fatigue of crosslinked and linear pvc foams under shear loading

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2004 23: 601Journal of Reinforced Plastics and CompositesKrishnan Kanny, Hassan Mahfuz, Tonnia Thomas and Shaik Jeelani

Fatigue of Crosslinked and Linear PVC Foams under Shear Loading

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Fatigue of Crosslinked and LinearPVC Foams under Shear Loading

KRISHNAN KANNY, HASSAN MAHFUZ,* TONNIA THOMAS AND SHAIK JEELANI

Chappie James Center Rm 103Tuskegee University

Tuskegee, Alabama, 36088, USA

ABSTRACT: When a sandwich structure is subjected to transverse loads, the face sheets carrybending moments as tensile and compressive stresses and the core carries transverse forces as shearstresses. The core is typically the weakest component of the structure and is the first to fail in shear.In this study the shear fatigue behavior of two closed-cell cellular PVC foams, Divinycell HD130(linear) and H130 (cross linked), with the same nominal density of 130 kg/m3, were investigated.Static shear tests reveal that HD130 foams are more ductile, have almost twice the energy absorptioncapability, and an extraordinary crack propagation resistance when compared to the H130 foams.Shear fatigue tests were conducted at room temperature, at a frequency of 3Hz and at a stress ratio,R¼ 0.1 on the HD130 and H130 foams. S–N curves were generated and shear fatigue characteristicswere determined. The number of cycles to failure for the linear foams was substantially higher thanthat of the cross-linked PVC foams. HD foams have smaller cells with thicker faces and edges. Thismicrostructure supports absorption of larger amounts of liquid resin forming a resin rich subinterface zone just below the actual core–skin interface. The high intrinsic toughness of the subinterface delays the initiation of fatigue cracks and thereby increases the fatigue life of the HDfoams. For both foams, shear deformation occurs without volume change and the materials fail byshearing in the vicinity of the centerline of the specimen along the longitudinal axis. In both casesnumerous 45� shear cracks form across the width of the specimen and are equidistantly spaced alongthe length of the specimen. The occurrence of these through the thickness shear cracks signals thefinal failure event during fatigue. Details of the experimental investigation and the evaluation of thefatigue performance are presented.

KEY WORDS: foam core, shear fatigue, cross-linked, linear cores.

INTRODUCTION

IN MANY APPLICATIONS sandwich structures are subjected to transverse loads. If thefacings of the sandwich construction are designed so that they are elastically stable, the

most critical stress to which the core is subjected is shear [1]. The core in a sandwichcomposite is usually made from PVC foam, which may be either linear (HD130) or cross-linked (H130). The cross-linked H130 PVC is more rigid, has higher mechanicalproperties, and is less heat sensitive than linear foams [2]. When such sandwich beamsundergo repetitive transverse loads, their constituents are subjected to different kinds of

*Author to whom correspondence should be addressed. E-mail: [email protected]

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loading; the face sheets exhibit almost entirely membrane tension/compression and thecore pure shear. A common failure of sandwich construction is the so called ‘‘core shearfailure’ in which the core fails when the shear stress reaches its critical value [3]. In aprevious study [4] on the flexural fatigue behavior of foam core sandwich structures it wasfound that numerous small cracks initiated in the core, in the sub interface area at or nearthe point of loading. The cracks grew together and propagated on the compression side ofthe beam, immediately below the sub interface, parallel to beam until they reached somecritical length. Subsequently, the crack kinked at an angle of approximately 45� toward thetension side. The crack then propagated in the core parallel to the beam beforedelamination occurred at the edges. A similar finding on a lower density core was reportedin [5] where fatigue tests were performed on R75 sandwich beams. Shipsha et al. [6]performed tests on H100 beams and found that the crack continuously propagated alongthe interface, in the core material, below the layer of resin rich cells with diagonalsecondary fracture cracks. In all cases the core shear stresses produced globaldeformations. Thus a core must be chosen that would not fail under the appliedtransverse load and with a shear modulus high enough to give the required stiffness. Thecore is normally designed with a high margin of safety due to a lack of knowledge about itsfatigue properties while fatigue of the faces are easily included in the design since fatigueproperties are relatively well known [7]. The fact that the foam cores are viscoelastic makesthe problem of fatigue more complex especially with linear foams.

The mechanical behavior of cellular foams for simple stress states such as uniaxialtension and compression has been studied extensively in the literature [8–11]. Limitedstudies on multiaxial behaviors have been studied and are those by [3,12–14]. Uniaxialtensile, compressive, and shear tests along the in-plane and through the thicknessdirections of H100 and H250 cellular foams were performed. H100 material showed nearlyisotropic behavior, while H250 showed orthotropic behavior with a higher stiffness alongthe through the thickness than in the in-plane direction. Many researchers have examinedthe behavior of foam materials and the results are compiled in a comprehensive text byGibson and Ashby [15]. The text covers simple micro mechanical equations based onmechanics of materials analysis that relate the properties of the foam to structure of thecells and the properties of the solid material. Information relating to the solid is sometimesnot easily available. In any event, a more detailed characterization was considerednecessary particularly when two micro-structurally different foams having identicaldensity are subjected to fatigue under pure shear loading. To our knowledge no work hasso far been performed on foam materials, under shear fatigue. Detailed description of thefatigue tests and their analyses ensues in the following sections.

EXPERIMENTAL

Material

Two closed-cell thermoplastic PVC foams of nominal density 130 kg/m3 wereinvestigated in this study. The main difference in the foams is the level of cross-linking.HD130 PVC foams are linear, hereafter referred to as HD130, and H130 PVC foams arecross-linked and will hereafter be referred to as H130.

These closed-cell PVC foams are used in almost every type of sandwich applicationvarying from pure insulation applications to aerospace and marine structures and arehence the most widely used of all foams. In marine applications, HD130 foams are used

602 K. KANNY ET AL.




below the water line where repetitive slamming occurs, and H130 foams are used above thewater line.

The foams are supplied in the form of large sheets, 12.5mm thick. Material properties assupplied by the manufacturer DIAB, are listed in Table 1.

Quasi-static Shear Tests

Five replicate HD130 and H130 specimen of dimension 40mm� 160mm were cut from12.5mm thick as supplied panels, using a diamond coated steel blade, as per ASTMC273-61standard test method [16]. The specimen was bonded between the two parallel loading steelplates as shown in the test set up in Figure 1(a) which shows a schematic of the shear fatiguetest fixture. The arrows indicate the direction of loading. The steel plates were truly parallelsince a small deviation in parallelism of the loading plates can cause considerable errors inthe calculation of the shear strength and shear modulus [17]. The thickness of the steelloading plates were increased to 20mm to insure that the loads was carried by the foamspecimen and not transferred to the steel plates. A two-part epoxy, Hysol EA 9309.3 NAwas used as the adhesive to bond the foam to the steel plates. The epoxy was allowed to cureat room temperature for a minimum of 48 h prior to testing. The fixture was installed ina servo hydraulic testing machine (MTS) fitted with a 100 kN load cell as shown inFigure 1(b). The tests were conducted at room temperature in displacement control at acrosshead speed of 1.27mm/min. A Keyence laser displacement unit coupled to a RD-50Rcontroller, shown in Figure 1(b) was installed to measure the sliding movement of theloading plates relative to each other in the direction parallel to the loading plates.

Fatigue Test

Shear fatigue tests were performed in accordance to ASTM 394-62 [18] at roomtemperature under load control on the foam specimens at a load ratio of R ¼ Pminj j=Pmaxj j ¼ 0:1, using the MTS machine at a frequency of 3Hz. The run out cycle numberwas set at 106 cycles. Fatigue data for a minimum of four specimens of each of the foamtypes were generated at stress levels of: 95, 85, 75, 65, 55 and 45% of the static shearstrength. During the cycling process, regular inspection of the fatigue specimen was made.The damage mechanism and crack path was continuously monitored. The initiation ofeach new crack, the corresponding number of cycles and the total number of cracks tofailure was recorded.

Pre/Post Fracture Examination

Virgin surfaces were examined in a JEOL JSM 5800 scanning electron microscope.The specimens were glued to an aluminum base and coated with gold to prevent charge

Table 1. Properties of foams as specified by DIAB.

Property Unit H130 HD130

Density kg/m3 130 130Shear strength MPa 2.0 1.6Shear modulus MPa 52 32

Fatigue of Crosslinked and Linear PVC Foams 603




build-up by the electrons absorbed by the specimen. Postfractured specimens werephotographed with a digital camera.

RESULTS AND DISCUSSION

Static Tests

These tests were conducted primarily to obtain strength values for the fatigue tests.The load was applied to the H130 and HD130 specimen via the steel plates as shown in

(a)

(c)

(b)

c

r

L

P

γ = tanθ r/c

τ = P/Lb

P

Figure 1. (a) Schematic of shear test fixture; (b) Photograph showing experimental setup; (c) Schematic ofspecimen deformed along its length.

604 K. KANNY ET AL.




Figure 1(a). The laser displacement unit recorded displacement of the moving steel platerelative to the fixed plate. This displacement was used to calculate the shearing strain, �.Figure 2 shows representative stress–strain (�–�) curves for HD130 and H130 foams. Thefailure loads of both materials were similar. Upon reaching the critical load the specimenelongated up to a threshold value whereupon a small crack formed in the upper section ofthe core. Thereafter rapid shearing of the core occurred. The failure mechanism for bothcross-linked and linear foams was similar. HD130 foams demonstrated more ductilebehavior than H130 foams. This ductility is evident by the longer shear deformation zonefor HD130 seen in Figure 2. Elongation of the HD130 was approximately twice than thatof H130 foams. The large difference in the shear elongation is probably related to thestructure of the cross linked H130 PVC polymer which hinders elongation [19]. The shearstrength and shear modulus of the HD130 foams were approximately 6 and 55% lowerthan that of the H130 foams respectively. An approximation of the area under the curvesin Figure 2 indicates that the energy absorption capability of the HD130 foams is almost100% more than the H130 foams. Mechanical properties of HD130 and H130 foamsdetermined from the experiment are in good agreement with the data supplied by themanufacturer, shown in Table 1. Figure 3 shows a schematic of a foam specimen subjectedto static shear load. The foam specimen deformed as shown in Figure 3. The first crackinitiated at the free edge in the uppermost section of the specimen adjacent to the epoxyinterface. The crack then propagated parallel to the plate for approximately 3–5mm afterwhich, it kinked into the core moving diagonally toward the opposite end. In a fewspecimens free edge effects occurred, i.e. the foam specimen tore away from the plate ateither of the free ends in the upper corners. The fractured surfaces of the HD and H foamsare shown in Figure 4. HD foams show closely spaced shearing lines, which is indicative ofthe small cell size and possibly the better cohesion properties of HD cells whereas H foamshave a very uneven failure surface mainly because of the larger cell sizes and porous natureof this foam. The damaged surface of the linear foam indicates more ductile failure with

0 0.2 0.4 0.6

γ

0

4E+005

8E+005

1.2E+006

1.6E+006

2E+006

τ(P

a) HD130

H130

Figure 2. Stress–strain curves for H130 and HD130 foams.





the pulling out and stretching of the cells while the cross-linked foams behavedmacroscopically as quasi-brittle materials.

Fatigue Tests

A standard S/N diagram with the shear stress normalized with the ultimate static failurestress in shear is presented in Figure 5. The number of cycles is plotted on a logarithmic

(a) (b)Figure 4. Photographs of the damaged surfaces of (a) HD and (b) H foams taken in the direction of view ‘A’.

Deformed Core

Direction of Loading

View A ofdamaged surface

Interface

MovingPlate

Fi xed Plate

Figure 3. Schematic of deformed specimen showing crack propagation.

606 K. KANNY ET AL.




x-axis scale and the lines are power function curve fits. It is seen in Figure 5 that at each ofthe stress levels, the number of cycles to failure for HD foams was at least ten times higherthan that of H130 foam specimen. Accordingly, HD130 foams reaches fatigue threshold of106 cycles in the 60–65% range and the H130 foams reached the same fatigue threshold inthe 50–55% range. In a previous study [4] the flexural fatigue behavior of sandwichcomposites made with HD and H130 cores were characterized. The tests were run atrelatively lower loads in simple bending, at a frequency of 3Hz and at a stress ratioR¼ 0.1. The flexural fatigue data was found to be consistent with the shear data presentedhere i.e. the fatigue life of HD structures at every stress levels was significantly higher thanthat of the H130 structures. The flexural fatigue data however, showed more scatter thanthe shear fatigue data. The large scatter was probably due to the complex failuremodes that occurred in the heterogeneous sandwich structure subjected to flexural loads.

The damage formation process in both the cross-linked and linear foams was similarand a schematic of the crack formation and propagation is given in Figure 6(a),(b).Shortly prior to failure, numerous small cracks form in the foam just below the interfacearea on the side of the fixed plate (Side b). The cracks coalesce into a more dominantcrack, which then propagate parallel to the steel plate. The crack then kinks at an angle ofapproximately 45� into the core, propagating toward the moving plate (Side a). The crackarrests at the interface area (Side a), apparently having insufficient energy at the crack tipto penetrate the cured epoxy. Upon the onset of the first crack, similar cracks appear in thecore on side ‘‘b’’ at fairly equidistant locations along the length of the specimen. Each ofthese cracks propagates in the same way as the first until final tearing and separation ofthe plates occur. Figure 7(a),(b) shows the damaged surface of HD130 foam specimen. Thecracks run across the entire width of the specimen for both categories. For the given lengthof specimen, irrespective of the stress level, a total of approximately 20 number of cracksformed on the HD specimen prior to tearing and separation of the plates, as opposed to 15

1000 10000 100000 1000000No of Cycles (N)

0.4

0.6

0.8

1

τ/τ U

LT

HD130

H130

Figure 5. S–N curves for HD130 and H130 specimen. Stress ratio, R¼ 0.1 and frequency f¼ 3Hz.





number of cracks in the case of H specimen. This suggests that there is a crack saturationpoint prior to failure, which is associated with the length and type of foam specimen beingused. It must be noted that the cracks counted here are the ones that traverse from the justbelow the interface of the moving plate to the interface at the fixed plate. Smaller, lessdominant cracks were not counted. Figure 8 shows a plot of the number of cracks formedas a function of the number of cycles. As seen in the figure, the crack saturation wasreminiscent of the characteristic damage state (CDS) during fatigue lifetime of compositelaminates [20]. In a composite laminate damage usually occurs in three phases. Phase Ioccurs in the first 10–15% of life, during which damage is developed at a very rapid rate.Phase II corresponds to the next 70–80% of the fatigue life, during which time damage

(a) (b)

Interface

Foam Core

Fatigue Cracks

Moving Plate (Side a)

Fixed Plate(Side b)

Fatigue Cracks

Separationof platesalong line

Figure 6. (a) Schematic of crack formation in the core; (b) Schematic showing the line along which finalshearing occurs.

(a) (b)

Photograph “b”end view

Photographside view

Figure 7. (a),(b) Front and side view of a failed HD130 foam specimen after 2�105 cycles.

608 K. KANNY ET AL.




continues to initiate and grow, but at a slower rate than in Phase I. However at the end ofPhase II, the laminate was severely damaged to the level where continued cyclic loadingaccelerated the damage process during Phase III, the final 10–15% of life. A differentscenario however, is observed during the shear fatigue of foams. Phase I, as shown inFigure 8, accounts for approximately 80% of the fatigue life of both H and HD materials.During this time no damage was visible externally, however it was unclear as to the extentof damage within the foam itself. Toward the end of Phase I, a single crack appeared inupper section of the specimen, this was followed by a few more cracks forming fairlyrapidly. Figure 8 shows that the crack initiation for H130 occurred after just 3500 cyclesand for HD after 35,000 cycles. Phase II was marked by a temporary saturation of thenumber of cracks. In some instances a few cracks did initiate and grow but at a muchslower rate than at the end of Phase I. Continued cyclic loading during Phase IIIaccelerated the damage process and a threshold number of cracks formed. This wasfollowed by tearing of the foams up until final separation of the test plates (Phase IV). Notsurprisingly, the shear cracks seen here are similar to the single shear crack that occurredin sandwich beams subjected to flexural loads [4]. Under shear and flexural loads, fatiguecracks kinks in the foam immediately below the epoxy and resin interface respectively. It isbelieved that the adhesive epoxy used to bond the core to the steel plates penetrates thepartly open cells on the foam surface and fill them up to form an interface layer betweenthe skin and the top surface of the core. In addition to this, we believe that as the resin getsfilled into the partially opened cells, it also soaks around and down the cell walls andedges. When the resin is cured, these soaked cell materials become stronger than theregular dry foam cells just underneath. A sub-interface is therefore created between theseso-called soaked and dry form cells, which are apparently weaker than the actual core–skin interface mentioned earlier. It is also noticed in Figure 8 that the number of cyclesrequired to form an equal number of cracks within any of the phases described earlier, is

0 20000 40000 60000

No. of Cycles (N)

0

5

10

15

20

25

No.

of

Cra

cks

HD130H130

Phase I

Phase II

Phase III

Phase IV

Crack initiationpoints

Figure 8. Crack formations as a function of the number of cycles to failure for H130 and HD130 tested at 85%of the ultimate load.





almost 10 times higher in HD than that of H foams. In other words, the formation ofcracks in HD foams during fatigue is somewhat delayed when compared with H foams.This delay in crack formation we believe is inherently connected with the debond fracturetoughness of the core material with the adhesively bonded plate. Surely, the debondstrength of HD was higher than that of H foam which caused the delay in the initiationand propagation of cracks. In order to check on this point, the debond fracture toughnessstudy conducted with H and HD foam core sandwich composites in a parallelinvestigation [21] was considered. In that study a set of sandwich specimens with H andHD foams were fabricated using S2-Glass face sheets. Debond fracture toughnessparameter (G1c) was then determined using a Tilted Sandwich Beam (TSB) configuration[22–24]. Test results indicated that the debond fracture toughness of HD (0.95 kJ/m2)foams was almost 1.6 times higher than that of H (0.59 kJ/m2) foam. It was concluded thatH and HD foams would perform almost in a similar manner if steel plates had been usedin place of S2-Glass as face sheets. While the variation in the magnitude of G1c explainedthe time delay in the formation of cracks, the question still remained as to why the fracturetoughness is higher with HD foam having identical density with H foam. On the otherhand, it was earlier shown in [23] that G1c values indeed increased with density. This calledfor an extensive SEM analysis of the cell structures of both categories.

SEM Analysis

Scanning electron microscopy (SEM) was performed on virgin HD130 and H130specimen and micrographs of the cell structures are shown in Figure 9(a),(b). Themicrographs show that HD130 foam has a fairly uniform distribution of irregular cells.The cells are of different size and shape with differing numbers of faces and edges and areat least 40% smaller than the corresponding H130 foam cells. Cell size was estimated fromenlarged photographs of foam specimen using a caliper. H130 foams on the other handhave fairly regular cell units that have a hexagonal structure. The cell walls of the HDfoams appear marginally thicker and the cell struts and plates are smaller than the H130foams. The cell wall thickness was estimated from enlarged photographs (same scale) usinga caliper. It was found on an average of five specimens that the cell wall thickness of theHD and H foams was 1 and 0.8mm respectively. A closer inspection of the micrographs in

(a) (b)

Figure 9. Micrographs of Virgin; (a) HD 130 and; (b) H 130.

610 K. KANNY ET AL.




Figure 9 reveals that there is an average of five cells across the width of micrograph (a) andthree across micrograph (b) The total length of cell edges of HD and H foams was found tobe 411 and 287mm respectively. It must be remembered that these are not the actualdimensions but rather a scaled value based on enlarged photographs. This estimate of thecell edge length was found by adding the perimeter of each cell. The length of a cell edgeadjacent to two cells was counted once only. An estimate of the cross sectional area of thecell edges is made by multiplying the total length of the cell edges by the thickness. It wasfound that the cross sectional area of the cell edges of the HD foams was approximately1.75 times that of the H130 foams. The ratio of the cross sectional area of the HD foam tothe H foams is very similar to the ratio of the fracture toughness. This supports the theorythat the thicker cell edges of the HD foams absorb more resin thereby making themtougher and less prone to premature failure.

CONCLUSIONS

The following conclusions are drawn from this investigation:

1. HD130 foams are more ductile than H130 foams and have a remarkable resistance tocrack propagation, at room temperature.

2. The energy absorption capability of the HD130 foams was almost 100% more than theH130 foams.

3. HD130 has better shear fatigue properties than H130 when tested at roomtemperatures. The number of cycles to failure for HD foams was at least 10 timeshigher than that of H130 foam specimen at every stress level.

4. HD foams have smaller cell size than H130 foams and a more uniform distribution.During the bonding process either with adhesives or with VARTM, liquid resin fills thepartially open foam cells and penetrates cell walls and edges forming a sub interphasezone consisting resin rich cells. In all cases fatigue cracks initiate immediatelyunderneath this zone.

5. As more resin infiltrates the cell walls, thicker edges, and open smaller cells of HDfoams, it causes the toughening of the cell material near the interface and therebymakes them more resilient to fracture cracks during fatigue which attributes to higherfatigue life.

ACKNOWLEDGMENTS

The authors would like to thank the Office of Naval Research (Grant No. N00014-90-J-11995) and the National Science Foundation (Grant No. HRD -976871) for supportingthis research.

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fatigue of crosslinked and linear pvc foams under shear loading

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