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
C ontents 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 2 Manchester 3D textiles - April 2008
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 3 Manchester 3D textiles - April 2008
R oad map: G eometrical model of the (deformed) unit cell Structure: weave / topology / interlacing – contacts, relative positions Textile mechanics “CAD” Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Meshing Textile mechanics FE mesh: Yarn volumes, contacts Deformations of the dry fabric: compression, tension, shear, bending FE 4 Manchester 3D textiles - April 2008
R oad map: P ermeability of the fabric Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Analytical “Voxelisation” Meshing “Hydraulic” Voxels in the unit cell Mesh of the unit cell (Navier-) Stokes solver Permeability of the fabric 5 Manchester 3D textiles - April 2008
R oad map: Micromechancisof composite Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections Orientation “Voxelisation” Meshing averaging Inclusions Voxels in the unit cell Mesh of the unit cell FE Stiffness of the composite Stress/strain fields; damage 6 Manchester 3D textiles - April 2008
WiseTex implementation P redictive Models of textile geometry models of and deformability composites mechanics P redictive models of T extile VR textile permeability F E packages 7 Manchester 3D textiles - April 2008
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 8 Manchester 3D textiles - April 2008
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 9 Manchester 3D textiles - April 2008
Warp interlacing: Matrix coding 1 2 3 level 0 1 0 1 2 � � warp 1 1 layer 1 2 3 4 � � 2 1 0 1 level 1 warp 2 � � 1 2 1 0 warp 3 � � layer 2 � � warp 4 0 1 2 1 � � 4 level 2 3 0 4 1 4-1 1 1 2 2 2 1 2-1 4-2 3 3 3 4 0 2-2 1 1 4-3 2 2 4 2-3 3 3 warp zones 10 Manchester 3D textiles - April 2008
“A lternating” / “missing” wefts more on the poster: G. Perie 11 Manchester 3D textiles - April 2008
C oding: 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 12 Manchester 3D textiles - April 2008
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 Textile mechanics Geometry: Placement of the yarns inside the (deformed) unit cell – yarn paths / directions / twist – yarn volumes / cross-sections 13 Manchester 3D textiles - April 2008
Input data 1 2 3 level 0 1 0 1 2 � � warp 1 1 layer 1 2 3 4 � � 2 1 0 1 Fabric weave, given by a matrix of warp levels level 1 warp 2 � � 1 2 1 0 warp 3 � � layer 2 � � warp 4 0 1 2 1 � � 4 level 2 Compression and bending behaviour of warp and weft - any number of different types of yarns Q d 2 d 1 Spacing of warp and weft yarns - can be non-uniform Shift between the weft layers in the warp direction. p Wa - defined by the weft insertion and battening process. mid-level 1 mid-level 2 � p We 14 Manchester 3D textiles - April 2008
E lementary crimp interval 6 z 5 4 A A 3 Q 2 h z(x) d 1 F 1 x � Z Q p 0 0 0.2 0.4 0.6 0.8 1 B d 2 h/p p 2 1 z B h � � � � � � � � � W B dx F z ( x ) : z ( 0 ) h / 2 ; z ( 0 ) 0 ; z ( p ) h / 2 ; z ( p ) 0 � � � � � � � � � � � � � � � � � 5 / 2 2 p p 2 � � 1 z � � � � � � 0 p 2 2 W 2 B h 1 z � � � � � � � � � Q F W B dx min � � � � � � � � � � � � 5 / 2 h ph p 2 2 � � 1 z � � � � � � 0 p 2 1 z 1 h z 1 h 1 x � � � � � � � � 2 � � 3 2 2 � � 4 x 6 x 1 A x x 1 x , x � � dx F � � � � � � � � � � � � � � � � � � � h 2 p 2 p 5 / 2 � � p p p 2 � � � � � � 1 z � � � � � � 0 Elastica approach is used for Characteristic functions of the crimp calculation of the characteristic interval are pre-calculated and functions defined by the ratio h/p 15 Manchester 3D textiles - April 2008
✄ ✄ ✁ ✂ ✂ ✄ ✂ ✄ ✄ ✂ ✄ ✄ ✄ ✄ ✄ ✄ � � ✄ ✄ ☎ ✂ ✄ ☎ ✂ ✄ ✁ ✆ ☎ ✝ ☎ ✄ ☎ ☎ F rom the weave coding to the internal geometry of the fabric weft crimp interval k’ weft j,l ; interval k 1 warp crimp interval k � x Z l We h jl We Z l+1 h jl+1 warp i weft j’,l’ z weft j,l+1 ; interval k 2 warp i weft crimp interval k’’ weft j’’,l’’ Unknown variables Number Equations Wa Wa Wa Wa B h B h 1 � � � � � � i i k i i k 1 Q F F � � � � � � � � ijl Wa Wa � Wa � Wa Wa � Wa � � � 2 p h p p h p � � � � � i k i k i k i k 1 i k 1 i k 1 � Dimensions of warp We We We We B h B h 1 � � � � � � L NWe Q � � � � jl jl jl jl and weft yarns � � Wa Wa Wa ij l F � � F � � 2 NWa NWe K d d ... � � � � � � �� � � jl 1 10 1 � � We We We We We We ik i i Wa 2 � � � � � � � p h p p h p � d l 1 j 1 � � � � jl k jl jl k jl k 1 jl jl k 1 2 ik � � � � � � Vertical positions of L We We We We We We Wa Z Z max ( z � shape , shape , d , d , d , d , d � � � � mid-planes of weft l 1 l tight jl jl 1 1 jlk 2 jlk 1 j , l 1 , k 2 j , l 1 , k 1 j k 1 1 21 21 , j k layers Z l We We We We h P h P ) � � , 1 , 1 , j l j l k jl jlk 2 2 Weft crimp heights L*NWe We We We Wa Wa Wa � � B h B � � h � � � � � � jlk jlk jl ik ik ik W F F � � min We � � � � � � � h Wa � Wa � We We p p p � p � jl i , k j , l , k � � ik ik jlk jlk � � 16 Manchester 3D textiles - April 2008
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 17 Manchester 3D textiles - April 2008
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 18 Manchester 3D textiles - April 2008
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