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Research Papers

Experiments on Elastic Polyether Polyurethane Foams Under Multiaxial Loading: Mechanical Response and Strain Fields

[+] Author and Article Information
Xiangyu Dai

Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801xdai1@illinois.edu

Tapan Sabuwala

Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801sabuwala@illinois.edu

Gustavo Gioia

Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801ggioia@illinois.edu

J. Appl. Mech 78(3), 031018 (Feb 17, 2011) (11 pages) doi:10.1115/1.4003190 History: Received June 07, 2010; Revised December 07, 2010; Posted December 08, 2010; Published February 17, 2011; Online February 17, 2011

We study experimentally the mechanical response of elastic polyether polyurethane (EPP) foams up to large strains over the range of commercially available densities and for a variety of loading conditions. To this end, we subject the foams in a set of EPP foams to five different tests, namely, compression along the rise direction, compression along a transverse direction, tension along the rise direction, simple shear combined with compression along the rise direction, and hydrostatic pressure combined with compression along the rise direction. The set of EPP foams consists of foams of five apparent densities ranging from 50.3kg/m3 to 221kg/m3. For each test and foam density, we report the mechanical response in the form of a stress-strain curve or a force-displacement curve. For some tests and foam densities, we use a digital image correlation method to measure the strain field on the surface of the foam. In a discussion of our experimental results, we put emphasis on the relation between the stress-strain or force-displacement curve recorded in a test and the attendant strain fields.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 8

Stress-strain curve of the foam of relative density ρ=0.038. Test 1. The stress-strain curve depends slightly on the size of the specimen. We use the larger specimen for DIC analysis. The applied strains at the points marked A, B, C, D, E, and F are 4.5%, 9.0%, 14.8%, 22.5%, 32.1%, and 44.9%, respectively. Inset: schematic of the test and the DIC frame of size 6.1×9.3 cm2.

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Figure 10

Plots of the displacement v as a function of the position on the transect marked with a dashed line on Fig. 9. Test 1. Inset: The same plots but with dotted lines connecting the kinks to show the process of nucleation and growth of the band of high local strain.

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Figure 11

Stress-strain curves of foams of five relative densities (ρ). Test 2.

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Figure 1

A simple cellular model of the microstructure of an EPP foam (8). (a) Four-bar cell and (b) periodic arrangement of identical cells.

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Figure 2

ATS machine and setup

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Figure 3

(a) TruePath system. (b) Sketch of the setup.

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Figure 4

Stress-strain curves of foams of five relative densities (ρ). Test 1.

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Figure 5

Stress-strain curve of the foam of relative density ρ=0.065. Test 1. The applied strains for the points marked A, B, C, E, F, and G are 4.2%, 10.3%, 16.3%, 22.3%, 28.4%, and 46.4%, respectively. The stress-strain curve depends slightly on the size of the specimen. We use the larger specimen for DIC analysis. Inset: schematic of the test and the DIC frame of size 7.0×6.0 cm2.

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Figure 6

Contour plots of the displacement v (inset of Fig. 5) in the foam of relative density ρ=0.065. Test 1. The contour plots of (a), (b), etc. correspond, respectively, to the points marked A, B, etc. on Fig. 5. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the rectangular DIC frame (inset of Fig. 5). The scale is 1 pixel=0.1 mm.

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Figure 7

Plots of the displacement v as a function of the position on the transect marked with a dashed line in Fig. 6. Test 1.

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Figure 9

Contour plots of the displacement v (inset of Fig. 8) in the foam of relative density ρ=0.038. Test 1. The contour plots of (a), (b), etc. correspond, respectively, to the points marked A, B, etc. on Fig. 8. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the rectangular DIC frame (inset of Fig. 8). The scale is 1 pixel=0.1 mm.

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Figure 15

Stress-strain curves of foams of five relative densities (ρ). Test 3.

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Figure 16

(a) A specimen ready for Test 4. (b) The same (schematic).

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Figure 17

Force-displacement curves of foams of five relative densities (ρ). Test 4.

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Figure 18

Force-displacement curve of the foam of relative density ρ=0.065. Test 4. The specimen size is 10×10×10 cm3 (used for DIC analysis). The displacements at the points marked A, B, C, D, E, and F are 2.7 mm, 7.2 mm, 11.4 mm, 13.7 mm, 18.9 mm, and 25.1 mm, respectively. Inset: schematic of the test and the DIC frame of size 8.2×8.0 cm2.

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Figure 12

Stress-strain curves of the foam of relative density ρ=0.030 compressed along two mutually perpendicular transverse directions (Test 2). The curves are practically indistinguishable, consistent with a foam that is transversely isotropic. The applied strains at the points marked A, B, C, D, E, and F are 10.4%, 20.8%, 31.2%, 41.6%, 51.9%, and 62.3%, respectively. Also shown is the stress-strain curve of the same foam compressed along the rise direction, for comparison. Inset: schematic of the test and the DIC frame of size 7.6×7.5 cm2.

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Figure 13

Contour plots of the displacement v (inset of Fig. 1) in the foam of lowest relative density (ρ=0.030). Test 2. The contour plots of (a), (b), etc. correspond, respectively, to the points marked A, B, etc. on Fig. 1. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the rectangular DIC frame (inset of Fig. 1). The scale is 1 pixel=0.1 mm.

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Figure 14

(a) A specimen ready for Test 3. (b) The same (schematic).

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Figure 19

Contour plots of the displacement v (inset of Fig. 1) in the foam of relative density ρ=0.065. Test 4. The contour plots of (a), (b), etc. corresponds, respectively, to the points marked A, B, etc. on Fig. 1. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the rectangular DIC frame of (inset of Fig. 1). The scale is 1 pixel=0.09 mm.

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Figure 20

Plots of the displacement v as a function of the position on the transect marked with a dashed line on Fig. 1. Test 4.

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Figure 21

Force-displacement curve of the foam of relative density ρ=0.038. Test 4. The force-displacement curve depends slightly on the size of the specimen. We use the larger specimen for DIC analysis. The displacements at the points marked A, B, C, D, E, and F are 2.5 mm, 8.5 mm, 16.0 mm, 24.2 mm, 30.1 mm, and 36.3 mm, respectively. Inset: schematic of the test and the DIC frame of size 8.6×8.3 cm2.

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Figure 22

Contour plots of the displacement v (inset of Fig. 2) in the foam of relative density ρ=0.038. Test 4. The contour plots of (a), (b), etc. correspond, respectively, to the points marked A, B, etc. on Fig. 2. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the DIC frame (inset of Fig. 2). The scale is 1 pixel=0.1 mm.

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Figure 23

Plots of the displacement v as a function of the position on the transect marked with a dashed line on Fig. 2. Test 4.

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Figure 24

Contour plots of the displacement u (inset of Fig. 2) in the foam of relative density ρ=0.038. Test 4. The contour plots of (a), (b), etc. correspond, respectively, to the points marked A, B, etc. on Fig. 2. The contour plots are mapped on the undeformed configuration so that the area covered by each contour plot is the DIC frame (inset of Fig. 2). The scale is 1 pixel=0.1 mm.

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Figure 25

Plots of the displacement u as a function of the position on the transect marked with a dashed line on Fig. 2. Test 4.

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Figure 26

Deviatoric stress-strain curves for foams of five relative densities (ρ) and three values of confining pressure (p). Test 5.

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Figure 27

Foam specimen, DIC frame, and finite element mesh

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