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TRANSCRIPT
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.