Fatigue and Damage Tolerance Edward Herba, January 29,2004

Fatigue: Failure mechanism due to cyclic loading.

Damage Tolerance: Fail Safe Design Concept

Fatigue: Failure mechanism due to cyclic loading.

Damage Tolerance: Fail Safe Design Concept

Overview

• Designing for fatigue: Safe Life vs Fail Safe

• Fail-Safe: Fatigue calculation

• Fail-Safe: Damage Tolerance

• Case studies: Crashes involving fatigue

crack propagation

• Fractography

• Summary

Safe-life

• 1952 DeHavilland Comet: World’s first Commercial Jet-liner.

• Designed with Safe-Life concept (tested for life, SF, discarded)

• Assumed no cracks during design lifetime.

• Stress in area of windows was 70% of UTS

• Explosive decompression due to cracking at square window

corners.

• Triggered new design concept: Fail-safe based on fatigue crack

growth, inspection procedures and multiple load paths.

1950’s Comet Aircraft Window

Fail Safe Design Concept

The engineer must :

1) accept all structural members to contain flaws.

2) determine the critical flaw size.

3) use reliable inspection methods and equipment to

monitor flaw size and orientation.

4) assure an appropriate interval between inspections.

5) replace components, parts and members when they

are no longer safe.

Flap track, body & linkages

• Function

• 2nd Load paths (fails-safe, damage tolerant)

• materials (2024 Al, 7075, Ti, Steel)

S-N curve

Requires many S-N curves for a Miner calcRequires many S-N curves for a Miner calc

Haigh Diagram for Fatigue Data

R=min/max

Lines of constant endurance

R=min/max

Lines of constant endurance

Cumulative Fatigue Damage

Fatigue damage= n1/N1 after n1 cycles at 1

where N1 is the life at 1 from the S-N curve.

Palmgren-Miner linear cumulative damage hypothesis:

Total Damage caused by a varying amplitude load

cycle is the summation of the damage caused by

each individual loading cycle.

(n1/N1 + n2/N2 + n3/N3 +... ) = 1

Total damage=1/LF

DSG/Fatigue life= 1/LF

Total damage=1/LF

DSG/Fatigue life= 1/LF

Fatigue Calculation

Damage Tolerance

Function: To determine the effects of cracks in the structure

Objective: To provide an inspection program so that cracks

will not propagate to a critical size under limit load prior to

detection.

Methods of Analysis:

Deterministic Analysis

Probabilistic Analysis

Probabilistic vs Deterministic Analysis

Probabilistic Analysis (residual fatigue analysis) is a method

to determine inspection interval when there is a:

• Multiple load path structure (2nd load path not inspectable)

• Insufficient results from fracture mechanics (acrit <adet)

Probabilistic Analysis (residual fatigue)

Inspection Interval is determined as follows:

Inspection Interval=DSG (1-Dpre) / FS•Dafterfailure

where DSG=Design Service Goal

Dpre=Pre-Damage of element 2 while 1 was intact for DSG

FS=Factor of safety

Dafterfailure=Damage in 2 after failure of element 1for DSG

*Assuming element 1 is 1st load path

Deterministic Analysis: Crack Growth

Linear Elastic Fracture Mechanics are used to

determine:

• Crack Growth due to cyclic loads

• Residual strength for a given crack length

• Critical crack length for a given stress level

Fracture Mechanics Assumptions:

• Crack propagation rate depends on K and R for a given

material and conditions.

• Failure occurs when K reaches its critical value (from this

residual strength and acrit can be calculated)

Crack Propagation

a (n) = ai + (da/dn)dn

where

ai = initial crack length (ex: detectable)

da/dn = crack propagation rate (depends on K , R)

n = number of load cycles

Crack Growth

Paris Law: da/dn=A( K)p

Forman Law:

da/dn=Cf ( K)nf

(1-R)Kf- K

Stress Intensity Factor, K

K= • Y • ( • a)

= max- min

Stress Intensity factor: Fracture Toughness, Kcrit

Stress Intensity factor = Stress at crack tip / nominal stress.

Fracture toughness is a material property

Stress Intensity factor = Stress at crack tip / nominal stress.

Fracture toughness is a material property

Critical Crack length & Residual Strength

limit is determined by static stress dept.

Specimen Orientation

•Fracture toughness of 7079 (40.5) is < 2024 (45.0)

•Fracture toughness very dependent on thickness

•Fracture Toughness affected by heat treatment (particles,

dislocations)

• L-T is worse than

L-S

• Shows crack

propagation rate

is dependent on

grain orientation

Sample Calc: Crack in skin over stringer

Stress Intensity Correction Function

Progression of Crack Calculation

Locations of MSD on aircraft

• B737 Aloha Airlines 1988: Explosive decompression (18’ section)

• Failure along fuselage skin longitudinal lap joint which had been epoxy bonded

• Epoxy to take most of loads

• Poor bonding transferred load to rivets and crack grew from rivet to rivet.

Aloha Airlines countersunk rivet where fatigue crack started.

• MSD at Lap joint

• Importance of inspectability (crack was hidden behind a frame)

• Small crack was spotted, joint was disassembled and a much

longer crack found underneath.

•Japan Airlines B747 Crash 1985 (explosive

decompression of fuselage)

•Repaired bulkhead after tail strike was not done

properly.

•Doubler was not continuous putting overload on

the skin.

•Fatigue cracks at rivet holes, then linked (MSD)

and then failure.

Japan Airlines: Bulkhead failure

Chicago DC-10 crash 1979

•Engine fell off during take-off

•Incorrect engine removal procedure caused

fracture to engine support.

•Fatigue crack growth then started at this

cracked upper flange of aft bulkhead.

•The residual strength of the component was

insufficient and complete failure occurred.

Fractography

• SEM showing fatigue striations (1 per cycle in stageII)

• multiple crack origins

Summary

• Fatigue: Miner Rule of linear accumulated

damage

• Damage Tolerance: Crack growth rate is

controlled by K, R

• Importance of surface finish, assembly,

inspectability.