Lomov Manchester 3D - KU Leuven · 2010-11-13 · Manchester 3D textiles - April 2008 1 Modellingof 3D woven fabrics and 3D reinforced composites: Challenges and solutions Stepan

Manchester 3D textiles - April 2008 1

Modellingof 3D woven fabrics and 3D reinforced composites: Challenges and solutions

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

Department MTM, Katholieke Universiteit Leuven


Modelling a 3D woven fabric/composite: Road map

… Coding the STRUCTURE …

… Modelling the GEOMETRY …

… Calculating COMPRESSION, TENSION and SHEAR (without FE?) …

… Calculating composite MICROMECHANICS (no need of FE!) …

… Building the finite element MESH …

… and BEYOND

Contents








… and BEYOND


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


Road map: Permeability of the fabric


“Voxelisation” Meshing

Voxels in the unit cell Mesh of the unit cell

(Navier-) Stokes solver

Permeability of the fabric

Analytical

“Hydraulic”


Road map: Micromechancis of composite


“Voxelisation” Meshing

Voxels in the unit cell Mesh of the unit cell

FE

Stiffness of the composite

Orientation averaging

Inclusions

Stress/strain fields; damage


WiseTex implementation

Predictive models of composites mechanics

Models of textile geometry and deformability

Predictive models of textile permeability

FE packages

Textile VR


Historical note

St.-Petersburg State University of Technology and Design

Institute of Technical Felts / “Nevskaya Manufactura”

• 1990 First version (DOS) of CETKA (=“net” in Russian) software: Internal geometry, mechanical properties and permeability of woven fabrics (one- and multi-layered)

• 1993 Windows version of CETKA

• 1998 CETKA 3.1, implementing “true” 3D fabric

• 1999 CETKA-KUL, including modules to transfer the data to micro-mechanical models of KUL

Katholieke Universiteit Leuven, Department MTM: WiseTex








… and BEYOND


Warp interlacing: Matrix coding

4

1 2 3

1 2 3 4 layer 1

layer 2

level 0

level 1

level 2

»»»»

¼

º

««««

¬

ª

1210

01211012

2101warp 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


“Alternating” / “missing” wefts

more on the poster: G. Perie


Coding: Challenges

The matrix coding covers all the warp-interlaced multi-layered weaves. It is implemented in easy-to-use graphical editor.

Challenges:

Connect the 3D weave coding with the coding used to control the loom (ScotWeave ?)

Weave architectures, not covered currently:

• Different weave count in the layers

• Weft-interlaced weaves

• “True” 3D weaves








… and BEYOND Structure: weave / topology / interlacing– contacts, relative positions


Textile mechanics


Fabric weave, given by a matrix of warp levels

Compression and bending behaviour of warp and weft

- any number of different types of yarns

Spacing of warp and weft yarns

- can be non-uniform

Shift between the weft layers in the warp direction.

- defined by the weft insertion and battening process.

Input data

4

1 2 3

1 2 3 4 layer 1

layer 2

level 0

level 1

level 2

»»»»

¼

º

««««

¬

ª

1210

01211012

2101warp 1

warp 2

warp 3

warp 4

pWa

mid-level 1mid-level 2

pWe'

d1

d2

Q


Elementary crimp interval

x

z

p

h z(x)

Q

Q

d2

d1

'Z

A

B

0)(;2/)(;0)0(;2/)0(:)( c� c pzhpzzhzxz

� � � �� ³ oc�cc

p

dxz

zBW

02/52

2

min12

1 N

� � � �px

xxxxph

Axxhz ¹̧

·©̈§ ��¸̧¹

·¨̈©§�� ,

21

116421 2223

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

A

F

h/p

� � � �� ¸̧¹

·¨̈©§ c�

cc ³ ph

Fp

Bdx

z

zBW

p NN0

2/52

2

121

� � ¸̧¹·¨̈©

§ ph

FphB

hW

QN22

� �� ¸̧¹

·¨̈©§ c�

cc ³ ph

Fp

dxz

zp

p 1

1

1

02/52

2

N

Characteristic functions of the crimp interval are pre-calculated and defined by the ratio h/p

Elastica approach is used for calculation of the characteristic functions


From the weave coding to the internal geometry of the fabric

warp i

warp crimp interval k

weft j’,l’

weft j’’,l’’

weft crimp interval k’

weft crimp interval k’’

weft j,l+1; interval k2

weft j,l; interval k1

hjlWe

hjl+1We

warp i z

Zl

Zl+1

'x

L*NWeWeft crimp heights

LVertical positions of mid-planes of weft layers Zl

Dimensions of warp and weft yarns

EquationsNumber Unknown variables

¸̧¹·

¨̈©§ �� ¦¦

� �

L

l

NWe

jjlKNWeNWa

1 1

2

Wejlh

1 10 12

...ij lWa Wa Waik i i Wa

ik

Qd d

dK � �§ · ¨ ¸© ¹ ¸̧¹

·¨̈©§

¸̧¹·

¨̈©§�¸̧¹

·¨̈©§�

¸̧¹·

¨̈©§

¸̧¹·¨̈©

§�¸̧¹·¨̈©

§

��

��

��

��

Wekjl

Wejl

Wejl

Wekjl

Wejl

Wekjl

Wejl

Wejl

Wekjl

Wejl

Waki

Waki

Waki

Waki

Wai

Waki

Waki

Waki

Waki

Wai

ijl

p

hF

hp

B

p

hF

hp

B

ph

Fhp

Bph

Fhp

BQ

11

1

1

11

21

21

� �)

,,,,,,(max

22

212111

,1,1,

1,1,2,1,1211,

1

Wejlk

Wejl

Weklj

Welj

Wakj

Weklj

Weklj

Wejlk

Wejlk

Wejl

Wejltight

kjll

PhPh

dddddshapeshapezZZ

��'�

��

��

� � � �min

,,,

o¸̧¹·

¨̈©§�¸̧¹

·¨̈©§ ¦¦�

kljWejlk

Wejl

Wejlk

Wejlk

Wejlk

kiWaik

Waik

Waik

Waik

Waik

p

hF

p

B

ph

Fp

BW

NN


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

Glass 3D woven: X-ray µCT and simulated

Carbon/epowy 3D woven: simulated and real cross-sections



Geometry: Challenges

1. Solution of the minimum energy problem: ill-defined optimisation problem, leading to instability in certain cases

2. Approximate assumptions in the geometrical model:

Flat middle surfaces of the weft layers

Constant crimp height for different crimp intervals of the same weft yarn

3. Symmetric and rigid shape of the cross-sections in the current algorithm. This leads to difficulties for high VF of the composite








… and BEYONDGeometry: 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

Textile mechanics


Models of textile deformability

Compression Biaxial and uniaxial tension

Shear Tension along warp

0

10

20

30

40

50

60

70

80

0 10 20 30 40

Deformation, %

Forc

e pe

r ya

rn, N

warp yarn computed

measured

measurements: Ph. Boisse


Deformability: Challenges

1. Approximate models:

contact regions

uncoupled bending/compression; tension/compression … resistance

lateral compression of the yarns

…

2. Limited validation. There are not many experimental data on deformability of 3D fabrics, hence validation of the models is limited.

3. Dead end. The “textile mechanics” models are a “dead end” for approximate textile mechanics. An attempt to make more complex and elaborate treatment of the interaction of the yarns encounters difficulties, which lead to finite element formulation of the problem. This gives generality to the solution – but throws away easy and mechanically clear formulation and speed of the calculations.








… and BEYOND


Stiffness of the composite

Inclusions


Yarns as a collection of curved segments

[C]

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


Curved segment as an equivalent ellipsoidal inclusion

, 3.14b Ra a

E E |

R2a

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


The result: assembly of equivalent inclusions

� � � ��

111

1

1

Strain concentration tensors:

,

Effective stiffness of the composite:

Mm m

m m m m

Meff m m

c c where

c

D D E D DD DE

E

D DD

D

� ��

§ · ª º � � �¨ ¸ « »¬ ¼© ¹

� �

¦

¦

A A I A A I S C C C

C C C C A Mori – Tanaka


Example: Stiffness of 3D woven carbon/epoxy composites


change: picks spacing

Exx Eyy








… and BEYOND


Interpenetration of yarn volumes: two approaches

Correction of the interpenetrating mesh in MeshTex – M. Zakoet al, Osaka University

MultiFil: Correction of yarn volumes build with WiseTex (left) into non-penetrating configuration (right) – D. Durville, Ecole Centrale Paris


Bogdanovich, A.E., Multi-scale modeling, stress and failure analyses of 3-D woven composites. Journal of Materials Science, 2006. 41(20): p. 6547-6590

Lomov, S.V., D.S. Ivanov, I. Verpoest, M. Zako, T. Kurashiki, H. Nakai, and S. Hirosawa Meso-FE modelling of textile composites: Road map, data flow and algorithms. Composites Science and Technology, 2007. 67: p. 1870-1891

…and beyond …


Conclusions

There exists a serious baggage of modelling approaches for 3D woven fabrics, implemented in software tools, which allows:

• Creation and easy varying weave architectures, (almost) without restriction of number of the yarns, layers, interlacing pattern or other complexity factors of the fabric weave

• Creation of geometrical models of internal structure of 3D fabrics, adequately representing yarn paths (hence crimp factors, hence overall parameters of the fabric, as areal density, tightness, porosity…)

• Calculation (with certain reservations vis-à-vis precision) of mechanical response of the fabric to compression, tension and shear

• Modelling of the geometry of deformed fabric

• Translation of the fabric geometry model into finite element model

• Calculation of effective properties of textile composites with precision conforming to requirements of macro-structural analysis of composite part

• Building meso-level FE models of unit cell of 3D woven composite and approach the problem of damage prediction

• Calculation of permeability of 3D textile


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Lomov Manchester 3D - KU Leuven · 2010-11-13 · Manchester 3D textiles - April 2008 1 Modellingof 3D woven fabrics and 3D reinforced composites: Challenges and solutions Stepan