J.-N. Périé, S. Calloch, C. Cluzel and F. Hild ANALYSIS OF A SHEAR TEST ON A C/C COMPOSITE BY USING DIGITAL IMAGE CORRELATION AND A DAMAGE MODEL J.-N. Périé, S. Calloch, C. Cluzel and F. Hild

EXPERIMENT / SIMULATION Aim: Understanding and modeling the multi-scale behavior of materials Model identification (coupons) and validation (mock-ups) EXPERIMENT / SIMULATION INTERACTIONS

Testing machines Tested objects Strains obtained by: experiment? computation?

Material Model and identification Shear test Conclusion

Some applications of Sepcarb®

Needled laminates [Cavalier] HR Carbon Fibers HM Carbon Fibers Needled laminates [Cavalier] Novoltex® Skinex® Multirex® Unidirectional or woven plies of ex-PAN fibers (preoxyded) + Ex-PAN fiber mat (preoxydised) Unidirectional or woven plies of HR Carbon fibers + Ex-PAN fiber mat (preoxydised) Yarns, unidirectional or woven plies of continuous or non-continuous HR Carbon fibers Preform manufacture (Stacking + Needling) Carbonization Pyrolysis (>1000°C) Chemical vapor infiltration

Plane preforms made of non-continuous fibers Unidirectional layers “C/C reinforced laminate” Layers of continuous fibers “X” Carbon preform + Carbon matrix stacked +“needled” and/or Layers of non-continuous fibers “Y” Some preforms … Plane preforms made of non-continuous fibers Needling Unidirectional layers Satin layers

Multirex® family Meso-undulations Macro-undulations No-undulation satin layers unidirectional plies 10 mm Macro-undulations (scale: n plies) ~1.5 mm ~3 mm Meso-undulations (scale: ply) 1.5 mm 0.5 mm No-undulation (scale: coupon)

Tension/compression tests at 0° and 45° on a [0y,90y]n satin Multirex® behavior Linear in continuous fiber direction Tension/compression tests at 0° and 45° on a [0y,90y]n satin Stress (MPa) Non linear for tension test in non-continuous fiber direction Non linear for 45° test

Model for a family of materials Identification procedure Validation on a set of composites Uniaxial tests Biaxial tests Displacement and strain field measurement

Material Model and identification Shear on C/C Composites Conclusion

Model designed for a family of materials brittle (rupture of fibres) Damage meso-model Meso-constituents Layers of continuous fibers Layers of non-continuous fibers Models “X” 2 damage parameters: d2 and d12 Transverse tension ≠ compression “Y” 3 damage parameters: d2 and d12 + d1 (in fiber direction) Fiber direction tension ≠ compression Hybrid laminate Model designed for a family of materials Kinetics of damage: gradual or brittle (rupture of fibres)

Anisotropic damage theory [Lad 83] State: damaged material strain energy mechanism? “crack opening” “crack closure” < a > +: positive part of a a°: initial value of a di = piecewise constant (meso level) Kinetics: Associated forces: “Energy-release rate” Effective stress d1 ( , , ) d12 or 2 ( , +b ) Mechanisms: friction and incomplete-closure of cracks Plasticity model with isotropic hardening Inelasticity

Elastic longi. and transverse energy Elastic parameters: 2 tensile tests on a hybrid [0x,90y]n Damage kinetics: 2 tensile tests on a [0y,90y]n satin Elastic shear energy Hyp: no change in d1 45° tension test d12(Yd12 ) kinetics Elastic longi. and transverse energy 0° tension test Hyp: d12 and d2 linked d1(Yd1 ) kinetics

Laminate 0y 90y Loading d1 d12 d2 Plies Plastic strains 0° tension test on a [0y,90y]n satin Stress (MPa) Test Simulation Mean L. Strain (%) Mean T. Strain (%) Simulation tool: classical laminate theory in the non-linear field

Material Model and identification Shear test Conclusion

Comparison between experiment/simulation [0y,90y]n C/C Composites Biaxial tests Comparison between experiment/simulation Uniaxial tests Heterogeneous strains Gages Strain fields CORRELILMT [Hild, Périé & Coret, 1999]

Video digital camera + ICPCI bus + PC Tensile machine CARDAN joint Long distance microscope CCD video camera PC C/C specimen Resolution : > 1Mpixels Coding : 8-12 bits File format : .bmp, .tiff, .jpeg… Interchangeable lenses Digital camera Argentic camera or video camera + scanner Scanning Electron Microscope ...

Principle of image correlation Displacement Scale of study: (only depends on magnification and pattern) micro 0.4mm meso Macro

Principle of correlation: displacement of 1D signal x+A x g g g g f x d Correlation product: g*f (FFT) ) ( * g FFT f = x d-A d d+A

Algorithm: CORRELILMT Reference image (t0) Deformed image (t) Choice of ZOI Pixel correlation Extraction of Displaced zone Windowing FFT correlation + interpolation Sub-pixel displacement increment FFT shift of displaced zone Convergence? Total displacement New zone? Strain computation Reference ZOI Shifted ZOI Yes DV DU FFT Correlation (precision: pixel) Max. Sub-pixel displacement (dU,dV) No Yes No

Shear test on [0y,90y]n C/C Composite (SEPCARB®) Fibres 100 mm 10 mm Macro-undulation (random distribution)

Optical strain field measurement ASTREE: Triaxial testing machine Image Acquisition Control

Boundary conditions: displacements Specimen: plate Boundary conditions: displacements Loading (elastic FEA)

Validation of geometry: shear damage in a ply FEA + Damlam [Clu 01]

Surface displacement field Gauges Artificial speckle Experimental boundary conditions x 30

8-bit signal - Size of ZOI: 64 pixels - ZOI shift: 32 pixels DIC Gauge 0.2% Strain (%) Time (s) Practical Precision (strain) ~10-4

Material heterogeneities ? Strain field Displacement field N°1 Material heterogeneities ? N°6 N°11 CORRELI2D FEA Boundary conditions

Shear damage d12 CORRELI2D Damlam Strain: Damage: Ply Ply CORRELI2D Coupling CORRELI2D FEA Damlam Strain: Damage:

Fiber damage d1 CORRELI2D Damlam Strain: Damage: Ply Ply CORRELI2D FEA Coupling CORRELI2D FEA Damlam Strain: Damage:

Brittle failure

Distributed shear damage (YET THERE ARE DEFECTS) Displacement field measurement (CORRELILMT) Experimental strain field (CORRELILMT) Computation (FEA) of strain field with experimental boundary conditions Evaluation of damage state: Damlam Distributed shear damage (YET THERE ARE DEFECTS) Onset of fiber damage ? Brittle failure

Material Model and identification Shear on C/C Composites Conclusion

Specific identification procedure Model implemented in Damlam Meso model 1 stacking sequence 2 meso constituents Specific identification procedure Model implemented in Damlam Mock-up design

Multiaxial experiment (mock-up) Displacement field measurement Experiment / Simulation coupling Experiment interpretation by using the material model

Inverse identification Understanding and modeling the multi-scale behavior of (composite) materials Measurement of fields (DIC) (texture = tracer) Numerical simulations Control of test Real-time simulation Inverse identification Multi-scale measurement Resolution of CCD cameras