1 11.03.2009 D.S.Ivanov, Pre-defence Outline Introduction - - PowerPoint PPT Presentation

ANALYSIS OF DAMAGE IN TEXTILE COMPOSITES

Dmitry S. Ivanov

Promotors:

• Prof. Stepan V. Lomov
• Prof. Ignaas Verpoest

Jury:

• Prof. Thomas Pardoen
• Prof. Dirk Roose

11.03.2009 D.S.Ivanov, Pre-defence

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Katholieke Universiteit Leuven Department of Metallurgy and Materials Engineering Composite Materials Group

• Prof. Ignaas Verpoest
• Prof. Dirk Roose
• Prof. Dirk Vandepitte
• Prof. Martine Wevers
• Prof. Masaru Zako

Chairman:

• Prof. Herman Neuckermans

Outline

• Introduction

–

Textile composites

–

Multi-scale modelling

–

Problem statement

• Experimental work

–

Methodology and materials

–

Mechanical response of the damaged composites

–

Damage evolution

• Multi-scale modelling

2

• Multi-scale modelling

–

Stress distribution in textile laminates

–

Novel out-of plane boundary conditions

–

Symmetry boundary conditions

• Damage modelling

–

Prediction of damage initiation

–

Main-stream element discount method

–

New damage modelling approach

–

Validation of the modelling

• Conclusions

Composite materials: applications

Aerospace: Sport:

wood metal Composite

% composit es in civil aircraf t

A320 A340 A380 A350 B787

10 20 30 40 50 60

www.itftennis.com

3

…, …, ETC.

Civil: Marine: Automotive:

Toyota 1/X

B747 A320

10 1970 1980 1990 2000 2010

Diversity of textile structures

3D woven Woven Braided

Patterns

4

Diversity = Architectures*Patterns*Lay-ups*Geometry*Textile deformations*…

Sheared Laminated Stitched Non crimp Knitted

Design concept: Meso-scale

3D woven Woven Braided

Patterns

UD fibre bundle

5

Meso scale → → → → Properties of UD and Matrix + Internal geometry + Boundary conditions

Sheared Laminated Stitched Non crimp Knitted

Damage development

Fibres Yarns Fabrics Parts

Patterns Hierarchy Failure initiation

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Patterns

Triaxial braided NCF 3D woven

Stability of crack system Failure initiation

% 4 ≈

epoxy failure

ε % 6 . ≈

UD

• nset

crack

ε

% 3 . ≈

composite textile

• nset

crack

ε

Stress concentration Fibres Yarn crimp

Problem statement

"The overall conclusion to be drawn is that a designer wishing to estimate the stress levels at which initial failure might occur in a multi-directional laminate, can only hope to get to within a ± ± ± ±50%, at best, based on current theories." Best criteria have been selected according to the principle: Conclusion of World-Wide Failure Exercise for UD laminated composite:

!

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"theories achieved predictions to within ±50% of the experimental values for 80% of the test features" Textile vs. UD laminated composites: Diversity of architectures↑ ↑ ↑ ↑ Geometrical complexity ↑ ↑ ↑ ↑ Mechanical stress factors (e.g. crimp, yarn interaction) ↑ ↑ ↑ ↑ 3D stress state↑ ↑ ↑ ↑ Failure mechanisms variability↑ ↑ ↑ ↑

Modelling loop

Reinforcement parameters

Part performance

Study of macro deformation Local reinforcement geometry

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Local stiffness Meso boundary conditions Physical evolution

• f the structure

Mechanical meso model of RVE

) (x ε

Macro strain at the point x

) (y ε x y

Meso stress-strain distribution

Outline

Introduction

–

Textile composites

–

Multi-scale modelling

–

Problem statement

Experimental work

–

Methodology and materials

–

Mechanical response of the damaged composites

–

Damage evolution Ch II

9

–

Damage evolution

Multi-scale modelling

–

Stress distribution in textile laminates

–

Novel out-of plane boundary conditions

–

Symmetry boundary conditions

Damage modelling

–

Prediction of damage initiation

–

Main-stream element discount method

–

New damage modelling approach

–

Validation of the modelling

Conclusions

Tests of carbon-epoxy composites

T700, 8-16 plies, Vf = 20-40% HTS 5631 Tenax fibres, T400 fibres, 10 plies, Vf = 45 %

The same manufacturing parameters and epoxy Biaxial non-crimp fabric Triaxial braided Quasi-UD woven Materials

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Load up to the predefined load levels

Vf = 20-40% HTS 5631 Tenax fibres, 4 layers, Vf = 44 % 10 plies, Vf = 45 %

Tensile test Acoustic emission Strain mapping Methodology diagram energy of failure events macro deformation degradation damage initiation meso strain Damage stages X-Ray Cross-sectioning SEM crack length Crack position/orientation Micro debonding crack density Delaminations Damage evolution

NCF, tensile

µ-damage + plasticity, fibre failure µ-d + plasticity + fibre

± 20, 30° ± 45°

Manufactured and tested by Thanh Troung Chi

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± 60, 70°

reorientation + m-cracking, separation of delaminated plies m-cracking, delaminated plies

NCF, tensile

µ-damage + plasticity, fibre failure µ-d + plasticity + fibre

± 20, 30° ± 45°

Manufactured and tested by Thanh Troung Chi

22 12

σ τ

1 . 7 −

1 . 3 −

• 20

±

• 30

±

• 45

±

12

± 60, 70°

reorientation + m-cracking, separation of delaminated plies m-cracking, delaminated plies 3 . 6 .

1 . 2

0, ± 45° 90, 0, ± 45° 90, ± 45°

Braided, tensile

MD

Slight degradation

BD

Similar to NCF ±60°

13

Low strain to failure despite the presence of the ±45° yarns

CD

Energy of AE events correlates with the degradation

Damage patterns

SEM

Crack density growth + crack length increase Total crack length correlates with AE energy and

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Inlay yarns Braiding yarns

X-ray images: CD Cross-section of the composite Loading

Inclined cracks Delaminations at the advanced stage of deformation Inter-yarn meso cracking, not much

• f µ-damage

Few cracks per yarn The similar orientation

• f the cracks in yarns of
• ne direction

stiffness degradation

Outline

Introduction

–

Textile composites

–

Multi-scale modelling

–

Problem statement

Experimental work

–

Methodology and materials

–

Mechanical response of the damaged composites

–

Damage evolution

15

–

Damage evolution

Multi-scale modelling

–

Stress distribution in textile laminates

–

Novel out-of plane boundary conditions

–

Symmetry boundary conditions

Damage modelling

–

Prediction of damage initiation

–

Main-stream element discount method

–

New damage modelling approach

–

Validation of the modelling

Conclusions

Ch III

Meso-FE: Road map

Geometric modeller Geometry corrector Meshing Assign material properties

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properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

Surface role

Experimental evidence of the surface effects Quasi-UD woven composite, delaminations in outer plies only Braided composite, MD: intra- yarn cracks in outer plies only

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Reference problem Extensive delaminations in surface plies ⇒ ⇒ ⇒ ⇒ Failure scenario governed by the number of plies

Comparison of stress

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Stress density function

Transverse stress in 90° ° ° ° yarns: volume fraction

• f elements with a particular stress value

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Stress distribution depends on the number of plies in a textile laminate

Deflection profiles

2 22 2 2

~ x u u ε − =

20

m u µ , ~

2

The less plies are in the laminate the higher the deflection The deflection for all the plies in the laminate is nearly the same The deflections of N-ply laminates are proportional to each other

New BC’s

( )

inner inner

• uter
• uter

E

N E

11 11 11 11

2 2 ε σ ε σ − + =

( )

inner ij ij

• uter

ij ij H

N E ε σ ε σ 2 2 − + = Energy of effective medium Energy of heterogeneous medium Outer and inner unit cells

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( )

E H

E E E − = ∆ λ

Number of the plies, N 2 3 4 5 6 Reference solutions 1.725 1.383 1.273 1.210 1.160 Numerical procedure 1.709 1.375 1.253 1.190 1.153 Deviation from the balance Minimisation of the deviation Optimum scaling coefficients

Analysis of the results

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3D test problem: twill woven

FE models are generated by MeshTex software, Osaka University, based on WiseTex geometry

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Displacement profiles: the same as 2D ⇒ ⇒ ⇒ ⇒ new BC’s can be used

Comparison of results

3.2 ÷ 16.5 3.6 ÷ 16.4 3.4 ÷ 16.1

yarns

• 90

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12 . 1 = λ

29.3 ÷ 134.4 49.7 ÷ 131.7 29.3 ÷ 132.8 Bottom outer ply of 6 ply laminate Periodic solution Surface solution, 6-ply Reference solution

yarns

Laminates with a ply shift

“Step”

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“Stairs”

Can one unit cell be representative in the case of laminates with an arbitrary ply shift? Which BC to apply?

Stress in laminate with an different ply shifts

“Stairs” “Step” “Periodic stacking”

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• 4.0 ÷

÷ ÷ ÷160.1

• 2.3 ÷

÷ ÷ ÷149.6 Stress in along the loading directions is dramatically influenced by the stacking sequence

• 2.5 ÷

÷ ÷ ÷126.9

Superposition of periodic profiles

To set the correct boundary conditions we have to predict the laminate deformed shape Periodic profile. Ply 1 Periodic profile. Ply 2 “Step”

∞ z

u ~

∞ z

u ~

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Superimposed profile Deformed profile of a textile laminate can be presented as a superposition of periodic profiles for each of the plies

( ) ( ) ( )

N u shift x u u shift x u shift x u u

z z z z z z

1 ... ) ~ max( 2 ~ ) ~ max( ~ ~ ~

3 2 1

              + + + + + + + + =

∞ ∞ ∞ ∞ ∞

Superposition of periodic profiles

To set the correct boundary conditions we have to predict the laminate deformed shape Periodic profile. Ply 1 Periodic profile. Ply 2 “Stairs”

∞ z

u ~

∞ z

u ~

28

Superimposed profile Deformed profile of a textile laminate can be presented as a superposition of periodic profiles for each of the plies

( ) ( ) ( )

N u shift x u u shift x u shift x u u

z z z z z z

1 ... ) ~ max( 2 ~ ) ~ max( ~ ~ ~

3 2 1

              + + + + + + + + =

∞ ∞ ∞ ∞ ∞

Actual and predicted profiles

m uz µ , ~ mm x ,

1

Superimposed/predicted profile “Step”-wise shift

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Average profile in the laminate Profiles along the inter-layer boundaries Predicted and average profiles are proportional ⇒ ⇒ ⇒ ⇒ Energy-based scaling is also applicable here The scatter of the profiles is bigger than in the periodic stacking

Actual and predicted profiles

m uz µ , ~ mm x ,

1

Superimposed/predicted profile “Stair”-wise shift

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Average profile in the laminate Profiles along the inter-layer boundaries Predicted and average profiles are proportional ⇒ ⇒ ⇒ ⇒ Energy-based scaling is also applicable here The scatter of the profiles is bigger than in the periodic stacking

BC: braided composite for quarter

• f UC

γ γ γ γ = – 1, if j, k = = 1, if j, k = γA 1,3 or 2,3; 1,1/ 2,2/ 3,3 or 1,2 γB 1,2 or 1,3; 1,1/ 2,2/ 3,3 or 2,3 γC 1,2 or 2,3; 1,1/ 2,2/ 3,3 or 1,3

ij j n in i

d ) ( u ) ( u ε γα = − 1 2

• j,k - fixed indexes – point out the macro

A

α B α C α

Based on idea of J.Whitcomb

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Face A j,k - fixed indexes – point out the macro deformation

Faces {(1) →(2)} γ γ γ γ α α α α d x2=–a (A) (x1, x2, x3) → (- x1, - x2, x3) γA Rotation around the x3 axis by π (bottom -top) (0, w, 0) x1= –x2 (B) (x1, x2, x3) → (-x2, -x1, - x3) γB Rotation around the x′1 axis by π (bottom -right) (w, w,0) x1= x2 (C) (x1, x2, x3) → (x2, x1, -x3) γC Rotation around the x′2 axis by π (bottom -left) (-w, w,0)

Faces B and C

Outline

Introduction

–

Textile composites

–

Multi-scale modelling

–

Problem statement

Experimental work

–

Methodology and materials

–

Mechanical response of the damaged composites

–

Damage evolution

32

–

Damage evolution

Multi-scale modelling

–

Stress distribution in textile laminates

–

Novel out-of plane boundary conditions

–

Symmetry boundary conditions

Damage modelling

–

Prediction of damage initiation

–

Main-stream element discount method

–

New damage modelling approach

–

Validation of the modelling

Conclusions

Ch IV

Failure initiation

Puck criterion: the plane with highest risk factor of failure 90° angle in straight parts and 45-90° angle at the curved parts Braided composite

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Explains short cracks in the crimped composites NCF composite

Element discount method

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Non-realistic, “cross-fibre” predictions of damage zone propagation, and damage widening Reason: stress distribution around the damage zone

Damage modelling

1) Elementary damaged entity: segment 2) Orientation of the failure plane: Mohr-Hashin-Puck

concept

3) Degradation scheme of Murakami-Ohno

Crack plane defines the orientation of degradation Yarn segment: fibre orientation is constant

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3) Degradation scheme of Murakami-Ohno 4) Damage evolution law:

• 5) Combination: micro/plasticity and

damage

        =

cr

G Y d d ~

2

Damage ↔ energy release rate

) 1 2 ( ) 1 1 ( 2

12 12 2

d d d − − − − =

2

d

12

d

2 2 2 2

) 1 ( d E E − = ) 1 (

12 12 12

d G G − =

) 1 (

2 12 12

d v v − = ) 1 (

2 23 23

d v v − =

Damage evolution law

Ε ∂ Θ ∂ = Θ ∂ =

cr

~ Ε ∂ Θ ∂ = Θ ∂ =

2

Energy release rate due to increment of deformationΕ

µ icro meso

Mechanical interpretation

Damage evolution law:

        =

cr

G Y d d ~

2

Energy release rate Normalisation factor

= master function valid for any loading situation

( )

• nset

failure Y Gcr

2

~ ∝

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2

~ Y G d

cr

= ∂ ∂ ρ

ρ ∂ Ε ∂ Ε ∂ Θ ∂ = ∂ Θ ∂ = V a t G cr ~ d V d V Y ∂ Ε ∂ Ε ∂ Θ ∂ = ∂ Θ ∂ =

2

σ

ε Heterogeneous

a t

⇒ ⇒ ⇒ ⇒ Mechanical meaning of the normalisation factor: equal crack density at the moment of the failure onset Effective

cr

G Y ~

2

has the dimensions of crack density ρ

Damage evolution law: extraction

MPa

x,

σ % ,

x

ε

• 60

±

Damage

• nset

( ) ( )

12 12 12 12 12

1 G G d γ γ − =

Damage

• nset

37

In line with the assumptions of Zinoviev

( ) ( )

( ) ( )

2 23 23 2 12 12 13 33 12 11 2 22 22 22 2 12 2 12

2 1 1 1 γ γ ε ε ε ε G G C C d C d d d Y + + + + − − ∂ ∂ =

Results: NCF

± 20, 30° ± 45°

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± 60° ± 70°

Modelling of braided composite

Exp FEA – periodic BC FEA – symmetric BC

CD tensile test

39

MD tensile test

Local histories of deformation

40

% ,

22

ε

MPa ,

22

σ

% ,

12

γ

MPa ,

12

τ

MPa ,

22

σ

% ,

12

γ

MPa ,

12

τ

% ,

22

ε

⊥ 2

B

⊥ 1

B

Conclusions: general

1. The full chain of the textile composites analysis is presented. It incorporates: experimental investigation, meso-scale analysis, damage modelling, property identification, and model validation. 2. Experimental methodology for testing textile composite is established and applied to a spectrum of composite materials with

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various architectures. 3. Meso scale analysis for textile composites is extended for efficient modelling of textile laminates and complex triaxial structures 4. A need in novel damage modelling is demonstrated and the new concept is proposed

Conclusions: experiments

1. Dominant failure mechanisms, µ µ µ µ/plasticity and meso crack deformation mechanisms are distinguished. Their contribution to non-linearity is shown. 2. The crack geometry has been extensively studied by means of various experimental techniques

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3. Meso damage is described as competitive mechanism, crack length growth VS. number of cracks, with respect to the textile architecture. 4. It is found that acoustic emission energy, stiffness degradation, and density of m-cracks are directly related.

Conclusions: elastic analysis

1. The surface effect is found experimentally, shown numerically and explained 2. New analytical model is proposed. It accounts for the number of the plies and evaluates stress factors in textile laminate

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3. Novel boundary conditions for modelling the surface effects are introduced. It is shown that these BC’s allow to improve the solution and to decrease heavy computational needs of textile composite modelling 4. New symmetry BC’s for triaxial material are introduced

Conclusions: damage modelling

1. Damage initiation in textile composites is predicted and verified against experimental measurements 2. Paradox of main-stream damage mechanics – found and explained 3. Novel damage modelling

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3. Novel damage modelling

1. Segment degradation 2. Orientation of the degradation plane 3. One-parameter degradation scheme 4. New damage evolution law 5. Micro/plasticity + meso-damage

4. Validation: degradation, crack initiation, failure angle, failure mode

Thank you for attention

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