1. École Polytechnique Fédérale de Lausanne (EPFL),
TRACTION-SEPARATION RELATION IN DELAMINATION OF CROSS-PLY LAMINATES: EXPERIMENTAL CHARACTERIZATION AND NUMERICAL MODELING  
E. Farmand-Ashtiani, J. Cugnoni and J. Botsis
École Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
COMPTEST 2015
7th International Conference on Composites Testing and Model Identification, C. González, C. López, J. LLorca
IMDEA, 2015

2. Outline
Introduction: Delamination & bridging in carbon-epoxy composite
Motivation - objective
Methods :
Materials and specimens
Embedded FBG for internal strain measurements
Numerical /Analytical approach
Results :
Experimental
Analytical/numerical
Conclusions
Obviously I will close with some conclusions and perspectives

3. Delamination & bridging
Monotonic DCB testing of carbon-epoxy
Uniaxial interlaminar
Uniaxial intralaminar
Large Scale Bridging
Cross-ply
Improve the understanding of delamination tests
Specimen size is important
……………

4. Objective Observation Objective
ERR at initiation is well characterized and independent of the specimen thickness.
Propagation values rise up to a plateau value (R-curve):
- strong influence of geometry.
Objective
Characterise traction-separation tractions in cross-ply carbon epoxy composite use embedded FBG sensors for internal strain measurements during delamination. develop iterative numerical/analytical modelling and optimisation tools to evaluate relevant parameters and tractions.
Obviously I will close with some conclusions and perspectives

5. Materials & Methods Materials :
Carbon/epoxy prepreg, SE 70 from Gurit STTM, is used to fabricate a cross-ply composite plate (4×200×200 mm) with an asymmetric layup [0/90] 10.
An initial crack is introduced in the mid-plane of the plate at the 0/90 interface by inserting a 60 mm long, 20 μm thick release film.
Single mode optical fibers (SM28, 125 μm in diameter) with wavelength-multiplexed FBG sensors are embedded in the composite plates during the fabrication.
Specimens :
DCB specimens were produced with :
Thickess = 4 mm
Width = 12.5 and 25 mm
Length = 200 mm
Obviously I will close with some conclusions and perspectives

6. Materials & Methods
Optical fiber

7. Materials & Methods Materials properties :
The elastic constants are measured using:
a four point bending test of the unidirectional laminate (ASTM D7264/D7264M − 07) for the longitudinal modulus,
(ii) a transverse tensile test (ASTM D3039/D3039M − 08) for the transversal modulus and
(iii) a tensile test of the ±45° laminate (ASTM D3518/D3518M − 13) for the in-plane shear modulus.
Testing :
Displacement controlled of DCB specimens with 3 mm/min.
ERR is calculated using the compliance calibration :
Obviously I will close with some conclusions and perspectives
with

8. Delamination & bridging
Fracture resistance
Strong geometry effects

9. Delamination & bridging
Fracture resistance Strong geometry effects

10. Cross-ply : mechanisms
Side view z
Perspective view
Cross section
Longitudinal section

11. delamination : mechanisms
Cross-ply
Uniaxial

12. Strains : FBG – multiplexing
Intensity

13. Modelling of cross-ply laminates
Residual thermal stress
Mode mixity
Crack migration and wavy delamination path
Transverse fiber bridging …

14. Modelling of cross-ply laminates
Top view

15. Modelling of cross-ply laminates
Mode mixity at crack initiation is analyzed (VCCT method): 5%
Simulation of crack deviation by XFEM:

16. Methods : bridging tractions sb
Distributed strain data are used
Bridging stress distribution is taken as
A : maximum bridging stress stress, sbmax
A1/A2 : bridging zone length,
g : curvature sb A1
-A1/A2 g

17. Methods : bridging tractions sb
Define an error norm describing the difference between
the simulated and measured strains
mean value
Identification is reduced to the optimization problem
Find a such that with constraints :
Where
Adopt:
Non-linear least squares minimization
Trust region reflective Newtonian algorithm to solve the constrained non-linear least square optimization problem

18. Bridging tractions identification
Asymmetric layer-wise model.
Crack plane consisting of the original pre-crack at the 0/90 interface and the deviated path at the middle of neighboring 90 layer.
Parametric surface tractions.

19. Bridging tractions identification

20. Cohesive zone modelling

21. Cohesive zone modelling
Simulation of loading response
Crack growth prediction

22. Conclusions
Dlamination in cross-ply composite specimens is accompanied by large scale fiber bridging with strong geometry effects.
The identified traction-separation relation identified for delamination of the cross-ply specimen involves larger maximum stress at the crack tip and a smaller bridging zone length compared with the one of the unidirectional specimen of the same material and linear dimensions.
The iterative method, based on quasi-distributed strains from embedded sensors and numerical modeling, provides reliable results on traction – separation relations for prediction of delamination.

23. ERR calculation with projected crack length

24. Evaluation of bridging tractions
Direct Method
d * = d (a) Gb
GIC

25. Methods : bridging tractions sb25

26. Results : scaling parameter
Analysis and experiments confirm the increase in the
fiber bridging zone, zmax, with increasing thickness.
BUT the identified parameters σmax~2.1 MPa
and δmax ~12 mm, do not depend on the beam thickness.
Hypothesis (based on results & physical considerations):
σmax~2.1 MPa and δmax ~12 mm should be independent
of thickness for a given material system.

27. Methods : specimens specimen orientation Matrix rich zones
Interlaminar crack
Intralaminar crack
Matrix rich zones

28. Methods : FBG – multiplexing
Quasi-distributed sensing z
For each sensor 28

29. Conclusions

30. Studies on specimen size and layup dependence of delamination in layered composites
Ebrahim Farmand-ashtiani, EPFL, January 2015 30

31. Fracture surface observations (cross-ply)
Steady state
Crack growth direction
Crack initiation

32. Fracture surface observations (unidirectional)
Steady state
Crack growth direction
Crack initiation

33. Modelling of cross-ply laminates
Optical fiber

34. Modelling of cross-ply laminates
Damage criterion:
0⁰ layer: Micro Stain: 0.74 or Yield stress of fibers: 3100 MPa
90⁰ layer: Yield stress range epoxy matrix tested: 20 Mpa – 70 Mpa
Damage evolution: fracture energy at initiation (300 J/m2)