Aeronautics 1

4th International Conference on Composite Testing and Model IdentificationOctober 20-22, 2008Dayton, Ohio, USA

Aeronautics 2

An Inverse Method for Determining

the Stiffness of Impact Damage

in Laminated Composites

Pavel Sztefek and Robin Olsson

p.sztefek@imperial.ac.uk

r.olsson@imperial.ac.uk

4th International Conference on Composite Testing and Model IdentificationOctober 20-22, 2008Dayton, Ohio, USA

Aeronautics 3

Presentation Layout

Impact

Damage Inverse

Method

Tensile

Characterisation Compressive

Characterisation

Advanced

Issues

Aeronautics 4

Impact Damage

Aeronautics 5

Hail stones

Hail stones

Composites and Impact

AIRBUS A350

BOEING 787Dropped tools

Ground collision

Bird strike

Bird strike

Aeronautics 6

Problem of Impact Damage

Impact damage

Often invisible by naked

eye inspection

• Impact happens accidentally

• Impact often causes damage

• Damage reduces strength

• Damage affects buckling

• How much???

• STIFFNESS DISTRIBUTION IS KEY!!!Damage size

100 %

Str

ength

rete

ntion

Stress and stiffness distribution

Nature and severity of damage

0°

90°

fibre fracture

matrix crack

delamination

0 10 (mm) 0 10 20 (mm)

48 plies16 plies

Stress

Stiffness

Aeronautics 7

Inverse Method

Aeronautics 8

E0

E1

E2

Speckle photography

of a test specimen

Inverse method with

optimization routine

Matching of

displacements

Fundamentals of the approach

Displacement fields measured by

Digital Image Correlation - ARAMIS

Measured Data

Experiment

Predicted Data

FE Simulation

Error

Calculation

Gradient

Calculation

Numerical

Optimizer

StopCriterion Satisfied?

Final

Constitutive

Parameters

Yes

I n

v e

r s

e M

e t

h o

d

Inverse Method

Flowchart of the approach

Iterative updating of constitutive

material parameters in Finite Element

model - ABAQUS

Sztefek & Olsson (2008), Composites Part A.

Aeronautics 9

Aim

Seeking minimum of displacement error function by updating material parameters

Approach

Gradient method Steepest Descent combinedwith Davies, Swann, and Campey’s algorithm

Description

Mean squared error function:

Gradient and Search direction:

Parameter vector:

kkk g/gu =

Optimization Approach

ui

vi

u

v

Aexp

AFE

Parameter 1 (e.g. E)

Para

mete

r 2

(e.g

. ν)

Starting set of parameters

(e.g. undamaged material)

Minimum of a function

(e.g. correct material properties)

k-th gradient vector

calculation

k-th optimization

step

kkkk uxx 1

kk f P/g ΔΔ=

N

i

ii

v

v

u

u

Nf(x)

1

12

max

2

max

ΔΔ

Optimization search procedure

Aeronautics 11

Experiments

Aeronautics 12

Non-contact optical 3D deformation measuring system ARAMIS from GOM

Speckle pattern Before deformation During deformation

Digital Image Correlation System

DIC Principle

System type GOM ARAMIS 1.3 M

4 cameras in master and slave mode

Camera resolution 1280 1024 pixels

Measuring volume10 8 8 mm3 to

1.7 1.4 1.4 m3

Max. frame rate 12 Hz

Strain range 0.05% up to <100%

Strain accuracy up to 0.02%

Aeronautics 13

Overview of Experiments

Impact testing

Impactor

Boeing rig

Quasi-isotropic

Carbon/epoxy

Field of DIC

measurement

150 m

m

100 mm

4 mm thickness

x

y

14 J4 mm

14 mm

Fractographic findings

100 m

m

200 m

m

80 mm

4 mm thickness

x

y

Field of DIC

measurement

Tensile loading

Compressive loading

14 J4 mm

32 mm

Heterogeneous properties Apparent properties

Aeronautics 14

Tensile

Characterisation

Aeronautics 15

Experimental Setup

Aeronautics 16

Inverse Analysis

ABAQUS analysis

• Homogeneous isotropic thin shell

• Full-field boundary conditions

0

1

2

3

4

5

6

7

-40 -30 -20 -10 0 10 20 30 40

y-coordinate (mm)

No

rma

lis

ed

Str

ain

, e

x (

%)

0.30%

0.40%

0.85%

7 J2 mm

7 J

18 mm

2 mm

8 mm

14 mm

4 mm

ex (%)

2.0

1.5

1.0

0.5

0

□70 m

m

x

y

Aeronautics 17

Heterogeneous Material Parameters

2 mm, 5 J 2 mm, 7 J

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Young's Modulus

Poisson's Ratio

4 mm, 10 J 4 mm, 14 J

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Young's Modulus

Poisson's Ratio

2 mm, 7 J2 mm, 5 J 4 mm, 14 J4 mm, 10 J

5 J

14 mm

2 mm 7 J

18 mm

2 mm 4 mm 10 J

26 mm

14 J4 mm

32 mm

Aeronautics 18

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5 3

Local Average Strain, exav (%)

Lo

ca

l A

ve

rag

e S

tre

ss

, s

xav (

MP

a)

Nonlinear Material Behaviour

0.4%

Strain concentrations at different

applied (far-field) strains

0%

0.1%

0.2%

0.3%

0.8%

0.5%

0.6%

0.7%

0.85%

0.8%

0.4%

5%

4%

3%

2%

1%

0%

Heterogeneous nonlinearity

Aeronautics 19

Compressive

Characterisation

Aeronautics 20

Experimental and Optical Setup

xL

yL

zL

yL

zL

xL

From FRONT SIDE From BACK SIDE

yG

xG

zG

xG

yG

zG

xG

yG

zG

70 mm

90

mm

FRONT SIDE BACK SIDESeeing from front

Aeronautics 21

Full-field Benefits

(%)

(%)

(mm)

(mm)

Strain concentration Post-impact deflections Delamination opening

Aeronautics 22

Full-field Buckling Patterns

3D quarter cut

Observed area

Local

delamination

buckling

Global

buckling

0.3%

0.58%

Schematic buckling

Local and global buckling development

Aeronautics 23

In-plane and out-of-plane BCs

Out-of-plane BCs only

Finite Element Model

ABAQUS analysis

• Homogeneous isotropic thin shell

• Geometrically nonlinear analysis

• Full-field boundary conditions

4 mm 10 J 14 J4 mm 20 J4 mm

?

36 mm 32 mm 26 mm

Aeronautics 24

Apparent Material Parameters

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6

Applied Membrane Strain (%)

Ap

pare

nt

Yo

un

g's

Mo

du

lus (

GP

a)

0 J

10 J

14 J

20 J

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Applied Membrane Strain (%)

Ap

pare

nt

Po

isso

n's

Rati

o

0 J

10 J

14 J

20 J

Buckling patterns at different applied strains

0% 0.1% 0.2% 0.3%

0.4% 0.5% 0.58%

Aeronautics 25

Apparent Material Nonlinearity

-300

-250

-200

-150

-100

-50

0

-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.0

Local Average Strain, e xav (%)

Lo

cal A

vera

ge S

tress, s

xa

v (

MP

a)

0 J

10 J

14 J

20 J

Buckling patterns at different

applied strainsComparison of apparent material behaviours

0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.58%

Aeronautics 26

Advanced Issues

Aeronautics 27

Arbitrary and Multiple Damage Location200

mm

150 mm

23 mm

25 mm

Severe damage

Light damage

25

mm

30 m

m

5 × 5 grid model

6 concentric rings model

Numerically damaged plate

Damage localisation from

strain map

Aeronautics 28

Stiffness Reconstruction

Severe Damage

Benchmark

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Young's Modulus

Poisson's Ratio

Severe Damage

No offset

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's ModulusPoisson's Ratio

Severe Damage

2mm offset

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's Modulus

Poisson's Ratio

Severe Damage

5mm offset

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's Modulus

Poisson's Ratio

Severe Damage

No offset, noise 5%

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's Modulus

Poisson's Ratio

Light Damage

Benchmark

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Young's Modulus

Poisson's Ratio

Light Damage

5x5 grid, no offset, horizontal section

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's Modulus

Poisson's Ratio

Light Damage

5x5 grid, no offset, vertical section

0

0.2

0.4

0.6

0.8

1

1.2

-40 -30 -20 -10 0 10 20 30 40

Width Section (mm)

Rela

tive M

ate

rial P

ara

mete

rs

Benchmark E

Young's Modulus

Poisson's Ratio

Using 5x5 grid

Using 6 concentric rings

Aeronautics 29

Orthotropic Materials

Findings to date

• Load dependent material identification

• Geometry dependent material identification

Numerical test

Material set E1 E2 G12 12 Error in E1 Error in E2 Error in G12 Error in 12

Inner square 25 GPa 5 GPa 3 GPa 0.35 0.2% 0.1% 2.9% 2.8%

Middle square 35 GPa 10 GPa 4 GPa 0.2 9.4% 12.6% 4.3% 65%

Outer square 50 GPa 20 GPa 5.5 GPa 0.3 8.1% 8.9% 1.5% 40%

Aeronautics 30

Conclusions

• Inverse method using FEM coupled with DIC

• Applied to impact damage in laminates

• In-plane stiffness reduction in damage zone

• Material nonlinearity described

On-going Work

• Arbitrary and multiple damage location

• Impact damage in orthotropic laminates

Possible Future Applications

• Biomechanics

• Hot objects

• Aircraft inspection

Conclusions and Prospects

E0

E1

E2

Aeronautics 31

Pavel Sztefek and Robin Olsson

p.sztefek@imperial.ac.uk

r.olsson@imperial.ac.uk

Thank you for your attention

14 J4 mm

32 mm

14 J

14 mm

4 mm

-500

-250

0

250

500

-2 -1 0 1 2

Local Average Strain in Load. Direc. (%)

Lo

cal

Avera

ge S

tress i

n L

oad

. D

irec.

(MP

a)

CompressionTension, outer ringTension, middle ringTension, inner ring