Modellingof 3D woven fabrics and 3D reinforced composites: C - - PowerPoint PPT Presentation

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Modellingof 3D woven fabrics and 3D reinforced composites: C - - PowerPoint PPT Presentation

Apr 08, 2024 305 likes •637 views

Modellingof 3D woven fabrics and 3D reinforced composites: C hallenges and solutions Stepan V. LOMOV, Dmitry S. IVANOV, Guillaume PERIE, Ignaas VERPOEST Department MTM, Katholieke Universiteit Leuven 1 Manchester 3D textiles - April 2008

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Manchester 3D textiles - April 2008 1

Modellingof 3D woven fabrics and 3D reinforced composites: C hallenges and solutions

Stepan V. LOMOV, Dmitry S. IVANOV, Guillaume PERIE, Ignaas VERPOEST Department MTM, Katholieke Universiteit Leuven

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Manchester 3D textiles - April 2008 2

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

C

  • ntents
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Manchester 3D textiles - April 2008 3

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

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Manchester 3D textiles - April 2008 4

R

  • ad map: G

eometrical 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

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Manchester 3D textiles - April 2008 5

R

  • ad map: P

ermeability of the fabric

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections “Voxelisation” Meshing Voxels in the unit cell Mesh of the unit cell (Navier-) Stokes solver Permeability of the fabric Analytical “Hydraulic”

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R

  • ad map: Micromechancisof composite

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections “Voxelisation” Meshing Voxels in the unit cell Mesh of the unit cell FE Stiffness of the composite Orientation averaging Inclusions Stress/strain fields; damage

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WiseTex implementation

P redictive models of composites mechanics Models of textile geometry and deformability P redictive models of textile permeability F E packages T extile VR

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H istorical 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

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Manchester 3D textiles - April 2008 9

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

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Warp interlacing: Matrix coding

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

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Manchester 3D textiles - April 2008 11

“A lternating” / “missing” wefts

more on the poster: G. Perie

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C

  • ding: C

hallenges

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
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Manchester 3D textiles - April 2008 13

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

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 Textile mechanics

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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

  • 1

2 1 1 2 1 1 1 2 2 1 1

warp 1 warp 2 warp 3 warp 4

pWa

mid-level 1 mid-level 2

pWe

  • d1

d2 Q

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E lementary crimp interval

x z p h z(x) Q Q d2 d1 Z A B

) ( ; 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 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

  • 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

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F rom 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

hjl

We

hjl+1

We

warp i

z Zl Zl+1 x

L*NWe Weft crimp heights L Vertical positions of mid-planes of weft layers Zl Dimensions of warp and weft yarns Equations Number Unknown variables

  • 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

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E xamples 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 more on the poster: G. Perie

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G eometry: C hallenges

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

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Manchester 3D textiles - April 2008 19

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

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 Textile mechanics

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Models of textile deformability

Compression Biaxial and uniaxial tension Shear

Tension along warp

10 20 30 40 50 60 70 80 10 20 30 40 Deformation, % Force per yarn, N

warp yarn computed measured

measurements: Ph. Boisse

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D eformability: C hallenges

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.

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Manchester 3D textiles - April 2008 22

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

Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Stiffness of the composite Inclusions

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Y arns as a collection of curved segments

[C]

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

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C urved 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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T he result: assembly of equivalent inclusions

  • 1

1 1 1 1

Strain concentration tensors: , Effective stiffness of the composite:

M m m m m m m M eff m m

c c where c

  • A

A I A A I S C C C C C C C A

Mori – Tanaka

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E xample: S tiffness of 3D woven carbon/epoxy composites

more on the poster: G. Perie change: picks spacing Exx Eyy

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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

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Interpenetration of yarn volumes: two approaches

Correction of the interpenetrating mesh in MeshTex – M. Zako et al, Osaka University MultiFil: Correction of yarn volumes build with WiseTex (left) into non-penetrating configuration (right) – D. Durville, Ecole Centrale Paris

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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 …

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C

  • nclusions

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
  • f 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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L

  • ok at this!