material's fatigue

7/30/2019 Material's fatigue

1/25

Objective

Able to predict fatigue life of aircraftstructures under cyclic loadings

Aircraft fatigue analysis


2/25

Introduction

Prepared by :Dr. Dayang LailaWeek 3

Fatigue is a very important area of concern which willaffect the structural integrity.Approximately 75% of all aircraft structural failures

are due to fatigue.

Definition:Fatigue is a process of progressive permanentstructural change in a material subjected to

repeated cyclic applications of stressesassociated with operating loads. It is a failuremode that occurs as a result of large number of

fluctuations.


3/25

Prepared by :Dr. Dayang LailaWeek 2

A single load will not harm the structure if below static failure load, butif repeated many times, fatigue failure can occur.

Loads applied on aircraft structures are seldom static (monotonic) butusually fluctuate either above some mean stress or with completereversal in sign.

Endurance limit (fatigue limit) the highest stress level which thematerial can withstand for an infinite number of load cycles withoutfailure.

Fatigue failure initiates small (micro) cracks in the material whicheventually grow into large (macro) cracks. If not detected, will result incatastrophic failure.


4/25

Scope of problem

10% of all aircraft crashes are due to structuralfailure, but only 2-3% in civil aircraft.

Approximately 2/3 of all structural failures are dueto fatigue.

Historical disasters: DeHavilland Comet aircraft in1954. Fatigue cracks in the pressurized fuselage

structure initiated a fuselage decompression failure at a

high altitude.


5/25

Major cause of fatigue cracking

Design deficiencies (stresses too high, notch effects, etc)

Improper assembly (including damage by maintenance)

Corrosion added initiation (surface corrosion progressing inwards

causing strength deteriorates)Defective material

Fretting aided initiation (small scale rubbing movements andabrasion of adjacent parts)

Thermal aided initiation (caused by thermal expansion andcontraction)

High frequency stress fluctuations due to vibrations excited by jetor propeller noise.


6/25

Why structures fail due to fatigue?

Aircraft loads are cyclic and complex, depending routes andtypes of aircraft. If the fracture of a component is the primaryfailure mode, it is unlikely to be due to a simple event.


7/25

-stress concentrations at holes, sharp corners, cut-outs, etc willincrease the probability of fatigue failure. Fatigue cracks aremost likely to initiate at these stress concentration sites. It isvery important to get correct stresses in order to estimate

fatigue lives of structural components.


8/25

Elastic stress concentration


9/25

Definitions for fatigue analysis

Stress amplitude, Sa=0.5(Smax Smin)Mean stress, Sm=0.5(Smax + Smin)

S = Smax-Smin

R = Smin/Smax

Stress cycle: it is the smallest section of the stress-timefunction which is repeatedly periodically and identically.


10/25

Other examples of simple constant amplitude loading cycles.


11/25

Endurance, N the number of stress cyclesto failure for tests atconstant amplitudes.

Fatigue strength, Sam(N) the alternating stressat a specified meanstressthat give rise to an endurance N. Example: Sa0(10

4) denotes that

the alternating stress which under zero mean stress give rise to anendurance of 10000 cycles.

Fatigue limit, Sam(), or Se the highest level of alternating stress fora given mean stress at which the endurance may be regarded as infinite.In other words, it is the highest level of specified character which maybe applied for an infinite number of cycles.

Fatigue life the useful life as limited by fatigue. The criterionoflimitation maybe one of strength, performance or service ability. Inaeronautics the life may be expressed as flying hours, number offlights, number of applied loading cycles, etc.


12/25

Fatigue analysis under constantamplitude loading

Fatigue test on actual components are often impossible- high cost and time consuming.

Laboratory fatigue testing method:

Eg: Rotatingbending

machine.


13/25

Presentation of fatigue data

1. Fatigue limit (endurance limit)

2. S-N curve

experimental tests

Derived S-N curve

Statistical nature of fatigue

1. ESDU data sheet

From rotating bending tests, relationship was found betweenfatigue limit and ultimate tensile strength;

Se/Sult = 0.5 (steel, where mean stress is zero)


14/25

Example of fatigue curve

Example of S-N curve as a result of a number of fatigue test


15/25

Mean stress effects on fatigue life

In most applications, cyclic stress applied to a component is seldomfully reversed.

Higher tensile mean stress will decrease/increase fatigue life?


16/25

Combined effects of alternating andmean stress on fatigue endurance


17/25

Gerber, Goodman and Soderberg diagrams


18/25

Observations of models

1. The Soderberg line provides a conservative estimate offatigue life for most engineering alloys

2. Goodmans line matches experimental data quite closelyfor brittle metals, but is conservative for ductile alloys.

3. Gerbers parabola is generally good for ductile alloys.

Experience has shown that most test data liebetween the Gerber and Goodman diagrams.


19/25

In general, the most widely used design aid for estimating theeffect of mean stress on the alternating stress amplitude is theGoodman diagram, which at its simplest is shown below. Notethat the ratio OB/OA is a reasonable assessment of theReserve Factor or Safety Factor.


20/25

Fatigue analysis under variableamplitude loading

Constant amplitude loading not realistic.


21/25

Block loading spectrum

The load spectrum may be simplified by some multilevel stresspatterns(block loading spectrum). The stress cycles is divided intogroups characterized by stress magnitude and number of cycles.


22/25

Cumulative damage due to a varietyof stress amplitudes

Best known and widely used method for estimating thecumulative damage is known as the Palmgren-Miners rule, orMiners law.Hypothesis of the law: if the structure is subjected to ni

cycles at a stress amplitude of afor which the averagenumber of cycles to failure is Ni, then the amount of damage(Di) which will be caused by this particular stress amplitudewill be ni/Ni. In other words, for each stress level the fatiguedamage is

)(

)(

i

i

iNoadcyclesallowablel

ndcyclesappliedloaD


23/25

When fatigue loading involves many levels of stress amplitudes,the total damage is a sum of the different damage ratios andfailure should still occur when the ratio sum equals one.

In general form:

0.11

k

ii

ii

N

nD

Where k = number of stress levels in the loading spectrumi= i

thstress level

ni= number of cycles applied at i

Ni= fatigue life at i(from material S-N data)


24/25

Palmgren-Miners Linear CumulativeDamage Rule


25/25

Limitations of Palmgren-Minermethod

These effects are not accounted for:1. The effect of the order of the load applications (as

shown below)

2. Notch effect (such as fasteners holes, etc)

material's fatigue

Documents