Composites Light pdf

8/12/2019 Composites Light pdf

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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



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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)


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



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


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


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


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


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


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



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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



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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


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?



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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

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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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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.



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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.



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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


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



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Thermodynamic forces Yi=E/di

2. Intra-laminar failure for the UD(Cachansmodel)


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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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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Y11

Damage in the fiber direction d11

d11=1

Y12

Damage in shear d12 (d22)

Y012 Yc12YF12

d12=1


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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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




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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

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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


Example: [45/-45]2s


Virtual testing Procedure to

correlate the experimental tests

with simulation results


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copyrightLM

SInternational-2011


Loading_unloading scenarios

(6 to 7 cycles)

Identification of the damage/plasticity

Identification of the elastic properties



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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



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2.1 Degradation Process and Modelling 2.2 In-ply Damage Modelling

2.3 Delamination Modelling



3.1 The XFEM Method



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



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2. Cohesive elements approach for delamination

Including an imperfect interface

between two plies


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




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



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


Example of DCB Test

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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


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



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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2.1 Degradation Process and Modelling

2.2 In-ply Damage Modelling

2.3 Delamination Modelling



3.1 The XFEM Method



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



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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


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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




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Cohesive elements approach: zoom in the center of the structure, to check the contacts

between layers


Multiple contact conditions

taken into account to manage

potential reclosure of cracks




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copyrightLMSInternational01/08/2013


Displacement = 1.38 mm

Load = 4450 N


Load = 6050 N


Load = 6100 N


Load = 3000 N

Evolution of the interlaminar damage during the loading


52



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Damage in composites interface


Damage in composites interface


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293,332 do f

19264 volume elements

1221 contact elements

12664 interface elments

112,122 do f




553,889 do f




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



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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 mesomodel

Elastic behaviour



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- No delamination (in-situ tap test)

- No buckling (before fiber fracture)




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Strain along blade axis

Tests

Simulation

Increasing loading

Damage Image Correlation

(strain in longitudinal direction)

Documents

Composites Light pdf