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Forming simulation of a thermoforming i m u t e k n t e r - - PowerPoint PPT Presentation

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K AT H O L I E K E U N I V E R S I T E I T a l E n c g n i i n a e h e c r e i n M g - - D e d e n p a u k r t g e Forming simulation of a thermoforming i m u t e k n t e r W commingled woven textile

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D e e d p n a u r k t e g i m u e t n k r t e W E n l g a c i i n n e a e h r i c n e g M

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Introduction Constitutive model Forming study Conclusion

Forming simulation of a thermoforming commingled woven textile on a double dome

An Willems

Katholieke Universiteit Leuven Department of Mechanical Engineering Division PMA

April, 2008

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Introduction Constitutive model Forming study Conclusion

Outline

1

Introduction

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Constitutive model

3

Forming study Experiment Kinematic drape FE simulation Local shear angles

4

Conclusion

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D e e d p n a u r k t e g i m u e t n k r t e W E n l g a c i i n n e a e h r i c n e g M

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Introduction Constitutive model Forming study Conclusion

Outline

1

Introduction

2

Constitutive model

3

Forming study Experiment Kinematic drape FE simulation Local shear angles

4

Conclusion

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Introduction Constitutive model Forming study Conclusion

Specific properties of woven textile (prepregs)

Woven textile (prepreg): Multi-scale heterogeneous material Highly anisotropic: Efibre >> Eother directions Biaxial coupling:

Ft1 = f1(λ1, λ2), Ft2 = f2(λ1, λ2)

Low shear resistance → large shear deformation

Fshear = f (γ, T)

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Introduction Constitutive model Forming study Conclusion

Constitutive continuum model

Elastic continuum model based on nonlinear textile curves: Focus on in-plane behaviour → membrane element

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Introduction Constitutive model Forming study Conclusion

Constitutive model

1

Introduction

2

Constitutive model

3

Forming study Experiment Kinematic drape FE simulation Local shear angles

4

Conclusion

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Introduction Constitutive model Forming study Conclusion

The Non-orthogonal (NOCM) shear model

Pure shear deformation No normal stress: σ11

n = σ22 n = 0

FR(γ) → Fshear(γ) → σ12

n (γ) = σ21 n (γ)

step 1: Explicit definition of stress tensor σ(γ) in the non-orthogonal covariant frame.

[Woong-Ryeol Yu et al., Compos. Part. A., 36(8), 2005]

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Introduction Constitutive model Forming study Conclusion

The Non-orthogonal (NOCM) shear model

step 2: Express dσ

dγ in the orthonormal frame X”Y”

∆σxx = ∆σyy = ∆γ c ✒dFshear dγ tanγ + Fshear(tan2 γ + 1) ✓ ∆σxy = ∆γ c ✒dFshear dγ 1 cosγ + Fshear sinγ cos2 γ ✓

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Introduction Constitutive model Forming study Conclusion

The Non-orthogonal (NOCM) shear model

Arbitrary large deformations → X”Y” must be a co-rotational frame step 3: Define X”Y” as frame -45◦ rotated with respect to the fibre bisector frame

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Introduction Constitutive model Forming study Conclusion

The NOCM model: in-plane testing

Two shear curves: Pure shear: Accurate description of the shear resistance

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Introduction Constitutive model Forming study Conclusion

The NOCM model: in-plane testing

Simple shear: NOCM shear model: Accurate whenever yarn elongations remain small

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Experiment

1

Introduction

2

Constitutive model

3

Forming study Experiment Kinematic drape FE simulation Local shear angles

4

Conclusion

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Double Dome Forming

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D e e d p n a u r k t e g i m u e t n k r t e W E n l g a c i i n n e a e h r i c n e g M

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Double Dome Forming

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Double Dome Forming

Fabric RR2 (TPECU44): unbalanced twill 2/2 co-mingled glass-PP (Twintex)

case 1 case 2 Binder ring yes yes Binder force [N] 191 352 Blank Orientation [Θwarp] 45 Preheating temperature [◦C] 200 Mold temperature [◦C] 65-70 Punch speed [mm/s] 180

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Tracking local deformations

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Kinematic mapping

Quikform (ESI Group) Two starting points: midpoint and apex

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Shear resistance: bias test at 200◦ C

γC = γB 2 γA =

  • P. Harrison et al.,

Compos.Sci.Technol., 64(10-11) 2004

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Shear resistance: bias test at 200◦ C

  • J. Cao et al.,Compos.Part.A., in review (woven testing benchmark)

F ˙ u = Cs(γ) ˙ γAB + Cs( γ 2 ) ˙ γ 2 AC Cs(γ) = Fshear cos (γ) ✔ couple initial area ✕ = ✔ force initial length ✕

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Tensile resistance

Linearizing the biaxial tensile curves with 1/1 velocity ratio:

warp: 1.6 GPa weft: 10.6 GPa

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Predicting local deformations: case 1

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D e e d p n a u r k t e g i m u e t n k r t e W E n l g a c i i n n e a e h r i c n e g M

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Predicting local deformations: case 1

Kinematic prediction: starting point not very crucial Reasonable correspondence between experiment and FE simulation

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Predicting local deformations: case 2

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Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion

Predicting local deformations: case 2

Kinematic prediction: more sensitive to start conditions Larger discrepancy between experiment-FE and kinematic-FE

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Introduction Constitutive model Forming study Conclusion

Conclusion

1

Introduction

2

Constitutive model

3

Forming study Experiment Kinematic drape FE simulation Local shear angles

4

Conclusion

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Introduction Constitutive model Forming study Conclusion

Conclusion and future work

Conclusion Two forming case studies: 0◦ orientation: reasonable shear angle prediction by FE 45◦ orientation: larger discrepancy. Why? Future work Include (biaxial) tensile nonlinear curves Study sensitivity of shear angle predictions to material parameters and process conditions