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Composites Forming Analysis

Composites Forming Analysis. Remko Akkerman www.utwente.nl/ctw/pt r.akkerman@utwente.nl 26 th September 2013. Introduction. Scope Mechanisms Constitutive Models Implementation. Freedom of Design. The sky is the limit? Limits in FORMABILITY Which, why, where & how?.

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Composites Forming Analysis

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  1. Composites Forming Analysis RemkoAkkerman www.utwente.nl/ctw/pt r.akkerman@utwente.nl 26th September 2013

  2. Introduction • Scope • Mechanisms • Constitutive Models • Implementation

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

  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...

  5. Impregnation& consolidation quality residualstresses productdistortions joining,welding & bonding environmental loading mechanically induced stresses recycling crack initiation & crack growth After life Composite life line

  6. product geometry processsettings fibreorientation product properties composite properties fibre/matrixproperties Interrelations:Processing, Properties & Performance

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

  8. Forming Mechanisms

  9. Forming Mechanisms

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

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

  12. MaterialCharacterisation • Intra-ply shear (a) Picture frame. (b) Bias extension.

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

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

  15. ContinuumMechanics RECAP: ContinuumMechanics = Balance equations + Material ‘Laws’ + Formalism

  16. ContinuumMechanics Balance Equations • Conservation of mass • Conservation of energy • Conservation of momentum Material ‘Laws’ • Constitutiveequations,relatingforces & fluxes Formalism • Scalars, vectors, tensors • Deformationtheories

  17. Balance Equations • Conservation of mass • Conservation of momentum • Conservationof energy (1stLaw)

  18. ConstitutiveEquations • Relations betweenFluxes(transport of anextensivequantity) e.g. • andForces(gradient of an intensive quantity) e.g. • or, indeed, between stressesandstrains / strainrates e.g.

  19. Formalism • Scalars: e.g. • Vectors: e.g. • Tensors: e.g.

  20. Formalism • Single contraction, • Dyadicproduct,

  21. CompositesFormingProcessesbalanceequations • Viscous & elasticforces dominant (low Reynoldsnumber)Neglectinertia: • Neglectalso body forces: Stress equilibrium • Neglectcoolingduringforming(at leastinitially)

  22. CompositesFormingProcessesconstitutiveequations • Matrix response:Viscousvisco-elasticelasticlow modulus, O(1 MPa) • Fibre response: Elastichigh modulus, O(100 GPa) • Prepreg/laminate response:Elastic/high modulus - in fibredirectionVisco-elastic/low modulus - transverse dir.

  23. CompositesFormingProcessesconstitutiveequations Concluding: • Very high anisotropy • Large rotations & deformationspossibleexcept in the fibredirection udply woven fabric

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

  25. warp fill 1 2 Textiles: Woven Fabrics plain 3x1 twill 2x2 twill 5H satin

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

  27. b a a' b' Fibre Directions deformation

  28. ConstitutiveEquationsdefinition of strain Strain definition: Frame of reference: Which“l”? Total Lagrange or Updated Lagrange? Differential calculus:

  29. ConstitutiveEquationsdefinition of strain 3D Straindefinition: Goodforlinearelasticity But does itworkforCompositesForming?

  30. ConstitutiveEquationsdefinition of strain Rigidrotation:  Often non-zero axialstrain Exceptfor the “averageconfiguration”

  31. ConstitutiveEquationsdefinition of strain Averageconfiguration: But in whichdirection does the stress act?  Shouldbe in the FinalConfiguration! (considering the high anisotropy) INCONSISTENCY

  32. ConstitutiveEquationsdefinition of strain Result(tensile test simulation, E1/E2=105):  Exact straindefinitionrequired

  33. ConstitutiveEquationsdefinition of strain Large deformationtheory Deformationgradient: andalso:

  34. ConstitutiveEquationsdefinition of strain The usualpolardecomposition: (Rorthogonal, V&Usymmetric) maintainsanorthogonal basis which is usually wrong!

  35. ConstitutiveEquationsdefinition of strain Solution: multiplicative split (Rorthogonal, G non-symmetric), knowing suchthat andhence leadingto as the scalarfibrestrainϵ in directiona with

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

  37. Continuum model • Inextensibility: • or introduce • leads to

  38. Continuum model • Incompressibility: • Combine with • leads to

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

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

  41. ConstitutiveModelling • Continuummechanics • Alternative: Discrete approach (resin + fibre + structure) forinstanceusingmesoscopicmodelling

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

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

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

  45. Shear Locking Linear triangle (N1, N2, N3) Linear strains & rotations

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

  47. N3 y N1 x N2 Shear Locking N1 in the origin (0,0) Remaining d.o.f.s

  48. Shear Locking Suppress a single node Ni(i=2,3)  Shear locking ! Unless: xi=0or yi=0(i=2,3)  Edge coincides with fibre direction!

  49. Shear Locking • Result of locking: • Far too high stiffness • Spuriouswrinkles • Incorrect deformations • Example: bias extension

  50. Shear Locking • Alignedvsunalignedmesh (quads)

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