Part II

Sandwich Constructions

Composite materials used today are often in the form of a sandwich construction,

see Figure 8.5.A sandwich panel is built up by two thin skins, also called the

Face sheet

Adhesive

Honeycomb core(metal, composite or paper)

Face sheet

Figure 8.5: A sandwich construction.

facings, separated by a lightweight core. The core helps to increase the moment of

inertia such that the structure becomes efficient for resisting bending and buckling

loads. This is why sandwich panels are being used in applications where weight-

saving is critical, for instance in aircraft and in portable structures.

Sandwich designs are also used by nature itself for instance in a human skull

and in plants. While nature often uses the same material in the facings as in

the core and only vary the density, man-made sandwich panels usually consist of

different materials, or even structures, in the facings and in the core.A sandwich

construction is built up by different face- and core materials and forms, see Figure

8.6 and [35, p.18].

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Figure 8.6: Sandwich materials and forms.

9. Why use sandwich constructions?

The mechanical behavior of a sandwich panel depends on the properties of the

face and the core mateirals and on its geometry.

The Figure 9.1 shows how the sandwich design works, the so-called sandwich-

effect.

In Figure 9.2 we see the sandwich-effect in and aluminium-sandwich compared

to solid aluminium plates of different thickness.

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Figure 9.1: The sandwich effect.

Figure 9.2: Aluminium foam used as core material compared with aluminium plate.

120

9.1. Face materials

The face material in a sandwich panel can be made of almost any material that

can be formed into thin sheets. The properties we seek for in a face material are:

� high stiffness, which gives high �exural rigidity� high tensile and compressive strength� impact resistance� surface �nish� environmental resistance (chemical, UV, heat etc.)� wear resistanceThe most usual type of material used as facings are listed in the Table with a

summary of face materials.

Material

Metals: Mild steel

Stainless steel

Aluminium Alloy

Titanium Alloy

Wood: Pine

Plywood

Unidirectional �bre composites Carbon/Epoxy

(vf = 0.6− 0.7) Glass/Epoxy

Kevlar/Epoxy

Bi-directional �bre composites Kevlar/Polyester

(vf = 0.3− 0.4) Glass weave/Polyester

Glass WR /Polyester

Random �bres Glass CSM

(vf = 0.15− 0.25) SMC

, (9.1)

where WR=(woven roving), CSM= chopped strand mat, SMC = sheet mould-

ing compound and vf is the volume fraction of �bers.

The most used group of face-materials is the �bre composites since they have

a similar or even higher strength properties than metals, and are much easier to

fabricate. Also, the possibility to tailor the face materials because the anisotropic

behaviour of the �bres offer a very interesting addition. In this way �bres can be

placed in the direction where the loadcarrying is most important.

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Figure 9.3: Core exposed to shear.

9.2. Core materials and structures

The essential property of any core material is that it increases the thickness of the

laminate, without causing a great weight increase (engineering theory shows that

the �exural stiffness of any panel is proportional to the cube of its thickness). The

purpose of a core in a composite laminate is therefore to increase the laminate�s

stiffness by effectively �thickening� it with a low-density core material. This can

provide a dramatic increase in stiffness for very little additional weight.

Figure 9.3 shows a cored laminate under a bending load. Here, the sandwich

laminate can be likened to an I-beam, in which the laminate skins act as the

I-beam �ange, and the core materials act as the beam�s shear web. In this mode

of loading it can be seen that the upper skin is put into compression, the lower

skin into tension and the core into shear. It therefore follows that one of the most

important properties of a core is its shear strength and stiffness.

In addition, particularly when using lightweight, thin laminate skins, the core

must be capable of taking a compressive loading without premature failure. This

helps to prevent the thin skins from wrinkling, and failing in a buckling mode.

The properties of primary interest for the core:

� Low density (add little weight to the total weight of the sandwch)� Shear modulus (prevents wrinkling)� Shear strength (prevents wrinkling)� Stiffness perpendicular to the faces (prevents decrease in core thickness and

therefore a rapid decrease in the �exural rigidity)

� Thermal insulation� Acoustic insulationThere are four main groups of core material used,

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Figure 9.4: Honeycomb core.

� Foams� Honeycombs� Corrugated� Wood

9.2.1. Foam Cores

Foams are one of the most common forms of core material. They can be manu-

factured from a variety of synthetic polymers including polyvinyl chloride (PVC),

polystyrene (PS), polyurethane (PU), polymethyl methacrylamide (acrylic), poly-

etherimide (PEI) and styreneacrylonitrile (SAN). They can be supplied in densi-

ties ranging from less than 30kg/m3 to more than 300kg/m3, although the most

used densities for composite structures range from 40 to 200 kg/m3. They are

also available in a variety of thicknesses, typically from 5mm to 50mm.

9.2.2. Honeycomb Cores

Honeycomb cores are available in a variety of materials for sandwich structures,

which ranges from paper and card for low strength and stiffness, low load appli-

cations (such as domestic internal doors) to high strength and stiffness, extremely

lightweight components for aircraft structures. Honeycombs can be processed into

both �at and curved composite structures, and can be made to conform to curves

without excessive mechanical force or heating.

Figure 9.4 shows the usual honeycomb shape. The cells can be triangular,

square or hexagonal cells which also can be �lled with a rigid foam in order to

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provide a greater bond area for the skins, increases the mechanical properties of

the core by stabilising the cell walls and increases thermal and acoustic insulation

properties. The following materials are commonly used in honeycomb structures.

� Aluminium - Has been used since 1950, several alloys can be used, but in

comparison it is old and heavy.

� Glass �bre reinforced plastic - Has a high temperature resistance and goodinsulative properties, but is denser than other materials.

� Kraftpaper honeycoms - impregnated paper with resin to make it waterresistant. Good strength at low cost.

� Nomex honeycomb which is made from Nomex paper - a form of paper basedon KevlarTM (Aramid �bre), rather than cellulose �bres. High strength and

toughness with a low density makes it the most widely used honeycomb

core.The initial paper honeycomb is usually dipped in a phenolic resin to

produce a honeycomb core with high strength and very good �re resistance.

It is widely used for lightweight interior panels for aircraft in conjunction

with phenolic resins in the skins.Nomex honeycomb is becoming increas-

ingly used in high-performance non aerospace components due to its high

mechanical properties, low density and good long-term stability.

The �gures below give the shear strength and compressive strength in Figure

9.5 of some of the core materials described, plotted against their densities, in

addition to Figure 9.6 which shows prices of some core materials. All the �gures

have been obtained from manufacturers� data sheets.

Honeycombs can be made with several different cell shapes:

Hexagonal

The most common shape is the one shown at Figure 9.4, but this can only be

used in �at components.

Overexpanded

The honeycomb in Figure 9.7 is over expanded, so that the cells are rectangular.

This gives better properties in the web direction, but worse in the other, it can

therefore be curved in the ribbon direction only. This shape is used for single

curvature components.

124

Figure 9.5: Compressive strength and shear strength of some of the core materials

plotted against their densities.

Figure 9.6: Comparative prices of some core materials.

125

Figure 9.7: Overexpanded honeycomb structure.

Negative Poisson�s Ratio

Honeycombs can be made with negative Poissons Ratio, when the cell walls

are inverted as in Figure 9.8.

Figure 9.8: Honeycombs with negativ Poisson�s ratio.

Flex-core

Figure 9.9 shows a special core shape, which is created by pulling the hon-

eycomb in the opposite direction. It can curve in either direction, so is used for

irregular shapes.

9.2.3. Corrugated Cores

A corrugated core is shown in Figure 9.10.

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Figure 9.9: Honeycomb �ex core.

Figure 9.10: Corrugated core.

9.2.4. Wood Cores

Wood can be described as �nature�s honeycomb� because on a microscopic scale

you �nd that it consists of closed-cell structure. It has a similar structure to

that of a hexagonal honeycomb, and consequently good mechanical properties.

When used in a sandwich structure with the grain running perpendicular to the

plane of the skins, the resulting component shows properties similar to those made

with man-made honeycombs. However, despite various chemical treatments being

available, all wood cores are susceptible to moisture attack and will rot if not well

surrounded by laminate or resin. Wood is only used in large projects, as it has a

relatively high density, of at least 100kg/m3.

Balsa

The most commonly used wood core is end-grain balsa. Balsa wood cores �rst

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appeared in the 1940�s in �ying boat hulls, which were aluminium skinned and

balsa-cored to withstand the repeated impact of landing on water. This perfor-

mance led the marine industry to begin using end-grain balsa as a core material

in FRP construction. Apart from its high compressive properties, its advantages

include being a good thermal insulator offering good acoustic absorption. The

material will not deform when heated and acts as an insulating and ablative layer

in a �re, with the core charring slowly, allowing the non-exposed skin to remain

structurally sound. It also offers positive �otation and is easily worked with simple

tools and equipment.

Balsa core is available as contoured end-grain sheets 3 to 50mm thick on a

backing fabric, and rigid end-grain sheets up to 100mm thick. These sheets can

be provided ready resin-coated for vacuum-bagging, prepreg or pressure-based

manufacturing processes such as RTM. One of the disadvantages of balsa is its

high minimum density, with 100kg/m3 being a typical minimum. This problem

is exacerbated by the fact that balsa can absorb large quantities of resin during

lamination, although pre-sealing the foam can reduce this. Its use is therefore

normally restricted to projects where optimum weight saving is not required or in

locally highly stressed areas.

Balsa was the �rst material used as cores in load bearing sandwich structures

and is still often used as a core material.

Cedar

Another wood that is used sometimes as a core material is cedar. In marine

construction it is often the material used as the �core� in strip-plank construction,

with a composite skin on each side and the grain of the cedar running parallel to

the laminate faces. The cedar �bres run along the length of the boat giving fore

and aft stiffness while the �bres in the FRP skins are laid at ±45◦ giving torsionalrigidity, and protecting the wood.

9.3. Adhesives

Bonding of sandwich construction involve bonding of two very dissimilar con-

stituents, one solid and one softer cellular component, and the requirements con-

cerning bonding are therefore somewhat different than normal use. The adhesive

must be stronger than the tensile strength of the core. Some of the requirements

of the adhesives are:

Surface preparation

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The core and the face material have to be prepared before bonding, which

involves mechanically or chemically cleaning and sometimes priming.

Solvents

Core materials are often very sensitiv to certain solvents. For instance: Polystyrene

foams are sensitive to styrene (polyester and vinylester contains styrene), while

epoxies and polyurethanes may be used. Similar combinations needs to be inves-

tigated before bonding components.

Curing vapours

When curing, some adhesives (as phenolics) give off vapour when curing, which

can give rise to several bonding problems.

Bonding pressure

When pressure is needed to prevent pores to appear, be careful so that the

core will not fail due to the compression.

Adhesive viscosity

The adhesive must have exactly the right combination of surface wetting and

�ow. In the case of foam or balsa core, the viscosity should be low enough to

enable the adhesive to �ll the surface cells properly and leave as little as possible

trapped air. But the viscosity must not be too low,the the adhesive could be

squeezed out leaving too thin bonding line.

Bond thickness

If the bond is too thick, it adds extra unneccesary weight to the part. If it is

too thin, bonding will not be one properly.

Strength

The bond must be able to transfer the design loads, which means it must have

the desired tensile and shear strength, at the temperatures that might occur.

Thermal stresses

A frequent cause of debonding failures are thermal stresses. If for instance one

side is heated from sunligth it will deform due to thermal expansion. Most core

materials are very good insulators, and therefor it will be a very high thermal

gradient over the bond line. This lead to very high shear stresses in the bond

which may lead to debonding. In such environment, very ductile adhesives should

be chosen (high strain to failure).

Toughness

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Toughened adhesives which resist cracks better (improved impact resistance)

are on the market. They are ordinary resins which have elastomer particles added.

Viscoelastic properties

Highly viscoelastic adhesives may be advantageous for example where there

are high thermal gradients.

Curing shrinkage

As much as 7% decrease in volume can an adhesive (as polyesters) shrink when

its curing. This leads to high interface (bond) shear stresses and may decrease

the strength of adhesive joints.

Curing exotherm

Most adhesives exhibit an exotherm (curing process gives off heat) curing.

This is seldom a problem in thin bondings spread over a large area.

Different types of adhesives are for instance:

� Epoxy resins� Modi�ed epoxies� Phenolics� Polyurethanes Urethane acrylates� Polyester and vinylester resins

References:

Alulight products:

http://www.alulight.com/en/products/products.html

Composites:

http://www.users.globalnet.co.uk/~weeks/Composite%20Materials.htm

http://www.netcomposites.com/education.asp

http://www.baltek.com/

Fibres

http:// www.netcomposites.com/ education.asp?sequence=45

Foam cores:

http://www.netcomposites.com/education.asp

http://www.polymer-age.co.uk/techlink.htm

http://www.hexcelcomposites.com

Adhesives:

http://www.hexcelcomposites.com/products/honeycomb/sand_design_tech/hsdt_p04.html

130

http://www.hexcelcomposites.com/products/

Questions

�Why are sandwich constructions used?�What kind of face materials are used in sandwich constructions?�What kind of core materials and/or structures are used in sandwich construc-tions?

�What is the essential property of any core material�Is End Grain Balsa used as core material in sandwich construction? If yes, whatkind of products, and what are the advantages of this product? (http://www.baltek.com/)

�What kind of core materials are there? Explain the difference between them.�What reqirements must be taken into consideration when it comes to bondingsandwich-constructions with adhesives?

131

11. Design Procedures

Designing a sandwich element is very often an integrated process of sizing and

material selection in order to get some sort of optimum design with respect to

the objective you have chosen for instance weight, strength, or stiffness. Note

that all material systems have both advantages and disadvantages. Therefore it is

difficult to state some general terms about choosing materials. But, some material

related properties can still be considered despite the choice of material, such as

density of the core material. An optimum design of a sandwich construction is

very difficult to obtain because there are so many different constraints that the

problem becomes complex. But, considering the most important constraints and

using a simple optimization technique could be very useful in the design process.

The stiffness can be estimated as shown in the previous chapter. The strength

is depending on the failure mode, which is depending on the internal structure of

the sandwich as well as the applied loading.

11.1. Failure modes of sandwich panel

A sandwich panel must have the strength to carry the design loads without failing

in one of the possible failure modes. We have to design against and consider all

the failure modes to be sure of that the structure will not fail. Examples on failure

modes is shown in Figure 11.1. A sandwich construction will fail by the failure

mode which occurs at the lowest load. The optimum design is when two or more

failure modes occur at the same load. The failure modes can be found on the basis

of when the mode occur. Some of the failure modes is described in the following.

The skin and core materials should be able to withstand the tensile, compres-

sive and shear stresses induced by the design load. Also the adhesive must be

capable of transferring the shear stresses between skin and core. The sandwich

panel should also have sufficient bending and shear stiffness to prevent excessive

de�ection.

150

Figure 11.1: Some failure modes; a)face yielding/fracture, b) core shear failure, c) and

d) face wrinkling, e) general buckling, f) face dimpling, and g) local indentation.

(I) Face Yielding/fracture:

Face yielding/fracture occurs when the normal stress in the face σf equals or

exceeds the (yield) strength of the face material, σyf , such that:

σf =Mx

btfd=

PL

B3btfd≥ σyf .

(II) Face wrinkling:

Face wrinkling (local buckling) occurs when the normal stress in the face reaches

the wrinkling stress (the local instability stress). Wrinkling occurs when the com-

pressive stress in the face is

σf =Mx

btfd=

PL

B3btfd= 0.5 3

pEfEcGc. (11.1)

Hence, the wrinkling load is independent of the sandwich geometry, and is only a

function of the face and core properties. It is the core that has most in�uence on

the wrinkling load.

151

(III) Core shear failure:

Core shear failure occurs in a foam with a plastic-yield point when the principal

stresses satisfy the yield criterion. If the shear stress in the core is large compared

to the normal stress, failure occurs when the shear stress, τ c, equals or exceeds

the yield strength of the foam in shear, τ yc. The core failure is given by

τ cmax =Tx

bd=

P

B4bd≥ τ yc.

(IV) Failure of the adhesive bond (debonding):

Failure of the adhesive bond can occur due to overloading. Debonding (the adhe-

sive between the skin and the core fail) is the most difficult of the mechanisms to

analyze. The adhesive must have a strength equal or bigger than the shear stress

in the bonding line under loading which is almost the same as τ cmax. To avoid

debonding therefore

τ cmax =Tx

bd≤ τ ya

where τ ya is the yield shear stress in the adhesive. High thermal stresses, fa-

tigue,and aging are some of the reasons to debonding.

(V) Core indentation:

Core indentation is only a problem when loads are very localized and can be

avoided if we ensure that the load is distributed over a minimum area of at least

A ≥ P

σyc,

where σyc is the compressive strength of the core.

(VI) General buckling:

General buckling can occur in sandwich constructions due to the transverse shear

deformation. The transverse shear deformation must be accounted for, since this

decreases the bukling load compared with the ordinary Euler buckling cases. The

critical buckling load can be written as:

1

Pcr=1

Pb+1

Ps,

152

where Pb is the buckling load in pure bending, and Ps in pure shear, and they are

given as follows

Pb =n2π2(EI)eq

(βL)2

and Ps = (AG)eq ,

where β is the factor depending on the boundary conditions in Euler buckling.

(VII) Face dimpling (local buckling, or intercellular buckling):

Face dimpling may occur in sandwich structures with honeycomb or corrugated

as core material. For a square honeycomb this buckling stress equals

σf = 2.5Ef

µtf

a

¶2for Poissons ratio νf = 0.3,

where a is the length of the side of the cell. For hexagonal honeycombs the

buckling stress equals

σf =2Ef

1− ν2f

µtf

s

¶2≤ σyf ,

Ãwhen νf = 0.3 then σf ≈ 2. 2Ef

µtf

s

¶2!,

where s is the radius of the inscribed circle in the honeycomb cell.

(VIII) Fatigue:

Fatigue is said to cause more than 90% of all structural failures. For the face

material, a conservative way to use the fatie limit under which the material can

undrgo an in�nite number of load cycles without exhibiting any damage by taking

the allowable face stress σyf as the material fatigue stress at the given number

of load cycles and stress ratio. For the core material the reasoning is similar;

substitute the allowable shear stress τ yc with the fatigue limit. Be aware that

there is not always data for all materials available. Hopefully, more data will be

available in the future.

153

Figure 12.1: Failure modes with their corresponding failure loads.

12. Failure modes and failure loads

The different failure modes with the corresponding failure loads for a rectangular

sandwich beam is shown in Figure 12.1.

12.0.1. Failure-mode maps

Failure-mode maps can be used to design sandwich constructions in a way that

will improve the performance of the sandwich due to that no single component is

over-designed. The designer can choose the anticipated failure mode, or making

two different failure modes equally likely occur. Also, this is an advantage for

cases where certain failure modes should be avoided.

The dominant failure mode mechanism for a given design, is the one giving

157

failure at the lowest load. A transition in failure mechanism takes place when two

or more mechanisms have the same load. This information can be displayed as a

diagram or map (failure-mode map).The most important transitions we get from

equating pairs of the failure-mode equations are: face yielding - face wrinkling,

face yield - core shear and face wrinkling - core shear. Failure-mode maps can

be constructed from the failure-mode equations that comes out as a result of the

analysis of the different failure modes. For more information see [5], p. 363.

Transition equation between face yielding and face wrinkling Face yield-

ing/fracture occurs when

σf =|Mx|btfd

=PL

B3btfd=

P

B3btfLd= σyf .

hence the load P is given by

P = σyfB3bd

µtf

L

¶. (12.1)

Face wrinkling (local buckling) occurs when

σf =|Mx|btfd

=PL

B3btfd= 0.5 3

pEfEcGc.

Thus, P can be written as

P = 0.5B3

µtf

L

¶bdE

13

f E13c G

13c . (12.2)

Putting the two expressions in (12.1) and (12.2) equal to each other, we obtain

that

σyfB3bd

µtf

L

¶= 0.5B3

µtf

L

¶bdE

13

f E13c G

13c . (12.3)

As we see from (12.3) the expression tf/L is in both (12.1) and (12.2) which

means that this transition is independent of tf/L and therefore it appears as a

horizontal line. Also B3, b, and d appears on both sides, and (12.3) is reduced to

σyf = 0.5E13

f E13c G

13c (12.4)

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and then if we want the other axis to be the Youngs modulus of the core material,

we put

Ec =

σyf

0.5E13

f G13c

3

(12.5)

which is the transition equation for the failure-mode face yield and face wrinkling.

Transition equation between face yield and core shear Core shear failure

occurs when

τ cmax =Tx

bd=

P

B4bd≥ τ yc,

where

P = τ ycB4bd. (12.6)

Face yielding/fracture occurs when

σf =Mx

btfd=

PL

B3btfd= σyf ,

where

P = σyfB3btf

Ld. (12.7)

Putting the two expressions in (12.6) and (12.7) equal to each other

τ ycB4bd = σyfB3btf

Ld,

we obtain that the transition equation will be

tf

L=τ ycB4bd

σyfB3bd. (12.8)

Transition equation between face wrinkling and core shear Face wrin-

kling (local buckling) occurs when

σf =Mx

btfd=

PL

B3btfd= 0.5 3

pEfEcGc.

Hence,

P = 0.5B3

µtf

L

¶bdE

13

f E13c G

13c (12.9)

159

Core shear failure occurs when

τ cmax =Tx

bd=

P

B4bd≥ τ yc

and

P = τ ycB4bd. (12.10)

Putting the two expressions in (12.9) and (12.10) equal to each other, we get

0.5B3

µtf

L

¶bdE

13

f E13c G

13c = τ ycB4bd.

Hence the transition equation will be

µtf

L

¶=

B4τ yc

0.5B3E13

f E13c G

13c

. (12.11)

Summing up:The Face yield - Face wrinkling transition equation

Ec =

σyf

0.5E13

f G13c

3

, (1) (12.12)

the Face yield - Core shear transition equation

tf

L=τ ycB4

σyfB3, (2) (12.13)

and the Face wrinkling - Core shear transition equation

µtf

L

¶=

B4τ yc

0.5B3E13

f E13c G

13c

. (3) (12.14)

The failure modes are illustrated in the failure mode map in Figure 12.2, when

we use the result

Ec =

µρcρs

¶2Es (12.15)

160

Figure 12.2: A failure mode map for a sandwich construction.

161

Figure 12.3: The transition equations for the combinations of failure modes in a sand-

wich.

from [5], Cellular Solids, p. 186, 189 and 359, where ρc(is the same as ρ∗c) is the

density of the core, ρs is the density of the cell wall in the core-material , and Esis the Youngs modulus of the cell wall material in the core-material , and that the

Poissons ratio νc = 1/3. The transition equations for the remaining combinations

are summarised in Figure 12.3

We can ignore bond failure as for most cases the stress for bond failure is

considerably lower than that for face yield.

Exercise

Construct a failure-mode map for 3 point bend sandwich, which has GRP

faces and PVC foam core, and the following properties B3 = 4, B4 = 2, σyf =

100MPa, τ yc = 1.5MPa, Ef = 20000MPa, Ec = 100MPa, and Gc = 40MPa.

162

Hints: (12.12), will be

Ec =

σyf

0.5E13

f G13c

3

=

Ã100

0.5 (20000)13 (40)

13

!3= 10,

(12.13) will be,tf

L=τ ycB4

σyfB3=(1.5) 2

(100) 4= 0.0075,

and (12.14)

µtf

L

¶=

B4τ yc

0.5B3E13

f E13c G

13c

=2 (1.5)

0.5 (4) (20000)13 (Ec)

13 (40)

13

=0.016

(Ec)13

Equations in the mode-map:

a³Ec,

tfL

´=

163