1. Characterization of impact damage in fibre reinforced composite plates using embedded FBG sensors J. Frieden*, J. Cugnoni, J. Botsis, Th. Gmür CompTest2011 5th International Conference on Composites Testing and Model Identification 14 Feb 2011 - 17 Feb 2011, Ecole Polytechnique Fédérale de Lausanne, Switzerland Swiss National Science Foundation, grant N° 116715

2. Objectives Primary objective of this work: Impact localization and damage identification in CFRP plates with FBG sensors Methods: Interpolation-based impact localization method using high rate FBG signals Inverse numerical-experimental damage identification method based on eigenfrequency changes and homogenized damage model

3. Objectives Primary objective of this work: Impact localization and damage identification in CFRP plates with FBG sensors Today’s focus: Influence of impact damage on the plate’s eigenfrequencies measured with FBG sensors Experimental characterisation of impact damage Finite element model of the plate with impact damage that reproduces the change of eigenfrequencies  Application

4. Introduction: Materials and specimen CFRP cross-ply plate with 28 UD plies [0° 2, 90° 2, 0° 2, 90° 2, 0° 2, 90° 2, 0° 2 ] s Embedded FBG sensors Reference: Frieden J. et al, Composite Structures, 2010 Cross-section of plate

5. Sensitivity of eigenfrequencies to damage Intact plate: Experimental modal analysis Damaged plate: Experimental modal analysis Impact 1.7J – 6.7J Experiment carried out on 8 plates using different impact energies.

6. Sensitivity of eigenfrequencies to damage Relative frequency changes as a function of impact energy

7. High resolution X-ray computed tomography SkyScan, model 1076 Aluminium filter : 1 mm thickness X-ray source voltage : 100 kV X-ray source power : 10 W Exposure time : 1750 ms Experimental damage characterization Damaged CFRP plate

8. Experimental damage characterization Impact Location Intralaminar cracks are rare and their occurrence is limited to a region located just beneath the impact point Cross-section (Cut through plate thickness) Impact energy : 5.1 J CT Resolution: 9 μm/pixel Distance between cross-section images: 9 μm Total of 10 000 images Convert to black & white images 2 mm

9. Experimental damage characterization Absorbed energy per unit of delamination area of 280 J/m 2.

10. Detailed 3D delamination model FE model in Abaqus 6.8-2: Numerical modal analysis 20-nodes brick elements with reduced stiffness matrix integration Mesh interfaces without node connection between plies Element size : 2 mm x 2 mm

11. Discrete delamination model FE model in Abaqus 6.8-2: Numerical modal analysis 20-nodes brick elements with reduced stiffness matrix integration Mesh interfaces without node connection between plies Element size : 2 mm x 2 mm Eigenfrequency changes are mainly due to delamination type damage

12. Homogenized damage model Projected damage shape: Rhombic area Diagonal damage tensor D: Affected: Transverse shear moduli Not affected: Longitudinal, transverse and through-the-thickness Young’s moduli In-plane shear modulus Poisson’s ratio Incident energy [J]3.375.066.75 Projected area [cm 2 ]10.716.020.720.6 Length [mm]56.772.087.481.6 Width [mm]37.847.247.3 Material properties: Through-the-thickness homogenized material properties

13. Homogenized damage model Diagonal damage tensor D: Affected: Transverse shear moduli Not affected: Longitudinal, transverse and through-the-thickness Young’s moduli In-plane shear modulus Poisson’s ratio Values of D 13 and D 23 identified through least square optimization: Minimize error between experimentally measured frequency change and numerically calculated frequency change Projected damage shape: Rhombic area Material properties: Through-the-thickness homogenized material properties

14. Homogenized damage model Diagonal damage tensor D: Affected: Transverse shear moduli Not affected: Longitudinal, transverse and through-the-thickness Young’s moduli In-plane shear modulus Poisson’s ratio Values of D 13 and D 23 identified through least square optimization: Minimize error between experimentally measured frequency change and numerically calculated frequency change Incident energy [J]3.375.066.75 D 13 [%]84.486.188.491.9 D 23 [%]85.590.292.593.9 Projected damage shape: Rhombic area Material properties: Through-the-thickness homogenized material properties

15. Prediction of eigenfrequency change Experimentally measured damage size Using the previously determined values of D 13 and D 23

16. Damage identification procedure Values of D 13 and D 23 are fixed to 94 % Parameters to identify: Damage position Damage surface Damage aspect ratio Reduce discrepancy between experimentally measured eigenfrequency changes and numerically calculated eigenfrequency changes Iterative minimization algorithm: Levenberg-Maquardt

17. Application example Impact energy: 3.4 J Predict the impact location Identify damage size and position

18. Application Reference measurements before impact: Arrival time delays for interpolation-based localization method Eigenfrequencies of intact plate

19. Application: Reference data Non-destructive hammer impacts Grid of 3 x 3 reference points Acquisition rate of FBG sensors : 1 GHz Arrival time delays obtained by threshold method

20. Application: Reference data Non-destructive hammer excitation Grid of 3 x 3 reference points Acquisition rate of FBG sensors : 100 kHz Eigenfrequencies obtained by modal curve fitting FRF

21. Application: Impact Impact with energy of 3.4 J Acquisition rate of FBG sensors : 1 GHz

22. Application: Impact Impact with energy of 3.4 J Acquisition rate of FBG sensors : 1 GHz

23. Application: Identification of damage Experimental data

24. Application: Identification of damage Parameters to identify: Damage position Damage surface Damage aspect ratio Initial guess for the damage identification: Predicted impact location Damage surface = 1 cm 2 Damage aspect ratio = 1 Experimental data

25. Application: Identification of damage Convergence graph Identification results Predicted eigenfrequency changes compared to experimental eigenfrequency changes

26. Conclusion Embedded FBG sensors provide very accurate strain data for modal analysis and acoustic wave sensing. The eigenfrequency changes can be mainly attributed to delamination type damage. The simple homogenized damage model allows to reproduce the eigenfrequency changes. The damage size can be identified by a numerical- experimental optimization method based on eigenfrequency changes.

27. Thank you

28. Introduction: Fast FBG interrogation

29. FBG sensors for modal analysis 1 st mode 3 rd mode 2 nd mode 4 th mode