Damage Tolerance Philosophy for Bonded Aircraft Structures Towards a generic assessment approach 6-7-2009 Dr. C.D. Rans Aerospace Materials 27-05-2009 Faculty of Aerospace Engineering Delft University of Technology Challenge the future
Possible Damage Scenarios Generic Bonded Structure Adherent damage Bond line damage Damage tolerance approach to deal with all three scenarios Adherent and bond line damage Damage Tolerant Philosophy for Bonded Aircraft Structures 2 | 27
I Have Seen This Before! Coupled Adherent and Bond Line Damage FMLs Crack opening Crack opening constraint constraint Can this be translated to Delamination at Delamination at Fatigue crack Fatigue crack generic bonded structures? metal-fiber interfaces metal-fiber interfaces growth metals growth metals Damage Tolerant Philosophy for Bonded Aircraft Structures 3 | 27
1. Prediction Approach Damage Tolerant Philosophy for Bonded Aircraft Structures 4 | 27
What Do We Need? Required Prediction Approaches • Bond line delamination growth • Adherent damage growth • Damage interaction Damage Tolerant Philosophy for Bonded Aircraft Structures 5 | 27
Adherent Crack Growth Prediction Approach • Fracture Mechanics description using Paris type relation • Mode I crack growth • Empirical relation for R-ratio effects da n dN = Δ C ( K ) cg cg eff ( ) ( ) Δ = + + − 2 K 0.55 0.33 R 0.12 R 1 R K eff max Damage Tolerant Philosophy for Bonded Aircraft Structures 6 | 27
Bond Line Delamination Growth Prediction Approach • Fracture Mechanics description using Paris type relation • Mode II delamination growth • Reformulated strain energy release rate range db dN = Δ n C ( G ) d d II Δ ≠ − G G G II II II max min ( ) 2 = − G G II II max min Damage Tolerant Philosophy for Bonded Aircraft Structures 7 | 27
Mode II Growth Assumption Bond Line Delamination Growth • Adhesive joints designed to -2 10 transfer load through shear -3 10 • Mode II assumption supported by test data -4 10 db/dN [mm/cycle] • FML delamination characterization -5 10 • Composite laminates -6 10 • Damage growth, not initiation -7 10 -8 10 -9 10 0.2 0.4 0.6 0.8 1 √ G max - √ G min [MPa mm] Data obtained from Alderliesten et al. (2006) Damage Tolerant Philosophy for Bonded Aircraft Structures 8 | 27
Strain Energy Release Rate Range Bond Line Delamination Growth • Linear elastic fracture mechanics description • Principle of Similitude • Principle of Superposition = + + G G G G T I II III 2 ⎡ ⎤ = + + + G G G G � ⎣ ⎦ I I (1) I (2) I (3) Δ ≠ − G G G 2 II II II ⎡ ⎤ = + + + G G G G � max min ⎣ ⎦ ( ) II II (1) II (2) II (3) 2 = − G G 2 II II ⎡ ⎤ = + + + max min G G G G � ⎣ ⎦ III III (1) III (2) III (3) Damage Tolerant Philosophy for Bonded Aircraft Structures 9 | 27
Strain Energy Release Rate Range Bond Line Delamination Growth • Illustrate with Mode I DCB specimen 2 P dC = G I 2 b da For identical crack and specimen geometries = ⋅ 2 G const P I Compare applied loading to obtain the same Δ G for 2 different R-ratios Damage Tolerant Philosophy for Bonded Aircraft Structures 10 | 27
Strain Energy Release Rate Range Bond Line Delamination Growth = ⋅ 2 G const P I Damage Tolerant Philosophy for Bonded Aircraft Structures 11 | 27
Strain Energy Release Rate Range Bond Line Delamination Growth • Advantages of new formulation • Removal of residual stress influence on SERR range • Permits use of superposition in analysis • R-ratio effects can be studied Data obtained from Lin and Kao (1996) -5 -5 10 10 Post-stretched (C2) Post-stretched (C2) Post-stretched (C4) Post-stretched (C4) Post-stretched (C6) Post-stretched (C6) -6 -6 10 10 As cured (C2) As cured (C2) As cured (C4) As cured (C4) db/dN [m/cycle] db/dN [m/cycle] As cured (C6) As cured (C6) -7 -7 10 10 -8 -8 10 10 -9 -9 10 10 -10 -10 10 10 1 2 3 1 2 3 10 10 10 10 10 10 2 [(J/m 2 ] ( √ G max - √ G min ) 2 )] G max - G min [J/m Damage Tolerant Philosophy for Bonded Aircraft Structures 12 | 27
Damage Interaction Prediction Approach • Discretize damage area • Enforce displacement compatibility between adherents • Determine load redistribution resulting from damages • Superposition of load redistribution on damage growth Damage Tolerant Philosophy for Bonded Aircraft Structures 13 | 27
Displacement Compatibility Damage Interaction Damage Tolerant Philosophy for Bonded Aircraft Structures 14 | 27
Displacement Compatibility Damage Interaction • Cracked adherent = − v v v P P 1 br • Undamaged adherent δ = δ + δ + δ P P ad 2 br Over delamination length, b = δ → v P br Damage Tolerant Philosophy for Bonded Aircraft Structures 15 | 27
Influence on Damage Growth Damage Interaction • Superposition of bridging load = − K K K P P 1 br = G f P P P ( , , ) 1 2 br • Implementation • Analytical solutions • FEM Discretization into 1-D damage interaction zones Damage Tolerant Philosophy for Bonded Aircraft Structures 16 | 27
2. Case Studies Damage Tolerant Philosophy for Bonded Aircraft Structures 17 | 27
Bonded Patch Repair Case Studies • Predict edge delamination growth behaviour • Adherents undamaged • Delamination growth model only • Initiation assumed at 1 st load cycle • Approximate as a 1-D problem Damage Tolerant Philosophy for Bonded Aircraft Structures 18 | 27
Bonded Patch Repair Case Studies • Good agreement in damage 100 growth rates S max = 106 MPa S max = 120 MPa • Shift in data due to damage 80 initiation behaviour experimental measurement 60 b [mm] 40 20 mode II prediction 0 0 20 40 60 80 100 N [kcycles] Damage Tolerant Philosophy for Bonded Aircraft Structures 19 | 27
FML Panel with a Bonded Strap Case Studies • Cracked Glare panel with an intact bonded titanium strap • Damages • Cracked metal layers of FML • Delamination between metallic and fibre FML layers • Delamination between strap and FML • Superposition of multiple bridging effects = − − K K K K farfield br FML , br stiffner , G , G C-scan FML stiffener Damage Tolerant Philosophy for Bonded Aircraft Structures 20 | 27
FML Panel with a Bonded Strap Case Studies Data obtained from Rodi (2007) 20 front left front right 18 delamination shape Rear Left Rear Right • Prediction Prediction 16 14 • Intact central strap 12 b [mm] 10 8 6 4 2 0 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 x [mm] 0.0002 0.08 crack opening displacement da 0.00018 0.07 0.00016 0.06 0.00014 dN Crack opening V(x) [mm] da/dN [mm/cycle] 0.05 0.00012 0.04 0.0001 0.00008 0.03 0.00006 0.02 0.00004 0.01 0.00002 0 0 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 Crack length [mm] x [mm] Damage Tolerant Philosophy for Bonded Aircraft Structures 21 | 27
FML Panel with a Bonded Strap Case Studies • Prediction • Broken central strap = − + K K K K farfield br FML , br stiffner , Data obtained from Rodi (2007) 0.003 0.25 crack opening displacement da 0.0025 0.2 dN 0.002 Crack opening V(x) [mm] da/dN [mm/cycle] 0.15 0.0015 0.1 0.001 0.05 0.0005 0 0 12.5 22.5 32.5 42.5 52.5 62.5 72.5 82.5 12.5 22.5 32.5 42.5 52.5 62.5 72.5 82.5 x [mm] Crack length [mm] Damage Tolerant Philosophy for Bonded Aircraft Structures 22 | 27
Metallic Skin with Bonded Stiffeners Case Studies • Predict crack growth in stiffened panel • Aluminum skin • 7 bonded aluminum stringers • 7 bonded aluminum straps • Central stringer initially broken • Stiffener failure assumption • Superimpose bridging effects of all stringers + ∑ = K K K farfield stiffeners G 1 , � , G stiffner stiffnerN Damage Tolerant Philosophy for Bonded Aircraft Structures 23 | 27
Metallic Skin with Bonded Stiffeners Case Studies 0 10 15000 st Doubler st Stringer Broken Stringer 1 1 da/dN [mm/cycle] -1 10 10000 N [cycles] -2 10 5000 -3 10 0 0 50 100 150 200 250 a [mm] Damage Tolerant Philosophy for Bonded Aircraft Structures 24 | 27
Summary • Damage tolerance analysis philosophy • Simultaneous analysis of adherent and bond line damage • Linear elastic fracture mechanics description of damage growth • Damage interaction through displacement compatibility and superposition • Philosophy demonstrated to work for bonded metallic and hybrid structures • Cracked metal adherents • Bond line delamination growth • Crack opening displacement Damage Tolerant Philosophy for Bonded Aircraft Structures 25 | 27
Summary • Potential for composite structures • Stiffness reduction in damaged composite • Determination of load redistribution through displacement compatibility (superposition of effects) • Requires further work and understanding of composite damage growth • Potential power of superposition and linear elastic fracture mechanics for delamination growth prediction • Proper formulation of SERR range Damage Tolerant Philosophy for Bonded Aircraft Structures 26 | 27
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