Multiscale analyses of the behaviour and damage of composite materials

Transcription

1 Multiscale analyses of the behaviour and damage of composite materials Presented by Didier BAPTISTE ENSAM, LIM, UMR CNRS boulevard de l hôpital l PARIS, France Research works from: K.Derrien, J.Fitoussi,, F. Meraghni, E.Lepen, G.Guo,, M. Levesque, Z.Jendli.

2 Variability of the short fibres orientation From B. Ohl, Schneider

3 Microtomography X: volume view of the fibres distribution From B. OLH, Schneide

4 Example of a dispersed microstructure: S.M.C.

5 What are the difficulties? Mechanical properties depending on the analysed zone of the structure. Initial anisotropy depending on the distribution of fibres orientation Evolution of this anisotropy with the loading

6 Difficulties of the macroscopic approach Tensile tests in different directions Many tensile tests with unloading to determine the evolution of all the stiffness parameters due to damage Identification of a macroscopic behaviour law taking into account damage evolution.. (exemple SMC: 27 coefficients)

7 Objective: Experimental determination of all the mechanical properties from: one given distribution of the microstructure One loading direction

8 Objective Prediction of the mechanical properties for other distributions of microstructure for other path loadings (other directions, bi-traction, shear,.)

9 Objective Identification of an anisotropic behaviour law from the simulation of loading tests on a R.V.E. for other distributions of the microstructure and different loading paths. VIRTUAL TEST MACHINE

10 MULTI-SCALE BEHAVIOUR MODELLING PROCESS Statistical approach:weibull Local failure criteria Matrix Homogenization Model: Mori and Tanaka Reinforcement: Matrix Behaviour law: Distributions: Elasticity Aspect ratio Damage Viscoelasticity Orientation, Micro-cracks cracks Plasticity Volume fraction, Mechanical properties Experimental investigation Loading -unloading tests In situ tensile test inside SEM Quantification of micro cracks kinetics Equivalent homogeneous material

11 MICRO MACRO BEHAVIOUR MODELLING Objective: To predict the composite properties from the components ones. Σ = L(?) E imp DESCRIPTION of the Representative Volume Element E imp ellipsoïdes (λ i, fv i, θ i, φ i ) Σ = < σ i > i=0, N HOMOGENEISATION LOCALIZATION σ 0 = L 0 ε 0 σ r = L r ε r BEHAVIOUR ε 0 =B 0 Ε ε r =B r Ε

12 Interface damage criterion σ Interfacial stresses calculated by Mori and Tanaka model Σ τ Orientation θ Interfacial criterion:(σ/σ 0 ) 2 + (τ/τ 0 ) 2 < R interface

13 interface damage law: Statistical approach σ Damaged interface σ Interface Failure Probability: Pf=Vfd/Vf =1-exp[(((σ/σ 0 ) 2 + (τ/τ 0 ) 2 )/σ u )] m = Volume fraction of broken interface fibre/ Volume Fraction of total fibre for a given orientation (σ 0,τ 0, m) = f (ε)( Interface mechanical properties. Undamaged interface

14 Failure particule criterion Diap Katell Σ Σ Σ Σ Σ = 494 MPa Al-SiCp Σ = 509 MPa

15 Reinforcement failure law σ 3 Brittle fracture of the reinforcement Damage criterion: σ< R particule σ : Maximun principal stress in the particule σ 1 σ 2 Statistical particule failure law Pr ( σ, V ) = 1 exp V V 0 σ σu m V : Particule volume

16 Matrix damage law Matrix cracking Cavity growth criterion or Cracks density Maximum cracks density = 1 exp σ σu m 1 dr 9 = ε R 43 2 p e h σ m h ( + fp) σ e σ: stresses in the matrix

17 Modelling of the damaged microstructure

18 Simulation of a stress- strain response Σ Mori et Tanaka : Building of the stress-strain answer by an incremental method Local damage criteria Δd (θ) Σ = Σ + δσ Introduction of a crack volume fraction (new microstructure)

19 Identification of the material parameters of the behaviour law Distribution of reinforcement : Tomography Ultrasonic waves Flow numerical simulation of the process

20 Microtomography From B. Olh Schneider ESRF

21 Ultrasonics measurement Specimen Wave propagation time measurement under bi-tension Ultrasonic transducers

22 Determination of the distribution of fibres Transvers Vitesse wave des OT (m/s) rate Angle de rotation de l'échantillon ( ) Rotation angle of the specimen C ii = ρ v OL ² C ij = ρ v OT ² C comp = f (f v,f(θ),c m,c r ) Mori and Tanaka model: volume fraction and distribution of fibres orientation

23 Damage quantification at the microscale In situ tensile test ( inside a S.E.M.) 10 cm Specimen Microscopic damage

24 High strain rate damage caracterisation Tensile test up to 20m/s Specimen σ Fuse 36*9*3,2 mm 3 Quantitative analyses of damage at the microscopic scale

25 Evolution of damage for SMC Stress (MPa) Stage 2 Damag e initiatio n Stage 3 Micro-cracks coalescence and damage accumulation 20 0 Stage 1 Elastic behaviour St rain (%)

26 Quantification of damage evolution d microscopic s-1 8 s s-1 ε_ult ε dε/dt (%) d= Number of broken interface fibres Total number of fibres

27 Identification of the visco- damage law at the micro scale The interface failure criterion is a function of the strain rate. d=p r = 1 - exp[(σ/σ 0 ) 2 +(τ/τ 0 ) 2 ] m PROB-OPT DOM-EXP PROB-INT (σ 0,τ 0, m) = f ( ). ε Identification (matlab( matlab) minimisation algorithme: Levenberge marquardt + Hessien calculation d-micro m/s STRAIN déformation (%) Model Experiments 8/s 20/s STRAIN

28 Prediction of the lost of stiffness Strain rate: Exp. 20 s E11 (MPa) Mod E11-eps s-1(Simulation) E11-eps11(élastique)-- 20s-1(Expérience) STRAIN Déformation ε 11(%)

29 Prediction of the anisotropic evolution of all the stiffness coefficients E1/E1 (MPa) s-1 20 s s s-1 20 s s Déformation ε11 (%) Déformation ε11 (%) Anisotropic stiffness evolution of composite SMC-R26 For strain rates: , 20 et 250 s - 1. E2/E2 (MPa) E3/E3 (MPa) s s s Déformation ε11 (%) G23/G23 (MPa) s-1 20 s s-1 G13/G13 (MPa) s-1 20 s s-1 G12/G12 (MPa) s-1 20 s s Déformation ε11 (%) Déformation ε11 (%) Déformation ε11 (%)

30 Prediction of the macroscopic behaviour Elasticity + plasticity + damage + failure 600 Al-SiCp 500 Σ (MPa) % modèle m=4 15% expérience 20% modèle m=4 20% expérience STRAIN Déformation macroscopique en % from K.DERRIEN

31 Prediction of the macroscopic behaviour Elasticity + plasticity with kinematic and isotropic hardening + damage Al-Al2O Stress (Mpa) expérience simulation -0,01-0,006-0, ,002 0,006 0,01 Total strain From E. LEPEN

32 Prediction of the macroscopic behaviour Elasticity + viscodamage S.M.C ε =150 s Tensile stress (MPa) ε =22 s -1 Model 22s-1: stress-strain22 Model 22s-1: stress-strain1 Experimental (22 s-1) Mode 150s-1: stress-strain11 Mode 150s-1l: stress-strain22 Experimental (150 s-1) ε 22 ε ,5 0 0,5 1 1,5 2 2,5 Strain (%) ε 11 From Z. JENDLI

33 Prediction of the macroscopic behaviour Non linear viscoelasticity Stress (MPa) Glass reinforced thermoplastic 10 MPa/s - Model 10 MPa/s - FE 1 MPa/s - Model 1 MPa/s - FE 0.1 MPa/s - Model 0.1 MPa/s - FE Strain (%) From M. LEVESQUE

34 Prediction of the effect of the different microstructure

35 Prediction of the effect of the different microstructure

36 Prediction of the effect of the different microstructure

37 Prediction of the behaviour and damage evolution for different loading paths. Fibres Distribution d'orientation distribution des fibres 0,05 Contrainte (MPa) STRESS ,04 Simulation micro-macro Matériaux CIC RANGER 0,03 Fi/Ff Comparaison C.I.C. simulation-expérience 0,02 Essais quasistatiques 0,01 0 Experiences Endo interface seul sans Model endo matricielle Fibre à 90 Loading in the 90 direction Fibre à 0 Loading in the Endo 0 interface + endo matricielle direction 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Déformation (%) STRAIN From J.FITOUSSI

38 Prediction of the behaviour under multiaxial sollicitations Objective: to perform virtual multiaxial tests (bi( bi- tension, shear+tension,..) To identify of a macroscopic damage criterion To identify the evolution of this damage surface with loading

39 Simulation of different loading paths : Iso-damage criterion S.M.C. From G. GUO

40 Iso-damage surface evolution 60 0/1 σ2 S.M.C. Iso relative fraction of broken interface fibres -1/1 1/ % 5% 1% 30% 20% σ1-20 Biaxial loading paths From J. FITOUSSI

41 Micro damage evolution for different biaxial loading paths Volume fraction of broken interface fibres function of the fibres orientation:vfb Vfb Tension 18MPa Vfb Bi-tension 18MPa Vfb Angle Tension-compression 18MPa Angle Angle

42 Heterogeneous structure behaviour simulation Theses virtual tests allow to identify a three dimensionnal anisotropic behaviour law. Possibility to perform finite elements calculations: 2 solutions: 1. Macroscopic law identified by the micro macro relationship 2. Micro-macro model introduced in the FEM code (Umat( Umat, Abaqus)

43 Integrated Design Finite elements calculations of the process to get the distribution of fibres orientation. Finite elements calculations of the deformation and damage of an heterogeneous structure taking into account the spatial distribution of the microstructure.

44 Coupling of process simulation with structure design simulation F.E. MESH Different material data files mesh Moldflow Simulation of the process ( ex: Moldflow, ) Interpolation of the fibres orientation matrices Mesh (ex:radioss,abaqus ) Imput material data file Simulation of the deformation and the damage of the structure

45 Simulation of the mould filling by injection of short fibres composites. From P. CHINESTA

46 Prediction of the fibres orientation From P. CHINESTA

47 Simulation of bending + torsion of S.M.C. structure ABAQUS+ UMAT MICRO-MACRO LAW From G. GUO

48 Simulation of the behaviour of a structure using a micro-maco maco law for S.M.C. Force (N) ,50% -1,00% -0,50% 0,00% 0,50% 1,00% 1,50% 2,00% Longitudinal strain ε22(%) F. E. Face in traction Test, Face in traction F.E. Face in compression Test, Face in compression From G. GUO

49 Simulation of the lost of stiffness due to damage Longitudinal Young s modulus (GPa) thickness (mm) width (mm) From G. GUO

50 Futur: Possibility to simulate the behaviour of a real heterogeneous composite structure 0 à 5% 5 à 10% 10 à 15% 15 à 20% 20 à 25 % 25 à 30% 35 à 40% 40 à 45% Different volume fraction, different distribution of fibres orientation. due to the injection process. From P. COUDRON INOPLAST

51 CONCLUSION Discontinuous reinforcement laws based on homogeneisation techniques Introduction of micro damage laws for each damage mechanisms Identification of the mic-mac mac law from ultrasonic measurements, tomography,, and in situ tensile tests Prediction of the macroscopic behavior and damage effect up to failure for multiaxial stress states Prediction of the deformation and damage of an heterogeneous structure by coupling process and structure finite elements simulations.

52 THANK YOU