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Composites Forming Analysis Remko Akkerman 26 th September 2013.

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Presentation on theme: "Composites Forming Analysis Remko Akkerman 26 th September 2013."— Presentation transcript:

1 Composites Forming Analysis Remko Akkerman 26 th September 2013

2 Introduction Scope Mechanisms Constitutive Models Implementation 2

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

4 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

5 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

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

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

8 Forming Mechanisms 8

9 9

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

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

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

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

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

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

16 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

17 Balance Equations 17

18 Constitutive Equations 18

19 Formalism 19

20 Formalism 20

21 Composites Forming Processes balance equations 21

22 Composites Forming Processes constitutive equations 22

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

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

25 Textiles: Woven Fabrics plain3x1 twill2x2 twill5H satin warp fill

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

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

28 Constitutive Equations definition of strain 28

29 Constitutive Equations definition of strain 29

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

31 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

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

33 Constitutive Equations definition of strain 33

34 Constitutive Equations definition of strain 34

35 Constitutive Equations definition of strain 35

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

37 Continuum model Inextensibility: or introduce leads to 37

38 Continuum model Incompressibility: Combine with leads to 38

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

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

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

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

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

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

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

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

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

48 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

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

50 Shear Locking Aligned vs unaligned mesh (quads) 50

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

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

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

54 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

55 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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