Textile Preforms for Composites 1. Introduction 2. Fibres and yarns - - PDF document

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Textile Preforms for Composites

• 1. Introduction
• 2. Fibres and yarns
• 3. Textiles in general
• 4. Fabrics: NCF – Woven – Braided – Knitted – 3D – Spaced
• 5. Modelling of textile composites

Stepan V. Lomov Department MTM – KU Leuven

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 2

Contents

1. Introduction 2. Geometrical models of textile reinforcement internal architecture 3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling

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1. Introduction 2. Geometrical models of textile reinforcement internal architecture 3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling S.V. Lomov 27.07.2012

Textile composites: meso-scale as a bridge to Macro

x z p h z(x) Q Q d2 d1 Z A B

Internal architecture of the reinforcement Deformation resistance and change of geometry Compr. Shear Tension Bending Perme- ability

M R=1/ K

Drapeability and formability Impregnation Production Mechanical properties and damage Performance Structural analysis

4 4 S.V. Lomov - Textile Preforms for Composites - 5. Modelling 4

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Мodels

Unit cell Manufacturing Pefomance Internal architecture of the reinforcement Deformation resistance and change of geometry Permeability Drapeability and formability Impregnation Mechanical properties and damage Structural analysis

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 5 6

Software

Unit cell Manufacturing Performance Internal architecture of the reinforcement Deformation resistance and change of geometry Permeability Drapeability and formability Impregnation Mechanical properties and damage Structural analysis WiseTex TexGen FlowTex CFD WiseTex Abaqus TexComp Abaqus ANSYS PAM-RTM LCM RTM-Works PAM-FORM QuikForm CoData Abaqus Nastran РАМ-SYSPLY Abaqus PAM-CRASH ANSYS

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 6

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WiseTex software package: Virtual textiles and textile composites

• commercialised by K.U.Leuven R&D
• integrated in SYSPLY package of ESI Group

6 industrial licenses 30+ university licenses

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 7

Textile structures in WiseTex

Woven Braided NCF Laminates Knitted

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 8

5

Smart composites

AE sensor

• n-board

computer super- computer structural health analysis decision on maintenance

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 9 10

1. Introduction 2. Geometrical models of textile reinforcement internal architecture

• A model of internal geometry of (2D or 3D) woven fabric
• From geometrical model to finite elements

3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 10

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Road map: Geometrical model of the (deformed) unit cell

Structure: weave / topology / interlacing – contacts, relative positions Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Deformations of the dry fabric: compression, tension, shear, bending FE mesh: Yarn volumes, contacts Textile mechanics Textile mechanics FE “CAD” Meshing

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 11

Road map: Geometrical model of the (deformed) unit cell

Structure: weave / topology / interlacing – contacts, relative positions Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Deformations of the dry fabric: compression, tension, shear, bending FE mesh: Yarn volumes, contacts Textile mechanics Textile mechanics FE “CAD” Meshing

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 12

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Woven fabric: Detailed road map

Weave model Elementary bent intervals Crimp height and yarn thickness Yarn properties Ends/picks count Weave coding Yarn shapes Full description of the geometry Input Distance between the layers

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 13

Weave model: matrix coding

warp zones NWa yarns in a warp zone NWaZ[iWa] weft rows NWe weft layers L

4 1 2 3 1 2 3 4 layer 1 layer 2 level 0 level 1 level 2

            1 2 1 1 2 1 1 1 2 2 1 1

warp 1 warp 2 warp 3 warp 4

1 2-1 2-2 2-3 3 4-1 4-2 4-3 0 4 1 1 2 2 3 3 4 0 1 1 2 2 3 3

1 2 3 4

warp zones

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers S.V. Lomov - Textile Preforms for Composites - 5. Modelling 14

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Elementary bent intervals

base weft yarns elementary bent interval: warp iWa iWa, iWaInt

iWe1 iWe2

Elementary bent interval iWaInt of warp yarn iWa 1. Numbers of base weft yarns iWe1, iWe2 2. Position of the yarn vis-à-vis the base pos1, pos2 pos2 = BELOW pos1 = OVER

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers S.V. Lomov - Textile Preforms for Composites - 5. Modelling 15

Yarn shape in a bent interval – 1

element e    

   

 

   

 

 

e e e e s P B A e e e e s P B A

B A s P W s P B A W

e e e e e e

, | min min ; , min

) ( , , ,

Problem B: find the positions of the ends of the bent interval (crimp heights) Problem A: find the shape P(s) for the given end positions

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers S.V. Lomov - Textile Preforms for Composites - 5. Modelling 16

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Yarn shape in a bent interval – 2

h_We d11_We d21_We d12_We d22_We base contour p d11_Wa h_Wa

• distance between base

contours: picks count

• dimensions: compression

resistance

• crimp height: equilibrium of

bending forces

) ( ; 2 / ) ( ; ) ( ; 2 / ) ( : ) (        p z h p z z h z x z

     

 



     

p

dx z z B W

2 / 5 2 2

min 1 2 1 

 

 

p x x x x x p h A x x h z                      , 2 1 1 1 6 4 2 1

2 2 2 3

z(x)

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 17

Characteristic functions of bent intervals

h_We d11_We d21_We d12_We d22_We p d11_Wa h_Wa

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 A F h/p

     

 

 

             



p h F p B dx z z B W

p

 

2 / 5 2 2

1 2 1

 

          p h F ph B h W Q  2 2

   

 

             



p h F p dx z z p

p

1 1 1

2 / 5 2 2



energy transversal force average curvature z(x) main parameter: h/p main property B(k)

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 18

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Distance between the layers

 

) , , , , , , ( max

2 2 21 21 1 1

, 1 , 1 , 1 , 1 , 2 , 1 , 1 2 1 1 , 1 We jlk We jl We k l j We l j Wa k j We k l j We k l j We jlk We jlk We jl We jl tight k j l l

P h P h d d d d d shape shape z Z Z     

       level 1 level 2

pWe 

shift of the layers

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers

weft j,l+1; interval k2 weft j,l; interval k1

hjl

We

hjl+1

We

warp i

z Zl Zl+1 x

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 19

Compressibility of the yarns d1 d2 Q

5 . ... 3 . 1 2 10 2 2 10 1 1

; ) ( ) (

 

       d Q d d Q d

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers S.V. Lomov - Textile Preforms for Composites - 5. Modelling 20

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Crimp heights: minimum energy – 1

element e    

   

 

   

 

 

e e e e s P B A e e e e s P B A

B A s P W s P B A W

e e e e e e

, | min min ; , min

) ( , , ,

Problem B: find the positions of the ends of the bent interval (crimp heights) Problem A: find the shape P(s) for the given end positions

Weave model Elementary bent intervals Crimp, yarn thickness Yarn prop. Ends / picks Weave coding Yarn shapes Full description of the geometry Input Distance between layers S.V. Lomov - Textile Preforms for Composites - 5. Modelling 21

Crimp heights: minimum energy – 2

x z p h z(x) Q Q d2 d1 Z A B

warp i warp crimp interval k weft j’,l’ weft j’’,l’’ weft crimp interval k’ weft crimp interval k’’

   

min

, , ,

                  

 

 k l j We jlk We jl We jlk We jlk We jlk k i Wa ik Wa ik Wa ik Wa ik Wa ik

p h F p B p h F p B W  

minimum energy:

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 22

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Full system of equations

warp i warp crimp interval k weft j’,l’ weft j’’,l’’ weft crimp interval k’ weft crimp interval k’’

warps NWa weft layers L weft rows NWe

Unknown variables Number Equations Dimensions of warp and weft yarns Vertical positions

• f mid-planes of

weft layers Zl L Weft crimp heights L*NWe

         



  L l NWe j jl

K NWe NWa

1 1

2

We jl

h

1 10 1 2

...

ij l Wa Wa Wa ik i i Wa ik

Q d d d 

 

                                                          

                      We k jl We jl We jl We k jl We jl We k jl We jl We jl We k jl We jl Wa k i Wa k i Wa k i Wa k i Wa i Wa k i Wa k i Wa k i Wa k i Wa i ijl

p h F h p B p h F h p B p h F h p B p h F h p B Q

1 1 1 1 1 1

2 1 2 1

 

) , , , , , , ( max

2 2 21 21 1 1

, 1 , 1 , 1 , 1 , 2 , 1 , 1 2 1 1 , 1 We jlk We jl We k l j We l j Wa k j We k l j We k l j We jlk We jlk We jl We jl tight k j l l

P h P h d d d d d shape shape z Z Z     

      

   

min

, , ,

                  

 

 k l j We jlk We jl We jlk We jlk We jlk k i Wa ik Wa ik Wa ik Wa ik Wa ik

p h F p B p h F p B W  

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 23

The flowchart of the solution

hWe

lj=0

calculate Q for all contacts warp/weft calculate d for all contacts warp/weft calculate Zl solve energy equation (l,j) for hWe

lj, all other

hWe given max|hWe

lj- holdWe lj|<prec

no yes

h,%

0 2 4 6 5 10 15 iterations

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 24

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Description of internal geometry

O r(s)

X Y Z 

t a1 a2 O d2 d1

Each segment:

• direction
• curvature
• two dimensions
• average Vf

Unit cell: dimensions X,Y,Z number of yarns Each yarn: set of segments

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 25

Examples of calculations of internal geometry of 3D fabrics/composites

Glass 3D woven: X-ray µCT and simulated Carbon/epoxy 3D woven: simulated and real cross-sections

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 26

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Visualisation

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 27 28

1. Introduction 2. Geometrical models of textile reinforcement internal architecture

• A model of internal geometry of (2D or 3D) woven fabric
• From geometrical model to finite elements

3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 28

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Road map: Geometrical model of the (deformed) unit cell

Structure: weave / topology / interlacing – contacts, relative positions Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Deformations of the dry fabric: compression, tension, shear, bending FE mesh: Yarn volumes, contacts Textile mechanics Textile mechanics FE “CAD” Meshing

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 29

A gallery of finite element models

3-axial braid knitted plain weave 3D woven stitched NCF

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 30

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meso-FE: Road map

Geometric modeller Geometry corrector Meshing Assign material properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

N+1 N N+2

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 31

meso-FE: Road map

Geometric modeller Geometry corrector Meshing Assign material properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

N+1 N N+2

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 32

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Yarn volumes

O r(s)

X Y Z 

t a1 a2 O d2 d1 P f Vf

Fibre structure of the yarns Solid model

N+1 N N+2

Orthotropy of the impregnated yarns

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 33

Orthotropy of the impregnated yarns

2 1 3

 

              

f m f m m f t f

E E V E E E E V E V E

22 33 22 11 11

1 1 1                       

f m f m f m f m

G G V G G G G V G G G

23 23 12 13 12

1 1 1 1

 

1 2 1

23 22 23 12 13 12

      G E V V

m f f f

     Chamis model

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 34

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Interpenetration of the volumes

no interpenetration (rare) “vertical” interpenetration complex interpenetration The correction of the geometry should preserve:

• verall fibre volume fraction in the composite (dimensions of the unit cell and

amount of fibres in all the yarns)

• average fibre volume fraction in the yarns in realistic bounds (< 70…75%)

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 35

Manual correction

1 2 3

p0 1 p11 p0 2 p1 2 s1 s2 p0 1 p11 s1 s2 1 p01=p11 P02=p1 2 s1 s2 p01=p11 6 2 3 4 5 7 1

• 1. First interpenetration type
• 2. Second interpenetration type
• 3. Third interpenetration type

6 2 3 4 5 7 1

[1]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 36

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Interpenetration of the volumes: correction via inermediary FEA z

• z

Deformation Splitting Separation

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 37

Example of the volume correction: 3-axial braid

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 38

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Contact surfaces

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 39

Mesh interpolation

x z y

sx sx

x z y 320(MPa) 60(MPa)

fine mesh Global and local mesh

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 40

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Voxels

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 41 42

1. Introduction 2. Geometrical models of textile reinforcement internal architecture 3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 42

22 What is a forming simulation?

Given: 1. Preforms characterisation 2. Mould geometry 3. Mould temperature 4. Forming speed Calculate: 1. Wrinkling 2. Waste 3. Local shear and other local parameters of the reinforcement

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 43

Optimise forming operation

1. Mould geometry (radii of curvature...) 2. Blank orientation 3. Configuration of a blank-holder and blank-holder tension 4. Forming temperature and evenness of the temperature distribution 5. Forming speed main optimisation parameter: WRINKLING

[2]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 44

23 Optimise impregnation

Permeability of textile depends on local volume fraction and local shear Local volume fraction and local shear depend on local deformation Local deformation depends on draping of the preform

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 45

Forming  impregnation The front is not round – the preform is anisotropic Distribution of shear angles  local permeability

shear angles impregnation: PAM-RTM

images: ESI Group

Drape: PAM-QuikForm front movement

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 46

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Example

Constant permeability Accounting for the preform deformation

images: ESI Group

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 47

Optimise performance

Stiffness of composite depends on local orientation of the fibres Local orientation of the fibres depends on local deformation Local deformation depends on draping of the preform

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 48

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Forming  structural analysis

WiseTex Local deformation parameters (thickness, shear…) Forming: QUIKFORM Internal geometry Local stiffness [Q] FE analysis: SYSPLY

Stress/strain fields

TexComp

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 49

Key result: Distribution of shear angle of the preform



locking

images: Kristof Vanclooster

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 50

26 Cloth draping

Well advanced simulations of garments

[3]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 51

Principle of kinematic draping simulation

1. NO mechanical properties 2. DEPENDS on the initial choice of principal directions

[4]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 52

27 Good predictions for symmetrical configurations...

warp parallel to the cylinder axis

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 53

… may be very bad for asymmetrical situations

warp at 45° to the cylinder axis assumed in kinematic draping and real advancement of draping

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 54

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Finite element simulations of draping: Example – 1

[5]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 55

Expicit FE solution

[5]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 56

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Stages of PAM-FORM analysis

[6]

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 57

Material model for textile fabrics – 1

shear diagram viscous matrix non-linear tension

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 58

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Material model for textile fabrics – 2

0.002 0.004 0.006 0.008 0.01 0.012 0.014 10 20 30 40 50 Shear angle, ° Shear force, N/mm

50 100 150 200 250 300 0.2 0.4 0.6 0.8 1

EpsX, % Fx per yarn, N

effective viscosity is different from the viscosity of the matrix shear tension viscosity

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 59

Problems of kinematic draping solved!

kinematic draping PAM-FORM

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 60

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WiseTex models of deformations of textiles

Compression Uni- and Biaxial tension Shear

(un)bending + compression of yarns work of compressive force Q on change of thickness db = change of bending energy of yarns dW

d2Wa d2We q d1Wa d1We Qij

 T T Q h

Wa

p

• Friction between the yarns
• Lateral compression of the yarns
• (Un) bending of the yarns
• Torsion of the yarns
• Vertical displacement of the yarns

T T Q

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 61

FE modelling of deformations of textiles

images: Ph. Boisse

shear tension

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 62

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63

1. Introduction 2. Geometrical models of textile reinforcement internal architecture 3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 63

Simulation of impregnation

Input:

• mould geometry
• permeability of the textile
• resin viscosity
• positions of inlets and

vents

• pressure drop

Output:

• movement of the flow front
• dry spots
• impregnation time

       p Κ grad v 

Darcy equation

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 64

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Solution of Darcy equation

       p Κ grad v 

Assumption: front moves with velocity <v> = ideal wetting inlets vents front iso-chrones

Meyer et al 2004 S.V. Lomov - Textile Preforms for Composites - 5. Modelling 65

Calculation of preform permeability

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections “Voxels” Meshing Voxel-mesh FE mech (Navier-) Stokes solver Fabric permeability Analytical “Hydraulic”

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 66

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Darcy permeability: homogenised (Navier-) Stokes solution p = 0

<u> <u>

p = p u(A) - u(A´) = const(A) AA´= periodic translation A A´

x y z

K K K            K

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 67

Geometrical models and voxel mesh Reinforcement model Voxel model

woven, monofilaments quasi-UD woven, carbon non-woven, glass NCF, carbon

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(Navier-) Stokes solution

Requirements:

• Automated
• Fast and accurate
• Accurate in narrow channels
• Periodic boundary conditions
• Sheared unit cell

Implementation:

• Navier-Stokes:

(adapted) NaSt3d staggered grid

• Stokes

collocated grid stabilisation term PETSc package, GMRES(m) Navier-Stokes: staggered grid, difficulty with isolated cells F S F

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 69

Boundary conditions: faces of the unit cell and internal boundaries

wall and internal boundary Г velocity pressure (Stokes equation) => Re = 0.05

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FlowTex: Integration with WiseTex and GUI

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 71

Experimental validation: Overview

Ky Kx

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37

Coupled meso-macro simulation

WiseTex Local reinforcement deformation Process model Local reinforcement geometry Local permeability

[K]

Filling simulation

Processing parameters

FlowTex

stand-alone application

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Necessary performance of mass-simulations

10,000 finite elements

• r…

90 values of shear angles (0°, 1°, 2°…) and 5 degrees of compression = = about 450 calculation variants 3h calculation time  2 s per fabric configuration

5 s

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38

75

1. Introduction 2. Geometrical models of textile reinforcement internal architecture 3. Models of textile reinforcement deformability 4. Models of textile reinforcement permeability 5. Mechanical properties of textile composites, damage 6. Conclusion: Models integration

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Road map: Micromechanics of textile composites

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections “Voxels” Meching Voxel - partitioning FE mesh FE Stiffness Orientation averaging Inclusions Stress-strain fields, damage

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39

Stiffness: Simple model neglecting yarn crimp

90 90 90 90 90

P T P T h h h h h VF VF VF     

woven laminate  UD laminate

two plies representing warp and weft

90° 0° h_0° h_90° linear density of warp/weft and ends/picks count Assumption: iso-strain

90

C C C h h h h

90

 

Stiffness matrix Approximation: Young’s modulus

90 90

E h h E h h E  

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Orientation averaging

The textile structure is subdivided into elements; each element is represented by a UD composite CSi GCS Vi

       

 

   

      

N i i N i i i i m eff

V V V GCS CS V GCS GCS

1 1

; 1 C C C

effective stiffness of the composite matrix stiffness stiffness of elements Assumption: iso-strain

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40

S.V. Lomov - Textile Preforms for Composites - 5. Modelling

Example: 3D woven glass/epoxy composite

exp OA E1, GPa 24.3±1.2 22.7 E2, GPa 25.1±2.34 22.8 E3, GPa n/a 10.1 G12, GPa n/a 3.38 ν12 0.141±0.071 0.109 ν13 n/a 0.377 ν23 n/a 0.380 E45º, GPa 12.9±0.5 10.7 G45º, GPa n/a 10.3 ν45º 0.502±0.21 0.581 Vf, % E1,GPa E2,E3, GPa 12 , 13 23 G12, G13, GPa G23, GPa 3D weave, warp 2275 tex 64.1 47.2 10.8 0.266 0.440 4.24 3.73 3D weave, warp 1100 tex 60.1 44.5 9.7 0.271 0.445 3.79 3.35 3D weave, Z 276 tex 78.0 56.8 16.7 0.252 0.414 6.73 5.9 3D weave, fill 1470 tex 59.1 43.7 9.44 0.272 0.447 3.69 3.26

W F Z W

Elastic properties of the impregnated yarns

Areal density, g/m2 3255 Thickness, mm 2.6 Ends, 1/cm 2.76

• Picks. 1/cm

2.64 Z-yarns, 1/cm 2.76 VF, % 48.9

79

Method of Inclusions: Yarns as a collection of curved segments

[C]

The yarn segment is NOT circular, but has two different diameters

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81

Curved segment as an equivalent ellipsoidal inclusion

, 3.14 b R a a    

R 2a 2b 1. Volume fraction of each equivalent ellipsoid in the unit cell corresponds to the volume fraction of the segment which it represents. 2. The elongation of the equivalent ellipsoid depends on the curvature of the segment. 3. The stiffness of the ellipsoid inclusion is equal to the homogenised local stiffness in the segment. 4. For a non-circular yarn the ellipsoid has all the three axis different 5. The equivalent ellipsoids are NOT a physical substitution of the yarn segments; they are merely mathematical means to calculate the stress-strain states in the segments, using Eshelby tensors

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Flowchart

Geometrical preprocessor Textile data Internal geometry of textile and partitioning into segments Segment processor Matrix and fibre data Assembly of equivalent ellipsoidal inclusions Mori – Tanaka homogenisation Homogenisation

• n micro-level

Homogenised stiffness

• f the composite

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42 Software: WiseTex and TexComp (KULeuven) Models of textile geometry and deformability Predictive models of composites mechanics

Models of internal structure and deformation of unit cell of textile reinforcement:

• woven 2D and 3D
• braided bi- and triaxial
• knitted

Homogenisation of stiffness of textile composite, based on the method of inclusions: any textile reinforcement described by WiseTex, including deformed (sheared, compressed, tensed)

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Comparison

5.13 4.95 5.65 5.25 5.44

0.00

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

GE001_G

GE002_G GE012_G

G

W iseTex/ TexCom p Experim ent

glass/epoxy

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43 Stiffness prediction: FE and inclusions

exp OA Inclusions FE @49.3 E1, GPa 24.3±1.2 22.7 24.2 23.6 E2, GPa 25.1±2.34 22.8 24.2 23.7 E3, GPa n/a 10.1 9.1 9.5 ν12 0.141±0.071 0.109 0.161 0.128 ν13 n/a 0.377 0.370 0.365 ν23 n/a 0.380 0.368 0.359

no real need in FE for the stiffness prediction

W F Z W

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Road map: Micromechanics of textile composites

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections “Voxels” Meching Voxel - partitioning FE mesh FE Stiffness Orientation averaging Inclusions Stress-strain fields, damage

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44

87

meso-FE: Road map

Geometric modeller Geometry corrector Meshing Assign material properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

N+1 N N+2

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Solving meso-FE problem

   

 

   

 

           

| | ( ) | ( ) |

Homogenised stiffness : 0; 1 2 1 1

ijkl kpq l j ipq ipq q ip p iq pq ij ijkl kpq l kl ijkl ijpq pkl q ij UC UC UC UC

C U U U C U C C U d d V V       s       s           

 

C 2 1

     

( ) ,

Local stress-strain field =

pq ij p q ij

v s s  x x      

, ,

Homogenised stress-strain field ( )

ijkl k lj i i ij ijkl k l

C u f u v C u  s

 

         u x x x x x x



FE FE

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89

Example: Finite element model of 3D woven composite

Mesh in the yarns Full mesh Clearance between yarns 0.005 mm Resin layer on the surface 0.005 mm VF 43.7% (WiseTex: 48.9%) Total elements 20768 Penetrating nodes corrected 3000 Max aspect ratio 469 Max aspect ratio in yarns 60

WiseTex Tex MeshTex Tex

Correct representation of measurable parameters:

• areal density
• thickness
• verall fibre volume fraction
• ends/picks count
• yarn dimensions

Simplifications:

• elliptical shape of yarn cross-sections
• constant dimensions of Z-yarns
• VF inside yarns up to 90% (Z-yarns)

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Strains on the surface of the composite

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46

Stress-strain diagram

50 100 150 200 250 300 350 400 450 500 0.5 1 1.5 2 2.5 3 eps, % sig, MPa exp

elastic solution

S.V. Lomov - Textile Preforms for Composites - 5. Modelling 91 92

Damage model – 1

Damage initiation: Hoffmann

2 9 2 8 2 7 6 5 4 2 3 2 2 2 1

) ( ) ( ) (

LT ZL TZ Z T L T L L Z Z T

C C C C C C C C C F    s s s s s s s s s                                                                                                 

2 9 2 8 2 7 6 5 4 3 2 1

1 , 1 , 1 1 1 , 1 1 , 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1

s LT s ZL s TZ c Z t Z c T t T c L t L c Z t Z c T t T c L t L c T t T c L t L c Z t Z c L t L c Z t Z c T t T

F C F C F C F F C F F C F F C F F F F F F C F F F F F F C F F F F F F C

Definition of the damage mode

L T Z

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93

Damage model – 2

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Tensile diagrams, 3D composite

• correct modelling of degradation
• f stiffness
• reasonable evaluation of damage

initiation threshold

• qualitative representation of

intensity of damage

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95

Progressive damage, 3D composite

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References

1. Bedogni, E., D.S. Ivanov, S.V. Lomov, A. Pirondi, M. Vettori, and I. Verpoest, Creating finite element model of 3D woven fabrics and composites: semi-authomated solution of interpenetration problem, in 15th European Conference on Composite Materials (ECCM-15). 2012: Venice. p. electronic edition, s.p. 2. Lamers, E.A.D., S. Wijskamp, and R. Akkerman, Modelling shape distortions in composite products, in Proceedings ESAFORM-2004. 2004:

• Trondheim. p. 365-368.

3. http://www.optitex.com/ 4. Sozer, E.M., S. Bickerton, and S.G. Advani, On-line strategic control of liquid composite mould filling process. Composites Part A: Applied Science and Manufacturing, 2000. 31(12): p. 1383-1394. 5. http://www.esi-group.com/ 6. Duhovic, M., P. Mitschang, and D. Bhattacharyya, Modelling approach for the prediction of stitch influence during woven fabric draping. Composites Part A, 2011. 42: p. 968–978.

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