Fatigue

Question 1

What is a top-level definition of fatigue?

Answer 1

• Repeated cyclic loading.
• Accumulation of microscopic fatigue damage at a defect/flaw.
• Crack formation and growth.
• Catastrophic failure.

Question 2

How does the microscopic fatigue damage arise?

Answer 2

• Microscopic fatigue damage is traced to localised plastic deformation, even if the applied global stress is well below the material elastic limit.
• Stress concentrations at flaws can produce dislocations which increase and move with high stresses.
• These dislocations impede one another and then must form new surfaces (by cracking) to continue absorbing energy.

Question 3

What is the difference between ‘safe life’ and ‘fail safe’ for design analysis?

Answer 3

Safe Life:

• Fatigue analysis.
• Assumes no initial macroscopic flaws.
• For safety critical design.

Fail Safe:

• Fracture analysis.
• Assumes initial macroscopic flaws.
• For most easily inspected components.

Question 4

Describe the key aspects of a cyclic stress-strain plot, in the form of a hysteresis curve.

Answer 4

• Area within the loop is the work done/ energy absorbed by the material on each complete load cycle.
• Associated with the accumulated fatigue damage.

Question 5

Detail the two key cyclic-dependant changes in material properties. How can the changes be identified from hysteresis curves?

Answer 5

The fatigued stress-strain response may not be the same as the un-fatigued stress-strain response. Material flow and fracture will change; elastic modulus will not!

• Cyclic hardening (high stress for a given strain).
• Cyclic softening (lower stress for a given strain).

The stress-strain curves can be generated from the hysteresis peaks.

Question 6

What energies are responsible for crack initiation and propagation?

Answer 6

Crack initiation (fatigue) - plastic strain energy.
Crack propagation (fracture) - elastic strain energy.

Question 7

Define fatigue toughness.

Answer 7

The sum of the individual hysteresis energy increments over the fatigue life, denoted by ‘W_p’.

Question 8

List the factors affecting initiation and Stage 1 growth.

Answer 8

• Material under tension or compression.
• Dependant on shear-slip formation.
• In direction of max shear stress planes.
• Dependant on surface properties.
• Slow growth.

Question 9

List the factors affecting propagation and Stage 2 growth.

Answer 9

• Predominantly under tension.
• Dependant on stress concentration at crack tip.
• Growth on planes of maximum tensile stress.
• Characterised by shell markings.

Question 10

Define dislocations.

Answer 10

• Defects that cause lattice distortion centred around a line.
• Extra half plane of atoms in the lattice.

Question 11

What is the ‘critical resolved shear stress (tau_crss)’?

Answer 11

A resolved shear stress ‘tau_r’ may be produced on a slip system, causing the dislocation to move on the slip plane in the slip direction.

I.e. when sigma -> tau_r >= tau_crss (where tau_r = F_r / A_slip plane)

then slip occurs!

Question 12

How do molecular structures affect slip?

Answer 12

FCC:

• Low tau_crss (0.35-0.70)
• 12 slip systems.
• Cross slip can occur.
• Ductile.

BCC:

• High tau_crss (35-70)
• 48 slip systems.
• Cross-slip can occur.
• Strong.

HCP:

• Low tau_crss (0.35-0.70)
• 3 slip systems (increased by alloying/heating to elevated temperatures).
• Cross-slip cannot occur (unless slip-systems increase, as above).
• Relatively brittle.

Question 13

What are the two regimes of fatigue life?

Answer 13

1) Low cycle fatigue @ <50,000 cycles (high stress).

2) High cycle fatigue @ >50,000 cycles (low stress).

Question 14

Describe some key attributes of low-cycle fatigue.

Answer 14

• Carried out under strain control to prevent ‘runaway’ instabilities common under high stress.
• Superimposes elastic and plastic strain components.
• Manson-Coffin relations are available to estimate the plastic line.
• The ‘Transition Life’ the the point at which the components of elastic (low stress = long lives) and plastic strain (high stress = short lives) are equal, and marks the point where each strain component dominate.

Question 15

Describe some key attributes of high-cycle fatigue.

Answer 15

• Typically characterised by stress-life ‘S-N’ diagrams for constant amplitude tests (I.e. fully reversed, zero mean cyclic stresses).
• Fatigue/endurance limit ‘S_inf’ is the reversed cyclic stress that can be sustained for effectively infinite fatigue life.
• Fatigue/endurance strength ‘S_N’ is the reversed cyclic stress that can be sustained for a given life of N (typically 10^6) cycles.

Question 16

What are ‘safe’ design curves?

Answer 16

Safe design curves are S-N curves that are factored by life or stress factors to account for scatter of fatigue lives. This occurs despite using (apparently) identical materials!

Question 17

What is the R-ratio, when describing load cycles with non-zero means?

Answer 17

The ratio of minimum to maximum cyclic stresses.

Question 18

What happens to fatigue life with:
A) Tensile mean stress
B) Compressive mean stress

Answer 18

A) Tensile = reduce fatigue life (opening cracks).

B) Compressive = increase fatigue life (closing cracks).

Question 19

Does creep of mean stresses occur under load control?

Answer 19

Yes - if the material has different tensile and compressive responses then creep will occur, even under fully-reversed cyclic stresses.

Question 20

What are residual stresses? Where may they be useful?

Answer 20

Residual stresses are effectively local, internal mean stresses which act in addition to any externally applied stress. They are always balanced within the material.

• Peening of mild steel (10x increase in fatigue life).
• Cold working drilled holes to delay cracking onset.

Question 21

What is an ‘over-load’? What are its effects?

Answer 21

An over-load is a single high load occurring on a typically cyclic loading. They create residual stresses at notches of the opposite sign in stress concentration regions.

Question 22

Describe the ‘fatigue notch sensitivity parameter’.

Answer 22

The fatigue notch sensitivity parameter ‘q’ is defined on the fatigue reduction factor ‘K_f’ and static mono tonic stress concentration factor ‘K_t’.

Full notch sensitivity: K_f = K_t, q = 1.
Full notch insensitivity: K_f = 1, q = 0.

Question 23

Describe ‘cycle counting methods’ for the idealisation of complex service loading histories. What are some assumptions?

Answer 23

Counting methods reduce complex, variable amplitude load sequences to sets of constant amplitude cycles, described by peak-trough values or mean-alternating values.
Assumptions:
- Cycle not time-dependant.
- Independent of loading wave-form.
- Independent of load sequence.

Question 24

Describe the ‘Range-Pair-Range “Rainflow”’ counting method. List the assumptions.

Answer 24

This method selects pairs of load reversals which correspond to closed hysteresis loops, assuming that:

• These represent discrete damage events.
• The damage caused by a large event is not affected by its interruption to complete a small stress-strain loop, simply added to the total as its own event.
• Material memory effect, which results in continuous hysterisis curves for interrupted events.

Question 25

What is a ‘load spectrum’?

Answer 25

A load specturm is a range of constant amplitude, counted cycles represented by ‘exceedence curves’, which themselves are cumulative,active distribution function curves.

Question 26

Describe the combination of up and down peaks, in regards to exceedence curves.

Answer 26

• For a relatively symmetric load peak distribution function (e.g. gust loading), the cumulative spectrum exceedence curves are usually drawn for the up-peaks only. This whole spectrum is then assumed to be symmetric about the mean.
• For a distinctly unsymmetric load peak distribution functions (e.g. manoeuvre loading), the up and down peaks are paired by the counting method or exceedence curve pairing of those with the same frequency of occurrence.

Question 27

Describe ‘spectrum extrapolation’.

Answer 27

The distribution shape obtained from a limited sample of load history can be extrapolated to produce a load history representing a total aircraft lifetime or even aircraft fleet lifetime.

Question 28

Describe ‘load spectrum distribution forms’.

Answer 28

Exceedence curves allow results from different spectrum tests to be correlated. The availability of recognised load spectrum distributions enables the assessment of the load spectrum of a particular structure in the design stage. This allows a fatigue life estimation to be made before even a prototype is available.

Question 29

Describe ‘step-load histogram approximations’.

Answer 29

Exceedence curves can be stepped in load level increments to provide a set of simple constant-amplitude blocks to simulate the spectrum in a ‘programmed block test’ or to provide input data for cumulative damage analysis.

Question 30

Name two standard load spectra. What are the differences?

Answer 30

TWIST (Transport Wing Standard Test):

• Civil
• Gust-dominated
• Symmetric
• Separate taxi

FALSTAFF (Fighter Aircraft Loading Standard for Fatigue):

• Military
• Manoeuvre-dominated
• Asymmetric
• Taxi included

Question 31

List and describe the assumptions associated with the simplification of load spectra.

Answer 31

Database:
- Load factor histories are usually obtained from the centre of gravity measurements from a number of different aircraft, representing a certain type.

Size of spectrum block:
- Overall number of flights in a spectrum definition must be limited to a convenient size and yet represent the expected aircraft loading.

Omission of low loads (range filtering):
- To limit the number of load cycles, only the load ranges above a given size are included (assumes smaller loads are not damaging).

Truncation of high loads:
- Spectrum high load truncation is arbitrarily applied based on material response. For metals, low occurrences of high loads can create beneficial plastic zones and increase fatigue life. Since they can not be predicted to occur at regular intervals, they are not included in fatigue test spectra.

Sequence effect:
- Most of the original load sequence information is lost and an idealised sequence of cyclic loads is arbitrarily regenerated in block form.

Loading wave-form shape and rate effect:
- Counting methods result in loss of load wave-form shape and rate. Arbitrary sine-wave loading and convenient load frequencies are used.

Question 32

What are ‘Constant Life Diagrams’? Why are they used?

Answer 32

• Constant life diagrams consist of curves defining the combination of mean and alternating stresses which cause failure at a particular life.
• They are used as S-N fatigue data is usually limited to a relatively small base of three or four R-ratios.

Question 33

What can be calculated from Goodman ‘Constant Life’ diagrams?

Answer 33

Life:
- For a given cyclic stress, S-N data and static strength.

Allowable combinations of mean and alternating stresses:
- for a given life, S-N data and static strength.

Question 34

What is the basis of the Palmgreen and Miner ‘Linear Cumulative Damage (LCD)’ rule?

Answer 34

• Damage is assumed proportional to n/N.
  
  • n = number of applied cycles at equivalent endurance strength.
  • N = number of constant amplitude cycles to cause failure at that endurance stress.
• The damage ratios of each set of cycles is summed and failure may be assumed to occur when the sum adds up to 1.

Question 35

What are the assumptions of the Palmgreen and Miner ‘Linear Cumulative Damage (LCD)’ rule?

Answer 35

• The damage accumulated is assumed to be independent of the current damage state.
• Damage accumulation is assumed to be independent of the order of the loading.

Question 36

List four methods of increasing fatigue life.

Answer 36

• Pick material with good fatigue resistance to crack initiation and propagation.
• Avoid Aluminium alloys with high yield to ultimate strength ratios.
• Ensure proper heat treatments are applied.
• Account for manufacturing method.

Question 37

List six manufacturing methods that can contribute to an increase in fatigue life.

Answer 37

• Proper cleaning of surface treatments.
• Protective finishes.
• Minimise wear of fretting surfaces due to relative sliding.
• Shot peen surfaces to be chrome plated.
• Check mechanical surface finish (e.g. roughness).
• Check use of shims.

Question 38

List six joint configurations that may contribute an increase to fatigue life.

Answer 38

• Limit countersink depth.
• Use cold-worked holes.
• Ensure current fastener selection and installation.
• Use interference fit.
• Avoid eccentricity.
• Avoid blind areas.

Question 39

List five design details that may contribute to an increase in fatigue life.

Answer 39

• Large cut-out radii.
• Large corner/bend radii.
• Avoid eccentricities and sudden discontinuities.
• Avoid interacting stress concentrations.
• Use a ‘fatigue quality index’.