufacturer. Factors such as strain-rate and specimen size will also influencethe material behavior of polymer foams, as do some other factors like temperature, anisotropy andloading conditions. In this study the loading condition will vary; the other factors will be keptconstant.

2.1 Deformation mechanisms of foams

The stress-strain responses of foams in compression tests show likewise properties for differenttypes of foams. Figure 1 shows typical schematic compressive and tensile stress-strain responsesfor an elastomeric foam and for an elasto-plastic foam.

Figure 1: The two figures to the left show elastomeric and elasto-plastic compressive stress-strainresponses, the two figures to the right show the tensile stress-strain responses for those materials[1].

When looking at the stress-strain responses of both materials in compression, they start at lowstrains with a region of linear elasticity which is followed by a long collapse plateau in whichthe stress does not vary much. The curves end with a fast increase in stress which is called thedensification region. Each region is determined by a different mechanism of deformation. A foamcan be plastic in compression but brittle in tension, since a crack can concentrate the stress in asingle point, which causes the material to fracture fast in tension.

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The first region,linear elasticity, is controlled by cell wall bending in case of open-celled foams,and stretching of the cell walls in case of closed-celled foams. The Young’s modulus E∗ is theinitial slope of the stress-strain response of the polymer foam. When strains are small, the foamwill have an elastic response.

The collapse plateau is associated with collapse of the cells. The plateau region is different forelastomeric foams and elasto-plastic foams. An elastomeric foam has a plateau which is determinedby elastic buckling of cell walls while an elasto-plastic foam has a plateau determined by theformation of plastic hinges. If a foam is fully elastomeric then there is no plastic deformation, andthe foam will return to its original deformation when no stresses are applied. An elasto-plasticmaterial the foam does have a plastic region.

When the cells of a foam almost completely collapsed on themselves, then the opposing cellwalls touch and if the strain is increased it compresses the solid itself, causing a final regionof rapidly rising stress, called as densification. The slope of this densification approaches theYoung’s modulus of the solid polymer of the foam. Increasing the relative density of the foamincreases the Young’s modulus of the total foam, which raises the plateau stress and reduces thestrain at which densification begins. When a closed-cell foam is compressed, the cell fluid orgas is also compressed, leads to an additional stress on the cell walls. When a open-celled foamis compressed, the deformation forces the fluid to flow from cell to cell causing viscous effects,which also generates a resistance force. The existence of plastic hinges in the elasto-plastic foamcauses a long and nearly flat plateau which is ideal for energy absorbtion (area under the stress-strain curve). Plastic collapse in the elasto-plastic foams causes the material to crumble, whichcan rupture the cell walls and allow gas to escape. The material behavior in that case is like aopen-celled foam.

When looking at the stress-strain responses of both materials in tension, they start with thesame linear elasticity region as the materials in compression. In this case the cell walls also bend(open-celled foams) or stretch(closed-celled foams) only in the opposite direction compared tocompression. For an elastomeric foam this followed by a region in which the stress continues torise with increasing strain, caused by the alignment of the cell walls. Unlike compression, thecell walls cannot buckle and therefore there is no plateau in tension. Instead the cell walls whichlie at an angle to the tension direction, rotate towards this direction, causing an alignment invertical direction. This increases the density of the foam until it almost reaches the density of thesolid polymer material itself at higher strains. An elasto-plastic foam has the region of elasticityfollowed by a plastic yield, before the alignment of the cell walls. This is probably caused byrupturing of the closed-celled foams because of pressure buildup in the cells. This temperorarilyreduces the amount of stress, but causes a plastic deformation. After this region the cell wallsalign just like the elastomeric foams. Images of the buckling of open-celled foams in compressionand alignment of closed-celled foams in tensile are shown in Figure 2 on the next page.

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Figure 2: Top:Schematic representation of the buckling of open foam cell walls in compression.The left image shows the undeformed state, the right image shows the buckling of the cell walls.Bottem:Schematic representation of rotation and stress buildup of closed-celled foams under tensilestress[1].

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3 Materials

Tests have been performed on two polymer foams that both have different properties. The firstmaterial is a polystyrene based foam called IMPAXX, which is used in automotive industries forcrash protection. The second foam is polyurethane-based foam used for interior, like car seats.This foam will simply be referred to as PUR.

3.1 IMPAXX

IMPAXX is an energy absorbing foam which is ideal to absorb impacts. IMPAXX foams are highlyengineered polystyrene-based thermoplastic foams. It is formed by extruding polystyrene polymerwhich contains a halogen that has been formulated with blowing agents and other additives. Theblowing agents expand when pressure is released at the extrusion die to form the foam. Theresulting foam is strong and lightweight and is designed to maximize the efficiency and minimizethe weight. IMPAXX foams are mainly used for automotive applications. Their function is toabsorb the impact energy in the event of a crash and the foams are for instance installed withinbumpers or doors. IMPAXX can have different densities, but the main supply is IMPAXX 300,IMPAXX 500 or IMPAXX 700, which have a corresponding density of 38.5 kg

m3 , 40.4 kgm3 and 44.7

kgm3 [2]. All IMPAXX foams have a closed-cell structure, which can be shown with a ScanningElectron Microscope (SEM), see figure 3. For the experiments the IMPAXX 500 has been chosen.IMPAXX is said to have small temperature dependence, so all tests will be executed at a constantroom temperature, about 293 K.

Figure 3: Scanning Electron Microscope image of the closed-celled IMPAXX 500 structure[2].

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3.2 PUR

This flexible foam is used for example in seating interior of vehicles. This foam has an open-celledstructure which can again be shown with a SEM, see Figure 4. The material behavior of PUR issimilar to elastomeric foams. Polyurethane is any polymer consisting of a chain of carbon joinedby urethane links. Polyurethane polymers can be built of many different components, and theycover a wide range of stiffness, hardness, and densities. The PUR used for the experiments has adensity of 39 kg

m3 .

Figure 4: Scanning Electron Microscope image of the open-celled PUR structure[2].

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4 Experimental

4.1 Mechanical testing

Figure 5: Example of a Zwickstatic testing machine.

The machine used for the experiments is a Zwick static mechanicaltesting machine, which has enough displacement range and force toperform the experiments. A picture of such a testing machine canbe seen in Figure 5. The machine basically consists of a motor,a power cell, a clamping system and a lift system. The powercell used in the experiments is a 2.5 kN cell, which means it canmeasure forces up to 2.5 kN.

4.1.1 IMPAXX sample preparation

Compression testingSince the difference in volume will be measured, it is practical to

use axis metric samples so cylindrical samples are used. IMPAXXmaterial has been supplied in plates with a thickness of about30 mm. For the compression samples, a diameter of 50 mm hasbeen chosen to get several samples from one plate. The samplesare made by using a cavity drilling machine with the appropriatediameter. In the Zwick these samples are compressed between twocylindrical plates with a strain speed of 0.01 s−1, up to a verticalstrain of εln = 0.66 . compression. Before starting the experiment, the top clamp is moved upuntil there is enough space for a sample to easily fit between them. At this moment there is nocontact between the top clamp and the sample, so the force the machine is measuring will beset to zero. After that the top clamp is lowered while carefully monitoring the force. When themachine registers a small force (about 5 N), this means it has just barely come into contact withthe sample and the experiment can begin. The camera will start to record while the top clampmoves down and compresses the sample. An IMPAXX 500 compression sample can be seen infigure 6.

Tensile testingIn a tensile test the sample is pulled apart. In order to do this, the clamping system requires

an area on which it can transfer its force. This is best achieved by using friction, since this wouldonly slightly disturb the material itself near the grip point, and the rest of the sample remainsvalid for testing. Testing samples for the tensile test are long strokes taken from the IMPAXXplates, with high length compared to width and thickness. The dimensions are about 10x30x300mm. The clamps used in the machine have a specific shape in order to clamp the ends of thesamples and hold them. Unfortunately, when the ends are clamped enough to hold the samplein place, the ends are extremely deformed. Nearly all air has been removed which causes thematerial to fracture at the ends where the local stresses are a lot higher. In order to hold thesamples in place, a special add-on has been designed which is placed on top of the ends of thesamples[3]. The add-on consists of 2 plates of steel of dimensions 1x30x100 mm, and a block ofPVC, dimensions 10x30x50 mm. The steel plates are glued onto the top and bottom at the endof the sample, and onto the top and bottom of the PVC block. This allows us to put the frictionforce of the machine onto the hard polymer and upper half of the steel plates, who can resist thatforce without deforming like the IMPAXX. The glue makes sure the IMPAXX remains connectedto lower half of the steel plates, and therefore also transfers the force applied by the machine. AIMPAXX tensile sample can be seen in figure 6. With the IMPAXX-samples properly modified,they are placed within the Zwick machine. When the clamps are properly tightened the camerastarts the measurement and the top clamp moves up with a strain rate of 0.001s−1. At a certain

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moment in time the IMPAXX fractures and the experiment is repeated with a new sample.

4.1.2 PUR sample preparation

Compression testingThe test setup is almost the same as the IMPAXX 500 compression test, but the samples have

slightly different dimensions (diameter 60 mm instead of 50mm). These samples are prepared byusing waterjet cutting, a method which uses a narrow jet of water with high pressure and velocityto cut through material. The main advantage is that this cutting method does not disturb thefoam’s material structure.The material is presumed elastic, so there is the option to use eachsample more than once. In order to verify this, the first sample has been compressed multipletimes and the stress-strain response has been measured. This test has also been done for thebeam-shaped tensile samples. These samples are also pressed between 2 cylindrical plates with astrain speed of 0.01 s−1, up to a vertical strain of εln = 0.66 . The top clamp is lowered until avery small force of about 0.2 N is detected, then the camera is switched on and the experimentcan begin. The reason this force is much lower then the 5N of the IMPAXX samples is becausethe force needed for deformation is much lower. A force of 5N would cause the material to becompressed to much before the testing begins.A PUR compression sample can be seen in figure 6.

Tensile testingThis setup is also like the IMPAXX tensile test; however, since this material is elastic, it can

be clamped normally without disturbing the rest of the sample. These samples will also be usedmultiple times. Figure 6 shows an image of a PUR tensile sample

Figure 6: Left image: Example of an IMPAXX compression sample (left) and a PUR compressionsample (right). Middle image: Example of a IMPAXX tensile sample with add-on. Right image:Example of a PUR tensile test sample, with the original to the right and a sprayed sample forAramis to the left.

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4.2 Photo-acquisition

The images made by the camera are analyzed by using two different methods; Digital ImageCorrelation (DIC) and Aramis

4.2.1 Digital Image Correlation

This technique uses the gray-scale difference between the sample and the background to measurethe macroscopic changes in diameter and length. Using a Matlab program, a gray-scale limit isset. Everything above the gray-scale limit becomes black, everything below it white, resulting ina binary image. If the sample gray-scale is significantly different from the background this willcause the sample to look white with a black boundary around it. This boundary can then easilybe tracked and compared to the boundary in the next image, which gives the macroscopic strain in2D. The advantage of this method is that it requires little time to prepare the gray-scale difference(good lighting is enough in most cases) and calculate the strains. The disadvantage is that theentire sample is viewed as one piece; any local structural changes cannot be seen.

4.2.2 Aramis

This is an advanced technique which can determine locale strains. An image is taken and onceagain converted to grayscale. By using the computer program Aramis an area on the samplecan be selected. This area is divided in many smaller ones of only a few pixels in size. Such asquare contains gray dots in a configuration which is unique for that square. Aramis will searchall these squares again in the next photo, where they have been displaced. After all photos havebeen analyzed the general and local displacement are calculated for all those squares. Twentypoints on the initial area have been chosen for this experiment to analyze further, calculating thelocal strains and general strains. The advantage of this method is that you can specify points ofwhich you want the strains calculated, thus having the ability to check for differences betweendifferent areas of samples. A disadvantage is the need for unique gray dots. Reflections will alsocause trouble since a ”unique” white spot in a square suddenly disappears in the next, which leadsto a miscalculation in that square. In order to prevent this, a thin gray film has been sprayedover the sample, it will minimize the reflections and also provide more unique features. An otherdisadvantage is that it takes quite long to analyze 20 points per sample. Therefore this methodwill only be used to verify the results of the DIC and see if there are local effects.

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As can be seen in Figure 7, the curves are rather identical, the largest difference between the 2methods is at the tip, where the maximum difference encountered was a difference of 0.044 strain,a difference of 10%. This is taken as an acceptable error, since both methods have unknown errors,and therefore the DIC method is used for the rest of the experiments.

Figure 7: Vertical strain vs time of a PUR tensile sample. Both methods are shown, the left imageshows the total vertical strain, the right image shows a zoom of the tip.

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5 Results

This section will discuss the results from the experiments described in Chapter 4. To describethe volume effects of the samples, the Poisson’s ratio has been chosen. This ratio describesthe relationship between strain in the loading direction (vertical strain in this case) and in thedirection 90 ◦ from this loading direction (horizontal strain in this case). This Poisson’s ratio canbe described by ν = − εyy

εxx, with εyy the strain in the direction parallel to the loading and εyy the

strain in the direction perpendicular to the loading. The results start by showing the stress-straincurve in compression, this is used to validate the material assumptions (elastomeric, elasto-plastic)made in Chapter 3. The engineering stress is used, defined as σeng = F

A0, the A0 standing for

the original surface area on which the force F is applied. All strains used in this article are truestrains, meaning that if the strain was originally calculated as linear it has been converted to truestrain by using εln = ln(εlin+1). When testing the IMPAXX and PUR samples data was acquiredfrom the machine and from the photo-acquisition. The machine data provided the vertical strain,εyy , and the force needed for the compression or tensile testing. The photo-acquisition providedthe vertical strain εyy and the horizontal strain εxx. Since the machine and the photo-acquisitionboth give a value for the vertical strain, these two can be compared to see if the photo-acquisitioncan calculate the vertical displacement as decent as the machine. This comparison has been donewith the IMPAXX compression tests, the results are shown in figure 8. The Poisson’s ratio hasbeen calculated for both cases for all compression samples and the differences are very little. Itcan therefore be assumed that the horizontal strain measurement using this method will also bevery accurate.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

True strain [−]

Poi

sson

s’R

atio

[−]

−−− IMPAXX Compression, image εyy

O IMPAXX Compression, machine εyy

Figure 8: Comparison between using the vertical strain of the machine to calculate the Poisson’sratio or using the vertical strain of the image.

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5.1 IMPAXX results

Figure 9 shows the stress-strain response of IMPAXX during testing. If we compare it with thebottom left figure of figure 1, it can be seen that the densification area has nearly been reached,but it is hard to make a difference between the elastic and elasto-plastic curve, since they lookmuch alike during the compression. However, when the stress is released, the material does notreturn to its original state, which can be explained by a plastic deformation, thus making thematerial indeed elasto-plastic.

0 0.2 0.4 0.6 0.80

2

4

6

8

x 105

True strain ε (−)

Eng

inee

ring

stre

ss σ

(N

/m2 )

IMPAXX Compression

Figure 9: Stress-strain response of an IMPAXX compression sample.

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The Poisson’s ratio of samples in compression and the average Poisson’s ratio at low strain canbe seen in Figure 10.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

True strain [−]

Poi

sson

s’R

atio

[−]

IMPAXX Compression

Mean IMPAXX Compression

Figure 10: Compression test with IMPAXX samples. The black dot represents the average Pois-son’s ratio.

Values of the Poisson’s ratio at a strain smaller then 0.01 strain have not been shown, since thesevalues are incorrect due to being so close to deviation by zero. The Poisson’s ratio for very smallstrains is near 0.22, which is rather low for polymer foams who on average have a Poisson’s ratioaround 0.33 [1]. At higher strains the Poisson’s ratio drops dramatically until it is almost 0. Thismeans there is almost no change in diameter of the IMPAXX foam under compression. This couldbe explained by fast collapsing of the cell wands. The closed-celled structure crumbles, rupturingwalls and allowing air to flow out.

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In order to plot the Poisson’s ratio for the tensile testing the actual data has not been used but aapproximation. This is shown in the left image of figure 11 for a single sample. The approximationwas necessary since the raw data varies a lot between a Poisson’s ratio of 0.20 and 0.25, while thegeneral line can clearly be seen.

0 0.005 0.01 0.015 0.02 0.025 0.030

0.05

0.1

0.15

0.2

0.25

0.3

strain [−]

Poi

sson

s’R

atio

[−]

Fitted dataRaw data

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

True strain [−]

Poi

sson

s’R

atio

[−]

−−− IMPAXX CompressionO Mean IMPAXX Compression−−− IMPAXX TensileO Mean IMPAXX Tensile

Figure 11: Left image: Tensile test with a single IMPAXX sample. The blue curve representsthe actual data, the red curve the approximation. Right image: Tensile and compression tests ofIMPAXX in one figure, the black dots represent the averages of the compression samples and theaverage of the tensile samples.

When we look at the tensile test results, it can be seen that these results differ more from eachother then the compression results. The Poisson’s Ratio is between 0.15 and 0.25 and appearsto be rather constant with increasing strain. The starting Poisson’s ratio is the same as forcompression, as is expected of linear elasticity. However, IMPAXX in tensile testing was a brittlematerial, which caused it to fracture at low strains. To verify how the tensile curves go when morestrain is applied, the usage of a closed-celled rubber material would be needed. At lower strains,it seems the material has the same Poisson’s ratio in compression and tensile stresses. This is offcourse expected of the elastic region of the material. The instant the cell wands are aligned causesthe critical stress to be reached and a crack in the material.

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5.2 PUR results

Figure 12 shows the stress-strain response during testing.

0 0.2 0.4 0.6 0.8 10

0.4

0.8

1.2

1.6

2

2.4x 10

4

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

True strain ε (−)

Eng

inee

ring

stre

ss σ

(N

/m2 )

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

−−− PUR Tensile sample 1

−−− PUR Tensile sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

−−− PUR Compression sample 1

−−− PUR Compression sample 2 to 6

Figure 12: Stress-strain response of an IMPAXX compression sample.

The figure shows multiple tests, which were done in order to verify the elasticity of the sample.All 6 tests show elastic behavior, since they return to zero strain when decompressed, but the firsttest shows a slightly different stress-strain response then the following tests. This can clearly beseen with the compression samples, in tensile testing this phenomenal also occurred, this is justless visible in the graph. The phenomenal could occur because certain errors in the microstructureare ”repaired” during this first test, either by breaking some connections or bending them. Itcould be that while manufacturing the foam thin cell walls were created which rupture during thefirst test. The 5 tests after this first one show very identical behavior, so these will mainly be usedfor analysis.

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0 0.2 0.4 0.6

0

0.1

0.2

0.3

0.4−−− PUR compression, test 1

O PUR compression, test 2 to 6

−−− PUR compression, test 1

O PUR compression, test 2 to 6

−−− PUR compression, test 1

O PUR compression, test 2 to 6

−−− PUR compression, test 1

O PUR compression, test 2 to 6

−−− PUR compression, test 1

O PUR compression, test 2 to 6

−−− PUR compression, test 1

O PUR compression, test 2 to 6

True strain [−]

Poi

sson

’s r

atio

[−]

0 0.05 0.1 0.150.2

0.3

0.4

−−− PUR tensile, test 1

O PUR tensile, test 2 to 6

True strain [−]

Poi

sson

’s r

atio

[−]

0 0.2 0.4 0.6

0

0.1

0.2

0.3

0.4

O PUR compression

O PUR tensile

True strain [−]

Poi

sson

’s r

atio

[−]

Figure 13: Left image: Compression test with a PUR sample. Middle image: Tensile test of aPUR sample. Right image: A single test of a PUR sample in compression and tensile.

The compression sample shown in the figure 13 shows a decrease in Poisson’s ratio after startingat a value 0.3. This decrease is not as rapid as the IMPAXX compression which suggest bendingof the walls instead of collapse as the main mechanism. The first test results differs from theother 5, as could also be seen in the stress-strain curve. This is true for both compressive andtensile testing. The tensile testing shows a starting value of 0.3, as is expected, since in the linearelasticity region it should be the same as in compressive testing, but then the Poisson’s ratioincreases to a Poisson’s ratio of 0.4 over a strain of 0.1. This could also clearly be seen during theexperiments, as the compression sample expanded little while the tensile sample contracted ratherfast. This is quite unexpected, since although PUR has a different deformation mechanism fortensile and compression (stretching and buckling), the difference in Poisson’s ratio between themis very large considering it is the same material. If we assume the tensile behavior to continueto have an increase of its Poisson’s ratio it might increase to 0.5 and become an incompressiblematerial. Testing with higher strains should be performed to verify this.

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5.3 Comparison between IMPAXX and PUR

The following figure shows all the data from IMPAXX and PUR.

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

PUR CompressionPUR Tensile

True strain [−]

Poi

sson

s’R

atio

[−]

IMPAXX CompressionIMPAXX Tensile

Figure 14: Poisson’s ratio of IMPAXX and PUR, for both compression and tensile tests. A single,representative, test has been shown to prevent the curves from interfering with each other.

First the compression samples will be compared. There is a large difference between these; IM-PAXX collapses immediately while PUR makes a slow progress of bending which causes thePoisson’s ratio to lower at a nearly constant rate. At a strain of 0.5 both materials have thesame Poisson’s ratio of practically 0, but the IMPAXX is still as wide as at the beginning of thetest while PUR has already grown in diameter. The tensile tests are hard to compare because ofthe relatively small strain the IMPAXX sample could withstand before cracking. However if weassume the curve to remain as constant as it is, it shows a lesser contraction then the PUR foam.This could be described by the brittleness under tensile stresses, the structure is more reluctantto bend its walls, causing higher stresses and less contraction.

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6 Conclusion

The volume changes of closed-celled and open-celled materials differs from what one might expect.The closed-celled foam IMPAXX under compression collapsed almost immediately, causing it tohave a Poisson’s ratio close to zero and therefore practically maintaining its original diameter. Thecollapse could be described by the inability to bend the structure’s walls. The closed walls buildup stress and then suddenly collapse. PUR, the open-celled foam, does not have the restrictedclosed cell structure and can bend the honeycomb structure in response to the stress. This causesthe material to change in diameter, but maintain its structure, causing elastic behavior when thestress is removed. The Poisson’s ratio slowly decreases when the strain goes higher (from 0.3 to 0over 0.7 strain), caused by the angle at which the structure must deform. (ref chapter 2) Whentensile testing, the IMPAXX forms a crack when applying a small vertical strain causing it tofracture. Obviously, at such a small strain, the volume effects are nearly invisible. The fracture isagain caused by pressure buildup of the brittle structure, which then ruptures at a cell wall. ThePUR shows a rather strange volume change when in tensile testing. When under tensile testingthe Poisson’s ratio increases from 0.3 to 0.4 over a small strain, which makes the thinning of thesample compared to the widening of the compression test very large. This could be caused by thedifferent deformation mechanisms structure, causing it to contract better in one direction then theother. However, more tests with different materials need to be done in order to verify this.

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References

[1] Gibson LJ, Ashby MF,Cellular solids - Structures and properties, 2nd Edition, 1997.

[2] David de Vries, Coaches: J.G.F. Wismans, J.A.W. van Dommelen, Characterization of poly-meric foams, MT 09.22, Internal Report (2009)

[3] Gdoutos EE, Daniel IM, Wang KA, Failure of cellular foams under multiaxial loading, Depart-ment of Civil Engineering, Northwestern University, Evanston, IL 60208-3020, USA, 2001

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