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 20157th 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):

- strong influence of geometry.

Observation

Objective

Materials & Methods

Specimens :DCB specimens were produced with :Thickess = 4 mmWidth = 12.5 and 25 mmLength = 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

2

P dCG

b da nC Ba

Delamination & bridging

Fracture resistance Strong geometry effects

Delamination & bridging

Fracture resistance Strong geometry effects

Cross-ply : mechanismsSide view

Perspective view Cross section

Longitudinal section

z

delamination : mechanisms

Cross-ply Uniaxial

,

0,

1B ie z

B i

p

Inte

nsity

Strains : FBG – multiplexing

1.Residual thermal stress2.Mode mixity3.Crack migration and wavy delamination path 4.Transverse fiber bridging5.…

Modelling of cross-ply laminates

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 b

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

as

1 2( , ) zb z e A A z

b

z

A1

-A1/A2

z

maxz

A1 : maximum bridging stress stress, bmax

-A1/A2 : bridging zone length, : curvature

1 2 max

max

1 2 max 1 2

( , ) 0;

( , ) 0 0;

, , /

zb

b

z e A A z for z z

z for z z

with A A and z A A

α

α

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 minimization2. Trust region reflective Newtonian algorithm to solve the

constrained non-linear least square optimization problem

mean value

Methods : bridging tractions b

21( ) ( , )

2F zα f α

( , ) ( )( , )

( )z z

z

z zz

z

αf α

Find such that with constraints :

Where 1 2 2 3 0 2 3( ) , , , ,u a a g α

min ( )F α

( ) 0ig

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 d

Bridging tractions identification

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.

ERR calculation with projected crack length

Evaluation of bridging tractions

i

*

0

II )( J GdG b

*)( *d

d I b

G

Gb GIC

* = (a)

Evaluation of bridging tractions: Direct Method

Methods : bridging tractions b

4

40b

xx

d w x b x

dx E I

1a xb max

0

a xx e

a a

3 2

1 2 3 45

4 1 1

6 2

a xmax 0

0 xx

b a x ew x C x C x C x C

a a E I

2

1 22 3

2 a xmax 0

analytical0 xx

b a x ed w xx z z C x C

dx a a E I

4

41 0a xmax

xx 0

d w x b a xe

dx E I a a

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.

Interlaminar crackIntralaminar crack

Methods : specimens

specimen orientation

Matrix rich zones

Methods : FBG – multiplexing

Quasi-distributed sensing

For each sensor B,kz,k

e B0,k

(1 p )

k=1,2,3,....(sensor number)

z

Conclusions

Studies on specimen size and layup dependence of delamination in layered composites

Ebrahim Farmand-ashtiani, EPFL, January 2015

30

Fracture surface observations (cross-ply)C

rack

gro

wth

dire

ctio

n

Crack initiation

Steady state

Fracture surface observations (unidirectional)C

rack

gro

wth

dire

ctio

n

Crack initiation

Steady state

Optical fiber

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)

Modelling of cross-ply laminates