Fatigue

Question 1

Define fatigue

Answer 1

Progressive localised damage to a material under repeated or oscillating loads

Question 2

Define low-cycle fatigue

Answer 2

Fatigue in which there are few cycles to failure - plastic deformation occurs in each cycle and there is hysteresis.

Question 3

Define high-cycle fatigue

Answer 3

Fatigue wherein there is no macroscopic plasticity and the stress-strain curve is linear - there are many cycles to failure

Question 4

Give three methods for analyzing fatigue

Answer 4

Fracture mechanics - consider the behaviour of existing cracks
Stress-based - relates stress to lifespan, empirical
Strain-based - relates strain during low-cycle fatigue to lifespan

Question 5

Define fatigue limit

Answer 5

A threshold stress below which fatigue is never seen in a material - typically caused by interstitial atoms that pin dislocations and prevent localised plasticity

Question 6

What is the stress range, Δσ? How does it relate to stress amplitude, σa?

Answer 6

The difference between the maximum and minimum stress in a cycle. Stress amplitude is a half the value of stress range.

Question 7

Does mean stress alter a component’s lifetime?

Answer 7

YES

Question 8

What is the definition of th R-value?

Answer 8

σmin / σmax

Question 9

What is the Basquin model?

Answer 9

A mathematical model of stress-lifespan for a given component of the form
σar = AN^B
Where σa is the stress amplitude, N is the number of cycles to failure, and A, B are constants

Question 10

What is the fatigue strength coefficient, σf’?

Answer 10

σf’ = A / 2^B

Corresponds to the projected failure stress at half a cycle [one reversal]

Question 11

How are fatigue safety factors defined?

Answer 11

In terms of stress of lifetime: they are the ratio of the design stress/lifetime to the expected stress/lifetime

Question 12

What are typical values for Xs and Xn, safety factors for fatigue stress and lifetime respectively?

Answer 12

1.5 and 15 respectively

Question 13

What is difference between a gross and net section?

Answer 13

A gross section is equivalent to the area described by the outer boundaries, the net section is equivalent to the true area of the section

Question 14

When designing a component to withstand fatigue, what should you be asking?

Answer 14

Have I ensured the maximum stress is less than the fatigue limit/endurance limit of the component’s material?

Question 15

What is the endurance limit?

Answer 15

A stress at which a material will last some large number of cycles (between 10 and 100 million)

Question 16

How is a material’s endurance limit estimated?

Answer 16

σ_{e} = m σ_{ts}

Where m is in the range 0.4 - 0.6 for most metals.

Question 17

Why is the approximation for a material’s endurance limit, σ_{e} = m σ_{ts}, not valid for highly strengthened materials?

Answer 17

Strengthened materials aren’t plastic at the tips of cracks (unlike their unstrengthened counterparts) - this is essential to limit crack propagation

Question 18

What factors influence a material’s endurance limit?

Answer 18

Material factor (empirical, assume 0.5 w/out other info)
Surface quality
Stress concentration factor (mk = 1/K)
Reliability (mr)
Size effect (bigger components are more likely to have defects)
Loading type (mt)

Question 19

How does a tensile mean stress affect a component’s lifetime?

Answer 19

Typically reduces lifetime

Question 20

How does a compressive mean stress affect a component’s lifetime?

Answer 20

Usually increases lifetime

Question 21

What is σar?

Answer 21

Stress amplitude for fully reversed loading (i.e. the equivalent stress were the mean stress zero)

Question 22

What generic expression relates stress amplitude with a mean stress present to equivalent stress amplitude w/ zero mean stress? What is the name of this expression?

Answer 22

σa = σar [ 1 - (σm/σu)^x ]

> The constant life equation

Question 23

Give four constant-life equation variables

Answer 23

Goodman: x = 1, σu&raquo_space; σts
Modified Goodman: x = 1, σu&raquo_space; σf’
Gerber: x = 2, σu&raquo_space; σts
Soderberg: x = 1, σu&raquo_space; σy

Question 24

You are analyzing a notched component that has a mean stress and is being periodically loaded. What must you account for when applying the constant life equation?

Answer 24

The stress concentration factor attributable to the notch - ensure the σm and σa used in the CLE encompass this.

Question 25

Do you need to worry about stress concentration of mean stresses in a notched component fabricated from a ductile material?

Answer 25

No - the material’s ductility means that high mean stresses cause plastic flow which mitigates the effects of the notch.

Question 26

What is the Palmgren-Miner rule, and how can it be applied?

Answer 26

Assume that a component has a certain amount of fatigue life available - loading at different stresses for given numbers of cycles consumes certain fractions of this lifespan. (Nb. pertains to variable loading scenarios)