Multiscale analyses of the behaviour and damage of composite materials Presented by Didier BAPTISTE ENSAM, LIM, UMR CNRS 8006 151 boulevard de l hôpital l 75013 PARIS, France Research works from: K.Derrien, J.Fitoussi,, F. Meraghni, E.Lepen, G.Guo,, M. Levesque, Z.Jendli.
Variability of the short fibres orientation From B. Ohl, Schneider
Microtomography X: volume view of the fibres distribution From B. OLH, Schneide
Example of a dispersed microstructure: S.M.C.
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
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)
Objective: Experimental determination of all the mechanical properties from: one given distribution of the microstructure One loading direction
Objective Prediction of the mechanical properties for other distributions of microstructure for other path loadings (other directions, bi-traction, shear,.)
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
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
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
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
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
Failure particule criterion Diap Katell Σ Σ Σ Σ Σ = 494 MPa Al-SiCp Σ = 509 MPa
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
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
Modelling of the damaged microstructure
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)
Identification of the material parameters of the behaviour law Distribution of reinforcement : Tomography Ultrasonic waves Flow numerical simulation of the process
Microtomography From B. Olh Schneider ESRF
Ultrasonics measurement Specimen Wave propagation time measurement under bi-tension Ultrasonic transducers
Determination of the distribution of fibres Transvers Vitesse wave des OT (m/s) rate 1620 1600 1580 1560 1540 1520 1500 1480 0 30 60 90 120 150 180 210 240 270 300 330 360 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
Damage quantification at the microscale In situ tensile test ( inside a S.E.M.) 10 cm Specimen Microscopic damage
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
Evolution of damage for SMC 140 120 100 Stress (MPa) 80 60 40 Stage 2 Damag e initiatio n Stage 3 Micro-cracks coalescence and damage accumulation 20 0 Stage 1 Elastic behaviour 0 0.5 1 1.5 2 2.5 St rain (%)
Quantification of damage evolution d microscopic 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0.0002 s-1 8 s-1 20.5 s-1 ε_ult 0 0 0.5 1 1.5 2 ε dε/dt (%) d= Number of broken interface fibres Total number of fibres
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 0.4 0.35 PROB-OPT DOM-EXP PROB-INT (σ 0,τ 0, m) = f ( ). ε Identification (matlab( matlab) minimisation algorithme: Levenberge marquardt + Hessien calculation d-micro 0.3 0.25 0.2 0.15 0.1 0.05 3 m/s 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 STRAIN déformation (%) Model Experiments 8/s 20/s STRAIN
Prediction of the lost of stiffness 14000 12000 Strain rate: Exp. 20 s -1 10000 E11 (MPa) 8000 6000 Mod. 4000 E11-eps11-- 20s-1(Simulation) E11-eps11(élastique)-- 20s-1(Expérience) 2000 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 STRAIN Déformation ε 11(%)
Prediction of the anisotropic evolution of all the stiffness coefficients 1.2 1.2 1.2 1.0 1.0 1.0 E1/E1 (MPa) 0.8 0.6 0.4 250 s-1 20 s-1 0.2 2.10-4 s-1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 0.8 0.6 0.4 250 s-1 20 s-1 0.2 2.10-4 s-1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Déformation ε11 (%) Déformation ε11 (%) Anisotropic stiffness evolution of composite SMC-R26 For strain rates: 2.10-4, 20 et 250 s - 1. E2/E2 (MPa) E3/E3 (MPa) 0.8 0.6 0.4 250 s-1 0.2 20 s-1 2.10-4 s-1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Déformation ε11 (%) 3 2 1 1.2 1.2 1.2 1.0 1.0 1.0 G23/G23 (MPa) 0.8 0.6 0.4 0.2 250 s-1 20 s-1 2.10-4 s-1 G13/G13 (MPa) 0.8 0.6 0.4 0.2 250 s-1 20 s-1 2.10-4 s-1 G12/G12 (MPa) 0.8 0.6 0.4 0.2 250 s-1 20 s-1 2.10-4 s-1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Déformation ε11 (%) 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Déformation ε11 (%) 0.0 0.0 0.5 1.0 1.5 2.0 2.5 Déformation ε11 (%)
Prediction of the macroscopic behaviour Elasticity + plasticity + damage + failure 600 Al-SiCp 500 Σ (MPa) 400 300 200 100 15% modèle m=4 15% expérience 20% modèle m=4 20% expérience 0 0 1 2 3 4 5 STRAIN Déformation macroscopique en % from K.DERRIEN
Prediction of the macroscopic behaviour Elasticity + plasticity with kinematic and isotropic hardening + damage Al-Al2O3 200 100 Stress (Mpa) 0-100 -200 expérience simulation -0,01-0,006-0,002 0 0,002 0,006 0,01 Total strain From E. LEPEN
Prediction of the macroscopic behaviour Elasticity + viscodamage S.M.C. 160 140 ε =150 s -1 120 Tensile stress (MPa) 100 80 60 40 20 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 ε11 0-1 -0,5 0 0,5 1 1,5 2 2,5 Strain (%) ε 11 From Z. JENDLI
Prediction of the macroscopic behaviour Non linear viscoelasticity Stress (MPa) 20 18 16 14 12 10 8 6 4 2 0 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 0 0.2 0.4 0.6 0.8 1 Strain (%) From M. LEVESQUE
Prediction of the effect of the different microstructure
Prediction of the effect of the different microstructure
Prediction of the effect of the different microstructure
Prediction of the behaviour and damage evolution for different loading paths. Fibres Distribution d'orientation distribution des fibres 0,05 Contrainte (MPa) STRESS 70 60 50 40 30 20 10 0 0,04 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
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
Simulation of different loading paths : Iso-damage criterion S.M.C. From G. GUO
Iso-damage surface evolution 60 0/1 σ2 S.M.C. Iso relative fraction of broken interface fibres -1/1 1/1 40 20 0 10% 5% 1% 30% 20% -60-40 -20 0 20 40 60 σ1-20 Biaxial loading paths -40-60 From J. FITOUSSI
Micro damage evolution for different biaxial loading paths Volume fraction of broken interface fibres function of the fibres orientation:vfb Vfb 0.045 0.04 0.035 0.03 0.025 0.02 Tension 18MPa 0.015 0.01 0.005 Vfb 0.045 0.04 0.035 0.03 Bi-tension 18MPa Vfb 0.25 0.2 0-100 -80-60 -40-20 0 20 40 60 80 100 Angle Tension-compression 18MPa 0.025 0.15 0.02 0.015 0.1 0.01 0.05 0.005 0-100 -80-60 -40-20 0 20 40 60 80 100 Angle 0-100 -80-60 -40-20 0 20 40 60 80 100 Angle
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)
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.
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
Simulation of the mould filling by injection of short fibres composites. From P. CHINESTA
Prediction of the fibres orientation From P. CHINESTA
Simulation of bending + torsion of S.M.C. structure ABAQUS+ UMAT MICRO-MACRO LAW From G. GUO
Simulation of the behaviour of a structure using a micro-maco maco law for S.M.C. Force (N) 450 400 350 300 250 200 150 100 50 0-1,50% -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
Simulation of the lost of stiffness due to damage Longitudinal Young s modulus (GPa) 15 12.5 10 7.5 5 2.5 0 6 0.25 1 1.5 2.25 2.75 1.5 3.5 4 4.75 thickness (mm) 9 28.5 24 21 16.5 13.5 width (mm) From G. GUO
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
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.
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