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H. CHALAL, F. MERAGHNI , F. PIERRON & M. GRÉDIAC *

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.

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H. CHALAL, F. MERAGHNI , F. PIERRON & M. GRÉDIAC *

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  1. 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. Introduction The Virtual Fields Method Damage Meso-modelling Non linear Constitutive Law Implementation Application : Iosipescu Configuration Test Results : Numerical Aspects and Parametric Study Conclusions OUTLINE

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

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

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

  6. Damage Meso-modelling • Non linearity of the behaviour is assumed to be due mainly to damage. • Anisotropic Damage : Meso-model proposed by Ladevèze (1986) In-plane stress  In the present work :  only the in-plane shear damage is considered • damage evolution is modelled by a quadratic function of the shear strain dss = K/Qss . s2

  7. , P (resulting force) : Known Non Linear Behaviour Law In-plane orthotropic composite Qxx, Qyy, Qxy, Qss, K : Unknown parameters PVW Identification requires at least 5 different virtual fields

  8. =0 =0 =0 =0 =1 Uy(1)* : first special virtual displacement According to the same scheme, Qyy Qxy, Qss and K are determined ……... Virtual Fields Method To extract Qxx..

  9. IMPLEMENTATION • Actual strain fields : Experimental measurements using optical methods • ( grid method, ESPI, …) • 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

  10. RESULTS • 15000 (2D) 4-nodes plane stress element (CPS4) • Finite element model (ABAQUS 6.2- UMAT) C A B In-plane shear strain field simulated for the damaged composite Unnotched Iosipescu specimen

  11. FE inputs RESULTS UD : Glass /epoxy (M10) composite Linear shear response Non-linear shear response

  12. RESULTS UD : Glass /epoxy (M10) composite Identification from Noisy Data Amplitude noise = b . Max(mean(|ex|), mean(|ey|), mean(|gs|))  = 5%  = 10%

  13. 15000 elements L SENSITIVITY TO THE LENGTH UD : Glass /epoxy (M10) composite Increasing L : bending stresses increase Decreasing L : shear and transverse compression stresses increase Optimal L ?

  14. L SENSITIVITY TO THE LENGTH Noisy strain fields UD : Glass /epoxy (M10) composite Mean values of 30 identifications

  15. SENSITIVITY TO THE ORTHOTROPIC RATIO UD : Glass /epoxy (M10) composite (r = Qxx /Qyy = 2.5) UD : Carbon/epoxy (T300/914) r = 13.7 both materials L=30 mm

  16. SENSITIVITY TO THE ORTHOTROPIC RATIO Identification from Noisy Data  = 5% L=30 mm is probably not the optimal length for the T300/914

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

  18. FURTHER WORK • Identification : Off-axis orthotropic behaviour Coupling terms (6 constants to be identified simultaneously) • Coupled damage model

  19. Convergence spatiale

  20. 9600 elements L SPATIAL CONVERGENCE

  21. 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 linearequations system • Resolution : direct and simultaneous determination of the parameters

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