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

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

Delamination & bridging

Uniaxial interlaminar

Monotonic DCB testing of carbon-epoxy

Large Scale Bridging

Specimen size is important

…………….........

Uniaxial intralaminar

Cross-ply

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.

ERR at initiation is well characterized and independent of the specimen thickness. Propagation values rise up to a plateau value (R-curve): -Large scale bridging & strong influence of geometry.

Observation

Objective

Materials & Methods

Specimens : DCB specimens were produced with : Thickess = 4 mm Width = 12.5 and 25 mm Length = 200 mm

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.

Optical fiber

Materials & Methods

Materials & Methods

with

Materials properties : The elastic constants are measured using: (i) a four point bending test of the unidirectional laminate (ASTM

D7264/D7264M − 07) for the longitudinal modulus, (ii) (ii) a transverse tensile test (ASTM D3039/D3039M − 08) for

the transversal modulus and (iii) (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 :

2

2P dCG

b da= nC Ba=

Delamination & bridging

Fracture resistance

Delamination & bridging

Fracture resistance Strong geometry & orientation effects

Cross-ply : mechanisms Side view

Perspective view Cross section

Longitudinal section

z

ERR calculation with projected crack length

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60

ERR

(J/m

2)

Crack advance (mm)

Nominal crack length

Scaled crack length

( ),

0,

1B ie z

B i

pλ

ελ∆

= −

Inte

nsity

Strains : FBG – multiplexing

Strain at each FBG sensor is given by

1. Residual thermal stress 2. Mode mixity 3. Crack migration and wavy delamination path 4. Transverse fiber bridging 5. ……

Modelling of cross-ply laminates

-250.00

-200.00

-150.00

-100.00

-50.00

0.000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Axia

l res

idua

l mic

ro-s

trai

n (-)

Distance through the laminate thickness (mm)

Top view

Modelling of cross-ply laminates

Mode mixity at crack initiation is analyzed (VCCT method): 5%

Simulation of crack deviation by XFEM:

Modelling of cross-ply laminates

Methods : bridging tractions σb

• Distributed strain data are used • Bridging stress distribution is taken as

( )1 2( , ) zb z e A A z−γσ α = +

σ b

z

A1

-A1/A2

γ z

maxz

A1 : maximum bridging stress stress, σbmax -A1/A2 : bridging zone length, γ : curvature

( ) [ ][ ]

[ ]

1 2 max

max

1 2 max 1 2

( , ) 0;( , ) 0 0;

, , /

zb

b

z e A A z for z zz for z z

with A A and z A A

γσσ

γ

− = + ∈ = ∉

= = −

αα

α

Define an error norm describing the difference between the simulated and measured strains

Identification is reduced to the optimization problem

Adopt: 1. Non-linear least squares minimization 2. Trust region reflective Newtonian algorithm to solve the constrained

non-linear least square optimization problem

mean value

Methods : bridging tractions σb

21( ) ( , )2

F z=α f α( , ) ( )

( , )( )

z z

z

z zzz

αf α ε εε

−=

Find α such that with constraints : Where 1 2 2 3 0 2 3( ) , , , ,u a aα α σ α α α α = − − − + g α

min ( )F αα

( ) 0ig α ≥

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.

Bridging tractions identification

( )0

max

b bG dδ

σ δ δ= ∫

Bridging tractions identification

From ( )zbσ we obtain ( )bσ δ

Cohesive zone modelling

Simulation of loading response Crack growth prediction

Cohesive zone modelling

Conclusions

1. Dlamination in cross-ply composite specimens is accompanied by large scale fiber bridging with strong geometry effects.

2. 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.

3. 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.

References

E. FARMAND-ASHTIANI, J. CUGNONI, J. BOTSIS, ‘Specimen thickness dependence of large scale fiber bridging in mode I interlaminar fracture of carbon epoxy composite’, International Journal of Solids and Structures, 55, 2015, pp. 58–65. B. D. MANSHADI, A. P. VASSILOPOULOS & J. BOTSIS, ‘A combined experimental/numerical study of the scaling effects on mode-I delamination of GFRP’, Composites Science and Technology, 83, 2013, pp. 32–39. S. STUTZ, J. CUGNONI & J. BOTSIS, ‘Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing’, Composites Science and Technology, 71, 2011, pp. 443-449. Acknowledgement The authors acknowledge the financial support from the Swiss National Science Foundation under Grant 200020_137937/1.