damage tolerance of sandwich structures - modelling ... · conference on damage in composite...

Conference on Damage in Composite Materials, Stuttgart, 18.-19.09.2006

Jan Teßmer, Luise Kärger, Uwe Pfeiffer, Anja Wetzel

Damage Tolerance of Sandwich Structures- Modelling, Analysis and Testing -

Institute of Composite Structures and Adaptive Systems 2

High Performance Composites in Aerospace Structures

ROSETTA

Formel 1ARIANEAntenna

A380

ARIANE



MonolithicComposites

Sandwich Structures withComposite Face sheets

Textile Composites


1 Double shell structures (Sandwiches)

2 Impact analysis

3 Residual strength analysis

ExperimentsSimulation tool CODACDamage ModellingSimulation results

4 Non-destructive Testing

CAI-TestsGeometrical non-linear simulation using ABAQUSSimulation results

Air-coupled Ultrasonic Testing for SandwichesSignal Processing for monolithic CFRP (skins)


1 Double shell structures

core

outer skin

inner skin

Ref.:Element S89: Kärger, Wetzel, Rolfes, Rohwer. Computers & Structures 84. 2006.Element S815: Wetzel, Kärger, Rolfes, Rohwer. Computers & Structures 83. 2005.

Development of two new shell elements

Modelling requirementsby accounting for the specific deformation behaviour:- fast for being used in the design process- sufficiently accurate


0

0 2

0

00

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥= + +⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦⎣ ⎦

L L xL

L L L yL L

L L zL zL

u uv v z zw w

ψψψ ϕ

15 dof per node

Element S815: 3-layered shell element with 3-D stress analysis(Sandwich element with 8 nodes and 15 dof per node)

Kinematics of layer L :

Layer-wise full 3D-material law:

L L L=σ C ε

Stress computation: • in-plane stresses: material law• transv. shear stresses: equilibrium approach by Rolfes & Rohwer• transv. normal stress: material law and equilibrium approach

3xψ

0 01u u=

03uz3

x

z

z2z1

02u

02w

03w

2xψ

1xψ

h3

h2

h1/2h1/2

core

outerskin

0 01w w=

initial state

deformed state

innerskin




2 Impact analysis







2 Impact analysis: ExperimentsTests conducted at ILR, TU Dresden

Force-time histories:

completely supported panel

top skin core top skin core

1 Joule damage: 4 Joule damage:


2 Impact analysis: Simulation tool CODAC

• CODAC = Composite Damage Tolerance Analysis Code

• fast evaluation of impact damage and residual strength of composite structures

• Finite Element Method

Impactor (Ø25.4 mm):• point mass • parabolically distributed surface load

Transient impact analysis:• dynamic FEA with Newmark time integration• application of Hertzian contact law


2 Impact analysis: Modelling of core damage

Degradation:

11 12 13

22 23

33

44

*11 12 13

*22 23

*33

55

*44

*55

*6 666

sym.

xxxx

yyyy

zzzz

yzyz

xzxz

xyxy

C C CC C

CC

D D

C

DD D

DD

DD C

εσεσεσγτγτγτ

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥

=⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥

⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦⎣ ⎦

absorbed energy

Dij > 0

ε

σ

crushσuσ

elastic-plastic behaviour

Failure criterion:

Ref.: Petras, Sutcliffe (2000)

1⎛ ⎞ ⎛ ⎞ ⎛ ⎞

+ + ≥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

n n nyzzz xz

cc cls cts

τσ τσ τ τ

- transverse shear and compression failure of honeycomb core- criterion by Besant et al.:

Ref.: Kärger, Baaran, Teßmer. Composite Structures. 2006


2 Impact analysis: Modelling of skin damage

Kra

ft

Weg

phase 2

fibre breakage in a few laminas:- degradation of membran stiffness

by degradation factor D11- further stiffness components without

considerable influence on impact response

( ) ( )( ) ( ) ( )( ) ( ) ( )

( )( )

( )

11 0 00 0 00 0 0

00

0

D⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

3-point bending test: phase 3

bending failure

fibre breakage in all laminas:- skin tears- simulation stops

(fracture mechanical modelsor energy based damagemechanical models withcontinuous degradation are needed)

phase 1

all laminas intact:linear-elastic material behaviour

forc

e

displacement


2 Impact analysis: Simulation results4J Impact

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6t / ms

F / k

N

no degradation

experiments

with core degradation

with core & skin degradation

Core damage:

no degradation

computed core damage

measured core damage

core degradation(upper bound)

core & skin degradation

(lower bound)

Force time history:



2 Impact analysis







3 Residual strength analysis: CAI-Tests

CAI-Test-Equipment:

Failure phenomenon:• impacted face sheet: dent propagation transverse to the loading direction

• failure of the impacted face sheet: buckling across the whole specimen width sudden load decrease

• further load increase• failure of second face sheet

Source: ILR TU Dresden


0

20

40

60

80

100

120

0 100 200 300 400 500 600

Zeit

Kraf

t

0J1J2J4J6J10J15J

0°

1 2 43

6 7

8

9 10 11 12 13

Test data:• Force vs. time • Strain vs. time at specified location

Strain gage positions on front and back side

Force vs. strain for 4 Joule specimen: higher compression on the front side compared to the back side (bending)

Forc

e

Time

-125

-105

-85

-65

-45

-25

-5-12000 -10000 -8000 -6000 -4000 -2000 0

Dehnung

Kra

ft

DMS 03 DMS 04DMS 08 DMS 09DMS 10 DMS 11DMS 12 DMS 13

3 Residual strength analysis: CAI-Tests


3 Residual strength analysis: Non-linear simulation using ABAQUS

Non-linear FE analysis of impacted face sheet:• uniaxial in-plane loading (displacement-driven, ∆u)• face sheet supported by springs representing the core• including initial dent, face sheet and core damage due to impact• including core damage growth• using automatic stabilization because of local instabilities

initial dent∆u

u = v = w = 0

w = 0

w = 0

v = w = 0

face sheet damage:soft inclusion (stiffness reduction)

core damage:stiffness reduction

0 < Dij < 1

ε

σ

crushσultσ

elastic-plastic behaviour

face sheet supportedby springs:


3 Residual strength analysis: Simulation results

Dent growth with increasing in-plane loading:


0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5(-1) Displacement / mm

(-1) F

orce

/ kN

Experimental failure load Experimental onset of non-linearitySlopeABAQUS

m/m-10

0

10

20

30

40

50

60

-20000 -16000 -12000 -8000 -4000 0

Strain in

Forc

e in

kN

DMS10_ABAQUS

DMS10_Test

DMS11_ABAQUS

DMS11_Test

DMS12_ABAQUS

DMS12_Test

3 Residual strength analysis: Simulation results

4 Joule specimen: force vs. displacement ∆u 4 Joule specimen: force vs. strain

For 4 Joule damage, Dij=0.7, kcore=Ezz/h, Ezz and σult according to data sheet, σplat/ σult = 0.3:

• very good correlation between experimental failure load and maximum load of ABAQUS simulation

• good correlation between experiment and ABAQUS simulation for strains at strain gage locations

Strain in µm/m



2 Impact analysis







Sandwich inspection with water coupling

Optimal frequency forSandwiches: <500kHz=> Bad Focussing,low spatial resolution


Air-coupled Ultrasonics

Benefits:Contact free, without coupling mediaConstant and reproducible couplingNo incoming water<500kHz and focussed

Challenges:Bad acoustic matchingMore than 160 dB amplitude loss

ApproachTransducers with optimised matching layersOptimised transmitter and receiver electronics

Our resultsSignal-to-noise ratio in transmission: 30 dBNarrow band, strongly focussing transducersBest choice for sandwich testing

Sound pressure

0dB

-50

-100

-150

-200

Test spcimenz.B. CFRP ReceiverTransmitter

Water coupling(for comparison)

Air coupling

-21 dB

-93 dB

-24 dB

-162 dB -156 dB

-18 dB

Wat

erco

uplin

gA

ir co

uplin

g


CFRP: High and frequency-specific sound attenuation

Transmitter ReceiverdB dB

Arrow thickness ~ wavelengthArrow length ~ amplitude

= signified microstructure

f = 3 MHz

f = 2 MHz

f = 1 MHz

f = 3 MHz

f = 2 MHz

f = 1 MHz

Loss by scattering is dominating at high frequencies

The HF fraction is attenuated superproportional

delivered signal:E.g. same amplitude at 1, 2 and 3 MHz

Transmission:Spectrum shifted to low frequencies

Institute of Composite Structures and Adaptive Systems 23Depth [mm]15 30 45

100

50

0

-50

-100

Processed A-Scan

Depth [mm]15 30 45

Frequency

[MHz]

4

3

2

1

0

5Processed Spectrogram

Depth [mm]15 30 45

4

3

2

1

0

5Spectrogram

STFT

Inve

rse

STFT

Frequency

[MHz]

Depth [mm]15 300 45

4

3

2

1

0

5Correction Matrix Γ(d,f)

Depth [mm]15 30 45

Amplitude [%]

100

50

0

-50

-100

A-Scan (+DAC)

Frequency

[MHz]

Spectral Distance Amplitude Correction „SDAC“

-80 -60 -40 -20 0Amplitude spectrum [dB]

-20 -10 0 10 20Amplification [dB]


Stringer Specimen: Analysis of Layer Echoes

Gate 1:0.2 – 0.8μs„shallow“ Gate 2:

0.8 – 1.4μs„middle“

Gate 3:1.4 – 2.0μs„deep“

Gate 0:Interfacetrigger


Flaw Detection in various depths(Time-of-Flight D-Scans)

shallow

middle

deep

unprocessed SDAC processedSDAC: Spectral Distance Amplitude Correction


Impact

NDT:Detection and Characterization

Residual Strength

Simulation

Impact

DAMAGE



Impact

NDT:Detection and Characterization

Residual Strength

Simulation

Impact

DAMAGE


Thank you for your Attention!Contact: [email protected]

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