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MORI-TANAKA MEAN-FIELD HOMOGENIZATION
BASED FAILURE PREDICTIONS OF A SHORT
FIBER COMPOSITE BUTT-JOINT
COMPTEST 2015
Bas Tijs 1, Wouter Wilson 2, 3, Steyn Westbeek 3, Max Markestein 1
1 Fokker
Aerostructures B.V., Industrieweg 4, 3351 LB, Papendrecht, The Netherlands
Fokker Landing Gear B.V., Grasbeemd 28, 5705 DG, Helmond, The Netherlands
3 Eindhoven University of Technology, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands
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Content
1. Skin-stringer butt-joint connection
2. Modelling approach
3. Manufacturing & testing of dogbones
4. Detailed butt-joint testing & predictions
5. Conclusion & future work
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Skin-stringer butt-joint connection
Manufacturing concept of butt-joint
Thermoplastic pre-forms are
co-consolidated to skin lay-up
during skin consolidation
Skin UD lay-up
Web laminate
Cap laminate
Injection moulded
filler
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Skin-stringer butt-joint connection
Anisotropy of Short Fiber Reinforced Plastic filler
Anisotropy of Short
Fiber Reinforced filler
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Modelling approach
Parametric butt-joint model
Parametric Abaqus butt-joint model:
LARC04 UVARM implemented to
monitor first ply & matrix failure in skin
(developed by C.S. Lopes)
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Parametric:
- Loading: 3PB or Peel
- Layup
- Span
- Filler geometry
- Filler material (UMAT)
Modelling approach
Two modelling approaches
1) Approach based on test-data, using default ABAQUS functionality:
• Input elastic properties of compound:
- E1, E2, nu12 measured
- Other elastic properties estimated by M-T method
•
Input plasticity & damage curve:
- Plasticity with Hill’s potential function for anisotropic behaviour
- Ductile damage with tabular displacement input
•
Perform parameter studies on geometry:
Filler geometry, skin layup, span, loading
2) M-T ABAQUS User-defined Material routine (UMAT) :
• Input: matrix, fiber & geometrical properties
• Input: Resin plasticity & damage constants
• Perform parameter studies on compound & geometry:
Matrix and/or fiber type, Fiber orientation, aspect ratio, volume fraction
Filler geometry, skin layup, span, loading
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Modelling approach
Mori-Tanaka Mean-Field Homogenization
• Smeared out micro scale information
Volume averaging
via volume fraction
• Based on the Eshelby inclusion problem
• Only non-elastic phenomena in the resin
– Isotropic damage => logarithmic damage growth until exponential
rapid failure
– Plasticity => power law hardening rule
• Update Eshelby tensor according to new resin Poisson’s ratio
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Modelling approach
Mori-Tanaka Mean-Field Homogenization
Fiber :
inclusion angle
aspect ratio
volume fraction
(4 fibers, 2 rotation planes for 3D implementation)
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Modelling approach
Mori-Tanaka Mean-Field Homogenization
• Predict elastic properties (Matlab model)
a = 10
xi = 0.2
• Predict coefficients of thermal expansion
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Manufacturing & testing of dogbones
Manufacturing of dogbones
Injection molded dogbones
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Injection molded plates
* ref. Modeling of short fiber reinforced injection moulded Composite, A Kulkarni, NANOSTRUC 2012
Manufacturing & testing of dogbones
Static test results for different orientations
0-deg
Moderate
orientation
Low
orientation
90-deg
(not tested in
tension)
(remark: as moulded behaviour is different then after co-consolidation)
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Manufacturing & testing of dogbones
Plasticity & Damage
The damage can be
determined from the
change in stiffness
Plastic (residual) strain
12
* ref. Modelling the nonlinear shear stress–strain response of glass fibre-reinforced composites
Van Paepegem, Composites Science and Technology 66 (2006)
Detailed butt-joint testing & predictions
3-Point-Bending versus Peel
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Detailed butt-joint testing & predictions
Failure prediction
Drop in load due to
filler failure: thermal
stress released
Residual
displacement: skin
back in “straight”
situation after release
of thermal stresses
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•
•
The initial stiffness (1-2)
Failure of the filler (2-3)
Residual stiffness (3-4)
Conclusion & future work
Conclusion:
•
•
Two approaches applied for predicting the strength of SFRP butt-joint
Mean-field homogenization model developed with planar fiber inclusions
–
•
•
•
•
Easy prediction of:
–
–
–
Elastic properties
Thermal expansion
Plasticity / Failure
–
As a function of:
–
–
–
–
Matrix and/or fiber type
Fiber orientation
Fiber aspect ratio
Fiber volume fraction
UMAT implementation for elasto-plastic-damage behavior
Matlab implementation to predict: Elastic properties, CTE’s
Cyclic tests used to distinguish between plasticity and damage
Failure mode in filler well captured
Future work:
•
•
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Parameter studies on geometry & compound
Extensive model validation: different compounds, loading, geometry