The Mechanics and Behavior of Hybrid Sandwich Structures

Michael RiceCorey Fleischer

Professor Marc Zupan

Funding provided by: NASA Goddard SFC DDF Program and Lockheed-Martin Maritime Systems

26 October 2006FEMCI Workshop 2006

CoreCore

Face Sheets

12;

3bhII

My==σ

c

t

l

Ecσc τ c

Ef σf τf

c

t

l

Ecσc τ c

Ef σf τf

Introduction to Sandwich Panels

•The equations governing the response of a beam in bending can be given by:

3

48lEIF

=δ

• Define the relative density, ρ, of a panel as the mass of the panel divided by the mass of a solid block with the same enclosed volume.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

s

c

ρρ

ρ

y

20 mm20 mm

15 mm15 mm

Core Topologies

Metallic face sheets

Polymer foam and carbon fiber pins

10 mm

150 μm150 μm150 μm150 μm

50 mm50 mm50 mm50 mm

10 mm10 mm

Core Classification

Relative Density, ρc/ρs

σ σy

Bending Dominated Architectures

11

3/21

Stretching Dominated Architectures • For the same relative density

material the modulus and initial yield strength of a stretching-dominated core is much greater than that of bending dominated core.

Load

StretchingArchitecture

Load

BendingArchitecture

Load 10 mm

5 mm

Deshpande, V.S., Ashby, M.F., and Fleck, N.A. “Foam Topology bending vs stretching dominated architectures,”Acta Materialia, Volume 49, 2001.

Hybrid Materials

Mat

eria

l Pro

perty

1

Material Property 2

RM

WB

WL

BB

Adapted From Ashby

Hybrid Sandwich Panels

Polymer foam

Specifics: Foam Density 31kg/m3

Pin Volume Fraction 3%Pin Angle 22°Face Sheet Thickness 1.5mm

Insertion of the rods

Lay-up and cure face sheets

0

4

8

0 0.2 0.4

Stre

ss (M

Pa)

Strain

(b) 10mm Core

Pin Reinforced Core

Polymer Foam0

4

8

0 0.2 0.4

Stre

ss (M

Pa)

Strain

(b) 10mm Core

Pin Reinforced Core

Polymer Foam

Uniaxial Compression Results:

• Pins can be thought of as Euler columns on an elastic foundation.

• Synergistic interactions between the pins and foam.

• The foam reinforces the “Euler columns” by stabilization against buckling.

Pins Only

Sandwiches in Three-Point Bend:

• In order to take full advantage of the structural efficiency gains offered by sandwich panels, a robust understanding of the bending response is needed.

• We identify possible collapse modes for each beam geometry and use an upper bound work balance analysis to predict collapse loads.

c

t

l

Ecσc τ c

Ef σf τf

c

t

l

Ecσc τ c

Ef σf τf

Sandwich Beam Collapse Modes:

Indentation is likely to occur in panels with weak cores and thin face sheets, or in panels with high core thickness to span ratios.

INDENTATION:

Relatively thick panels loaded transversely carry the shear loading primarily in the core of the panel and can initiate collapse by the shearing failure of the core.

Failure of the face sheets is typical of beams with thin cores and long spans owing to the tensile or compressive stresses resulting from the bending moment.

CORE SHEAR: FACE FAILURE:

cfbtF σσ4= cfbc

lbtF σσ

344 2

+=( )

cf lbc

ltcbtF σσ

24+

+=

Failure Mode Map

• Map displays the initial collapse of a simply supported sandwich beam.

• Map takes axes of non-dimensional ratios of core thickness to face sheet thickness as a function of core thickness to beam span.

• Plotting non-dimensional parameters, the map displays all possible beam geometries for a given material.

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4

t=t/c

c=c/l

C B

A

Indentation

Core Shear

Face Yield

Bend Experimental Results:

0

20

40

60

Load

/ W

idth

(N/m

m) (B) Failed by Indentation

0

10

20

30

5 10 15Displacement (mm)

(C) Failed by Core Shear

0

20

40(A) Failed by Core Shear

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4

t=t/c

c=c/l

C B

A

IndentationCore Shear

Face Yield

Analysis of Failure Modes:

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4

t=t/c

c=c/l

C B

A

IndentationCoreShear

Face Yield

20mm

Central Roller

Comparison with Competing Cores:

Pin reinforced cores exhibit a dramatic increase in stiffness as well as a much higher failure load prior to collapse.

References: Tagarielli, V.L. and Fleck, N.A., 2003Steeves, C. A and Fleck, N.A., 2004

1

2

3

4

0 0.1 0.3 0.5St

ress

(MPa

)Strain (mm/mm)

Compression X-cor (20 mm thick)

Al Honeycomb(25.4 mm thick)

Unreinforced Foam

0

100

200

0 0.02 0.04Displacement/Span (mm/mm)

Forc

e/(W

idth

*Den

sity

) (N

m2 /k

g)

Three-Point Bend

X-cor

Al Honeycomb

Metal Foam

Nomex PVC

Stochastic Cores- Pumice

•Pumice is a natural aggregate formed during volcanic eruptions with properties similar to an engineering ceramic foam.

•Very Inexpensive

•Can be combined with a pyramidal core to produce a hybrid type sandwich structure

500 mm 50 mm

Pumice Pyramidal Hybrid

0

2

4

6

8

10

0 0.1 0.2 0.3 0.4 0.5

Nom

inal

Stre

ss

Nominal Strain

Hybrid Pumice-Pyramidal

Pyramidal

Pumice

• Pumice acts as a reinforcing phase to the pyramidal cores.

• The resultant strength behavior is additive.

Wv=6.43 MJ/m3

Wm=17.5 kJ/Kg

Wv=2.24 MJ/m3

Wm=12.3 kJ/Kg

Wv=0.886MJ/m3

Wm=1.18 kJ/Kg

Conclusions:

Lower Pin Density

Higher Pin Density

• Hybrid sandwich structures offer exciting potential in weight critical applications.

• Comparison of the hybrid pin reinforced sandwich core response with competing cores demonstrates that the panels outperform other sandwich structures in both stiffness and load carry capacity.

• Hybrid Pumice Pyramidal panel results show that this topology can exhibit increased strength and energy absorption capabilities.

• Future studies on these hybrid panels are required for further understanding of the deformation mechanisms.