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Composites Forming Analysis Remko Akkerman 26 th September 2013

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Introduction Scope Mechanisms Constitutive Models Implementation 2

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Freedom of Design The sky is the limit? Limits in FORMABILITY Which, why, where & how? 3

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Composite Life line What is a material, what is a structure? What is a Forming Process? Micro is close to Meso is close to Macro... 4

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residual stresses product distortions mechanically induced stresses crack initiation & crack growth Impregnation & consolidation quality joining, welding & bonding environmental loading Composite life line After life recycling 5

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process settings productproperties fibre orientation fibre/matrix properties compositeproperties productgeometry Interrelations: Processing, Properties & Performance 6

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Forming Processes Consolidation Drape (pre-forming) Press Forming Compression Molding.... 7

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Forming Mechanisms 8

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Deformation Limits Form ability Low resistance to shear & bending High anisotropy Negligible fibre extension Low compressive strength (fibre buckling) 10

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Formability Analysis... From deformation mechanisms... to material characterisation... to constitutive modelling... to process modelling... and formability prediction 11

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Material Characterisation Intra-ply shear (a) Picture frame. (b) Bias extension. 12

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Material Characterisation Bi-axial response Crimp leads to non-linear behaviour depending on the warp/weft strain ratio 13

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Material Characterisation Ply/tool and Ply/ply Friction Tool/ply friction (glass/PP) Shear stress vs pressure. 14

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Continuum Mechanics RECAP: Continuum Mechanics = Balance equations + Material Laws + Formalism 15

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Continuum Mechanics Balance Equations Conservation of mass Conservation of energy Conservation of momentum Material Laws Constitutive equations, relating forces & fluxes Formalism Scalars, vectors, tensors Deformation theories 16

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Balance Equations 17

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Constitutive Equations 18

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Formalism 19

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Formalism 20

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Composites Forming Processes balance equations 21

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Composites Forming Processes constitutive equations 22

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Composites Forming Processes constitutive equations Concluding: Very high anisotropy Large rotations & deformations possible except in the fibre direction 23 woven fabric ud ply

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Reinforcement structures … some terminology Unidirectional Biaxial (weft & warp) Triaxial …. 24

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Textiles: Woven Fabrics plain3x1 twill2x2 twill5H satin warp fill

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Fibre Directions unit vectors a, b deformation gradient F rate of deformation D a b 26

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Fibre Directions a'a' b'b' a b deformation 27

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Constitutive Equations definition of strain 28

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Constitutive Equations definition of strain 29

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Constitutive Equations definition of strain Rigid rotation: Often non-zero axial strain Except for the average configuration 30

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Constitutive Equations definition of strain Average configuration: But in which direction does the stress act? Should be in the Final Configuration! (considering the high anisotropy) 31 INCONSISTENCY

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Constitutive Equations definition of strain Result (tensile test simulation, E 1 /E 2 =10 5 ): Exact strain definition required 32

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Constitutive Equations definition of strain 33

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Constitutive Equations definition of strain 34

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Constitutive Equations definition of strain 35

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Continuum model Now directional properties f (a,b) Recall incompressible isotropic viscous fluids: 36

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Continuum model Inextensibility: or introduce leads to 37

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Continuum model Incompressibility: Combine with leads to 38

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Continuum model extra stress Form-invariance under rigid rotations: isotropic function of its arguments Assume linearity, leads to: with 39

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Continuum model Fabric Reinforced Fluid (FRF) model Can be simplified by symmetry considerations (sense of a, b, fabric symmetry) 40

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Constitutive Modelling 1.Continuum mechanics 2.Alternative: Discrete approach (resin + fibre + structure) for instance using mesoscopic modelling 41

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Mesoscopic modelling Composite property prediction from mesostructure Shear response from FE model 42

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Mesoscopic modelling Composite property prediction from mesostructure Biaxial 2D 3D Triaxial 2D Knit Multiaxial 2D (NCF) TexGen, WiseTex, etc 43

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Implementation issues Accuracy especially concerning fibre directions Consistent tangent (as above) Shear locking (due to large stiffness differences) 44

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Shear Locking Linear triangle (N 1, N 2, N 3 ) Linear strains & rotations 45

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Shear Locking Fibres in x and y direction (inextensibility) Eliminate rigid body displacements 46

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Shear Locking N 1 in the origin (0,0) Remaining d.o.f.s x y N1N1 N3N3 N2N2 47

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Shear Locking Suppress a single node N i (i=2,3) Shear locking ! Unless: x i =0 or y i =0 (i=2,3) Edge coincides with fibre direction! 48

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Shear Locking Result of locking: Far too high stiffness Spurious wrinkles Incorrect deformations Example: bias extension 49

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Shear Locking Aligned vs unaligned mesh (quads) 50

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Shear Locking Aligned vs unaligned mesh (triangles) Force vs Displacement 51

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UD laminates: 52 Process Modelling INCLUDE RELEVANT DEFORMATION MECHANISMS Intra-ply shear Inter-ply shear Laminate bending

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Process Modelling Reduction of trial & error Production process simulation of wing leading edge stiffeners Benchmarking experiments + analysis + modelling 53

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Recap: Formability Analysis of Composites Very high anisotropy Highly Sensitive to Fibre Directions – use exact (non linearised) strain definition Shear Locking for non-aligned meshes Stiff systems – Consistent Tangent Operators to prevent divergence 54

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Composites Forming Processes numerical aspects In summary: Very high anisotropy Highly Sensitive to Fibre Directions – use exact (non linearised) strain definition Shear Locking for non-aligned meshes Stiff systems – Consistent Tangent Operators to prevent divergence 55

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