Crack Trajectory Prediction in Thin Shells Using FE Analysis 6th International Conference on Computation of Shell and Spatial Structures Cornell University and NASA Langley Research Center A.D. Spear1 J.D. Hochhalter1 A.R. Ingraffea2 E.H. Glaessgen3 1 Graduate Research Assistant, Cornell University 2 Principal Investigator, Cornell University 3 Grant Monitor, NASA Langley Research Center

Outline Motivation & objectives Relevant past work Point-source damage: HOW TO LAND SAFELY? Fatigue damage: HOW MANY MORE FLIGHTS? Relevant past work Improvements in physics-based modeling Incorporating the nano- & micro-scales Current technical challenges

Point-source damage: HOW TO LAND SAFELY? Airbus A300 damaged by surface-to-air missile www.youtube.com/watch?v=DUstvXSytRc

Point-source damage: Objectives Develop finite element-based analyses to predict growth of point-source damage within airframe structures under realistic conditions and in real-time Interface real-time damage assessment with control systems to provide a damage-dependent flight envelope to restrict structural loads in the presence of severe damage

Point-source damage: Technical approach Generic aircraft component damaged by surface-to-air missile Stiffeners Skin Idealized Damage Airbus A300 damaged by surface-to-air missile Integrate information from on-board sensors to characterize damage Develop interface with control system Reduced model Response surface Recast structural component as a lower order model (i.e. equivalent plate) Get the sensor description of inflicted damage and compute updated allowable load in real-time Parameterize damage configurations Store a response surface of computed allowable load given the damage configuration and query in real-time Response surface Damaged Area www.youtube.com/watch?v=DUstvXSytRc http://www.free-online-private-pilot-ground-school.com/aircraft-structure.html

Point-source damage: Predicting damage configurations Before Impact Projectile Projectile 0 degrees 45 degrees After Impact T. Krishnamurthy and J.T. Wang, NASA Langley Research Center

Point-source damage: Response surface method Original Load Allowable Global Finite Element Model Decrease Load Allowable YES Store New Load Allowable in Response Surface Extract Local Boundary Conditions Catastrophic Crack Growth? NO Parameterized Damage State Local Finite Element Model Explicit Crack Growth Simulation

Outline Motivation & objectives Relevant past work Point source damage: HOW TO LAND SAFELY? Fatigue damage: HOW MANY MORE FLIGHTS? Relevant past work Improvements in physics-based modeling Incorporating the nano- & micro-scales Current technical challenges

Fatigue damage: HOW MANY MORE FLIGHTS? April 28, 1988. Aloha Airlines Flight 243 levels off at 7,000 meters... Small cracks start at each rivet hole… 25 mm …then link to form a lead crack The plane, a B-737-200, had flown 89,680 flights, an average of 13 per day over its 19 year lifetime. A “high time” aircraft has flown 60,000 flights.

FRANC3D-ABAQUS interface for crack growth simulation Displacement in z-direction Fatigue damage: Relevant past work [inch] -0.16 FRANC3D-ABAQUS interface for crack growth simulation Global-Local Hierarchical Modeling Maximum tangential stress for crack trajectory Experimental determination of phenomenological material constants: - crack tip opening angle, CTOA - critical radius, rc Initial crack z -1.10 measured Internal cabin pressure, P What about -slanted crack growth? influence of fundamental fatigue damage mechanisms? the inherent stochastic nature? predicted ui ui

Improvements in physics-based modeling: Modeling crack front with 3D finite elements Shell-to-solid couple

Improvements in physics-based modeling: Modeling crack front with 3D finite elements RD RD SEM’s of 7075-T651 (R. Campman, CMU)

Improvements in physics-based modeling: Considering common damage mechanisms Loading Direction (a) Incubation – the process that leads to the first appearance of a cracked particle (b) Nucleation – the appearance event of a crack in the matrix (c) Propagation – the process of crack extension governed by microstructural heterogeneities Stage I – Slip along a single band Stage II – Slip along multiple bands, causing crack propagation subnormal to the global tensile direction (a) (b) (c) b 10 mm a c 250 mm Stage I/II illustration from: C. Laird, 1967. 100 Cycle: Cycle: 1 Cycle: 3000 Cycle: SEM/OIM courtesy of Northrop Grumman Corporation

Improvements in physics-based modeling: Incorporating the nano- & micro-scales FCC polycrystal plasticity for grains & linear elastic, isotropic for particles 1 Cycle @ 1% strain in simple tension, along RD-axis

Improvements in physics-based Modeling: Incorporating the nano- & micro-scales Molecular dynamics simulation Grain Boundary Crack Incubated crack

Technical Challenges Incorporating nano- & micro-scale simulation in a computationally feasible manner Determination of damage configurations and assessment during flight Better physical understanding of the governing mechanisms for crack growth Why does CTOA appear to work? Interpolating between damage states Development of real-time interface with control system