1 28.07.2009 ICCM 2009 Outline Introduction Textile composites - - PowerPoint PPT Presentation

Analysis of Failure in Textile Composites via Meso- Damage Mechanics: Effect of lay-up

28.07.2009 ICCM 2009

1

Dmitry S. IVANOV, Stepan V. LOMOV, Ignaas VERPOEST

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

Outline

Introduction

–

Textile composites

–

Multi-scale concept

–

Problem statement

Mechanical insight

–

Deformation mechanisms in textile laminates

–

Energy-based scaling procedure for boundary conditions for unit cell in N-ply laminate

2

cell in N-ply laminate

–

Modelling of delaminations via new BC’s

–

Damage modelling: ERR model + Zinoviev’s assumptions

Examples: experiments and FEA

–

1-ply and multi-ply composites

–

Plain weave and 3D composites

–

Triaxial braided composites

Conclusions

Diversity of textile structures

3D woven Woven Braided

Patterns

3

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

4

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

Sheared Laminated Stitched Non crimp Knitted

Outline

• Introduction

–

Textile composites

–

Multi-scale concept

–

Problem statement

• Mechanical insight

–

Deformation mechanisms in textile laminates

–

Energy-based scaling procedure for novel boundary conditions for unit cell in N-ply laminate

–

Modelling of delaminations via new BC’s

5

–

Modelling of delaminations via new BC’s

–

Damage modelling: ERR model + Zinoviev’s assumptions

• Examples: 2D and 3D glass-epoxy composites

–

Comparison: 1-ply and multi-ply composites

–

Comparison: plain weave and 3D composites

–

FEA vs. experiments: local strain distribution

–

FEA vs. experiment: stress-strain diagrams

• Conclusions

Through-the-thickness non- homogeneity

Reference problem

6

Reasons:

(1) The moment caused by force misbalance is compensated by the stress distribution in the

• uter plies ∆

∆ ∆ ∆F (2) A high inter-0° ° ° °-yarn shear

7

(2) A high inter-0° ° ° °-yarn shear stress S is zeroed at the surface Effective E-modulus

2 11 12 12 11 11 1

ε γ τ σ ε + ≈

eff

E

Deflection profiles

2 22 2 2

~ x u u ε − =

8

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

9

( )

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

10

3D test problem: twill woven

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

11

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

Laminates with a ply shift

“Step”

12

“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” Stress along the loading directions “Periodic stacking”

13

• 4.0 ÷

÷ ÷ ÷160.1

• 2.3 ÷

÷ ÷ ÷149.6

• 2.5 ÷

÷ ÷ ÷126.9

• 0.02 ÷

÷ ÷ ÷0.33 %

• 0.08 ÷

÷ ÷ ÷0.28 % 0.02 ÷ ÷ ÷ ÷0.24 % Surface strain map Average surface strain 0.1002 % 0.1002 % 0.1003 %

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 ~

14

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 ~

15

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

16

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

17

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

Outline

• Introduction

–

Textile composites

–

Multi-scale concept

–

Problem statement

• Mechanical insight

–

Deformation mechanisms in textile laminates

–

Energy-based scaling procedure for novel boundary conditions for unit cell in N-ply laminate

–

Modelling of delaminations via new BC’s

18

–

Modelling of delaminations via new BC’s

–

Damage modelling: ERR model + Zinoviev’s assumptions

• Examples: 2D and 3D glass-epoxy composites

–

Comparison: 1-ply and multi-ply composites

–

Comparison: plain weave and 3D composites

–

FEA vs. experiments: local strain distribution

–

FEA vs. experiment: stress-strain diagrams

• Conclusions

Modelling of delaminations via novel BC’s

Delamination can be modelled by “releasing” the interlayer boundary of single UC from the prescribed BC’s Periodic profile. Ply 1 Periodic profile. Ply 2 “Step”

∞ z

u ~

∞ z

u ~

Zero-traction surface

19

Superimposed profile Thus, 1-ply solution can be effective for the modelling delamination in the entire laminate Delamination No need to insert the cohesive elements

Outline

• Introduction

–

Textile composites

–

Multi-scale concept

–

Problem statement

• Mechanical insight

–

Deformation mechanisms in textile laminates

–

Energy-based scaling procedure for novel boundary conditions for unit cell in N-ply laminate

–

Modelling of delaminations via new BC’s

20

–

Modelling of delaminations via new BC’s

–

Damage modelling: ERR model + Zinoviev’s assumptions

• Examples

–

1-ply and multi-ply plain weave composites

–

3D composites

–

Triaxail braided composite

• Conclusions

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

21

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

• 5) Combination: micro/plasticity and

damage

        = Y Y d d

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

MPa

x,

σ % ,

x

ε

• 60

±

Damage

• nset

( )

12 12 12 12

1 Y Y d − = γ

Damage

• nset

22

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 + + + + − − ∂ ∂ =

Outline

• Introduction

–

Textile composites

–

Multi-scale concept

–

Problem statement

• Mechanical insight

–

Deformation mechanisms in textile laminates

–

Energy-based scaling procedure

–

Boundary conditions for unit cell in N-ply laminate

–

Modelling of delaminations via new BC’s Damage modelling: ERR model + Zinoviev’s assumptions

23

–

Damage modelling: ERR model + Zinoviev’s assumptions

• Examples: experiments and FEA

–

1-ply and multi-ply composites

–

Plain weave and 3D composites

–

Triaxial braided composites

• Conclusions
• S. V. Lomov, A. E. Bogdanovich, D. S. Ivanov, D. Mungalov, M. Karahan, I. Verpoest

A comparative study of tensile properties of non-crimp 3D orthogonal weave and multi-layer plain weave E- glass composites. Part 1: Materials, methods and principal results; Part 2: Comprehensive experimental results Composites Part A, In Press Materials are provided by 3Tex Inc, USA

Surface strain

24

Damage accumulation mechanisms

Loading direction

25

Matrix intra-yarn cracks: 90° ° ° ° yarns Matrix intra-yarn cracks: 0° ° ° ° yarns Inter-ply delaminations Fibre rupture

Comparison of 1-ply and 4-ply composites

MPa , σ

4-ply composite Approaching of 4-ply composite curve to the 1-ply composite curve: effect of delaminations

26 % , ε

1-ply composite

FE vs. experiment: plain weave

MPa , σ

4-ply composite FE-4 ply-sym FE-1 ply

27 % , ε

1-ply composite

FE vs. experiment: plain weave

MPa , σ

4-ply composite FE-4 ply-sym FE-1 ply

28 % , ε

1-ply composite Delamination onset

3D NCF textile composites

MPa , σ

FE-4 ply-sym

29 % , ε

Triaxial braided composite

Exp FEA – periodic BC FEA – symmetric BC

CD tensile test

30

MD tensile test

Conclusions

1. Ply shift is hardly ever considered to be an important mechanical factor 2. But: Inter-layer shift creates huge diversity of the strain fields and failure scenario’s. 3. Novel BC account for the number of plies, ply shift, surface

31

3. Novel BC account for the number of plies, ply shift, surface

• effects. They improve the solution and decrease heavy

computational needs of textile composite modelling 4. Novel BC’s can be used for effective modelling of delamination 5. Damage modelling: Orientation of degradation plane + Simple degradation scheme + ERR-model + Post-critical assumptions + Correct BC’s = ok.