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 University2 Principal Investigator, Cornell University3 Grant Monitor, NASA Langley Research Center

Outline

• Motivation & objectivesi. Point-source damage: HOW TO LAND SAFELY?ii. Fatigue damage: HOW MANY MORE FLIGHTS?

• Relevant past work• Improvements in physics-based modeling

– Incorporating the nano- & micro-scales

• Current technical challenges

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Point-source damage: HOW TO LAND SAFELY?

www.youtube.com/watch?v=DUstvXSytRc

Airbus A300 damaged by surface-to-air missile

3

1) Develop finite element-based analyses to predict growth of point-source damage within airframe structures under realistic conditions and in real-time

2) 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

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Point-source damage: Objectives

Response surface

Point-source damage: Technical approach

Airbus A300 damaged by surface-to-air missile

Stiffeners

Skin

IdealizedDamage

Generic aircraft component damaged by surface-to-air missile

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• Integrate information from on-board sensors to characterize damage

• Develop interface with control system

• Parameterize damage configurations

• Store a response surface of computed allowable load given the damage configuration and query in real-time

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

Reduced model

http://www.free-online-private-pilot-ground-school.com/aircraft-structure.htmlwww.youtube.com/watch?v=DUstvXSytRc

Damaged Area

Point-source damage:Predicting damage configurations

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Before Impact

After Impact

0 degrees 45 degrees

T. Krishnamurthy and J.T. Wang, NASA Langley Research Center

Projectile Projectile

Original Load Allowable

Parameterized Damage State

Global Finite Element Model

Local Finite Element Model

Catastrophic Crack Growth?

Extract Local Boundary Conditions

Explicit Crack Growth Simulation

Decrease Load Allowable

Store New Load Allowable in Response Surface

YES

NO

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Point-source damage: Response surface method

Outline

• Motivation & objectives– 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

8

Fatigue damage: HOW MANY MORE FLIGHTS?

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.

April 28, 1988. Aloha Airlines Flight 243levels off at 7,000 meters...

25 mm

Small cracks start at each rivet hole…

…then link to form a lead crack

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ui10

Global-Local Hierarchical Modeling

ui

Internal cabin pressure, P

Initial crack

Fatigue damage: Relevant past

workFRANC3D-ABAQUS interface

for crack growth simulation

Displacement in z-direction

-1.10

-0.16[inch]

z

measured

predicted

What about -slanted crack growth?-influence of fundamental fatigue damage mechanisms?-the inherent stochastic nature?

Maximum tangential stress for crack trajectoryExperimental determination of phenomenological material

constants:- crack tip opening angle, CTOA- critical radius, rc

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Improvements in physics-based modeling: Modeling crack front with 3D finite elements

Shell-to-solid couple

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Improvements in physics-based modeling: Modeling crack front with 3D finite elements

SEM’s of 7075-T651 (R. Campman, CMU)

RDRD

Improvements in physics-based modeling: Considering common damage mechanisms

• (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

250 m

a

b

c

SEM/OIM courtesy of Northrop Grumman Corporation

Stage I/II illustration from:

C. Laird, 1967.

0Cycle: 1Cycle:

(a)

100Cycle:

(b)

3000Cycle:

(c)

10 m

Loading Direction

7075-T651

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– 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

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Improvements in physics-based Modeling: Incorporating the nano- & micro-scales

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Incubated crack

Grain Boundary

Molecular dynamics simulation

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

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