4th international conference on composite testing and ... · bird strike bird strike. aeronautics 6...
TRANSCRIPT
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
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
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