David Ashby

Sandwich Panel Optimisation

Contents

PageIntroduction 1Method 2Results 5Discussion 7Conclusion 7

Introduction

The aim of this report is to determine the optimal design for a sandwich panel. A sandwich panel is constructed of a lightweight but thick core material with a thin but stiff skin material bonded to each side of it. This has the advantage of being able to have an overall low density whilst achieving a high second moment of area giving the panel a high bending stiffness. To determine an optimal design the ideal combination of skin materials and core materials as well as their thicknesses need to be found. The choice of skin materials are Fibre glass, Carbon Fibre and Aluminium. The choice for cores are PVC foam (with a thickness up to 100mm) and Aluminium Honeycomb. To determine the optimal design the lightest panel that won’t fail or deflect more than 1/150 th of its span when a line load of 10kN/m is applied centrally to a simply supported panel spanning 4m, needs to be found. The panel must not fail by skin failure, core shear or local crushing. There are six failure modes (shown below in figure 1) for sandwich panels which must all be considered and will act as the constraints for the problem.

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Skin tensile failure

Skin compressive failure

Core shear failure

Skin-core debonding

Skin wrinkling

Core crushing

Figure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modesFigure 1: Sandwich panel failure modes

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Method

To determine the lightest design, excel will be used to plot failure maps for the 6 different combinations of skin and core materials. These failure maps will be a plot of core thickness against skin thickness at the point where each of the failure modes are met. The region where all criteria is satisfied will be identified then a line of constant mass plotted. This line will be altered until the minimum mass is found.

The failure modes of skin tensile failure, skin compressive failure and skin wrinkling can be combined to give the following equation for maximum skin stress:

Equation 1:

Where σmax is the maximum skin stress, W is load, b is panel breadth, c is core thickness, s is skin thickness and L is length of the panel.

The failure modes for core shear failure and skin-core debonding can be combined to create the following equation for the maximum core shear stress.

Equation 2:

Where τmax is the maximum shear stress, W is load, S is the shear force, b is panel breadth, c is core thickness and s is skin thickness.

The skin compressive stress required to cause wrinkling is represented with the following equation.

Equation 3: σ =35.0 CCS GEE

Where σ is the skin compressive stress, Es is skin Young’s modulus, Ec is core Young’s modulus and Gc is core shear modulus.

The maximum load that can be applied before the core will crush is represented with the following equation.

Equation 4: W

Where W is load, b is panel breadth, s is skin thickness, σ c is the core compressive strength and σ sis the skin tensile strength.

Finally, for 3-point bending the maximum deflection is shown with the following equation.

Equation 5: d=dbending+dshear=

WL3

4 b (Es (h3−c3)+Ec c3 )+ WL4 b (c+s )Gc

2

σmax=3WL

2b ( (c+2 s )2−c2 )= 3WL8bs (c+s )

τmax=S

b (c+s )= W2b (c+s)

=2bs √σ cσ s

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Where d is the deflection, W is load, b is panel breadth, h is overall panel thickness, c is core thickness, s is skin thickness, Es is skin Young’s modulus, Ec is core Young’s modulus and Gc is core shear modulus.

These five equations are then each rearranged into an equation for skin thickness in terms of core thickness (see the example below). In excel a column is made with values of core thickness ranging from 0mm to 30mm increasing in increments of 0.1mm. The adjacent column is used to find the skin thickness that satisfies the failure mode equation, when the core thickness equals that in the left hand column. These values of core and skin thickness are then plotted on the failure map. This process is repeated for the other 4 equations to create the failure map.

Example: Fiberglass skins with a PVC foam Core, Max skin stress

Equation 1 can be rearranged to give

s2 + cs – A = 0

Where A is a constant equal to −3WL8bσmax

=−3×10000×48×1×3.5×108

=−4.285714×10−5

Therefore, s = −c±√c2−4×1×−4.285714×10−5

2×1

To determine the optimal design the mass per square meter has to be minimized. To find this the equation following equation is used.

Equation 6: M=cρc+2 sρs

Where M is the mass per m2, c is the core thickness, s is the skin thickness, ρc is the core density and ρ s is the skin density.

This equation is rearranged similarly to the previous ones to give skin thickness as a function of core thickness. The same technique as before is used to find the corresponding skin and core thicknesses which are then plotted on the failure map. The value for the mass is then altered until this line for constant mass just touches the point at which all failure modes are satisfied. Then this point is

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Figure 2: Excel spreadsheet for determining the relationship between core and skin thickness for max skin stress

David Ashby

determined and this gives the optimal dimensions for the skin and core. This process is then repeated or the other 5 combinations of skin and core materials.

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Results

-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025

Fibreglass/PVC Foam

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 91.4kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025

Fibreglass/Honeycomb

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 49.4kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

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-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025

Carbon Fibre/PVC Foam

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 42.0kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025

Carbon Fibre/Honeycomb

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 31.2kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

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-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025Aluminium/PVC Foam

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 57.6kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

-0.1 0.1 0.30

0.005

0.01

0.015

0.02

0.025Aluminium/Honeycomb

Max Skin Stress

Max Core Shear Stress

Max Core Thickness

Penetration

Deflection

Mass = 38.4kg/m

Optimal Mass

Core Thickness(m)

Skin

Thi

ckne

ss (m

)

Panel Core Thickness (mm) Skin Thickness (mm) Mass (kg/m)Fibreglass/PVC Foam 100 4.68 91.4Fibreglass/Al Honeycomb 205 1.15 49.4Carbon Fibre/PVC Foam 100 1.50 42.0Carbon Fibre/Al Honeycomb 130 0.87 31.2Aluminium/PVC Foam 100 1.50 57.6Aluminium/Al Honeycomb 160 0.57 38.4

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Discussion

It can be seen from the graphs that all sandwich panels with an Aluminium Honeycomb core, which meet the specification, are lighter than when the same skin is used with a PVC foam core. This is due to the honeycombs lower density and higher young’s modulus. Also, as the PVC foam is only available in sizes up to 100mm thickness this become one of the two main limiting factors, along with the deflection, in designs that use it. This means that the skin has to be much thicker, when using PVC foam, and as all the skin materials are at least 25 times the density of the foam this has a big impact on the weight. In all designs the deflection is the main limiting factor.

The panels with fibreglass skins are the heaviest, this is despite the skin having the second lowest density of 1,800 kg.m-3 as opposed to 2,800 kg.m-3 for aluminium and 1,500 kg.m-3 for carbon fibre. However, it’s young’s modulus, of 21GPa, is significantly lower than that of carbon fibre or aluminium, both are 70GPa. This means the skin has to be much thicker, and, where possible, its core thicker than for the other two materials making it the heaviest.

The panel with the lowest mass, 31.2kg/m for a 4 m span, is constructed of 0.87mm carbon fibre skins with 130mm aluminium honeycomb core. It’s not surprising that this is the lightest design as carbon fibre has the lowest density of the skin materials with the highest young’s modulus, compressive strength and tensile strength. Also, the core made of aluminium honeycomb has the lowest density of the core materials and the highest young’s modulus, shear modulus, compressive and shear strength.

Conclusion

The optimal design for a honeycomb panel is one constructed of 0.87mm carbon fibre skins with a 130mm aluminium honeycomb core and a total mass of 31.2kg/m for a 4m span. The main limitation in all designs is the deflection and in designs that use PVC the maximum thickness of the core is the other limiting factor. However, a carbon fibre panel would be more expensive to produce than one with aluminium or fibreglass skins. Aluminium skins with an aluminium honeycomb core is only 7.2kg/m heavier and would be considerably cheaper. However, as this is for an aerospace application the lowest weight is probably more crucial so the carbon fibre skins and aluminium core is the best solution.

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