1. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 DIRECT IDENTIFICATION OF THE DAMAGED BEHAVIOUR OF COMPOSITE MATERIALS USING THE VIRTUAL FIELDS METHOD H. CHALAL, F. MERAGHNI, F. PIERRON & M. GRÉDIAC* LMPF, JE 2381 – ENSAM Châlons en Champagne *LERMES – Univ. Blaise Pascal, Clermont Ferrand II Université Blaise Pascal

2. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 OUTLINE Introduction The Virtual Fields Method Damage Meso-modelling Non linear Constitutive Law Implementation Application : Iosipescu Configuration Test Results : Numerical Aspects and Parametric Study Conclusions

3. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 INTRODUCTION Objective To identify an in-plane non-linear behaviour law for orthotropic composite materials - Performing several mechanical tests - Unable to extract the coupling terms (tensoriel damage approach)  Local strain measurements Inverse problem Heterogeneous stress fields Usual technique : Novel Strategy Involves the whole set of material parameters Whole-Field Measurements Whole-Field Measurements ( great amount of information)  Uniform stain/stress fields (closed-form solution) (no closed-form solution)

4. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 How to link WFM to the identified parameters ? Among the techniques : FE models Updating Iterative process Need to introduce initial values Novel strategy for in-plane orthotropic composites : The Virtual Fields Method (VFM) : Grédiac M. (1989) Whole-kinematic fields are processed INTRODUCTION Principle : Global equilibrium of a structure Principle of Virtual Work

5. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 How to find virtual kinematic fields ? (filtering information) - analytically ( found intuitively) - automatic generation Special virtual fields (recent improvements) Grédiac M. proposed polynomial functions Virtual Fields Method K 2 K 1 x y S 3 S 2 S 1 L H Thickness : e u y ~ u y ~ P Unnotched Iosipescu test

6. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Damage Meso-modelling Anisotropic Damage : Meso-model proposed by Ladevèze (1986)  damage evolution is modelled by a quadratic function of the shear strain function of the shear strain d ss = K/Q ss.  s 2 d ss = K/Q ss.  s 2  only the in-plane shear damage is considered   In the present work : Non linearity of the behaviour is assumed to be due mainly to damage. In-plane stress

7. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Non Linear Behaviour Law PVW Identification requires at least 5 different virtual fields Known, P (resulting force) : Known Unknown parameters Q xx, Q yy, Q xy, Q ss, K : Unknown parameters In-plane orthotropic composite

8. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 =1 =0 U y (1) * : first special virtual displacement To extract Q xx.. According to the same scheme, Q yy Q xy, Q ss and K are determined ……... Virtual Fields Method

9. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 In the present study, these are numerically simulated using FE analysis  FE Implementation of the considered behaviour law  development of a UMAT (ABAQUS) routine : Incremental stress estimation IMPLEMENTATION Actual strain fields : Experimental measurements using optical methods ( grid method, ESPI, …) ( grid method, ESPI, …)

10. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 A C B RESULTS Finite element model (ABAQUS 6.2- UMAT)  15000 (2D) 4-nodes plane stress element (CPS4) In-plane shear strain field simulated for the damaged composite Unnotched Iosipescu specimen

11. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Linear shear responseNon-linear shear response RESULTS UD : Glass /epoxy (M10) composite FE inputs

12. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Identification from Noisy Data  = 5%  = 10% Amplitude noise = . Max(mean(|  x |), mean(|  y |), mean(|  s |)) RESULTS UD : Glass /epoxy (M10) composite

13. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 L 15000 elements SENSITIVITY TO THE LENGTH Increasing L : bending stresses increase Decreasing L : shear and transverse compression stresses increase Optimal L ? UD : Glass /epoxy (M10) composite

14. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 L Noisy strain fields Mean values of 30 identifications SENSITIVITY TO THE LENGTH UD : Glass /epoxy (M10) composite

15. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 UD : Carbon/epoxy (T300/914) r = 13.7 SENSITIVITY TO THE ORTHOTROPIC RATIO both materials L=30 mm UD : Glass /epoxy (M10) composite (r = Q xx /Q yy = 2.5)

16. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Identification from Noisy Data  = 5% L=30 mm is probably not the optimal length for the T300/914 SENSITIVITY TO THE ORTHOTROPIC RATIO

17. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 CONCLUSION Capability of the VFM to process Whole-fields measurments Identification of material parameters governing a damage model VFM : proved numerically robust and less sensitive to moderate noisy data Interaction between specimen length and material orthotropic ratio VFM : less sensitive to the specimen length when the strain gradients are well described (numerically or experimentally)

18. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Identification : Off-axis orthotropic behaviour  Coupling terms (6 constants to be identified simultaneously) (6 constants to be identified simultaneously) FURTHER WORK Coupled damage model

19. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003

20. Convergence spatiale

21. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 L 9600 elements SPATIAL CONVERGENCE

22. CompTest 2003 : ENSAM-Châlons en Champagne, 28-30 January 2003 Virtual Fields Method Global equilibrium of a structure Principle Principle of Virtual Work Basic idea : Grédiac M. (1989) Known : P (global load),  and specimen geometry Introduction of the behaviour law which form is a priori known Writing : PVW with as many virtual fields (u * ) as unknown parameters A set of linear equations system Resolution : direct and simultaneous determination of the parameters