Analysis of a cracked plateCasa Day 16/11/05

Aloha Airlines Flight 243

Motivation

Honolulu International Airport, Hawaii

At 24000 feet… loud clap

No visual exterior inspection (nor required)

Flight attendant swept out of the cabin

1 dead, 65 injured

$5 million damage

Peel Test

45º

Force Displacement (constant speed)

Nickel layer

Substrate

Peel-Test Support

Uniaxial Stress

Stress

Strain

A F

Displacement Gradient

Displacement Gradient

Displacement

Approximation

Strain Tensor

rigid body motions

deformations

symmetric

symmetric

skew-symmetric

Strain Tensor

Physical Interpretation

diagonal

off-diagonal

Stress Tensor

Traction

Cauchy Stress

Equation of motion

Balance of linear momentum

Balance of angular momentum

body force

density

Equation of motion

Summary

Equations Unknowns

3

6

6

6

3

9

+ +

15

constitutive equations

15

6

Constitutive Equations

Lamé Moduli

Linear Elasticity:

Young’s Modulus

Poisson’s Ratio

Problem Description

Continuum Mechanics

Boundary Conditions

Plane Stress

Continuum Mechanics

Domain decomposition

Macro equations, Micro equations

Schwarz

ExampleDifference between

successive iterations for uu1

u2-u1

u1-u0 5.13

u2-u1 1.16x10-1

u3-u2 6.56x10-2

u4-u3 5.86x10-2

Future Work

- Grain structure

- Time

- Convergence analysis