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Research Papers

# Test Method Development and Determination of Three-Dimensional Strength and Failure Modes of Polyvinyl Chloride Structural FoamsPUBLIC ACCESS

[+] Author and Article Information
Akira Miyase

National Wind Energy Center,
University of Houston,
5000 Gulf Freeway,
Building 3, Room 152B,
Houston, TX 77204-0931
e-mail: amiyase@uh.edu

Su Su Wang

National Wind Energy Center,
University of Houston,
5000 Gulf Freeway,
Building 3, Room 152B,
Houston, TX 77204-0931
e-mail: sswang@uh.edu

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 30, 2016; final manuscript received January 30, 2017; published online March 27, 2017. Assoc. Editor: Erdogan Madenci.

J. Eng. Mater. Technol 139(3), 031006 (Mar 27, 2017) (7 pages) Paper No: MATS-16-1246; doi: 10.1115/1.4036068 History: Received August 30, 2016; Revised January 30, 2017

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## Introduction

High-performance load-bearing sandwich structures are often constructed with fiber-reinforced polymer-matrix composite skins and lightweight structural foam core materials. They can be found in aerospace, marine, automotive, and wind energy applications. The sandwich structural performance depends not only on the fiber composite skin but also on the core material, as well as on adhesive bonding between them. In-depth knowledge of foam material strength and mechanics, as well as associated failure modes, is essential in design, performance, and reliability of the sandwich structure.

Among different core foams, rigid PVC structural foams are the most widely used. The PVC foam is known to have anisotropic cell microstructure and exhibits in-plane isotropy and out-of-plane (i.e., foam rise direction) orthotropy. Although limited foam nominal mechanical properties in out-of-plane directions are reported [1], its in-plane properties are generally not available. Since the foam in a sandwich structure is generally subjected to not only in-plane loads but also out-of-plane stresses, its strength behavior and associated failure modes must be determined accurately and properly, for design and integrity of the sandwich structure.

The ASTM Standard tests for evaluation of foam strengths under tension [2] and compression [3] require specimens with a geometric aspect ratio (i.e., gauge length/width) equal or less than one. The low aspect ratio generally introduces a nonuniform strain field within the gauge region due to grip-end constraints [4], leading to local damage and premature failure. Most available information on mechanical properties and failure strength of PVC foams in the literature is determined with the standard test methods, due to their simplicity. Recognizing the problems associated with the ASTM Standard tests, several researchers [59] have studied foam deformation and strengths under different loading modes, using test methods other than the ASTM Standards, and show large variation and dependency on specimen dimensions and geometry, and the test methods.

The objectives of this study are to: (1) develop proper test methods for accurate determination of strengths and failure modes of foam materials under different loading modes (compression, tension and shear), (2) obtain directionally dependent strength properties and failure modes of PVC foams along different material directions under different loading modes, and (3) provide microstructure models and experimental data for a complementary study [10] on development of micromechanics theory and prediction for use in design and reliability of large composite sandwich structures. A comprehensive test program was conducted on the commonly used Divinycell H80 PVC foam. Foam deformations, failure strengths, and failure modes in in-plane and out-of-plane (i.e., rise) directions under compression, tension, and shear were investigated. Of particular interests are the effects of specimen geometry and gauge-section aspect ratio on foam strength properties, and damage and failure modes in different loading modes.

## Experiments

###### Material.

The foam material used in the study was Divinycell H80 PVC foam with a nominal density of 80 kg/m3. Test specimens were made from a sheet of the foam with dimensions of approximately 1.2 m by 1.2 m and 50.8 mm. To study its directionally dependent properties in various loading modes, a coordinate system shown in Fig. 1 was introduced. As shown in the figure, directions 1 and 2 (in-plane directions) were mutually perpendicular alongside edges of the foam panel. The three-direction was the out-of-plane (foam rise) direction.

The foam cell microstructure and density in the planar direction and in the out-of-plane direction of the H80 foam sheet were examined previously.

###### Compression Test Specimen.

Initial tests on straight-side foam specimens in compression showed damage occurring near specimen surfaces outside of the gauge region. Therefore, compression test specimens of square cross sections with reduced gauge-section width WGS (Fig. 2) were used. To fabricate the test specimens, a slightly over-sized specimen blank was cut first with a table saw. The specimen blank was grounded with a series of Emery papers (down to 1000 grit). The prismatic specimen with a square cross section was 50.8 mm in length. The density of each specimen was determined from its volume and weight. After foam elastic property measurements, the cross section of the prismatic specimen was reduced by machining all four side surfaces with a milling cutter to make a reduced gauge section (Fig. 2). The milled surfaces were then grounded with Emery papers to the reduced gauge section width (WGS).

###### Tensile Test Specimen.

The overall foam tensile specimen geometry and dimensions are shown in Fig. 3. An approximately 3 mm oversized specimen blank was cut from a foam sheet. The specimen blanks were ground to a rectangular shape with predetermined width, length, and thickness using a series of Emery papers to 1000 grit. Dimensions and weight of each specimen were measured and its density was determined. The specimen gauge section was machined with a milling cutter, and the machined surfaces were grounded with Emery papers.

The specimen for out-of-plane (rise direction) strength determination contained five pieces of foam taken in the out-of-plane direction and glued together with an epoxy adhesive. The centerpiece was then machined into the 50.8-mm gauge section. The thickness of all test specimens was 12.7 mm.

###### Shear Test Specimen.

After an oversized specimen blank was cut from the foam sheet by a table saw, the shear test specimen was grounded to the final dimensions of 25.4 mm width, 114.3 mm length, and 9.5 mm thickness (Fig. 4). The specimen had a length-to-thickness ratio of 12 in accordance with ASTM Standard C273 [11]. The density of each specimen was also determined individually. The specimen was adhesively bonded onto shear loading plates using an epoxy adhesive.

###### Experimental Setup.

The experimental setups for compression, tensile, and shear mechanical tests of the foam were described in detail. Briefly, the compression test setup in a servohydraulic load frame consisted of aluminum loading platens, and two axial and two lateral extensometers. The two sets of extensometers were positioned 180 deg apart to obtain average strains. The axial extensometer had a gauge length of 25.4 mm.

The tensile test setup included mechanically tightened flat-face grips, two axial extensometers positioned 180 deg apart, and one lateral extensometer. The same axial and lateral extensometers used for the compression test were employed for the tension tests.

The fixture design for the foam shear test was similar to that of ASTM Standard C273 [11]. The small shear specimen required a scaledown, in-house built shear fixture. To measure the relative displacements of the two loading plates, two clip gauges were used.

###### Experimental Procedure and Data Acquisition.

All tests were conducted in a servohydraulic material test system. In each test, load and displacement signals from extensometers and clip gauges were recorded by a data acquisition system. All tests were run in a displacement-controlled mode at a nominal strain rate of 1.4 to 1.6%/min in an ambient temperature condition.

## Results and Discussion

###### Compression Tests.

With the aforementioned compression test methods, specimen design and fixtures foam compression failure were observed to occur within the specimen gauge section, resulting in accurate and reproducible compressive stress–strain data and failure strength of the H80 foam.

Typical compressive stress–strain curves of the foam in the out-of-plane direction are shown in Fig. 5 for specimens with different gauge-section dimensions.

The foam compressive stress–strain behavior exhibited an initial linear region, followed by significantly nonlinear deformation before the maximum stress (i.e., $S33−$, compressive strength in the rise direction) was reached. Thereafter, the compressive stress dropped off gradually and reached a constant value. All compression tests were terminated at axial compressive strain less than 15% because the capacity limit of the extensometers was reached.

The effect of gauge-section aspect ratio on foam rise-direction compressive strength ($S33−$) obtained is shown in Fig. 6. Little difference was observed in the compressive failure strengths of the foam specimens with different gauge-section dimensions. However, a slight increase in stress–strain nonlinearity was found for the specimens with smaller gauge-section dimensions, revealing the effect of gauge-section aspect ratio on the compressive strength in the rise direction of the foam.

In-plane compressive stress–strain relationships and failure strength along one- and two-directions of the foam are shown in Figs. 7(a) and 7(b). Characteristics of the in-plane compressive stress–strain behavior were very similar to those of the out-of-plane compression. The effect of gauge-section aspect ratio on the in-plane compressive strength ($S11−$ and $S22−$) is also shown in Fig. 6. As in the case of out-of-plane compression, the in-plane compressive strength was not affected by the cross section size of the specimen. The compression test results show that failure strength in one and two directions were almost identical, regardless of the loading direction in the 1-2 plane of the foam.

###### Tensile Tests.

The out-of-plane (rise-direction) tensile foam failure strength in specimens with different cross sections is shown in Fig. 8. The effect of specimen gauge-section geometry on tensile strengths in different loading directions is shown in Fig. 9. Regardless of the specimen gauge-section dimension, the failure strength in the rise direction showed almost no change. The validity of the tensile specimen geometry introduced in the study is clearly demonstrated for proper determination of the foam tensile strength.

In-plane (one and two directions) tensile failure strength of the foam in specimens with different cross sections is determined in Figs. 10(a) and 10(b). The in-plane tensile failure strength was not affected by the specimen gauge section aspect ratio. The results also show that failure strengths in one and two directions were almost identical, regardless of the loading direction in the 1-2 plane of the foam.

###### Compressive Strength.

In Fig. 11, a comparison is made on the H80 PVC foam compressive strengths in in-plane and out-of-plane (rise) directions. The foam compressive strength and stiffness were much higher in the three direction (rise direction) than those in the in-plane direction (one and two directions). The compressive strength ($S33−$) in the out-of-plane direction was found to occur at a smaller strain ($ε3u−$) than those ($ε1u−$ and $ε2u−$) in the in-plane directions. The directionally dependent strength of the H80 foam resulted from the orthotropic cell microstructure and stretching of the cell wall material in the rise direction.

###### Tensile Damage.

In-plane and rise direction tensile stress–strain curves up to failure are shown in Fig. 13 for the H80 PVC foam. In the rise (out-of-plane) direction, both foam strength and stiffness were much higher than those in the in-plane direction. However, foam failure strain in the out-of-plane direction was much smaller than that in the in-plane direction.

###### Transverse (Rise Direction) and In-Plane Shear Strengths.

Transverse shear strengths in 1-3 and 2-3 planes (rise direction) and in-plane shear strengths in 1-2 and 2-1 planes of the H80 foam were obtained from the experiments and the results are summarized in Table 1. The transverse shear strength and stiffness of the H80 PVC foam were found much higher than those of the in-plane shear.

The transverse and in-plane shear stress–strain relationships and failure strength of the H80 PVC foam are shown in Fig. 14. In all shear loading cases, an initial linearity was followed by a highly nonlinear region, and subsequently a nearly constant region where the resulting shear strain increased without an increase in applied shear stress. The shear strengths (S13, S23, S12, and S21) shown in Table 1 were the maximum shear stresses reached in the flat regions of the shear stress–strain curves.

###### Compression Failure.

Typical macroscopic foam failure modes observed in a compression specimen are shown in Fig. 18(a). The foam was compressed in the out-of-plane (i.e., rise) direction to the maximum compressive strain ($ε3−$  ∼ 13.2%). A narrow band of local bulging, nearly normal to the loading direction, was observed on all four side surfaces. The failure region was examined microscopically by sectioning the specimen and polishing the surface with Emery papers. As shown in Fig. 18(b), crimped and collapsed cells were clearly observed in the band of the bulged region.

###### Tensile Failure.

All foam specimens failed in the same manner regardless of the tensile loading direction (transverse or in-plane). A tensile-fractured specimen tested in the out-of-plane direction is shown in Fig. 19(a). Macroscopically, the specimen failed by a single crack across the entire cross section normal to the loading direction. Microscopically, no visible cell damage in the vicinity of the fracture surface was observed (Fig. 19(b)).

###### Shear Failure.

Despite the large shear deformation observed in the shear test, no visible macroscopic damage was observed after the specimen was unloaded. The failed shear specimen was examined microscopically. Typical microscopic shear failure modes observed in the specimen are shown in Fig. 20. Noticeable changes were observed in foam cell shape and cell orientation, as well as microcracks in foam cell walls. The microscopic shear damage and failure modes observed clearly indicate that cell elongation, rotation, realignment, and cracking along and normal to the 45 deg direction all contributed to the macroscopic foam shear failure.

## Conclusions

Proper test methods for accurate determination of strength and failure modes of closed-cell polymer-based foams were developed. With the methods, different loading modes were applied in the tests and the results validated, including compression, tension and shear with loading along in-plane and out-of-plane (foam rise) directions. The effects of specimen geometry and gauge-section aspect ratio on failure strength were examined in detail. Based on the results obtained, the following conclusions may be drawn:

1. (1)Compressive strength of a polymer-based foam can be accurately determined from the experimental methods developed. Foam specimens of a proper gauge-section aspect ratio exhibit consistent true failure strengths. With the properly designed specimen, compressive failure always occurs within its gauge region away from specimen ends and failure strength is independent of gauge-section dimensions.
2. (2)The H80 PVC foam compressive strength in the in-plane direction is directionally independent. However, the out-of-plane (rise direction) compressive strength is much higher than that in the in-plane direction. The same foam strength characteristics are also observed in tensile loading.
3. (3)Failure strength of H80 PVC foam is transversely isotropic with the 1-2 plane as the plane of isotropy, due to its cell microstructure.
4. (4)Shear strength of the PVC foam is highly dependent on the shear loading direction. Transverse (out-of-plane) shear strength is much higher than those in the in-plane direction.
5. (5)Different failure modes govern the H80 PVC foam strengths, depending on loading modes and directions.
6. (6)Foam compressive failure modes feature localized cell crushing and collapse in a narrow band across the entire specimen regardless of the loading direction.
7. (7)Under tension, foam failure results from fracture of cell walls, leading to a single macroscopic crack across the entire gauge cross section.
8. (8)Foam shear failure modes are generally complex, including foam cell elongation, rotation, and realignment, together with localized foam cell-wall cracking, along and normal to the principal stress (i.e., ±45 deg) directions.

## Acknowledgements

Critical discussions and input by Dr. K. H. Lo of National Wind Energy (NWEC) are greatly appreciated. The work reported in the paper was supported in part by the U.S. Department of Energy through Grant DE-EE0000295 to the NWEC at University of Houston. The financial support for the research is gratefully acknowledged.

## References

Divinycell, H. , 2009, “ Technical Data,” DIAB Group, Laholm, Sweden.
ASTM, 2010, “ Standard Test Method for Tensile and Tensile Adhesion Properties of Rigid Cellular Plastics,” ASTM International, West Conshohocken, PA, Standard No. ASTM D-1623.
ASTM, 2009, “ Standard Test Method for Compressive Properties of Rigid Cellular Plastics,” ASTM International, West Conshohocken, PA, Standard No. ASTM D-1621.
Zhang, S. , Dulieu-Barton, J. M. , Fruehmann, R. K. , and Thomsen, O. T. , 2012, “ A Methodology for Obtaining Material Properties of Polymeric Foam at Elevated Temperatures,” Exp. Mech., 52(1), pp. 3–15.
Abot, J. L. , 2000, “ Fabrication, Testing and Analysis of Composite Sandwich Beams,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Gdoutos, E. E. , Daniel, I. M. , and Wang, K. A. , 2002, “ Failure of Cellular Foams Under Multiaxial Loading,” Composites, Part A, 33(2), pp. 163–176.
Viana, G. M. , and Carlsson, L. A. , 2002, “ Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams,” J. Sandwich Struct. Mater., 4(2), pp. 99–113.
Abot, J. L. , Daniel, I. M. , and Gdoutos, E. E. , 2002, “ Contact Law for Composite Sandwich Beams,” J. Sandwich Struct. Mater., 4(2), pp. 157–173.
Daniel, I. M. , 2009, “ Influence of Core Properties on the Failure of Composite Sandwich Beams,” J. Mech. Mater. Struct., 4(7–8), pp. 1271–1286.
Lo, K. H. , Miyase, A. , and Wang, S. S. , 2017, “ Strength Prediction for Rigid Closed Cell PVC Foams,” Composites Engineering and Applications Center (CEAC), University of Houston, Houston, Texas, Technical Report No. CEAC-TR-16-1010.
ASTM, 2011, “ Standard Test Method for Shear Properties of Sandwich Core Materials,” ASTM International, West Conshohocken, PA, Standard No. ASTM C273.
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## References

Divinycell, H. , 2009, “ Technical Data,” DIAB Group, Laholm, Sweden.
ASTM, 2010, “ Standard Test Method for Tensile and Tensile Adhesion Properties of Rigid Cellular Plastics,” ASTM International, West Conshohocken, PA, Standard No. ASTM D-1623.
ASTM, 2009, “ Standard Test Method for Compressive Properties of Rigid Cellular Plastics,” ASTM International, West Conshohocken, PA, Standard No. ASTM D-1621.
Zhang, S. , Dulieu-Barton, J. M. , Fruehmann, R. K. , and Thomsen, O. T. , 2012, “ A Methodology for Obtaining Material Properties of Polymeric Foam at Elevated Temperatures,” Exp. Mech., 52(1), pp. 3–15.
Abot, J. L. , 2000, “ Fabrication, Testing and Analysis of Composite Sandwich Beams,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Gdoutos, E. E. , Daniel, I. M. , and Wang, K. A. , 2002, “ Failure of Cellular Foams Under Multiaxial Loading,” Composites, Part A, 33(2), pp. 163–176.
Viana, G. M. , and Carlsson, L. A. , 2002, “ Mechanical Properties and Fracture Characterization of Cross-Linked PVC Foams,” J. Sandwich Struct. Mater., 4(2), pp. 99–113.
Abot, J. L. , Daniel, I. M. , and Gdoutos, E. E. , 2002, “ Contact Law for Composite Sandwich Beams,” J. Sandwich Struct. Mater., 4(2), pp. 157–173.
Daniel, I. M. , 2009, “ Influence of Core Properties on the Failure of Composite Sandwich Beams,” J. Mech. Mater. Struct., 4(7–8), pp. 1271–1286.
Lo, K. H. , Miyase, A. , and Wang, S. S. , 2017, “ Strength Prediction for Rigid Closed Cell PVC Foams,” Composites Engineering and Applications Center (CEAC), University of Houston, Houston, Texas, Technical Report No. CEAC-TR-16-1010.
ASTM, 2011, “ Standard Test Method for Shear Properties of Sandwich Core Materials,” ASTM International, West Conshohocken, PA, Standard No. ASTM C273.

## Figures

Fig. 1

Coordinates for directionally dependent strength properties of H80 PVC foam

Fig. 2

Foam compression test specimen geometry with reduced gauge section

Fig. 3

Foam tensile test specimen geometry and dimensions

Fig. 4

Shear test specimen geometry and dimensions

Fig. 5

Rise-direction compressive stress–strain curves of H80 PVC foam specimen with different gauge section dimensions

Fig. 6

Effect of gauge-section aspect ratio, LGS/WGS, on compressive failure strengths of H80 PVC foam

Fig. 7

Compressive stress–strain behavior and failure strength of H80 PVC foam in (a) one-direction and (b) two-direction (specimens with different gauge-section dimensions)

Fig. 8

Out-of-plane (rise-direction) tensile stress–strain behavior and failure strength of H80 PVC foam (in specimens with different gauge-section geometry)

Fig. 9

Effect of gauge-section aspect ratio on tensile strengths of H80 PVC foam

Fig. 10

Tensile stress–strain behavior and failure strength in (a) one-direction and (b) two-direction of H80 PVC foam in specimens with different gauge section geometry

Fig. 11

Directionally dependent compressive stress–strain behavior and failure strength of H80 PVC foam (WGS = 19 mm, LGS/WGS = 1.60)

Fig. 12

Fig. 13

Tensile stress–strain behavior and failure strength in different loading directions of H80 PVC foam

Fig. 14

In-plane and out-of-plane shear stress–strain curves and failure strengths of H80 PVC foam

Fig. 15

Fig. 16

Fig. 17

Glass transition temperature of H80 PVC foam polymer from differential scanning calorimeter (DSC) experiment

Fig. 18

Compression failure modes in H80 PVC foam: (a) bulge band in test specimen and (b) microscopic damage with crimpled and collapsed cells

Fig. 19

Tensile failure modes of H80 PVC foam: (a) fractured test specimen (WGS = 12.7 mm) and (b) foam cells near fracture surface

Fig. 20

Microscopic cell damage and failure modes in foam transverse shear failure (specimen subjected to shear strain, γ23 = 0.29)

## Tables

Table 1 Transverse and in-plane shear strengths of H80 PVC foam

## Errata

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