Lomov Manchester 3D - KU Leuven · 2010-11-13 · Manchester 3D textiles - April 2008 1 Modellingof...
Transcript of Lomov Manchester 3D - KU Leuven · 2010-11-13 · Manchester 3D textiles - April 2008 1 Modellingof...
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
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
Contents
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
Manchester 3D textiles - April 2008 4
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
Manchester 3D textiles - April 2008 5
Road map: Permeability 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”
Manchester 3D textiles - April 2008 6
Road map: Micromechancis of 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
Manchester 3D textiles - April 2008 7
WiseTex implementation
Predictive models of composites mechanics
Models of textile geometry and deformability
Predictive models of textile permeability
FE packages
Textile VR
Manchester 3D textiles - April 2008 8
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
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
Manchester 3D textiles - April 2008 10
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
Manchester 3D textiles - April 2008 11
“Alternating” / “missing” wefts
more on the poster: G. Perie
Manchester 3D textiles - April 2008 12
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
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
Manchester 3D textiles - April 2008 14
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
Manchester 3D textiles - April 2008 15
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
Manchester 3D textiles - April 2008 16
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
Manchester 3D textiles - April 2008 17
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
more on the poster: G. Perie
Manchester 3D textiles - April 2008 18
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
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 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
Manchester 3D textiles - April 2008 20
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
Manchester 3D textiles - April 2008 21
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.
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
Manchester 3D textiles - April 2008 23
Yarns as a collection of curved segments
[C]
The yarn segment is NOT circular, but has two different diameters
Manchester 3D textiles - April 2008 24
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
Manchester 3D textiles - April 2008 25
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
Manchester 3D textiles - April 2008 26
Example: Stiffness of 3D woven carbon/epoxy composites
more on the poster: G. Perie
change: picks spacing
Exx Eyy
Manchester 3D textiles - April 2008 27
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
Manchester 3D textiles - April 2008 28
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
Manchester 3D textiles - April 2008 29
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 …
Manchester 3D textiles - April 2008 30
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
Manchester 3D textiles - April 2008 31
Look at this!