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 on a double dome An Willems Introduction Katholieke Universiteit Leuven Constitutive model Department of Mechanical Engineering Forming study Division PMA Conclusion April, 2008
Outline 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 - - Introduction 1 D e d e n p a u k r t g e i m u t e k n t e r W Constitutive model 2 Forming study 3 Introduction Experiment Constitutive model Kinematic drape Forming study FE simulation Conclusion Local shear angles Conclusion 4
Outline 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 - - Introduction 1 D e d e n p a u k r t g e i m u t e k n t e r W Constitutive model 2 Forming study 3 Introduction Experiment Constitutive model Kinematic drape Forming study FE simulation Conclusion Local shear angles Conclusion 4
Specific properties of woven textile (prepregs) 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 Woven textile (prepreg): a e h e c r e i n M g - - Multi-scale heterogeneous material D e d e n p a u k r t g e i m u Highly anisotropic: E fibre >> E other directions t e k n t e r W Biaxial coupling: F t 1 = f 1 ( λ 1 , λ 2 ), F t 2 = f 2 ( λ 1 , λ 2 ) Low shear resistance → large shear deformation F shear = f ( γ, T ) Introduction Constitutive model Forming study Conclusion
Constitutive continuum model 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 Elastic continuum model based on nonlinear textile a e h e c r e i n M g curves: - - D e d e n p a u k r t g e i m u t e k n t e r W Introduction Constitutive model Forming study Conclusion Focus on in-plane behaviour → membrane element
Constitutive model 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 - - Introduction 1 D e d e n p a u k r t g e i m u t e k n t e r W Constitutive model 2 Forming study 3 Introduction Experiment Constitutive model Kinematic drape Forming study FE simulation Conclusion Local shear angles Conclusion 4
The Non-orthogonal (NOCM) shear model 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 i m u t e k n t e r W Introduction Constitutive model Pure shear deformation Forming study Conclusion No normal stress: σ 11 n = σ 22 n = 0 F R ( γ ) → F shear ( γ ) → σ 12 n ( γ ) = σ 21 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]
The Non-orthogonal (NOCM) shear model 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 i m u t e k n t e r W Introduction Constitutive model Forming study step 2: Conclusion Express d σ d γ in the orthonormal frame X ” Y ” ✒ dF shear ✓ ∆ γ tan γ + F shear (tan 2 γ + 1) ∆ σ xx = ∆ σ yy = c d γ ∆ γ ✒ dF shear 1 ✓ cos γ + F shear sin γ ∆ σ xy = cos 2 γ c d γ
The Non-orthogonal (NOCM) shear model K AT H O L I E K E U N I V E R S I T E I T Arbitrary large deformations → X ” Y ” must be a co-rotational frame a l E n c g n i i n a e h e c r e i n M g step 3: - - D e d e n Define X ” Y ” as frame -45 ◦ rotated with respect to the fibre bisector p a u k r t g e i m u t e k n t e r W frame Introduction Constitutive model Forming study Conclusion
The NOCM model: in-plane testing 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 Two shear curves: a e h e c r e i n M g - - D e d e n p a u k r t g e i m u t e k n t e r W Introduction Constitutive model Pure shear: Accurate description of the shear resistance Forming study Conclusion
The NOCM model: in-plane testing 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 Simple shear: a e h e c r e i n M g - - D e d e n p a u k r t g e i m u t e k n t e r W Introduction Constitutive model Forming study NOCM shear model: Conclusion Accurate whenever yarn elongations remain small
Experiment 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 - - Introduction 1 D e d e n p a u k r t g e i m u t e k n t e r W Constitutive model 2 Forming study 3 Introduction Experiment Constitutive model Kinematic drape Forming study Experiment FE simulation Kinematic drape FE simulation Local shear angles Local shear angles Conclusion Conclusion 4
Double Dome Forming 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Double Dome Forming 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Double Dome Forming 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 Fabric RR2 (TPECU44): - - D e d e n p a u k r t g e i m u t e k n t e r W unbalanced twill 2/2 co-mingled glass-PP (Twintex) case 1 case 2 Introduction Binder ring yes yes Constitutive model Forming study Binder force [N] 191 352 Experiment Kinematic drape Blank Orientation [Θ warp ] 0 45 FE simulation Local shear angles Conclusion Preheating temperature [ ◦ C] 200 Mold temperature [ ◦ C] 65-70 Punch speed [mm/s] 180
Tracking local deformations 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Kinematic mapping 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 Quikform (ESI Group) e i n M g - - D e d e Two starting points: midpoint and apex n p a u k r t g e i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Shear resistance: bias test at 200 ◦ C 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles γ B = γ C Conclusion 2 P. Harrison et al., = 0 γ A Compos.Sci.Technol., 64(10-11) 2004
Shear resistance: bias test at 200 ◦ C 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation J. Cao et al.,Compos.Part.A., in review (woven testing benchmark) Local shear angles Conclusion 2 ) ˙ γ A B + C s ( γ γ F ˙ u = C s ( γ ) ˙ 2 A C C s ( γ ) = F shear cos ( γ ) ✔ ✕ ✔ ✕ couple force = initial area initial length
Tensile resistance 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 Linearizing the biaxial tensile curves with 1/1 velocity ratio: a e h e c r e i n M g - - D e d e n p a u k r t g e i m u t e k n t e r W warp: 1.6 GPa weft: 10.6 GPa Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Predicting local deformations: case 1 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion
Predicting local deformations: case 1 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 i m u t e k n t e r W Introduction Constitutive model Forming study Experiment Kinematic drape FE simulation Local shear angles Conclusion Kinematic prediction: starting point not very crucial Reasonable correspondence between experiment and FE simulation
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