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SAMCEF Mecano
The Best Way to Predict Non-Linear Flexible Dynamic Behavior
Composites and Advanced
Structural AnalysisModeling and Simulation Seminar
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FUNDAMENTAL OFCOMPOSITES STRUCTURES1
Composites and Advanced Structural Analysis
2
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LMS Samtech Composite Solution
3 copyright LMS International - 2012
LMS Samtech 35 years of experience in:
Engineering Service Activities
Software Development
Important reference customers in aeronautic field :
Reference in other sectors :
Numerous collaboration with top class research center
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LMS offers for composite modeling
Laminates
SandwichesContinuous fibers
Short fibers
Filament
Winding
4
copyrightLMS
Interna
tional01/08/2013
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Comprehensive library of dedicated multi-layered elements
Composite Shell
Transverse shear deformable thick shell element
Based on Classical Lamination Theory
Can be used for sandwich constructions modeling within scope of CLT
Composite Volume
Classic formulation (3D Solid)
1 ply/element OR several/element
Composite Volumic Shell formulation (2D Solid) shell-like behavior
Composite Membrane (inflatable structures)
2D : Axisymmetric, Plane Stress, Plane Strain,
Multi-harmonic : When the loading or/and the structure response is non axi-
symmetrical
Composites Analyses in LMS SAMTECH Solver
Finite Elements
Multi Layer Element
ShellVolume
Ply 1
Ply 2
Ply N
1 FE
5 copyright LMS International - 2012
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Composites Analyses in LMS SAMTECH Solver
Samtech Solvers package is a suite of several modules dedicated for specific applications
Composite modeling are standard capabilities of every LMS Samtech Solvers
Data exchange between solver are simplified :
Input data files are the same
Capabilities of chaining/ Co-simulation / Mapping data (ie thermal/structural)
6 copyright LMS International - 2012
Stress, Strain,
Frequencies,
Temperature
Strength Analysis
First-ply failure, Failure
Indices
Displayed : critical ply,
values, load case
Classic Failure Analysis
To collapse
From Linear Buckling to
Advanced non linear
algorithm : RIKS,
Buckling, Post Buckling
Classic criteria or
Automatic simulation of
material degradation to
model progressive Intra
laminar or Inter laminar
damage
Damage in composite
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Independent tool or integrated in Caesam Framework : Multi-disciplinary, Multi-model
Design variables : Continuous, Discrete, Integer, Non numeric Analysis Multidisciplinary & Response Any computable value
Composites Analyses in LMS SAMTECH Solver
7 copyright LMS International - 2012
Optimization with
geometric non linarites
(buckling, post-buckling,
collapse)
Local Optimization
Optimization wrt ply
thickness & fibers
orientation
Local Optimization
Stacking Sequence
Optimization
Local Optimization
Very Large scale of
Optimization problems
(e.g. topological
optimization)
Global Optimization
Open System Design of Experiments UpdatingGradient Optimization Genetic Algorithm
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LMS Samtech Linear Solver
Complete Family of Linear solvers:
Static Modal Analysis
Stability Analysis
Response to a harmonic force
Response to an arbitrary excitation
8 copyright LMS International - 2012
Load
Displacement
Features :
Extended library of Finite Elements including composite (all), fracture mechanics(static)
Can handle contact if relative displacements are small (static)
Chaining between solver is simplified (between solvers, same solvers)
Parallel Solver available
Stage #1 Stage #3
Stage #2 Stage #4
Referencesector
Complete
3-D structure
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LMS Samtech Non-Linear Solver
9 copyright LMS International - 2012
Non-linear flexible mechatronic simulation
Contact conditions
Large displacements and rotations
Library of material laws:
Classic linear behavior
Advanced behavior: Composite, plastic ...
Large library of kinematic joints: rigid and flexible
Multi-Body Simulation in Finite Elements Models
Multi-Body SimulationNon-linear capabilitiesFinite Element Analysis Digital Control
Rigid bodies
Flexible meshed parts
Contactwith friction
Flexible Dynamics ensures
Accurate dynamic loads
Vibration level assessment
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Dedicated Graphic User Interface
Non Linear
10 copyright LMS International - 2012
Dedicated pre-processing, user friendly environment allowing easy definition and
interactive checking of:
Material properties (Linear or Non-linear)
Individual ply creation (material, angle, thickness)
Laminates creation (lay-ups)
Data library storage
Laminates assignment to FE mesh
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Dedicated Graphic User Interface
Non Linear
11 copyright LMS International - 2012
Specific post-processing procedure : Ply by ply result recovery (stress/strain/failure criteria)
Critical ply selection (large range of failure theories)
Critical load case
Damage distribution
Ply selection
(composite viewer)
Element selection
(cursor)
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Results on the structure:
Composite Viewer
13 copyright LMS International - 2012
Display the value of the criteria in all
the laminate structure
Select 1 element
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Solution:
SAMCEF solution, with our dedicated tool for compositemodeling
SAMCEF solution,with efficient solvers for modal analysis
Benefits:
Better knowledgeof the composite structure, to support the
physical prototype
Influence of the design parameters on structural behavior
Challenges:
To build a model of the Metisse concept car, with a carbody made of composite
Evaluate thedynamic behavior and thetorsional rigidity
Propose a modelling procedureto support the physical
prototype
Modal analysis of a concept car
15 copyright LMS International - 2012
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Challenge:
Make forecasts of the future test results
(composite structure)
Develop composites FE methods
Solution:
Parametric Finite Element model
Use SAMCEF Linear solution & SAMCEF
Mecano solver
Benefits: Good correlations with reference tests
Methods fully integrated in Airbus application
for certification (ISAMI)
Engineering Service : Airbus Composite Method
Development
16 copyright LMS International - 2012
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Failure Criteria
Failure criteria are used to extend the use of strength data measured from tensile,
compressive and shear uni-axial tests, and that are compared to a combined stress states.
As far as failure for a laminated material are concerned, 2 failure levels can be considered :
1. the First Ply Failure (FPF) based on Failure Criteria
2D or 3D at the ply level:
2. Progressive Failure Analysis based on a Continuum Damage Mechanics
Progressive Ply Failure (UD or Fabric)
Delamination (Interface Model)
Cf Chapter 2
17 copyright LMS International - 2012
Maximum stress criteria
Stress ratio / Strain ratio
Rice and Tracey criterion
Hoffman criteria
Puck
Tsai Hill Quadratic
Tsai Wu
Hashin Multicriterion
Maximum total strain criteria
Maximum mechanical strain criteria
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Failure Criteria
First Ply Failure leads to a very conservative design
Meanwhile, Progressive Failure Analysis is not widely used because of the difficulty to
achieve a design with a full confidence
The presence of cracks leads to a decrease of the stiffness of the matrix resulting to
a load transfer to the fibers or to the surrounding plies.
This stress redistribution assessment is the objective of a simulation that will
integrate the damage laws of the components of the composite structure Last Ply Failure
Questions the designers face:
Whatsthe residual strength of the structure beyond the initiation of the damage?
How is the stress re-distribution within the structure?
Can the structure withstand the applied loads?
But How to do?
18 copyright LMS International - 2012
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PROGRESSIVE FAILURESIMULATION2
Composites and Advanced Structural Analysis
19
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Scope of the presentation
1Fundamental of Composites Structures
1.1 Definition & Advantages of Composites Structures
1.2 Modelling Aspects and Failure Criteria
2Progressive Failure Simulation in Composites structures
2.1 Degradation Process Modelling 2.2 In-ply Damage Modelling
2.3Delamination Modelling
2.4 Industrial Cases
3 Crack Propagation in Metallic Structure
3.1 The XFEM Method
3.2 Applications Cases
4 Optimization of Buckling/Post Buckling behaviour of a composite stiffened
Panel
20
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Failure mechanisms in composite
A correct prediction of the damage in the composite structures is essential for the design
of their structural application
Because of their heterogeneous structure, different scales of analysis can be defined:
Fiber (10 m)
Laminated structure (1-10 mm)
Elementary ply (100 m)
At the ply level, the degradation mechanisms are:
1. Fiber/Matrix decohesion with a limited diffusive damage
2. Transverse cracking of the matrix (through the thickness of the ply)
3. Fiber breaking
21 copyright LMS International - 201221 copyright LMS International - 2012
1 2
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Failure mechanisms in composite
Between the ply, the degradation mechanisms are:
1. Limited diffusive delamination
2. Local delamination, induced by the transverse cracks
When the damage become significant, the interaction between these mechanismsbecomes essential in the evolution of the condition of the structure:
Their chaining generates a re-distribution of the stresses, which is at the origin of
the complete breaking
Often, these mechanisms happen within a significant range of the loading.
A good understanding and an accurate modeling of these degradation mechanisms is
thus a requirement for the design of composites structures.
22 copyright LMS International - 201222 copyright LMS International - 2012
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Failure mechanisms in composite
The proposed approach is based on the Damage Modeling Theory and consider the
laminated structure as a stacking of elementary components with different nature: Ply
Interface
For each degradation mechanism, a damage indicator is defined at the meso-scale
according to the assumptions:
Ply and Interface can be modeled as Continuum Elasto-plastic and Damage-able
Media.
The damage is constant through the thickness but can be different between each ply
In a first version, there is no interaction between damage in the ply and damage in the
interface
A new meso-model has been recently introduced.
23 copyright LMS International - 201223 copyright LMS International - 2012
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Solutions available in SAMCEF, for
damage analysis of compositesIntra-laminar failure Inter-laminar failure
Failure modes in laminated composites
Cohesive elements approach
Fracture mechanics approach (VCE)
User material
24 copyright LMS International - 2012
Damage model for the UD/woven ply
Progressive rupture of the ply
Advanced non local damage model, with strong
interaction with delaminatrion
Short fibers
Classical strength criteria
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2. Damage model for UD/Fabric (P. Ladeveze - LMT Cachan)
Damage in compositesply model
2
3
Damage in 1st (fiber) direction
Damage in 3rd (matrix) direction (only in traction, not in compression)
Damage in 2nd (matrix) direction (only in traction, not in compression)
Damage in 12/13 directions (shear)
1
12
2313
25 copyright LMS International - 2012
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Damage in compositesply model
Thermodynamic forces Yi=E/di
2. Intra-laminar failure for the UD(Cachansmodel)
26 copyright LMS International - 2012
3 damage variables (11; 22; 12)
d11: Damage in the fiber direction (fiber breaking)
d22: Damage in transverse direction (matrix cracking in
traction)
d12: Damage in the shear plane, reflecting decohesion
between fiber/matrix
Very often: Plane stress assumption
Coupling between directions
Transverse Direction: Damage only in Traction, not in Compression
The damaged-material strain energy is :
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Damage in compositesply model
2. Intra-laminar failure for the UD(Cachansmodel)
27 copyright LMS International - 2012
A damage is computed and is a function of the thermodynamic forces:
11 = 0 11 11+11 111
11 >
11+,
11 > 0
11 >
11,
11 > 0
12 = 12012 120 12 1,22 1,12 12
1
22 = 31212 1,22 1,22 22 1
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Damage in compositesply model
2. Intra-laminar failure for the UD(Cachansmodel)
Y11
Damage in the fiber direction d11
d11=1
Y12
Damage in shear d12 (d22)
Y012 Yc12YF12
d12=1
28 copyright LMS International - 2012
Fragile/Brittle failure of the fibers
After a limit, which is not a macro-
value
Ductile failure of the matrix
Plasticity taken into account
Permanent deformation after unloading
Coupling is introduced:
Once d12 or d22 is equal to 1, then d22 or d12 respectively is set to 1
Once the ply is broken in the transverse direction bec. of too many cracks in the
matrix, the resistance in shear vanishes; the opposite is also true.
Y011
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Damage in compositesply model
pKpR
pRRapf
0~~~~~,~ 02
33
2
22
22
23
2
13
2
12
Non linearity in the fiber direction
Plasticity in the matrix: Definition of effective stresses (coupled with damage)Introduction of yield criteria and hardening law
12
13
22
23
12
12
33
33
33
22
22
22
11
11
13
23
12
33
22
11
1
1
1
1
1
1
~
~
~
~
~
~
d
d
d
d
d
d
Traction test, with unloading, on a [45,-45]s lay-up
29 copyright LMS International - 2012
2. Intra-laminar failure for the UD(Cachansmodel)
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Material Testing and behaviour identification
Challenges:
The identification of the parameters of the model can be donebased on a set of simple tests at the coupon level
Solution:
LMS Samtech knowledge for parameter identification
Identification procedure is clearly defined
02322
223
01312
213
01212
212
332202
023
331101
013
221101
012
0322
2
3303
2
3302
2
220222
2
220111
2
11
)1(2)1(2)1(2
)1(222)1(2)1(2
GdGdGd
EEE
EdEEEdEded
Benefits: Virtual material testing, with the non linearities
Haveaccurate material modelsfor the progressive
damage modeling,easy to use
Input for detailled sizing
Coupon level
30
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copyrightLM
SInternational-2011
Damage in compositesparameters identification
[0/90]2s
[45/-45]2s
[0/90]2s
[67,5/-67,5]2s
Set of tests at the coupon level
Upper face
FLFL
L_U
T_
U
Lower face
FL
FL
L_LT_
L
Instrumentation of the coupons
+ tests on holed plates for non local parameters
The procedure to identify the parameters of each model is clearly identified
Traction/Compression
on a laminate at 0 and
90 for fiber direction
behavior
Test on 45/-45 for
the matrix properties
Test on 67.5/-67.5
for the coupling
between shear and
transverse damage
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copyrightLM
SInternational-2011
Damage in compositesparameters identification
Example: [45/-45]2s
The procedure to identify the parameters of each model is clearly identified
Virtual testing Procedure to
correlate the experimental tests
with simulation results
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copyrightLM
SInternational-2011
Damage in compositesparameters identification
Loading_unloading scenarios
(6 to 7 cycles)
Identification of the damage/plasticity
Identification of the elastic properties
The procedure to identify the parameters of each model is clearly identified
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Damage in compositesply model
3. Intra-laminar failure for woven fabrics (Hochardsmodel)
E = potential
Ei0, Gi
0= initial moduli (undamaged)
dij= damages [0;1]
02322
223
01312
213
01212
212
332202
023
03
233
0322
233
02
222
0222
222
331101
013
221101
012
0111
211
)1(2
)1(2)1(22)1(2
2)1(2)1(2
Gd
GdGdEEEd
EEdEEEdE
023
223
013
213
01212
212
332202
023
03
233
0222
222
331101
013
221101
012
0111
211
2
2)1(22
)1(2)1(2
G
GGdEE
EdEEEdE
1
2
34 copyright LMS International - 2012
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Scope of the presentation
1Fundamental of Composites Structures
1.1 Definition & Advantages of Composites Structures
1.2 Modelling Aspects and Failure Criteria
2Progressive Failure Simulation in Composites structures
2.1 Degradation Process and Modelling 2.2 In-ply Damage Modelling
2.3 Delamination Modelling
2.4 Industrial Cases
3 Crack Propagation in Metallic Structure
3.1 The XFEM Method
3.2 Applications Cases
4 Optimization of Buckling/Post Buckling behaviour of a composite stiffened
Panel
35
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In SAMCEF
Damage in composites - interface
1. Fracture mechanics approach Which crack is dangerous ?
What is the propagation load ?
2. Cohesive elements approach Which crack is dangerous ?
What is the propagation load ?
What is the maximum load ?
What is the residual stiffness during propagation ?
Inter-laminar failure: delamination
Automatic
crack
propagation
No automatic crack
propagation
Inter-laminar failure: delamination
Delamination = Separation of adjacent plies
at locations sensitive to transverse effects
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GI GIC
=> Crack prop agat ion
120
140
160
180
200
220
240
0 5 10 15 20 25
Crack width (mm)
EnergyreleaserateGI(J/m)
Computed values
Limiting value
At the crack front:
GI
GIC
Toughness reachedand exceeded
1. Fracture Mechanics approach for delamination : VCE Approach
Damage in composites - interface
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2. Cohesive elements approach for delamination
Including an imperfect interface
between two plies
Damage in composites - interface
39 copyright LMS International - 2012Properties of the interface
Tension
Opening
f
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233
0
2
1
eId kY I231
0
2
1IId kY II
2320
2
1IIId kY III
2. Thermodynamic forces ("forces in the interface")
3. Equivalent thermodynamic force (with the 3 modes effects)
/1
sup
IIIC
III
IIC
II
IC
IIC
t G
Y
G
Y
G
YGY
232
0231
0233
0233
0)1()1()1(
2
1ee IIIIIIIIIIIII dkdkdkkE
1. Potential in the interface elements
4. Only one resulting damage variable
dddd IIIIII
)(Yhd
5. Evolution of the damage wrt the thermodynamic force
Y
d1
40 copyright LMS International - 2012
2. Cohesive elements approach for delamination
Damage in composites - interface
D i it i t f
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Library of cohesive models
0
30
60
90
120
150
180
0 1 2 3 4 5 6
Displacement w (mm)
Load(N)
Numerical results Analytical reference
Max imum load
Residual st i f fness
Propagat ion
load
Crack propagation
Non linear analysis
2. Cohesive elements approach for delamination
Damage in composites - interface
P t f M t i l L
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Parameters of Material Law
Standard tests should be performed to define the material law coefficient
42 copyright LMS International - 2012
Example of DCB Test
016/016
Material Law Type of test requiredTransverse stiffness of the interface: kI
0 x Fit on DCBFirst shear stiffness of the interface: kII
0 x Fit on ENFSecond shear stiffness of the interface: kIII
0 x kIII0 = kII0GIc: fracture toughness in mode I x DCBGIIc: fracture toughness in mode II X ENFGIIIc: fracture toughness in mode III X GIIIc=GIIca: coupling parameter between the modes MMBThreshold for thermodynamic force: Y0t (X) Fit on DCB and ENFExponent (X) Fit on DCB and ENFTau, Adel: parameters for the delay effect x Fit on DCB and ENF
DCB : Double Cantilever Beam
ENF : End Notched Flexure
MMB test (Mixed Mode Bending)
D i it t id tifi ti
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copyrightLMS
International-2011
Damage in compositesparameters identification
The procedure to identify the values for the model parameters is known
Properties of the interface (for delamination)
DCB
Double Cantilever Beam
MMB
Mixed Mode Bending
ENF
End Notched Flexure
A li ti D i it i t f
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Fracture mechanics approach
Application Damage in composites - interface
45 copyright LMS International - 2012
Cohesive elements approach
crack
Comparison between SAMCEF and other commercial FE code:
Academic Case: Propagation in Mode I DCB test
(Refined Mesh at the crack front)
S f th t ti
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Scope of the presentation
1Fundamental of Composites Structures
1.1 Definition & Advantages of Composites Structures
1.2 Modelling Aspects and Failure Criteria
2Progressive Failure Simulation in Composites structures
2.1 Degradation Process and Modelling
2.2 In-ply Damage Modelling
2.3 Delamination Modelling
2.4 Industrial Cases
3 Crack Propagation in Metallic Structure
3.1 The XFEM Method
3.2 Applications Cases
4 Optimization of Buckling/Post Buckling behaviour of a composite stiffened
Panel
47
St t l C t D i i A ti
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Structural Components Design in Aeronautics
80mm
50mm
Existing crack
Existing cracks
20mm
Cap (4 plies)[45/90/0/-45]
Skin (9 plies)[0/90/45/0/-45/90/0/45/-45]
Imposed displacement
Flange- left part (4 plies)
[-45/90/0/45]
Clamp
Benefits
Non-Linear laws with damage for plies and
interfaces
Contact introduced between all interface to simulate
the closing of cracks Presence of initial cracks
Very large models : parallel procedure Determination of the propagation load and the
maximum load
Location of initial cracks
0
2000
4000
6000
8000
10000
12000
0 0.5 1 1.5 2 2.5
Displacement w (mm)
Load(N)
Propagation load
Maximum load
copyrightLMSInternational
Composite T-Stiffener (Airbus Supplier France)
48
Element level
Structural Components Design in Aeronautics
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Structural Components Design in Aeronautics
copyrightLMSInternational01/08/2013
Energy release rates by mode: VCE
Evolution of the criterion: VCE
Most critical crack identification
Propagation Laods
IIIc
III
IIc
II
Ic
I
G
G
G
G
G
G
Full 3D case
Presence of the 3 modes
Composite T-Stiffener (Airbus Supplier France)
49
Damage in composites - interface
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Cohesive elements approach
Damage in composites - interface
0
1000
2000
3000
4000
5000
6000
7000
0 0.5 1 1.5 2 2.5 3 3.5 4
Vertical displacement (mm)
Reaction(N)
112122 ddl
293332 ddl
553889 ddl
First damage d =
1 (propagation
load)
Interface elements
Deformation at collapse
Load - displacement curve for different element sizes
Composite T-Stiffener (Airbus Supplier France)
Damage in composites - interface
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Cohesive elements approach: zoom in the center of the structure, to check the contacts
between layers
Damage in composites - interface
Multiple contact conditions
taken into account to manage
potential reclosure of cracks
Composite T-Stiffener (Airbus Supplier France)
Structural Components Design in Aeronautics
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Structural Components Design in Aeronautics
copyrightLMSInternational01/08/2013
Composite T-Stiffener (Airbus Supplier France)
Displacement = 1.38 mm
Load = 4450 N
Displacement = 1.98 mm
Load = 6050 N
Displacement = 2.16 mm
Load = 6100 N
Displacement = 2.25 mm
Load = 3000 N
Evolution of the interlaminar damage during the loading
Cohesive elements approach
52
Damage in composites - interface
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Cohesive elements approach
Damage in composites interface
Composite T-Stiffener (Airbus Supplier France)
Damage in composites interface
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Damage in composites - interface
293,332 do f
19264 volume elements
1221 contact elements
12664 interface elments
112,122 do f
7164 volume elements
639 contact elements
4410 interface elments
553,889 do f
37064 volume elements
2550 contact elements
22884 interface elments
2
2
3
7
4
1
1
1
553889
553889
293332
112122
6700
6700
6530
6720
285
854
524
44
Speed-up = 3
Efficiency = 75%
Mean le(mm) Number ofprocessors Size of theproblem
(dof)
Maximumload (N) CPU to reach2.35mm
(minutes)
Damage in composites
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Damage in composites
Bend specimen4 points bending
Inter-laminar damage
AIRBUS GERMANY BENCHMARK
4 Points Bending Experimental device for a curved beam
Damage in Composites
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Damage in Composites
1stdelamination (violent)
Value in agreement with experimentalresults (including dispersion) Courtesy of Airbus
2nddelamination
Determination of the successive delamination loads
AIRBUS GERMANY BENCHMARK
4 Points Bending Experimental device for a curved beam copyrightLMS
Internatio
nal01/08/2013
Identify the critical
interface
56
Structural Components Design in Aeronautics
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Structural Components Design in Aeronautics
Example 1: AIRBUS GERMANY BENCHMARK
4 Points Bending Experimental device for a curved beam
Delamination starts at the edges
Need a 3D modelingIf S33 Interlaminar decreases =damage appears !
Understanding of the delamination process
57
Damage in a composite blade
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Challenge:
Tail rotor blade with central notch
Rotor blade skin: glass fiber/ epoxy matrix with a 45 lay-up
Study made in collaboration with Eurocopter and EADS IW for
3rd ECCOMAS Thematic Conference on the Mechanical
Response of Composites
Solution:
Full model: all blade components modeled (foam, spar, etc.)
Combined bending/torsion loading 150000 multilayered solid elements
Damage model only in zone around the notch
Benefits:
Very good correlation with test
Better understanding of the non-linear behavior of the structure
Damage in a composite blade
58 copyright LMS International - 2012
Damage mesomodel
Elastic behaviour
Damage in a composite blade
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- No delamination (in-situ tap test)
- No buckling (before fiber fracture)
Damage in a composite blade
Damage in a composite blade
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55/55
Damage in a composite blade
Strain along blade axis
Tests
Simulation
Increasing loading
Damage Image Correlation
(strain in longitudinal direction)