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Camanho2008.pdf
Faculdade de Engenharia da Universidade do Porto Departamento de Engenharia Mecânica e Gestão Industrial Numerical simulation of damage in composites: current status and future developments Pedro P Camanho University of Porto Portugal Carlos G Dávila NASA Langley Research Center Hampton, VA, USA Contents 9 Introduction. 9 Finite Element models for damage and fracture of composites • Delamination. • Intralaminar damage. 9 Applications. 9 Conclusions. Introduction Building Block Integration. Structural Levels of Analysis Full Scale Article Analysis Chronological Sequence Specimen Complexity Certification Methodology (Mil-Hbk.-17) Static/ Fatigue Verification of Design Data and Methodology Components Sub-components No T Structural Elements es Development of Design Data tin g Design Allowables Coupons Material Selection and Qualifications Coupons Number of Specimens • High-fidelity Progressive Damage Analysis •reduced reliance on testing reduced non-recurring costs •faster design process •more accurate design tools reduced recurring costs Introduction • The failure of composites is a progressive event; even fiber failure may not be catastrophic • Emerging composite DT requirements – need for life/residual strength prediction, including damage onset and growth • Scale effects • Virtual testing: • load incrementation without user’s intervention • reduced testing • Applications: • detail design • failure investigations Introduction +45° Matrix cracking delamination -45° -45° Matrix cracking 0° Fibre fracture (kinck) Introduction Modeling Modeling Complexities Complexities •• Failure Failure of of unidirectional unidirectional plies plies •• Failure Failure of of laminated laminated composites composites (in-situ) (in-situ) •• Material Material nonlinearity nonlinearity •• Material Material degradation degradation laws laws •• Thermal Thermal residual residual stresses stresses •• Finite Finite Element Element implem. implem. (mesh (mesh effects) effects) •• Effects Effects of of stress stress gradients gradients & & notches notches •• Built-up Built-up structures structures •• Stitched Stitched composites composites and and textiles textiles •• Delamination Delamination growth growth •• Damage Damage mode mode interaction interaction σR ϕ σR Introduction Through-the-thickness crack • fracture mechanics and modifications • strain softening Ply Damage • continuum damage modeling (CDM) • strength-based methods • micromechanics approach Delamination/Debonding • fracture mechanics approaches (FM) • decohesion elements Introduction Finite Element representation of failure process x Strong discontinuity Band of localized strain separated by two weak discontinuities Continuous profile of localised strain Jirásek, ECCM-2001 Introduction Main difficulties Strain softening constitutive models Bifurcation of the solution. • Non-local constitutive models. • Gradient methods. • Rate-dependence. • Inability of FEM to represent energy dissipated. • Localization. • Mesh dependence. • Include element characteristic length in constitutive model: W Fracture = AeW Cont ( ε u , h ) σ σ U σ U ε Energia = U × A × L Energia = U × A × L n ε ε Energia = U × A × L 2 n → ∞ ⇒ Energy → 0 Delamination VCCT +45° -45° GI = − 1 ⎡ ⎤ ' F v − v ( ) ∑ yi di d 'i ⎥⎦ 2∆b j ⎢⎣ i Delamination Objective Develop a methodology to predict progressive delamination • non self-similar delamination growth • capable of simultaneous delamination fronts • no post-process analyses required • no user intervention during analysis • works in conjunction with intra-ply damage simulations Approach: decohesion elements • Zero-thickness nonlinear elements simulate bond between layers. • Mixed-mode failure criterion combines stresses and energy release rates Delamination ⎛ σz ⎜ ⎝ T 2 + 2 ⎞ ⎛ τ xz ⎞ ⎛ τ yz ⎞ ⎟ +⎜ ⎟ +⎜ ⎟ =1 ⎠ ⎝ S ⎠ ⎝ S ⎠ 2 Mode I Mode II • Stress interaction law maps damage initiation • Mixed-mode critical Gcc maps delamination growth η ⎛ GII ⎞ Gc = GIc + (GIIc − GIc ) ⎜ ⎟ ⎝ GI + GII ⎠ Delamination MMB Specimen Force (N) AS4/PEEK Analysis (P. Camanho) Experimental (J. Reeder) Applied Displacement (mm) Intralaminar damage Matrix failure 2 σy 2 ⎛ σ y ⎞ ⎛ τ xy ⎞ ⎜ ⎟ +⎜ ⎟ =1 ⎝ Yt / c ⎠ ⎝ S c ⎠ Xt /c Xt / c , Yt / c , Sc =1 Fiber-matrix shear 2 Ply Strengths: σx Fiber damage σx τxy σx 2 ⎛ σ x ⎞ ⎛ τ xy ⎞ ⎜ ⎟ +⎜ ⎟ =1 ⎝ X c ⎠ ⎝ Sc ⎠ τxy Material Degradation Table Material state Elastic Properties FV1 FV2 Elastic E property 0 0 FV3 No failure Ex Ey υ xy Gxy Matrix failure Ex 0 0 Gxy 1 0 0 Fiber/matrix shear Ex Ey 0 0 0 1 0 Fiber damage Fiber buckling 0 0 0 0 0 0 1 0 Residual=E/1000 1 Failure criterion Intralaminar damage Ψ ( ε,d,T ) ∂Ψ σ= = (1 − d )C:ε ∂ε t t Fk := Φ k (σ ) − rk Free Energy per unit volume: Constitutive equation: Damage activation functions: Damage evolution: t t d = G ( rk ) Intralaminar damage Final biaxial failure stress envelope for (90/±30/90) E-glass/LY556 laminate. World Wide Failure Exercise Puck • International round robin to compare the most advanced failure criteria • Organized by Hinton & Soden (QinetiQ, UK), published in ’98, ‘02 • Cases of simplest constructions, e.g., no stress concentrations, or structural issues • Comparison indicates that strength prediction methodologies still immature. • What is the consensus? Intralaminar damage : σ22>0 and σ12 σ22 t T 0 2a σ22 0.3 Transverse Strength of 90 ° Ply, GPa Main unresolved issue: 9 ‘In-situ’ effects. T300/944 Dvorak, 1987 [±25/90n]s [252/-252/902]s [908]s Onset of delamination 0.2 [0/90n/0] Thin ply model Thin Thick 0.1 Thick ply model Unidirectional 0 0 0.4 0.8 1.2 1.6 Inner 90° Ply Thickness 2a, mm 2.0 Intralaminar damage: σ22<0 and σ12 Main unresolved issue: 9 Increase of strength when moderate transverse compression τ12 , MPa is combined with in-plane shear. Test (WWFE) σ22 120 100 80 60 Max Stress 40 Hashin 20 σ22 0 -160 -140 -120 -100 -80 -60 σ 22 , MPa -40 -20 0 Intralaminar damage LaRC03 Failure Criteria 3 (T) 3 (T) t 2a0 Matrix Crack 1(L) 2a0 σ22 Fibre kinck 2a0 2 L -XC ϕ σ11 σ22m σ11m -XC Intralaminar damage LaRC03 Failure Criteria Scotchply E-glass-LY556 T800-3900-2 CFRP laminate 160,0 LaRC03 Compressive stress, MPa 140,0 120,0 Max. Stress τ 12 [MPa] 100,0 80,0 Hashin 60,0 40,0 20,0 Hashin ‘73 [±θ]s LaRC02 Test, Shuart ‘89 α=00 α=44 0,0 -250,0 -200,0 -150,0 -100,0 -50,0 0,0 50,0 100,0 σ 22 [MPa] Lamination angle, degrees 0 α0=530 Applications Detail of notch tip Stitched/RFI Upper Wing Cover Panel 7-ply stack Potting Load ⎡ 45 / − 45 / 0 / 90 ⎤ ⎣ ⎦S Knife edges α Notch 5 43 in. z Potting y x 7 in. 19 in. Length of damage zone (in.) simulation 4 F 3 experiment E 2 D stitches C 1 B A 0 0 0.05 0.1 Applied end shortening (in.) 0.15 notch tip Conclusions Predicting Strength of Composites is Difficult 9 Calculation of stresses, strains, natural frequencies, buckling loads, is routine in aerospace industry. 9 Calculation of fracture and damage growth is not routine. Role of Progressive Damage Analysis 9 Simulates damage accumulation, load redistribution, and failure of a component. 9 Can reduce the cost of design certification. 9 Can lead to a better design. The technologies developed have a clear impact on the industry and services: 9 Abaqus Inc. selected the decohesion element developed to be implemented in version 6.5 of Abaqus FE code. 9 LaRC03 failure criteria selected to be implemented in Hypersizer. 9 Failure investigation of aircraft accident based on the technologies developed.