A comprehensive study has been conducted to develop proper test methods for accurate determination of failure strengths along different material directions of closed-cell polymer-based structural foams under different loading modes. The test methods developed are used to evaluate strengths and failure modes of commonly used H80 polyvinyl chloride (PVC) foam. The foam's out-of-plane anisotropic and in-plane isotropic cell microstructures are considered in the test methodology development. The effect of test specimen geometry on compressive deformation and failure properties is addressed, especially the aspect ratio of the specimen gauge section. Foam nonlinear constitutive relationships, strength and failure modes along both in-plane and out-of-plane (rise) directions are obtained in different loading modes. Experimental results reveal strong transversely isotropic characteristics of foam microstructure and strength properties. Compressive damage initiation and progression prior to failure are investigated in an incremental loading–unloading experiment. To evaluate foam in-plane and out-of-plane shear strengths, a scaled shear test method is also developed. Shear loading and unloading experiments are carried out to identify the causes of observed large shear damage and failure modes. The complex damage and failure modes in H80 PVC foam under different loading modes are examined, both macroscopically and microscopically.
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 , 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  and compression  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 , 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 [5–9] 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  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.
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.
Test Specimens and Sample Preparation
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 . The density of each specimen was also determined individually. The specimen was adhesively bonded onto shear loading plates using an epoxy adhesive.
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 . 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
Foam Test Method Development and Validity for Foam Strength Determination
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., , 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 () 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 ( and ) 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.
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.
Foam Strength Properties and Associated Damage
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 () in the out-of-plane direction was found to occur at a smaller strain () than those ( and ) 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.
Loading–unloading experiments were conducted to investigate foam compressive damage mechanisms and progression. Typical rise-direction compressive stress–strain curves are shown in Fig. 12 during incremental loading and unloading. No noticeable change in initial (loading) modulus was observed until the fourth loading cycle despite increasing nonlinearity and hysteresis. After reaching a peak stress, nearly 90% of its compressive strength in the fourth cycle, significant nonlinearity occurred at a lower stress in subsequent cycles. More significant reduction in modulus was observed after the foam was stressed beyond its compressive strength in the sixth cycle and appreciable macroscopic damage appeared. The macroscopic damage exhibited as narrow bulge bands on all four side surfaces. The localized damage extended across the entire cross section in the gauge region and resulted in large reduction of compression modulus. The residual strain accumulation during the repeated loading–unloading cycles was caused by progressive damage growth in the foam. The localization of damage in the foam also led to a small strain recovery of about 0.5% after 10 mins in the unloaded specimen after being strained more than 10% in compression.
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.
|S13 (MPa)||γ13u (%)||S23 (MPa)||γ23u (%)||S12 (MPa)||γ12u (%)||S21 (MPa)||γ21u (%)|
|S13 (MPa)||γ13u (%)||S23 (MPa)||γ23u (%)||S12 (MPa)||γ12u (%)||S21 (MPa)||γ21u (%)|
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.
Progressive Shear Damage.
In either transverse or in-plane shear, the H80 PVC foam exhibited large deformation without visible macroscopic damage. To investigate the cause of the large shear deformation observed, shear loading–unloading tests were performed on the foam specimens. The in-plane shear stress–strain curves obtained in repeated, incremental loading–unloading cycles are shown in Fig. 15. Up to the fifth loading–unloading cycle, no measurable change in shear modulus was observed even though the shear stress–strain curves showed significant nonlinearity and increasingly large hysteresis. Starting from the sixth cycle, the nonlinearity occurred at a small shear strain during loading. Residual shear strain in each fully unloaded state increased in subsequent cycles.
After the 11th loading–unloading cycle, the foam specimen was unloaded and the shear strain was monitored as shown in Fig. 16. Nearly 2.5% strain recovery was observed after 400 mins. A DSC scan of the H80 PVC foam polymer, shown in Fig. 17, revealed that its glass transition temperature was about 69 °C, which was about 50 °C above the ambient temperature at which the shear loading–unloading experiment was conducted. Thus, the time-dependent viscoelastic contribution to the observed foam shear deformation was small. As will be discussed in the subsequent section, microscopic cell-structure damage would be the major cause responsible for the shear failure mode.
Failure Modes of H80 Polyvinyl Chloride Foam
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 ( ∼ 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.
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)).
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.
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:
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.
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.
Failure strength of H80 PVC foam is transversely isotropic with the 1-2 plane as the plane of isotropy, due to its cell microstructure.
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.
Different failure modes govern the H80 PVC foam strengths, depending on loading modes and directions.
Foam compressive failure modes feature localized cell crushing and collapse in a narrow band across the entire specimen regardless of the loading direction.
Under tension, foam failure results from fracture of cell walls, leading to a single macroscopic crack across the entire gauge cross section.
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.
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.