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

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

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 …………….........

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

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

Materials & Methods Optical fiber

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

Delamination & bridging Fracture resistance Strong geometry effects

Delamination & bridging Fracture resistance Strong geometry effects

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

delamination : mechanisms Cross-ply Uniaxial

Strains : FBG – multiplexing Intensity

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

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:  

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

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

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.

Bridging tractions identification

Cohesive zone modelling

Cohesive zone modelling Simulation of loading response Crack growth prediction

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.

ERR calculation with projected crack length      

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

Methods : bridging tractions sb 25

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.

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

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

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) Steady state Crack growth direction Crack initiation

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

Modelling of cross-ply laminates 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)