Article

Debonding of composites structuralinsulated sandwich panels

Mohammed A Mousa and Nasim Uddin

Abstract

A new type of composites structural insulated panels (CSIPs) is presented in this article. These panels are proposed for

structural floor and wall applications. The developed composite panels are made of low-cost orthotropic thermoplastic

glass/polypropylene laminate as facesheets and expanded polystyrene foam as a core. CSIPs have a considerably high

facesheet/core moduli ratio. The common mode of failure of these panels is facesheet/core debonding. Accordingly, this

investigation presents models for interfacial tensile stress and critical wrinkling in-plane stress associated with debonding

of CSIPs. The facesheet in compression was modeled as a beam on a Winkler foundation. The proposed models were

validated using full-scale experimental testing for CSIPs floor and wall panels. Both type of panels failed by facesheet/

debonding with natural half-wavelength approximately equal to the core thickness.

Keywords

Sandwich structures, facesheet/core debonding, wrinkling, thermoplastic composites

Notation

b panel widtht thickness of glass-pp facesheetL panel lengthc core thicknessd total thickness of sandwich panell natural half-wavelength of the debonded part

wm out-of-plane displacement of the debondedpart

�z out-of-plane interfacial tensile stress�cr in-plane critical wrinkling stressEf longitudinal modulus of elasticity of glass-pp

facesheetsEc core modulus of elasticityG core shear modulus�xy Poisson’s ratio of facesheet in the xy-plane

Introduction

Sandwich structures consist of two stiff, thin facing,and lightweight thicker core. The concept of the sand-wich structures is similar to that of I-sections, in whichfacesheets carry the bending stresses while the coreresists the shear loads and stabilizes the faces againstbulking or wrinkling.1 The core also increases the

stiffness of the structure by holding the facesheetsapart. In general, core materials have lower mechanicalproperties compared to that of facesheets. For ordinarysandwich panels used in construction, the commoncore/facesheet thickness ratio ranges from 10 to 50while the moduli ratio varies from 50 to 1000.1 Thisarticle presents new a composite panel system,namely, composite structural insulated panels(CSIPs), which are developed by the authors. CSIPsare made of low-cost orthotropic thermoplastic glass/polypropylene (glass-PP) laminate as facesheets andexpanded polystyrene foam (EPS) as a core.Thermoplastics (TP) polymers offer advantages interms of short processing time, extended shelf life,and low-cost raw material. TP also possess the advan-tages of high toughness, superior impact property, andease of reshaping and recycling over thermoset polymercomposites. Several investigations have been conducted

Department of Civil, Construction and Environmental Engineering,

University of Alabama at Birmingham, USA.

Corresponding author:

Mohammed A Mousa, Department of Civil, Construction and

Environmental Engineering, University of Alabama at Birmingham,

Birmingham, AL 35294-4440, USA

Email: mmousa@uab.edu

Journal of Reinforced Plastics

and Composites

29(22) 3380–3391

! The Author(s) 2010

Reprints and permissions:

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DOI: 10.1177/0731684410380990

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at the University of Alabama at Birmingham (UAB) bythe authors and others on developing compositespanels for building applications using rigid and softcores with thermoset and thermoplastic facesheets.2–8

It was demonstrated by these studies that the developedpanels can provide much higher strength, stiffness, andcreep resistance than traditional ones that are madewith wood-based facing. The developed CSIPs havea considerably high facesheet/core moduli ratio(Ef/Ec¼ 12,500) compared to the ordinary sandwichconstruction. Further, CSIPs are characterized bylow-cost, high strength to weight ratio, and lower skillrequired for field construction, etc. These panels can beused for different elements in the structure, includingstructural elements (e.g., floors, roofs, and load-bearingwalls) and non-structural elements (e.g., non-load-bear-ing walls, lintels, and partitions).

A large number of investigations have been con-ducted on sandwich construction to study their behav-ior under different types of loadings including in-planeand out-plane loadings. A general review of failuremodes of composites sandwich construction was givenby Daniel et al.9 Failures modes for sandwich beamsinclude yielding of facesheet in tension, core shear fail-ure, and local buckling of facesheet in compressionwhich is know as wrinkling of facesheets. Failuresmodes of sandwich wall include global buckling, localbuckling ‘wrinkling’, and core failure. In case of globalbuckling, the core may exhibit a substantial shearingdeformation.10 A few global buckling formulas forsandwich formula can be found in the literature.11 Asfor wrinkling, several investigations have led to simpleformulas; the most known ones were developed byGough et al.12 and Hoff et al.13

The facesheet/core debonding is mainly caused dueto the wrinkling of facesheet in compression when thepanel is subjected to compressive loading. Deboningcould be preexisting due to manufacturing defects andin this case called ‘disbond’. Almost all of the previousstudies have focused on the modeling of pre-debondedsandwich panels. In this study, the focus is on thedebonding due to compressive loading. Further, thereis an apparent gap for modeling facesheet/core debond-ing for sandwich panels with considerably highfacesheet/core moduli ratio. Accordingly, this investi-gation also presents models for these types of sandwich

panels. Wrinkling is caused due to sudden localizedshort-wavelength buckling of facesheets in compres-sion. In case of wrinkling, the core acts as an elasticfoundation to the facesheets.10,11 It can take the form ofoutward or downward. If the buckling is outward it isknown as debonding, while if it is downward it isknown as core crushing (Figure 1). The former occursin case of sandwich panel with closed-cell cores (e.g.,EPS foam) while the latter normally happens in caseof sandwich panels with open-cell cores (e.g., honey-comb core).14

The wrinkling phenomenon is characterized by thecore/facesheets interaction, thus both tensile stressat the interface and compressive wrinkling stress arefunctions of the core and facing properties, andare independent of the geometrical properties and load-ing conditions. Since sandwich structures may exhibitlittle or no post-wrinkling load-carrying capability, fail-ure of these structures by facesheet wrinkling is typi-cally catastrophic. It has been demonstratedanalytically and experimentally that there will be nodebonding growth until the debonded region has buck-led.15–17 This means that an accurate estimate of thelocal buckling load or stress, in many cases, providesa lower bound on the failure load. In other words, accu-rate prediction of the local bucking load at debondingis important to the development of reliable and efficientsandwich structures. There are three main categories ofwrinkling, as shown in Figure 2. Case (I) is known as

Figure 1. Upward and down wrinkling: (a) upward wrinkling

(debonding, case of solid cores); and (b) downward wrinkling

(core crushing, case of open-cell cores).

Figure 2. Types of wrinkling: (a) Case I: rigid base; (b) Case II: antisymmetrical; and (c) Case III: symmetrical.

Mousa and Uddin 3381

rigid base wrinkling or single-sided facesheet wrinkling.This case occurs in case of sandwich beam under purebending in which wrinkling is only likely to happen inthe compression face, or in pure compression when thesandwich panel has unsymmetrical facesheets with dif-ferent wrinkling loads, it can also occur in case thesandwich wall is loaded with eccentric load. Case II isknown as antisymmetrical wrinkling or in-plane mode.It occurs in a sandwich strut in which both facesheetsare subjected to equal compressive loads. The middleplane of the core does not remain undeformed and thethickness of the core is of significant importance toboth wavelength and the critical buckling. Case (III)is known as symmetrical wrinkling. This case is similarto Case II, it occurs in a sandwich strut in which bothfacesheets are subjected to equal compressive loads andis known as out-of-plane mode. This case gives ashorter natural wavelength and a higher stability failureload than both the other cases. The main objective ofthis paper is to develop models for the out-of-planeinterfacial tensile stress and the in-plane compressivewrinkling stress at the onset of the debonding forCSIPs sandwich panels that have a considerably highfacesheet/core moduli ratio and are made of orthotro-pic facesheet and solid cores. The study also includesfull-scale experimental testing as a case study todemonstrate the developed models.

Materials and specimens

To validate the models developed for stresses at debon-ding for CSIPs, four full-scale sandwich panels weretested. Two of them are full-scale floor panels whilethe other two are full-scale wall panels (Figure 3).The dimension for each panel is 4 ft� 8 ft(1219.2mm� 2438.4mm) as the typical dimension cur-rently used in the housing market.18

The large-scale sandwich specimens consisted of 5.5 in.(140mm) thick EPS foam sandwiched between two0.12 in. (3.04mm) thick glass/polypropylene (glass-PP)composite facesheets (Table 1). TP facesheet laminatesconsist of 70% bi-directional E-glass fibers impregnatedwith poly-propylene (PP) resin. TP offer promise interms of short processing time, extended shelf life, andlow-cost raw material. They can be reshaped andrecycled by reheating, and they also have superiorimpact properties. TP composites are produced byusing a hot-melt impregnation process, also called aDRIFT process.19 In this research, glass-PP compositesheets were directly obtained from the manufacturer.20

The mechanical properties of glass-pp facesheets arelisted in Table 2. Because of lower costs, good fire andthermal resistance, and excellent impact properties, EPSfoam was selected as the core for the sandwich. Table 3describes the properties of the EPS foam as provided bythe manufacturer.21 The glass-PP facesheets werebonded to the EPS core using a hot-melt thermoplasticspray adhesive. To insure quality of processing, CSIPswall panels tested in this study were manufactured at acasting and molding facility.

Modeling of facesheet/core debonding

During loading of the sandwich panel, two types ofstresses are developed at the facesheet in the compres-sion side; the first is a tensile stress at facesheet/coreinterface ‘�z’ while the other is a compressive criticalwrinkling stress in the facesheet of the deboned part

b

(a)

(b)

d

d

bc

t

t t

c

t

L

L

Figure 3. Schematic for CSIP specimens: (a) floor panels,

(b) wall panels.

Table 1. Dimensions of CSIP full-scale

specimens

t 0.12 in. (3.04 mm)

c 5.5 in. (140 mm)

d 5.74 in. (146.08 mm)

b 48 in. (1219.2 mm)

L 96 in. (2438.4 mm)

Table 2. Properties of the glass-PP facesheets

Nominal thickness, t 0.12 in. (3.04 mm)

Weight % of glass fiber 70%

Density (�f) 61 pcf (980 kg/m3)

Longitudinal modulus (Ex) 2,200,000 psi (15,169 MPa)

Transverse modulus (Ey) 2,200,000 psi (15,169 MPa)

Tensile strength 46,000 psi (317 MPa)

Flexural strength 60,000 psi (414 MPa)

In-plane Poisson’s ratio �xy

� �0.11

3382 Journal of Reinforced Plastics and Composites 29(22)

‘�cr’ (Figure 4). The debonding occurs when the tensilestress at the facesheet/core interface exceeds the tensilestrength of the core material. It is a common mode offailure of sandwich panels leading to the loss of panelstiffness. The facesheets under compression can bemodeled as a strut or beam supported by an elasticfoundation represented by the core. In the following adetail explanation for this model is presented.

The glass-PP facesheets under compression can bemodeled as a strut or beam supported by an elasticfoundation represented by the EPS foam core. Inother words, CSIP wrinkling can be modeled as aWinkler foundation. In the analysis of the behavior ofa long strut or beam supported by a continuous elasticmedium, the medium can be replaced by a set of closed-spaced springs (Figure 5); this phenomenon is normallyknown as Winkler hypothesis, and the facesheet in thiscase is called Winkler beam while core is known asWinkler foundation. For a beam supported by aWinkler foundation, the governing differential equationof the beam is given as:

Dfd4w

dx4þ P

d2w

dx2þ b�z ¼ 0, ð1Þ

where Df the flexural stiffness of the beam (facesheet),P is axial load developed in the facesheet due to load-ing, w is the displacement of the debonded part in

z-direction. �z is the interfacial tensile stress at face-sheet/core interface, and b is the width of the facesheet.

Interfacial tensile stress �zð Þ

Assume the springs’ (foundation) stiffness is repre-sented by a coefficient k. This coefficient representsthe force needed to displace the springs in a unit areaof the xy-plane through a unit displacement in thez-direction. Suppose this strut buckle into sinusoidalwaves with half-wavelength of l, which is equal to thedeboned length (Figure 7), the displacement of thebuckled portion in the z-direction can be expressed as:

w xð Þ ¼ wm sin�x

l, ð2Þ

where wm is the maximum displacement of the debonedpart (i.e., at l/2). The Winkler beam model assumes thatdisplacements of facesheet in compression are symmet-rical about the center line of the core while displace-ments the facesheet in tension are negligible. It shouldbe noted that, as demonstrated by earlier studies,11,22,23

the half-wavelength (l) of the debonded part is alwaysof same order as the thickness of the core. Similarobservation was made in this study, when experimentaltesting demonstrated that the debonded part is almostequal to the core thickness.

Interfacial stresses (sz) Critical wrinkling stress (scr)

Figure 4. Types of stresses at the compressive facesheet due to debonding.

Glass-PP facesheet is represented by long strut

EPS foam is represented by closed springs

Figure 5. Winkler foundation model.

Table 3. Properties of the EPS core

Nominal density 1 pcf (1:6� 107mg/m3)

Elastic modulus Ecð Þ 180–220 psi (1.2–1.5 MPa)

Flexural strength 25–30 psi (0.17–0.2 MPa)

Tensile strength 16–20 psi (0.11–0.14 MPa)

Shear modulus (G) 280–320 psi (1.9–2.2 MPa)

Shear strength 18–22 psi (0.1–0.15 MPa)

Poisson’s ratio 0.25

Mousa and Uddin 3383

As shown in Figure 6, the corresponding out-of-planstress (interfacial stress) that is required to displace thisportion of facesheet is given by:

�z ¼ k � w: ð3Þ

From (2) and (3), we get:

�z ¼ kwm sin�x

l: ð4Þ

To model the foundation stiffness k, many investiga-tions have been conducted. Sleight and Wang24 haveused this simplified definition for k:

k ¼Ez

tc: ð5Þ

This definition only satisfied two-dimensional equi-librium for a constant strain through the depth of thecore and a constant beam displacement, w (i.e.,w(x)¼wm). It is also applicable only for orthotropiccores (i.e., honeycomb). Niu et al.15 proposed the fol-lowing foundation term to incorporate the assumptionof plain strain condition in an isotropic core:

k ¼Ez 1� �ð Þ

tc 1� 2�ð Þ 1þ �ð Þ: ð6Þ

However, we are proposing in this study the stiffnessfoundation as suggested by Allen,11 in which the effectof the half-wavelength of the debonded facesheet isincluded as well as the wrinkling type unlike the previ-ous two models. It also used for solid core. The general

L Glass-PP facesheet

EPS foam

Wm

Z

X

Figure 6. Half-wavelength of the debonded facesheet in compression.

Figure 7. Experimental setup for full-scale floor testing according to ASTM-E-72-05.

3384 Journal of Reinforced Plastics and Composites 29(22)

equation for k to represent the three cases of wrinklingis expressed as:

k ¼Ec

c�2f �ð Þ: ð7Þ

where � is a function of the core thickness and half-wavelength of l and is given by �c

l .f(�) is a function of core Poisson’s ratio and � and

has a different equation for each case of wrinkling (as inFigure 2) as follows:

Case ðIÞ : f �ð Þ ¼2

�

3� �cð Þ sinh � cosh �þ 1þ �cð Þ�

1þ �cð Þ 3� �cð Þ2sinh2 �� 1þ �cð Þ

3�2,

ð8Þ

Case ðIIÞ : f �ð Þ ¼2

�

cosh �� 1

1þ �cð Þ 3� �cð Þ sinh �þ 1þ �cð Þ2�

,

ð9Þ

Case ðIIIÞ : f �ð Þ ¼cosh � þ 1

3 sinh � � ��c¼ 0ð Þ: ð10Þ

Thus, Equation (4) can be then rewritten as:

�z ¼Ec

c�2f �ð Þwm sin

�x

l: ð11Þ

Equation (11) represents the tensile stress at the face-sheet/core interface for a given displacement wmð Þ andhalf-wavelength (l) for the debonded facesheet. Thedebonding occurs when this stress exceeds the tensilestress of the core material. As seen from Equation(11), the interface stress is independent of the facesheetproperties and it only depends on the core propertiesas well as core thickness. It should be indicated thatthe lowest critical load that a compressive facesheetcan sustain is when the half-wavelength of the buckledform is approximately equal to the length of thefacesheet.

Critical wrinkling stress in the facesheet �crð Þ

The second stress that is associated with the debondingis the critical wrinkling stress in the facesheet in com-pression �crð Þ. This is a compressive in-plane stressdeveloped in the facesheet due to loading. This stresswas the focus of most of the previous studies that wereconducted on the wrinkling of facesheets in compres-sion, whereas the stress at the interface �zð Þ was notaddressed appropriately. The main reason for that isall of these studies were investigating sandwich panelswith pre-existing disbond that occur during themanufacturing of the panels. In this case, the interfacialstresses vanish at this region.

To model this stress �crð Þ, Recognizing Equation (2)for w(x) and Equation (11) for �zð Þ:

w xð Þ ¼ wm sin�x

l

�z ¼Ec

c�2f �ð Þwm sin

�x

l

Substitution of w(x) and (�z) in Equation (1) andrearranging the equation yields:

P�2

l2¼ b

Ec

c�2f �ð Þ þDf

�4

l4: ð12Þ

For orthotropic facesheets, referring to glass-PPfacesheet laminates, Df is given by:25

Df ¼bEft

3

121� �2xy

� �, ð13Þ

where �xy is the Poisson’s ratio of the facesheet in thexy-plane. This will considers the through thicknessanisotropy effect due to the orthotropic facesheets.Dividing Equation (12) by bt and substituting of Df,�l ¼

�c, recognizing that the wrinkling compressive

stress in the facesheet (�cr) is given as P/bt, this yields:

�cr ¼Ec

tcf �ð Þ þ

Ef

12

�

c

� �2

t2 1� �2xy

� �ð14Þ

Equation (14) represents the general theoretical for-mula for wrinkling compressive stress in the facesheetfor sandwich panel with orthotropic facesheets andsolid core (referring to CSIP). As can be noticed, thewrinkling stress �crð Þ is a function of the properties andthicknesses of facesheet and core unlike the interfacialtensile stress �zð Þ which is independent of the facesheetproperties and mainly depends on the core material.

Several investigations were conducted to predict thecritical wrinkling stress for all wrinkling cases. Most ofthese studies have led to empirical formulas. All theformulas of take the following form for sandwichpanels with solid cores (such as EPS foam):

�cr ¼ �1 EfEcGcð Þ1=3, ð15Þ

while for those with open-cell core (such as honey-comb), the stress takes the following form:

�cr ¼ �2Ef

ffiffiffiffiffiffiffiffiEctfEftc

r: ð16Þ

The value of the constant �1 in Equation (16) hasbeen suggested by various investigators (0.79 and 0.63by Gough et al.,12 0.76 by Cox et al.,26 0.91 and 0.5 by

Mousa and Uddin 3385

Hoff et al.,13 0.825 by Plantema27). The value of �2 wassuggested also by many investigators (0.82 byWilliams,28 1.732 by Hemp,29 and 0.961 by Yusuff30).From this discussion, it can be seen that there are dif-ferent thoughts regarding the calculation of the wrin-kling stress in the compressive facesheet. Further, mostof these studies considered only isotropic facesheetswhen the sandwich panels used to have isotropic face-sheets made of metal. In this study, the model derivedfor the wrinkling stress is taking into consideration theorthotropic facesheets and solid core. It is also appro-priate for the three cases of wrinkling. However, for thesake of comparison and the best formulation of theexperimental results, we are proposing a practical for-mula similar to the above models to predict the wrin-kling stress of the facesheets in compression for CSIPspanels.

Experimental procedure

The experimental testing was performed according tothe ASTM E-72-05 standard.31 This standard dealswith testing panels for structural building applications.The deflection at the mid-span was recorded using alinear variable displacement transducer (LVDT) witha capacity of measuring deflection up to 150mm.Strain gages with gage factor of 2.085 were attachedat the geometric center on both sides of each panel torecord the strains of the facesheets at the tensile andcompression sides. A load cell with a capacity of 13.5kip (60 kN) was used to measure the load. The LVDT,load cell, and the strain gages were connected to thedata acquisition machine, which in turn recorded thedata using Strain Smart software. A preload of 1 kNwas applied initially to ensure that all of the instru-ments were working adequately. The floor panelswere tested using a four-point bend setup, as shownin Figure 7. The load was applied through a bottlejack of capacity 6 metric tons distributed over thepanel using a spreader I-beam.

For most compression-loaded members, the line ofaction of the load does not act at the centroid due todimension and construction errors. Accordingly,ASTM E-7224 recommends that these walls should betested under eccentric compressive load by applying theload uniformly to the top cross section of the panelsalong a line parallel to the inside face at one-third thepanels thickness from inside which corresponds to aneccentricity of to h/6 from the wall centroid. A steelroller of 1 in. (25mm) diameter welded to the 0.24 in.(6.25mm) thick steel plate was used to distribute theload uniformly along the top edge of the panel. The topand bottom edges of the panel were constrained toavoid premature debonding at the edges once the loadwas applied (Figure 8). The structural behavior of the

panel was analyzed by measuring surface strains on theboth faces of the panels. A loading ram was used toapply the compressive load.

At a load of 1.8 kip (8 kN), floor panels failed bylocalized debonding between the core and top facesheet(facesheet in compression) in the maximum flexuralzone in compression (Figure 9(a)). For CSIP wallpanels, they also failed by localized debonding betweenthe core and facesheets in the maximum compressionside (Figure 9(b)). As seen from Figure 8, both panelsfailed due Case I of debonding which is known assingle-sided or rigid base wrinkling case. This ismainly because of the panels were subjected to bendingmoment which creates a compression on one side andtension on the other side. The debonding occurs onlyon the compression side. It should be noticed here thatfloor panels were subjected to pure moment while wallpanels were subjected to a combination of axial loadand moment resulting from the eccentric loading whichcreates a tension on one side and compression on theother side. As seen clearly from Figure 9, both floor andwall panels recorded same half- wavelength (l) and alsosame maximum out-of-plane displacement of thedebonded facesheet (wm). Therefore, the expected inter-facial tensile stress will be the same for wall and floorpanels. This strongly validates that fact that the inter-facial tensile stress is independent of the geometricalproperties and loading conditions.

Figure 8. Experimental setup for the full-scale wall testing

according to ASTM-E-72-05.

3386 Journal of Reinforced Plastics and Composites 29(22)

Validation of the experimental results

Validation of the interfacial tensile stress �zð Þ

As shown in Figure 9, the half-wavelength is almostequal to the core thickness (140mm) and the maximumout-of-plane displacement of the debonded facesheet isalmost 10mm for both panels. Therefore, the function �can be determined as follows:

� ¼�c

l¼�x140

140¼ 3:14

As observed in the experiment: wm (10mm) repre-sents 7% of the core thickness (140mm), c¼ l, sinsin�x=l¼ unity since the stress is calculated at themiddle. Accordingly, and for the design purpose,

Equation (7) can be rewritten as:

�z ¼ 0:07�2f �ð ÞEc ð17Þ

Since Case I is the control case for floor and wallspanels, f (�) is determined according to Equation (8):

f �ð Þ¼

2

3:14

3�0:25ð Þsinh 3:14ð Þcosh 3:14ð Þþ 1þ0:25ð Þ 3:14ð Þ

1þ0:25ð Þ 3�0:25ð Þ2sinh2 3:14ð Þ� 1þ0:25ð Þ

3 3:14ð Þ2

¼0:191

Thus, the interfacial out-of-plane stress facesheet/core interfaces can be then determined from Equation(17) as follows:

�z¼ 0:07�2 0:191ð Þ 1:2ð Þ ¼ 0:16MPa¼ 23:8psi

Figure 9. Failure of the CSIPs at the peak load: (a) failure of CSIP floor panel under out-of-plane loading, (b) failure of CSIP wall panel

under eccentric in-plane loading: both types of panel are Case I of wrinkling (wm¼ 10 mm, l¼ core thickness¼ 140 mm).

Mousa and Uddin 3387

As seen from Table 2, the maximum tensile strengthof the EPS core is 20 psi. As previously mentioned,the debonding occurs when the interfacial stressexceeds the tensile strength of the core material. Asdemonstrated from the model, the out-of-plane stress(23.8 psi) has just exceeded the tensile strength of thecore material (20 psi) causing the debonding failure forboth wall and floor panels. Figure 10 illustrates thesevalues.

Validation of critical wrinkling stressin the facesheet �crð Þ

The wrinkling stress formula (Equation (14)) of thefacesheets in compression was also validated using thefour CSIP large scale panels (two for floor and two forwall applications). Figures 11 and 12 show the load–strain curves for floor and wall panels, respectively. As

shown in the figures, the compression strain at thedebonding is almost the same for floor and wallpanels (0.0005 for floor and 0.00055 for wall). Again,this validates the criteria that the facesheet wrinklingstress is independent of loading and boundary condi-tions. This strain results an experimental wrinklingstress of:

�cr Exp: ¼ "Exp: � Ef

For floor panels:

�cr Exp: ¼ 0:0005 15, 169ð Þ ¼ 7:58MPa:

For wall panels:

�cr Exp: ¼ 0:00055 15, 169ð Þ ¼ 8:34MPa:

Core tensilestrength=20psi

L

X

Glass-PP facesheet

EPS foam

wm

Z

sz=23.8psi

Figure 10. Out-of-plane stress of CSIP panels.

Figure 11. Load vs. strain for CSIP floor panels.

3388 Journal of Reinforced Plastics and Composites 29(22)

The theoretical wrinkling stress can be calculatedusing Equation (14) considering Case I of wrinklingsince both types of panels were debonded at one sideonly due to the bending moment.

� ¼�c

l¼�x140

140¼ 3:14

Since Case I is the control case for floor and wallspanels, f(�) is determined according to Equation (8):

f �ð Þ¼

2

3:14

3�0:25ð Þsinh 3:14ð Þcosh 3:14ð Þþ 1þ0:25ð Þ 3:14ð Þ

1þ0:25ð Þ 3�0:25ð Þ2sinh2 3:14ð Þ� 1þ0:25ð Þ

3 3:14ð Þ2

¼0:191

Accordingly, the theoretical wrinkling stress can becalculated using Equation (15) as follows:

�cr¼Ec

tcf �ð Þþ

Ef

12

�

c

� �2

t2 1��2xy

� �

¼1:2

3:04140ð Þ 0:191ð Þþ

15,169

12

3:14

140

� �2

3:04ð Þ2 1�0:112� �

¼16:43MPa

Comparing the experimental value of the wrinklingstress (8.34MPa for wall and 7.58MPa for floor) withthe theoretical value predicted by the proposed model(16.43MPa), It can be noticed that the experimentalvalue is almost one-half of the theoretical one. This

was common for most of the previous work conductedon wrinkling stress (e.g., Hoff et al.,6 the constant wentfrom 0.91 to 0.5 to fit the experimental results). Thus,these studies have proposed an empirical formula tocorrelate with the experiments. In this case, the mainreason for this difference is the much lower mechanicalproperties of the core compared to that of the face-sheets in which the ratio of facesheet modulus to thatof the core is the highest ratio that been used for asandwich panel till to date (Ef/Ec¼ 12,500). It can benoticed that the critical wrinkling stress of the floor orwall can be predicted using Equation (16) with �1¼0.25. Accordingly, to fit of the experimental results,the following empirical formula is therefore proposedto predict the wrinkling stress of the CSIPs taking intoconsideration the orthotropic facesheets:

�cr ¼ 0:25 EfEcGcð Þ1=3 1� �2xy

� �: ð18Þ

By comparing the proposed constant (0.25) with theother constants previously proposed for sandwichstructures, it can be noticed this constant is smallerthan the ones that have been used before. The mainreasons for that include the orthotropic facesheet usedin the study and the high moduli ratio of the facesheetto the core.

Summary and conclusions

In this article, a new type of sandwich panel, namely,CSIPs, was developed for structural floor and

Figure 12. Load vs. strain at the mid-height of CSIP wall panels.

Mousa and Uddin 3389

wall applications. CSIPs are made of orthotropic glass-PP facesheets and EPS foam core with considerablyhigh face/core moduli ratio (Ef/Ec¼ 12,500). This typeof panels normally fails by debonding. Two models forinterfacial tensile stress and in-plane critical wrinklingstress were developed for CSIPs. Full-scale testing wasconducted to demonstrate the efficiency of the devel-oped models. The following are the main conclusionsof the present study:

1. Two models for interfacial tensile stress and criticalwrinkling stress were proposed for CSIPs. The wrin-kling stress �crð Þ is a function of the properties andthicknesses of facesheet and core whereas the inter-facial tensile stress �zð Þ is independent of the face-sheet properties and mainly depends on the corematerial.

2. Full-scale CSIPs panels failed by localized debond-ing between the core and facesheets in the maximumcompression side with natural half-wavelengthapproximately equal to the core thickness (l¼ c).Case I of debonding was observed for both typesof panels. This mode of failure is known as wrinklingof the facesheet in compression, which is caused by asudden local buckling of the facesheets. This mode ismainly because of the out-of-plane interfacial stress(�z) exceeded the core tensile strength.

3. The interfacial tensile stress model was validated bydemonstrating the close proximity to the experimen-tal results. The results proved that the predictedinterfacial stress is higher than core tensile strengthand therefore, debonding was the general mode offailure. This validates the criteria that the interfacialstress in independent of loading and boundary con-ditions and depends only on the core properties. Thismodel is given by:

�z ¼ 0:07�2f �ð ÞEc

4. The proposed theoretical model for the critical wrin-kling stress that based on the Winkler foundationmodel less conservatively predicted the actual wrin-kling stress. Accordingly, the following empiricalformula was proposed to predict the critical wrin-kling stress at the debonding for CSIP panelsconsidering the orthotropic facesheets:

�cr ¼ 0:25 EfEcGcð Þ1=3 1� �2xy

� �

Acknowledgments

The authors would also like to thank Dr Amol Vaidyafor his help in the experimental results.

Funding

This work was supported by National ScienceFoundation (NSF) [grant number CMMI-0825938].

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