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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