Mr Hocine CHALAL, Dr Fodil MERAGHNI, Dr Stéphane AVRIL, Professor Fabrice PIERRON

1. Paris Châlons en Champagne SEM Xth International Congress – Costa Mesa, 2004 Experimental strategy to identify the non-linear behaviour of composite materials from full-field strain measurements Mr Hocine CHALAL, Dr Fodil MERAGHNI, Dr Stéphane AVRIL, Professor Fabrice PIERRON LMPF Research Group ENSAM Châlons en Champagne France

2. PLAN • Introduction • The Virtual Fields Method • Extension to damage non-linearity • Experiments and Results • Conclusion

3. Introduction The VFM Experiments/Results Conclusion 0° tensile test 3 tests 4 parameters 90° tensile test shear test (off-axis) Local strain measurements • Usual strategies for in-plane orthotropic elastic moduli measurements Uniform stress fields (closed-form solution) Spatial stress distribution

4. Introduction The VFM Experiments/Results Conclusion 1 test FE model updating Virtual Fields Method • Novelstrategy for material parameter identification Heterogeneous stress fields (no closed-form solution) Inverse problem

5. Introduction The VFM Experiments/Results Conclusion Damage law Retrieve from a heterogeneous strain map • In-plane shear non linearity

6. Introduction The VFM Experiments/Results Conclusion Principle of virtual work • Principle Global equilibrium of structure Choice of virtual fields

7. Introduction The VFM Experiments/Results Conclusion Over S2 Uniform virtual shear

8. Introduction The VFM Experiments/Results Conclusion In-plane elastic orthotropywith shear damage Plane stress Material homogeneous

9. Introduction The VFM Experiments/Results Conclusion Finally if the fields are « well chosen » Special virtual fields optimized to resist to noise in data Need to choose other virtual fields

10. Introduction The VFM Experiments/Results Conclusion • Experimental set-up

11. Introduction The VFM Experiments/Results Conclusion Grid glued on the specimen Difference Spatial phase shifting Loading Phase map (undeformed state) Phase map (deformed state) • The grid method • Developped by Prof. Yves SURREL

12. Introduction The VFM Experiments/Results Conclusion Cross grid of pitch p=100 µm p Sampling 4 pixels / period • The grid method: • Printed on a photosensitive film (postscript file) • Film is glued onto specimen (white glue)

13. Introduction The VFM Experiments/Results Conclusion • Experimental details • CCD Camera (8bits, 1280×1024) • 60 mm focal lens • Frangyne software • Field of view: 30 mm by 20 mm • 4 pixels /period • Smoothing phase maps: 33 x 33, twice • Differentiation: 33 x 33 pixels

14. Introduction The VFM Experiments/Results Conclusion ey ex es • Strain maps Sensitivity to out-of-plane displacements 1 mm – 4 mdef Corrected by 120 mdef

15. Introduction The VFM Experiments/Results Conclusion K 1990 44.9 12.2 3.86 3.78 Reference (GPa) Coeff. var (%) 31 0.7 2.8 2.4 7.3 Identified (GPa) 56 27 - 3.6 1500 Rel. diff. (%) 25 130 * -5 -25 • Identification results • Special virtual fields

16. Introduction The VFM Experiments/Results Conclusion • In-plane strain response

17. Introduction The VFM Experiments/Results Conclusion • Conclusions • VFM: process strain maps • VFM: Material non-linearity • Good results if information there • Problem: out-of-plane displacements • Problem: what test? • Perspectives • Fibres at an angle (45° ?) • Design of new tests adapted to VFM • Improve measurements