Design and Sizing of Structure for Safe Service Lifeunder Fatigue Loading

Fatigue from a structural mechanics point of view

TMMI09 Vibrations and Fatigue, December 15, 2015

Life Design Principles

Fail-safeSafety-by-design

Damage toleranceSafety-by-inspection

StaticSafety-by-margin

Safe-lifeSafety-by-retirement

Safe-Life → Safety-by-Retirement

No defects are considered to exist in new constructions.

Establish an allowable usage time so that all structures will be removed from servicebefore the worst one suffer fatigue failure.

No inspections necessary.

Durability Analysis

Design for inspectability and redundancy (multiple load paths) or crack arrestors so thatstructure can tolerate large damages.

Inspections shall be performed frequently enough to ensure the detection of cracksprior to strength to fall below the lowest acceptable limit = residual strengthrequirement

No requirement limits the period of use

Fail-safe→ Safety-by-Design

Fail-Safe designs

The wing’s bending material is mainly concentrated the flanges of the beams. Thebeam alone is the primary load carrier.

Rough sections of the beams leads to high fracture growth rate for any fatigue crackand short critical crack lengths.

If one tries to maintain security using inspections, it would require unrealisticallyshort inspection intervals. It is better to replace the lower flange after a usagecorresponding safe life.

i.e. Not Fail-safe, classify the structure as Safe-Life structure

Three beams with divided flanges (two L- profiles for each beam) gives improved fail-safe characteristics.

Although fatigue crack would grow relatively quickly and result in complete failure ofan L – profile, the beam retains the wing’s main load carrying capacity .

Further distribution of the wing’s bending material on both beam flanges andstringers, besides the load carrying wing skin, brings improvements in tworespects :

1. When the number of parallel collaborating elements increase, any loss of anelement due to fatigue failure will result in a relatively mild impact on theresidual strength .

2. Closely spaced stringers reduces the growth rate of any skin cracks, and willalso increase the critical crack length for any skin cracks , i.e. makes the skinmore damage tolerant.

By dividing the skin in several "planks" it is even possible to allow a skin plate crack togrow beyond critical length with a possibility of unstable growth.

At any unstable crack growth, it is possible to tolerate a complete plank to get lostand still maintain a satisfactory residual strength of the complete wing section .

Comparison between beam flange and stringer reinforced panel:

Although the difference in the damage tolerance is large , there exists nodistinct difference between safe-life behavior and fail-safe behavior. It isonly a question of degree difference, which, however, has great practicalsignificance in the determination of the inspection procedures

Crack like defects of the specified size areconsidered to exist already in new constructions

Slow Crack Growth - Non inspectableDetermine an allowed usage time < half the time needed for the strength, due tocrack growth, to be reduced below the residual strength requirement .

Slow Crack Growth - inspectableEstablish a safe inspection interval < half the time needed for the strength, due tocrack growth, to be reduced below the residual strength requirement .No limitations of the period of use.

Fail SafeAfter the total failure of a load path, or for unstable fracture growth with followingcrack arrest , shall the remaining life be at least two inspection intervals beforestrength reduced down to residual strength requirement .No limitations of the period of use

Damage Tolerance→ Safety-by-Inspection

Damage Tolerance AnalysisC

RAC

KLE

NG

TH

LIFE

critical crack length (ac)

max allowable crack length (af)

visually detectable crack length (ad-v)

detectable crack length (ad-NDI)needs special NDI

safe inspectioninteval - NDI

Initial flawquality (ai)

ad

Slow crack growthNon-inspectable life

safe inspectioninteval - visual

Attachments- bolted joints- lugs- bolts

Stress concentrations- holes- thickness steps- radii- stiffener run-out- eccentricity

Fatigue prone components

Structural configuration

Operational loadingVariable amplitude

Test specimen

Test loadingConstant amplitude

Manufacturing and surfacetreatment effects

Environmental effects

Fatigue analysis task

Fatigue and Damage Tolerance ManagementRe

gula

tions

&Sp

ecifi

catio

ns

Structural Analysis

Mission Analysis

Loads Analysis

Local Analysis

Product Model

Manufacturing

Service

Flight Testing

Service Loads Monitoring

Structural TestingDetails Complete A/C

Mission Parameters§ accelerations§ angular velocities§ speed§ altitude§ control surface deflections§ thrust§ fuel consumption§ store configurations

Mission Segments§ safety and function tests§ ground manoeuvring§ combat manoeuvring§ store separation§ gun firing§ landing

Mission Types§ basic training§ air-to-air§ air-to-surface§ reconnaissance

CLIMBCRUISERETURN

DESCENT

LANDING

CRUISE

INTERCEPT

AIR COMBAT

Example: Combat Air Patrol

Operational Analysis

Operational profile – influence on loads

Principles of loads model

flightparameters

wind tunnel measurements

calculation of balancedloading of airframe

§ flight control system§ aeroelasticity

configurationdata unit load cases

pressure distributions

acceleration distributions

CFD analysis

Selection and extraction of localload sequences for anystructural part of the model

Pressure distributionM=1.2, b=6o

Pressure distributionM=0.9, a=6o

internal pressurestemperaturespoint loads

Solution of unitload cases

Loading

Material properties

Failure criterion

• Effective stress

• Damage accumulation

CalculatedFatigue life

Allowedservice life

Safety factor

Fatigue life calculation under safe life principles

Structural configuration

Fatigue Strength data – Basic

SD 23-0212: κ- Factors for Aluminium,Surface Treatments

Adjustment factors (examples)

• Surface Treatments• Machining Operations• Temperature Exposure

SD 23-0215: κ- Factors for Aluminium,Combined Operations and Corrosion Protection

LUG – Life Enhancement by CX & RB – AA7010-T3651

Fatigue Test Results:

• The points of crack initiation are located to the holesurface

•A ratio of 2 - 2.5 is obtained when the fatigue life of thebasic lug and the expanded lug are compared

Local stress analysis – example of a bolted joint

5000 10000 15000 20000

Time step

Left

inne

rele

von

torq

ueM

Mmax

Mmin

Load sequence

0- +

STRESS

The Rain Flow Count Algorithm

1 cycle: -5 +51 cycle: 0 +51 cycle: 0 +21 cycle: -3 -1

A

A

G

G

H

H

E

E

C

C

B

B

F

F

D

D

Rain flow count and the materials stress-strain hysteresis loop

Fatigue Damage Model

Palmgren – Miners cumulative damage law

iN1D =D

o

j

1i i

i DNnDD ==D=å å

=

During timeT0

å= NnDFatigue life ended when Reach the value 1

1NnD ==åValue Is reached at time 00 DTT =

Fatigue life is calculated

0T

0

Nn

TT

÷øö

çèæ

=

å

101 103 105 107 109N

25

Sa

102 103 104 105

Reference period T0

-10

10

30

50

n

S

n =N200

10000

Sm = 15

Sm = (40+(-10))/2Sa = (40-(-10))/2

Fatigue Damage Model – Example – Max Load Truncation

nz

Truncation Level

s = 24 x nz

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Fatigue Damage Model – Example – Max Load Truncation

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Fatigue Damage Model – Example – Max Load Truncation

PAGE 32

Fatigue Damage Model – Insufficiency

• A moderate number cycles to high maximum tensilestresses are promoting fatigue life because they leave localresidual compressive stresses at stress concentrations.According to cumulative damage hypothesis all cycles thatexceed the fatigue limit are damaging.

• The beneficial effect is enhanced if the high stress cyclesare spread throughout the loading block compared tooccur close together in time (sequence effect). Thecumulative damage hypothesis is not able to take intoaccount the order of loads.

• Stress variations with low compressive stresses are moreharmful than what corresponds to partial damage sincesuch variations after leave unfavorable tensile residualstresses.

• The unfavorable effect is enhanced if the compressivestresses are scattered throughout the sequence.

Fatigue Damage Model – A Reflection

Stress cycles less than the fatigue limit gives no contribution to partial damage atN = ∞. In reality, these small stress cycles reduce figigue life by accelerating thegrowth of previously formed cracks, promote fretting corrosion or help toextinguish favorable residual stress state.

103

104

105

106

107

40

60

80

100

150

250

300

Log(N)

Log(Ds

)

8k4 <<

k

1

k

2

1

1

2

NN

÷÷ø

öççè

æss

=

( ) 34.02.11NN 612 ==Increase of stress with 20% reduce life to 1/3

Decrease of stress with 10% doubles the life ( ) 9.19.01NN 612 ==

Margins using safety factors on:

§ Loads - design for larger loads than expected to occur

§ Usage period - design for a larger number of loads than expected

§ Fatigue strength - design using materials data which is worse than available test data.

Apply combinations of these factors in order to obtain a probability of failure which is inacceptable levels

Safety against fatigue

A probability of failure in the range of 10-3 means that one construction out of 1000 is expectedto fail.

To determine the safety factor required to achieve this failure probability or less with testing isnot feasible

Collection of operating experience get usually only failure data for the extremely worstspecimens.

To gain insight into these low probabilities must extrapolations be used i.e. to choose aprobability model and a probability distribution.

§ Prerequisites for loadswhat is the expected scatter? What are the design load cases? Median values or do theyrepresent severe conditions which only a few structures are exposed to?

§ Prerequisites for material strengthWhat kind of materials data is available? Is it average data or reduced data?

§ UncertaintiesAre there any uncertainties in the calculations? Is there sufficient support for adjustments oftest data (surface treatment, etc.)

§ TargetWhat is acceptable failure probability

Sizing with requirements that no stresses may exceed the fatigue limit

Choice of safety factor fs

Assuming that the stress is normally distributed, the required reduction factor fs for afailure probability of 10-3 can be determined

ss s

ss

f×-

=09.350max

50max Material smax 50 ss ss / smax 50 fs18-8 490 25 0.05 1.18

SAE 4340 393 27 0.07 1.27

7075-T6 227 17 0.08 1.31

103 104 105 106 107

smax 50

fs

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Severe design spectra and reduced materials data

Level of severity corresponds to zstandard deviations and can beexpressed as a factor

nszdimn 10

nnf ×==

Equivalent to a total factor on life0x ³D

NnT fff ×=

Nf Reduction factor on materialsdataDx

log fn

log fN

2 sn = log fn

log fT

Average spectrum (50% exceedings)

Design spectrum (2.3% exceedings)

Sequences for test verification

addition of overloadsfor test verification ofcomposite structures

elimination of insignificantcycles for metallic

elimination ofpeak loads

structures

truncation fortest verificationof metallicstructures

insignificant cyclesfor compositestructures

Test # 5.1.7.3 Wing to fuselage attachment

Test # 5.3.6.1 Canard wing and pivot

Test # 5.1.17.2 Rear fuselage with fin and rudder

Full-scale test programme - Airframe (examples)

Mechanical systems - test overview

Flight control system§ servo actuators (SL+DT)§ pedal housing (SL+DT)§ control stick assembly (SL+DT)§ leading edge flap control system

Landing gear system§ nose and main landing gear (SL)§ actuators (SL)§ wheels and brakes (SL)

Escape and oxygen system§ pressure vessel (SL)

Hydraulic system§ tubes and fittings (SL)§ pumps (SL)§ valve units (SL)§ accumulators (SL)

Secondary power systems§ auxiliary power unit (SL)§ air turbine starter (SL)§ aircraft gear box (SL)§ power transmission shaft (SL)

SL = Safe LifeDT = Damage Tolerance

Environmental system§ reduce and shut off valve (SL)§ heat exchangers (SL)§ engine bleed systems (SL)

Gun and armament install.§ gun deflector (SL+DT)§ gun fwd attachment (SL+DT)§ weapon pylons (SL)

Fuel system§ engine feed pipe (SL+DT)§ refuelling transfer units (SL)§ cooling and transfer pipe (SL)

Damage tolerance test verification of servo actuators

§ Two test articles§ 40 artificial defects inserted§ Fatigue crack growth from 33 defects

Case StudiesEvolution of Requirements

Fail of Fail-Safe

Lusaka - Boeing 707-321C

May 14, 197747621 hours & 16723 flights

• Take-off Nairobi: 07.17• Approach Lusaka: 09.28

Failed Tailplane Spar